Component Sizing[LINK]
In EnergyPlus each HVAC component sizes itself. Each
component module contains a sizing subroutine. When a
component is called for the first time in a simulation, it
reads in its user specified input data and then calls the
sizing subroutine. This routine checks the autosizable input
fields for missing data and calculates the data when
needed.
A number of high-level variables are used in the sizing
subroutines.
CurDuctType (in DataSizing) contains the
information about the current duct type. The types can be
main, cooling, heating or
other.
CurZoneEqNum (in DataSizing) is the
current zone equipment set index and indicates that the
component is a piece of zone equipment and should size itself
using the zone sizing data arrays.
CurSysNum (in DataSizing) is the current
air loop index and indicates that the component is part of the
primary air system and should size itself using the system
sizing data arrays.
Fan sizing is done in subroutine SizeFan.
Max Flow Rate[LINK]
If the fan is part of the central air system then check the
duct type.
For duct type = main, other or default
\[\dot Vfan,max =
DesMainVolFlowsys\]
For duct type=cooling
\[\dot Vfan,max =
DesCoolVolFlowsys\]
For duct type=heating
\[\dot Vfan,max =
DesHeatVolFlowsys\]
If the fan is zone equipment then check whether it is part
of a component that only does heating.
For heating only \(\dot Vfan,max
= DesHeatVolFlowzone\);
Otherwise \(\dot Vfan,max =
Max(DesHeatVolFlowzone,DesCoolVolFlowzone)\)
If the max fan flow rate is less than
SmallAirVolFlow the max flow rate is set to zero.
Coil:Cooling:Water[LINK]
The sizing is done in function SizeWaterCoil of
module WaterCoils
Initial Calculations[LINK]
For central cooling coils, the first step is to determine
the design air flow rate, load, and design air entering and
exit conditions. The coil design air flow rate is not
generally the same as the maximum system air flow rate (used
to size the central fans). The cooling coil peak load (either
sensible or total) can occur at a different time than the
system peak flow rate. Hence the coil air entering conditions
can be different than those at the peak system flow rate.
Also, the method of controlling the coil’s cooling output may
also affect coil design flow rate as well as the coil design
exit temperature and humidity.
By choosing Type of Load to Size On =
Sensible or Total in Sizing:System
the user indicates to the program to save the cooling coil air
flow rate and system air conditions (mixed, return, outside)
at the time of either the system cooling sensible or total
load peak. Note that the choice
VentilationRequirement uses the time of the sensible
peak.
Choosing Central Cooling Capacity Control Method =
VAV, Bypass, VT, or OnOff
indicates which type of cooling output control the program
should assume when calculating the design air flow rate. The
function GetCoilDesFlowT in module
ReportSizingManager calculates the air flow rate and
exit air temperature for each capacity control method.
VAV: \({T_{cc,exit}} =
{T_{cool,supply}}\) and \({\dot V_{cc,air}} = {\dot
m_{cc,air,peak}}/{\rho _{air}}\)
Bypass: \({T_{cc,exit}} =
{T_{cool,supply}}\) and \({\dot V_{cc,air}} = {\dot
V_{cc,air,max}}(\max [0,\min [1,({T_{mix,atpeak}} -
{T_{sup,avg}})/({T_{mix,atpeak}} - {T_{cc,exit}})]])\)
where \({T_{sup,avg}} =
{T_{zones,avg}} - \sum\limits_{zones} {{{\dot
Q}_{sens,atpeak}}} /({\rho _{air}}{c_{p,air}}{\dot
V_{cool,air,max}})\)
VT: \({T_{cc,exit}} = \max
[{T_{cool,supply}},({T_{zones,avg}} - \sum\limits_{zones}
{{{\dot Q}_{sens,atpeak}}} /({\rho _{air}}{c_{p,air}}{\dot
V_{cool,air,max}}))]\) and \({\dot V_{cc,air}} = {\dot
V_{cc,air,max}}\)
OnOff: \({T_{cc,exit}} =
{T_{cool,supply}}\) and \({\dot V_{cc,air}} = {\dot
V_{sys,air,max}}\)
\({c_{p,air}}\): the specific heat
of air [J/kg°C]
\({\dot m_{cc,air,peak}}\):
the air mass flow rate through the cooling coil at the
sensible or total system peak cooling load
[m3/s]
\(\sum\limits_{zones} {{{\dot
Q}_{sens,atpeak}}}\): sum of the zone sensible cooling
loads at the time of the peak system cooling load.
\({\rho _{air}}\): the
density of air [kg/m3]
\({T_{cc,exit}}\): the design
cooling coil exit temperature [°C]
\({T_{cool,supply}}\): the
supply air temperature for cooling specified in Sizing:System
[°C]
\({T_{mix,atpeak}}\): the
mixed air temperature at the time of the system peak cooling
load [°C]
\({T_{zones,avg}}\): the
average zone temperature at the time of the system peak
cooling load [°C]
\({\dot V_{cc,air}}\): the
design volumetric air flow rate through the cooling coil
[m3/s]. This is the flow rate at either the sensible or total
cooling load peak from the design period calculations.
\({\dot V_{cool,air,max}}\):
the maximum cooling volumetric air flow rate from the design
calculations [m3/s]. This flow rate occurs at the maximum zone
cooling demand.
\({\dot V_{sys,air,max}}\):
the maximum volumetric air flow rate from the design
calculations [m3/s]. This flow rate occurs at either the
maximum zone cooling or heating demand.
Design Coil Load (W)[LINK]
Design coil load (cooling capacity) is not an input for
Coil:Cooling:Water.
It is used for calculating the design water flow rate.
The design load \({\dot
Q_{coil,des}}\) is calculated using:
\[{\dot Q_{coil,des}} = {\dot
m_{a,coil,des}}({h_{a,coil,des,in}} -
{h_{a,coil,des,out}})\]
where
\({h_{a,coil,des,in}}\) is
the coil design inlet air enthalpy [J/kg];
\({h_{a,coil,des,out}}\)
is the coil design outlet air enthalpy [J/kg]; and
\({\dot m_{a,coil,des}}\)
is the coil design air mass flow rate [kg/s].
The design air mass flow rate depends on the location of
the coil. If the coil is in the outside air stream the flow
rate is set to \({\rho _{air}}{\dot
V_{a,coil,oa,des}}\), where \({\dot V_{a,coil,oa,des}}\) is the
design outside air volumetric flow rate for the system.
Otherwise \({\dot
m_{a,coil,des}}\) is set to \({\rho _{air}}{\dot V_{cc,air}}\)
where \({\dot V_{cc,air}}\)
is calculated above in the Initial Calculations section.
To obtain the inlet and outlet enthalpies, we need the
inlet and outlet temperatures and humidity ratios. The inlet
and outlet conditions depend on whether the coil is in the
outside air stream and if it is not, whether or not there is
outside air preconditioning.
- Coil in outside air stream
\({T_{air,in,des}} =
{T_{out,cool,atpeak}}\) (the outside air temperature at
the design cooling peak)
\({T_{air,out,des}} =
{T_{sys,precool}}\) (the specified Precool Design
Temperature from the Sizing:System
object).
\({W_{air,in,des}} =
{W_{out,cool,atpeak}}\) (the outside humidity ratio at
the design cooling peak)
\({W_{air,out,des}} =
{W_{sys,precool}}\) (the specified Precool Design
Humidity Ratio from the Sizing:System
object)
- Coil in main air stream, no preconditioning of outside air
\({T_{air,in,des}} =
{T_{mix,cool,atpeak}}\) (the mixed air temperature at
the design cooling peak)
\({W_{air,in,des}} =
{W_{mix,cool,atpeak}}\) (the mixed air humidity ratio
at the design cooling peak)
Tair,out,des is set to
*Tcc,exit calculated above in the Initial
Calculation section
\({W_{air,out,des}} =
{W_{sup,cool}}\) (the specified Central Cooling
Design Supply Air Humidity Ratio from the Sizing:System
object)
- Coil in main air stream, outside air preconditioned. The
outside air fraction is calculated as \({f_{oa}} = {\dot V_{air,out,des}}/{\dot
V_{cc,air}}\) where \({\dot
V_{cc,air}}\) is calculated above
\({T_{air,in,des}} =
{f_{oa}}{T_{precool}} + (1 -
{f_{oa}}){T_{ret,cool,atpeak}}\) where \({T_{precool}}\) is the specified
Precool Design Temperature from
System:Sizing. \({T_{ret,cool,atpeak}}\) is the
return temperature at the system cooling peak load.
\({W_{air,in,des}} =
{f_{oa}}{W_{precool}} + (1 -
{f_{oa}}){W_{ret,cool,atpeak}}\) where \({W_{precool}}\) is the specified
Precool Design Humidity Ratio from Sizing:System
and \({W_{ret,cool,atpeak}}\)
is the return humidity ratio at the system cooling peak
load.
Tair,out,des and
Wair,out,des are defined as in 2).
With the inlet and outlet conditions established, we can
obtain the inlet and outlet enthalpies:
hair,coil,des,in =
PsyHFnTdbW(Tair,in,des,
Wair,in,des)
hair,coil,des,out =
PsyHFnTdbW(Tair,out,des,
Wair,out,des)
where PsyHFnTdbW is the EnergyPlus function for
calculating air specific enthalpy given the air temperature
and humidity ratio. We now have all we need to calculate \({\dot Q_{coil,des}}\).
If the coil is part of an AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction
unit or an ZoneHVAC:FourPipeFanCoil,
the cooling load (cooling capacity) is passed down from the
terminal unit or fan coil sizing calculations. Otherwise the
load is defined as:
\({\dot Q_{coil,des}} = {\dot
m_{a,coil,des}}({h_{a,coil,des,in}} -
{h_{a,coil,des,out}})\)
where
\({h_{a,coil,des,in}}\) is the coil
design inlet air enthalpy [J/kg];
\({h_{a,coil,des,out}}\) is
the coil design outlet air enthalpy [J/kg]; and
\({\dot m_{a,coil,des}}\) is
the coil design air mass flow rate [kg/s].
The enthalpies are given by:
\[{h_{air,coil,des,in}} =
PsyHFnTdbW({T_{air,in,des}},{W_{air,in,des}})\]
\[{h_{air,coil,des,out}} =
PsyHFnTdbW({T_{air,out,des}},{W_{air,out,des}})\]
where Tair,in,des and
Wair,in,des are the coil inlet design
conditions. For coils in terminal units these are set at the
system level to the system design supply air temperature. For
zonal usits they are set to design return air, mixed air, or
outside air as appropriate to the unit.
Tair,out,des is set to the zone cooling
design supply air temperature as specified in the
Zone:Sizing inputs. Wair,out,des
is set to the zone cooling design supply air humidity ratio as
specified in the Zone:Sizing inputs.
Design Water Flow Rate
(m3/s)[LINK]
The design water volumetric flow rate is calculated
using:
\[{\dot V_{w,coil,des}} = {\dot
Q_{coil,des}}/({\rho _w}{c_{p,w}}\Delta
{T_{w,des}})\]
where \(\Delta T_{w,des}\)
is just the Loop Design Temperature Difference user
input from Sizing:Plant
(if the coil is in the outside air stream, ½ the Loop
Design Temperature Difference is used).
If the coil is part of an AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction
unit or a ZoneHVAC:FourPipeFanCoil,
the chilled water flow rate is passed down from the terminal
unit or fan coil sizing calculations. Otherwise the flow is
set to:
\[{\dot V_{w,coil,des}} = {\dot
Q_{coil,des}}/({\rho _w}{c_{p,w}}\Delta
{T_{w,des}})\]
where \(\Delta T_{w,des}\)
is just the Loop Design Temperature Difference user
input from Sizing:Plant.
\({\dot Q_{coil,des}}\) is
calculated as described above.
Design Air Flow Rate[LINK]
The design air volumetric flow rate for the system cooling
coil is set to:
- the design outside air flow rate if the coil is in the
outside air stream;
- the coil design flow rate from function
GetCoilDesFlowT described in section “Initial
Calculations”;
- the design flow rate set by the parent component (such as
a unitary system) containing the cooling coil.
Zone
chilled water coils are always part of a zone HVAC component.
In almost all cases the design flow rate is passed down from
the design flow rate of the parent component. Otherwise if the
parent component does cooling only the flow rate for the coil
is set to the zone design cooling flow rate. And if the parent
component does both cooling and heating, the coil flow rate is
set to the maximum of the zone design cooling and heating flow
rates.
Design Inlet Air
Temperature[LINK]
The inlet air temperature depends on whether the coil is in
the outside air stream and if it is not, whether or not there
is outside air preconditioning.
Coil in outside air stream: \({T_{air,in,des}} =
{T_{out,cool,atpeak}}\) (the outside air temperature at
the design cooling peak). Coil in main air stream, no
preconditioning of outside air: \({T_{air,in,des}} =
{T_{mix,cool,atpeak}}\) (the mixed air temperature at
the design cooling peak). Coil in main air stream, outside air
preconditioned. The outside air fraction is calculated as
\({f_{oa}} = {\dot
V_{air,out,des}}/{\dot V_{cc,air}}\), where \({\dot V_{cc,air}}\) is calculated
above. Then \({T_{air,in,des}} =
{f_{oa}}{T_{precool}} + (1 -
{f_{oa}}){T_{ret,cool,atpeak}}\) where \({T_{precool}}\) is the specified
Precool Design Temperature from
System:Sizing. \({T_{ret,cool,atpeak}}\) is the
return temperature at the system cooling peak load.
The design inlet temperature depends on whether the coil is
in a terminal unit or a zonal unit, and where the coil is
positioned within the unit.
- For the
AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction
terminal unit the design inlet temperature is set to the zone
temperature at the time of the zone cooling peak, since the
coil is located in the induced air stream.
- For fan coil units the design inlet temperature is set to
the mixed air temperature: \({T_{air,in,des}} =
{f_{oa}}{T_{oa,coolpeak}} + (1 -
{f_{oa}}){T_{z,coolpeak}}\) where \({f_{oa}} = {\rho _a}{\dot
V_{z,oa,des}}/{\dot m_{z,cool,des}}\).
- In all other cases the design inlet temperature is set to
the zone design cooling coil inlet temperature which is
calculated in the zone sizing simulation and is basically the
same calculation as the fan coil unit.
Design Outlet Air
Temperature[LINK]
The outlet air temperature depends on whether the coil is
in the outside air stream.
- Coil in outside air stream:
Tair,out,des =
Tsys,des,precool (the specified
Precool Design Temperature from the
Sizing:System object).
- Coil in main air stream: the design outlet air temperature
is set to the temperature calculated in the Initial
Calculation section above
If the coil is part of an AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction
unit, then:
\[{\dot Q_{coil,des}} =
{c_{p,air}}{\rho _{air}}{\dot V_{w,coil,des}}\Delta
{T_{w,des}}\]
\[{T_1} = {T_{air,in,des}} -
{\dot Q_{coil,des}}/({\rho _{air}}{c_{p,air}}{\dot
V_{air,coil,des}})\]
\[{T_2} = {T_{w,out,des}} +
2\]
\[{T_{air,out,des}} = \max
({T_1},{T_2})\]
For all other cases Tair,out,des is set
to Tz,sup,des (the zone design supply air
temperature as specified in Sizing:Zone).
Design Inlet Air
Humidity Ratio[LINK]
The design inlet humidity ratio depends on whether the coil
is in the outside air stream and if it is not, whether or not
there is outside air preconditioning.
- Coil in outside air stream: \({W_{air,in,des}} =
{W_{out,cool,atpeak}}\) (the outside air humidity ratio
at the design cooling peak).
- Coil in main air stream, no preconditioning of outside
air: \({W_{air,in,des}} =
{W_{mix,cool,atpeak}}\) (the mixed air humidity ratio
at the design cooling peak).
- Coil in main air stream, outside air preconditioned. The
outside air fraction is calculated as \({f_{oa}} = {\dot V_{air,out,des}}/{\dot
V_{cc,air}}\), where \({\dot
V_{cc,air}}\) is calculated above. Then \({W_{air,in,des}} = {f_{oa}}{W_{precool}}
+ (1 - {f_{oa}}){W_{ret,cool,atpeak}}\) where \({W_{precool}}\) is the specified
Precool Design Humidity Ratio from
System:Sizing. \({W_{ret,cool,atpeak}}\) is the
return air humidity ratio at the system cooling peak
load.
The design inlet humidity depends on whether the coil is in
a terminal unit or a zonal unit, and where the coil is
positioned within the unit.
- For the
AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction
terminal unit the design inlet humidity ratio is set to the
zone humidity ratio at the time of the zone cooling peak,
since the coil is located in the induced air stream.
- For fan coil units the design inlet humidity ratio is set
to the mixed air humidity ratio: \({W_{air,in,des}} =
{f_{oa}}{W_{oa,coolpeak}} + (1 -
{f_{oa}}){W_{z,coolpeak}}\) where \({f_{oa}} = {\rho _a}{\dot
V_{z,oa,des}}/{\dot m_{z,cool,des}}\).
- In all other cases the design inlet temperature is set to
the zone design cooling coil inlet humidity ratio which is
calculated in the zone sizing simulation and is basically the
same calculation as the fan coil unit.
Design Outlet Air
Humidity Ratio[LINK]
The outlet air humidity ratio depends on whether the coil
is in the outside air stream.
- Coil in outside air stream:
Wair,out,des =
Wsys,des,precool (the specified
Precool Design Humidity Ratio from the
Sizing:System object)
- Coil in main air stream: \({W_{air,out,des}} =
PsyWFnTdbRhPb({T_{air,out,des}},0.9,{P_{air,std}})\)
where PsyWFnTdbRhPb is the EnergyPlus psychrometric
function to calculate humidity ratio from drybulb temperature,
relative humidity, and atmospheric pressure. The design outlet
humidity ratio is being set to the humidity ratio at 90%
relative humidity and design outlet temperature.
If the coil is part of an AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction
unit, then: get the dewpoint temperature at
Wair,in,des:
\({T_{dp,in}} =
PsyTdpFnWPb({W_{air,in,des}},{P_{air,std}})\).
If Tdp,in ≤ Tw,in,des
set Wair,out,des =
Wair,in,des. Otherwise set
\({W_{air,out,des}} = \min
(PsyWFnTdbRhPb({T_{air,out,des}},0.9,{P_{air,std}}),{W_{air,in,des}})\)
If the coil is not part of an AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction
unit, set Wair,out,des to
Wz,sup,des (the zone design supply air
humidity ratio as specified in Sizing:Zone).
Design Inlet Water
Temperature[LINK]
The Design Inlet Water Temperature is set to the Design
Loop Exit Temperature specified in the Sizing:Plant
object for the water loop serving this coil.
The Design Inlet Water Temperature is set to the Design
Loop Exit Temperature specified in the Sizing:Plant
object for the water loop serving this coil.
Coil:Cooling:Water:DetailedGeometry
Sizing[LINK]
The sizing is done in subroutine SizeWaterCoil
Max Water Flow Rate of
Coil[LINK]
The calculation is identical to that done for Coil:Cooling:Water.
Number of Tubes per Row[LINK]
\[Ntube/row = {\mathop{\rm
Int}\nolimits} ({\rm{13750}}\dot Vcoil,water,max)\]
Ntube/row=Max(Ntube/row,3)
Depending on the duct type, get the coil design air flow
rate.
For duct type = main, other or default
\[\dot mair,des = \rho
airDesMainVolFlowsys\]
for duct type=cooling
\[\dot mair,des = \rho
airDesCoolVolFlowsys\]
for duct type=heating
\[\dot mair,des = \rho
airDesHeatVolFlowsys\]
\[Dfin = 0.335\dot
mair,des\]
Minimum Air Flow Area[LINK]
Depending on the duct type, get the coil design air flow
rate.
For duct type = main, other or default
\[\dot mair,des = \rho
airDesMainVolFlowsys\]
for duct type=cooling
\[\dot mair,des = \rho
airDesCoolVolFlowsys\]
for duct type=heating
\[\dot mair,des = \rho
airDesHeatVolFlowsys\]
\[AMinAirFlow = 0.44\dot
mair,des\]
Fin Surface Area[LINK]
Depending on the duct type, get the coil design air flow
rate.
For duct type = main, other or default
\[\dot mair,des = \rho
airDesMainVolFlowsys\]
for duct type=cooling
\[\dot mair,des = \rho
airDesCoolVolFlowsys\]
for duct type=heating
\[\dot mair,des = \rho
airDesHeatVolFlowsys\]
\[AFinSurf = 78.5\dot
mair,des\]
Total Tube Inside Area[LINK]
A~tube,total
inside=4.4Dtube,insideNtube
rowsNtubes/row~
Where Dtube,inside is the tube inside
diameter.
Tube Outside Surf Area[LINK]
Atube,outside=4.1Dtube,outsideN~tube
rowsNtubes/row~
Where Dtube,outside is the tube outside
diameter.
Depthcoil=Depth~tube spacing~
N~tube rows~
Coil:Cooling:WaterToAirHeatPump:EquationFit
Sizing[LINK]
The sizing is done in subroutine
SizeHVACWaterToAir
Rated Air Flow Rate[LINK]
The calculation is identical to that done for Coil:Cooling:Water.
Rated Water Flow Rate[LINK]
The calculation is identical to that done for Coil:Cooling:Water,
which is the coil design load divided by the Loop Design
Temperature Difference user input from Sizing:Plant.
If there is a companion heating coil, the heating coil design
load is used so that both modes will have the same rated water
flow rate. For sizing the plant loop serving this coil, only
one half of this flow rate is used since both the cooling and
heating coil will save a flow rate but only one of these coils
will operate at a time.
Rated Total Cooling
Capacity[LINK]
The calculation for coil operating temperatures (inlet and
outlet) are identical to that done for Coil:Cooling:Water.
The following calculations are then performed to determine the
rated total cooling capacity.
\[{T_{WB,ratio}} = \frac{\left(
{{T_{WB,air,in,des}} + 273.15\,C}
\right)}{283.15C}\]
\[{T_{S,ratio}} = \frac{29.44C +
273.15C}{283.15C}\]
where:
\({T_{WB,ratio}}\) = ratio
of load-side inlet air wet-bulb temperature in Kelvin to a
reference temperature
\({T_{S,ratio}}\) = ratio
of source-side inlet water temperature in Kelvin to a
reference temperature
TCC1 = user input for Total Cooling Capacity Coefficient
1
TCC2 = user input for Total Cooling Capacity Coefficient
2
TCC3 = user input for Total Cooling Capacity Coefficient
3
TCC4 = user input for Total Cooling Capacity Coefficient
4
TCC5 = user input for Total Cooling Capacity Coefficient
5
\[TotCapTempModFac = \,TCC1 +
TCC2\left( {{T_{WB,ratio}}} \right) + TCC3\left(
{{T_{S,ratio}}} \right) + TCC4 + TCC5\]
The 4th and 5th coefficient (TCC4 and
TCC5) used in the above equation are multipliers for the
load-side and source-side flow ratios, respectively. For
sizing, these ratios are assumed to be 1.
The enthalpy of the entering air is then compared with the
enthalpy of the exiting air. The calculations for air enthalpy
are identical to that done for Coil:Cooling:Water.
If the entering air enthalpy is less than the exiting air
enthalpy, a reference value of 48,000 J/kg is used as the
entering air enthalpy. If the TotCapTempModFac calculation
above yields 0 as the result, a value of 1 is used in the
following calculation. If the design air mass flow rate is
determined to be less than a very small flow value (0.001
kg/s) or the capacity calculated here is less than 0, the coil
total cooling capacity is set equal to 0.
Rated Sensible
Cooling Capacity[LINK]
The calculation for coil operating temperatures (inlet and
outlet) are identical to that done for Coil:Cooling:Water.
The following calculations are then performed to determine the
rated sensible cooling capacity.
\[{T_{DB,ratio}} =
\frac{(T_{DB,air,in,des} + 273.15C}{283.15C}\]
\[{T_{S,ratio}} = \frac{(29.44C
+ 273.15C}{283.15C}\]
where:
\({T_{DB,ratio}}\) = ratio
of load-side inlet air dry-bulb temperature in Kelvin to a
reference temperature
SCC1 = user input for Sensible Cooling Capacity Coefficient
1
SCC2 = user input for Sensible Cooling Capacity Coefficient
2
SCC3 = user input for Sensible Cooling Capacity Coefficient
3
SCC4 = user input for Sensible Cooling Capacity Coefficient
4
SCC5 = user input for Sensible Cooling Capacity Coefficient
5
SCC6 = user input for Sensible Cooling Capacity Coefficient
6
\[\begin{array}{l}SensCapTempModFac =
\,SCC1 + SCC2\left( {{T_{DB,ratio}}} \right) + SCC3\left(
{{T_{WB,ratio}}} \right) + SCC4\left( {{T_{S,ratio}}}
\right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,
+ SCC5 + SCC6\end{array}\]
The 5th and 6th coefficient (SCC5 and
SCC6) used in the above equation are multipliers for the
load-side and source-side flow ratios, respectively. For
sizing, these ratios are assumed to be 1.
The dry-bulb temperature of the entering air is then
compared with the dry-bulb temperature of the exiting air. The
calculations for air dry-bulb temperature are identical to
that done for Coil:Cooling:Water.
If the entering air dry-bulb temperature is less than the
exiting air dry-bulb temperature, a reference value of 24 C is
used as the entering air dry-bulb temperature. If the
SensCapTempModFac calculation above yields 0 as the result, a
value of 1 is used in the following calculation. If the design
air mass flow rate is determined to be less than a very small
flow value (0.001 kg/s) or the capacity calculated here is
less than 0, the coil sensible cooling capacity is set equal
to 0.
Coil:Cooling:WaterToAirHeatPump:VariableSpeedEquationFit
Sizing[LINK]
For the cooling coil of VS WSHP, we specify a nominal speed
level. During the sizing calculation, the Rated Air Volume
Flow Rate, the Rated Water Volume Flow Rate and the Rated
Total Cooling Capacity at the Selected Nominal Speed Level are
determined in the same way as the Coil:Cooling:WaterToAirHeatPump:EquationFit
object. The sensible heat transfer rate is not allowed for
auto-sizing, instead, it is a function of the rated air and
water flow rates, rated total cooling capacity and the
Reference Unit SHR at the nominal speed level. The default
nominal speed level is the highest speed. However, the model
allows the user to select a nominal speed level rather than
the highest.
Rated Air Flow Rate[LINK]
The calculation is identical to that done for Coil:Cooling:WaterToAirHeatPump:EquationFit.
Rated Water Flow Rate[LINK]
The calculation is identical to that done for Coil:Cooling:WaterToAirHeatPump:EquationFit
, which is the coil design load divided by the Loop Design
Temperature Difference user input from Sizing:Plant.
If there is a companion heating coil, the heating coil design
load is used so that both modes will have the same rated water
flow rate. For sizing the plant loop serving this coil, only
one half of this flow rate is used since both the cooling and
heating coil will save a flow rate but only one of these coils
will operate at a time.
Rated Total Cooling
Capacity[LINK]
The calculation for coil operating temperatures (inlet and
outlet) are identical to that done for Coil:Cooling:WaterToAirHeatPump:EquationFit.
The calculations for air enthalpy are similar to that done for
Coil:Cooling:WaterToAirHeatPump:EquationFit.
The difference is in calculating the total cooling capacity
temperature modifier function at the selected nominal speed
level, as below:
\[TotCapTempModFra{c_{NominalSpeed}} =
{\rm{a}} + {\rm{b*}}W{B_i} + c*WB_i^2 + {\rm{d*EWT}} +
e*EW{T^2} + f*W{B_i}*EWT\]
where
WBi = wet-bulb temperature of the air entering
the heating coil, °C
EWT = entering water temperature, °C
a-f = regression curve-fit coefficients.
If the entering air enthalpy is less than the exiting air
enthalpy, a reference value of 48,000 J/kg is used as the
entering air enthalpy. If the TotCapTempModFac
calculation above yields 0 as the result, a value of 1 is used
in the following calculation. If the rated air mass flow rate
is determined to be less than a very small flow value (0.001
kg/s) or the capacity calculated here is less than 0, the coil
total cooling capacity is set equal to 0.
If Hin > Hout Then
\[{\dot Q_{coil,rated,total}} =
{m_{air,rated}}({H_{in}} -
{H_{out}})/TotCapTempModFra{c_{NominalSpeed}}\]
Else
\[{\dot Q_{coil,rated,total}} =
{m_{air,rated}}(48000 -
{H_{out}})/TotCapTempModFra{c_{NominalSpeed}}\]
End If
Coil:Heating:WaterToAirHeatPump:EquationFit
Sizing[LINK]
The sizing is done in subroutine
SizeHVACWaterToAir.
Rated Air Flow Rate[LINK]
The calculation is identical to that done for Coil:Cooling:Water.
Rated Water Flow Rate[LINK]
The calculation is identical to that done for Coil:Cooling:Water
, which is the coil design load divided by the Loop Design
Temperature Difference user input from Sizing:Plant.
For sizing the plant loop serving this coil, only one half of
this flow rate is used since both the cooling and heating coil
will save a flow rate but only one of these coils will operate
at a time.
Rated Total Heating
Capacity[LINK]
The rated total heating capacity is set equal to the rated
total cooling capacity.
Coil:Heating:WaterToAirHeatPump:VariableSpeedEquationFit
Sizing[LINK]
For the heating coil of VS WSHP, we specify a nominal speed
level. During the sizing calculation, the Rated Air Volume
Flow Rate and the Rated Water Volume Flow Rate are determined
in the same way as the Coil:Heating:WaterToAirHeatPump:EquationFit
object. On the other hand, the Rated Heating Capacity at the
Selected Nominal Speed Level should be the same as the total
cooling capacity of its corresponding cooling coil, which has
to be sized first. The default nominal speed level will be the
highest speed. However, the model allows the user to select a
nominal speed level rather than the highest.
Rated Air Flow Rate[LINK]
The calculation is identical to that done for Coil:Cooling:WaterToAirHeatPump:EquationFit.
Rated Water Flow Rate[LINK]
The calculation is identical to that done for Coil:Cooling:WaterToAirHeatPump:EquationFit,
which is the coil design load divided by the Loop Design
Temperature Difference user input from Sizing:Plant.
For sizing the plant loop serving this coil, only one half of
this flow rate is used since both the cooling and heating coil
will save a flow rate but only one of these coils will operate
at a time.
Rated Total Heating
Capacity[LINK]
The rated total heating capacity is set equal to the rated
total cooling capacity.
Coil:Heating:Water
Sizing[LINK]
The sizing is done in subroutine
SizeWaterCoil.
Max Water Flow Rate of
Coil[LINK]
With the coil load from the system design data array and
the user specified (in a Sizing:Plant
object) design hot water temperature fall, calculate the max
water flow rate:
\[\dot Vcoil,water,max =
HeatCapsys/(Cp,water\rho water\Delta Tplt,hw,des)\]
Using the zone design coil inlet and supply air conditions
calculate the design coil load.
If the coil is not part of an induction unit then obtain
the coil inlet temperature from the zone design data
array;
Tin,air=
DesHeatCoilInTempzone
If the coil is part of an induction unit take into account
the induced air:
Fracminflow =
MinFlowFraczone
Tin,air =
DesHeatCoilInTempzone
Fracminflow +
ZoneTempAtHeatPeakzone(1
Fracminflow)
Tout,air =
HeatDesTempzone
Wout,air =
HeatDesHumRatzone
If the coil is part of a terminal unit the mass flow rate
is determined by the volumetric flow rate of the terminal
unit:
\[\dot mair,des = \rho air\dot
mair,des,tu\]
Otherwise the design flow is obtained from the zone design
data array:
\[\dot mair,des =
DesHeatMassFlowzone\]
\[Qcoil,des = cp,air\dot
mair,des(Tout,air - Tin,air)\]
Here cp,air is calculated at the outlet
humidity and the average of the inlet and outlet
temperatures.
With the coil load and the user specified (in a Sizing:Plant
object) design hot water temperature decrease, calculate the
max water flow rate:
\[\dot Vcoil,water,max =
Qcoil,des/(Cp,water\rho water\Delta Tplt,hw,des)\]
UA of the Coil[LINK]
To obtain the UA of the coil, we specify the model inputs
(other than the UA) at design conditions and the design coil
load that the coil must meet. Then we numerically invert the
coil model to solve for the UA that will enable the coil to
meet the design coil load given the specified inputs.
The design coil load is the system design sensible cooling
capacity;
Qcoil,des=
HeatCapsys
The required inputs for the simple coil model are:
Tin,air=
HeatMixTempsys
Win,air=
HeatMixHumRatsys
Tin,water=
ExitTempplt,hw,des
\[\dot min,water = \rho
water\dot Vcoil,water,max\]
Depending on the duct type, get the coil design air flow
rate.
For duct type = main, other or default
\(\dot min,air = \rho
airDesMainVolFlowsys\)
for duct type=cooling
\(\dot min,air = \rho
airDesCoolVolFlowsys\)
for duct type=heating
\[\dot min,air = \rho
airDesHeatVolFlowsys\]
We now have all the data needed to obtain UA. The numerical
inversion is carried out by calling subroutine
SolveRegulaFalsi. This is a general utility routine
for finding the zero of a function. In this case it finds the
UA that will zero the residual function - the difference
between the design coil load and the coil output divided by
the design coil load. The residual is calculated in the
function SimpleHeatingCoilUAResidual.
If the coil is not part of an induction unit then obtain
the coil inlet temperature from the zone design data
array;
Tin,air =
DesHeatCoilInTempzone
If the coil is part of an induction unit take into account
the induced air:
Fracminflow =
MinFlowFraczone
Tin,air =
DesHeatCoilInTempzone
Fracminflow +
ZoneTempAtHeatPeakzone(1
Fracminflow)
Win,air=
DesHeatCoilInHumRatzone
Tin,water=
ExitTempplt,hw,des
\[\dot min,water = \rho
water\dot Vcoil,water,max\]
Tout,air =
HeatDesTempzone
Wout,air =
HeatDesHumRatzone
If the coil is part of a terminal unit the mass flow rate
is determined by the volumetric flow rate of the terminal
unit:
\[\dot mair,des = \rho air\dot
mair,des,tu\]
Otherwise the design flow is obtained from the zone design
data array:
\[\dot mair,des =
DesHeatMassFlowzone\]
\[\dot Qcoil,des = cp,air\dot
mair,des(Tout,air - Tin,air)\]
Here cp,air is calculated at the outlet
humidity and the average of the inlet and outlet
temperatures.
We now have all the data needed to obtain UA. The numerical
inversion is carried out by calling subroutine
SolveRegulaFalsi. This is a general utility routine
for finding the zero of a function. In this case it finds the
UA that will zero the residual function - the difference
between the design coil load and the coil output divided by
the design coil load. The residual is calculated in the
function SimpleHeatingCoilUAResidual.
Coil:Heating:Steam
Sizing[LINK]
The sizing is done in subroutine
SizeSteamCoil.
Maximum Steam Flow Rate[LINK]
The maximum steam volumetric flow rate is calculated
using:
The steam density (\({\rho
_{steam}}\)) is for saturated steam at 100°C (101325.0
Pa) and hfg is the latent heat of
vaporization of water at 100°C (101325.0 Pa).
Cp,w is the heat capacity of saturated
water (condensate) at 100°C (101325.0 Pa) and \(\Delta {T_{sc}}\) is the Degree
of Subcooling defined in the Coil:Heating:Steam
object input. The design coil load
Loadcoil,des is calculated from:
\[Loa{d_{coil,des}} = {\dot
m_{air,des}}({c_{p,air}})({T_{air,coil,des,out}} -
{T_{air,coil,des,in}})\]
The design air mass flow rate depends on the location of
the coil (duct type). For duct type = main, the flow
rate is set to
airDesMainVolFlowsysMinSysAirFlowRatio.
If the coil is in a cooling duct the flow rate is set to
airDesCoolVolFlowsysMinSysAirFlowRatio.
If the coil is in a heating duct the flow rate is set to
airDesHeatVolFlowsys. If the
coil is in any other kind of duct, the flow rate is set to
airDesMainVolFlowsys.
For sizing, the design outlet air temperature
(Tair,coil,des,out) is the Central Heating
Design Supply Air Temperature specified in the Sizing:System
object.
The design inlet air temperature depends on whether the
coil is being sized for 100% outdoor air or minimum outdoor
air flow (per 100% Outdoor Air in Heating input field in the
Sizing:System
object).
- Sizing based on 100% Outdoor Air in Heating
Tair,coil,des,in =
HeatOutTempsys (the outdoor air
temperature at the design heating peak)
- Sizing based on minimum outdoor air flow. The outdoor air
fraction is calculated as Fracoa **=
DesOutAirVolFlowsys / DesVolFlow.
DesVolFlow is \(\frac{\dot{m}_{air,des}}{\rho_{air}}\).
Tair,coil,des,in =
Fracoa HeatOutTempsys
+ (1. - Fracoa)
HeatRetTempsys (see Table 41. System
Sizing Data)
If the coil is part of an AirTerminal:SingleDuct:*
unit (e.g., AirTerminal:SingleDuct:ConstantVolume:Reheat,
AirTerminal:SingleDuct:VAV:Reheat,
AirTerminal:SingleDuct:SeriesPIU:Reheat,
etc.), the maximum steam flow rate is set equal to the
terminal unit’s maximum steam flow rate. Otherwise (e.g., the
zone-level coil is part of ZoneHVAC:PackagedTerminalAirConditioner,
ZoneHVAC:UnitVentilator,
ZoneHVAC:UnitHeater
or ZoneHVAC:VentilatedSlab)
the calculation is similar to that at the system level. A
design load is calculated:
\[Loa{d_{coil,des}} = {\dot
m_{air,des}}({c_{p,air}})({T_{air,coil,des,out}} -
{T_{air,coil,des,in}})\]
where:
\({\dot m_{air,des}}\)=
DesHeatMassFlowzone (see Table 40. Zone
Sizing Data)
Tair,coil,des,in =
DesHeatCoilInTempzone (see Table 40)
Tair,coil,des,out =
HeatDesTempzone (user input from Sizing:Zone
object)
\({c_{p,air}}\) = Specific
heat of air (evaluated at the average of inlet and outlet air
temperatures, and at the zone heating design supply air
humidity ratio HeatDesHumRatzone [user
input from Sizing:Zone
object])
The terms in the denominator of this equation
(ρsteam, hfg, etc.)
are evaluated in the same way as described above for steam
System Coils.
Sizing of
Gas and Electric Heating Coils[LINK]
The sizing calculation is done in subroutine
SizeHeatingCoil in module HeatingCoils.
Nominal Capacity of the
Coil[LINK]
The value is obtained from the system design array.
Capnom=
HeatCapsys
The capacity is calculated from the design coil inlet and
outlet conditions.
If the coil is not part of an induction unit then obtain
the coil inlet temperature from the zone design data
array;
Tin,air =
DesHeatCoilInTempzone
If the coil is part of an induction unit take into account
the induced air:
Fracminflow =
MinFlowFraczone
Tin,air =
DesHeatCoilInTempzone
Fracminflow +
ZoneTempAtHeatPeakzone(1
Fracminflow)
Tout,air =
HeatDesTempzone
Wout,air =
HeatDesHumRatzone
Qcoil,des = Cp,air
DesHeatMassFlowzone(Tout,airTin,air)
Here cp,air is calculated at the outlet
humidity and the average of the inlet and outlet
temperatures.
DX Coil Sizing[LINK]
The sizing calculations are done in subroutine
SizeDXCoil in module DXCoils. This section
covers the sizing of the objects
Coil:Cooling:DX:SingleSpeed
Coil:Heating:DX:SingleSpeed
Coil:Cooling:DX:TwoSpeed
Rated Air Volume Flow
Rate[LINK]
The rated air flow rate is obtained from the system design
array.
\[\dot Vair,rated =
DesMainVolFlowsys\]
The rated air flow rate is the maximum of the heating and
cooling design flow rates from the zone design array.
\[\dot Vair,rated =
Max(DesCoolVolFlowzone,DesHeatVolFlowzone)\]
Rated Total Cooling
Capacity[LINK]
The rated cooling capacity is obtained by dividing the peak
cooling capacity by the Cooling Capacity Modifier
Curve evaluated at peak mixed wetbulb and outdoor drybulb
temperatures.
Tmix=
CoolMixTempsys
Wmix=CoolMixHumRatsys
Tsup=CoolSupTempsys
Wsup=CoolSupHumRatsys
Toutside=CoolOutTempsys
air=PsyRhoAirFnPbTdbW(pair,std,
Tmix,Wmix)
hmix=
PsyHFnTdbW(Tmix,Wmix)
hsup=
PsyHFnTdbW(Tsup,Wsup)
Tmix,wb=
PsyTwbFnTdbWPb(Tmix,Wmix,
pair,std)
CapModFac=CurveValue(CCapFTemp,Tmix,wb,Toutside)
\[CCappeak = \rho air\dot
Vair,rated(hmix - hsup)\]
CCaprated=CCappeak
CapModFac
We check that the design volume flow per total capacity is
within the prescribed range:
\[FlowCapRatio = \dot
Vair,rated/CCaprated\]
If FlowCapRatio <
FlowCapRatiomin then
\[CCaprated = \dot
Vair,rated/FlowCapRatiomin\]
If FlowCapRatio >
FlowCapRatiomax then
\[CCaprated = \dot
Vair,rated/FlowCapRatiomax\]
where
FlowCapRatiomin = 0.00004027
m3/s per watt (300 cfm/ton)
And
FlowCapRatiomax= 0.00006041
m3/s per watt (450 cfm/ton)
The sizing calculation for DX cooling coils for 100%
dedicated outdor air system (DOAS) are identical to regular DX
cooling coils. However, they operate operate at different flow
to capacity ratio ranges and are within the prescribed range
below:
FlowCapRatiomin = 0.00001677
m3/s per Watt (125 cfm/ton)
And
FlowCapRatiomax= 0.00003355
m3/s per Watt (250 cfm/ton)
The rated cooling capacity for zone coils is calculated in
the same manner as for system coils.
Tmix=
DesCoolCoilInTempzone
Wmix=
DesCoolCoilInHumRatzone
Tsup=
CoolDesTempzone
Wsup=
CoolDesHumRatzone
Toutside=Toutside,desday,peak
air=PsyRhoAirFnPbTdbW(pair,std,
Tmix,Wmix)
hmix=
PsyHFnTdbW(Tmix,Wmix)
hsup=
PsyHFnTdbW(Tsup,Wsup)
Tmix,wb=
PsyTwbFnTdbWPb(Tmix,Wmix,
pair,std)
CapModFac=CurveValue(CCapFTemp,Tmix,wb,Toutside)
\[CCappeak = \rho air\dot
Vair,rated(hmix - hsup)\]
CCaprated=CCappeak
CapModFac
We check that the design volume flow per total capacity is
within the prescribed range:
\[FlowCapRatio = \dot
Vair,rated/CCaprated\]
If FlowCapRatio <
FlowCapRatiomin then
\[CCaprated = \dot
Vair,rated/FlowCapRatiomin\]
If FlowCapRatio >
FlowCapRatiomax then
\[CCaprated = \dot
Vair,rated/FlowCapRatiomax\]
where
FlowCapRatiomin = 0.00004027
m3/s per watt (300 cfm/ton)
And
FlowCapRatiomax= 0.00006041
m3/s per watt (450 cfm/ton)
We check the design flow to the total cooling capacity rato
for dedicated zone outdoor unit DX cooling coils to be within
the limits prescribed below:
FlowCapRatiomin = 0.00001677
m3/s per Watt (125 cfm/ton)
And
FlowCapRatiomax= 0.00003355
m3/s per Watt (250 cfm/ton)
Rated Total Heating
Capacity[LINK]
For Coil:Heating:DX:SingleSpeed
the rated heating capacity is set equal to the cooling
capacity.
The rated sensible heat ratio is calculated to be the
sensible cooling (from rated inlet conditions to user
specified supply conditions) divided by the total cooling
(from rated inlet to specified supply).
Tin,rated= 26.6667 oC (80
oF)
Win,rated= 0.01125 (corresponds to 80
oF drybulb, 67 oF wetbulb)
Cp,air=
PsyCpAirFnWTdb(Win,rated,
Tin,rated)
For system coils
Tsup=CoolSupTempsys
Wsup=CoolSupHumRatsys
For zone coils
Tsup=
CoolDesTempzone
Wsup=
CoolDesHumRatzone
Then
hrated=
PsyHFnTdbW(Tin,rated,
Win,rated)
hsup=
PsyHFnTdbW(Tsup,
Wsup)
hrated,sup=hratedhsup
Qsrated,sup=Cp,air(Tin,ratedTsup)
SHRrated=Qsrated,suphrated,sup
Evaporative
Condenser Air Volume Flow Rate[LINK]
The evaporative condenser air volume flow rate
(m3/s) is set to 0.000114 m3/s per watt
(850 cfm/ton) times the total rated cooling capacity.
Evaporative
Condenser Air Volume Flow Rate, Low Speed[LINK]
The evaporative condenser air volume flow rate, low speed
(m3/s) is set to 1/3 times 0.000114 m3/s
per watt (850 cfm/ton) times the total rated cooling
capacity.
Evaporative
Condenser Pump Rated Power Consumption[LINK]
The evaporative condenser pump rated power consumption is
set equal to the total cooling capacity times 0.004266 watts
pump power per watt capacity (15 W/ton).
Evaporative
Condenser Pump Rated Power Consumption, Low Speed[LINK]
The evaporative condenser pump rated power consumption, low
speed, is set equal to 1/3 times the total cooling capacity
times 0.004266 watts pump power per watt capacity (15
W/ton).
Rated Air Volume
Flow Rate, low speed[LINK]
The rated air volume flow rate, low speed, is set equal to
1/3 times the full rated air volume flow rate.
Rated Total
Cooling Capacity, Low Speed[LINK]
The rated total cooling capacity, low speed, is set equal
to 1/3 times the full rated total cooling capacity.
Rated SHR, low speed[LINK]
The rated sensible heat ratio, low speed, is set equal to
the full speed SHR.
Resistive Defrost
Heater Capacity[LINK]
For the heat pump the resistive defrost heat capacity is
set equal to the cooling capacity.
DX MultiSpeed Coil
Sizing[LINK]
The sizing calculations are done in subroutine
SizeDXCoil in module DXCoils. This section
covers the sizing of the objects
The rated air volume flow rate, rated total cooling
capacity, rated heating capacity, rated SHR, evaporative
condenser air volume flow rate, evaporative condenser pump
rated power consumption at the highest speed are sized in the
same ways as DX Coil Sizing.
After the sizes are determined at the highest speed, the
sizes in the rest of speeds are assumed to
\[Valu{e_n} =
\frac{n}{{NumberOfSpeed}}*Valu{e_{NumberOfSpeed}}\]
where
Valuen= Any autosizable variable at Speed n,
except SHR
SHRn = SHRNumberOfSpeed
n= Speed Index number from 1 to NumberOfSpeed-1
NumberOfSpeed= The highest speed number
Coil:Cooling:DX:VariableSpeed
Sizing[LINK]
For the variable-speed DX cooling coil, we specify a
nominal speed level. During the sizing calculation, the Rated
Total Cooling Capacity at the Selected Nominal Speed Level is
determined in the same way as the Coil:Cooling:DX:SingleSpeed
object. If the user chooses to autosize the Rated Air Volume
Flow Rate, the flow rate, as compared to the Rated Total
Cooling Capacity, is sized to have the same ratio as the air
volume flow rate to the total cooling capacity at the nominal
speed, of the Reference Unit. The sensible heat transfer rate
is not allowed for auto-sizing, instead, it is a function of
the rated air flow, rated total cooling capacity and the
Reference Unit SHR at the nominal speed level. The default
nominal speed level is the highest speed. However, the model
allows the user to select a nominal speed level rather than
the highest.
Rated Total Cooling Capacity
The calculation for coil operating temperatures (inlet and
outlet) are identical to that done for Coil:Cooling:DX:SingleSpeed.
The calculations for air enthalpy are similar to that done for
Coil:Cooling:DX:SingleSpeed.
The difference is in calculating the total cooling capacity
temperature modifier function at the selected nominal speed
level, as below:
\[TotCapTempModFra{c_{NominalSpeed}} =
{\rm{a}} + {\rm{b*}}W{B_i} + c*WB_i^2 + {\rm{d*}}D{B_o} +
e*D{B_o}{T^2} + f*W{B_i}*D{B_o}\]
where
WBi = wet-bulb temperature of the air entering
the cooling coil, °C
DBo = condenser entering air temperature, °C
a-f = regression curve-fit coefficients.
If the entering air enthalpy is less than the exiting air
enthalpy, a reference value of 48,000 J/kg is used as the
entering air enthalpy. If the TotCapTempModFac
calculation above yields 0 as the result, a value of 1 is used
in the following calculation. If the rated air mass flow rate
is determined to be less than a very small flow value (0.001
kg/s) or the capacity calculated here is less than 0, the coil
total cooling capacity is set equal to 0.
If Hin > Hout Then
\[{\dot Q_{coil,rated,total}} =
{m_{air,rated}}({H_{in}} -
{H_{out}})/TotCapTempModFra{c_{NominalSpeed}}\]
Else
\[{\dot Q_{coil,rated,total}} =
{m_{air,rated}}(48000 -
{H_{out}})/TotCapTempModFra{c_{NominalSpeed}}\]
End If
The other sizing procedures, e.g. evaporative condenser
pump, etc., are the same as Coil:Cooling:DX:SingleSpeed.
Coil:Heating:DX:VariableSpeed
Sizing[LINK]
For the variable-speed DX heating coil, we specify a
nominal speed level. During the sizing calculation, the Rated
Heating Capacity at the Selected Nominal Speed Level should be
the same as the total cooling capacity of its corresponding
cooling coil, which has to be sized first. The default nominal
speed level will be the highest speed. However, the model
allows the user to select a nominal speed level rather than
the highest. If the user chooses to autosize the Rated Air
Volume Flow Rate, the flow rate, as compared to the Rated
Heating Capacity, is sized to have the same ratio as the air
volume flow rate to the heating capacity at the nominal speed,
of the Reference Unit. The other sizing procedures are the
same as Coil:Heating:DX:SingleSpeed.
The loop pumps’ autosizable inputs are nominal volumetric
flow rate and nominal power consumption. We have
Efftot=EffmotEffimpeller
The motor efficiency is an input. Since we need the total
efficiency to calculate the nominal power consumption we
assume an impeller efficiency of 0,78 for purposes of
sizing.
Rated Volumetric Flow
Rate[LINK]
This is just set equal to the design loop demand obtained
from summing the needs of the components on the demand side of
the loop.
Rated Power Consumption[LINK]
\[\dot Qnom = Hnom\dot
Vnom/Efftot\]
Hnom, the nominal head, is an
input.
Electric Chiller Sizing[LINK]
Generally chillers will need nominal cooling capacity,
evaporator flow rate and condenser flow rate. All 3 quantities
can be straightforwardly obtained using the user specified
loop sizing data and the loop design flow rates.
All chillers on a loop are sized to meet the full loop
load. If there are multiple chillers on a loop that call for
autosizing, they will all be assigned the same cooling
capacity and evaporator flow rate.
Nominal Cooling
Capacity[LINK]
\[\dot Qchiller,nom = Cp,w\rho
w\Delta Tloop,des\dot Vloop,des\]
where
Cp,w is the specific heat of water at 5
oC;
w is the density of water at standard
conditions (5.05 oC);
Tloop,des is the chilled water loop
design temperature rise;
\(\dot Vloop,des\) is the
loop design volumetric flow rate.
Design
Evaporator Volumetric Water Flow Rate[LINK]
\[\dot Vevap,des = \dot
Vloop,des\]
Design
Condenser Volumetric Water Flow Rate[LINK]
\[\dot Vcond,des = \dot
Qchiller,nom(1 + 1/COPchiller,nom)/(\Delta Tloop,desCp,w\rho
w)\]
where
Cp,w is the specific heat of water at
design condenser inlet temperature;
w is the density of water at standard
conditions (5.05 oC);
Tloop,des is the chilled water loop
design temperature rise;
COPchiller,nom is the chiller nominal
COP.
Boiler Sizing
Generally boilers will need nominal heating capacity and
rate. Both quantities can be straightforwardly obtained using
the user specified loop sizing data and the loop design flow
rates.
All boilers on a loop are sized to meet the full loop load.
If there are multiple boilers on a loop that call for
autosizing, they will all be assigned the same heating
capacity and flow rate.
Nominal Capacity[LINK]
\[\dot Qboiler,nom = Cp,w\rho
w\Delta Tloop,des\dot Vloop,des\]
where
Cp,w is the specific heat of water at
the boiler design outlet temperature;
w is the density of water at standard
conditions (5.05 oC);
Tloop,des is the hot water loop design
temperature decrease;
\(\dot Vloop,des\) is the
loop design volumetric flow rate.
Design
Evaporator Volumetric Water Flow Rate[LINK]
\[\dot Vdes = \dot
Vloop,des\]
Plant Heat Exchanger
Sizing[LINK]
The sizing of plant heat exchanger component (object:
HeatExchanger:FluidToFluid) involves determining design flow
rates for both sides, a UA value, and a nominal capacity for
reporting. The component has a sizing factor for fine control
and uses the design temperatures defined in the Sizing:Plant
object.
The Loop Supply Side design flow rate, \({\dot V_{Sup,\;des}}\), is set
equal to the design flow rate for that loop, multiplied by the
component sizing factor, \({f_{comp}}\).
\[{\dot V_{Sup,\;des}} = {\dot
V_{loop,des}}*{f_{comp}}\]
The Loop Demand Side design flow rate,\(\;{\dot V_{Dmd,\;des}}\) , is set
equal to the Loop Supply Side design flow rate.
\[{\dot V_{Dmd,\;des}} = {\dot
V_{Sup,\;des}}\]
The design heat transfer capacity and UA for the heat
exchanger are calculated using the design temperatures for the
two plant loops. The loop design temperature difference for
the Loop Supply Side, \(\Delta
{T_{SupLoop,Des}}\), is used to determine a nominal
capacity.
\[\dot Q = {\mathop V\limits^.
_{Sup,\;des}}\rho {c_p}\Delta {T_{SupLoop,Des}}\]
A loop-to-loop design temperature difference, \(\Delta {T_{LoopToLoop,\;Des}}\),
is determined depending on the nature of the plant loop
connected to the Loop Supply Side. The Sizing:Plant
object includes classifications for the type of loop that
include Heating, Steam, Cooling, or Condenser. For Cooling and
Condenser loop types, the loop design temperature difference
is added to the design exit temperature for the Loop Supply
Side, \({T_{SupLoop,Exit}}\).
For Heating and Stem loop types, the loop design temperature
difference is subtracted from the design exit temperature.
This adjusted supply side temperature is then compared to the
design exit temperature for the Loop Demand Side,\(\;{T_{DmdLoop,Exit}}\) .
\(\Delta {T_{LoopToLoop,Des}} =
\left( {{T_{SupLoop,Exit}} + \Delta {T_{SupLoop,Des}}} \right)
- {T_{DmdLoop,Exit}}\) (Cooling, Condenser)
\(\Delta {T_{LoopToLoop,Des}} =
\left( {{T_{SupLoop,Exit}} - \Delta {T_{SupLoop,Des}}} \right)
- {T_{DmdLoop,Exit}}\) (Heating, Steam)
\[\Delta {T_{LoopToLoop,Des}} =
MAX\left( {ABS\left( {\Delta {T_{LoopToLoop,Des}}}
\right),2.0} \right)\]
The UA (U-Factor Time Area Value) is determined by assuming
that the target capacity can be delivered for the loop-to-loop
temperature difference which after substituting and
rearranging becomes:
A nominal capacity for the heat exchanger is determined
from the design flow rates and UA (regardless of if they were
automatically sized or input by the user) and the expected
operating temperatures of the two loops. The loop operating
temperatures are obtained from the input in Sizing:Plant
object if it is present for that loop. If no Sizing:Plant
is present then the loop’s overall setpoint is used (if the
loop’s load scheme is DualSetpointDeadband then the average of
the high and low setpoints is used). The full heat exchanger
model is then calculated for the maximum loop flow rates and
expected loop temperatures as inlets to the heat exchanger.
The absolute value for the model result for heat transfer rate
is then used as the capacity of the heat exchanger. This
capacity is reported and may be used for controls based on
operation scheme.
Humidifier Sizing[LINK]
The rated power, or nominal electric power input of an
Electric Steam Humidifier (Humidifier:Steam:Electric) is
calculated from user specified rated capacity
(m3/s) and the enthalpy change of the water from a
reference temperature (20.0°C) to saturated steam at 100.0°C.
Autosizing procedure assumes that electrical heating element
in the humidifier heat the water from the reference
temperature and generate saturated steam at 100°C, and
electric to thermal energy conversion efficiency of
100.0%.
\[{P_{rated}} = {\dot V_{rated}}
\cdot {\rho _w} \cdot \left( {{h_{fg}} + {C_{p,w}} \cdot
\Delta {T_w}} \right)\]
where
Cp,w is the specific heat of water at
average temperature ((100+20)/2 = 60.0 °C), (J/kgK);
\(\rho_w\) is the
density of water at standard conditions (5.05 °C);
\(\Delta T_w\) is the
sensible temperature rise of water (100.0 - 20.0=80.0
°C);
\({\dot V_{rated}}\)
is the rated capacity of the humidifier in volumetric flow
rate.
hfg is the latent heat of vaporization of
water at 100.0°C, (J/kg);
Gas Fired Humidifier
Sizing[LINK]
The rated power, or nominal gas use rate of a gas steam
humidifier (Humidifier:Steam:Gas) is calculated from user
specified rated volumetric capacity (m3/s) and the enthalpy
change of the water from a reference temperature of 20.0°C to
a saturated steam at 100.0°C. Autosizing procedure assumes
that gas heater in the humidifier convert the water from the
reference temperature and generate saturated steam at 100°C,
using gas to thermal energy conversion rated thermal
efficiency.
Rated Gas Use Rate
The rated or nominal gas use rate is given by:
\[Q_{NG,nom} =
\frac{\dot{V}_{cap,nom}\rho_w\left(h_{fg}+c_{p,w}\Delta
T_w\right)}{\eta_{rated}}\]
Where,
Cp,w is the specific heat of water at
average temperature ((100+20)/2 = 60.0 °C), (J/kgK);
\(\rho_w\) is the
density of water at standard conditions (5.05 °C);
\(\Delta T_w\) is the
sensible temperature rise of water (100.0 - 20.0=80.0
°C);
\({\dot V_{cap,nom}}\)
is the rated or nominal capacity of the humidifier,
(m3/s)
hfg is the latent heat of vaporization of
water at 100.0°C, (J/kg);
\(\eta_{rated}\) is
the thermal efficiency at rated conditions;
Rated Capacity[LINK]
\[{\dot m_w} = {\dot
m_a}({\omega _o} - {\omega _i})\]
where
\(\dot{m}_w\) is water
mass flow rate, kg/s;
\(\dot{m}_a\) is
design air mass flow rate, kg/s;
\(\omega_o\) is design
outlet humidity ratio, kg-water/kg-air;
\(\omega_i\) is design
inlet humidity ratio, kg-water/kg-air.
The air mass flow rate and humidity ratios are determined
based upon zone design conditions. If the unit is part of zone
equipment, then:
\[{\dot m_a} =
Max(DesCoolVolFlo{w_{zone}},DesHeatVolFlo{w_{zone}}) \cdot
{\rho _a}\]
\[{\omega _i} =
Min(OutHumRatAtCoolPea{k_{zone}},OutHumRatAtHeatPea{k_{zone}})\]
\[{\omega _o} =
Max(ZoneHumRatAtCoolPea{k_{zone}},ZoneHumRatAtHeatPea{k_{zone}})\]
where
- \(\rho_a\) is the density
of air at design conditions, kg/s.
If the unit is part of the central air system, then check
if outdoor air system is present. If outdoor air system is
part of the air loop and design outdoor air flow rate is
greater than zero, then:
\[{\dot m_a} =
DesOutAirVolFlo{w_{sys}} \cdot {\rho _a}\]
\[{\omega _i} =
Min(CoolOutHumRa{t_{sys}},HeatOutHumRa{t_{sys}})\]
\[{\omega _o} =
Max(CoolSupHumRa{t_{sys}},HeatSupHumRa{t_{sys}})\]
Otherwise, air mass flow rate is determined as follows:
for duct type = main
\({\dot m_a} =
DesMainAirVolFlo{w_{sys}} \cdot {\rho _a}\)
for duct type = cooling
\[{\dot m_a} =
DesCoolVolFlo{w_{sys}} \cdot {\rho _a}\]
for duct type = heating
\[{\dot m_a} =
DesHeatVolFlo{w_{sys}} \cdot {\rho _a}\]
for duct type = other
\({\dot m_a} =
DesMainVolFlo{w_{sys}} \cdot {\rho _a}\),
and the humidity ratios are:
\[{\omega _i} =
Min(CoolMixHumRa{t_{sys}},HeatMixHumRa{t_{sys}})\]
\[{\omega _o} =
Max(CoolSupHumRa{t_{sys}},HeatSupHumRa{t_{sys}})\]
Gas Fired Humidifier
Sizing[LINK]
The rated power, or nominal gas use rate of a gas steam
humidifier (Humidifier:Steam:Gas) is calculated from user
specified rated volumetric capacity (m3/s) and the
enthalpy change of the water from a reference temperature of
20.0°C to a saturated steam at 100.0°C. Autosizing procedure
assumes that gas heater in the humidifier convert the water
from the reference temperature and generate saturated steam at
100°C, using gas to thermal energy conversion rated thermal
efficiency.
Rated Gas Use Rate[LINK]
The rated or nominal gas use rate is given by:
\[{Q_{NG,{\kern 1pt} nom}} =
\frac{{{{\dot V}_{cap,{\kern 1pt} nom}} \cdot {\rho _w} \cdot
\left( {{h_{fg}} + {c_{p,w}} \cdot \Delta {T_w}}
\right)}}{{{\eta _{rated}}}}\]
Where,
Cp,w = specific heat of water at
average temperature ((100+20)/2 = 60.0 °C), (J/kgK);
\(\rho_w\) = density of
water at standard condition (5.05 °C);
\(\Delta T_w\) = sensible
temperature rise of water (100.0 – 20.0=80.0 °C);
\({\dot V_{cap,{\kern 1pt}
nom}}\) = rated or nominal capacity of the humidifier,
(m3/s)
hfg = latent heat of vaporization of
water at 100.0°C, (J/kg);
\(\eta_{rated}\) = thermal
efficiency at rated condition;
Cooling Tower Sizing[LINK]
The quantities needed to autosize a cooling tower include
the design water flow rate, the nominal fan power and air flow
rate, and the tower UA. This data may be need to be given at
more than one operating point:, for instance - high speed fan,
low speed fan and free convection.
EnergyPlus provides two input choices: the user can input
the design water flow rate and tower UA at each operating
point or the tower nominal capacity (and let the program
calculate the water flow rate and UA). Choice of input method
will affect the sizing calculations in ways noted below.
Design Water Flow Rate[LINK]
If Tower Performance Input Method =
UFactorTimesAreaAndDesignWaterFlowRate then
\[\dot Vtower,w,des = \dot
Vloop,des\]
If Tower Performance Input Method =
NominalCapacity then
\[\dot Vtower,w,des = 5.382E -
8\dot Qtower,nom\]
where 5.38210-08 is m3/s per watt
corresponds to the rule-of-thumb of sizing the tower flow rate
at 3 gallons per minute per ton. For the CoolingTower:VariableSpeed:Merkel
model with NominalCapacity input method, the user can input
the value used to scale design water flow rate from nominal
capacity and the default is 5.38210-08
m3/s/W.
Fan Power at Design
Air Flow Rate[LINK]
The nominal fan power is sized to be 0.0105 times the
design load.
If Tower Performance Input Method =
UFactorTimesAreaAndDesignWaterFlowRate then
\[\dot Qtower,nom = Cp,w\rho
w\dot Vtower,w,des\Delta Tloop,des\]
where
Cp,w is the specific heat of water at
the condenser loop design exit temperature;
w is the density of water at standard
conditions (5.05 oC);
Tloop,des is the condenser water loop
design temperature rise;
Finally
\[\dot Qfan,nom = 0.0105\dot
Qtower,nom\]
For the CoolingTower:VariableSpeed:Merkel
model, the design fan power is determined using a scaling
factor, in units of Watts per Watt, that can be input by the
user. The default value is 0.0105 which is the same as
above.
Design Air Flow Rate[LINK]
We assume a fan efficiency of 0.5 and a fan pressure rise
of 190 Pascals. Then
\[\dot Vtower,air,des = \dot
Qfan,nom0.5\rho air/190\]
where
air is the density of air at standard
conditions.
For the CoolingTower:VariableSpeed:Merkel
model, the design air flow rate is determined from the nominal
capacity using a scaling factor, \({f_{airflow/W}}\),in units of
m3/s/W. The default value is
2.76316*10-5. When the input field is left blank,
the default is used as follows
\[{\dot V_{tower,air,des}} =
{\dot Q_{tower,nom}} \bullet {f_{airflow/W}} \bullet
\frac{{101325}}{{{P_{std,altitude}}}}\]
where, \({P_{std,altitude}}\) is the
standard barometric pressure for the location’s elevation.
When the input field is filled with a hard value, the
pressure scaling is not used
\[{\dot V_{tower,air,des}} =
{\dot Q_{tower,nom}} \bullet {f_{airflow/W}}\]
Tower UA Value
at Design Air Flow Rate[LINK]
To obtain the UA of the tower, we specify the model inputs
(other than the UA) at design conditions and the design tower
load that the tower must meet. Then we numerically invert the
tower model to solve for the UA that will enable the tower to
meet the design tower load given the specified inputs.
The design tower load is:
for Tower Performance Input Method =
UFactorTimesAreaAndDesignWaterFlowRate
\[\dot Qtower,des = Cp,w\rho
w\dot Vtower,w,des\Delta Tloop,des\]
for Tower Performance Input Method =
NominalCapacity
\(\dot Qtower,des = 1.25\dot
Qtower,nom\) (to allow for compressor heat)
Where, \({f_{des,heat,ratio}}\) is the
ratio of actual heat rejection capacity to nominal capacity.
This ratio is available as a user input with a default value
of 1.25 (to allow for compressor heat).
Then we assign the inputs needed for the model.
Tin,air=35 oC (95
oF design air inlet temperature)
Tin,air,wb=25.6 oC (78
oF design air inlet wetbulb temperature)
Win is calculated from the entering air
drybulb and wetbulb.
The inlet water mass flow rate is just the design
volumetric flow rate times the density of water.
The inlet water temperature is set slightly differently for
the 2 input methods. For
UFactorTimesAreaAndDesignWaterFlowRate
Tin,water=Tloop,exit,desTloop,des
NominalCapacity
Tin,water=35 oC (95
oF design inlet water temperature).
We now have all the data needed to obtain UA. The
numerical inversion is carried out by calling subroutine
SolveRegulaFalsi. This is a general utility routine for
finding the zero of a function. In this case it finds the UA
that will zero the residual function - the difference between
the design tower load and the tower output divided by the
design tower load. The residual is calculated in the function
SimpleTowerUAResidual.
Air Flow Rate at Low
Fan Speed[LINK]
The nominal air flow rate at low fan speed is set to a
fraction of the full speed air flow rate. The fraction is
available for user input in the field called Low Fan Speed Air
Flow Rate Sizing Factor. The default is 0.5.
Fan Power at Low Fan
Speed[LINK]
The fan power at low fan speed is set to a fraction of the
fan power at full speed. The fraction is available for user
input in the field called Low Fan Speed Fan Power Sizing
Factor. The default is 0.16.
Tower UA Value at Low
Fan Speed[LINK]
For Tower Performance Input Method =
UFactorTimesAreaAndDesignWaterFlowRate the low speed
UA is set to a fraction of the full speed UA. The fraction is
available for user input in the field called Low Fan Speed
U-Factor Times Area Sizing Factor. The default is 0.6. For
Tower Performance Input Method =
NominalCapacity the low speed UA is calculated in the
same manner as the full speed UA using \(\dot Qtower,nom,lowspeed\)
instead of \(\dot
Qtower,nom\) .
Air Flow Rate
in Free Convection Regime[LINK]
The free convection air flow rate is set to a fraction of
the full air flow rate. The fraction is available for user
input in the field called Free Convection Regime Air Flow Rate
Sizing Factor. The default is 0.1.
Tower UA
Value in Free Convection Regime[LINK]
For Tower Performance Input Method = UA and
Design Water Flow Rate the low speed UA is set to a
fraction of the full speed UA. The fraction is available for
user input in the field called Free Convection U-Factor Times
Area Value Sizing Factor. The default is 0.1. For Tower
Performance Input Method = NominalCapacity the
low speed UA is calculated in the same manner as the full
speed UA using \(\dot
Qtower,nom,freeconv\) instead of \(\dot Qtower,nom\) .
Fluid Cooler Sizing[LINK]
The quantities needed to autosize a fluid cooler include
the design water flow rate, the nominal fan power, air flow
rate, and the fluid cooler UA. This data may need to be given
at more than one operating point:, for instance - high speed
fan and low speed fan.
EnergyPlus provides two input choices: the user can input
the design water flow rate and fluid cooler UA at each
operating point or the fluid cooler nominal capacity and the
water flow rate (and let the program calculate UA). Choice of
input method will affect the sizing calculations in ways noted
below.
Design Water Flow Rate[LINK]
The design water flow rate is sized as follows
\[{\dot V_{fluidcooler,w,des}} =
{\dot V_{loop,des}}\]
Fan Power at
Design Air Flow Rate[LINK]
The nominal fan power is sized to be 0.0105 times the
design load.
If Performance Input Method =
UFactorTimesAreaAndDesignWaterFlowRate then
\[{\dot Q_{fluidcooler,nom}} =
{C_{p,w}} \bullet {\rho _w} \bullet {\dot
V_{fluidcooler,w,des}} \bullet \Delta
{T_{loop,des}}\]
where
Cp,w is the specific heat of water at
the condenser loop design exit temperature;
w is the density of water at standard
conditions (5.05 oC);
Tloop,des is the condenser water loop
design temperature rise;
Finally
\[{\dot Q_{fan,nom}} = 0.0105
\bullet {\dot Q_{fluidcooler,nom}}\]
\[{\dot Q_{fan,nom}} = 0.0105
\bullet {\dot Q_{fluidcooler,nom}}\]
Where
\({\dot
Q_{fluidcooler,nom}}\) is provided by the user.
Design Air Flow Rate[LINK]
- For Performance Input Method =
UFactorTimesAreaAndDesignWaterFlowRate
\[{\dot Q_{fluidcooler,nom}} =
{C_{p,w}} \bullet {\rho _w} \bullet {\dot
V_{fluidcooler,w,des}} \bullet \Delta
{T_{loop,des}}\]
- For Performance Input Method = NominalCapacity
\({\dot
Q_{fluidcooler,nom}}\) is provided by the user.
\[{\dot V_{fluidcooler,air,des}}
= {\dot Q_{fluidcooler,nom}}/({T_{in,water}} -
{T_{in,air}})\*4\]
Where,
Tin,water= Design entering water
temperature provided by the user
Tin,air= Design air inlet temperature
provided by the user
Fluid
cooler UA Value at Design Air Flow Rate[LINK]
To obtain the UA of the fluid cooler, we specify the model
inputs (other than the UA) at design conditions and the design
fluid cooler load that the fluid cooler must meet. Then we
numerically invert the fluid cooler model to solve for the UA
that will enable the fluid cooler to meet the design fluid
cooler load given the specified inputs.
The design fluid cooler load is:
- For Performance Input Method =
UFactorTimesAreaAndDesignWaterFlowRate
\[{\dot Q_{fluidcooler,nom}} =
{C_{p,w}} \bullet {\rho _w} \bullet {\dot
V_{fluidcooler,w,des}} \bullet \Delta
{T_{loop,des}}\]
- For Performance Input Method = NominalCapacity
\({\dot
Q_{fluidcooler,nom}}\) is provided by the user.
Then we assign the inputs needed for the model.
Tin,air= Design air inlet temperature
provided by the user
Tin,air,wb= Design air inlet wetbulb
temperature provided by the user
Win is calculated from the entering air
drybulb and wetbulb.
The inlet water mass flow rate is just the design entering
volumetric flow rate times the density of water.
The inlet water temperature is set slightly differently for
the 2 input methods. For
- UFactorTimesAreaAndDesignWaterFlowRate
\[{T_{in,water}} =
{T_{loop,exit,des}} + \Delta {T_{loop,des}}\]
\[{T_{in,water}} =
Provided\,by\,the\,user\]
We now have all the data needed to obtain UA. The
numerical inversion is carried out by calling subroutine
SolveRegulaFalsi. This is a general utility routine for
finding the zero of a function. In this case it finds the UA
that will zero the residual function - the difference between
the design fluid cooler load and the fluid cooler output
divided by the design fluid cooler load. The residual is
calculated in the function
SimpleFluidCoolerUAResidual.
Air Flow Rate at Low
Fan Speed[LINK]
The nominal air flow rate at low fan speed is set to a
fraction of the full speed air flow rate. The fraction is
available for user input in the field called Low Fan Speed Air
Flow Rate Sizing Factor. The default is 0.5.
Fan Power at Low Fan
Speed[LINK]
The fan power at low fan speed is set to a fraction of the
fan power at full speed. The fraction is available for user
input in the field called Low Fan Speed Fan Power Sizing
Factor. The default is 0.16.
Fluid cooler
UA Value at Low Fan Speed[LINK]
For Performance Input Method =
UFactorTimesAreaAndDesignWaterFlowRate the low speed
UA is set to a fraction of the full speed UA. . The fraction
is available for user input in the field called Low Fan Speed
U-Factor Times Area Sizing Factor. The default is 0.6. For
Performance Input Method = NominalCapacity
the low speed UA is calculated in the same manner as the full
speed UA using \({\dot
Q_{fluidcooler,nom,lowspeed}}\) instead of \({\dot Q_{fluidcooler,nom}}\).
Evaporative Fluid
cooler Sizing[LINK]
The quantities needed to autosize an evaporative fluid
cooler include the design water flow rate, the nominal fan
power, air flow rate, and the fluid cooler UA. This data may
need to be given at more than one operating point:, for
instance - high speed fan and low speed fan.
EnergyPlus provides three input choices: the user can input
the design water flow rate and fluid cooler UA at each
operating point
(UFactorTimesAreaAndDesignWaterFlowRate) or the fluid
cooler design capacity and the water flow rate and let the
program calculate UA (UserSpecifiedDesignCapacity) or
only the fluid cooler design capacity and let the program
calculate UA and the water flow rate
(StandardDesignCapacity). Choice of input method will
affect the sizing calculations in ways noted below.
Design Water Flow Rate[LINK]
If Performance Input Method =
StandardDesignCapacity then
Else
\[{\dot V_{fluidcooler,w,des}} =
{\dot V_{loop,des}}\]
where 5.38210-08 is m3/s per watt
corresponds to the rule-of-thumb of sizing the fluid cooler
flow rate at 3 gallons per minute per ton.
Fan Power at
Design Air Flow Rate[LINK]
The design fan power is sized to be 0.0105 times the design
load.
If Performance Input Method =
UFactorTimesAreaAndDesignWaterFlowRate then
\[{\dot Q_{fluidcooler,design}}
= {C_{p,w}} \bullet {\rho _w} \bullet {\dot
V_{fluidcooler,w,des}} \bullet \Delta
{T_{loop,des}}\]
where
Cp,w is the specific heat of water at
the condenser loop design exit temperature;
w is the density of water at standard
conditions (5.05 oC);
Tloop,des is the condenser water loop
design temperature rise;
Finally
\[{\dot Q_{fan,design}} = 0.0105
\bullet {\dot Q_{fluidcooler,design}}\]
\[{\dot Q_{fan,design}} = 0.0105
\bullet {\dot Q_{fluidcooler,design}}\]
Where
\({\dot
Q_{fluidcooler,design}}\) is the design capacity
provided by the user for the other two performance input
methods
Design Air Flow Rate[LINK]
We assume a fan efficiency of 0.5 and a fan pressure rise
of 190 Pascals. Then
\[{\dot V_{fluidcooler,air,des}}
= {\dot Q_{fan,design}} \bullet 0.5 \bullet {\rho
_{air}}/190\]
where
\(\rho_{air}\) is the
density of air at standard conditions.
Fluid
cooler UA Value at Design Air Flow Rate[LINK]
To obtain the UA of the evaporative fluid cooler, we
specify the model inputs (other than the UA) at design
conditions and the design fluid cooler load that the fluid
cooler must meet. Then we numerically invert the fluid cooler
model to solve for the UA that will enable the fluid cooler to
meet the design fluid cooler load given the specified
inputs.
The design fluid cooler load is:
- For Performance Input Method =
UFactorTimesAreaAndDesignWaterFlowRate
\[{\dot Q_{fluidcooler,design}}
= {C_{p,w}} \bullet {\rho _w} \bullet {\dot
V_{fluidcooler,w,des}} \bullet \Delta
{T_{loop,des}}\]
- For Performance Input Method = StandardDesignCapacity
\({\dot Q_{fluidcooler,design}} =
1.25 \bullet {\dot Q_{fluidcooler,standarddesign}}\)
(to allow for compressor heat)
Then we assign the inputs needed for the model.
Tin,air= 35 oC (95
oF design air inlet temperature)
Tin,air,wb= 25.6 oC (78
oF design air inlet wetbulb temperature)
Win is calculated from the entering air
drybulb and wetbulb.
- For Performance Input Method =
UserSpecifiedDesignCapacity
\[{\dot Q_{fluidcooler,design}}
= {\dot Q_{fluidcooler,userspecifieddesign}}\]
Where, \({f_{des,heat,ratio}}\) is the
ratio of actual heat rejection capacity to nominal capacity.
This ratio is available as a user input with a default value
of 1.25 (to allow for compressor heat)
Then we assign the inputs needed for the model.
Tin,air= Design air inlet temperature
provided by the user
Tin,air,wb= Design air inlet wetbulb
temperature provided by the user
Win is calculated from the entering air
drybulb and wetbulb.
The inlet water mass flow rate is just the design entering
volumetric flow rate times the density of water.
The inlet water temperature is set slightly differently for
the 3 input methods. For
- UFactorTimesAreaAndDesignWaterFlowRate
\[{T_{in,water}} =
{T_{loop,exit,des}} + \Delta {T_{loop,des}}\]
\[{T_{in,water}} = 35^\circ
C\;(95^\circ
F\,design\,inlet\,water\,temperature)\]
- UserSpecifiedDesignCapacity
\[{T_{in,water}} =
Provided\,by\,the\,user\]
We now have all the data needed to obtain UA. The
numerical inversion is carried out by calling subroutine
SolveRegulaFalsi. This is a general utility routine for
finding the zero of a function. In this case it finds the UA
that will zero the residual function - the difference between
the design fluid cooler load and the fluid cooler output
divided by the design fluid cooler load. The residual is
calculated in the function
SimpleEvapFluidCoolerUAResidual.
Air Flow Rate at Low
Fan Speed[LINK]
The design air flow rate at low fan speed is set to a
fraction of the full speed air flow rate. The fraction is
available for user input in the field called Low Fan Speed Air
Flow Rate Sizing Factor. The default is 0.5.
Fan Power at Low Fan
Speed[LINK]
The fan power at low fan speed is set to a fraction of the
fan power at full speed. The fraction is available for user
input in the field called Low Fan Speed Fan Power Sizing
Factor. The default is 0.16.
Fluid cooler
UA Value at Low Fan Speed[LINK]
For Performance Input Method =
UFactorTimesAreaAndDesignWaterFlowRate the low speed
UA is set to a fraction of the full speed UA. The fraction is
available for user input in the field called Low Fan Speed
U-Factor Times Area Sizing Factor. The default is 0.6. For
Performance Input Method =
StandardDesignCapacity (and similarly for
UserSpecifiedDesignCapacity method) the low speed UA
is calculated in the same manner as the full speed UA using
\({\dot
Q_{fluidcooler,standarddesign,lowspeed}}\) instead of
\({\dot
Q_{fluidcooler,standarddesign}}\).
Fan Coil Unit Sizing[LINK]
Fan Coil units are compound components: each unit contains
a fan, hot water coil, chilled water coil and outside air
mixer. The inputs that may need to be autosized are the
nominal unit air flow rate, the maximum hot and chilled water
flow rates, and the design outside air flow rate. The data
needed for sizing the units is obtained from the zone design
arrays and the user specified plant sizing input.
Maximum Air Flow Rate[LINK]
\[\dot Vair,max =
Max(DesCoolVolFlowzone,DesHeatVolFlowzone)\]
Maximum Outside Air
Flow Rate[LINK]
\[\dot Voutsideair,max =
Min(MinOAzone,\dot Vair,max)\]
Maximum Hot Water Flow[LINK]
Tcoil,in=DesHeatCoilInTempzone
Tcoil,out=HeatDesTempzone
\[\dot Qcoil,des =
cp,airDesHeatMassFlowzone(Tout,coil - Tin,coil)\]
\[\dot Vmax,hw = \dot
Qcoil,des/(cp,w\rho w\Delta Tloop,des)\]
where
cp,air is evaluated at the average of
the inlet & outlet temperatures and the coil outlet
humidity ratio.
Maximum Cold Water Flow[LINK]
Tcoil,in=DesColdCoilInTempzone
Tcoil,out=ColdDesTempzone
Wcoil,in=
DesCoolCoilInHumRatzone
Wcoil,out=
CoolDesHumRatzone
Hcoil,in=
PsyHFnTdbW(Tcoil,in,
Wcoil,in)
Hcoil,out=
PsyHFnTdbW(Tcoil,out,
Wcoil,out)
\[\dot Qcoil,des =
DesCoolMassFlowzone(hin,coil - hout,coil)\]
\[\dot Vmax,hw = \dot
Qcoil,des/(cp,w\rho w\Delta Tloop,des)\]
where
cp,air is evaluated at the average of
the inlet & outlet temperatures and the coil outlet
humidity ratio.
Window Air Conditioner
Sizing[LINK]
Window
air conditioners are compound components: each unit contains a
fan, a DX coil and an outside air mixer. The inputs that may
need to be autosized are the nominal unit air flow rate and
the design outside air flow rate. The data needed for sizing
the units is obtained from the zone design arrays.
Maximum Air Flow Rate[LINK]
\[{\dot V_{air,max}} =
DesCoolVolFlo{w_{max}}\]
Maximum Outside Air
Flow Rate[LINK]
\[\dot Voutsideair,max =
Min(MinOAzone,\dot Vair,max)\]
Unit Ventilator Sizing[LINK]
Unit ventilators are compound components: each unit
contains an outdoor air mixer, a fan, a heating coil, and a
cooling coil. The inputs that may need to be autosized are the
maximum supply air flow rate and the maximum/minimum outside
air flow rates. The data needed for sizing the units is
obtained from the zone design arrays.
Maximum Air Flow Rate[LINK]
If both the cooling and heating coil are present, then:
\[{\dot
V_{{\rm{supplyair,max}}}} =
MAX(DesCoolVolFlowzone,DesHeatVolFlowzone)\]
If only the heating coil is present, then:
\[{\dot
V_{{\rm{supplyair,max}}}} = DesHeatVolFlowzone\]
If only cooling coil is present, then:
\[{\dot V_{{\rm{supplyair,
max}}}} = DesCoolVolFlowzone\]
If neither heating nor cooling coil is present, then:
\[{\dot
V_{{\rm{supplyair,max}}}} = MinOAzone\]
Maximum Outside Air
Flow Rate[LINK]
\[{\dot V_{outsideair,\max }} =
{\dot V_{air,\max }}\]
Minimum Outside Air
Flow Rate[LINK]
\[{\dot V_{outsideair,\min }} =
Min(MinOAzone,{\dot V_{air,\max }})\]
Packaged Terminal
Heat Pump Sizing[LINK]
Packaged terminal heat pumps are compound components: each
unit contains a supply air fan, a DX cooling coil, a DX
heating coil, a GAS or ELECTRIC supplemental heating coil, and
an outside air mixer. The inputs that may need to be autosized
are the supply air and outside air volumetric air flow rates
during cooling operation, heating operation, and when no
cooling or heating is needed. In addition, the maximum supply
air temperature from the supplemental heater can also be
automatically selected. The data needed for sizing the units
are obtained from the zone design arrays.
Supply
air volumetric flow rate during cooling operation[LINK]
\[{\mathop V\limits^
\cdot _{SA\,\,,\,cooling}} =
\,\,MAX(DesCoolVolFlowzone,\,DesHeatVolFlowzone)\]
Supply
air volumetric flow rate during heating operation[LINK]
\[{\mathop V\limits^
\cdot _{SA\,\,,\,heating}} =
\,\,MAX(DesCoolVolFlowzone,\,DesHeatVolFlowzone)\]
Supply
air volumetric flow rate when no cooling or heating is
needed[LINK]
\[{\mathop V\limits^
\cdot _{SA\,,\,no\,cool\,or\,heat}} =
\,\,MAX(DesCoolVolFlowzone,\,DesHeatVolFlowzone)\]
Outside
air volumetric flow rate during cooling operation[LINK]
\[{\mathop V\limits^
\cdot _{OA\,,\,\,cooling}} =
{\rm{MIN}}(MinO{A_{zone}},{\mathop {\,V}\limits^
\cdot _{SA\,,\,\,cooling}})\]
Outside
air volumetric flow rate during heating operation[LINK]
\[{\mathop V\limits^
\cdot _{OA\,,\,\,heating}} =
{\rm{MIN}}(MinO{A_{zone}},{\mathop {\,V}\limits^
\cdot _{SA\,,\,\,heating}})\]
Outside
air volumetric flow rate when no cooling or heating is
needed[LINK]
\[{\mathop V\limits^
\cdot _{OA\,,\,no\,\,cool\,or\,heat}} =
{\rm{MIN}}(MinO{A_{zone}},{\mathop {\,V}\limits^
\cdot _{SA\,,\,no\,\,cool\,or\,heat}})\]
Maximum
supply air temperature from supplemental heater[LINK]
\[{T_{SA,\max }} =
HeatDesTem{p_{zone}}\]
MultiSpeed Heat Pump
Sizing[LINK]
MultiSpeed heat pumps are compound components: each unit
contains a supply air fan, a multispeed DX cooling coil, a
multispeed DX heating coil, and a GAS or ELECTRIC supplemental
heating coil. The inputs that may need to be autosized are the
supply air volumetric air flow rates during cooling operation,
heating operation, and when no cooling or heating is needed.
The data needed for sizing the units are obtained from the
controlled zone design arrays.
Supply
air volumetric flow rate during cooling operation at the
highest speed[LINK]
\[{\mathop V\limits^
\cdot _{SA\,\,,\,cooling}} =
\,\,MAX(DesCoolVolFlowzone,\,DesHeatVolFlowzone)/ZoneFraction\]
Supply
air volumetric flow rate during heating operation at the
highest speed[LINK]
\[{\mathop V\limits^
\cdot _{SA\,\,,\,heating}} =
\,\,MAX(DesCoolVolFlowzone,\,DesHeatVolFlowzone)/ZoneFraction\]
Supply
air volumetric flow rate when no cooling or heating is
needed[LINK]
\[{\mathop V\limits^
\cdot _{SA\,,\,no\,cool\,or\,heat}} =
\,\,MAX(DesCoolVolFlowzone,\,DesHeatVolFlowzone)/ZoneFraction\]
where
ZoneFraction = Fraction of the total volume flow that goes
through the controlling zone
Supply
air volumetric flow rate during cooling operation at Speed n
(1 to NumberOfSpeed-1)[LINK]
\[{\mathop V\limits^
\cdot _{SA\,\,,\,cooling,n}} =
\frac{n}{{NumberOfSpeed}}{\mathop V\limits^
\cdot _{SA\,\,,\,cooling}}\]
Supply
air volumetric flow rate during heating operation at Speed n
(1 to NumberOfSpeed-1)[LINK]
\[{\mathop V\limits^
\cdot _{SA\,\,,\,heating,n}} =
\frac{n}{{NumberOfSpeed}}{\mathop V\limits^
\cdot _{SA\,\,,\,heating}}\]
where
n= Speed Index number from 1 to NumberOfSpeed-1
NumberOfSpeed= The highest speed number
Single Duct Terminal
Units[LINK]
These are all the EnergyPlus components whose names begin
with “AirTerminal:SingleDuct:” (except for Cooled
Beam units). This includes Uncontrolled,
ConstantVolume:Reheat, VAV:NoReheat, VAV:Reheat,
VAV:Reheat:VariableSpeedFan, VAV:HeatAndCool:NoReheat,
VAV:HeatAndCool:Reheat, SeriesPIU:Reheat,
ParallelPIU:Reheat, and
ConstantVolume:FourPipeInduction. The inputs that may
need to be autosized are the various maximum air flow rates
through the unit, minimum air flow rates, and maximum hot
water and/or chilled water flow rates if heating or cooling
coils are present.
Note: all zone design flow rates and loads
referenced below may have been altered by system sizing
inputs. For instance, if the user specifies a Cooling
Design Air Flow Method = Flow/System and specifies a
Cooling Design Air Flow Rate the zone cooling design
values will be altered to match the specified system flow
rate.
Maximum Air Flow Rate[LINK]
\[{\dot V_{air,\max
,{\rm{terminal}}}} =
Max(DesCoolVolFlowzone,DesHeatVolFlowzone)\]
Maximum Heating Air
Flow Rate[LINK]
\[{\dot
V_{air,max,heat,terminal}} = DesHeatVolFlowzone\]
Maximum
Primary and Secondary Air Flow Rates[LINK]
For the PIU terminal units, the maximum primary and
secondary air flow rates are sized to the same value as the
maximum total air flow rate.
Minimum Air Flow Rate[LINK]
Basically minimum air flow rates are sized to the
ventilation air requirement. This may be more or less
complicated.
For the PIU’s, the minimum primary air flow fraction is set
to
\(\mathop {MinOA}\nolimits_{zone}
/{\dot V_{air,max,primary,terminal}}\).
For other VAV terminal units
\[{\dot V_{air,min,terminal}} =
Fra{c_{air,\min }}*DesVolFlowzone\]
where, Fracair,min corresponds to the minimum flow
fraction of the teminal unit. This value is provided as user
input, typically as the field “Zone
Minimum Air Flow Fraction.” For the VAV terminals that allow
scheduling minimum flow fraction (e.g.,
AirTerminal:SingleDuct:VAV:Reheat), there are two ways that
Fracair,min can be determined. If a value is entered
in the input field Constant Minimum Air Flow Fraction, then it
is always used for Fracair,min. If the mimimum air
flow fraction method is “Schedule” and the Constant Minimum
Air Flow Fraction is left blank, then the program uses the
average of the minimum and maximum values in the schedule for
Fracair,min.
Fan On Flow Fraction[LINK]
For the parallel PIU, this is set to the minimum primary
air flow fraction.
Max Hot Water Flow[LINK]
\[{T_{coil,in}} =
DesHeatCoilInTem{p_{zone}}\]
\[{T_{coil,out}} =
HeatDesTem{p_{zone}}\]
The coil load and max hot water flow rate are then:
\[\dot Qcoil,des = cp,air\rho
air\dot Vair,coil,heating(Tout,coil - Tin,coil)\]
\[\dot Vmax,hw = \dot
Qcoil,des/(cp,w\rho w\Delta Tloop,des)\]
where
cp,air is evaluated at the average of
the inlet & outlet temperatures and the coil outlet
humidity ratio.
The four-pipe induction unit sizes the heating coil
differently: to meet the zone load rather than match the
design zone supply temperature. The load on the hot water coil
is then the zone load minus whatever the central system
does.
\[{\dot Q_{coil,des}} = {\dot
Q_{zone,des}} - {c_{p,air}}{\rho _{air}}{\dot
V_{air,primary,des}}({T_{coil,in}} -
{T_{zone,heatpeak}})\]
where
\[{T_{coil,in}} =
DesHeatCoilInTem{p_{zone}}\]
\[{T_{zone,heatpeak}} =
ZoneTempAtHeatPea{k_{zone}}\]
\[{\dot V_{air,primary,des}} =
{\dot V_{air,max,terminal}}/(1 + {R_{induc}})\]
Max Chilled Water Flow[LINK]
The chilled water flow for the four-pipe induction unit is
sized analogously to the hot water flow.
Indirect
Evaporative Cooler Sizing[LINK]
The model for the object called EvaporativeCooler:Indirect:ResearchSpecial
has a field for the secondary fan flow rate that can be
autosized.
Secondary Fan Flow Rate[LINK]
The secondary fan is not part of an airstream that is
directly modeled in EnergyPlus. Because the primary side air
flows can be autosized as part of the air system, it is
convenent to also scale the size of the secondary flow. If the
cooler is part of the main loop of a central air system, then
the secondary fan flow rate is sized to equal to the main
design flow rate.
\[\dot Vfan,max =
DesMainVolFlowsys\]
If the cooler is part of the outdoor air path of a central
air system, then the secondary fan flow rate is sized to be
the maximum of either the design minimum outdoor air flow rate
or one-half of the main design flow rate.
\[{\dot V_{fan,\max }} =
MAX({\rm{DesOutAirVolFlow,
0}}{\rm{.5\*DesMainVolFlow)}}\]
Secondary DX Coils
Sizing[LINK]
The secondary DX coils model does not have a standalone
object and it is models as add–on feature to the DX Coils.
When the secondary DX coil is added to a primary DX cooling
coil, the heat rejected to secondary zone is sensible only and
is treated as tnternal gain, hence secondary air flow rate is
not required in the model. Where as when the secondary DX coil
is added to a primary DX heating coil, then the heat removed
from secondary zone may have sensible and latent components
and is treated as tnternal gain. The sensible/latent component
split among other parameters requires secondary coil air flow
rate. Hence secondary coil air flow rate sizing is added based
on the primary DX cooling coil only.
\[{\dot V_{SecCoil}} = {\dot
V_{PriHeatCoil}} \cdot ScalingFactor\]
Where,
\({\dot V_{SecCoil}}\) =
the secondary coil design air flow rate (m3/s)
\({\dot V_{PriHeatCoil}}\)
= the primary heating DX coil design air flow rate, (kg/s)
\(ScalingFactor\) =
secondary DX coil air flow rarte scaling factor (-)
Desiccant Dehumidifier
Sizing[LINK]
The sizing of dehumidifier with no fans is done in
subroutine SizeDesiccantDehumidifier.
Nominal Process Air
Flow Rate[LINK]
If the unit is part of zone equipment, then:
\[{\dot V_p} =
Max(DesCoolVolFlo{w_{zone}},DesHeatVolFlo{w_{zone}})\]
If the unit is part of the central air system, then check
if outdoor air system is present. If outdoor air system is
part of the air loop and design outdoor air flow rate is
greater than zero, then:
\[{\dot V_p} =
DesOutAirVolFlo{w_{sys}}\]
Otherwise, nominal process air flow rate is determined as
follows:
for duct type = main
\({\dot V_p} =
DesMainVolFlo{w_{sys}}\)
for duct type = cooling
\[{\dot V_p} =
DesCoolVolFlo{w_{sys}}\]
for duct type = heating
\[{\dot V_p} =
DesHeatVolFlo{w_{sys}}\]
for duct type = other
\[{\dot V_p} =
DesMainVolFlo{w_{sys}}\]
Evaporative Cooler
Sizing[LINK]
The sizing of evaporative cooler objects is done in
subroutine SizeEvapCooler.
Secondary Fan Flow
Rate[LINK]
\[\dot V =
DesMainVolFlo{w_{sys}}\]
Note that it is only applicable to indirect CELdek pad
object.
Direct Pad Area[LINK]
As from the continuity equation, the area of direct pad is
directly determined by assuming face air velocity of 3m/s
as:
\[{A_{pad}} =
\frac{{DesMainVolFlo{w_{sys}}}}{V}\]
where
Apad is area of direct pad,
m2
V is face air velocity, m/s
Direct Pad Depth[LINK]
The solution of the following regression equation is used,
assuming saturation effectiveness of 70% and face air velocity
of 3m/s:
ɛ = 0.792714 + 0.958569D - 0.25193V - 1.03215D2 +
0.0262659V2 + 0.914869DV
- 1.48241VD2 - 0.018992 D V3 +
1.13137D3V + 0.0327622 D2V3 -
0.145384D3V2
where
Heat Recovery Sizing[LINK]
The sizing of heat exchanger objects is done in subroutine
SizeHeatRecovery.
Nominal Supply Air Flow
Rate[LINK]
If the unit is part of zone equipment, then:
\[{\dot V_p} =
Max(DesCoolVolFlo{w_{zone}},DesHeatVolFlo{w_{zone}})\]
If the unit is part of the central air system, then check
if outdoor air system is present. If outdoor air system is
part of the air loop and design outdoor air flow rate is
greater than zero, then:
\[{\dot V_p} =
DesOutAirVolFlo{w_{sys}}\]
Otherwise, nominal supply air flow rate is determined as
follows:
for duct type = main
\({\dot V_p} =
DesMainVolFlo{w_{sys}}\)
for duct type = cooling
\[{\dot V_p} =
DesCoolVolFlo{w_{sys}}\]
for duct type = heating
\[{\dot V_p} =
DesHeatVolFlo{w_{sys}}\]
for duct type = other
\[{\dot V_p} =
DesMainVolFlo{w_{sys}}\]
Nominal Supply Air
Flow Rate[LINK]
It is assumed to be equal to the nominal supply air flow
rate.
Low Temperature
Radiant System Sizing[LINK]
The sizing is done in subroutine
SizeLowTempRadiantSystem.
ZoneHVAC:LowTemperatureRadiant:Electric:[LINK]
Nominal Capacity[LINK]
\[Cap = DesHeatLoa{d_{zone}}
\cdot HeatSizingFactor\]
ZoneHVAC:LowTemperatureRadiant:VariableFlow:[LINK]
Maximum Hot Water Flow[LINK]
\[{\dot V_h} =
\frac{{DesHeatLoa{d_{zone}} \cdot HeatSizingFactor}}{{\Delta
{T_h} \cdot {c_{p,h}} \cdot {\rho _h}}}\]
where
Vh is maximum hot water flow rate,
m3/s
cp,h is specific heat of hot water at
reference condition (60°C), J/kgK
h is the density of water at reference
condition (60°C), kg/m3
Maximum Cool Water Flow[LINK]
\[{\dot V_c} =
\frac{{DesCoolLoa{d_{zone}} \cdot CoolSizingFactor}}{{\Delta
{T_c} \cdot {c_{p,c}} \cdot {\rho _c}}}\]
Vc is maximum chilled water flow rate,
m3/s
cp,c is specific heat of hot water at
reference condition (5°C), J/kgK
c is the density of chilled water at
reference condition (5°C), kg/m3
Hydronic Tubing Length[LINK]
\[TubeLength =
\frac{{TotalSurfaceArea}}{{TubeSpacing}}\]
Note that tube spacing is assumed to be 0.15m.
ZoneHVAC:LowTemperatureRadiant:ConstantFlow:[LINK]
Rated Flow Rate[LINK]
The object provides both cooling and heating, and also
operates in a single operating mode such as cooling-only or
heating-only mode. Thus, the rated flow rate is determined,
depending upon the operating mode of the unit. If the unit
operates in a single operating mode, either design chilled
water or hot water flow rate is chosen. The larger of the two
is chosen if the unit provides both cooling and heating. The
flow rates are determined in the same fashion to the variable
flow system above.
Hydronic Tubing Length[LINK]
The length of hydronic tube is determined as described in
the variable flow radiant system above.
Unitary System Sizing[LINK]
The AirloopHVAC:UnitarySystem object incorporates all coils
types and fans as a complete packaged system. The fans and
coils are optional allowing virtually any system type to be
modeled. Sizing of this object depends on the coils selected.
For single coil systems, the associated air flow rate is used
as the operating flow rate (i.e., cooling or heating). For
systems with both a cooling and heating coil, this methodology
still applies except for DX systems (Heat Pumps) where the
greater of the cooling or heating air flow rate is used. Heat
pumps are defined as systems having both a DX cooling and DX
heating coil. Other AirloopHVAC equipment models use the
greater of the cooling and heating flow rates. The inputs that
may need to be autosized are the supply air air volumetric air
flow rates during cooling operation, heating operation, and
when no cooling or heating is needed. The data needed for
sizing the units are obtained from the zone design arrays.
Supply Air Flow Rate:[LINK]
Supply air volumetric flow rate during cooling
operation
\[\dot{V}_{SA,cooling} =
\rm{DesCoolVolFlow}_{zone}/\rm{ZoneFraction}\]
Supply air volumetric flow rate during heating
operation
\[\dot{V}_{SA,heating} =
\rm{DesHeatVolFlow}_{zone}/\rm{ZoneFraction}\]
Supply air volumetric flow rate when DX coils are
used as a system
\[\dot{V}_{SA} =
MAX(\rm{DesCoolVolFlow}_{zone}, \rm{DesHeatVolFlow}_{zone}) /
\rm{ZoneFraction}\]
where
ZoneFraction = Fraction of the total volume flow
that goes through the controlling zone
The unitary system object also allows scalable sizing as
follows:
Flow Per Floor Area:
\[\dot{V}_{SA} =
(\rm{FlowPerFloorArea})(\rm{TotalFloorArea})\]
Fraction of Autosized Cooling Value:
\[\dot{V}_{SA,cooling} =
\dot{V}_{SA,des,coolings}(\rm{FractionOfCoolingValue})\]
Fraction of Autosized Heating Value:
\[\dot{V}_{SA,heating} =
\dot{V}_{SA,des,heatings}(\rm{FractionOfHeatingValue})\]
Flow Per Cooling Capacity
\[\dot{V}_{SA,cooling} =
\dot{Q}_{coil,des,cooling}(\rm{FractionOfCoolingValue})\]
Flow Per Heating Capacity
\[\dot{V}_{SA,heating} =
\dot{Q}_{coil,des,heating}(\rm{FractionOfCoolingValue})\]
The maximum supply air temperature can also be
automatically selected. The value is determined from the Sizing:Zone
or Sizing:System
object depending on where the object is used in the simulation
(i.e., as zone or air loop equipment).
Maximum supply air temperature
\[T_{SA,max} =
\rm{HeatDesTemp}_{\rm{ZoneOrSystem}}\]
Component Sizing[LINK]
Introduction[LINK]
In EnergyPlus each HVAC component sizes itself. Each component module contains a sizing subroutine. When a component is called for the first time in a simulation, it reads in its user specified input data and then calls the sizing subroutine. This routine checks the autosizable input fields for missing data and calculates the data when needed.
A number of high-level variables are used in the sizing subroutines.
CurDuctType (in DataSizing) contains the information about the current duct type. The types can be main, cooling, heating or other.
CurZoneEqNum (in DataSizing) is the current zone equipment set index and indicates that the component is a piece of zone equipment and should size itself using the zone sizing data arrays.
CurSysNum (in DataSizing) is the current air loop index and indicates that the component is part of the primary air system and should size itself using the system sizing data arrays.
Fan Sizing[LINK]
Fan sizing is done in subroutine SizeFan.
Max Flow Rate[LINK]
If the fan is part of the central air system then check the duct type.
For duct type = main, other or default
\[\dot Vfan,max = DesMainVolFlowsys\]
For duct type=cooling
\[\dot Vfan,max = DesCoolVolFlowsys\]
For duct type=heating
\[\dot Vfan,max = DesHeatVolFlowsys\]
If the fan is zone equipment then check whether it is part of a component that only does heating.
For heating only \(\dot Vfan,max = DesHeatVolFlowzone\);
Otherwise \(\dot Vfan,max = Max(DesHeatVolFlowzone,DesCoolVolFlowzone)\)
If the max fan flow rate is less than SmallAirVolFlow the max flow rate is set to zero.
Coil:Cooling:Water[LINK]
The sizing is done in function SizeWaterCoil of module WaterCoils
Initial Calculations[LINK]
System Coils[LINK]
For central cooling coils, the first step is to determine the design air flow rate, load, and design air entering and exit conditions. The coil design air flow rate is not generally the same as the maximum system air flow rate (used to size the central fans). The cooling coil peak load (either sensible or total) can occur at a different time than the system peak flow rate. Hence the coil air entering conditions can be different than those at the peak system flow rate. Also, the method of controlling the coil’s cooling output may also affect coil design flow rate as well as the coil design exit temperature and humidity.
By choosing Type of Load to Size On = Sensible or Total in Sizing:System the user indicates to the program to save the cooling coil air flow rate and system air conditions (mixed, return, outside) at the time of either the system cooling sensible or total load peak. Note that the choice VentilationRequirement uses the time of the sensible peak.
Choosing Central Cooling Capacity Control Method = VAV, Bypass, VT, or OnOff indicates which type of cooling output control the program should assume when calculating the design air flow rate. The function GetCoilDesFlowT in module ReportSizingManager calculates the air flow rate and exit air temperature for each capacity control method.
VAV: \({T_{cc,exit}} = {T_{cool,supply}}\) and \({\dot V_{cc,air}} = {\dot m_{cc,air,peak}}/{\rho _{air}}\)
Bypass: \({T_{cc,exit}} = {T_{cool,supply}}\) and \({\dot V_{cc,air}} = {\dot V_{cc,air,max}}(\max [0,\min [1,({T_{mix,atpeak}} - {T_{sup,avg}})/({T_{mix,atpeak}} - {T_{cc,exit}})]])\) where \({T_{sup,avg}} = {T_{zones,avg}} - \sum\limits_{zones} {{{\dot Q}_{sens,atpeak}}} /({\rho _{air}}{c_{p,air}}{\dot V_{cool,air,max}})\)
VT: \({T_{cc,exit}} = \max [{T_{cool,supply}},({T_{zones,avg}} - \sum\limits_{zones} {{{\dot Q}_{sens,atpeak}}} /({\rho _{air}}{c_{p,air}}{\dot V_{cool,air,max}}))]\) and \({\dot V_{cc,air}} = {\dot V_{cc,air,max}}\)
OnOff: \({T_{cc,exit}} = {T_{cool,supply}}\) and \({\dot V_{cc,air}} = {\dot V_{sys,air,max}}\)
\({\dot m_{cc,air,peak}}\): the air mass flow rate through the cooling coil at the sensible or total system peak cooling load [m3/s]
\(\sum\limits_{zones} {{{\dot Q}_{sens,atpeak}}}\): sum of the zone sensible cooling loads at the time of the peak system cooling load.
\({\rho _{air}}\): the density of air [kg/m3]
\({T_{cc,exit}}\): the design cooling coil exit temperature [°C]
\({T_{cool,supply}}\): the supply air temperature for cooling specified in Sizing:System [°C]
\({T_{mix,atpeak}}\): the mixed air temperature at the time of the system peak cooling load [°C]
\({T_{zones,avg}}\): the average zone temperature at the time of the system peak cooling load [°C]
\({\dot V_{cc,air}}\): the design volumetric air flow rate through the cooling coil [m3/s]. This is the flow rate at either the sensible or total cooling load peak from the design period calculations.
\({\dot V_{cool,air,max}}\): the maximum cooling volumetric air flow rate from the design calculations [m3/s]. This flow rate occurs at the maximum zone cooling demand.
\({\dot V_{sys,air,max}}\): the maximum volumetric air flow rate from the design calculations [m3/s]. This flow rate occurs at either the maximum zone cooling or heating demand.
Design Coil Load (W)[LINK]
Design coil load (cooling capacity) is not an input for Coil:Cooling:Water. It is used for calculating the design water flow rate.
System Coils[LINK]
The design load \({\dot Q_{coil,des}}\) is calculated using:
\[{\dot Q_{coil,des}} = {\dot m_{a,coil,des}}({h_{a,coil,des,in}} - {h_{a,coil,des,out}})\]
where
\({h_{a,coil,des,in}}\) is the coil design inlet air enthalpy [J/kg];
\({h_{a,coil,des,out}}\) is the coil design outlet air enthalpy [J/kg]; and
\({\dot m_{a,coil,des}}\) is the coil design air mass flow rate [kg/s].
The design air mass flow rate depends on the location of the coil. If the coil is in the outside air stream the flow rate is set to \({\rho _{air}}{\dot V_{a,coil,oa,des}}\), where \({\dot V_{a,coil,oa,des}}\) is the design outside air volumetric flow rate for the system. Otherwise \({\dot m_{a,coil,des}}\) is set to \({\rho _{air}}{\dot V_{cc,air}}\) where \({\dot V_{cc,air}}\) is calculated above in the Initial Calculations section.
To obtain the inlet and outlet enthalpies, we need the inlet and outlet temperatures and humidity ratios. The inlet and outlet conditions depend on whether the coil is in the outside air stream and if it is not, whether or not there is outside air preconditioning.
\({T_{air,in,des}} = {T_{out,cool,atpeak}}\) (the outside air temperature at the design cooling peak)
\({T_{air,out,des}} = {T_{sys,precool}}\) (the specified Precool Design Temperature from the Sizing:System object).
\({W_{air,in,des}} = {W_{out,cool,atpeak}}\) (the outside humidity ratio at the design cooling peak)
\({W_{air,out,des}} = {W_{sys,precool}}\) (the specified Precool Design Humidity Ratio from the Sizing:System object)
\({T_{air,in,des}} = {T_{mix,cool,atpeak}}\) (the mixed air temperature at the design cooling peak)
\({W_{air,in,des}} = {W_{mix,cool,atpeak}}\) (the mixed air humidity ratio at the design cooling peak)
Tair,out,des is set to *Tcc,exit calculated above in the Initial Calculation section
\({W_{air,out,des}} = {W_{sup,cool}}\) (the specified Central Cooling Design Supply Air Humidity Ratio from the Sizing:System object)
Tair,out,des and Wair,out,des are defined as in 2).\({T_{air,in,des}} = {f_{oa}}{T_{precool}} + (1 - {f_{oa}}){T_{ret,cool,atpeak}}\) where \({T_{precool}}\) is the specified Precool Design Temperature from System:Sizing. \({T_{ret,cool,atpeak}}\) is the return temperature at the system cooling peak load.
\({W_{air,in,des}} = {f_{oa}}{W_{precool}} + (1 - {f_{oa}}){W_{ret,cool,atpeak}}\) where \({W_{precool}}\) is the specified Precool Design Humidity Ratio from Sizing:System and \({W_{ret,cool,atpeak}}\) is the return humidity ratio at the system cooling peak load.
With the inlet and outlet conditions established, we can obtain the inlet and outlet enthalpies:
hair,coil,des,in = PsyHFnTdbW(Tair,in,des, Wair,in,des)
hair,coil,des,out = PsyHFnTdbW(Tair,out,des, Wair,out,des)
where PsyHFnTdbW is the EnergyPlus function for calculating air specific enthalpy given the air temperature and humidity ratio. We now have all we need to calculate \({\dot Q_{coil,des}}\).
Zone Coils[LINK]
If the coil is part of an AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction unit or an ZoneHVAC:FourPipeFanCoil, the cooling load (cooling capacity) is passed down from the terminal unit or fan coil sizing calculations. Otherwise the load is defined as:
\({\dot Q_{coil,des}} = {\dot m_{a,coil,des}}({h_{a,coil,des,in}} - {h_{a,coil,des,out}})\)
where
\({h_{a,coil,des,out}}\) is the coil design outlet air enthalpy [J/kg]; and
\({\dot m_{a,coil,des}}\) is the coil design air mass flow rate [kg/s].
The enthalpies are given by:
\[{h_{air,coil,des,in}} = PsyHFnTdbW({T_{air,in,des}},{W_{air,in,des}})\]
\[{h_{air,coil,des,out}} = PsyHFnTdbW({T_{air,out,des}},{W_{air,out,des}})\]
where Tair,in,des and Wair,in,des are the coil inlet design conditions. For coils in terminal units these are set at the system level to the system design supply air temperature. For zonal usits they are set to design return air, mixed air, or outside air as appropriate to the unit. Tair,out,des is set to the zone cooling design supply air temperature as specified in the Zone:Sizing inputs. Wair,out,des is set to the zone cooling design supply air humidity ratio as specified in the Zone:Sizing inputs.
Design Water Flow Rate (m3/s)[LINK]
System Coils[LINK]
The design water volumetric flow rate is calculated using:
\[{\dot V_{w,coil,des}} = {\dot Q_{coil,des}}/({\rho _w}{c_{p,w}}\Delta {T_{w,des}})\]
where \(\Delta T_{w,des}\) is just the Loop Design Temperature Difference user input from Sizing:Plant (if the coil is in the outside air stream, ½ the Loop Design Temperature Difference is used).
Zone Coils[LINK]
If the coil is part of an AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction unit or a ZoneHVAC:FourPipeFanCoil, the chilled water flow rate is passed down from the terminal unit or fan coil sizing calculations. Otherwise the flow is set to:
\[{\dot V_{w,coil,des}} = {\dot Q_{coil,des}}/({\rho _w}{c_{p,w}}\Delta {T_{w,des}})\]
where \(\Delta T_{w,des}\) is just the Loop Design Temperature Difference user input from Sizing:Plant. \({\dot Q_{coil,des}}\) is calculated as described above.
Design Air Flow Rate[LINK]
System Coils[LINK]
The design air volumetric flow rate for the system cooling coil is set to:
Zone Coils[LINK]
Zone chilled water coils are always part of a zone HVAC component. In almost all cases the design flow rate is passed down from the design flow rate of the parent component. Otherwise if the parent component does cooling only the flow rate for the coil is set to the zone design cooling flow rate. And if the parent component does both cooling and heating, the coil flow rate is set to the maximum of the zone design cooling and heating flow rates.
Design Inlet Air Temperature[LINK]
System Coils[LINK]
The inlet air temperature depends on whether the coil is in the outside air stream and if it is not, whether or not there is outside air preconditioning.
Coil in outside air stream: \({T_{air,in,des}} = {T_{out,cool,atpeak}}\) (the outside air temperature at the design cooling peak). Coil in main air stream, no preconditioning of outside air: \({T_{air,in,des}} = {T_{mix,cool,atpeak}}\) (the mixed air temperature at the design cooling peak). Coil in main air stream, outside air preconditioned. The outside air fraction is calculated as \({f_{oa}} = {\dot V_{air,out,des}}/{\dot V_{cc,air}}\), where \({\dot V_{cc,air}}\) is calculated above. Then \({T_{air,in,des}} = {f_{oa}}{T_{precool}} + (1 - {f_{oa}}){T_{ret,cool,atpeak}}\) where \({T_{precool}}\) is the specified Precool Design Temperature from System:Sizing. \({T_{ret,cool,atpeak}}\) is the return temperature at the system cooling peak load.
Zone Coils[LINK]
The design inlet temperature depends on whether the coil is in a terminal unit or a zonal unit, and where the coil is positioned within the unit.
Design Outlet Air Temperature[LINK]
System Coils[LINK]
The outlet air temperature depends on whether the coil is in the outside air stream.
Zone Coils[LINK]
If the coil is part of an AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction unit, then:
\[{\dot Q_{coil,des}} = {c_{p,air}}{\rho _{air}}{\dot V_{w,coil,des}}\Delta {T_{w,des}}\]
\[{T_1} = {T_{air,in,des}} - {\dot Q_{coil,des}}/({\rho _{air}}{c_{p,air}}{\dot V_{air,coil,des}})\]
\[{T_2} = {T_{w,out,des}} + 2\]
\[{T_{air,out,des}} = \max ({T_1},{T_2})\]
For all other cases Tair,out,des is set to Tz,sup,des (the zone design supply air temperature as specified in Sizing:Zone).
Design Inlet Air Humidity Ratio[LINK]
System Coils[LINK]
The design inlet humidity ratio depends on whether the coil is in the outside air stream and if it is not, whether or not there is outside air preconditioning.
Zone Coils[LINK]
The design inlet humidity depends on whether the coil is in a terminal unit or a zonal unit, and where the coil is positioned within the unit.
Design Outlet Air Humidity Ratio[LINK]
System Coils[LINK]
The outlet air humidity ratio depends on whether the coil is in the outside air stream.
Zone Coils[LINK]
If the coil is part of an AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction unit, then: get the dewpoint temperature at Wair,in,des:
If Tdp,in ≤ Tw,in,des set Wair,out,des = Wair,in,des. Otherwise set
\({W_{air,out,des}} = \min (PsyWFnTdbRhPb({T_{air,out,des}},0.9,{P_{air,std}}),{W_{air,in,des}})\)
If the coil is not part of an AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction unit, set Wair,out,des to Wz,sup,des (the zone design supply air humidity ratio as specified in Sizing:Zone).
Design Inlet Water Temperature[LINK]
System Coils[LINK]
The Design Inlet Water Temperature is set to the Design Loop Exit Temperature specified in the Sizing:Plant object for the water loop serving this coil.
Zone Coils[LINK]
The Design Inlet Water Temperature is set to the Design Loop Exit Temperature specified in the Sizing:Plant object for the water loop serving this coil.
Coil:Cooling:Water:DetailedGeometry Sizing[LINK]
The sizing is done in subroutine SizeWaterCoil
Max Water Flow Rate of Coil[LINK]
The calculation is identical to that done for Coil:Cooling:Water.
Number of Tubes per Row[LINK]
\[Ntube/row = {\mathop{\rm Int}\nolimits} ({\rm{13750}}\dot Vcoil,water,max)\]
Ntube/row=Max(Ntube/row,3)
Fin Diameter[LINK]
Depending on the duct type, get the coil design air flow rate.
For duct type = main, other or default
\[\dot mair,des = \rho airDesMainVolFlowsys\]
for duct type=cooling
\[\dot mair,des = \rho airDesCoolVolFlowsys\]
for duct type=heating
\[\dot mair,des = \rho airDesHeatVolFlowsys\]
\[Dfin = 0.335\dot mair,des\]
Minimum Air Flow Area[LINK]
Depending on the duct type, get the coil design air flow rate.
For duct type = main, other or default
\[\dot mair,des = \rho airDesMainVolFlowsys\]
for duct type=cooling
\[\dot mair,des = \rho airDesCoolVolFlowsys\]
for duct type=heating
\[\dot mair,des = \rho airDesHeatVolFlowsys\]
\[AMinAirFlow = 0.44\dot mair,des\]
Fin Surface Area[LINK]
Depending on the duct type, get the coil design air flow rate.
For duct type = main, other or default
\[\dot mair,des = \rho airDesMainVolFlowsys\]
for duct type=cooling
\[\dot mair,des = \rho airDesCoolVolFlowsys\]
for duct type=heating
\[\dot mair,des = \rho airDesHeatVolFlowsys\]
\[AFinSurf = 78.5\dot mair,des\]
Total Tube Inside Area[LINK]
A~tube,total inside=4.4Dtube,insideNtube rowsNtubes/row~
Where Dtube,inside is the tube inside diameter.
Tube Outside Surf Area[LINK]
Atube,outside=4.1Dtube,outsideN~tube rowsNtubes/row~
Where Dtube,outside is the tube outside diameter.
Coil Depth[LINK]
Depthcoil=Depth~tube spacing~ N~tube rows~
Coil:Cooling:WaterToAirHeatPump:EquationFit Sizing[LINK]
The sizing is done in subroutine SizeHVACWaterToAir
Rated Air Flow Rate[LINK]
The calculation is identical to that done for Coil:Cooling:Water.
Rated Water Flow Rate[LINK]
The calculation is identical to that done for Coil:Cooling:Water, which is the coil design load divided by the Loop Design Temperature Difference user input from Sizing:Plant. If there is a companion heating coil, the heating coil design load is used so that both modes will have the same rated water flow rate. For sizing the plant loop serving this coil, only one half of this flow rate is used since both the cooling and heating coil will save a flow rate but only one of these coils will operate at a time.
Rated Total Cooling Capacity[LINK]
The calculation for coil operating temperatures (inlet and outlet) are identical to that done for Coil:Cooling:Water. The following calculations are then performed to determine the rated total cooling capacity.
\[{T_{WB,ratio}} = \frac{\left( {{T_{WB,air,in,des}} + 273.15\,C} \right)}{283.15C}\]
\[{T_{S,ratio}} = \frac{29.44C + 273.15C}{283.15C}\]
where:
\({T_{WB,ratio}}\) = ratio of load-side inlet air wet-bulb temperature in Kelvin to a reference temperature
\({T_{S,ratio}}\) = ratio of source-side inlet water temperature in Kelvin to a reference temperature
TCC1 = user input for Total Cooling Capacity Coefficient 1
TCC2 = user input for Total Cooling Capacity Coefficient 2
TCC3 = user input for Total Cooling Capacity Coefficient 3
TCC4 = user input for Total Cooling Capacity Coefficient 4
TCC5 = user input for Total Cooling Capacity Coefficient 5
\[TotCapTempModFac = \,TCC1 + TCC2\left( {{T_{WB,ratio}}} \right) + TCC3\left( {{T_{S,ratio}}} \right) + TCC4 + TCC5\]
The 4th and 5th coefficient (TCC4 and TCC5) used in the above equation are multipliers for the load-side and source-side flow ratios, respectively. For sizing, these ratios are assumed to be 1.
The enthalpy of the entering air is then compared with the enthalpy of the exiting air. The calculations for air enthalpy are identical to that done for Coil:Cooling:Water. If the entering air enthalpy is less than the exiting air enthalpy, a reference value of 48,000 J/kg is used as the entering air enthalpy. If the TotCapTempModFac calculation above yields 0 as the result, a value of 1 is used in the following calculation. If the design air mass flow rate is determined to be less than a very small flow value (0.001 kg/s) or the capacity calculated here is less than 0, the coil total cooling capacity is set equal to 0.
Rated Sensible Cooling Capacity[LINK]
The calculation for coil operating temperatures (inlet and outlet) are identical to that done for Coil:Cooling:Water. The following calculations are then performed to determine the rated sensible cooling capacity.
\[{T_{DB,ratio}} = \frac{(T_{DB,air,in,des} + 273.15C}{283.15C}\]
\[{T_{S,ratio}} = \frac{(29.44C + 273.15C}{283.15C}\]
where:
\({T_{DB,ratio}}\) = ratio of load-side inlet air dry-bulb temperature in Kelvin to a reference temperature
SCC1 = user input for Sensible Cooling Capacity Coefficient 1
SCC2 = user input for Sensible Cooling Capacity Coefficient 2
SCC3 = user input for Sensible Cooling Capacity Coefficient 3
SCC4 = user input for Sensible Cooling Capacity Coefficient 4
SCC5 = user input for Sensible Cooling Capacity Coefficient 5
SCC6 = user input for Sensible Cooling Capacity Coefficient 6
\[\begin{array}{l}SensCapTempModFac = \,SCC1 + SCC2\left( {{T_{DB,ratio}}} \right) + SCC3\left( {{T_{WB,ratio}}} \right) + SCC4\left( {{T_{S,ratio}}} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + SCC5 + SCC6\end{array}\]
The 5th and 6th coefficient (SCC5 and SCC6) used in the above equation are multipliers for the load-side and source-side flow ratios, respectively. For sizing, these ratios are assumed to be 1.
The dry-bulb temperature of the entering air is then compared with the dry-bulb temperature of the exiting air. The calculations for air dry-bulb temperature are identical to that done for Coil:Cooling:Water. If the entering air dry-bulb temperature is less than the exiting air dry-bulb temperature, a reference value of 24 C is used as the entering air dry-bulb temperature. If the SensCapTempModFac calculation above yields 0 as the result, a value of 1 is used in the following calculation. If the design air mass flow rate is determined to be less than a very small flow value (0.001 kg/s) or the capacity calculated here is less than 0, the coil sensible cooling capacity is set equal to 0.
Coil:Cooling:WaterToAirHeatPump:VariableSpeedEquationFit Sizing[LINK]
For the cooling coil of VS WSHP, we specify a nominal speed level. During the sizing calculation, the Rated Air Volume Flow Rate, the Rated Water Volume Flow Rate and the Rated Total Cooling Capacity at the Selected Nominal Speed Level are determined in the same way as the Coil:Cooling:WaterToAirHeatPump:EquationFit object. The sensible heat transfer rate is not allowed for auto-sizing, instead, it is a function of the rated air and water flow rates, rated total cooling capacity and the Reference Unit SHR at the nominal speed level. The default nominal speed level is the highest speed. However, the model allows the user to select a nominal speed level rather than the highest.
Rated Air Flow Rate[LINK]
The calculation is identical to that done for Coil:Cooling:WaterToAirHeatPump:EquationFit.
Rated Water Flow Rate[LINK]
The calculation is identical to that done for Coil:Cooling:WaterToAirHeatPump:EquationFit , which is the coil design load divided by the Loop Design Temperature Difference user input from Sizing:Plant. If there is a companion heating coil, the heating coil design load is used so that both modes will have the same rated water flow rate. For sizing the plant loop serving this coil, only one half of this flow rate is used since both the cooling and heating coil will save a flow rate but only one of these coils will operate at a time.
Rated Total Cooling Capacity[LINK]
The calculation for coil operating temperatures (inlet and outlet) are identical to that done for Coil:Cooling:WaterToAirHeatPump:EquationFit. The calculations for air enthalpy are similar to that done for Coil:Cooling:WaterToAirHeatPump:EquationFit. The difference is in calculating the total cooling capacity temperature modifier function at the selected nominal speed level, as below:
\[TotCapTempModFra{c_{NominalSpeed}} = {\rm{a}} + {\rm{b*}}W{B_i} + c*WB_i^2 + {\rm{d*EWT}} + e*EW{T^2} + f*W{B_i}*EWT\]
where
WBi = wet-bulb temperature of the air entering the heating coil, °C
EWT = entering water temperature, °C
a-f = regression curve-fit coefficients.
If the entering air enthalpy is less than the exiting air enthalpy, a reference value of 48,000 J/kg is used as the entering air enthalpy. If the TotCapTempModFac calculation above yields 0 as the result, a value of 1 is used in the following calculation. If the rated air mass flow rate is determined to be less than a very small flow value (0.001 kg/s) or the capacity calculated here is less than 0, the coil total cooling capacity is set equal to 0.
If Hin > Hout Then
\[{\dot Q_{coil,rated,total}} = {m_{air,rated}}({H_{in}} - {H_{out}})/TotCapTempModFra{c_{NominalSpeed}}\]
Else
\[{\dot Q_{coil,rated,total}} = {m_{air,rated}}(48000 - {H_{out}})/TotCapTempModFra{c_{NominalSpeed}}\]
End If
Coil:Heating:WaterToAirHeatPump:EquationFit Sizing[LINK]
The sizing is done in subroutine SizeHVACWaterToAir.
Rated Air Flow Rate[LINK]
The calculation is identical to that done for Coil:Cooling:Water.
Rated Water Flow Rate[LINK]
The calculation is identical to that done for Coil:Cooling:Water , which is the coil design load divided by the Loop Design Temperature Difference user input from Sizing:Plant. For sizing the plant loop serving this coil, only one half of this flow rate is used since both the cooling and heating coil will save a flow rate but only one of these coils will operate at a time.
Rated Total Heating Capacity[LINK]
The rated total heating capacity is set equal to the rated total cooling capacity.
Coil:Heating:WaterToAirHeatPump:VariableSpeedEquationFit Sizing[LINK]
For the heating coil of VS WSHP, we specify a nominal speed level. During the sizing calculation, the Rated Air Volume Flow Rate and the Rated Water Volume Flow Rate are determined in the same way as the Coil:Heating:WaterToAirHeatPump:EquationFit object. On the other hand, the Rated Heating Capacity at the Selected Nominal Speed Level should be the same as the total cooling capacity of its corresponding cooling coil, which has to be sized first. The default nominal speed level will be the highest speed. However, the model allows the user to select a nominal speed level rather than the highest.
Rated Air Flow Rate[LINK]
The calculation is identical to that done for Coil:Cooling:WaterToAirHeatPump:EquationFit.
Rated Water Flow Rate[LINK]
The calculation is identical to that done for Coil:Cooling:WaterToAirHeatPump:EquationFit, which is the coil design load divided by the Loop Design Temperature Difference user input from Sizing:Plant. For sizing the plant loop serving this coil, only one half of this flow rate is used since both the cooling and heating coil will save a flow rate but only one of these coils will operate at a time.
Rated Total Heating Capacity[LINK]
The rated total heating capacity is set equal to the rated total cooling capacity.
Coil:Heating:Water Sizing[LINK]
The sizing is done in subroutine SizeWaterCoil.
Max Water Flow Rate of Coil[LINK]
System Coils[LINK]
With the coil load from the system design data array and the user specified (in a Sizing:Plant object) design hot water temperature fall, calculate the max water flow rate:
\[\dot Vcoil,water,max = HeatCapsys/(Cp,water\rho water\Delta Tplt,hw,des)\]
Zone Coils[LINK]
Using the zone design coil inlet and supply air conditions calculate the design coil load.
If the coil is not part of an induction unit then obtain the coil inlet temperature from the zone design data array;
Tin,air= DesHeatCoilInTempzone
If the coil is part of an induction unit take into account the induced air:
Fracminflow = MinFlowFraczone
Tin,air = DesHeatCoilInTempzone Fracminflow + ZoneTempAtHeatPeakzone(1 Fracminflow)
Tout,air = HeatDesTempzone
Wout,air = HeatDesHumRatzone
If the coil is part of a terminal unit the mass flow rate is determined by the volumetric flow rate of the terminal unit:
\[\dot mair,des = \rho air\dot mair,des,tu\]
Otherwise the design flow is obtained from the zone design data array:
\[\dot mair,des = DesHeatMassFlowzone\]
\[Qcoil,des = cp,air\dot mair,des(Tout,air - Tin,air)\]
Here cp,air is calculated at the outlet humidity and the average of the inlet and outlet temperatures.
With the coil load and the user specified (in a Sizing:Plant object) design hot water temperature decrease, calculate the max water flow rate:
\[\dot Vcoil,water,max = Qcoil,des/(Cp,water\rho water\Delta Tplt,hw,des)\]
UA of the Coil[LINK]
To obtain the UA of the coil, we specify the model inputs (other than the UA) at design conditions and the design coil load that the coil must meet. Then we numerically invert the coil model to solve for the UA that will enable the coil to meet the design coil load given the specified inputs.
System Coils[LINK]
The design coil load is the system design sensible cooling capacity;
Qcoil,des= HeatCapsys
The required inputs for the simple coil model are:
Tin,air= HeatMixTempsys
Win,air= HeatMixHumRatsys
Tin,water= ExitTempplt,hw,des
\[\dot min,water = \rho water\dot Vcoil,water,max\]
Depending on the duct type, get the coil design air flow rate.
For duct type = main, other or default
\(\dot min,air = \rho airDesMainVolFlowsys\)
for duct type=cooling
\(\dot min,air = \rho airDesCoolVolFlowsys\)
for duct type=heating
\[\dot min,air = \rho airDesHeatVolFlowsys\]
We now have all the data needed to obtain UA. The numerical inversion is carried out by calling subroutine SolveRegulaFalsi. This is a general utility routine for finding the zero of a function. In this case it finds the UA that will zero the residual function - the difference between the design coil load and the coil output divided by the design coil load. The residual is calculated in the function SimpleHeatingCoilUAResidual.
Zone Coils[LINK]
If the coil is not part of an induction unit then obtain the coil inlet temperature from the zone design data array;
Tin,air = DesHeatCoilInTempzone
If the coil is part of an induction unit take into account the induced air:
Fracminflow = MinFlowFraczone
Tin,air = DesHeatCoilInTempzone Fracminflow +
ZoneTempAtHeatPeakzone(1 Fracminflow)
Win,air= DesHeatCoilInHumRatzone
Tin,water= ExitTempplt,hw,des
\[\dot min,water = \rho water\dot Vcoil,water,max\]
Tout,air = HeatDesTempzone
Wout,air = HeatDesHumRatzone
If the coil is part of a terminal unit the mass flow rate is determined by the volumetric flow rate of the terminal unit:
\[\dot mair,des = \rho air\dot mair,des,tu\]
Otherwise the design flow is obtained from the zone design data array:
\[\dot mair,des = DesHeatMassFlowzone\]
\[\dot Qcoil,des = cp,air\dot mair,des(Tout,air - Tin,air)\]
Here cp,air is calculated at the outlet humidity and the average of the inlet and outlet temperatures.
We now have all the data needed to obtain UA. The numerical inversion is carried out by calling subroutine SolveRegulaFalsi. This is a general utility routine for finding the zero of a function. In this case it finds the UA that will zero the residual function - the difference between the design coil load and the coil output divided by the design coil load. The residual is calculated in the function SimpleHeatingCoilUAResidual.
Coil:Heating:Steam Sizing[LINK]
The sizing is done in subroutine SizeSteamCoil.
Maximum Steam Flow Rate[LINK]
System Coils[LINK]
The maximum steam volumetric flow rate is calculated using:
The steam density (\({\rho _{steam}}\)) is for saturated steam at 100°C (101325.0 Pa) and hfg is the latent heat of vaporization of water at 100°C (101325.0 Pa). Cp,w is the heat capacity of saturated water (condensate) at 100°C (101325.0 Pa) and \(\Delta {T_{sc}}\) is the Degree of Subcooling defined in the Coil:Heating:Steam object input. The design coil load Loadcoil,des is calculated from:
\[Loa{d_{coil,des}} = {\dot m_{air,des}}({c_{p,air}})({T_{air,coil,des,out}} - {T_{air,coil,des,in}})\]
The design air mass flow rate depends on the location of the coil (duct type). For duct type = main, the flow rate is set to airDesMainVolFlowsysMinSysAirFlowRatio. If the coil is in a cooling duct the flow rate is set to airDesCoolVolFlowsysMinSysAirFlowRatio. If the coil is in a heating duct the flow rate is set to airDesHeatVolFlowsys. If the coil is in any other kind of duct, the flow rate is set to airDesMainVolFlowsys.
For sizing, the design outlet air temperature (Tair,coil,des,out) is the Central Heating Design Supply Air Temperature specified in the Sizing:System object.
The design inlet air temperature depends on whether the coil is being sized for 100% outdoor air or minimum outdoor air flow (per 100% Outdoor Air in Heating input field in the Sizing:System object).
Tair,coil,des,in = HeatOutTempsys (the outdoor air temperature at the design heating peak)
Tair,coil,des,in = Fracoa HeatOutTempsys + (1. - Fracoa) HeatRetTempsys (see Table 41. System Sizing Data)
Zone Coils[LINK]
If the coil is part of an AirTerminal:SingleDuct:* unit (e.g., AirTerminal:SingleDuct:ConstantVolume:Reheat, AirTerminal:SingleDuct:VAV:Reheat, AirTerminal:SingleDuct:SeriesPIU:Reheat, etc.), the maximum steam flow rate is set equal to the terminal unit’s maximum steam flow rate. Otherwise (e.g., the zone-level coil is part of ZoneHVAC:PackagedTerminalAirConditioner, ZoneHVAC:UnitVentilator, ZoneHVAC:UnitHeater or ZoneHVAC:VentilatedSlab) the calculation is similar to that at the system level. A design load is calculated:
\[Loa{d_{coil,des}} = {\dot m_{air,des}}({c_{p,air}})({T_{air,coil,des,out}} - {T_{air,coil,des,in}})\]
where:
\({\dot m_{air,des}}\)= DesHeatMassFlowzone (see Table 40. Zone Sizing Data)
Tair,coil,des,in = DesHeatCoilInTempzone (see Table 40)
Tair,coil,des,out = HeatDesTempzone (user input from Sizing:Zone object)
\({c_{p,air}}\) = Specific heat of air (evaluated at the average of inlet and outlet air temperatures, and at the zone heating design supply air humidity ratio HeatDesHumRatzone [user input from Sizing:Zone object])
The terms in the denominator of this equation (ρsteam, hfg, etc.) are evaluated in the same way as described above for steam System Coils.
Sizing of Gas and Electric Heating Coils[LINK]
The sizing calculation is done in subroutine SizeHeatingCoil in module HeatingCoils.
Nominal Capacity of the Coil[LINK]
System Coils[LINK]
The value is obtained from the system design array.
Capnom= HeatCapsys
Zone Coils[LINK]
The capacity is calculated from the design coil inlet and outlet conditions.
If the coil is not part of an induction unit then obtain the coil inlet temperature from the zone design data array;
Tin,air = DesHeatCoilInTempzone
If the coil is part of an induction unit take into account the induced air:
Fracminflow = MinFlowFraczone
Tin,air = DesHeatCoilInTempzone Fracminflow +
ZoneTempAtHeatPeakzone(1 Fracminflow)
Tout,air = HeatDesTempzone
Wout,air = HeatDesHumRatzone
Qcoil,des = Cp,air DesHeatMassFlowzone(Tout,airTin,air)
Here cp,air is calculated at the outlet humidity and the average of the inlet and outlet temperatures.
DX Coil Sizing[LINK]
The sizing calculations are done in subroutine SizeDXCoil in module DXCoils. This section covers the sizing of the objects
Coil:Cooling:DX:SingleSpeed
Coil:Heating:DX:SingleSpeed
Coil:Cooling:DX:TwoSpeed
Rated Air Volume Flow Rate[LINK]
System Coils[LINK]
The rated air flow rate is obtained from the system design array.
\[\dot Vair,rated = DesMainVolFlowsys\]
Zone Coils[LINK]
The rated air flow rate is the maximum of the heating and cooling design flow rates from the zone design array.
\[\dot Vair,rated = Max(DesCoolVolFlowzone,DesHeatVolFlowzone)\]
Rated Total Cooling Capacity[LINK]
System Coils[LINK]
The rated cooling capacity is obtained by dividing the peak cooling capacity by the Cooling Capacity Modifier Curve evaluated at peak mixed wetbulb and outdoor drybulb temperatures.
Tmix= CoolMixTempsys
Wmix=CoolMixHumRatsys
Tsup=CoolSupTempsys
Wsup=CoolSupHumRatsys
Toutside=CoolOutTempsys
air=PsyRhoAirFnPbTdbW(pair,std, Tmix,Wmix)
hmix= PsyHFnTdbW(Tmix,Wmix)
hsup= PsyHFnTdbW(Tsup,Wsup)
Tmix,wb= PsyTwbFnTdbWPb(Tmix,Wmix, pair,std)
CapModFac=CurveValue(CCapFTemp,Tmix,wb,Toutside)
\[CCappeak = \rho air\dot Vair,rated(hmix - hsup)\]
CCaprated=CCappeak CapModFac
We check that the design volume flow per total capacity is within the prescribed range:
\[FlowCapRatio = \dot Vair,rated/CCaprated\]
If FlowCapRatio < FlowCapRatiomin then
\[CCaprated = \dot Vair,rated/FlowCapRatiomin\]
If FlowCapRatio > FlowCapRatiomax then
\[CCaprated = \dot Vair,rated/FlowCapRatiomax\]
where
FlowCapRatiomin = 0.00004027 m3/s per watt (300 cfm/ton)
And
FlowCapRatiomax= 0.00006041 m3/s per watt (450 cfm/ton)
The sizing calculation for DX cooling coils for 100% dedicated outdor air system (DOAS) are identical to regular DX cooling coils. However, they operate operate at different flow to capacity ratio ranges and are within the prescribed range below:
FlowCapRatiomin = 0.00001677 m3/s per Watt (125 cfm/ton)
And
FlowCapRatiomax= 0.00003355 m3/s per Watt (250 cfm/ton)
Zone Coils[LINK]
The rated cooling capacity for zone coils is calculated in the same manner as for system coils.
Tmix= DesCoolCoilInTempzone
Wmix= DesCoolCoilInHumRatzone
Tsup= CoolDesTempzone
Wsup= CoolDesHumRatzone
Toutside=Toutside,desday,peak
air=PsyRhoAirFnPbTdbW(pair,std, Tmix,Wmix)
hmix= PsyHFnTdbW(Tmix,Wmix)
hsup= PsyHFnTdbW(Tsup,Wsup)
Tmix,wb= PsyTwbFnTdbWPb(Tmix,Wmix, pair,std)
CapModFac=CurveValue(CCapFTemp,Tmix,wb,Toutside)
\[CCappeak = \rho air\dot Vair,rated(hmix - hsup)\]
CCaprated=CCappeak CapModFac
We check that the design volume flow per total capacity is within the prescribed range:
\[FlowCapRatio = \dot Vair,rated/CCaprated\]
If FlowCapRatio < FlowCapRatiomin then
\[CCaprated = \dot Vair,rated/FlowCapRatiomin\]
If FlowCapRatio > FlowCapRatiomax then
\[CCaprated = \dot Vair,rated/FlowCapRatiomax\]
where
FlowCapRatiomin = 0.00004027 m3/s per watt (300 cfm/ton)
And
FlowCapRatiomax= 0.00006041 m3/s per watt (450 cfm/ton)
We check the design flow to the total cooling capacity rato for dedicated zone outdoor unit DX cooling coils to be within the limits prescribed below:
FlowCapRatiomin = 0.00001677 m3/s per Watt (125 cfm/ton)
And
FlowCapRatiomax= 0.00003355 m3/s per Watt (250 cfm/ton)
Rated Total Heating Capacity[LINK]
For Coil:Heating:DX:SingleSpeed the rated heating capacity is set equal to the cooling capacity.
Rated SHR[LINK]
The rated sensible heat ratio is calculated to be the sensible cooling (from rated inlet conditions to user specified supply conditions) divided by the total cooling (from rated inlet to specified supply).
Tin,rated= 26.6667 oC (80 oF)
Win,rated= 0.01125 (corresponds to 80 oF drybulb, 67 oF wetbulb)
Cp,air= PsyCpAirFnWTdb(Win,rated, Tin,rated)
For system coils
Tsup=CoolSupTempsys
Wsup=CoolSupHumRatsys
For zone coils
Tsup= CoolDesTempzone
Wsup= CoolDesHumRatzone
Then
hrated= PsyHFnTdbW(Tin,rated, Win,rated)
hsup= PsyHFnTdbW(Tsup, Wsup)
hrated,sup=hratedhsup
Qsrated,sup=Cp,air(Tin,ratedTsup)
SHRrated=Qsrated,suphrated,sup
Evaporative Condenser Air Volume Flow Rate[LINK]
The evaporative condenser air volume flow rate (m3/s) is set to 0.000114 m3/s per watt (850 cfm/ton) times the total rated cooling capacity.
Evaporative Condenser Air Volume Flow Rate, Low Speed[LINK]
The evaporative condenser air volume flow rate, low speed (m3/s) is set to 1/3 times 0.000114 m3/s per watt (850 cfm/ton) times the total rated cooling capacity.
Evaporative Condenser Pump Rated Power Consumption[LINK]
The evaporative condenser pump rated power consumption is set equal to the total cooling capacity times 0.004266 watts pump power per watt capacity (15 W/ton).
Evaporative Condenser Pump Rated Power Consumption, Low Speed[LINK]
The evaporative condenser pump rated power consumption, low speed, is set equal to 1/3 times the total cooling capacity times 0.004266 watts pump power per watt capacity (15 W/ton).
Rated Air Volume Flow Rate, low speed[LINK]
The rated air volume flow rate, low speed, is set equal to 1/3 times the full rated air volume flow rate.
Rated Total Cooling Capacity, Low Speed[LINK]
The rated total cooling capacity, low speed, is set equal to 1/3 times the full rated total cooling capacity.
Rated SHR, low speed[LINK]
The rated sensible heat ratio, low speed, is set equal to the full speed SHR.
Resistive Defrost Heater Capacity[LINK]
For the heat pump the resistive defrost heat capacity is set equal to the cooling capacity.
DX MultiSpeed Coil Sizing[LINK]
The sizing calculations are done in subroutine SizeDXCoil in module DXCoils. This section covers the sizing of the objects
Coil:Heating:DX:MultiSpeed
Coil:Cooling:DX: MultiSpeed
The rated air volume flow rate, rated total cooling capacity, rated heating capacity, rated SHR, evaporative condenser air volume flow rate, evaporative condenser pump rated power consumption at the highest speed are sized in the same ways as DX Coil Sizing.
After the sizes are determined at the highest speed, the sizes in the rest of speeds are assumed to
\[Valu{e_n} = \frac{n}{{NumberOfSpeed}}*Valu{e_{NumberOfSpeed}}\]
where
Valuen= Any autosizable variable at Speed n, except SHR
SHRn = SHRNumberOfSpeed
n= Speed Index number from 1 to NumberOfSpeed-1
NumberOfSpeed= The highest speed number
Coil:Cooling:DX:VariableSpeed Sizing[LINK]
For the variable-speed DX cooling coil, we specify a nominal speed level. During the sizing calculation, the Rated Total Cooling Capacity at the Selected Nominal Speed Level is determined in the same way as the Coil:Cooling:DX:SingleSpeed object. If the user chooses to autosize the Rated Air Volume Flow Rate, the flow rate, as compared to the Rated Total Cooling Capacity, is sized to have the same ratio as the air volume flow rate to the total cooling capacity at the nominal speed, of the Reference Unit. The sensible heat transfer rate is not allowed for auto-sizing, instead, it is a function of the rated air flow, rated total cooling capacity and the Reference Unit SHR at the nominal speed level. The default nominal speed level is the highest speed. However, the model allows the user to select a nominal speed level rather than the highest.
Rated Total Cooling Capacity
The calculation for coil operating temperatures (inlet and outlet) are identical to that done for Coil:Cooling:DX:SingleSpeed. The calculations for air enthalpy are similar to that done for Coil:Cooling:DX:SingleSpeed. The difference is in calculating the total cooling capacity temperature modifier function at the selected nominal speed level, as below:
\[TotCapTempModFra{c_{NominalSpeed}} = {\rm{a}} + {\rm{b*}}W{B_i} + c*WB_i^2 + {\rm{d*}}D{B_o} + e*D{B_o}{T^2} + f*W{B_i}*D{B_o}\]
where
WBi = wet-bulb temperature of the air entering the cooling coil, °C
DBo = condenser entering air temperature, °C
a-f = regression curve-fit coefficients.
If the entering air enthalpy is less than the exiting air enthalpy, a reference value of 48,000 J/kg is used as the entering air enthalpy. If the TotCapTempModFac calculation above yields 0 as the result, a value of 1 is used in the following calculation. If the rated air mass flow rate is determined to be less than a very small flow value (0.001 kg/s) or the capacity calculated here is less than 0, the coil total cooling capacity is set equal to 0.
If Hin > Hout Then
\[{\dot Q_{coil,rated,total}} = {m_{air,rated}}({H_{in}} - {H_{out}})/TotCapTempModFra{c_{NominalSpeed}}\]
Else
\[{\dot Q_{coil,rated,total}} = {m_{air,rated}}(48000 - {H_{out}})/TotCapTempModFra{c_{NominalSpeed}}\]
End If
The other sizing procedures, e.g. evaporative condenser pump, etc., are the same as Coil:Cooling:DX:SingleSpeed.
Coil:Heating:DX:VariableSpeed Sizing[LINK]
For the variable-speed DX heating coil, we specify a nominal speed level. During the sizing calculation, the Rated Heating Capacity at the Selected Nominal Speed Level should be the same as the total cooling capacity of its corresponding cooling coil, which has to be sized first. The default nominal speed level will be the highest speed. However, the model allows the user to select a nominal speed level rather than the highest. If the user chooses to autosize the Rated Air Volume Flow Rate, the flow rate, as compared to the Rated Heating Capacity, is sized to have the same ratio as the air volume flow rate to the heating capacity at the nominal speed, of the Reference Unit. The other sizing procedures are the same as Coil:Heating:DX:SingleSpeed.
Pump Sizing[LINK]
The loop pumps’ autosizable inputs are nominal volumetric flow rate and nominal power consumption. We have
Efftot=EffmotEffimpeller
The motor efficiency is an input. Since we need the total efficiency to calculate the nominal power consumption we assume an impeller efficiency of 0,78 for purposes of sizing.
Rated Volumetric Flow Rate[LINK]
This is just set equal to the design loop demand obtained from summing the needs of the components on the demand side of the loop.
Rated Power Consumption[LINK]
\[\dot Qnom = Hnom\dot Vnom/Efftot\]
Hnom, the nominal head, is an input.
Electric Chiller Sizing[LINK]
Generally chillers will need nominal cooling capacity, evaporator flow rate and condenser flow rate. All 3 quantities can be straightforwardly obtained using the user specified loop sizing data and the loop design flow rates.
All chillers on a loop are sized to meet the full loop load. If there are multiple chillers on a loop that call for autosizing, they will all be assigned the same cooling capacity and evaporator flow rate.
Nominal Cooling Capacity[LINK]
\[\dot Qchiller,nom = Cp,w\rho w\Delta Tloop,des\dot Vloop,des\]
where
Cp,w is the specific heat of water at 5 oC;
w is the density of water at standard conditions (5.05 oC);
Tloop,des is the chilled water loop design temperature rise;
\(\dot Vloop,des\) is the loop design volumetric flow rate.
Design Evaporator Volumetric Water Flow Rate[LINK]
\[\dot Vevap,des = \dot Vloop,des\]
Design Condenser Volumetric Water Flow Rate[LINK]
\[\dot Vcond,des = \dot Qchiller,nom(1 + 1/COPchiller,nom)/(\Delta Tloop,desCp,w\rho w)\]
where
Cp,w is the specific heat of water at design condenser inlet temperature;
w is the density of water at standard conditions (5.05 oC);
Tloop,des is the chilled water loop design temperature rise;
COPchiller,nom is the chiller nominal COP.
Boiler Sizing
Generally boilers will need nominal heating capacity and rate. Both quantities can be straightforwardly obtained using the user specified loop sizing data and the loop design flow rates.
All boilers on a loop are sized to meet the full loop load. If there are multiple boilers on a loop that call for autosizing, they will all be assigned the same heating capacity and flow rate.
Nominal Capacity[LINK]
\[\dot Qboiler,nom = Cp,w\rho w\Delta Tloop,des\dot Vloop,des\]
where
Cp,w is the specific heat of water at the boiler design outlet temperature;
w is the density of water at standard conditions (5.05 oC);
Tloop,des is the hot water loop design temperature decrease;
\(\dot Vloop,des\) is the loop design volumetric flow rate.
Design Evaporator Volumetric Water Flow Rate[LINK]
\[\dot Vdes = \dot Vloop,des\]
Plant Heat Exchanger Sizing[LINK]
The sizing of plant heat exchanger component (object: HeatExchanger:FluidToFluid) involves determining design flow rates for both sides, a UA value, and a nominal capacity for reporting. The component has a sizing factor for fine control and uses the design temperatures defined in the Sizing:Plant object.
The Loop Supply Side design flow rate, \({\dot V_{Sup,\;des}}\), is set equal to the design flow rate for that loop, multiplied by the component sizing factor, \({f_{comp}}\).
\[{\dot V_{Sup,\;des}} = {\dot V_{loop,des}}*{f_{comp}}\]
The Loop Demand Side design flow rate,\(\;{\dot V_{Dmd,\;des}}\) , is set equal to the Loop Supply Side design flow rate.
\[{\dot V_{Dmd,\;des}} = {\dot V_{Sup,\;des}}\]
The design heat transfer capacity and UA for the heat exchanger are calculated using the design temperatures for the two plant loops. The loop design temperature difference for the Loop Supply Side, \(\Delta {T_{SupLoop,Des}}\), is used to determine a nominal capacity.
\[\dot Q = {\mathop V\limits^. _{Sup,\;des}}\rho {c_p}\Delta {T_{SupLoop,Des}}\]
A loop-to-loop design temperature difference, \(\Delta {T_{LoopToLoop,\;Des}}\), is determined depending on the nature of the plant loop connected to the Loop Supply Side. The Sizing:Plant object includes classifications for the type of loop that include Heating, Steam, Cooling, or Condenser. For Cooling and Condenser loop types, the loop design temperature difference is added to the design exit temperature for the Loop Supply Side, \({T_{SupLoop,Exit}}\). For Heating and Stem loop types, the loop design temperature difference is subtracted from the design exit temperature. This adjusted supply side temperature is then compared to the design exit temperature for the Loop Demand Side,\(\;{T_{DmdLoop,Exit}}\) .
\(\Delta {T_{LoopToLoop,Des}} = \left( {{T_{SupLoop,Exit}} + \Delta {T_{SupLoop,Des}}} \right) - {T_{DmdLoop,Exit}}\) (Cooling, Condenser)
\(\Delta {T_{LoopToLoop,Des}} = \left( {{T_{SupLoop,Exit}} - \Delta {T_{SupLoop,Des}}} \right) - {T_{DmdLoop,Exit}}\) (Heating, Steam)
\[\Delta {T_{LoopToLoop,Des}} = MAX\left( {ABS\left( {\Delta {T_{LoopToLoop,Des}}} \right),2.0} \right)\]
The UA (U-Factor Time Area Value) is determined by assuming that the target capacity can be delivered for the loop-to-loop temperature difference which after substituting and rearranging becomes:
A nominal capacity for the heat exchanger is determined from the design flow rates and UA (regardless of if they were automatically sized or input by the user) and the expected operating temperatures of the two loops. The loop operating temperatures are obtained from the input in Sizing:Plant object if it is present for that loop. If no Sizing:Plant is present then the loop’s overall setpoint is used (if the loop’s load scheme is DualSetpointDeadband then the average of the high and low setpoints is used). The full heat exchanger model is then calculated for the maximum loop flow rates and expected loop temperatures as inlets to the heat exchanger. The absolute value for the model result for heat transfer rate is then used as the capacity of the heat exchanger. This capacity is reported and may be used for controls based on operation scheme.
Humidifier Sizing[LINK]
The rated power, or nominal electric power input of an Electric Steam Humidifier (Humidifier:Steam:Electric) is calculated from user specified rated capacity (m3/s) and the enthalpy change of the water from a reference temperature (20.0°C) to saturated steam at 100.0°C. Autosizing procedure assumes that electrical heating element in the humidifier heat the water from the reference temperature and generate saturated steam at 100°C, and electric to thermal energy conversion efficiency of 100.0%.
Rated Power[LINK]
\[{P_{rated}} = {\dot V_{rated}} \cdot {\rho _w} \cdot \left( {{h_{fg}} + {C_{p,w}} \cdot \Delta {T_w}} \right)\]
where
Cp,w is the specific heat of water at average temperature ((100+20)/2 = 60.0 °C), (J/kgK);
\(\rho_w\) is the density of water at standard conditions (5.05 °C);
\(\Delta T_w\) is the sensible temperature rise of water (100.0 - 20.0=80.0 °C);
\({\dot V_{rated}}\) is the rated capacity of the humidifier in volumetric flow rate.
hfg is the latent heat of vaporization of water at 100.0°C, (J/kg);
Gas Fired Humidifier Sizing[LINK]
The rated power, or nominal gas use rate of a gas steam humidifier (Humidifier:Steam:Gas) is calculated from user specified rated volumetric capacity (m3/s) and the enthalpy change of the water from a reference temperature of 20.0°C to a saturated steam at 100.0°C. Autosizing procedure assumes that gas heater in the humidifier convert the water from the reference temperature and generate saturated steam at 100°C, using gas to thermal energy conversion rated thermal efficiency.
Rated Gas Use Rate
The rated or nominal gas use rate is given by:
\[Q_{NG,nom} = \frac{\dot{V}_{cap,nom}\rho_w\left(h_{fg}+c_{p,w}\Delta T_w\right)}{\eta_{rated}}\]
Where,
Cp,w is the specific heat of water at average temperature ((100+20)/2 = 60.0 °C), (J/kgK);
\(\rho_w\) is the density of water at standard conditions (5.05 °C);
\(\Delta T_w\) is the sensible temperature rise of water (100.0 - 20.0=80.0 °C);
\({\dot V_{cap,nom}}\) is the rated or nominal capacity of the humidifier, (m3/s)
hfg is the latent heat of vaporization of water at 100.0°C, (J/kg);
\(\eta_{rated}\) is the thermal efficiency at rated conditions;
Rated Capacity[LINK]
\[{\dot m_w} = {\dot m_a}({\omega _o} - {\omega _i})\]
where
\(\dot{m}_w\) is water mass flow rate, kg/s;
\(\dot{m}_a\) is design air mass flow rate, kg/s;
\(\omega_o\) is design outlet humidity ratio, kg-water/kg-air;
\(\omega_i\) is design inlet humidity ratio, kg-water/kg-air.
The air mass flow rate and humidity ratios are determined based upon zone design conditions. If the unit is part of zone equipment, then:
\[{\dot m_a} = Max(DesCoolVolFlo{w_{zone}},DesHeatVolFlo{w_{zone}}) \cdot {\rho _a}\]
\[{\omega _i} = Min(OutHumRatAtCoolPea{k_{zone}},OutHumRatAtHeatPea{k_{zone}})\]
\[{\omega _o} = Max(ZoneHumRatAtCoolPea{k_{zone}},ZoneHumRatAtHeatPea{k_{zone}})\]
where
If the unit is part of the central air system, then check if outdoor air system is present. If outdoor air system is part of the air loop and design outdoor air flow rate is greater than zero, then:
\[{\dot m_a} = DesOutAirVolFlo{w_{sys}} \cdot {\rho _a}\]
\[{\omega _i} = Min(CoolOutHumRa{t_{sys}},HeatOutHumRa{t_{sys}})\]
\[{\omega _o} = Max(CoolSupHumRa{t_{sys}},HeatSupHumRa{t_{sys}})\]
Otherwise, air mass flow rate is determined as follows:
for duct type = main
\({\dot m_a} = DesMainAirVolFlo{w_{sys}} \cdot {\rho _a}\)
for duct type = cooling
\[{\dot m_a} = DesCoolVolFlo{w_{sys}} \cdot {\rho _a}\]
for duct type = heating
\[{\dot m_a} = DesHeatVolFlo{w_{sys}} \cdot {\rho _a}\]
for duct type = other
\({\dot m_a} = DesMainVolFlo{w_{sys}} \cdot {\rho _a}\),
and the humidity ratios are:
\[{\omega _i} = Min(CoolMixHumRa{t_{sys}},HeatMixHumRa{t_{sys}})\]
\[{\omega _o} = Max(CoolSupHumRa{t_{sys}},HeatSupHumRa{t_{sys}})\]
Gas Fired Humidifier Sizing[LINK]
The rated power, or nominal gas use rate of a gas steam humidifier (Humidifier:Steam:Gas) is calculated from user specified rated volumetric capacity (m3/s) and the enthalpy change of the water from a reference temperature of 20.0°C to a saturated steam at 100.0°C. Autosizing procedure assumes that gas heater in the humidifier convert the water from the reference temperature and generate saturated steam at 100°C, using gas to thermal energy conversion rated thermal efficiency.
Rated Gas Use Rate[LINK]
The rated or nominal gas use rate is given by:
\[{Q_{NG,{\kern 1pt} nom}} = \frac{{{{\dot V}_{cap,{\kern 1pt} nom}} \cdot {\rho _w} \cdot \left( {{h_{fg}} + {c_{p,w}} \cdot \Delta {T_w}} \right)}}{{{\eta _{rated}}}}\]
Where,
Cp,w = specific heat of water at average temperature ((100+20)/2 = 60.0 °C), (J/kgK);
\(\rho_w\) = density of water at standard condition (5.05 °C);
\(\Delta T_w\) = sensible temperature rise of water (100.0 – 20.0=80.0 °C);
\({\dot V_{cap,{\kern 1pt} nom}}\) = rated or nominal capacity of the humidifier, (m3/s)
hfg = latent heat of vaporization of water at 100.0°C, (J/kg);
\(\eta_{rated}\) = thermal efficiency at rated condition;
Cooling Tower Sizing[LINK]
The quantities needed to autosize a cooling tower include the design water flow rate, the nominal fan power and air flow rate, and the tower UA. This data may be need to be given at more than one operating point:, for instance - high speed fan, low speed fan and free convection.
EnergyPlus provides two input choices: the user can input the design water flow rate and tower UA at each operating point or the tower nominal capacity (and let the program calculate the water flow rate and UA). Choice of input method will affect the sizing calculations in ways noted below.
Design Water Flow Rate[LINK]
If Tower Performance Input Method = UFactorTimesAreaAndDesignWaterFlowRate then
\[\dot Vtower,w,des = \dot Vloop,des\]
If Tower Performance Input Method = NominalCapacity then
\[\dot Vtower,w,des = 5.382E - 8\dot Qtower,nom\]
where 5.38210-08 is m3/s per watt corresponds to the rule-of-thumb of sizing the tower flow rate at 3 gallons per minute per ton. For the CoolingTower:VariableSpeed:Merkel model with NominalCapacity input method, the user can input the value used to scale design water flow rate from nominal capacity and the default is 5.38210-08 m3/s/W.
Fan Power at Design Air Flow Rate[LINK]
The nominal fan power is sized to be 0.0105 times the design load.
If Tower Performance Input Method = UFactorTimesAreaAndDesignWaterFlowRate then
\[\dot Qtower,nom = Cp,w\rho w\dot Vtower,w,des\Delta Tloop,des\]
where
Cp,w is the specific heat of water at the condenser loop design exit temperature;
w is the density of water at standard conditions (5.05 oC);
Tloop,des is the condenser water loop design temperature rise;
Finally
\[\dot Qfan,nom = 0.0105\dot Qtower,nom\]
For the CoolingTower:VariableSpeed:Merkel model, the design fan power is determined using a scaling factor, in units of Watts per Watt, that can be input by the user. The default value is 0.0105 which is the same as above.
Design Air Flow Rate[LINK]
We assume a fan efficiency of 0.5 and a fan pressure rise of 190 Pascals. Then
\[\dot Vtower,air,des = \dot Qfan,nom0.5\rho air/190\]
where
air is the density of air at standard conditions.
For the CoolingTower:VariableSpeed:Merkel model, the design air flow rate is determined from the nominal capacity using a scaling factor, \({f_{airflow/W}}\),in units of m3/s/W. The default value is 2.76316*10-5. When the input field is left blank, the default is used as follows
\[{\dot V_{tower,air,des}} = {\dot Q_{tower,nom}} \bullet {f_{airflow/W}} \bullet \frac{{101325}}{{{P_{std,altitude}}}}\]
where, \({P_{std,altitude}}\) is the standard barometric pressure for the location’s elevation.
When the input field is filled with a hard value, the pressure scaling is not used
\[{\dot V_{tower,air,des}} = {\dot Q_{tower,nom}} \bullet {f_{airflow/W}}\]
Tower UA Value at Design Air Flow Rate[LINK]
To obtain the UA of the tower, we specify the model inputs (other than the UA) at design conditions and the design tower load that the tower must meet. Then we numerically invert the tower model to solve for the UA that will enable the tower to meet the design tower load given the specified inputs.
The design tower load is:
for Tower Performance Input Method = UFactorTimesAreaAndDesignWaterFlowRate
\[\dot Qtower,des = Cp,w\rho w\dot Vtower,w,des\Delta Tloop,des\]
for Tower Performance Input Method = NominalCapacity
\(\dot Qtower,des = 1.25\dot Qtower,nom\) (to allow for compressor heat)
Where, \({f_{des,heat,ratio}}\) is the ratio of actual heat rejection capacity to nominal capacity. This ratio is available as a user input with a default value of 1.25 (to allow for compressor heat).
Then we assign the inputs needed for the model.
Tin,air=35 oC (95 oF design air inlet temperature)
Tin,air,wb=25.6 oC (78 oF design air inlet wetbulb temperature)
Win is calculated from the entering air drybulb and wetbulb.
The inlet water mass flow rate is just the design volumetric flow rate times the density of water.
The inlet water temperature is set slightly differently for the 2 input methods. For
UFactorTimesAreaAndDesignWaterFlowRate
Tin,water=Tloop,exit,desTloop,des
NominalCapacity
Tin,water=35 oC (95 oF design inlet water temperature).
We now have all the data needed to obtain UA. The numerical inversion is carried out by calling subroutine SolveRegulaFalsi. This is a general utility routine for finding the zero of a function. In this case it finds the UA that will zero the residual function - the difference between the design tower load and the tower output divided by the design tower load. The residual is calculated in the function SimpleTowerUAResidual.
Air Flow Rate at Low Fan Speed[LINK]
The nominal air flow rate at low fan speed is set to a fraction of the full speed air flow rate. The fraction is available for user input in the field called Low Fan Speed Air Flow Rate Sizing Factor. The default is 0.5.
Fan Power at Low Fan Speed[LINK]
The fan power at low fan speed is set to a fraction of the fan power at full speed. The fraction is available for user input in the field called Low Fan Speed Fan Power Sizing Factor. The default is 0.16.
Tower UA Value at Low Fan Speed[LINK]
For Tower Performance Input Method = UFactorTimesAreaAndDesignWaterFlowRate the low speed UA is set to a fraction of the full speed UA. The fraction is available for user input in the field called Low Fan Speed U-Factor Times Area Sizing Factor. The default is 0.6. For Tower Performance Input Method = NominalCapacity the low speed UA is calculated in the same manner as the full speed UA using \(\dot Qtower,nom,lowspeed\) instead of \(\dot Qtower,nom\) .
Air Flow Rate in Free Convection Regime[LINK]
The free convection air flow rate is set to a fraction of the full air flow rate. The fraction is available for user input in the field called Free Convection Regime Air Flow Rate Sizing Factor. The default is 0.1.
Tower UA Value in Free Convection Regime[LINK]
For Tower Performance Input Method = UA and Design Water Flow Rate the low speed UA is set to a fraction of the full speed UA. The fraction is available for user input in the field called Free Convection U-Factor Times Area Value Sizing Factor. The default is 0.1. For Tower Performance Input Method = NominalCapacity the low speed UA is calculated in the same manner as the full speed UA using \(\dot Qtower,nom,freeconv\) instead of \(\dot Qtower,nom\) .
Fluid Cooler Sizing[LINK]
The quantities needed to autosize a fluid cooler include the design water flow rate, the nominal fan power, air flow rate, and the fluid cooler UA. This data may need to be given at more than one operating point:, for instance - high speed fan and low speed fan.
EnergyPlus provides two input choices: the user can input the design water flow rate and fluid cooler UA at each operating point or the fluid cooler nominal capacity and the water flow rate (and let the program calculate UA). Choice of input method will affect the sizing calculations in ways noted below.
Design Water Flow Rate[LINK]
The design water flow rate is sized as follows
\[{\dot V_{fluidcooler,w,des}} = {\dot V_{loop,des}}\]
Fan Power at Design Air Flow Rate[LINK]
The nominal fan power is sized to be 0.0105 times the design load.
If Performance Input Method = UFactorTimesAreaAndDesignWaterFlowRate then
\[{\dot Q_{fluidcooler,nom}} = {C_{p,w}} \bullet {\rho _w} \bullet {\dot V_{fluidcooler,w,des}} \bullet \Delta {T_{loop,des}}\]
where
Cp,w is the specific heat of water at the condenser loop design exit temperature;
w is the density of water at standard conditions (5.05 oC);
Tloop,des is the condenser water loop design temperature rise;
Finally
\[{\dot Q_{fan,nom}} = 0.0105 \bullet {\dot Q_{fluidcooler,nom}}\]
Elseif ****Performance Input Method = NominalCapacity then**[LINK]
\[{\dot Q_{fan,nom}} = 0.0105 \bullet {\dot Q_{fluidcooler,nom}}\]
Where
\({\dot Q_{fluidcooler,nom}}\) is provided by the user.
Design Air Flow Rate[LINK]
\[{\dot Q_{fluidcooler,nom}} = {C_{p,w}} \bullet {\rho _w} \bullet {\dot V_{fluidcooler,w,des}} \bullet \Delta {T_{loop,des}}\]
\({\dot Q_{fluidcooler,nom}}\) is provided by the user.
\[{\dot V_{fluidcooler,air,des}} = {\dot Q_{fluidcooler,nom}}/({T_{in,water}} - {T_{in,air}})\*4\]
Where,
Tin,water= Design entering water temperature provided by the user
Tin,air= Design air inlet temperature provided by the user
Fluid cooler UA Value at Design Air Flow Rate[LINK]
To obtain the UA of the fluid cooler, we specify the model inputs (other than the UA) at design conditions and the design fluid cooler load that the fluid cooler must meet. Then we numerically invert the fluid cooler model to solve for the UA that will enable the fluid cooler to meet the design fluid cooler load given the specified inputs.
The design fluid cooler load is:
\[{\dot Q_{fluidcooler,nom}} = {C_{p,w}} \bullet {\rho _w} \bullet {\dot V_{fluidcooler,w,des}} \bullet \Delta {T_{loop,des}}\]
\({\dot Q_{fluidcooler,nom}}\) is provided by the user.
Then we assign the inputs needed for the model.
Tin,air= Design air inlet temperature provided by the user
Tin,air,wb= Design air inlet wetbulb temperature provided by the user
Win is calculated from the entering air drybulb and wetbulb.
The inlet water mass flow rate is just the design entering volumetric flow rate times the density of water.
The inlet water temperature is set slightly differently for the 2 input methods. For
\[{T_{in,water}} = {T_{loop,exit,des}} + \Delta {T_{loop,des}}\]
\[{T_{in,water}} = Provided\,by\,the\,user\]
We now have all the data needed to obtain UA. The numerical inversion is carried out by calling subroutine SolveRegulaFalsi. This is a general utility routine for finding the zero of a function. In this case it finds the UA that will zero the residual function - the difference between the design fluid cooler load and the fluid cooler output divided by the design fluid cooler load. The residual is calculated in the function SimpleFluidCoolerUAResidual.
Air Flow Rate at Low Fan Speed[LINK]
The nominal air flow rate at low fan speed is set to a fraction of the full speed air flow rate. The fraction is available for user input in the field called Low Fan Speed Air Flow Rate Sizing Factor. The default is 0.5.
Fan Power at Low Fan Speed[LINK]
The fan power at low fan speed is set to a fraction of the fan power at full speed. The fraction is available for user input in the field called Low Fan Speed Fan Power Sizing Factor. The default is 0.16.
Fluid cooler UA Value at Low Fan Speed[LINK]
For Performance Input Method = UFactorTimesAreaAndDesignWaterFlowRate the low speed UA is set to a fraction of the full speed UA. . The fraction is available for user input in the field called Low Fan Speed U-Factor Times Area Sizing Factor. The default is 0.6. For Performance Input Method = NominalCapacity the low speed UA is calculated in the same manner as the full speed UA using \({\dot Q_{fluidcooler,nom,lowspeed}}\) instead of \({\dot Q_{fluidcooler,nom}}\).
Evaporative Fluid cooler Sizing[LINK]
The quantities needed to autosize an evaporative fluid cooler include the design water flow rate, the nominal fan power, air flow rate, and the fluid cooler UA. This data may need to be given at more than one operating point:, for instance - high speed fan and low speed fan.
EnergyPlus provides three input choices: the user can input the design water flow rate and fluid cooler UA at each operating point (UFactorTimesAreaAndDesignWaterFlowRate) or the fluid cooler design capacity and the water flow rate and let the program calculate UA (UserSpecifiedDesignCapacity) or only the fluid cooler design capacity and let the program calculate UA and the water flow rate (StandardDesignCapacity). Choice of input method will affect the sizing calculations in ways noted below.
Design Water Flow Rate[LINK]
If Performance Input Method = StandardDesignCapacity then
Else
\[{\dot V_{fluidcooler,w,des}} = {\dot V_{loop,des}}\]
where 5.38210-08 is m3/s per watt corresponds to the rule-of-thumb of sizing the fluid cooler flow rate at 3 gallons per minute per ton.
Fan Power at Design Air Flow Rate[LINK]
The design fan power is sized to be 0.0105 times the design load.
If Performance Input Method = UFactorTimesAreaAndDesignWaterFlowRate then
\[{\dot Q_{fluidcooler,design}} = {C_{p,w}} \bullet {\rho _w} \bullet {\dot V_{fluidcooler,w,des}} \bullet \Delta {T_{loop,des}}\]
where
Cp,w is the specific heat of water at the condenser loop design exit temperature;
w is the density of water at standard conditions (5.05 oC);
Tloop,des is the condenser water loop design temperature rise;
Finally
\[{\dot Q_{fan,design}} = 0.0105 \bullet {\dot Q_{fluidcooler,design}}\]
Else[LINK]
\[{\dot Q_{fan,design}} = 0.0105 \bullet {\dot Q_{fluidcooler,design}}\]
Where
\({\dot Q_{fluidcooler,design}}\) is the design capacity provided by the user for the other two performance input methods
Design Air Flow Rate[LINK]
We assume a fan efficiency of 0.5 and a fan pressure rise of 190 Pascals. Then
\[{\dot V_{fluidcooler,air,des}} = {\dot Q_{fan,design}} \bullet 0.5 \bullet {\rho _{air}}/190\]
where
\(\rho_{air}\) is the density of air at standard conditions.
Fluid cooler UA Value at Design Air Flow Rate[LINK]
To obtain the UA of the evaporative fluid cooler, we specify the model inputs (other than the UA) at design conditions and the design fluid cooler load that the fluid cooler must meet. Then we numerically invert the fluid cooler model to solve for the UA that will enable the fluid cooler to meet the design fluid cooler load given the specified inputs.
The design fluid cooler load is:
\[{\dot Q_{fluidcooler,design}} = {C_{p,w}} \bullet {\rho _w} \bullet {\dot V_{fluidcooler,w,des}} \bullet \Delta {T_{loop,des}}\]
\({\dot Q_{fluidcooler,design}} = 1.25 \bullet {\dot Q_{fluidcooler,standarddesign}}\) (to allow for compressor heat)
Then we assign the inputs needed for the model.
Tin,air= 35 oC (95 oF design air inlet temperature)
Tin,air,wb= 25.6 oC (78 oF design air inlet wetbulb temperature)
Win is calculated from the entering air drybulb and wetbulb.
\[{\dot Q_{fluidcooler,design}} = {\dot Q_{fluidcooler,userspecifieddesign}}\]
Where, \({f_{des,heat,ratio}}\) is the ratio of actual heat rejection capacity to nominal capacity. This ratio is available as a user input with a default value of 1.25 (to allow for compressor heat)
Then we assign the inputs needed for the model.
Tin,air= Design air inlet temperature provided by the user
Tin,air,wb= Design air inlet wetbulb temperature provided by the user
Win is calculated from the entering air drybulb and wetbulb.
The inlet water mass flow rate is just the design entering volumetric flow rate times the density of water.
The inlet water temperature is set slightly differently for the 3 input methods. For
\[{T_{in,water}} = {T_{loop,exit,des}} + \Delta {T_{loop,des}}\]
\[{T_{in,water}} = 35^\circ C\;(95^\circ F\,design\,inlet\,water\,temperature)\]
\[{T_{in,water}} = Provided\,by\,the\,user\]
We now have all the data needed to obtain UA. The numerical inversion is carried out by calling subroutine SolveRegulaFalsi. This is a general utility routine for finding the zero of a function. In this case it finds the UA that will zero the residual function - the difference between the design fluid cooler load and the fluid cooler output divided by the design fluid cooler load. The residual is calculated in the function SimpleEvapFluidCoolerUAResidual.
Air Flow Rate at Low Fan Speed[LINK]
The design air flow rate at low fan speed is set to a fraction of the full speed air flow rate. The fraction is available for user input in the field called Low Fan Speed Air Flow Rate Sizing Factor. The default is 0.5.
Fan Power at Low Fan Speed[LINK]
The fan power at low fan speed is set to a fraction of the fan power at full speed. The fraction is available for user input in the field called Low Fan Speed Fan Power Sizing Factor. The default is 0.16.
Fluid cooler UA Value at Low Fan Speed[LINK]
For Performance Input Method = UFactorTimesAreaAndDesignWaterFlowRate the low speed UA is set to a fraction of the full speed UA. The fraction is available for user input in the field called Low Fan Speed U-Factor Times Area Sizing Factor. The default is 0.6. For Performance Input Method = StandardDesignCapacity (and similarly for UserSpecifiedDesignCapacity method) the low speed UA is calculated in the same manner as the full speed UA using \({\dot Q_{fluidcooler,standarddesign,lowspeed}}\) instead of \({\dot Q_{fluidcooler,standarddesign}}\).
Fan Coil Unit Sizing[LINK]
Fan Coil units are compound components: each unit contains a fan, hot water coil, chilled water coil and outside air mixer. The inputs that may need to be autosized are the nominal unit air flow rate, the maximum hot and chilled water flow rates, and the design outside air flow rate. The data needed for sizing the units is obtained from the zone design arrays and the user specified plant sizing input.
Maximum Air Flow Rate[LINK]
\[\dot Vair,max = Max(DesCoolVolFlowzone,DesHeatVolFlowzone)\]
Maximum Outside Air Flow Rate[LINK]
\[\dot Voutsideair,max = Min(MinOAzone,\dot Vair,max)\]
Maximum Hot Water Flow[LINK]
Tcoil,in=DesHeatCoilInTempzone
Tcoil,out=HeatDesTempzone
\[\dot Qcoil,des = cp,airDesHeatMassFlowzone(Tout,coil - Tin,coil)\]
\[\dot Vmax,hw = \dot Qcoil,des/(cp,w\rho w\Delta Tloop,des)\]
where
cp,air is evaluated at the average of the inlet & outlet temperatures and the coil outlet humidity ratio.
Maximum Cold Water Flow[LINK]
Tcoil,in=DesColdCoilInTempzone
Tcoil,out=ColdDesTempzone
Wcoil,in= DesCoolCoilInHumRatzone
Wcoil,out= CoolDesHumRatzone
Hcoil,in= PsyHFnTdbW(Tcoil,in, Wcoil,in)
Hcoil,out= PsyHFnTdbW(Tcoil,out, Wcoil,out)
\[\dot Qcoil,des = DesCoolMassFlowzone(hin,coil - hout,coil)\]
\[\dot Vmax,hw = \dot Qcoil,des/(cp,w\rho w\Delta Tloop,des)\]
where
cp,air is evaluated at the average of the inlet & outlet temperatures and the coil outlet humidity ratio.
Window Air Conditioner Sizing[LINK]
Window air conditioners are compound components: each unit contains a fan, a DX coil and an outside air mixer. The inputs that may need to be autosized are the nominal unit air flow rate and the design outside air flow rate. The data needed for sizing the units is obtained from the zone design arrays.
Maximum Air Flow Rate[LINK]
\[{\dot V_{air,max}} = DesCoolVolFlo{w_{max}}\]
Maximum Outside Air Flow Rate[LINK]
\[\dot Voutsideair,max = Min(MinOAzone,\dot Vair,max)\]
Unit Ventilator Sizing[LINK]
Unit ventilators are compound components: each unit contains an outdoor air mixer, a fan, a heating coil, and a cooling coil. The inputs that may need to be autosized are the maximum supply air flow rate and the maximum/minimum outside air flow rates. The data needed for sizing the units is obtained from the zone design arrays.
Maximum Air Flow Rate[LINK]
If both the cooling and heating coil are present, then:
\[{\dot V_{{\rm{supplyair,max}}}} = MAX(DesCoolVolFlowzone,DesHeatVolFlowzone)\]
If only the heating coil is present, then:
\[{\dot V_{{\rm{supplyair,max}}}} = DesHeatVolFlowzone\]
If only cooling coil is present, then:
\[{\dot V_{{\rm{supplyair, max}}}} = DesCoolVolFlowzone\]
If neither heating nor cooling coil is present, then:
\[{\dot V_{{\rm{supplyair,max}}}} = MinOAzone\]
Maximum Outside Air Flow Rate[LINK]
\[{\dot V_{outsideair,\max }} = {\dot V_{air,\max }}\]
Minimum Outside Air Flow Rate[LINK]
\[{\dot V_{outsideair,\min }} = Min(MinOAzone,{\dot V_{air,\max }})\]
Packaged Terminal Heat Pump Sizing[LINK]
Packaged terminal heat pumps are compound components: each unit contains a supply air fan, a DX cooling coil, a DX heating coil, a GAS or ELECTRIC supplemental heating coil, and an outside air mixer. The inputs that may need to be autosized are the supply air and outside air volumetric air flow rates during cooling operation, heating operation, and when no cooling or heating is needed. In addition, the maximum supply air temperature from the supplemental heater can also be automatically selected. The data needed for sizing the units are obtained from the zone design arrays.
Supply air volumetric flow rate during cooling operation[LINK]
\[{\mathop V\limits^ \cdot _{SA\,\,,\,cooling}} = \,\,MAX(DesCoolVolFlowzone,\,DesHeatVolFlowzone)\]
Supply air volumetric flow rate during heating operation[LINK]
\[{\mathop V\limits^ \cdot _{SA\,\,,\,heating}} = \,\,MAX(DesCoolVolFlowzone,\,DesHeatVolFlowzone)\]
Supply air volumetric flow rate when no cooling or heating is needed[LINK]
\[{\mathop V\limits^ \cdot _{SA\,,\,no\,cool\,or\,heat}} = \,\,MAX(DesCoolVolFlowzone,\,DesHeatVolFlowzone)\]
Outside air volumetric flow rate during cooling operation[LINK]
\[{\mathop V\limits^ \cdot _{OA\,,\,\,cooling}} = {\rm{MIN}}(MinO{A_{zone}},{\mathop {\,V}\limits^ \cdot _{SA\,,\,\,cooling}})\]
Outside air volumetric flow rate during heating operation[LINK]
\[{\mathop V\limits^ \cdot _{OA\,,\,\,heating}} = {\rm{MIN}}(MinO{A_{zone}},{\mathop {\,V}\limits^ \cdot _{SA\,,\,\,heating}})\]
Outside air volumetric flow rate when no cooling or heating is needed[LINK]
\[{\mathop V\limits^ \cdot _{OA\,,\,no\,\,cool\,or\,heat}} = {\rm{MIN}}(MinO{A_{zone}},{\mathop {\,V}\limits^ \cdot _{SA\,,\,no\,\,cool\,or\,heat}})\]
Maximum supply air temperature from supplemental heater[LINK]
\[{T_{SA,\max }} = HeatDesTem{p_{zone}}\]
MultiSpeed Heat Pump Sizing[LINK]
MultiSpeed heat pumps are compound components: each unit contains a supply air fan, a multispeed DX cooling coil, a multispeed DX heating coil, and a GAS or ELECTRIC supplemental heating coil. The inputs that may need to be autosized are the supply air volumetric air flow rates during cooling operation, heating operation, and when no cooling or heating is needed. The data needed for sizing the units are obtained from the controlled zone design arrays.
Supply air volumetric flow rate during cooling operation at the highest speed[LINK]
\[{\mathop V\limits^ \cdot _{SA\,\,,\,cooling}} = \,\,MAX(DesCoolVolFlowzone,\,DesHeatVolFlowzone)/ZoneFraction\]
Supply air volumetric flow rate during heating operation at the highest speed[LINK]
\[{\mathop V\limits^ \cdot _{SA\,\,,\,heating}} = \,\,MAX(DesCoolVolFlowzone,\,DesHeatVolFlowzone)/ZoneFraction\]
Supply air volumetric flow rate when no cooling or heating is needed[LINK]
\[{\mathop V\limits^ \cdot _{SA\,,\,no\,cool\,or\,heat}} = \,\,MAX(DesCoolVolFlowzone,\,DesHeatVolFlowzone)/ZoneFraction\]
where
ZoneFraction = Fraction of the total volume flow that goes through the controlling zone
Supply air volumetric flow rate during cooling operation at Speed n (1 to NumberOfSpeed-1)[LINK]
\[{\mathop V\limits^ \cdot _{SA\,\,,\,cooling,n}} = \frac{n}{{NumberOfSpeed}}{\mathop V\limits^ \cdot _{SA\,\,,\,cooling}}\]
Supply air volumetric flow rate during heating operation at Speed n (1 to NumberOfSpeed-1)[LINK]
\[{\mathop V\limits^ \cdot _{SA\,\,,\,heating,n}} = \frac{n}{{NumberOfSpeed}}{\mathop V\limits^ \cdot _{SA\,\,,\,heating}}\]
where
n= Speed Index number from 1 to NumberOfSpeed-1
NumberOfSpeed= The highest speed number
Single Duct Terminal Units[LINK]
These are all the EnergyPlus components whose names begin with “AirTerminal:SingleDuct:” (except for Cooled Beam units). This includes Uncontrolled, ConstantVolume:Reheat, VAV:NoReheat, VAV:Reheat, VAV:Reheat:VariableSpeedFan, VAV:HeatAndCool:NoReheat, VAV:HeatAndCool:Reheat, SeriesPIU:Reheat, ParallelPIU:Reheat, and ConstantVolume:FourPipeInduction. The inputs that may need to be autosized are the various maximum air flow rates through the unit, minimum air flow rates, and maximum hot water and/or chilled water flow rates if heating or cooling coils are present.
Note: all zone design flow rates and loads referenced below may have been altered by system sizing inputs. For instance, if the user specifies a Cooling Design Air Flow Method = Flow/System and specifies a Cooling Design Air Flow Rate the zone cooling design values will be altered to match the specified system flow rate.
Maximum Air Flow Rate[LINK]
\[{\dot V_{air,\max ,{\rm{terminal}}}} = Max(DesCoolVolFlowzone,DesHeatVolFlowzone)\]
Maximum Heating Air Flow Rate[LINK]
\[{\dot V_{air,max,heat,terminal}} = DesHeatVolFlowzone\]
Maximum Primary and Secondary Air Flow Rates[LINK]
For the PIU terminal units, the maximum primary and secondary air flow rates are sized to the same value as the maximum total air flow rate.
Minimum Air Flow Rate[LINK]
Basically minimum air flow rates are sized to the ventilation air requirement. This may be more or less complicated.
For the PIU’s, the minimum primary air flow fraction is set to
\(\mathop {MinOA}\nolimits_{zone} /{\dot V_{air,max,primary,terminal}}\).
For other VAV terminal units
\[{\dot V_{air,min,terminal}} = Fra{c_{air,\min }}*DesVolFlowzone\]
where, Fracair,min corresponds to the minimum flow fraction of the teminal unit. This value is provided as user input, typically as the field “Zone Minimum Air Flow Fraction.” For the VAV terminals that allow scheduling minimum flow fraction (e.g., AirTerminal:SingleDuct:VAV:Reheat), there are two ways that Fracair,min can be determined. If a value is entered in the input field Constant Minimum Air Flow Fraction, then it is always used for Fracair,min. If the mimimum air flow fraction method is “Schedule” and the Constant Minimum Air Flow Fraction is left blank, then the program uses the average of the minimum and maximum values in the schedule for Fracair,min.
Fan On Flow Fraction[LINK]
For the parallel PIU, this is set to the minimum primary air flow fraction.
Max Hot Water Flow[LINK]
\[{T_{coil,in}} = DesHeatCoilInTem{p_{zone}}\]
\[{T_{coil,out}} = HeatDesTem{p_{zone}}\]
The coil load and max hot water flow rate are then:
\[\dot Qcoil,des = cp,air\rho air\dot Vair,coil,heating(Tout,coil - Tin,coil)\]
\[\dot Vmax,hw = \dot Qcoil,des/(cp,w\rho w\Delta Tloop,des)\]
where
cp,air is evaluated at the average of the inlet & outlet temperatures and the coil outlet humidity ratio.
The four-pipe induction unit sizes the heating coil differently: to meet the zone load rather than match the design zone supply temperature. The load on the hot water coil is then the zone load minus whatever the central system does.
\[{\dot Q_{coil,des}} = {\dot Q_{zone,des}} - {c_{p,air}}{\rho _{air}}{\dot V_{air,primary,des}}({T_{coil,in}} - {T_{zone,heatpeak}})\]
where
\[{T_{coil,in}} = DesHeatCoilInTem{p_{zone}}\]
\[{T_{zone,heatpeak}} = ZoneTempAtHeatPea{k_{zone}}\]
\[{\dot V_{air,primary,des}} = {\dot V_{air,max,terminal}}/(1 + {R_{induc}})\]
Max Chilled Water Flow[LINK]
The chilled water flow for the four-pipe induction unit is sized analogously to the hot water flow.
Indirect Evaporative Cooler Sizing[LINK]
The model for the object called EvaporativeCooler:Indirect:ResearchSpecial has a field for the secondary fan flow rate that can be autosized.
Secondary Fan Flow Rate[LINK]
The secondary fan is not part of an airstream that is directly modeled in EnergyPlus. Because the primary side air flows can be autosized as part of the air system, it is convenent to also scale the size of the secondary flow. If the cooler is part of the main loop of a central air system, then the secondary fan flow rate is sized to equal to the main design flow rate.
\[\dot Vfan,max = DesMainVolFlowsys\]
If the cooler is part of the outdoor air path of a central air system, then the secondary fan flow rate is sized to be the maximum of either the design minimum outdoor air flow rate or one-half of the main design flow rate.
\[{\dot V_{fan,\max }} = MAX({\rm{DesOutAirVolFlow, 0}}{\rm{.5\*DesMainVolFlow)}}\]
Secondary DX Coils Sizing[LINK]
The secondary DX coils model does not have a standalone object and it is models as add–on feature to the DX Coils. When the secondary DX coil is added to a primary DX cooling coil, the heat rejected to secondary zone is sensible only and is treated as tnternal gain, hence secondary air flow rate is not required in the model. Where as when the secondary DX coil is added to a primary DX heating coil, then the heat removed from secondary zone may have sensible and latent components and is treated as tnternal gain. The sensible/latent component split among other parameters requires secondary coil air flow rate. Hence secondary coil air flow rate sizing is added based on the primary DX cooling coil only.
\[{\dot V_{SecCoil}} = {\dot V_{PriHeatCoil}} \cdot ScalingFactor\]
Where,
\({\dot V_{SecCoil}}\) = the secondary coil design air flow rate (m3/s)
\({\dot V_{PriHeatCoil}}\) = the primary heating DX coil design air flow rate, (kg/s)
\(ScalingFactor\) = secondary DX coil air flow rarte scaling factor (-)
Desiccant Dehumidifier Sizing[LINK]
The sizing of dehumidifier with no fans is done in subroutine SizeDesiccantDehumidifier.
Nominal Process Air Flow Rate[LINK]
If the unit is part of zone equipment, then:
\[{\dot V_p} = Max(DesCoolVolFlo{w_{zone}},DesHeatVolFlo{w_{zone}})\]
If the unit is part of the central air system, then check if outdoor air system is present. If outdoor air system is part of the air loop and design outdoor air flow rate is greater than zero, then:
\[{\dot V_p} = DesOutAirVolFlo{w_{sys}}\]
Otherwise, nominal process air flow rate is determined as follows:
for duct type = main
\({\dot V_p} = DesMainVolFlo{w_{sys}}\)
for duct type = cooling
\[{\dot V_p} = DesCoolVolFlo{w_{sys}}\]
for duct type = heating
\[{\dot V_p} = DesHeatVolFlo{w_{sys}}\]
for duct type = other
\[{\dot V_p} = DesMainVolFlo{w_{sys}}\]
Evaporative Cooler Sizing[LINK]
The sizing of evaporative cooler objects is done in subroutine SizeEvapCooler.
Secondary Fan Flow Rate[LINK]
\[\dot V = DesMainVolFlo{w_{sys}}\]
Note that it is only applicable to indirect CELdek pad object.
Direct Pad Area[LINK]
As from the continuity equation, the area of direct pad is directly determined by assuming face air velocity of 3m/s as:
\[{A_{pad}} = \frac{{DesMainVolFlo{w_{sys}}}}{V}\]
where
Apad is area of direct pad, m2
V is face air velocity, m/s
Direct Pad Depth[LINK]
The solution of the following regression equation is used, assuming saturation effectiveness of 70% and face air velocity of 3m/s:
ɛ = 0.792714 + 0.958569D - 0.25193V - 1.03215D2 + 0.0262659V2 + 0.914869DV
where
D is depth of pad, m
ɛ is saturation effectiveness
Heat Recovery Sizing[LINK]
The sizing of heat exchanger objects is done in subroutine SizeHeatRecovery.
Nominal Supply Air Flow Rate[LINK]
If the unit is part of zone equipment, then:
\[{\dot V_p} = Max(DesCoolVolFlo{w_{zone}},DesHeatVolFlo{w_{zone}})\]
If the unit is part of the central air system, then check if outdoor air system is present. If outdoor air system is part of the air loop and design outdoor air flow rate is greater than zero, then:
\[{\dot V_p} = DesOutAirVolFlo{w_{sys}}\]
Otherwise, nominal supply air flow rate is determined as follows:
for duct type = main
\({\dot V_p} = DesMainVolFlo{w_{sys}}\)
for duct type = cooling
\[{\dot V_p} = DesCoolVolFlo{w_{sys}}\]
for duct type = heating
\[{\dot V_p} = DesHeatVolFlo{w_{sys}}\]
for duct type = other
\[{\dot V_p} = DesMainVolFlo{w_{sys}}\]
Nominal Supply Air Flow Rate[LINK]
It is assumed to be equal to the nominal supply air flow rate.
Low Temperature Radiant System Sizing[LINK]
The sizing is done in subroutine SizeLowTempRadiantSystem.
ZoneHVAC:LowTemperatureRadiant:Electric:[LINK]
Nominal Capacity[LINK]
\[Cap = DesHeatLoa{d_{zone}} \cdot HeatSizingFactor\]
ZoneHVAC:LowTemperatureRadiant:VariableFlow:[LINK]
Maximum Hot Water Flow[LINK]
\[{\dot V_h} = \frac{{DesHeatLoa{d_{zone}} \cdot HeatSizingFactor}}{{\Delta {T_h} \cdot {c_{p,h}} \cdot {\rho _h}}}\]
where
Vh is maximum hot water flow rate, m3/s
cp,h is specific heat of hot water at reference condition (60°C), J/kgK
h is the density of water at reference condition (60°C), kg/m3
Maximum Cool Water Flow[LINK]
\[{\dot V_c} = \frac{{DesCoolLoa{d_{zone}} \cdot CoolSizingFactor}}{{\Delta {T_c} \cdot {c_{p,c}} \cdot {\rho _c}}}\]
Vc is maximum chilled water flow rate, m3/s
cp,c is specific heat of hot water at reference condition (5°C), J/kgK
c is the density of chilled water at reference condition (5°C), kg/m3
Hydronic Tubing Length[LINK]
\[TubeLength = \frac{{TotalSurfaceArea}}{{TubeSpacing}}\]
Note that tube spacing is assumed to be 0.15m.
ZoneHVAC:LowTemperatureRadiant:ConstantFlow:[LINK]
Rated Flow Rate[LINK]
The object provides both cooling and heating, and also operates in a single operating mode such as cooling-only or heating-only mode. Thus, the rated flow rate is determined, depending upon the operating mode of the unit. If the unit operates in a single operating mode, either design chilled water or hot water flow rate is chosen. The larger of the two is chosen if the unit provides both cooling and heating. The flow rates are determined in the same fashion to the variable flow system above.
Hydronic Tubing Length[LINK]
The length of hydronic tube is determined as described in the variable flow radiant system above.
Unitary System Sizing[LINK]
The AirloopHVAC:UnitarySystem object incorporates all coils types and fans as a complete packaged system. The fans and coils are optional allowing virtually any system type to be modeled. Sizing of this object depends on the coils selected. For single coil systems, the associated air flow rate is used as the operating flow rate (i.e., cooling or heating). For systems with both a cooling and heating coil, this methodology still applies except for DX systems (Heat Pumps) where the greater of the cooling or heating air flow rate is used. Heat pumps are defined as systems having both a DX cooling and DX heating coil. Other AirloopHVAC equipment models use the greater of the cooling and heating flow rates. The inputs that may need to be autosized are the supply air air volumetric air flow rates during cooling operation, heating operation, and when no cooling or heating is needed. The data needed for sizing the units are obtained from the zone design arrays.
Supply Air Flow Rate:[LINK]
Supply air volumetric flow rate during cooling operation
\[\dot{V}_{SA,cooling} = \rm{DesCoolVolFlow}_{zone}/\rm{ZoneFraction}\]
Supply air volumetric flow rate during heating operation
\[\dot{V}_{SA,heating} = \rm{DesHeatVolFlow}_{zone}/\rm{ZoneFraction}\]
Supply air volumetric flow rate when DX coils are used as a system
\[\dot{V}_{SA} = MAX(\rm{DesCoolVolFlow}_{zone}, \rm{DesHeatVolFlow}_{zone}) / \rm{ZoneFraction}\]
where
ZoneFraction = Fraction of the total volume flow that goes through the controlling zone
The unitary system object also allows scalable sizing as follows:
Flow Per Floor Area:
\[\dot{V}_{SA} = (\rm{FlowPerFloorArea})(\rm{TotalFloorArea})\]
Fraction of Autosized Cooling Value:
\[\dot{V}_{SA,cooling} = \dot{V}_{SA,des,coolings}(\rm{FractionOfCoolingValue})\]
Fraction of Autosized Heating Value:
\[\dot{V}_{SA,heating} = \dot{V}_{SA,des,heatings}(\rm{FractionOfHeatingValue})\]
Flow Per Cooling Capacity
\[\dot{V}_{SA,cooling} = \dot{Q}_{coil,des,cooling}(\rm{FractionOfCoolingValue})\]
Flow Per Heating Capacity
\[\dot{V}_{SA,heating} = \dot{Q}_{coil,des,heating}(\rm{FractionOfCoolingValue})\]
The maximum supply air temperature can also be automatically selected. The value is determined from the Sizing:Zone or Sizing:System object depending on where the object is used in the simulation (i.e., as zone or air loop equipment).
Maximum supply air temperature
\[T_{SA,max} = \rm{HeatDesTemp}_{\rm{ZoneOrSystem}}\]
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