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, ${\dot{V}}_{fan,max}={\text{DesMainVolFlow}}_{sys}$.

For duct type = cooling, ${\dot{V}}_{fan,max}={\text{DesCoolVolFlow}}_{sys}$.

For duct type = heating, ${\dot{V}}_{fan,max}={\text{DesHeatVolFlow}}_{sys}$.

If the fan is zone equipment then check whether it is part of a component that only does heating.

For heating only ${\dot{V}}_{fan,max}={\text{DesHeatVolFlow}}_{zone}$.

Otherwise ${\dot{V}}_{fan,max}=max({\text{DesHeatVolFlow}}_{zone},{\text{DesCoolVolFlow}}_{zone})$.

If the max fan flow rate is less than SmallAirVolFlow the max flow rate is set to zero.

Design Fan Heat[LINK]

The design fan heat added to the air stream is calculated using fan model inputs of maximum volume flow rate, pressure rise, fan total efficiency and motor efficiency. For multi-speed fans, the highest air volume flow rate is used in the calculation. Fan heat is accounted for when sizing cooling coils.

Where:

$$P_{fan,des}=({\dot{V}}_{fan,des}\ast \Delta P)/e_{tot,des}$$ $${\dot{Q}}_{fan,heat,des}=e_{motor,des}\ast P_{fan,des}+(P_{fan,des}-(e_{motor,des}\ast P_{fan,des}\left)\right)\ast f_{motorinair}$$

and:

• $P_{fan,des}$ : fan design total power (W)

• ${\dot{V}}_{fan,des}$ : fan design volume flow rate (m3/s)

• $\Delta P$ : fan pressure rise (Pa)

• $e_{tot,des}$ : fan total efficiency

• ${\dot{Q}}_{fan,heat,des}$ : design fan heat to air stream (W)

• $e_{motor,des}$ : fan motor efficiency

• $f_{motorinair}$ : motor in air stream fraction

The design fan temperature rise (C) due to fan heat is added to the cooling coil inlet air temperature or subtracted from the cooling coil outlet air temperature during sizing calculations as appropriate for blow-through or draw-through fan configurations, respectively. The calculation uses a straight-forward inversion of the classic $Q=\dot{m}\ast Cp\ast \Delta T$ equation as:

$$T_{fan,heat,des}={\dot{Q}}_{fan,heat,des}/(C_{p,air}\ast {\rho }_{air}\ast {\dot{V}}_{fan,des})$$

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.

@lp4in@ Control Method & Calculations
VAV & $\begin{array}{cc}{T}_{cc,exit}& =T_{cool,supply}\\ {\dot{V}}_{cc,air}& =\frac{{\dot{m}}_{cc,air,peak}}{{\rho }_{air}}\end{array}$
Bypass & $\begin{array}{cc}{T}_{cc,exit}& =T_{cool,supply}\\ {\dot{V}}_{cc,air}& ={\dot{V}}_{cc,air,max}\cdot max(0,min(1,\frac{T_{mix,at-peak}-T_{sup,avg}}{T_{mix,at-peak}-T_{cc,exit}}))\end{array}$
VT & $\begin{array}{cc}{T}_{cc,exit}& =max(T_{cool,supply},T_{sup,avg})\\ {\dot{V}}_{cc,air}& ={\dot{V}}_{cc,air,max}\end{array}$
OnOff & $\begin{array}{cc}{T}_{cc,exit}& =T_{cool,supply}\\ {\dot{V}}_{cc,air}& ={\dot{V}}_{sys,air,max}\end{array}$
Where:

$$T_{sup,avg}=T_{zones,avg}-\sum _{zones}\frac{{\dot{Q}}_{sens,at-peak}}{{\rho }_{air}{c}_{p,air}{\dot{V}}_{cool,air,max}}$$

and:

• $C_{p,air}$ : the specific heat of air (J/kgC)

• ${\dot{m}}_{cc,air,peak}$ : the air mass flow rate through the cooling coil at the sensible or total system peak cooling load (m${}^3$/s)

• ${\sum }_{zones}{\dot{Q}}_{sens,at-peak}$ : sum of the zone sensible cooling loads at the time of the peak system cooling load

• ${\rho }_{air}$ : the density of air (kg/m${}^3$)

• $T_{cc,exit}$ : the design cooling coil exit temperature (c)

• $T_{cool,supply}$ : the supply air temperature for cooling specified in Sizing:System (C)

• $T_{mix,at-peak}$ : 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 (m${}^3$/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 (m${}^3$/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 (m${}^3$/s). This flow rate occurs at either the maximum zone cooling or heating demand.

Design Coil Load - System Coils[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 is calculated as:

$${\dot{Q}}_{coil,des}={\dot{m}}_{a,coil,des}(h_{a,coil,des,in}-h_{a,coil,des,out})+{\dot{Q}}_{fan,heat,des}$$

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)

• ${\dot{m}}_{a,coil,des}$ : is the coil design air mass flow rate (kg/s)

• ${\dot{Q}}_{fan,heat,des}$ : is the design fan heat (W) - see Section 1.3

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, it 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:[LINK]

• $T_{air,in,des}=T_{out,cool,at-peak}$ (the outside air temperature at the design cooling peak)

• $T_{air,out,des}=T_{sys,precool}$ (the specified Precool Design Temperature from the System:Sizing object)

• $W_{air,in,des}=W_{out,cool,at-peak}$ (the outside humidity ratio at the design cooling peak)

• $W_{air,out,des}=W_{sys,precool}$ (the specified Precool Design Humidity Ratio from the System:Sizing object)

Coil in main air stream, no preconditioning of outside air[LINK]

• $T_{air,in,des}=T_{mix,cool,at-peak}$ (the mixed air temperature at the design cooling peak. Plus the design fan temperature rise due to fan heat, + $T_{fan,heat,des}$, for blow through configuration - see Section 1.3)

• $W_{air,in,des}=W_{mix,cool,at-peak}$ (the mixed humidity ratio at the design cooling peak)

• $T_{air,out,des}=T_{cc,exit}$ (calculated above in the Initial Calculation section. Minus the design fan temperature rise due to fan heat, - $T_{fan,heat,des}$, for draw through configuration - see Section 1.3)

• $W_{air,out,des}=W_{sup,cool}$ (the specified Central Cooling Design Supply Air Humidity Ratio from the Sizing:System object)

Coil in main air stream, outside air preconditioned[LINK]

The oustide air fraction is calculated as (where V${}_{cc,air}$ is calculated as above):

• $f_{oa}=\frac{{\dot{V}}_{air,out,des}}{{\dot{V}}_{cc,air}}$

• $T_{air,in,des}=f_{oa}{T}_{precool}+(1-f_{oa})T_{ret,cool,at-peak}$ (Precool temperature is the specified Precool Design Temperature from System:Sizing Manager; T_ret_cool_at-peak is the return temperature at the system cooling peak load. Plus the design fan temperature rise due to fan heat, + $T_{fan,heat,des}$, for blow through configuration - see Section 1.3)

• $W_{air,in,des}=f_{oa}{W}_{precool}+(1-f_{oa})W_{ret,cool,at-peak}$ (Precool humidity ratio is the specified Precool Design Humidity Ratio from System:Sizing Manager; W_ret_cool_at-peak is the return humidity ratio at the system cooling peak load)

• $T_{air,out,des}=T_{cc,exit}$ (calculated above in the Initial Calculation section. Minus the design fan temperature rise due to fan heat, - $T_{fan,heat,des}$, for draw through configuration - see Section 1.3))

• $W_{air,out,des}=W_{sup,cool}$ (the specified Central Cooling Design Supply Air Humidity Ratio from the Sizing:System object)

With the inlet and outlet conditions established, we can obtain the inlet and outlet enthalpies:

$$\begin{array}{cc}{h}_{air,coil,des,in}& =\text{PsyHFnTdbW}(T_{air,in,des},W_{air,in,des})\\ h_{air,coil,des,out}& =\text{PsyHFnTdbW}(T_{air,out,des},W_{air,out,des})\end{array}$$

Where PsyHFnTdbW is the EnergyPlus function for calculation air specific enthalpy given the air temperature and humidity ratio. We now have all we need to calculate the design coil capacity, ${\dot{Q}}_{coil,des}$ .

Design Coil Load - 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:

$${\dot{Q}}_{coil,des}={\dot{m}}_{a,coil,des}(h_{a,coil,des,in}-h_{a,coil,des,out})+{\dot{Q}}_{fan,heat,des}$$

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)

• ${\dot{m}}_{a,coil,des}$ : is the coil design air mass flow rate (kg/s)

• ${\dot{Q}}_{fan,heat,des}$ : is the design fan heat (W) - see Section 1.3

The enthalpies are given by:

$$\begin{array}{cc}{h}_{air,coil,des,in}& =\text{PsyHFnTdbW}(T_{air,in,des},W_{air,in,des})\\ h_{air,coil,des,out}& =\text{PsyHFnTdbW}(T_{air,out,des},W_{air,out,des})\end{array}$$ Where the inputs to those functions 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 units they are set to design return air, mixed air, or outside air as appropriate to the unit. T${}_{air,out,des}$ is set to the zone cooling design supply air temperature as specified in the Zone:Sizing inputs. W${}_{air,out,des}$ is set to the zone cooling design supply air humidity ratio as specified in the Zone:Sizing inputs.

Design Water Flow Rate (m${}^3$/s) - System Coils[LINK]

The design water volumetric flow rate is calculated using:

$${\dot{V}}_{w,coil,des}=\frac{{\dot{Q}}_{coil,des}}{{\rho }_w{c}_{p,w}\Delta T_{w,des}}$$

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, 1/2 the Loop Design Temperature Difference is used). The design coil load Load${}_{coil,des}$ is calculated from:

$$Loa{d}_{coil,des}=AirMassFlowRat{e}_{coil,des}\cdot (h_{air,coil,des,in}-h_{air,coil,des,out})$$

Design Water Flow Rate (m${}^3$/s) - Zone Coils[LINK]

If the coil is part of an AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction unit or an 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:

$${\dot{V}}_{w,coil,des}=\frac{{\dot{Q}}_{coil,des}}{{\rho }_w{c}_{p,w}\Delta T_{w,des}}$$

Where $\Delta T_{w,des}$ is just the Loop Design Temperature Difference user input from Sizing:Plant.

Design Air Flow Rate - System Coils[LINK]

The design air volumetric flow rate for the system cooling coil is set to:

1. the design outside air flow rate if the coil is in the outside air stream;

2. the coil design flow rate from function GetCoilDesFlowT described in section “Initial Calculations”;

3. the design flow rate set by the parent component (such as a unitary system) containing the cooling coil.

Design Air Flow Rate - 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 Air Inlet Temperature - 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: $T_{air,in,des}=T_{out,cool,at-peak}$ (the outside air temperature set at the design cooling peak).

• Coil in main air stream, no preconditioning of outside air: $T_{air,in,des}=T_{mix,cool,at-peak}$ (the mixed air temperature at the cooling design peak. Plus the design fan temperature rise due to fan heat, + $T_{fan,heat,des}$, for blow through configuration - see Section 1.3).

• 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 $T_{air,in,des}=f_{oa}{T}_{precool}+(1-f_{oa})T_{ret,cool,at-peak}$ , where $T_{precool}$ is the specified Precool Design Temperature from System:Sizing, $T_{ret,cool,at-peak}$ is the return temperature at the system cooling peak load. Plus the design fan temperature rise due to fan heat, + $T_{fan,heat,des}$, for blow through configuration - see Section 1.3).

Design Air Inlet Temperature - 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. The design fan temperature rise is added to coil inlet temperature for blow-through or subtracted from the coil outlet air temperature for draw-through. Fan heat in either case results in a higher design coil load - see Section 1.3.

1. 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: $T_{air,in,des}=T_{zone,cool,peak}$

2. 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 $f_{oa}={\rho }_a{\dot{V}}_{z,oa,des}/{\dot{m}}_{z,cool,des}$

3. 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 Air Outlet Temperature - System Coils[LINK]

The outlet air temperature depends on whether the coil is in the outside air stream.

1. Coil in outside air stream: T${}_{air,out,des}$ = T${}_{sys,des,precool}$ (the specified Precool Design Temperature from the Sizing:System object).

2. Coil in main air stream: the design outlet air temperature is set to the temperature calculated in the Initial Calculation section above.

Design Air Outlet Temperature - Zone Coils[LINK]

If the coil is part of an AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction unit, then:

$$\begin{array}{cc}{\dot{Q}}_{coil,des}& =c_{p,air}{\rho }_{air}{\dot{V}}_{w,coil,des}\Delta T_{w,des}\\ T_1& =T_{air,in,des}-{\dot{Q}}_{coil,des}/\left({\rho }_{air}{c}_{p,air}{\dot{V}}_{air,coil,des}\right)\\ T_2& =T_{w,out,des}+2\\ T_{air,out,des}& =max(T_1,T_2)\end{array}$$

For all other cases T${}_{air,out,des}$ is set to T${}_{z,sup,des}$ (the zone design supply air temperature as specified in Sizing:Zone).

Design Inlet Air Humidity Ratio - 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.

• Coil in outside air stream: $W_{air,in,des}=W_{out,cool,at-peak}$ (the outside air humidity ratio at the design cooling peak).

• Coil in main air stream, no preconditioning of outside air: $W_{air,in,des}=W_{mix,cool,at-peak}$ (the mixed air humidity ratio at the cooling design 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 $W_{air,in,des}=f_{oa}{W}_{precool}+(1-f_{oa})W_{ret,cool,at-peak}$ , where $W_{precool}$ is the specified Precool Design Humidity Ratio from System:Sizing, and $W_{ret,cool,at-peak}$ is the return humidity ratio at the system cooling peak load.

Design Air Inlet Humidity Ratio - Zone Coils[LINK]

The design inlet humidity ratio depends on whether the coil is in a terminal unit or a zonal unit, and where the coil is positioned within the unit.

1. 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.

2. 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 $f_{oa}={\rho }_a{\dot{V}}_{z,oa,des}/{\dot{m}}_{z,cool,des}$

3. In all other cases the design inlet humidity ratio is set to the zone design cooling coil inlet hunidity 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 - System Coils[LINK]

The outlet air humidity ratio depends on whether the coil is in the outside air stream.

• Coil in outside air stream: W${}_{air,out,des}$ = W${}_{sys,des,precool}$ (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.

Design Outlet Air Humidity Ratio - Zone Coils[LINK]

• If the coil is part of an AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction unit, then:

• Get the dewpoint temperature at W${}_{air,in,des}$: $T_{dp,in}=\text{PsyTdpFnWPb}(W_{air,in,des},P_{air,std})$

• If T${}_{dp,in}$ < = T${}_{w,in,des}$ set W${}_{air,out,des}$ = W${}_{air,in,des}$. Otherwise set W${}_{air,out,des}$ = min(PsyWFnTdbRhPb(T${}_{air,out,des}$,0.9,P${}_{air,std}$),W${}_{air,in,des}$)

Design Inlet Water Temperature - 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.

Design Inlet Water Temperature - 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]

$$N_{tube/row}=\mathrm{Int}(13750\cdot \dot{V}coil,water,max)$$

$$N_{tube/row}=\text{Max}(N_{tube/row},3)$$

Fin Diameter[LINK]

Depending on the duct type, get the coil design air flow rate.

For duct type = main, other or default

$${\dot{m}}_{air,des}={\rho }_{air}\cdot DesMainVolFlo{w}_{sys}$$

for duct type = cooling

$${\dot{m}}_{air,des}={\rho }_{air}\cdot DesCoolVolFlo{w}_{sys}$$

for duct type = heating

$${\dot{m}}_{air,des}={\rho }_{air}\cdot DesHeatVolFlo{w}_{sys}$$

$$D_{fin}=0.335\cdot {\dot{m}}_{air,des}$$

Minimum Air Flow Area[LINK]

Depending on the duct type, get the coil design air flow rate.

For duct type = main, other or default

$${\dot{m}}_{air,des}={\rho }_{air}\cdot DesMainVolFlo{w}_{sys}$$

for duct type = cooling

$${\dot{m}}_{air,des}={\rho }_{air}\cdot DesCoolVolFlo{w}_{sys}$$

for duct type = heating

$${\dot{m}}_{air,des}={\rho }_{air}\cdot DesHeatVolFlo{w}_{sys}$$

$$A_{MinAirFlow}=0.44\cdot {\dot{m}}_{air,des}$$

Fin Surface Area[LINK]

Depending on the duct type, get the coil design air flow rate.

For duct type = main, other or default

$${\dot{m}}_{air,des}={\rho }_{air}\cdot DesMainVolFlo{w}_{sys}$$

for duct type = cooling

$${\dot{m}}_{air,des}={\rho }_{air}\cdot DesCoolVolFlo{w}_{sys}$$

for duct type = heating

$${\dot{m}}_{air,des}={\rho }_{air}\cdot DesHeatVolFlo{w}_{sys}$$

$$A_{FinSurf}=78.5\cdot {\dot{m}}_{air,des}$$

Total Tube Inside Area[LINK]

$${\dot{Q}}_{coil,des,total}=\frac{{\dot{m}}_{air,des}(H_{in}-H_{out})}{TotCapTempModFac}+{\dot{Q}}_{fan,heat,des}$$

Where D${}_{tube,inside}$ is the tube inside diameter.

Tube Outside Surf Area[LINK]

$${\dot{Q}}_{coil,des,sensible}=\frac{{\dot{m}}_{air,des}{C}_{p,air,des}(T_{DB,in}-T_{DB,out})}{SensCapTempModFac}+{\dot{Q}}_{fan,heat,des}$$

Where D${}_{tube,outside}$ is the tube outside diameter.

Coil Depth[LINK]

$${\dot{Q}}_{coil,rated,total}=m_{air,rated}(H_{in}-H_{out})/TotCapTempModFra{c}_{NominalSpeed}$$

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.

$$T_{WB,ratio}=\frac{T_{WB,air,in,des}+273.15C}{283.15C}$$

$$T_{S,ratio}=\frac{29.44C+273.15C}{283.15C}$$

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

$$TotCapTempModFac=TCC1+TCC2\left(T_{WB,ratio}\right)+TCC3\left(T_{S,ratio}\right)+TCC4+TCC5$$

where:

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

The 4${}^{th}$ and 5${}^{th}$ 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.

$${\dot{Q}}_{coil,rated,total}=m_{air,rated}(48000-H_{out})/TotCapTempModFra{c}_{NominalSpeed}$$

Where:

• ${\dot{Q}}_{fan,heat,des}$ : is the design fan heat (W) - see Section 1.3

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

$$\begin{array}{cc}SensCapTempModFac& =SCC1+SCC2\left(T_{DB,ratio}\right)+SCC3\left(T_{WB,ratio}\right)\\ & +SCC4\left(T_{S,ratio}\right)+SCC5+SCC6\end{array}$$

where:

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

The 5${}^{th}$ and 6${}^{th}$ 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${}^{\circ }$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.

$${\dot{Q}}_{coil,rated,total}={\dot{Q}}_{coil,rated,total}+{\dot{Q}}_{fan,heat,des}$$

Where:

• ${\dot{Q}}_{fan,heat,des}$ : is the design fan heat (W) - see Section 1.3

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:

$$TotCapTempModFra{c}_{NominalSpeed}=a+b\ast W{B}_i+c\ast W{B}_i^2+d\ast EWT+e\ast EW{T}^2+f\ast W{B}_i\ast EWT$$

where:

WB${}_i$ = wet-bulb temperature of the air entering the heating coil, ${}^{\circ }$C

EWT = entering water temperature, ${}^{\circ }$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 H${}_{in}$ > H${}_{out}$ Then

$${\dot{V}}_{coil,water,max}=HeatCa{p}_{sys}/(C_{p,water}\cdot {\rho }_{water}\cdot \Delta T_{plt,hw,des})$$

Else

$${\dot{m}}_{air,des}={\rho }_{air}\cdot {\dot{m}}_{air,des,tu}$$

End If

$${\dot{m}}_{air,des}=DesHeatMassFlo{w}_{zone}$$

Where:

• ${\dot{Q}}_{fan,heat,des}$ : is the design fan heat (W) - see Section 1.3

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:

$$Q_{coil,des}=c_{p,air}{\dot{m}}_{air,des}\cdot (T_{out,air}-T_{in,air})$$

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:

T${}_{in,air}$ = DesHeatCoilInTemp${}_{zone}$

If the coil is part of an induction unit take into account the induced air:

Frac${}_{minflow}$ = MinFlowFrac${}_{zone}$

T${}_{in,air}$ = DesHeatCoilInTemp${}_{zone}$ * Frac${}_{minflow}$ +

ZoneTempAtHeatPeak${}_{zone}$ *(1- Frac${}_{minflow}$)

T${}_{out,air}$ = HeatDesTemp${}_{zone}$

W${}_{out,air}$ = HeatDesHumRat${}_{zone}$

If the coil is part of a terminal unit the mass flow rate is determined by the volumetric flow rate of the terminal unit:

$$FlowCapRati{o}_{min}=0.00004027m^3/sperwatt\left(300cfm/ton\right)$$

Otherwise the design flow is obtained from the zone design data array:

$$FlowCapRati{o}_{max}=0.00006041m^3/sperwatt\left(450cfm/ton\right)$$

$${\dot{m}}_{in,air}={\rho }_{air}\cdot DesHeatVolFlo{w}_{sys}$$

Here c${}_{p,air}$ 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:

$$T_{in,air}=DesHeatCoilInTem{p}_{zone}$$

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:

$$Fra{c}_{minflow}=MinFlowFra{c}_{zone}$$

The required inputs for the simple coil model are:

$$T_{in,air}=DesHeatCoilInTem{p}_{zone}\ast Fra{c}_{minflow}+$$

$$ZoneTempAtHeatPea{k}_{zone}\ast (1-Fra{c}_{minflow})$$

$$W_{in,air}=DesHeatCoilInHumRa{t}_{zone}$$

$$FlowCapRatio={\dot{V}}_{air,rated}/CCa{p}_{rated}$$

Depending on the duct type, get the coil design air flow rate.

For duct type = main, other or default

$${\dot{m}}_{in,water}={\rho }_{water}\cdot {\dot{V}}_{coil,water,max}$$

for duct type = cooling

$$T_{out,air}=HeatDesTem{p}_{zone}$$

for duct type = heating

$$W_{out,air}=HeatDesHumRa{t}_{zone}$$

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;

$${\dot{m}}_{air,des}={\rho }_{air}\cdot {\dot{m}}_{air,des,tu}$$

If the coil is part of an induction unit take into account the induced air:

$${\dot{m}}_{air,des}=DesHeatMassFlo{w}_{zone}$$

$${\dot{Q}}_{coil,des}=c_{p,air}\cdot {\dot{m}}_{air,des}\cdot (T_{out,air}-T_{in,air})$$

$${\dot{V}}_{air,rated}=DesMainVolFlo{w}_{sys}$$

$${\dot{V}}_{air,rated}=Max(DesCoolVolFlo{}^{}$$