## Engineering Reference — EnergyPlus 8.4

### Engineering Reference

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.

If the fan is part of the central air system then check the duct type.

For duct type = main, other or default,

For duct type = cooling,

For duct type = heating,

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

For heating only ;

Otherwise

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

The sizing is done in function SizeWaterCoil of module WaterCoils

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.
Cooling coil calculations for different capacity control methods
Control Method Calculations
VAV
Bypass
VT
OnOff

Where:

and:

• : the specific heat of air (J/kgC)

• : the air mass flow rate through the cooling coil at the sensible or total system peak cooling load (m3/s)

• : sum of the zone sensible cooling loads at the time of the peak system cooling load

• : the density of air (kg/m3)

• : the design cooling coil exit temperature (c)

• : the supply air temperature for cooling specified in Sizing:System (C)

• : the mixed air temperature at the time of the system peak cooling load (C)

• : the average zone temperature at the time of the system peak cooling load (C)

• : 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.

• : the maximum cooling volumetric air flow rate from the design calculations (m3/s). This flow rate occurs at the maximum zone cooling demand.

• : 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 (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:

Where:

• : is the coil design outlet air enthalpy (J/kg), and

• : 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

where is the design outside air volumetric flow rate for the system. Otherwise, it is set to:

where 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]

• (the outside air temperature at the design cooling peak)

• (the specified Precool Design Temperature from the System:Sizing object)

• (the outside humidity ratio at the design cooling peak)

• (the specified Precool Design Humidity Ratio from the System:Sizing object)

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

• (the mixed air temperature at the design cooling peak)

• (the mixed humidity ratio at the design cooling peak)

• (calculated above in the Initial Calculation section)

• (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 Vcc,air is calculated as above)

• (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)

• (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)

• (calculated above in the Initial Calculation section)

• (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:

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, .

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:

Where:

• : is the coil design outlet air enthalpy (J/kg), and

• : is the coil design air mass flow rate (kg/s)

The enthalpies are given by:

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. 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) - System Coils[LINK]

The design water volumetric flow rate is calculated using:

Where 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 Loadcoil,des is calculated from:

### Design Water Flow Rate (m3/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:

Where 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: (the outside air temperature set at the design cooling peak).

• Coil in main air stream, no preconditioning of outside air: (the mixed air temperature at the cooling design peak).

• Coil in main air stream, outside air preconditioned. The outside air fraction is calculated as , where is calculated above. Then , where is the specified Precool Design Temperature from System:Sizing, and is the return temperature at the system cooling peak load.

### 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.

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.

2. For fan coil units the design inlet temperature is set to the mixed air temperature: , where

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: Tair,out,des = Tsys,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:

For all other cases Tair,out,des is set to Tz,sup,des (the zone design supply air temperature as specified in Sizing:Zone).

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: (the outside air humidity ratio at the design cooling peak).

• Coil in main air stream, no preconditioning of outside air: (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 , where is calculated above. Then , where is the specified Precool Design Humidity Ratio from System:Sizing, and 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: , where

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: Wair,out,des = Wsys,des,precool (the specified Precool Design Humidity Ratio from the Sizing:System object)

• Coil in main air stream: Wair,out,des = PsyWFnTdbRhPb(Tair,out,des,0.9,Pair,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 Wair,in,des:

• If Tdp,in < = Tw,in,des set Wair,out,des = Wair,in,des. Otherwise set Wair,out,des = min(PsyWFnTdbRhPb(Tair,out,des,0.9,Pair,std),Wair,in,des)

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.

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 = Max(Ntube/row,3)

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

For duct type = main, other or default

for duct type = cooling

for duct type = heating

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

For duct type = main, other or default

for duct type = cooling

for duct type = heating

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

For duct type = main, other or default

for duct type = cooling

for duct type = heating

Atube,total\ inside = 4.4 *Dtube,inside *Ntube\ rows *Ntubes/row

Where Dtube,inside is the tube inside diameter.

Atube,outside = 4.1 *Dtube,outside *Ntube\ rows *Ntubes/row

Where Dtube,outside is the tube outside diameter.

Depthcoil = Depthtube\ spacing * Ntube\ rows

The sizing is done in subroutine SizeHVACWaterToAir

The calculation is identical to that done for Coil:Cooling:Water.

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.

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.

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

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.

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.

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

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.

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.

The calculation is identical to that done for Coil:Cooling:WaterToAirHeatPump:EquationFit.

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.

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:

where

WBi = wet-bulb temperature of the air entering the heating coil, degC

EWT = entering water temperature, degC

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

Else

End If

The sizing is done in subroutine SizeHVACWaterToAir.

The calculation is identical to that done for Coil:Cooling:Water.

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.

The rated total heating capacity is set equal to the rated total cooling capacity.

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.

The calculation is identical to that done for Coil:Cooling:WaterToAirHeatPump:EquationFit.

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.

The rated total heating capacity is set equal to the rated total cooling capacity.

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:

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 +

ZoneTempAtHeatPeak zone *(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:

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

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:

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

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

For duct type = main, other or default

for duct type = cooling

for duct type = heating

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 +

ZoneTempAtHeatPeak zone *(1- Fracminflow)

Win,air = DesHeatCoilInHumRatzone

Tin,water = ExitTempplt,hw,des

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:

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

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.

The sizing is done in subroutine SizeSteamCoil.

The maximum steam volumetric flow rate is calculated using:

The steam density ( ) is for saturated steam at 100 degC (101325.0 Pa) and hfg is the latent heat of vaporization of water at 100 degC (101325.0 Pa). Cp,w is the heat capacity of saturated water (condensate) at 100 degC (101325.0 Pa) and is the Degree of Subcooling defined in the Coil:Heating:Steam object input. The design coil load Loadcoil,des is calculated from:

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 rair *DesMainVolFlowsys *MinSysAirFlowRatio. If the coil is in a cooling duct the flow rate is set to rair *DesCoolVolFlowsys *MinSysAirFlowRatio. If the coil is in a heating duct the flow rate is set to rair *DesHeatVolFlowsys. If the coil is in any other kind of duct, the flow rate is set to rair *DesMainVolFlowsys.

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).

1. Sizing based on 100% Outdoor Air in Heating

Tair,coil,des,in = HeatOutTempsys (the outdoor air temperature at the design heating peak)

1. Sizing based on minimum outdoor air flow. The outdoor air fraction is calculated as Fracoa = DesOutAirVolFlowsys / DesVolFlow. DesVolFlow is .

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:

where:

= 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)

= 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 +

ZoneTempAtHeatPeak zone *(1- Fracminflow)

Tout,air = HeatDesTempzone

Wout,air = HeatDesHumRatzone

Qcoil,des = Cp,air * DesHeatMassFlowzone *(Tout,air-Tin,air)

Here cp,air is calculated at the outlet humidity and the average of the inlet and outlet temperatures.

The sizing calculations are done in subroutine SizeDXCoil in module DXCoils. This section covers the sizing of the objects

### Rated Air Volume Flow Rate[LINK]

The rated air flow rate is obtained from the system design array.

The rated air flow rate is the maximum of the heating and cooling design flow rates from the zone design array.

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

rair = 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)

CCaprated = CCappeak/ CapModFac

We check that the design volume flow per total capacity is within the prescribed range:

If FlowCapRatio < FlowCapRatiomin then

If FlowCapRatio > FlowCapRatiomax then

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

rair = 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)

CCaprated = CCappeak/ CapModFac

We check that the design volume flow per total capacity is within the prescribed range:

If FlowCapRatio < FlowCapRatiomin then

If FlowCapRatio > FlowCapRatiomax then

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)

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)

Dhrated,sup = hrated-hsup

DQsrated,sup = Cp,air *(Tin,rated-Tsup)

SHRrated = DQsrated,sup/Dhrated,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.

The rated sensible heat ratio, low speed, is set equal to the full speed SHR.

For the heat pump the resistive defrost heat capacity is set equal to the cooling capacity.

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

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

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:

where

WBi = wet-bulb temperature of the air entering thecooling coil, degC

DBo = condenser entering air temperature, degC

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

Else

End If

The other sizing procedures, e.g. evaporative condenser pump, etc., are the same as Coil:Cooling:DX:SingleSpeed.

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 = Effmot *Effimpeller

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.

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.

Hnom, the nominal head, is an input.

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.

where

Cp,w is the specific heat of water at 5 oC;

rw is the density of water at standard conditions (5.05 oC);

DTloop,des is the chilled water loop design temperature rise;

is the loop design volumetric flow rate.

### Design Condenser Volumetric Water Flow Rate[LINK]

where

Cp,w is the specific heat of water at design condenser inlet temperature;

rw is the density of water at standard conditions (5.05 oC);

DTloop,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.

where

Cp,w is the specific heat of water at the boiler design outlet temperature;

rw is the density of water at standard conditions (5.05 oC);

DTloop,des is the hot water loop design temperature decrease;

is the loop design volumetric flow rate.

### Design Evaporator Volumetric Water Flow Rate[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, , is set equal to the design flow rate for that loop, multiplied by the component sizing factor, .

The Loop Demand Side design flow rate, , is set equal to the Loop Supply Side design flow rate.

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, , is used to determine a nominal capacity.

A loop-to-loop design temperature difference, , 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, . 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, .

(Cooling, Condenser)

(Heating, Steam)

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.

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 degC) to saturated steam at 100.0 degC. Autosizing procedure assumes that electrical heating element in the humidifier heat the water from the reference temperature and generate saturated steam at 100 degC, and electric to thermal energy conversion efficiency of 100.0%.

where

Cp,w is the specific heat of water at average temperature ((100+20)/2 = 60.0 * degC), (J/kgK);*

rw is the density of water at standard conditions (5.05 * degC);*

DTw is the sensible temperature rise of water (100.0 - 20.0 = 80.0 * degC);*

is the rated capacity of the humidifier in volumetric flow rate.

hfg is the latent heat of vaporization of water at 100.0 degC, (J/kg);

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 degC to a saturated steam at 100.0 degC. Autosizing procedure assumes that gas heater in the humidifier convert the water from the reference temperature and generate saturated steam at 100 degC, using gas to thermal energy conversion rated thermal efficiency.

Rated Gas Use Rate

The rated or nominal gas use rate is given by:

Where,

• Cp,w: specific heat of water at average temperature ((100+20)/2 = 60.0 degC), (J/kgK);

• rho_w: density of water at standard condition (5.05 degC);

• DeltaTw: sensible temperature rise of water (100.0 - 20.0 = 80.0 degC);

• V_cap_nom: rated or nominal capacity of the humidifier, (m3/s)

• h_fg: latent heat of vaporization of water at 100.0 degC, (J/kg);

• eta_rated: thermal efficiency at rated condition;