# 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

˙Vfan,max=DesMainVolFlowsys

*F*or duct type=*cooling*

˙Vfan,max=DesCoolVolFlowsys

*F*or duct type=*heating*

˙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 ˙Vfan,max=DesHeatVolFlowzone;

Otherwise ˙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 subroutine SizeWaterCoil* of module *WaterCoils*

### Design Water Flow Rate (m^{3}/s)[LINK]

The design water volumetric flow rate is calculated using:

WaterVolFlowRatecoil,des=Loadcoil,desρw⋅cp,w⋅ΔTw,des

*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). The design coil load *Load*_{coil,des} is calculated from:

Loadcoil,des=AirMassFlowRatecoil,des⋅(hair,coil,des,in−hair,coil,des,out)

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 _{air}DesOutAirVolFlow_{sys} (the design outside air volumetric flow for the system). If the coil is in a cooling duct the flow rate is set to _{air}DesCoolVolFlow_{sys}. If the coil is in a heating duct the flow rate is set to _{air}DesHeatVolFlow_{sys}. If the coil is in the main duct (or any other kind of duct) the flow rate is set to _{air}DesMainVolFlow_{sys}.

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} = *CoolOutTemp*_{sys} (the outside air temperature at the design cooling peak)

*T*_{air,out,des} = *PrecoolTemp*_{sys} (the specified Precool Design Temperature from the *Sizing:System* object).

*W*_{air,in,des} = *CoolOutHumRat*_{sys} (the outside humidity ratio at the design cooling peak)

*W*_{air,out,des} = *PrecoolHumRat*_{sys} (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} = *CoolMixTemp*_{sys} (the mixed air temperature at the design cooling peak)

*W*_{air,in,des} = *CoolMixHumRat*_{sys} (the mixed air humidity ratio at the design cooling peak)

*T*_{air,out,des} = *CoolSupTemp*_{sys} (the specified Central Cooling Design Supply Air Temperature from the *Sizing:System* object)

*W*_{air,out,des} = *CoolSupHumRat*_{sys} (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 *Frac*_{oa} **= *DesOutAirVolFlow*_{sys} / *DesVolFlow*. *DesVolFlow* is just *AirMassFlowRate*_{coil,des} / _{air}.

*T*_{air,in,des}=*Frac*_{oa}*PrecoolTemp*_{sys} + (1. *Frac*_{oa})*CoolRetTemp*_{sys}(see Table 41. System Sizing Data)

*W*_{air,in,des}=*Frac*_{oa}PrecoolHumRat_{sys} + (1. *Frac*_{oa})*CoolRetHumRat*_{sys}

*T*_{air,out,des} = *CoolSupTemp*_{sys} (the specified Central Cooling Design Supply Air Temperature from the *Sizing:System* object)

*W*_{air,out,des} = *CoolSupHumRat*_{sys} (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:

*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 *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 *Load*_{coil,des} and *WaterVolFlowRate*_{coil,des}.

If the coil is part of an *AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction* unit, the water flow rate is set equal to the terminal unit’s chilled water flow rate. Otherwise (e.g., the zone-level coil is part of *ZoneHVAC:FourPipeFanCoil, ZoneHVAC:UnitVentilator or ZoneHVAC:VentilatedSlab*) the calculation is similar to that at the system level. A design load is calculated:

Loadcoil,des=AirMassFlowRatecoil,des⋅(hair,coil,des,in−hair,coil,des,out)

Where:

AirMassFlowRate_{coil,des}~~= DesCoolMassFlow_{zone} (see Table 40. Zone Sizing Data)

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})

T_{air,in,des} = DesCoolCoilInTemp_{zone} (see Table 40)

W_{air,in,des} = DesCoolCoilInHumRat_{zone} (see Table 40)

T_{air,out,des} = CoolDesTemp_{zone} (user input from Zone:Sizing object)

W_{air,out,des} = CoolDesHumRat_{zone} (user input from Zone:Sizing object)

WaterVolFlowRatecoil,des=Loadcoil,desρw⋅cp,w⋅ΔTw,des

where *T*_{w,des} is the *Loop Design Temperature Difference* user input from the *Sizing:Plant* object*.*

### Design Air Flow Rate[LINK]

The design air volumetric flow rate depends on the location of the coil. If the coil is in the outside air stream the flow rate is set to *DesOutAirVolFlow*_{sys}. If the coil is in a cooling duct the flow rate is set to *DesCoolVolFlow*_{sys}. If the coil is in a heating duct the flow rate is set to *DesHeatVolFlow*_{sys}. If the coil is in the main duct (or any other kind of duct) the flow rate is set to *DesMainVolFlow*_{sys}.

If the coil is part of an *AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction* unit, the design air volumetric flow rate is set equal to the flow rate of the terminal unit. For all other zone coils it is set equal to:

Max(DesCoolMassFlow_{zone},DesHeatMassFlow_{zone}) _{air}

### 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} = *CoolOutTemp*_{sys} (the outside air temperature at the design cooling peak).

Coil in main air stream, no preconditioning of outside air: *T*_{air,in} = *CoolMixTemp*_{sys} (the mixed air temperature at the design cooling peak).

Coil in main air stream, outside air preconditioned. The outside air fraction is calculated as *Frac*_{oa} **= *DesOutAirVolFlow*_{sys} / *DesVolFlow*. *DesVolFlow* is just *AirMassFlowRate*_{coil,des} / _{air}. Then

*T*_{air,in}=*Frac*_{oa}*PrecoolTemp*_{sys} + (1. *Frac*_{oa})*CoolRetTemp*_{sys}

If the coil is part of an *AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction* unit, the Design Inlet Air Temperature is set equal to *ZoneTempAtCoolPeak*_{zone} (see Table 40. Zone Sizing Data). For all other zone coils, it is set equal to *DesCoolCoilInTemp*_{zone} (see Table 40).

### 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: *T*_{air,out,des} = *PrecoolTemp*_{sys} (the specified Precool Design Temperature from the *Sizing:System* object).

Coil in main air stream: *T*_{air,out,des} = *CoolSupTemp*_{sys} (the specified Central Cooling Design Supply Air Temperature from the *Sizing:System* object)

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

Loadcoil,des=AirMassFlowRatecoil,des⋅ΔTw,des⋅cp,w⋅ρw

Tair,out,des=Tair,in,des−Loadcoil,des/(ρair⋅cp,air⋅CoolVolFlowcoil,air,des)

where *CoolVolFlow*_{coil,air,des} is the user input or previously autosized coil Design Air Flow Rate. For all other zone coils the Design Outlet Air Temperature is set to *CoolDesTemp*_{zone} (see Table 40. Zone Sizing Data).

### Design Inlet Air Humidity Ratio[LINK]

The inlet air 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} = *CoolOutHumRat*_{sys} (the outside humidity ratio at the design cooling peak).

Coil in main air stream, no preconditioning of outside air: *W*_{air,in,des} = *CoolMixHumRat*_{sys} (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 *Frac*_{oa} **= *DesOutAirVolFlow*_{sys} / *DesVolFlow*. *DesVolFlow* is just *AirMassFlowRate*_{coil,des} / _{air}. Then

*W*_{air,in,des}=*Frac*_{oa}PrecoolHumRat_{sys} + (1. *Frac*_{oa})*CoolRetHumRat*_{sys}

If the coil is part of an *AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction* unit, the Design Inlet Air Humidity Ratio is set equal to *ZoneHumRatAtCoolPeak*_{zone} (see Table 40. Zone Sizing Data). For all other zone coils, it is set equal to *DesCoolCoilInHumRat*_{zone} (see Table 40).

### 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: *W*_{air,out,des} = *PrecoolHumRat*_{sys} (the specified Precool Design Humidity Ratio from the *Sizing:System* object)

Coil in main air stream: *W*_{air,out,des} = *CoolSupHumRat*_{sys} (the specified Central Cooling Design Supply Air Humidity Ratio from the *Sizing:System* object)

The Design Outlet Air Humidity Ratio is set equal to *CoolDesHumRat*_{zone} (user input from *Zone:Sizing*).

### 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=Int(13750˙Vcoil,water,max)

*N*_{tube/row}=**Max**(*N*_{tube/row},3)

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

For duct type = *main, other* or default

˙mair,des=ρairDesMainVolFlowsys

*for duct type=cooling*

˙mair,des=ρairDesCoolVolFlowsys

*for duct type=heating*

˙mair,des=ρairDesHeatVolFlowsys

Dfin=0.335˙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

˙mair,des=ρairDesMainVolFlowsys

*for duct type=cooling*

˙mair,des=ρairDesCoolVolFlowsys

*for duct type=heating*

˙mair,des=ρairDesHeatVolFlowsys

AMinAirFlow=0.44˙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

˙mair,des=ρairDesMainVolFlowsys

*for duct type=cooling*

˙mair,des=ρairDesCoolVolFlowsys

*for duct type=heating*

˙mair,des=ρairDesHeatVolFlowsys

AFinSurf=78.5˙mair,des

### Total Tube Inside Area[LINK]

*A~tube,total inside*_{=4.4D}tube,inside_{N}tube rows_{N}tubes/row~

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

### Tube Outside Surf Area[LINK]

*A*_{tube,outside}=4.1*D*_{tube,outside}N~tube rows_{N}tubes/row~

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

*Depth*_{coil}=*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.

TWB,ratio=(TWB,air,in,des+273.15C)283.15C

TS,ratio=29.44C+273.15C283.15C

where:

TWB,ratio = ratio of load-side inlet air wet-bulb temperature in Kelvin to a reference temperature

TS,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(TWB,ratio)+TCC3(TS,ratio)+TCC4+TCC5

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.

### 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.

TDB,ratio=(TDB,air,in,des+273.15C283.15C

TS,ratio=(29.44C+273.15C283.15C

where:

TDB,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

SensCapTempModFac=SCC1+SCC2(TDB,ratio)+SCC3(TWB,ratio)+SCC4(TS,ratio)+SCC5+SCC6

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 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:

TotCapTempModFracNominalSpeed=a+b∗WBi+c∗WB2i+d∗EWT+e∗EWT2+f∗WBi∗EWT

where

WB_{i} = 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 H*_{in} > H_{out} Then

˙Qcoil,rated,total=mair,rated(Hin−Hout)/TotCapTempModFracNominalSpeed

*Else*

˙Qcoil,rated,total=mair,rated(48000−Hout)/TotCapTempModFracNominalSpeed

*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:

˙Vcoil,water,max=HeatCapsys/(Cp,waterρwaterΔTplt,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;

*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:

˙mair,des=ρair˙mair,des,tu

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

˙mair,des=DesHeatMassFlowzone

Qcoil,des=cp,air˙mair,des(Tout,air−Tin,air)

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:

˙Vcoil,water,max=Qcoil,des/(Cp,waterρwaterΔTplt,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;

*Q*_{coil,des}= *HeatCap*_{sys}

The required inputs for the simple coil model are:

*T*_{in,air}= *HeatMixTemp*_{sys}

*W*_{in,air}= *HeatMixHumRat*_{sys}

*T*_{in,water}= *ExitTemp*_{plt,hw,des}

˙min,water=ρwater˙Vcoil,water,max

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

For duct type = *main, other* or default

˙min,air=ρairDesMainVolFlowsys

*for duct type=cooling*

˙min,air=ρairDesCoolVolFlowsys

*for duct type=heating*

˙min,air=ρairDesHeatVolFlowsys

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;

*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})

*W*_{in,air}= *DesHeatCoilInHumRat*_{zone}

*T*_{in,water}= *ExitTemp*_{plt,hw,des}

˙min,water=ρwater˙Vcoil,water,max

*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:

˙mair,des=ρair˙mair,des,tu

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

˙mair,des=DesHeatMassFlowzone

˙Qcoil,des=cp,air˙mair,des(Tout,air−Tin,air)

Here *c*_{p,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 (ρsteam) is for saturated steam at 100°C (101325.0 Pa) and *h*_{fg} is the latent heat of vaporization of water at 100°C (101325.0 Pa). *C*_{p,w} is the heat capacity of saturated water (condensate) at 100°C (101325.0 Pa) and ΔTsc is the Degree of Subcooling defined in the Coil:Heating:Steam object input. The design coil load *Load*_{coil,des} is calculated from:

Loadcoil,des=˙mair,des(cp,air)(Tair,coil,des,out−Tair,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 _{air}DesMainVolFlow_{sys}MinSysAirFlowRatio. If the coil is in a cooling duct the flow rate is set to _{air}DesCoolVolFlow_{sys}MinSysAirFlowRatio. If the coil is in a heating duct the flow rate is set to _{air}DesHeatVolFlow_{sys}. If the coil is in any other kind of duct, the flow rate is set to _{air}DesMainVolFlow_{sys}.

For sizing, the design outlet air temperature (*T*_{air,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

*T*_{air,coil,des,in} = *HeatOutTemp*_{sys} (the outdoor air temperature at the design heating peak)

- Sizing based on minimum outdoor air flow. The outdoor air fraction is calculated as
*Frac*_{oa} **= *DesOutAirVolFlow*_{sys} / *DesVolFlow*. *DesVolFlow* is ˙mair,desρair.

*T*_{air,coil,des,in} = *Frac*_{oa} *HeatOutTemp*_{sys} + (1. - *Frac*_{oa}) *HeatRetTemp*_{sys} (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:

Loadcoil,des=˙mair,des(cp,air)(Tair,coil,des,out−Tair,coil,des,in)

where:

˙mair,des= *DesHeatMassFlow*_{zone} (see Table 40. Zone Sizing Data)

*T*_{air,coil,des,in} = *DesHeatCoilInTemp*_{zone} (see Table 40)

*T*_{air,coil,des,out} = *HeatDesTemp*_{zone} (user input from Sizing:Zone object)

cp,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 *HeatDesHumRat*_{zone} [user input from Sizing:Zone object])

The terms in the denominator of this equation (*ρ*_{steam}, *h*_{fg}, 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.

*Cap*_{nom}= *HeatCap*_{sys}

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;

*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}

*Q*_{coil,des} = *C*_{p,air} DesHeatMassFlow_{zone}(*T*_{out,air}T_{in,air})

Here *c*_{p,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.

˙Vair,rated=DesMainVolFlowsys

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

˙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.

*T*_{mix}= *CoolMixTemp*_{sys}

*W*_{mix}=*CoolMixHumRat*_{sys}

*T*_{sup}=*CoolSupTemp*_{sys}

*W*_{sup}=*CoolSupHumRat*_{sys}

*T*_{outside}=*CoolOutTemp*_{sys}

_{air}=*PsyRhoAirFnPbTdbW*(*p*_{air,std}, *T*_{mix},*W*_{mix})

*h*_{mix}= *PsyHFnTdbW*(*T*_{mix},*W*_{mix})

*h*_{sup}= *PsyHFnTdbW*(*T*_{sup},*W*_{sup})

*T*_{mix,wb}= *PsyTwbFnTdbWPb*(*T*_{mix},*W*_{mix}, *p*_{air,std})

*CapModFac*=*CurveValue*(CCapFTemp,*T*_{mix,wb},*T*_{outside})

CCappeak=ρair˙Vair,rated(hmix−hsup)

*CCap*_{rated}=*CCap*_{peak} CapModFac

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

FlowCapRatio=˙Vair,rated/CCaprated

If *FlowCapRatio* < *FlowCapRatio*_{min} then

CCaprated=˙Vair,rated/FlowCapRatiomin

If *FlowCapRatio* > *FlowCapRatio*_{max} then

CCaprated=˙Vair,rated/FlowCapRatiomax

where

*FlowCapRatio*_{min} = 0.00004027 m^{3}/s per watt (300 cfm/ton)

And

*FlowCapRatio*_{max}= 0.00006041 m^{3}/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:

*FlowCapRatio*_{min} = 0.00001677 m^{3}/s per Watt (125 cfm/ton)

And

*FlowCapRatio*_{max}= 0.00003355 m^{3}/s per Watt (250 cfm/ton)

The rated cooling capacity for zone coils is calculated in the same manner as for system coils.

*T*_{mix}= *DesCoolCoilInTemp*_{zone}

*W*_{mix}= *DesCoolCoilInHumRat*_{zone}

*T*_{sup}= *CoolDesTemp*_{zone}

*W*_{sup}= *CoolDesHumRat*_{zone}

*T*_{outside}=*T*_{outside},_{desday,peak}

_{air}=*PsyRhoAirFnPbTdbW*(*p*_{air,std}, *T*_{mix},*W*_{mix})

*h*_{mix}= *PsyHFnTdbW*(*T*_{mix},*W*_{mix})

*h*_{sup}= *PsyHFnTdbW*(*T*_{sup},*W*_{sup})

*T*_{mix,wb}= *PsyTwbFnTdbWPb*(*T*_{mix},*W*_{mix}, *p*_{air,std})

*CapModFac*=*CurveValue*(CCapFTemp,*T*_{mix,wb},*T*_{outside})

CCappeak=ρair˙Vair,rated(hmix−hsup)

*CCap*_{rated}=*CCap*_{peak} CapModFac

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

FlowCapRatio=˙Vair,rated/CCaprated

If *FlowCapRatio* < *FlowCapRatio*_{min} then

CCaprated=˙Vair,rated/FlowCapRatiomin

If *FlowCapRatio* > *FlowCapRatio*_{max} then

CCaprated=˙Vair,rated/FlowCapRatiomax

where

*FlowCapRatio*_{min} = 0.00004027 m^{3}/s per watt (300 cfm/ton)

And

*FlowCapRatio*_{max}= 0.00006041 m^{3}/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:

*FlowCapRatio*_{min} = 0.00001677 m^{3}/s per Watt (125 cfm/ton)

And

*FlowCapRatio*_{max}= 0.00003355 m^{3}/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).

*T*_{in,rated}= 26.6667 ^{o}C (80 ^{o}F)

*W*_{in,rated}= 0.01125 (corresponds to 80 ^{o}F drybulb, 67 ^{o}F wetbulb)

*C*_{p,air}= *PsyCpAirFnWTdb*(*W*_{in,rated}, *T*_{in,rated})

For system coils

*T*_{sup}=*CoolSupTemp*_{sys}

*W*_{sup}=*CoolSupHumRat*_{sys}

For zone coils

*T*_{sup}= *CoolDesTemp*_{zone}

*W*_{sup}= *CoolDesHumRat*_{zone}

Then

*h*_{rated}= *PsyHFnTdbW*(*T*_{in,rated}, *W*_{in,rated})

*h*_{sup}= *PsyHFnTdbW*(*T*_{sup}, *W*_{sup})

*h*_{rated,sup}=*h*_{rated}h_{sup}

*Qs*_{rated,sup}=*C*_{p,air}(*T*_{in,rated}T_{sup})

*SHR*_{rated}=*Qs*_{rated,sup}h_{rated,sup}

### Evaporative Condenser Air Volume Flow Rate[LINK]

The evaporative condenser air volume flow rate (m^{3}/s) is set to 0.000114 m^{3}/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 (m^{3}/s) is set to 1/3 times 0.000114 m^{3}/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

Valuen=nNumberOfSpeed∗ValueNumberOfSpeed

where

Value_{n}= Any autosizable variable at Speed n, except SHR

SHR_{n} = SHR_{NumberOfSpeed}

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:

TotCapTempModFracNominalSpeed=a+b∗WBi+c∗WB2i+d∗DBo+e∗DBoT2+f∗WBi∗DBo

where

WB_{i} = wet-bulb temperature of the air entering the cooling coil, °C

DB_{o} = 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 H*_{in} > H_{out} Then

˙Qcoil,rated,total=mair,rated(Hin−Hout)/TotCapTempModFracNominalSpeed

*Else*

˙Qcoil,rated,total=mair,rated(48000−Hout)/TotCapTempModFracNominalSpeed

*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

*Eff*_{tot}=*Eff*_{mot}Eff_{impeller}

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]

˙Qnom=Hnom˙Vnom/Efftot

*H*_{nom}, 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]

˙Qchiller,nom=Cp,wρwΔTloop,des˙Vloop,des

where

*C*_{p,w} is the specific heat of water at 5 ^{o}C;

_{w} is the density of water at standard conditions (5.05 ^{o}C);

*T*_{loop,des} is the chilled water loop design temperature rise;

˙Vloop,des is the loop design volumetric flow rate.

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

˙Vevap,des=˙Vloop,des

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

˙Vcond,des=˙Qchiller,nom(1+1/COPchiller,nom)/(ΔTloop,desCp,wρw)

where

*C*_{p,w} is the specific heat of water at design condenser inlet temperature;

_{w} is the density of water at standard conditions (5.05 ^{o}C);

*T*_{loop,des} is the chilled water loop design temperature rise;

*COP*_{chiller,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]

˙Qboiler,nom=Cp,wρwΔTloop,des˙Vloop,des

where

*C*_{p,w} is the specific heat of water at the boiler design outlet temperature;

_{w} is the density of water at standard conditions (5.05 ^{o}C);

*T*_{loop,des} is the hot water loop design temperature decrease;

˙Vloop,des is the loop design volumetric flow rate.

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

˙Vdes=˙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, ˙VSup,des, is set equal to the design flow rate for that loop, multiplied by the component sizing factor, fcomp.

˙VSup,des=˙Vloop,des∗fcomp

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

˙VDmd,des=˙VSup,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, ΔTSupLoop,Des, is used to determine a nominal capacity.

˙Q=.VSup,desρcpΔTSupLoop,Des

A loop-to-loop design temperature difference, ΔTLoopToLoop,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, TSupLoop,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,TDmdLoop,Exit .

ΔTLoopToLoop,Des=(TSupLoop,Exit+ΔTSupLoop,Des)−TDmdLoop,Exit (Cooling, Condenser)

ΔTLoopToLoop,Des=(TSupLoop,Exit−ΔTSupLoop,Des)−TDmdLoop,Exit (Heating, Steam)

ΔTLoopToLoop,Des=MAX(ABS(ΔTLoopToLoop,Des),2.0)

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 (m^{3}/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%.

Prated=˙Vrated⋅ρw⋅(hfg+Cp,w⋅ΔTw)

where

*C*_{p,w} is the specific heat of water at average temperature ((100+20)/2 = 60.0 °C), (J/kgK);

_{w} is the density of water at standard conditions (5.05 °C);

*T*_{w} is the sensible temperature rise of water (100.0 - 20.0=80.0 °C);

*˙Vrated is the rated capacity of the humidifier in volumetric flow rate.*

*h*_{fg} is the latent heat of vaporization of water at 100.0°C, (J/kg);

### Rated Capacity[LINK]

˙mw=˙ma(ωo−ωi)

where

*m*w *is water mass flow rate, kg/s;*

*m*a *is design air mass flow rate, kg/s;*

*ω*_{o} is design outlet humidity ratio, kg-water/kg-air;

*ω*_{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:

˙ma=Max(DesCoolVolFlowzone,DesHeatVolFlowzone)⋅ρa

ωi=Min(OutHumRatAtCoolPeakzone,OutHumRatAtHeatPeakzone)

ωo=Max(ZoneHumRatAtCoolPeakzone,ZoneHumRatAtHeatPeakzone)

where

_{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:

˙ma=DesOutAirVolFlowsys⋅ρa

ωi=Min(CoolOutHumRatsys,HeatOutHumRatsys)

ωo=Max(CoolSupHumRatsys,HeatSupHumRatsys)

Otherwise, air mass flow rate is determined as follows:

*for duct type = main*

*˙ma=DesMainAirVolFlowsys⋅ρa*

*for duct type = cooling*

˙ma=DesCoolVolFlowsys⋅ρa

*for duct type = heating*

˙ma=DesHeatVolFlowsys⋅ρa

*for duct type = other*

˙ma=DesMainVolFlowsys⋅ρa,

and the humidity ratios are:

ωi=Min(CoolMixHumRatsys,HeatMixHumRatsys)

ωo=Max(CoolSupHumRatsys,HeatSupHumRatsys)

## 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

˙Vtower,w,des=˙Vloop,des

If *Tower Performance Input Method* = *NominalCapacity* then

˙Vtower,w,des=5.382E−8˙Qtower,nom

where 5.38210^{-08} is m^{3}/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} m^{3}/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

˙Qtower,nom=Cp,wρw˙Vtower,w,desΔTloop,des

where

*C*_{p,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 ^{o}C);

*T*_{loop,des} is the condenser water loop design temperature rise;

Finally

˙Qfan,nom=0.0105˙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

˙Vtower,air,des=˙Qfan,nom0.5ρair/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, fairflow/W,in units of m^{3}/s/W. The default value is 2.76316*10^{-5}. When the input field is left blank, the default is used as follows

˙Vtower,air,des=˙Qtower,nom∙fairflow/W∙101325Pstd,altitude

where, Pstd,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

˙Vtower,air,des=˙Qtower,nom∙fairflow/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*

˙Qtower,des=Cp,wρw˙Vtower,w,desΔTloop,des

*for Tower Performance Input Method* = *NominalCapacity*

˙Qtower,des=1.25˙Qtower,nom (to allow for compressor heat)

Where, fdes,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.

*T*_{in,air}=35 ^{o}C (95 ^{o}F design air inlet temperature)

*T*_{in,air,wb}=25.6 ^{o}C (78 ^{o}F design air inlet wetbulb temperature)

*W*_{in} 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*

*T*_{in,water}=*T*_{loop,exit,des}T_{loop,des}

*NominalCapacity*

*T*_{in,water}=35 ^{o}C (95 ^{o}F 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 ˙Qtower,nom,lowspeed instead of ˙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 ˙Qtower,nom,freeconv instead of ˙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

˙Vfluidcooler,w,des=˙Vloop,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

˙Qfluidcooler,nom=Cp,w∙ρw∙˙Vfluidcooler,w,des∙ΔTloop,des

where

*C*_{p,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 ^{o}C);

*T*_{loop,des} is the condenser water loop design temperature rise;

Finally

˙Qfan,nom=0.0105∙˙Qfluidcooler,nom

˙Qfan,nom=0.0105∙˙Qfluidcooler,nom

Where

˙Qfluidcooler,nom is provided by the user.

### Design Air Flow Rate[LINK]

- For Performance Input Method = UFactorTimesAreaAndDesignWaterFlowRate

˙Qfluidcooler,nom=Cp,w∙ρw∙˙Vfluidcooler,w,des∙ΔTloop,des

- For Performance Input Method = NominalCapacity

˙Qfluidcooler,nom is provided by the user.

˙Vfluidcooler,air,des=˙Qfluidcooler,nom/(Tin,water−Tin,air)∗4

Where,

*T*_{in,water}= Design entering water temperature provided by the user

*T*_{in,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

˙Qfluidcooler,nom=Cp,w∙ρw∙˙Vfluidcooler,w,des∙ΔTloop,des

- For Performance Input Method = NominalCapacity

˙Qfluidcooler,nom is provided by the user.

Then we assign the inputs needed for the model.

*T*_{in,air}= Design air inlet temperature provided by the user

*T*_{in,air,wb}= Design air inlet wetbulb temperature provided by the user

*W*_{in} 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

Tin,water=Tloop,exit,des+ΔTloop,des

Tin,water=Providedbytheuser

*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 ˙Qfluidcooler,nom,lowspeed instead of ˙Qfluidcooler,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

˙Vfluidcooler,w,des=˙Vloop,des

where 5.38210^{-08} is m^{3}/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

˙Qfluidcooler,design=Cp,w∙ρw∙˙Vfluidcooler,w,des∙ΔTloop,des

where

*C*_{p,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 ^{o}C);

*T*_{loop,des} is the condenser water loop design temperature rise;

Finally

˙Qfan,design=0.0105∙˙Qfluidcooler,design

˙Qfan,design=0.0105∙˙Qfluidcooler,design

Where

˙Qfluidcooler,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

˙Vfluidcooler,air,des=˙Qfan,design∙0.5∙ρair/190

where

ρair 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

˙Qfluidcooler,design=Cp,w∙ρw∙˙Vfluidcooler,w,des∙ΔTloop,des

- For Performance Input Method = StandardDesignCapacity

˙Qfluidcooler,design=1.25∙˙Qfluidcooler,standarddesign (to allow for compressor heat)

Then we assign the inputs needed for the model.

*T*_{in,air}= 35 ^{o}C (95 ^{o}F design air inlet temperature)

*T*_{in,air,wb}= 25.6 ^{o}C (78 ^{o}F design air inlet wetbulb temperature)

*W*_{in} is calculated from the entering air drybulb and wetbulb.

- For Performance Input Method = UserSpecifiedDesignCapacity

˙Qfluidcooler,design=˙Qfluidcooler,userspecifieddesign

Where, fdes,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.

*T*_{in,air}= Design air inlet temperature provided by the user

*T*_{in,air,wb}= Design air inlet wetbulb temperature provided by the user

*W*_{in} 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

Tin,water=Tloop,exit,des+ΔTloop,des

Tin,water=35∘C(95∘Fdesigninletwatertemperature)

- UserSpecifiedDesignCapacity

Tin,water=Providedbytheuser

*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 ˙Qfluidcooler,standarddesign,lowspeed instead of ˙Qfluidcooler,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]

˙Vair,max=Max(DesCoolVolFlowzone,DesHeatVolFlowzone)

### Maximum Outside Air Flow Rate[LINK]

˙Voutsideair,max=Min(MinOAzone,˙Vair,max)

### Maximum Hot Water Flow[LINK]

*T*_{coil,in}=*DesHeatCoilInTemp*_{zone}

*T*_{coil,out}=*HeatDesTemp*_{zone}

˙Qcoil,des=cp,airDesHeatMassFlowzone(Tout,coil−Tin,coil)

˙Vmax,hw=˙Qcoil,des/(cp,wρwΔTloop,des)

where

*c*_{p,air} is evaluated at the average of the inlet & outlet temperatures and the coil outlet humidity ratio.

### Maximum Cold Water Flow[LINK]

*T*_{coil,in}=*DesColdCoilInTemp*_{zone}

*T*_{coil,out}=*ColdDesTemp*_{zone}

*W*_{coil,in}= *DesCoolCoilInHumRat*_{zone}

*W*_{coil,out}= *CoolDesHumRat*_{zone}

*H*_{coil,in}= *PsyHFnTdbW*(*T*_{coil,in}, *W*_{coil,in})

*H*_{coil,out}= *PsyHFnTdbW*(*T*_{coil,out}, *W*_{coil,out})

˙Qcoil,des=DesCoolMassFlowzone(hin,coil−hout,coil)

˙Vmax,hw=˙Qcoil,des/(cp,wρwΔTlo

## 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(inDataSizing) contains the information about the current duct type. The types can bemain,cooling,heatingorother.CurZoneEqNum(inDataSizing) 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(inDataSizing) 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, otheror default˙Vfan,max=DesMainVolFlowsys

For duct type=cooling˙Vfan,max=DesCoolVolFlowsys

For duct type=heating˙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 ˙Vfan,max=DesHeatVolFlowzone;

Otherwise ˙Vfan,max=Max(DesHeatVolFlowzone,DesCoolVolFlowzone)

If the max fan flow rate is less than

SmallAirVolFlowthe max flow rate is set to zero.## Coil:Cooling:Water[LINK]

The sizing is done in subroutine SizeWaterCoilof moduleWaterCoils## Design Water Flow Rate (m

^{3}/s)[LINK]## System Coils[LINK]

The design water volumetric flow rate is calculated using:

WaterVolFlowRatecoil,des=Loadcoil,desρw⋅cp,w⋅ΔTw,des

Tis just the_{w,des}Loop Design Temperature Differenceuser input fromSizing:Plant(if the coil is in the outside air stream, ½ theLoop Design Temperature Differenceis used). The design coil loadLoadis calculated from:_{coil,des}Loadcoil,des=AirMassFlowRatecoil,des⋅(hair,coil,des,in−hair,coil,des,out)

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

(the design outside air volumetric flow for the system). If the coil is in a cooling duct the flow rate is set to_{air}DesOutAirVolFlow_{sys}. If the coil is in a heating duct the flow rate is set to_{air}DesCoolVolFlow_{sys}. If the coil is in the main duct (or any other kind of duct) the flow rate is set to_{air}DesHeatVolFlow_{sys}._{air}DesMainVolFlow_{sys}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}CoolOutTemp(the outside air temperature at the design cooling peak)_{sys}T=_{air,out,des}PrecoolTemp(the specified Precool Design Temperature from the_{sys}Sizing:Systemobject).W=_{air,in,des}CoolOutHumRat(the outside humidity ratio at the design cooling peak)_{sys}W=_{air,out,des}PrecoolHumRat(the specified Precool Design Humidity Ratio from the_{sys}Sizing:Systemobject)Coil in main air stream, no preconditioning of outside air

T=_{air,in,des}CoolMixTemp(the mixed air temperature at the design cooling peak)_{sys}W=_{air,in,des}CoolMixHumRat(the mixed air humidity ratio at the design cooling peak)_{sys}T=_{air,out,des}CoolSupTemp(the specified Central Cooling Design Supply Air Temperature from the_{sys}Sizing:Systemobject)W=_{air,out,des}CoolSupHumRat(the specified Central Cooling Design Supply Air Humidity Ratio from the_{sys}Sizing:Systemobject)Coil in main air stream, outside air preconditioned. The outside air fraction is calculated as

Frac_{oa}**=DesOutAirVolFlow/_{sys}DesVolFlow.DesVolFlowis justAirMassFlowRate/_{coil,des}._{air}T=_{air,in,des}Frac_{oa}PrecoolTemp+ (1._{sys}Frac)_{oa}CoolRetTemp(see Table 41. System Sizing Data)_{sys}W=_{air,in,des}Frac+ (1._{oa}PrecoolHumRat_{sys}Frac)_{oa}CoolRetHumRat_{sys}T=_{air,out,des}CoolSupTemp(the specified Central Cooling Design Supply Air Temperature from the_{sys}Sizing:Systemobject)W=_{air,out,des}CoolSupHumRat(the specified Central Cooling Design Supply Air Humidity Ratio from the_{sys}Sizing:Systemobject)With the inlet and outlet conditions established, we can obtain the inlet and outlet enthalpies:

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

PsyHFnTdbWis the EnergyPlus function for calculating air specific enthalpy given the air temperature and humidity ratio. We now have all we need to calculateLoadand_{coil,des}WaterVolFlowRate._{coil,des}## Zone Coils[LINK]

If the coil is part of an

AirTerminal:SingleDuct:ConstantVolume:FourPipeInductionunit, the water flow rate is set equal to the terminal unit’s chilled water flow rate. Otherwise (e.g., the zone-level coil is part ofZoneHVAC:FourPipeFanCoil, ZoneHVAC:UnitVentilator or ZoneHVAC:VentilatedSlab) the calculation is similar to that at the system level. A design load is calculated:Loadcoil,des=AirMassFlowRatecoil,des⋅(hair,coil,des,in−hair,coil,des,out)

Where:

AirMassFlowRate

_{coil,des}~~= DesCoolMassFlow_{zone}(see Table 40. Zone Sizing Data)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})T

_{air,in,des}= DesCoolCoilInTemp_{zone}(see Table 40)W

_{air,in,des}= DesCoolCoilInHumRat_{zone}(see Table 40)T

_{air,out,des}= CoolDesTemp_{zone}(user input from Zone:Sizing object)W

_{air,out,des}= CoolDesHumRat_{zone}(user input from Zone:Sizing object)WaterVolFlowRatecoil,des=Loadcoil,desρw⋅cp,w⋅ΔTw,des

where

Tis the_{w,des}Loop Design Temperature Differenceuser input from theSizing:Plantobject.## Design Air Flow Rate[LINK]

## System Coils[LINK]

The design air volumetric flow rate depends on the location of the coil. If the coil is in the outside air stream the flow rate is set to

DesOutAirVolFlow. If the coil is in a cooling duct the flow rate is set to_{sys}DesCoolVolFlow. If the coil is in a heating duct the flow rate is set to_{sys}DesHeatVolFlow. If the coil is in the main duct (or any other kind of duct) the flow rate is set to_{sys}DesMainVolFlow._{sys}## Zone Coils[LINK]

If the coil is part of an

AirTerminal:SingleDuct:ConstantVolume:FourPipeInductionunit, the design air volumetric flow rate is set equal to the flow rate of the terminal unit. For all other zone coils it is set equal to:Max(DesCoolMassFlow

_{zone},DesHeatMassFlow_{zone})_{air}## 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}CoolOutTemp(the outside air temperature at the design cooling peak)._{sys}Coil in main air stream, no preconditioning of outside air:

T=_{air,in}CoolMixTemp(the mixed air temperature at the design cooling peak)._{sys}Coil in main air stream, outside air preconditioned. The outside air fraction is calculated as

Frac_{oa}**=DesOutAirVolFlow/_{sys}DesVolFlow.DesVolFlowis justAirMassFlowRate/_{coil,des}. Then_{air}T=_{air,in}Frac_{oa}PrecoolTemp+ (1._{sys}Frac)_{oa}CoolRetTemp_{sys}## Zone Coils[LINK]

If the coil is part of an

AirTerminal:SingleDuct:ConstantVolume:FourPipeInductionunit, the Design Inlet Air Temperature is set equal toZoneTempAtCoolPeak(see Table 40. Zone Sizing Data). For all other zone coils, it is set equal to_{zone}DesCoolCoilInTemp(see Table 40)._{zone}## Design Outlet Air Temperature[LINK]

## System Coils[LINK]

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

Coil in outside air stream:

T=_{air,out,des}PrecoolTemp(the specified Precool Design Temperature from the_{sys}Sizing:Systemobject).Coil in main air stream:

T=_{air,out,des}CoolSupTemp(the specified Central Cooling Design Supply Air Temperature from the_{sys}Sizing:Systemobject)## Zone Coils[LINK]

If the coil is part of an

AirTerminal:SingleDuct:ConstantVolume:FourPipeInductionunit, then:Loadcoil,des=AirMassFlowRatecoil,des⋅ΔTw,des⋅cp,w⋅ρw

Tair,out,des=Tair,in,des−Loadcoil,des/(ρair⋅cp,air⋅CoolVolFlowcoil,air,des)

where

CoolVolFlowis the user input or previously autosized coil Design Air Flow Rate. For all other zone coils the Design Outlet Air Temperature is set to_{coil,air,des}CoolDesTemp(see Table 40. Zone Sizing Data)._{zone}## Design Inlet Air Humidity Ratio[LINK]

## System Coils[LINK]

The inlet air 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}CoolOutHumRat(the outside humidity ratio at the design cooling peak)._{sys}Coil in main air stream, no preconditioning of outside air:

W=_{air,in,des}CoolMixHumRat(the mixed air humidity ratio at the design cooling peak)._{sys}Coil in main air stream, outside air preconditioned. The outside air fraction is calculated as

Frac_{oa}**=DesOutAirVolFlow/_{sys}DesVolFlow.DesVolFlowis justAirMassFlowRate/_{coil,des}. Then_{air}W=_{air,in,des}Frac+ (1._{oa}PrecoolHumRat_{sys}Frac)_{oa}CoolRetHumRat_{sys}## Zone Coils[LINK]

If the coil is part of an

AirTerminal:SingleDuct:ConstantVolume:FourPipeInductionunit, the Design Inlet Air Humidity Ratio is set equal toZoneHumRatAtCoolPeak(see Table 40. Zone Sizing Data). For all other zone coils, it is set equal to_{zone}DesCoolCoilInHumRat(see Table 40)._{zone}## 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.

Coil in outside air stream:

W=_{air,out,des}PrecoolHumRat(the specified Precool Design Humidity Ratio from the_{sys}Sizing:Systemobject)Coil in main air stream:

W=_{air,out,des}CoolSupHumRat(the specified Central Cooling Design Supply Air Humidity Ratio from the_{sys}Sizing:Systemobject)## Zone Coils[LINK]

The Design Outlet Air Humidity Ratio is set equal to

CoolDesHumRat(user input from_{zone}Zone:Sizing).## Design Inlet Water Temperature[LINK]

## System Coils[LINK]

The Design Inlet Water Temperature is set to the

Design Loop Exit Temperaturespecified in theSizing:Plantobject for the water loop serving this coil.## Zone Coils[LINK]

The Design Inlet Water Temperature is set to the

Design Loop Exit Temperaturespecified in theSizing:Plantobject 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=Int(13750˙Vcoil,water,max)

N=_{tube/row}Max(N,3)_{tube/row}## Fin Diameter[LINK]

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

For duct type =

main, otheror default˙mair,des=ρairDesMainVolFlowsys

for duct type=cooling˙mair,des=ρairDesCoolVolFlowsys

for duct type=heating˙mair,des=ρairDesHeatVolFlowsys

Dfin=0.335˙mair,des

## Minimum Air Flow Area[LINK]

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

For duct type =

main, otheror default˙mair,des=ρairDesMainVolFlowsys

for duct type=cooling˙mair,des=ρairDesCoolVolFlowsys

for duct type=heating˙mair,des=ρairDesHeatVolFlowsys

AMinAirFlow=0.44˙mair,des

## Fin Surface Area[LINK]

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

For duct type =

main, otheror default˙mair,des=ρairDesMainVolFlowsys

for duct type=cooling˙mair,des=ρairDesCoolVolFlowsys

for duct type=heating˙mair,des=ρairDesHeatVolFlowsys

AFinSurf=78.5˙mair,des

## Total Tube Inside Area[LINK]

A~tube,total inside_{=4.4D}tube,inside_{N}tube rows_{N}tubes/row~Where

Dis the tube inside diameter._{tube,inside}## Tube Outside Surf Area[LINK]

A=4.1_{tube,outside}D_{tube,outside}N~tube rows_{N}tubes/row~Where

Dis the tube outside diameter._{tube,outside}## Coil Depth[LINK]

Depth=_{coil}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 theLoop Design Temperature Differenceuser input fromSizing: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.TWB,ratio=(TWB,air,in,des+273.15C)283.15C

TS,ratio=29.44C+273.15C283.15C

where:

TWB,ratio = ratio of load-side inlet air wet-bulb temperature in Kelvin to a reference temperature

TS,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(TWB,ratio)+TCC3(TS,ratio)+TCC4+TCC5

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.## 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.TDB,ratio=(TDB,air,in,des+273.15C283.15C

TS,ratio=(29.44C+273.15C283.15C

where:

TDB,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

SensCapTempModFac=SCC1+SCC2(TDB,ratio)+SCC3(TWB,ratio)+SCC4(TS,ratio)+SCC5+SCC6

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 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:EquationFitobject. 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 theLoop Design Temperature Differenceuser input fromSizing: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 forCoil:Cooling:WaterToAirHeatPump:EquationFit.The difference is in calculating the total cooling capacity temperature modifier function at the selected nominal speed level, as below:TotCapTempModFracNominalSpeed=a+b∗WBi+c∗WB2i+d∗EWT+e∗EWT2+f∗WBi∗EWT

where

WB

_{i}= wet-bulb temperature of the air entering the heating coil, °CEWT = 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

TotCapTempModFaccalculation 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˙Qcoil,rated,total=mair,rated(Hin−Hout)/TotCapTempModFracNominalSpeed

Else˙Qcoil,rated,total=mair,rated(48000−Hout)/TotCapTempModFracNominalSpeed

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 theLoop Design Temperature Differenceuser input fromSizing: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:EquationFitobject. 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 Differenceuser input fromSizing: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:

˙Vcoil,water,max=HeatCapsys/(Cp,waterρwaterΔTplt,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;

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(1_{zone}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:

˙mair,des=ρair˙mair,des,tu

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

˙mair,des=DesHeatMassFlowzone

Qcoil,des=cp,air˙mair,des(Tout,air−Tin,air)

Here

cis calculated at the outlet humidity and the average of the inlet and outlet temperatures._{p,air}With the coil load and the user specified (in a Sizing:Plant object) design hot water temperature decrease, calculate the max water flow rate:

˙Vcoil,water,max=Qcoil,des/(Cp,waterρwaterΔTplt,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;

Q=_{coil,des}HeatCap_{sys}The required inputs for the simple coil model are:

T=_{in,air}HeatMixTemp_{sys}W=_{in,air}HeatMixHumRat_{sys}T=_{in,water}ExitTemp_{plt,hw,des}˙min,water=ρwater˙Vcoil,water,max

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

For duct type =

main, otheror default˙min,air=ρairDesMainVolFlowsys

for duct type=cooling˙min,air=ρairDesCoolVolFlowsys

for duct type=heating˙min,air=ρairDesHeatVolFlowsys

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 functionSimpleHeatingCoilUAResidual.## 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;

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(1_{zone}Frac)_{minflow}W=_{in,air}DesHeatCoilInHumRat_{zone}T=_{in,water}ExitTemp_{plt,hw,des}˙min,water=ρwater˙Vcoil,water,max

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:

˙mair,des=ρair˙mair,des,tu

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

˙mair,des=DesHeatMassFlowzone

˙Qcoil,des=cp,air˙mair,des(Tout,air−Tin,air)

Here

cis calculated at the outlet humidity and the average of the inlet and outlet temperatures._{p,air}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 functionSimpleHeatingCoilUAResidual.## 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 (ρsteam) is for saturated steam at 100°C (101325.0 Pa) and

his the latent heat of vaporization of water at 100°C (101325.0 Pa)._{fg}Cis the heat capacity of saturated water (condensate) at 100°C (101325.0 Pa) and ΔTsc is the Degree of Subcooling defined in the Coil:Heating:Steam object input. The design coil load_{p,w}Loadis calculated from:_{coil,des}Loadcoil,des=˙mair,des(cp,air)(Tair,coil,des,out−Tair,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. If the coil is in a cooling duct the flow rate is set to_{air}DesMainVolFlow_{sys}MinSysAirFlowRatio. If the coil is in a heating duct the flow rate is set to_{air}DesCoolVolFlow_{sys}MinSysAirFlowRatio. If the coil is in any other kind of duct, the flow rate is set to_{air}DesHeatVolFlow_{sys}._{air}DesMainVolFlow_{sys}For sizing, the design outlet air temperature (

T) is the Central Heating Design Supply Air Temperature specified in the Sizing:System object._{air,coil,des,out}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).

T=_{air,coil,des,in}HeatOutTemp(the outdoor air temperature at the design heating peak)_{sys}Frac_{oa}**=DesOutAirVolFlow/_{sys}DesVolFlow.DesVolFlowis ˙mair,desρair.T=_{air,coil,des,in}Frac_{oa}HeatOutTemp+ (1. -_{sys}Frac)_{oa}HeatRetTemp(see Table 41. System Sizing Data)_{sys}## 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 ofZoneHVAC:PackagedTerminalAirConditioner, ZoneHVAC:UnitVentilator, ZoneHVAC:UnitHeater or ZoneHVAC:VentilatedSlab) the calculation is similar to that at the system level. A design load is calculated:Loadcoil,des=˙mair,des(cp,air)(Tair,coil,des,out−Tair,coil,des,in)

where:

˙mair,des=

DesHeatMassFlow(see Table 40. Zone Sizing Data)_{zone}T=_{air,coil,des,in}DesHeatCoilInTemp(see Table 40)_{zone}T=_{air,coil,des,out}HeatDesTemp(user input from Sizing:Zone object)_{zone}cp,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

HeatDesHumRat[user input from Sizing:Zone object])_{zone}The terms in the denominator of this equation (

ρ,_{steam}h, etc.) are evaluated in the same way as described above for steam System Coils._{fg}## Sizing of Gas and Electric Heating Coils[LINK]

The sizing calculation is done in subroutine

SizeHeatingCoilin moduleHeatingCoils.## Nominal Capacity of the Coil[LINK]

## System Coils[LINK]

The value is obtained from the system design array.

Cap=_{nom}HeatCap_{sys}## 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;

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(1_{zone}Frac)_{minflow}T_{out,air}= HeatDesTemp_{zone}W_{out,air}= HeatDesHumRat_{zone}Q=_{coil,des}C(_{p,air}DesHeatMassFlow_{zone}T)_{out,air}T_{in,air}Here

cis calculated at the outlet humidity and the average of the inlet and outlet temperatures._{p,air}## DX Coil Sizing[LINK]

The sizing calculations are done in subroutine

SizeDXCoilin moduleDXCoils. This section covers the sizing of the objectsCoil: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.

˙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.

˙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 Curveevaluated at peak mixed wetbulb and outdoor drybulb temperatures.T=_{mix}CoolMixTemp_{sys}W=_{mix}CoolMixHumRat_{sys}T=_{sup}CoolSupTemp_{sys}W=_{sup}CoolSupHumRat_{sys}T=_{outside}CoolOutTemp_{sys}=_{air}PsyRhoAirFnPbTdbW(p,_{air,std}T,_{mix}W)_{mix}h=_{mix}PsyHFnTdbW(T,_{mix}W)_{mix}h=_{sup}PsyHFnTdbW(T,_{sup}W)_{sup}T=_{mix,wb}PsyTwbFnTdbWPb(T,_{mix}W,_{mix}p)_{air,std}CapModFac=CurveValue(CCapFTemp,T,_{mix,wb}T)_{outside}CCappeak=ρair˙Vair,rated(hmix−hsup)

CCap=_{rated}CCap_{peak}CapModFacWe check that the design volume flow per total capacity is within the prescribed range:

FlowCapRatio=˙Vair,rated/CCaprated

If

FlowCapRatio<FlowCapRatiothen_{min}CCaprated=˙Vair,rated/FlowCapRatiomin

If

FlowCapRatio>FlowCapRatiothen_{max}CCaprated=˙Vair,rated/FlowCapRatiomax

where

FlowCapRatio= 0.00004027 m_{min}^{3}/s per watt (300 cfm/ton)And

FlowCapRatio= 0.00006041 m_{max}^{3}/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:

FlowCapRatio= 0.00001677 m_{min}^{3}/s per Watt (125 cfm/ton)And

FlowCapRatio= 0.00003355 m_{max}^{3}/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.

T=_{mix}DesCoolCoilInTemp_{zone}W=_{mix}DesCoolCoilInHumRat_{zone}T=_{sup}CoolDesTemp_{zone}W=_{sup}CoolDesHumRat_{zone}T=_{outside}T_{outside},_{desday,peak}=_{air}PsyRhoAirFnPbTdbW(p,_{air,std}T,_{mix}W)_{mix}h=_{mix}PsyHFnTdbW(T,_{mix}W)_{mix}h=_{sup}PsyHFnTdbW(T,_{sup}W)_{sup}T=_{mix,wb}PsyTwbFnTdbWPb(T,_{mix}W,_{mix}p)_{air,std}CapModFac=CurveValue(CCapFTemp,T,_{mix,wb}T)_{outside}CCappeak=ρair˙Vair,rated(hmix−hsup)

CCap=_{rated}CCap_{peak}CapModFacWe check that the design volume flow per total capacity is within the prescribed range:

FlowCapRatio=˙Vair,rated/CCaprated

If

FlowCapRatio<FlowCapRatiothen_{min}CCaprated=˙Vair,rated/FlowCapRatiomin

If

FlowCapRatio>FlowCapRatiothen_{max}CCaprated=˙Vair,rated/FlowCapRatiomax

where

FlowCapRatio= 0.00004027 m_{min}^{3}/s per watt (300 cfm/ton)And

FlowCapRatio= 0.00006041 m_{max}^{3}/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:

FlowCapRatio= 0.00001677 m_{min}^{3}/s per Watt (125 cfm/ton)And

FlowCapRatio= 0.00003355 m_{max}^{3}/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).

T= 26.6667_{in,rated}^{o}C (80^{o}F)W= 0.01125 (corresponds to 80_{in,rated}^{o}F drybulb, 67^{o}F wetbulb)C=_{p,air}PsyCpAirFnWTdb(W,_{in,rated}T)_{in,rated}For system coils

T=_{sup}CoolSupTemp_{sys}W=_{sup}CoolSupHumRat_{sys}For zone coils

T=_{sup}CoolDesTemp_{zone}W=_{sup}CoolDesHumRat_{zone}Then

h=_{rated}PsyHFnTdbW(T,_{in,rated}W)_{in,rated}h=_{sup}PsyHFnTdbW(T,_{sup}W)_{sup}h_{rated,sup}=h_{rated}h_{sup}Qs=_{rated,sup}C(_{p,air}T)_{in,rated}T_{sup}SHR=_{rated}Qs_{rated,sup}h_{rated,sup}## Evaporative Condenser Air Volume Flow Rate[LINK]

The evaporative condenser air volume flow rate (m

^{3}/s) is set to 0.000114 m^{3}/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 (m

^{3}/s) is set to 1/3 times 0.000114 m^{3}/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

SizeDXCoilin moduleDXCoils. This section covers the sizing of the objectsCoil: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

Valuen=nNumberOfSpeed∗ValueNumberOfSpeed

where

Value

_{n}= Any autosizable variable at Speed n, except SHRSHR

_{n}= SHR_{NumberOfSpeed}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 CapacityThe 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:TotCapTempModFracNominalSpeed=a+b∗WBi+c∗WB2i+d∗DBo+e∗DBoT2+f∗WBi∗DBo

where

WB

_{i}= wet-bulb temperature of the air entering the cooling coil, °CDB

_{o}= condenser entering air temperature, °Ca-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

TotCapTempModFaccalculation 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˙Qcoil,rated,total=mair,rated(Hin−Hout)/TotCapTempModFracNominalSpeed

Else˙Qcoil,rated,total=mair,rated(48000−Hout)/TotCapTempModFracNominalSpeed

End IfThe 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

Eff=_{tot}Eff_{mot}Eff_{impeller}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]

˙Qnom=Hnom˙Vnom/Efftot

H, the nominal head, is an input._{nom}## 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]

˙Qchiller,nom=Cp,wρwΔTloop,des˙Vloop,des

where

Cis the specific heat of water at 5_{p,w}^{o}C;is the density of water at standard conditions (5.05_{w}^{o}C);Tis the chilled water loop design temperature rise;_{loop,des}˙Vloop,des is the loop design volumetric flow rate.

## Design Evaporator Volumetric Water Flow Rate[LINK]

˙Vevap,des=˙Vloop,des

## Design Condenser Volumetric Water Flow Rate[LINK]

˙Vcond,des=˙Qchiller,nom(1+1/COPchiller,nom)/(ΔTloop,desCp,wρw)

where

Cis the specific heat of water at design condenser inlet temperature;_{p,w}is the density of water at standard conditions (5.05_{w}^{o}C);Tis the chilled water loop design temperature rise;_{loop,des}COPis the chiller nominal COP._{chiller,nom}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]

˙Qboiler,nom=Cp,wρwΔTloop,des˙Vloop,des

where

Cis the specific heat of water at the boiler design outlet temperature;_{p,w}is the density of water at standard conditions (5.05_{w}^{o}C);Tis the hot water loop design temperature decrease;_{loop,des}˙Vloop,des is the loop design volumetric flow rate.

## Design Evaporator Volumetric Water Flow Rate[LINK]

˙Vdes=˙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, ˙VSup,des, is set equal to the design flow rate for that loop, multiplied by the component sizing factor, fcomp.

˙VSup,des=˙Vloop,des∗fcomp

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

˙VDmd,des=˙VSup,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, ΔTSupLoop,Des, is used to determine a nominal capacity.

˙Q=.VSup,desρcpΔTSupLoop,Des

A loop-to-loop design temperature difference, ΔTLoopToLoop,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, TSupLoop,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,TDmdLoop,Exit .

ΔTLoopToLoop,Des=(TSupLoop,Exit+ΔTSupLoop,Des)−TDmdLoop,Exit (Cooling, Condenser)

ΔTLoopToLoop,Des=(TSupLoop,Exit−ΔTSupLoop,Des)−TDmdLoop,Exit (Heating, Steam)

ΔTLoopToLoop,Des=MAX(ABS(ΔTLoopToLoop,Des),2.0)

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 (m

^{3}/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]

Prated=˙Vrated⋅ρw⋅(hfg+Cp,w⋅ΔTw)

where

C_{p,w}is the specific heat of water at average temperature ((100+20)/2 = 60.0 °C), (J/kgK);_{w}is the density of water at standard conditions (5.05 °C);T_{w}is the sensible temperature rise of water (100.0 - 20.0=80.0 °C);˙Vrated is the rated capacity of the humidifier in volumetric flow rate.h_{fg}is the latent heat of vaporization of water at 100.0°C, (J/kg);## Rated Capacity[LINK]

˙mw=˙ma(ωo−ωi)

where

mwis water mass flow rate, kg/s;mais design air mass flow rate, kg/s;ω_{o}is design outlet humidity ratio, kg-water/kg-air;ω_{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:

˙ma=Max(DesCoolVolFlowzone,DesHeatVolFlowzone)⋅ρa

ωi=Min(OutHumRatAtCoolPeakzone,OutHumRatAtHeatPeakzone)

ωo=Max(ZoneHumRatAtCoolPeakzone,ZoneHumRatAtHeatPeakzone)

where

_{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:

˙ma=DesOutAirVolFlowsys⋅ρa

ωi=Min(CoolOutHumRatsys,HeatOutHumRatsys)

ωo=Max(CoolSupHumRatsys,HeatSupHumRatsys)

Otherwise, air mass flow rate is determined as follows:

for duct type = main˙ma=DesMainAirVolFlowsys⋅ρafor duct type = cooling˙ma=DesCoolVolFlowsys⋅ρa

for duct type = heating˙ma=DesHeatVolFlowsys⋅ρa

for duct type = other˙ma=DesMainVolFlowsys⋅ρa,

and the humidity ratios are:

ωi=Min(CoolMixHumRatsys,HeatMixHumRatsys)

ωo=Max(CoolSupHumRatsys,HeatSupHumRatsys)

## 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=UFactorTimesAreaAndDesignWaterFlowRatethen˙Vtower,w,des=˙Vloop,des

If

Tower Performance Input Method=NominalCapacitythen˙Vtower,w,des=5.382E−8˙Qtower,nom

where 5.38210

^{-08}is m^{3}/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}m^{3}/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=UFactorTimesAreaAndDesignWaterFlowRatethen˙Qtower,nom=Cp,wρw˙Vtower,w,desΔTloop,des

where

Cis the specific heat of water at the condenser loop design exit temperature;_{p,w}is the density of water at standard conditions (5.05_{w}^{o}C);Tis the condenser water loop design temperature rise;_{loop,des}Finally

˙Qfan,nom=0.0105˙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

˙Vtower,air,des=˙Qfan,nom0.5ρair/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, fairflow/W,in units of m

^{3}/s/W. The default value is 2.76316*10^{-5}. When the input field is left blank, the default is used as follows˙Vtower,air,des=˙Qtower,nom∙fairflow/W∙101325Pstd,altitude

where, Pstd,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

˙Vtower,air,des=˙Qtower,nom∙fairflow/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˙Qtower,des=Cp,wρw˙Vtower,w,desΔTloop,des

for Tower Performance Input Method=NominalCapacity˙Qtower,des=1.25˙Qtower,nom (to allow for compressor heat)

Where, fdes,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.

T=35_{in,air}^{o}C (95^{o}F design air inlet temperature)T=25.6_{in,air,wb}^{o}C (78^{o}F design air inlet wetbulb temperature)Wis calculated from the entering air drybulb and wetbulb._{in}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

UFactorTimesAreaAndDesignWaterFlowRateT=_{in,water}T_{loop,exit,des}T_{loop,des}NominalCapacityT=35_{in,water}^{o}C (95^{o}F 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 functionSimpleTowerUAResidual.## 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=UFactorTimesAreaAndDesignWaterFlowRatethe 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. ForTower Performance Input Method=NominalCapacitythe low speed UA is calculated in the same manner as the full speed UA using ˙Qtower,nom,lowspeed instead of ˙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 Ratethe 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. ForTower Performance Input Method=NominalCapacitythe low speed UA is calculated in the same manner as the full speed UA using ˙Qtower,nom,freeconv instead of ˙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

˙Vfluidcooler,w,des=˙Vloop,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=UFactorTimesAreaAndDesignWaterFlowRatethen˙Qfluidcooler,nom=Cp,w∙ρw∙˙Vfluidcooler,w,des∙ΔTloop,des

where

Cis the specific heat of water at the condenser loop design exit temperature;_{p,w}is the density of water at standard conditions (5.05_{w}^{o}C);Tis the condenser water loop design temperature rise;_{loop,des}Finally

˙Qfan,nom=0.0105∙˙Qfluidcooler,nom

Elseif****Performance Input Method = NominalCapacity then**[LINK]˙Qfan,nom=0.0105∙˙Qfluidcooler,nom

Where

˙Qfluidcooler,nom is provided by the user.

## Design Air Flow Rate[LINK]

˙Qfluidcooler,nom=Cp,w∙ρw∙˙Vfluidcooler,w,des∙ΔTloop,des

˙Qfluidcooler,nom is provided by the user.

˙Vfluidcooler,air,des=˙Qfluidcooler,nom/(Tin,water−Tin,air)∗4

Where,

T= Design entering water temperature provided by the user_{in,water}T= Design air inlet temperature provided by the user_{in,air}## 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:

˙Qfluidcooler,nom=Cp,w∙ρw∙˙Vfluidcooler,w,des∙ΔTloop,des

˙Qfluidcooler,nom is provided by the user.

Then we assign the inputs needed for the model.

T= Design air inlet temperature provided by the user_{in,air}T= Design air inlet wetbulb temperature provided by the user_{in,air,wb}Wis calculated from the entering air drybulb and wetbulb._{in}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

Tin,water=Tloop,exit,des+ΔTloop,des

Tin,water=Providedbytheuser

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 functionSimpleFluidCoolerUAResidual.## 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=UFactorTimesAreaAndDesignWaterFlowRatethe 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. ForPerformance Input Method=NominalCapacitythe low speed UA is calculated in the same manner as the full speed UA using ˙Qfluidcooler,nom,lowspeed instead of ˙Qfluidcooler,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=StandardDesignCapacitythenElse

˙Vfluidcooler,w,des=˙Vloop,des

where 5.38210

^{-08}is m^{3}/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=UFactorTimesAreaAndDesignWaterFlowRatethen˙Qfluidcooler,design=Cp,w∙ρw∙˙Vfluidcooler,w,des∙ΔTloop,des

where

Cis the specific heat of water at the condenser loop design exit temperature;_{p,w}is the density of water at standard conditions (5.05_{w}^{o}C);Tis the condenser water loop design temperature rise;_{loop,des}Finally

˙Qfan,design=0.0105∙˙Qfluidcooler,design

Else[LINK]˙Qfan,design=0.0105∙˙Qfluidcooler,design

Where

˙Qfluidcooler,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

˙Vfluidcooler,air,des=˙Qfan,design∙0.5∙ρair/190

where

ρair 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:

˙Qfluidcooler,design=Cp,w∙ρw∙˙Vfluidcooler,w,des∙ΔTloop,des

˙Qfluidcooler,design=1.25∙˙Qfluidcooler,standarddesign (to allow for compressor heat)

Then we assign the inputs needed for the model.

T= 35_{in,air}^{o}C (95^{o}F design air inlet temperature)T= 25.6_{in,air,wb}^{o}C (78^{o}F design air inlet wetbulb temperature)Wis calculated from the entering air drybulb and wetbulb._{in}˙Qfluidcooler,design=˙Qfluidcooler,userspecifieddesign

Where, fdes,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.

T= Design air inlet temperature provided by the user_{in,air}T= Design air inlet wetbulb temperature provided by the user_{in,air,wb}Wis calculated from the entering air drybulb and wetbulb._{in}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

Tin,water=Tloop,exit,des+ΔTloop,des

Tin,water=35∘C(95∘Fdesigninletwatertemperature)

Tin,water=Providedbytheuser

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 functionSimpleEvapFluidCoolerUAResidual.## 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=UFactorTimesAreaAndDesignWaterFlowRatethe 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. ForPerformance Input Method=StandardDesignCapacity(and similarly forUserSpecifiedDesignCapacity method) the low speed UA is calculated in the same manner as the full speed UA using ˙Qfluidcooler,standarddesign,lowspeed instead of ˙Qfluidcooler,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]

˙Vair,max=Max(DesCoolVolFlowzone,DesHeatVolFlowzone)

## Maximum Outside Air Flow Rate[LINK]

˙Voutsideair,max=Min(MinOAzone,˙Vair,max)

## Maximum Hot Water Flow[LINK]

T=_{coil,in}DesHeatCoilInTemp_{zone}T=_{coil,out}HeatDesTemp_{zone}˙Qcoil,des=cp,airDesHeatMassFlowzone(Tout,coil−Tin,coil)

˙Vmax,hw=˙Qcoil,des/(cp,wρwΔTloop,des)

where

cis evaluated at the average of the inlet & outlet temperatures and the coil outlet humidity ratio._{p,air}## Maximum Cold Water Flow[LINK]

T=_{coil,in}DesColdCoilInTemp_{zone}T=_{coil,out}ColdDesTemp_{zone}W=_{coil,in}DesCoolCoilInHumRat_{zone}W=_{coil,out}CoolDesHumRat_{zone}H=_{coil,in}PsyHFnTdbW(T,_{coil,in}W)_{coil,in}H=_{coil,out}PsyHFnTdbW(T,_{coil,out}W)_{coil,out}˙Qcoil,des=DesCoolMassFlowzone(hin,coil−hout,coil)

˙Vmax,hw=˙Qcoil,des/(cp,wρwΔTlo