Refrigeration Equipment[LINK]

Overview[LINK]

EnergyPlus can model refrigerated case equipment consisting of a compressor rack, multiple refrigerated cases and walk-in coolers, secondary loop equipment, and optional heat reclaim air and water heating coils. The refrigerated case equipment models perform four major functions:

• calculate the electric consumption of refrigerated cases and walk-in coolers connected to a compressor rack

• determine the impact of refrigerated cases and walk-in coolers on zone cooling and dehumidification loads (i.e., case credits), including the effects of HVAC duct configuration

• calculate the electric consumption and COP of the compressor rack, and the electric and water (if applicable) consumption related to cooling the compressor rack’s condenser.

• determine the total amount of heat rejected by the compressor rack’s condenser and store this information for use by waste heat recovery models (e.g., using Desuperheater heating coil (object: Coil:Heating:Desuperheater) as an air reheat coil for high humidity control in a supermarket)

The case and walk-in models account for nearly all performance aspects of typical supermarket refrigeration equipment. Refrigerated case and walk-in performance are based on the combined effects of evaporator load, fan operation, lighting, defrost type, and anti-sweat heater operation. Optional air and water heating coils can be modeled to reclaim available waste heat (superheat) from the compressor rack.

The user has two options when describing the balance of the system. Energy used to cool the condenser is simulated in both approaches. The simplest option is to use a compressor rack object, combining the compressors and condenser into a single unit with the performance determined by the heat rejection environment and the total case load. An example schematic of a compressor rack system is shown in Figure 1 below.

A detailed refrigeration system object models compressor and condenser performance separately. The detailed refrigeration system also includes the ability to transfer refrigeration load from one system to another using subcoolers, cascade condensers, and secondary loops. An example schematic of the detailed refrigeration system is shown in Figure 2 below. Subcooler #2 is shown twice on Figure 2 because it represents a liquid suction heat exchanger. This type of subcooler uses the cool suction gas to subcool the warmer condensed liquid. Subcoolers #1 and #3 on Figure 2 represent mechanical subcoolers. These subcoolers are used to subcool the condensate on a lower-temperature system using the cold liquid refrigerant from a higher temperature system. On this example, only subcoolers #1 and #2 would be defined as a part of the refrigeration system. However, subcooler #3 would place a refrigerating load, similar to the load of a refrigerated case, on the system.

Four classes of secondary refrigeration loops can be modeled:

• a separate water loop is used to remove heat rejected by the condenser,

• a lower-temperature refrigeration system rejects heat to a higher-temperature refrigeration system via a cascade condenser,

• a fluid, such as a brine or glycol solution, is cooled in a secondary evaporator and is then circulated to chill the refrigerated cases and walk-ins, and

• a refrigerant, such as CO${}_2$, is partially evaporated in the refrigerated cases and walk-ins in a liquid-overfeed circuit, and then condensed in a secondary evaporator.

The first two classes of secondary loops are modeled using Refrigeration:System objects with Refrigeration:Condenser:WaterCooled and Refrigeration:Condenser:Cascade objects, respectively. Figure 2 shows how cascade condensers and secondary evaporators are treated as a refrigeration load on a primary detailed system. The second two classes are modeled with a Refrigeration:SecondarySystem object described later in this section.

The compressor rack, detailed and secondary refrigeration systems, refrigerated case, and other component models are described below. The optional air and water heating coils are described elsewhere in this document (Ref. objects Coil:Heating:Desuperheater and Coil:WaterHeating:Desuperheater).

Refrigeration Compressor Racks[LINK]

The refrigerated case compressor rack object works in conjunction with the refrigerated case and walk-in cooler objects (Refrigeration:Case and Refrigeration:WalkIn) to simulate the performance of a simple supermarket-type refrigeration system. This object (Refrigeration:CompressorRack) models the electric consumption of the rack compressors and the cooling of the compressor rack’s condenser. Heat removed from the refrigerated cases and walk-ins and compressor/condenser fan heat can be rejected either outdoors or to a zone. Compressor rack condenser waste heat can also be reclaimed for use by an optional air heating coil (Ref. object Coil:Heating:Desuperheater) or by a user-defined plant water loop (Ref. object Coil:WaterHeating:Desuperheater).

The performance of the compressor rack is simulated using the sum of the evaporator loads for all refrigerated cases and walk-ins connected to the rack. Whether a single refrigerated case is connected to a rack (e.g., stand-alone refrigerated case, meat cooler, or produce cooler) or several cases are connected to a rack, the rack electric consumption is calculated based on the total evaporator load for the connected cases and walk-ins and the coefficient of performance (COP) for the compressor rack. At least one refrigerated case or walk-in must be connected to the compressor rack. The model assumes the compressor rack has sufficient capacity to meet the connected refrigeration load for any simulation time step. Additionally, the model neglects compressor cycling losses at part-load conditions.

For condenser heat rejection to the outdoors, condenser cooling can be modeled as dry air cooling, wet evaporative cooling, or water loop cooling. Using evaporative cooling rather than dry air cooling will allow for more efficient condenser heat rejection based on the entering air approaching the wet-bulb temperature rather than the dry-bulb temperature. Analyses under the International Energy Agency’s (IEA) Heat Pumping Programme Annex 26 indicates that this measure can improve refrigeration system efficiency by up to 10% (IEA 2003). The use of an evaporative-cooled condenser requires a water pump and, optionally, a basin sump water heater (to protect against freezing). Makeup water will also be required to replace that lost by evaporation. In colder climates, some evaporative-cooled condensers are drained for the winter months and run as dry air units. This scenario can be modeled by using an optional evaporative condenser availability schedule.

The simulation of the evaporative cooled condenser utilizes an effective air dry-bulb temperature that is assumed to be the result of evaporation of water in the air stream (similar to object EvaporativeCooler:Direct:CelDekPad). As discussed below, this effective temperature is used by performance curves that are a function of temperature. While some designs of evaporative coolers use water film cascading across the condenser coil for evaporative cooling, the current model uses the effective temperature method as a surrogate for the more complex water film on coil calculations.

If the condenser heat rejection is specified as water cooled, an appropriate plant water loop must be defined by the user (see documentation on Plant/Condenser Loops for additional details about plant loops). This will include defining cooling supply components, such as pumps, water storage tanks, and cooling towers, as well as related branches, nodes, and connectors. The heat rejection from the refrigeration condenser is modeled as a cooling demand, which is satisfied by heat extraction devices (e.g., water tank and cooling tower) on the cooling supply side of a water loop. An example of such an arrangement is shown in Figure 3.

Compressor Energy Use[LINK]

Calculation of compressor rack electric power uses a simple model based on the total evaporator load (sum of the evaporator loads for all refrigerated cases and walk-ins connected to a rack) and the compressor rack operating COP which accounts for the air temperature entering the condenser:

$$CO{P}_{operating}=CO{P}_{design}\left(COPfTemp\right)$$

where:

$CO{P}_{operating}$ is the compressor coefficient of performance at actual operating conditions (W/W)

$CO{P}_{design}$ is the compressor coefficient of performance at design conditions (W/W)

$COPfTemp$ is the output of the normalized “Compressor Rack COP as a Function of Temperature Curve” (dimensionless).

Because the COP curve is defined only as a function of the condensing temperature, it is important that this curve definition corresponds to the lowest evaporating temperature served by the compressor rack. The air temperature used to evaluate the “Compressor Rack COP as a Function of Temperature Curve” depends on where the compressor rack’s condenser is located (Heat Rejection Location). When modeling condenser heat rejected directly to a zone (typical of a stand-alone packaged refrigerated case with integral condenser located in a building zone), the zone air dry-bulb temperature is used to calculate the change in compressor COP from the design value. If more than one refrigerated case and no walk-ins are attached to a compressor rack that rejects its condenser heat to a zone, then all cases served by this rack must reside in the same zone. When modeling a compressor rack serving at least one walk-in, OR with condenser heat rejected to outdoors, the refrigerated cases and walk-ins connected to this rack may be located in different zones. If the condenser type is specified as “Air Cooled”, the outdoor air dry-bulb temperature is used to evaluate the “Compressor Rack COP as a Function of Temperature Curve.” If the condenser type is specified as “Evap Cooled”, the air temperature leaving the condenser is related to the effectiveness of the evaporative cooling system. If the evaporative process were 100% effective, the effective temperature of air leaving the evaporative media would equal the air wet-bulb temperature. However, the efficiency of the direct evaporative process is typically less than 100%, and the effective temperature leaving the condenser is determined by:

$$T_{effective}=T_{owb}+(1-\epsilon )\ast [T_{odb}-T_{owb}]$$

where:

$T_{effective}$ is the effective dry-bulb temperature of air leaving the condenser cooling coil (${}^{\circ }$C)

$T_{owb}$ is the outdoor air wet-bulb temperature (${}^{\circ }$C)

$T_{odb}$ is the outdoor air dry-bulb temperature (${}^{\circ }$C)

$\epsilon$ is the evaporative condenser effectiveness.

If the user is modeling an evaporative cooled condenser and is using COPfTemp curve data (e.g., manufacturer’s data) based on wet-bulb temperature rather than dry-bulb temperature, the evaporative condenser effectiveness should be set to 1.0 for consistency.

If the condenser is water cooled, the effective temperature experienced by the condenser is based on the return water temperature from the plant loop heat rejection system (e.g., cooling tower) that is defined by the user. This return water temperature is typically related to the outdoor ambient conditions at each time step.

The electric power input to the rack compressor(s) is calculated for each simulation time step as the sum of the connected refrigerated case evaporator loads divided by the operating COP:

$$P_{rack}=\frac{\sum {\dot{Q}}_{case}+\sum {\dot{Q}}_{walkin}}{CO{P}_{operating}}$$

where:

$P_{rack}$ is the output variable “Refrigeration Compressor Rack Electric Power [W]”, electric power input to the rack compressor(s)

${\dot{Q}}_{case}$ is the evaporator load for each refrigerated case connected to the rack (W)

${\dot{Q}}_{walkin}$ is the refrigeration load for each walk-in connected to the rack (W).

Condenser Heat Rejection, Energy Use, and Water Use[LINK]

The compressor rack can reject heat to an air-, water-, or evaporative-cooled condenser. The condenser type determines the heat rejection temperature used for the compressor rack COP calculation. The compressor rack also allows superheat heat reclaim and heat rejection to a conditioned zone.

Condenser Fan Energy Use[LINK]

Condenser fan power for any simulation time step is calculated by multiplying the design fan power by the condenser fan power as a function of temperature curve.

$$P_{CondFan}=P_{CondFan,design}\left(CondFanfTemp\right)$$

where:

$P_{CondFan}$ is the output variable “Refrigeration Compressor Rack Condenser Fan Electric Energy [W]”

$P_{CondFan,design}$ is the design condenser fan power (W)

$CondFanfTemp$ is the output of the optional “Condenser Fan Power as a Function of Temperature Curve”.

Similar to the compressor rack energy use described above, the air temperature used to evaluate the “Condenser Fan Power as a Function of Temperature Curve” depends on where the condenser rack’s condenser is located (i.e., zone air dry-bulb temperature if the condenser is located in a zone, outdoor air dry-bulb temperature if the condenser is located outdoors and is specified as air cooled, or effective temperature if the condenser is outdoors and is specified as evaporative cooled). If the sum of the evaporator loads for the refrigerated cases connected to the rack is equal to zero, the condenser fan power is set equal to zero. If the user does not provide a “Condenser Fan Power as a Function of Temperature Curve”, then the model assumes the condenser fan power is at the design power level when any of the refrigerated cases connected to this rack are operating.

If the user is modeling an evaporative cooled condenser and is using CondFanfTemp curve data based on wet-bulb temperature rather than dry-bulb temperature, the evaporative condenser effectiveness should be set to 1.0 for consistency.

For a water cooled condenser, there is no fan load at the condenser (i.e., the water/refrigerant heat exchanger). Any fan load would be related to and accounted for at the heat rejection object (e.g., cooling tower).

Superheat Reclaim Heating Coil[LINK]

EnergyPlus can simulate waste heat being reclaimed from a compressor rack for use by a refrigerant-to-air or refrigerant to water heating coil. Heat reclaimed from the compressor rack is assumed to be recovered from the superheated refrigerant gas leaving the compressor(s) and does not directly impact the performance of the compressor rack or refrigerated cases connected to the rack. The total heat rejected by the condenser (in Watts) is calculated each time step as follows:

$${\dot{Q}}_{condenser}=(\sum {\dot{Q}}_{case}+\sum {\dot{Q}}_{walkin})(1+\frac{1}{CO{P}_{operating}})$$

The heat reclaim heating coil is able to transfer a fixed percentage of this total amount of rejected energy (not to exceed 30%) and use it to heat air and water. Refer to objects Coil:Heating:Desuperheater and Coil:WaterHeating:Desuperheater for a complete description of how these coils are modeled.

NOTE: When modeling a heat reclaim coil, the heat rejection location in the Refrigeration:CompressorRack object must be “Outdoors”. If the compressor rack heat rejection location is “Zone”, the total amount of waste heat available for reclaim (e.g., by a desuperheater heating coil) is set to zero by the compressor rack object and the simulation proceeds.

Heat Rejection to Zone[LINK]

The compressor rack model can simulate condenser heat being rejected to a zone. As explained previously, if this heat rejection option is selected then all refrigerated cases connected to the rack must be located in the same zone and a superheat heat reclaim heating coil can not be modeled (Ref. Superheat Reclaim Heating Coil).

The refrigerated case and walk-in objects (Refrigeration:Case and Refrigeration:WalkIn) already calculate and report the sensible case credits which impact the zone air heat balance (Ref. Sensible Case Credits). When refrigerated cases and/or walk-ins are served by a compressor rack that rejects condenser waste heat directly to the zone (e.g., a stand-alone refrigerated case with integral compressor and condenser), this condenser waste heat also impacts the zone air heat balance and offsets some or all of the sensible case credits.

If only cases are served, the amount of condenser waste heat rejected to the zone and/or the HVAC return air (zone return air path outlet node) is calculated and reported by the refrigerated case compressor rack object as follows:

$${\dot{Q}}_{Zone,heating}=\frac{\sum \left({\dot{Q}}_{case}[1-RAF]\right)}{\sum \left({\dot{Q}}_{case}\right)}\left({\dot{Q}}_{condenser}+P_{CondFan}\right)$$

$${\dot{Q}}_{HVAC,heating}=\left({\dot{Q}}_{condenser}+P_{CondFan}\right)-{\dot{Q}}_{zone,heating}$$

where:

${\dot{Q}}_{Zone,heating}$ is the output variable “Refrigeration Compressor Rack Zone Sensible Heating Rate” (W)

RAF is the return air factor for each case connected to the rack (Ref. Figure 4)

${\dot{Q}}_{HVAC,heating}$ is the output variable “Refrigeration Compressor Rack Return Air Sensible Heating Rate” (W).

If the HVAC system is off for a simulation time step (no return air mass flow), the rack condenser heat normally attributed to the HVAC return is set equal to zero and all condenser heat energy is applied to the zone air heat balance.

If, however, walk-in cooler(s) are also served by this compressor rack, no condenser heat is rejected to the HVAC return air. For walk-in cooler(s), the user must specify the zone that accepts the condenser heat rejection (because walk-ins can exchange heat with multiple zones). In that case:

$${\dot{Q}}_{Zone,heating}={\dot{Q}}_{condenser}+P_{CondFan}$$

Water Cooled Condenser[LINK]

If the refrigeration condenser is water cooled, a water plant loop must be defined in the input file. At a minimum, the loop must contain a pump and one or more heat sinks of sufficient capacity to remove the condenser heat load. In the system shown in Figure 3, the heat sinks are the water heater tank and the cooling tower. The water pump in the loop can be either constant (Ref. Pump:ConstantSpeed) or variable speed (Ref. Pump:VariableSpeed). A variable speed pump permits the loop flow to vary and allows for a setpoint to be established on the condenser outlet water temperature. As the refrigeration condenser heat load varies through time, the speed of the pump can be adjusted to achieve a mass flow consistent with a desired outlet water temperature according to

$$\dot{m}=\frac{Q_{condenser}}{c_p\cdot (T_{out}-T_{in})}$$

where:

$\dot{m}$ is the mass flow in the water loop

Q${}_{condenser}$ is the heat rejected by the condenser

c${}_p$ is the specific heat of water

T${}_{out}$ is the desired water outlet temperature

T${}_{in}$ is the return water inlet temperature.

The desired water outlet temperature is specified using a schedule, subject to a maximum water outlet temperature (input specified). The maximum temperature is typically defined by constraints on the refrigerant loop pressures and temperatures. The desired mass flow in the water loop to meet the temperature schedule is also compared to the user-supplied maximum flow rate. If the desired mass flow is greater than the maximum allowed flow, the flow rate is set to the maximum value and the resulting water outlet temperature is determined.

The return water inlet temperature is a function of the cooling system defined by the user. A minimum return water temperature may need to be taken into consideration to prevent lowering the resulting refrigerant condensing pressure to the point that refrigerant expansion valve operation becomes impaired. When ambient conditions produce low temperature warnings based on the minimum return water temperature, an outlet temperature setpoint control may need to be placed on the water heat sink object (e.g., cooling tower) to keep the return water temperature above the minimum.

If the water loop flow is constant (i.e., driven by a constant speed pump), then the outlet water temperature will vary with the amount of heat rejected by the condenser. Using the equation above, the resulting water outlet temperature is calculated as

$$T_{out}=\frac{Q_{condenser}}{c_p\cdot \dot{m}}+T_{in}$$

Evaporative Condenser Water Pump[LINK]

If the condenser type is specified as “Evap Cooled”, a water pump is required to circulate water in the evaporative condenser. The pump power can be input directly or be autocalculated using a relationship of 0.004266 W per watt [15 W/ton] of rated total cooling capacity where the total cooling capacity is the sum of the rated total cooling capacities for the refrigeration load connected to this compressor rack. Following manufacturer’s recommendations regarding the avoidance of scaling, the water pump does not cycle when there is no cooling demand (i.e., when the compressors are not running), but rather runs continuously. However, if the evaporative condenser availability schedule is set such that evaporative cooling is not available (e.g., during very cold months to avoid freezing), then the pump power consumption will be zero during that period.

Evaporative Condenser Water Consumption[LINK]

With evaporative cooling of the condenser’s entering air, makeup water is needed to replenish the water lost due to evaporation. The quantity required is calculated as the product of the air mass flow rate and the difference between the entering and leaving air humidity ratio, divided by the density of water. The air mass flow rate is determined by multiplying the evaporative condenser air volume flow rate times the density of the entering air (i.e., at the condenser air inlet node if provided, or outdoor air conditions [e.g., no adjustment for height above ground] if the condenser air inlet node field is left blank). The volumetric air flow rate is either specified directly in the user input or is autocalculated using the relationship 0.000144 m${}^3$/s per watt of rated total cooling capacity [850 cfm/ton] where the total cooling capacity is the sum of the rated total cooling capacities for the refrigerated cases and walk-ins connected to this compressor rack (Ref. Refrigeration:Case and Refrigeration:WalkIn). The air mass flow rate is multiplied by the variable CondFanfTemp, described above, to simulate the modulation of air flow by the condenser fans (e.g., staging, multi-speed, or variable speed) as a function of temperature. Mathematically,

$${\dot{V}}_{evaporation,makeup}=\frac{{\dot{m}}_{air}\left(CondFanfTemp\right)({\omega }_{air,outlet}-{\omega }_{air,inlet})}{{\rho }_{water}}$$

where:

$\stackrel{}{{\dot{V}}_{evaporation,makeup}}$ is the Refrigeration Compressor Rack Evaporative Condenser Water Volume Flow Rate (m${}^3$/s)

${\dot{m}}_{air}$ is the mass flow rate of air through the evaporative condenser (kg/s)

${\omega }_{air,outlet}$ is the humidity ratio of air leaving the evaporative media (kg${}_{water}$/kg${}_{dryair}$) based on the effective dry-bulb temperature T${}_{effective}$, as described above, outdoor air wet-bulb temperature, and outdoor barometric pressure

${\omega }_{air,inlet}$ is the humidity ratio of inlet air (kg${}_{water}$/kg${}_{dryair}$) based on conditions at the condenser air inlet node if provided, or outdoor air conditions (e.g., no adjustment for height above ground) if the condenser air inlet node field is left blank

${\rho }_{water}$ is the density of water evaluated at the effective air temperature (kg/m${}^3$).

The source of the makeup water may be specified as a water storage tank. If not specified, the makeup water is assumed to come from the building mains (Ref. Water Mains Temperatures).

Evaporative Condenser Basin Heater[LINK]

In cold climates, a basin heater may be needed to prevent freezing of the evaporative cooling water. This feature is included in the model whereby an electric basin heater provides heat to the sump water only when the condenser cooling system is idle (i.e., no refrigeration load) and when the outdoor air dry-bulb temperature is below a user-specified setpoint. Since heat balances and basin water temperatures are not explicitly determined, a linear loading relationship, as a function of the difference in outdoor air dry-bulb temperature and the setpoint temperature, is used calculate the power demand at a given time step by the basin heater.

$$P_{basinheater}=P_{heatercapacity}\ast (T_{setpoint}-T_{OutDb})$$

where:

$P_{basinheater}$ is the electric power demand for basin heater in current time step (W)

$P_{heatercapacity}$ is the electric heater capacity as a function of differential temperature (W/K)

$T_{setpoint}$ is the setpoint temperature below which the heater turns on (${}^{\circ }$C)

$T_{OutDb}$ is the outdoor air dry-bulb temperature (${}^{\circ }$C).

A default value for the basin heater capacity of 200 W/K has been established based on manufacturer data.

Evaporative Condenser Availability Schedule[LINK]

Some manufacturer’s evaporative cooling systems for refrigeration condensers permit seasonal draining in the colder months and operation as an air-cooled system during that time. This optional feature is available through an availability schedule. This is important in climates subject to freezing weather in order to avoid excessive ice formation on the condenser surfaces and surroundings. (The Availability Schedule is the correct way to model the use of evaporative condensers in cold climates. However, some users may take a single input description and use it to model a building with a refrigeration system in a variety of climates. To avoid modeling the use of evaporative coolers in freezing weather, the code includes a cutout to switch to dry operation whenever the outdoor drybulb temperature drops below 4${}^{\circ }$C.) During periods when evaporative cooling is not available, the outdoor condenser behaves as an air-cooled system with no water consumption or pump and basin heater loads. The effective temperature of air entering the condenser coil during this period (used to evaluate COPfTemp and CondFanfTemp) is equal to the outdoor air dry-bulb temperature at the condenser air inlet node if provided, or outdoor air conditions (e.g., no adjustment for height above ground) if the condenser air inlet node field is left blank.

Refrigerated Cases[LINK]

The refrigerated case object (Refrigration:Case) works in conjunction with the compressor rack, detailed refrigeration system, or secondary refrigeration system object (Refrigeration:CompressorRack, Refrigeration:System, or Refrigeration:SecondarySystem) to simulate the performance of a refrigerated case system. The refrigerated case model uses performance information at rated conditions along with performance curves for latent case credits and defrost heat load to determine performance at off-rated conditions. Energy use for lights, fans and anti-sweat heaters is modeled based on inputs for nominal power, schedules, and control type. The refrigerated case model accounts for the sensible and latent heat exchange with the surrounding environment (termed “case credits”) which impacts the temperature and humidity in the zone where the case is located. The simplified model described here provides the flexibility to simulate a broad range of refrigerated case types.

The total load on the refrigerated case evaporator is made up of various components:

$${\dot{Q}}_{case}={\dot{Q}}_{walls}+{\dot{Q}}_{rad}+{\dot{Q}}_{inf,sens}+{\dot{Q}}_{inf,lat}+{\dot{Q}}_{lights}+{\dot{Q}}_{as}+{\dot{Q}}_{def}+{\dot{Q}}_{fan}+{\dot{Q}}_{restock}$$

where:

${\dot{Q}}_{case}$ is the total load on the refrigerated case evaporator (W)

${\dot{Q}}_{walls}$ is the heat transfer through case walls due to the difference between the refrigerated case operating dry-bulb temperature and the zone air dry-bulb temperature (W)

${\dot{Q}}_{rad}$ is the radiant heat transfer to the refrigerated case (W)

${\dot{Q}}_{inf,sens}$ is the sensible heat transfer by air infiltration to the refrigerated case through the air curtain or via door openings (W)

${\dot{Q}}_{inf,lat}$ is the latent heat transfer by air infiltration to the refrigerated case through the air curtain or via door openings (W)

${\dot{Q}}_{lights}$ is the lighting heat load (W)

${\dot{Q}}_{as}$ is the anti-sweat heater load (W)

${\dot{Q}}_{def}$ is the defrost heat load (W)

${\dot{Q}}_{fan}$ is the fan heat load (W)

${\dot{Q}}_{restock}$ is the sensible load on the refrigerated case due to restocking of products that are at a higher temperature than the case (W).

The model assumes that these load components are known for a refrigerated case at rated ambient air conditions (typically 23.9${}^{\circ }$C [75${}^{\circ }$F] and 55% relative humidity) and the specified case operating temperature. A combination of user input curves and fixed correlations (defined within EnergyPlus) adjust for case performance at off-rated conditions. Several of the load components are typically provided by the case manufacturer (e.g., total rated load, fan, lighting, anti-sweat heater, and defrost loads). The remaining load components are not usually provided by the manufacturer and must be estimated (heat conduction through case walls, radiation heat transfer, sensible/latent air infiltration, and restocking).

For estimating the latent air infiltration load, the model requires that the user provide the latent heat ratio (LHR) for the refrigerated case at rated conditions. Research results are available to provide guidance in selecting this value (ASHRAE 2002, Howell 1993a, Howell 1993b). The rated LHR for refrigerated cases typically ranges from 0.1 to 0.3 depending on case configuration (e.g., glass door reach-in versus multi-deck open case) and case operating temperature.

The case loads due to wall heat conduction, radiation, and sensible air infiltration are estimated by the model as a single lumped value (sensible case credits). The sensible case credits are calculated by subtracting the known loads at rated conditions (fan, lighting, anti-sweat heater, defrost and latent case credits) from the rated total cooling capacity of the case which is provided by the case manufacturer (${\dot{Q}}_{case,rated}$).

Using these assumptions and the schedule inputs provided by the user, the refrigerated case evaporator load components in Equation [eq:TotalLoadRefCaseEvaporator] are determined for each simulation time step. The variation in certain loads with respect to changes in ambient air temperature and/or humidity (e.g., latent and sensible case credits, defrost load, and anti-sweat heater load) are factored into the calculation based on user-provided inputs or by the model itself.

Whenever the total heat load on the case is greater than the available evaporator capacity, such as during defrost (when the evaporator capacity is set to zero) or restocking, the load is accumulated to be met during subsequent time steps. This accounts for the energy required to bring the case back down to the rated operating temperature even though the rise in case temperature during defrost or restocking is not explicitly modeled. Following defrost, it may take multiple time steps to meet this accumulated load.

The specific calculations for case evaporator load components and electric power for these loads (as applicable) are provided below.

Case Evaporator Fan[LINK]

The refrigerated case evaporator fan electric power is calculated for each simulation time step as the product of the operating case fan power per unit length of case, the length of the refrigerated case, and the fraction of time that the case is not being defrosted. For cases with hot-gas or electric defrost (with or without temperature termination), the fan is disabled during the entire scheduled defrost drip-down time period. The evaporator fan operates continuously for off-cycle defrost or no defrost.

$$P_{fan}={P^{\prime }}_{fan,oper}\left(L_{case}\right)\left(1-SC{H}_{defrost,dripdown}\right)$$

where:

$P_{fan}$ is the output variable “Refrigerated Case Evaporator Fan Electric Power [W]”

${P^{\prime }}_{fan,oper}$ is the operating case fan power per unit length (W/m)

$L_{case}$ is the case length (m)

$SC{H}_{defrost,dripdown}$ is the fraction of time case is being defrosted (0 to 1), including drip-down period (based on the defrost drip-down schedule) for hot-gas or electric defrost. For off-cycle defrost or no defrost, this value is set to zero for this calculation.

The model assumes that the evaporator fan is entirely contained within the thermal envelope of the case, and that all fan power results in a direct heat load on the case evaporator:

$${\dot{Q}}_{fan}=P_{fan}$$

Case Lighting[LINK]

The refrigerated case lighting electric power is calculated for each simulation time step as the product of the installed case lighting power per unit length of case, the lighting schedule value, and the length of the refrigerated case:

$$P_{lights}=P{}_{lights,installed}^{\prime }\left(L_{case}\right)\left(SC{H}_{lights}\right)$$

where:

$P_{lights}$ is the output variable “Refrigerated Case Lighting Electric Power [W]”

$P{}_{lights,installed}^{\prime }$ is the installed case lighting power per unit length (W/m)

$SC{H}_{lights}$ is the case lighting schedule value (0 to 1).

A maximum schedule value of 1.0 means the lights are fully on at the installed case lighting power level. Schedule values of 0.0 indicate the lights are off and 0.5 at half-power.

The user can specify the fraction of lighting energy that directly contributes to the case evaporator heat load:

$${\dot{Q}}_{lights}=P_{lights}\left(F_l\right)$$

where $F_l$ is the fraction of lighting energy to case.

The remainder of the lighting energy (1 - F${}_l$) is a heating load to the zone where the case is located, which is discussed further in section Sensible Case Credits below. This fraction (1 - F${}_l$) can be used to represent lighting ballasts and/or bulbs located outside the air curtain of the refrigerated case.

Anti-Sweat Heater Performance[LINK]

Anti-sweat heaters warm the refrigerated case rails or doors to provide protection from moisture condensation. Different anti-sweat heater control strategies are used depending on the case temperature and the type of anti-sweat heater installed. Several types of anti-sweat heater control strategies can be simulated with this model: constant, linear variation with ambient relative humidity or dewpoint temperature, and a theoretical model that determines the minimum anti-sweat heater power required to maintain the case surface just above the temperature where condensation would occur. Additionally, anti-sweat heater performance can be disregarded if the type of refrigerated case does not warrant its use. For the control strategies described below (except “None” and “Constant Method”), the model does not allow the anti-sweat heater power to be less than the minimum power nor greater than the case anti-sweat heater power specified by the user. Each anti-sweat heater control type is described in detail below.

None[LINK]

Used for refrigerated cases that do not require an anti-sweat heater.

$${\dot{Q}}_{as}=0$$

where ${\dot{Q}}_{as}$ is the anti-sweat heater load on the case evaporator (W).

Constant Method[LINK]

For refrigerated cases requiring constant anti-sweat heater output, the power use is simply calculated as the case anti-sweat heater power per unit length multiplied by the length of the case. This method is used when the manufacturer recommends that cycling of the heaters not occur.

$$P_{as}={P^{\prime }}_{as}\left(L_{case}\right)$$

where:

$P_{as}$ is the output variable “Refrigerated Case Anti-Sweat Heater Electric Power” (W)

${P^{\prime }}_{as}$ is the case anti-sweat heater power per unit length (W).

Relative Humidity Method[LINK]

Anti-sweat heater power can be reduced at lower ambient relative humidity levels to save energy while still protecting from moisture condensation on cold surfaces. For this control type, anti-sweat heater power use is reduced linearly based on case anti-sweat heater power at the rated ambient relative humidity (typically 55% RH), the relative humidity specified by the user where no anti-sweat heater power is required, and the relative humidity of the ambient (zone) air surrounding the case.

$$P_{as}={P^{\prime }}_{as}\left(L_{case}\right)\left(1-\left[\frac{R{H}_{rated}-R{H}_{air}}{R{H}_{rated}-R{H}_{min}}\right]\right)$$

where:

$R{H}_{air}$ is the relative humidity of the ambient (zone) air (%)

$R{H}_{rated}$ is the rated ambient relative humidity (%)

$R{H}_{min}$ is the relative humidity at zero anti-sweat heater energy (%).

Dewpoint Method[LINK]

Anti-sweat heater power can also be reduced as a function of ambient air dewpoint temperature based on a similar correlation to that used by the relative humidity method. This control method varies the anti-sweat heater power linearly based on the ambient air dewpoint temperature, the case operating temperature, and the rated ambient dewpoint temperature (calculated by the model using the rated ambient temperature and rated ambient relative humidity entered by the user).

$$P_{as}={P^{\prime }}_{as}\left(L_{case}\right)\left(\frac{T_{dp,air}-T_{case}}{T_{dp,rated}-T_{case}}\right)$$

where:

$T_{dp,air}$ is the dewpoint temperature of the ambient (zone) air (${}^{\circ }$C)

$T_{dp,rated}$ is the rated ambient dewpoint temperature (${}^{\circ }$C)

$T_{case}$ is the case operating temperature (${}^{\circ }$C).

Heat Balance Method[LINK]

A theoretical model may also be used to simulate the performance of anti-sweat heater operation at various indoor dewpoint temperatures (Henderson and Khattar 1999). The model calculates that amount of heat required to hold the case or door surface at (or slightly above) the dewpoint temperature of the ambient air using the following simple heat balance equation:

$$P_{as}=\left(\frac{\left(T_{dp,air}-T_{db,air}\right)H_{case}}{R_{air}}+\frac{\left(T_{dp,air}-T_{case}\right)H_{case}}{R_{case}}\right)L_{case}$$

where:

$T_{dp,air}$ is the dewpoint temperature of the ambient (zone) air (${}^{\circ }$C)

$T_{db,air}$ is the dry-bulb temperature of the ambient (zone) air (${}^{\circ }$C)

$H_{case}$ is the height of the case (m)

$R_{air}$ is the air film resistance (assumed constant at 0.3169 m${}^2$-${}^{\circ }$C/W)

$R_{case}$ is the heat transfer resistance of case (m${}^2$-${}^{\circ }$C/W)

$T_{case}$ is the case operating temperature (${}^{\circ }$C)

$L_{case}$ is the case length (m).

The model above provides a linear relationship of anti-sweat heater power with varying ambient air dewpoint temperature at constant ambient air dry-bulb and case temperatures. By assuming that the ‘nominal’ anti-sweat heater power entered by the user is required to avoid moisture condensation at rated ambient air conditions, the value of $R_{case}$ can be determined by rearranging the equation and solving as follows:

$$R_{case}=\frac{\left(T_{dp,rated}-T_{case}\right)}{\left(\frac{{P^{\prime }}_{as}}{H_{case}}\right)-\left(\frac{T_{dp,rated}-T_{db,rated}}{R_{air}}\right)}$$

where $T_{db,rated}$ is the rated ambient temperature (${}^{\circ }$C)

With R${}_{case}$ known, P${}_{as}$ can be calculated for each simulation time step using the actual ambient (zone) air dry-bulb and dewpoint temperatures.

All Anti-Sweat Heater Control Methods[LINK]

For all control methods, the user can specify the fraction of anti-sweat heater energy that directly contributes to the case evaporator heat load:

$${\dot{Q}}_{as}=P_{as}\left(F_{as}\right)$$

where $F_{as}$ is the fraction of anti-sweat heater energy to case.

The remainder of the anti-sweat heater energy (1 - F${}_{as}$) is a heating load to the zone where the case is located, which is discussed further in section Sensible Case Credits below.

Case Restocking[LINK]

The impact of restocking the refrigerated case with product that is not at the case operating temperature is modeled with the case restocking schedule. The schedule is entered as a heat gain rate per unit length of the refrigerated case (W/m). The heat load due to restocking is calculated as the scheduled load multiplied by the length of the refrigerated case. The load due to product restocking is assumed to be only sensible (temperature) heat; a latent (moisture) component is not modeled.

$${\dot{Q}}_{restock}=SC{H}_{restock}\left(L_{case}\right)$$

where $SC{H}_{restock}$ is the refrigerated case restocking schedule value (W/m).

The restocking heat load is removed by the refrigerated case evaporator any time the case is not being defrosted and excess sensible cooling capacity is available. If the evaporator cooling capacity is insufficient to remove the entire restocking load, the unmet portion is carried over to the next simulation time step.

Case Defrost[LINK]

Eight refrigerated case defrost strategies can be simulated: none, off-cycle, electric, electric with temperature termination, hot-gas, hot-gas with temperature termination, hot-brine, and hot-brine with temperature termination. Some research has shown that the defrost times for cases defrosted using hot brine can be significantly shorter than defrost times for electric or hot gas.(Terrell, W. J. Jr., 1999) For each of these strategies, the refrigerated case evaporator is turned off for the required time period to allow accumulated frost to melt. Additional time can be scheduled (drip-down) to allow the water to drip from the evaporator and drain from the case.

Refrigerated cases typically require a specific number of defrost cycles per day for a pre-determined length of time. Refer to manufacturer’s recommendations for proper defrost frequency and duration. For example, a refrigerated case may have a single defrost period each day with defrost scheduled from 7:00 – 7:40 am and defrost drip-down scheduled from 7:00 – 7:55 am. Notice the drip-down schedule and the defrost schedule start at the same time, and the drip-down schedule is longer than the defrost schedule. These schedules should normally repeat for each day of the year.

For electric, hot gas, and hot brine defrost types, energy use by the defrost heater occurs during the scheduled defrost period. For defrost with temperature termination, the energy is also multiplied by the defrost ratio simulating a defrost duration shorter than the defined (maximum) period. For all non-electric defrost types, defrost electric power is set equal to zero (and is not available as an output variable). For hot gas and hot brine defrost types in cases served by a detailed system, the condenser heat rejection load is reduced by the amount of heat recovered for use in the defrost system. This condenser credit is not applied for the simple compressor rack system.

If DefrostType is electric, then:

$$P_{def}={P^{\prime }}_{def}{L}_{case}SC{H}_{defrost}$$

Else if DefrostType is ElectricWithTempTermination, then:

$$P_{def}={P^{\prime }}_{def}{L}_{case}SC{H}_{defrost}\left(DefrostRatio\right)$$

Otherwise:

$$P_{def}=0.0$$

where:

$P_{def}$ is the output variable “Refrigerated Case Defrost Electric Power” (W)

${P^{\prime }}_{def}$ is the case defrost power per unit length (W)

$L_{case}$ is the case length (m)

$SC{H}_{defrost}$ is the case defrost schedule value (0 to 1)

$DefrostRatio$ is the fraction of maximum defrost time, used with temperature termination.

Frost accumulation on the case evaporator will vary with the humidity level in the ambient air surrounding the case. Therefore, defrost heater operation can be reduced when ambient air humidity levels are low. Several methods are used to reduce unnecessary defrost heater operation, including terminating heater operation when the measured evaporator temperature indicates that the accumulated frost has been completely melted. For modeling refrigerated cases with temperature-terminated defrost, EnergyPlus allows the user to specify a defrost energy correction curve to account for variations in defrost energy as ambient air humidity levels change. The user can select from four correction curve types: None, Case Temperature Method, Relative Humidity Method, or Dewpoint Method.

For type None (default):

$$DefrostRatio=1$$

For type Case Temperature Method:

$$DefrostRatio=1-(R{H}_{rated}-R{H}_{air})(a+b{T}_{case}+c{T}_{case}^2+d{T}_{case}^3)$$

For type RH Method:

$$DefrostRatio=e+f\left(R{H}_{air}\right)+g\left(R{H}_{air}^2\right)+h\left(R{H}_{air}^3\right)$$

For type Dewpoint Method:

$$DefrostRatio=i+j{T}_{dp,air}+k{T}_{dp,air}^2+l{T}_{dp,air}^3$$

where:

$R{H}_{rated}$ is the rated ambient relative humidity (%)

$R{H}_{air}$ is the relative humidity of the ambient (zone) air (%)

$T_{case}$ is the case operating temperature (${}^{\circ }$C)

$T_{dp,air}$ is the dewpoint temperature of the ambient (zone) air (${}^{\circ }$C)

a, …, l is the user-defined coefficients using a cubic curve object (Curve:Cubic).

The user specifies the defrost energy correction curve type and the name of the cubic curve object (Curve:Cubic) that defines the curve coefficients. Representative curve coefficients for curve type “Case Temperature Method” are provided in Table 1.

As mentioned above, the refrigerated case evaporator is turned off while it is being defrosted. Heat gains during defrost must be removed once the defrost period (drip-down schedule) has ended. The model assumes that heat gains due to defrost heater operation are at least partially offset by converting accumulated frost to liquid water (condensate) which drains from the case. Frost accumulation during each simulation time step is estimated by the model using the actual latent heat transfer to the refrigerated case and the heat of vaporization plus the heat of fusion for water. The model assumes that frost is not accumulated on the evaporator during the defrost drip-down time period.

$$Frost=Frost+\left(\frac{{\dot{Q}}_{case,rated}\left(L_{case}\right)\left(RT{F}_{rated}\right)\left(LH{R}_{rated}\right)\left(LatentRatio\right)\left(t_{zn}\right)}{\left(h_f+h_{fg}\right)}\right)\left(1-SC{H}_{defrost,dripdown}\right)$$

where:

$Frost$is the amount of accumulated frost on the case evaporator (kg)

${\dot{Q}}_{case,rated}$ is the case rated total cooling capacity per unit length (W/m)

$L_{case}$ is the case length (m)

$RT{F}_{rated}$ is the runtime fraction of the refrigerated case at rated conditions

$LH{R}_{rated}$ is the latent heat ratio of the refrigerated case at rated conditions

$LatentRatio$ is the ratio of actual latent load to rated latent load on the case, based on latent case credit curve (see section Latent Case Credits below)

$t_{zn}$ is the duration of zone simulation time step (s)

$h_{fg}$ is the heat of vaporization of water (assumed constant at 2,498,000 J/kg)

$h_f$ is the heat of fusion of water (335,000 J/kg)

$SC{H}_{defrost,dripdown}$ is the defrost drip-down schedule value (0 to 1).

During defrost (SCHdefrost), the model assumes that the hot gas, hot brine, or electric heater energy directly contributes to melting the frost (heat of fusion of water). Defrost energy not attributed to melting frost from the evaporator coil results in a heat load on the refrigerated case evaporator (${\dot{Q}}_{def}$). When the defrost drip-down time period ends, this defrost energy heat load is added to the actual case load (up to the maximum evaporator capacity) until the total defrost energy heat load is removed (which may take several simulation time steps).

If DefrostType is Electric, HotGas, or HotBrine, then:

$${\dot{Q}}_{def}=max[0.0,(P_{def}^{\prime }{L}_{case}SC{H}_{def}-\frac{Frost\left(h_f\right)}{t_{zn}})]$$

Otherwise:

$${\dot{Q}}_{def}=0.0$$

where ${\dot{Q}}_{def}$ is the defrost heat load (W).

Sensible Case Credits[LINK]

Refrigerated cases remove sensible energy from the surrounding environment (termed “sensible case credits”). In this model, the sensible case credits are composed of wall heat conduction, radiation heat transfer, and sensible heat transfer by air infiltration (${\dot{Q}}_{walls}$ + ${\dot{Q}}_{rad}$ + ${\dot{Q}}_{inf,sens}$ in Equation [eq:TotalLoadRefCaseEvaporator]). To quantify this energy transfer, the model first calculates the rated sensible case credits by subtracting the known loads at rated conditions (fan, lighting, and anti-sweat heater) from the rated sensible cooling capacity of the case. It should be noted that the lighting and fan heat discussed here are for standard-efficiency equipment. Manufacturers typically provide ratings for both standard and high-efficiency fan and lighting equipment; however, the standard equipment is used to determine rated sensible case credits. (Some manufacturers no longer include any lighting in their rated capacity values. For these cases, P’${}_{lights,std}$ will equal zero.)

$$\dot{Q}c{c}_{sens,rated}=\left[{\dot{Q}}_{case,rated}\left(RT{F}_{rated}\right)\left(1-LH{R}_{rated}\right)-{P^{\prime }}_{lights,std}\left(F_l\right)-{P^{\prime }}_{as}\left(F_{as}\right)-{P^{\prime }}_{fan,std}\right]L_{case}$$

where:

$\dot{Q}c{c}_{sens,rated}$ is the sensible case credits at rated conditions (W)

${\dot{Q}}_{case,rated}$ is the case rated total cooling capacity per unit length (W/m)

$RT{F}_{rated}$ is the runtime fraction of the refrigerated case at rated conditions

$LH{R}_{rated}$ is the latent heat ratio of the refrigerated case at rated conditions

${P^{\prime }}_{lights,std}$ is the standard case lighting power per unit length (W/m)

$F_l$ is the fraction of lighting energy to case

${P^{\prime }}_{as}$ is the case anti-sweat heater power per unit length (W)

$F_{as}$ is the fraction of anti-sweat heater energy to case

${P^{\prime }}_{fan,std}$ is the standard case fan power per unit length (W/m)

$L_{case}$ is the case length (m).

For every simulation time step, the rated sensible case credits are then adjusted to account for variations at off-rated ambient air temperatures. The model also allows the user to define a case credit fraction using a schedule object. This case credit fraction can be useful for modeling cases that operate differently during specific time periods. For example, metal or plastic coverings may be installed on refrigerated display cases during unoccupied hours which would significantly reduce case credits (e.g., air infiltration) compared to occupied hours when the coverings are removed. If the user does not define a case credit fraction schedule, then the fraction is assumed to be 1 for the entire simulation.

$$\dot{Q}c{c}_{sens}=\dot{Q}c{c}_{sens,rated}\left(\frac{T_{db,air}-T_{case}}{T_{db,rated}-T_{case}}\right)\left(SC{H}_{cc}\right)$$

where:

$\dot{Q}c{c}_{sens}$ is the sensible case credits adjusted for ambient temperature and case credit fraction (W)

$T_{db,air}$ is the dry-bulb temperature of the ambient (zone) air (${}^{\circ }$C)

$T_{case}$ is the case operating temperature (${}^{\circ }$C)

$T_{db,rated}$ is the rated ambient (zone) dry-bulb temperature (${}^{\circ }$C)

$SC{H}_{cc}$ is the case credit fraction (schedule value, 0 to 1).

The sensible case credits calculated above are considered heat loads on the refrigerated case evaporator. The net impact of the case credits on the surrounding zone includes adjustment for the portion of the lighting and anti-sweat heater power that does not directly contribute to the case evaporator load. Sensible case credits are negative values when heat is removed from the zone load.

$$\dot{Q}c{c}_{sens,NET}=P_{lights}(1-F_l)+P_{as}(1-F_{as})-\dot{Q}c{c}_{sens}$$

where:

$\dot{Q}c{c}_{sens,NET}$ is the net impact of the sensible case credits on the surrounding zone, negative for cooling (W)

$P_{lights}$ is the case lighting electric power (W)

$F_l$ is the fraction of lighting energy to case

$P_{as}$ is the anti-sweat heater electric power (W)

$F_{as}$ is the fraction of anti-sweat heater energy to case.

When refrigerated cases are served by a compressor rack that rejects condenser waste heat directly to the zone (e.g., a stand-alone refrigerated case with integral compressor and condenser), this condenser waste heat offsets some or all of the sensible case credits. The amount of condenser waste heat rejected to the zone is calculated and reported by the refrigerated case compressor rack object (Ref. Heat Rejection to Zone).

Latent Case Credits[LINK]

Refrigerated cases also remove latent energy (moisture) from the surrounding environment (termed “latent case credits”). In this model, the latent case credit is composed solely of the latent heat transfer by air infiltration ${\dot{Q}}_{inf,lat}$ in Equation [eq:TotalLoadRefCaseEvaporator]. The latent case credits are calculated as the product of the case length and the total cooling capacity per unit length, latent heat ratio, and runtime fraction at rated conditions. As described previously (Ref. Sensible Case Credits), a case credit fraction schedule is used to model cases that operate differently during specific time periods. The same case credit fraction is used to modify both the sensible and latent case credits. If the user does not define a case credit fraction schedule, then the fraction is assumed to be 1 for the entire simulation. The calculation of latent case credits also includes a factor (LatentRatio) that accounts for lower ambient humidity levels. Latent case credits are set to zero during the defrost-dripdown periods.

$${\dot{Q}}_{inf,lat}=-\dot{Q}c{c}_{lat}={\dot{Q}}_{case,rated}\left(LH{R}_{rated}\right)\left(RT{F}_{rated}\right)\left(SC{H}_{cc}\right)\left(LatentRatio\right)L_{case}$$

where:

${\dot{Q}}_{inf,lat}$ is the latent load on the refrigerated case evaporator at current ambient conditions (W)

$\dot{Q}c{c}_{lat}$ is the latent case credit impact on zone load, negative for dehumidification (W)

${\dot{Q}}_{case,rated}$ is the case rated total cooling capacity per unit length (W/m)

$LH{R}_{rated}$ is the latent heat ratio of the refrigerated case at rated conditions

$RT{F}_{rated}$ is the runtime fraction of the refrigerated case at rated conditions

SCH${}_{CC}$ is the case credit fraction (schedule value, 0 to 1)

$LatentRatio$ is the ratio of actual latent load to rated latent load on the case, based on latent case credit curve

$L_{case}$ is the case length (m).

Latent load on the refrigerated case evaporator will vary with ambient humidity levels. Therefore, the refrigerated case model allows the user to specify a latent case credit curve to adjust case credits based on ambient humidity, and the user can select from three curve types: Case Temperature Method, Relative Humidity Method, or Dewpoint Method.

If CurveType is Case Temperature Method:

$$LatentRatio=1-(R{H}_{rated}-R{H}_{air})(m+n{T}_{case}+o{T}_{case}^2+p{T}_{case}^3)$$

Else if CurveType is RH Method:

$$LatentRatio=q+r\left(R{H}_{air}\right)+s\left(R{H}_{air}^2\right)+t\left(R{H}_{air}^3\right)$$

Else if CurveType is Dewpoint Method:

$$LatentRatio=u+v{T}_{dp,air}+w{T}_{dp,air}^2+x{T}_{dp,air}^3$$

where:

$R{H}_{rated}$ is the rated ambient relative humidity (%)

$R{H}_{air}$ is the relative humidity of the ambient (zone) air (%)

$T_{case}$ is the case operating temperature (${}^{\circ }$C)

$T_{dp,air}$ is the dewpoint temperature of the ambient (zone) air (${}^{\circ }$C)

m, …, x is the user-defined coefficients using a cubic curve object (Curve:Cubic).

The user specifies the latent case credit curve type and the name of the cubic curve object (Curve:Cubic) that defines the curve coefficients. Representative curve coefficients for curve type “Case Temperature Method” are provided in Table 2.

Refrigerated Case Credits With Under Case Return Air[LINK]

For certain refrigerated case types, the sensible case credits provided to the zone can create an uncomfortably cold environment in the surrounding area. For this reason, return air ducts are frequently placed behind these cases to draw this cold air under the case and direct it back to the HVAC system. This reduces localized over-cooling and improves occupant comfort.

Since under case return ducts reduce the temperature and humidity of the air being recirculated to the HVAC system, this can impact HVAC system performance. Figure 4 shows the relationship that is used by the refrigerated case model to determine the fraction of case credits that directly cool and dehumidify the HVAC system return air. This fraction, referred to as the Return Air Factor (RAF), is a function of the fraction of the HVAC system return air that comes from under the cases. The remaining fraction of the case credits (1-RAF) becomes part of the overall zone air energy balance. If the HVAC system is off for a simulation time step (no return air mass flow), the sensible and latent case credits normally attributed to the HVAC return are set equal to zero (even though they get calculated and reported here as non-zero values) and all case credit energy is applied to the zone air heat balance.

$$\dot{Q}c{c}_{sens,zone}=\dot{Q}c{c}_{sens,NET}\left(1-RAF\right)$$

$$\dot{Q}c{c}_{lat,zone}=\dot{Q}c{c}_{lat}\left(1-RAF\right)$$

$$\dot{Q}c{c}_{sens,HVAC}=\dot{Q}c{c}_{sens,NET}\left(RAF\right)$$

$$\dot{Q}c{c}_{lat,HVAC}=\dot{Q}c{c}_{lat}\left(RAF\right)$$

where:

$\dot{Q}c{c}_{sens,zone}$ is the sensible case credit applied to the zone air heat balance (W)

$\dot{Q}c{c}_{lat,zone}$ is the latent case credit applied to the zone air heat balance (W)

$\dot{Q}c{c}_{sens,HVAC}$ is the sensible case credit applied to the HVAC return air (zone return air path outlet node) (W)

$\dot{Q}c{c}_{lat,HVAC}$ is the latent case credit applied to the HVAC return air (zone return air path outlet node) (W)

RAF is the return air factor (see Figure 4 above).

Variable Evaporator Temperature[LINK]

Control systems are now available that increase the evaporator temperature to improve compressor efficiency whenever the total loads on a system are less than the system capacity. To model these systems, a variable evaporator temperature is an option available with the detailed refrigeration system object (Refrigeration:System). If this option is selected, the model will compare the refrigeration load on each case to the load at rated conditions. If the case load in a particular time step is less than the rated load, an acceptable elevated evaporator temperature is determined for that case. The evaporator temperature for the whole refrigeration system is then set by the minimum evaporator temperature needed for any particular case.

$$L{F}_{case}=\frac{{\dot{Q}}_{case,actual}}{{\dot{Q}}_{case,rated}}$$

$$T_{Evap,Allowed}=T_{case}-L{F}_{case}(T_{case}-T_{Evap,Design})$$

where:

$L{F}_{case}$ is the load factor for a particular case

$T_{Evap}$ is the evaporator temperature (${}^{\circ }$C).

Walk-In Coolers and Freezers[LINK]

The walk-in object (Refrigeration:WalkIn) is another type of refrigeration load that can be placed on either a refrigeration compressor rack, detailed refrigeration system, or secondary refrigeration system object (Refrigeration:CompressorRack, Refrigeration:System, or Refrigeration:SecondarySystem). Walk-in coolers and freezers differ from refrigerated cases in that they may have surfaces facing more than one zone and in that they are always equipped with doors, that is, they do not have open shelves. Their sensible and latent exchange with zones is therefore calculated in a different manner than for refrigerated cases. Also, the walk-in model does not interact directly with the HVAC system, that is, the return air fraction option available in the refrigerated case model is not included.

The walk-in cooler performance is based on the ASHRAE load model, which includes infiltration through door openings and sensible loss through walls/ceilings described by the user for each zone.(ASHRAE 2006d, ASHRAE 2006e, Gosney, W.B., Olama, G.A.-L. 1975) All equipment loads (fan, light, heaters) are modeled as well. Sensible and latent exchange with multiple adjoining zones is included. A master schedule is used for the Walk In operation and additional schedules control the lights, defrost, and heater operation. Just as for cases, unmet refrigeration loads are accumulated to be met the following time step. This usually occurs during defrost and restocking.

Walk-In Sensible and Latent Heat Exchange[LINK]

A walk-in can exchange both sensible and latent energy with multiple zones. The heat transfer calculations are performed separately for each zone so that the heat transfer impact, or zone credits, can be determined. The area of all walls and ceilings facing each zone are described by the user by their thermal conductance and area. Sensible energy exchange takes place between these surfaces and the surrounding zones. Because these walls interface with conditioned zones at relatively constant temperatures, this heat exchange is modeled very simply:

$$Q_{SurfacesZn}=U_{SurfacesZn}\cdot A_{SurfacesZn}\cdot \Delta T_{Zn}$$

$$Q_{DoorSensZn}=U_{DoorZn}\cdot Are{a}_{DoorZn}\cdot \Delta T_{Zn}$$

The heat transfer through the floor is similarly modeled.

$$Q_{Floor}=A_{Floor}x{U}_{Floor}x(T_{Ground}-T_{WalkIn})$$

Where:

$A_{Floor}$ is the area of the walkin floor (m${}^2$)

$A_{SurfacesZn}$ is the area of surfaces facing Zone n (m${}^2$)

$Q_{DoorSensZn}$ is the sensible heat transfer through the closed door(s) facing Zone n (W)

$Q_{surfacesZn}$ is the sensible heat transfer through walls and ceilings facing Zone n (W)

$T_{Ground}$ is the ground temperature (${}^{\circ }$C)

$T_{WalkIn}$ is the walk-in operating temperature (${}^{\circ }$C)

$U_{Floor}$ is the thermal conductance of floor (W/m${}^2$-K)

$U_{DoorZn}$ is the thermal conductance of doors facing Zone n (W/m${}^2$-K)

$U_{SurfacesZn}$ is the thermal conductance of surfaces facing Zone n (W/m${}^2$-K)

$\Delta T_{Zn}$ is the difference between walk-in operating temperature and Zone n drybulb temperature (${}^{\circ }$C).

Infiltration through doorways places both a sensible and a latent load upon the walk-in, and corresponding credits upon the adjacent zone. Two types of doors are available, nominally called ‘stock’ and ‘glass’ doors, to enable the user to model doors that differ in thermal conductance, door protection type, and frequency of opening. The sensible and latent infiltration loads are modeled according to the guidance specified in (ASHRAE 2006d, ASHRAE 2009, and Gosney and Olama, 1975). The air within the cooler is assumed to be at 90% relative humidity. Equal air exchange is assumed, that is, the mass of dry air infiltrating into the walkin is assumed to equal the mass of dry air infiltrating out of the walkin.

$$Q_{Infiltration}=Q_{FullFlow}\cdot Facto{r}_{DoorOpen}\cdot Facto{r}_{Flow}\cdot (1-Facto{r}_{Protection})$$

$$Q_{FullFlow}=0.221\ast A_{Door}(h_{ZoneAir}-h_{AirWalkIn}){\rho }_{AirWalkIn}(1-{\rho }_{ZoneAir}/{\rho }_{AirWalkIn}{)}^{0.5}(g\ast H_{Door}{)}^{0.5}Facto{r}_{Density}$$

$$Facto{r}_{Density}=\left(2/\right(1+\left({\rho }_{AirWalkIn}/{\rho }_{ZoneAir}{)}^{0.333}\right){)}^{1.5}$$

$$m_{DryAir}=Q_{Infiltration}/(h_{ZoneAir}-h_{AirWalkIn})$$

$$m_{Water}=m_{DryAir}\cdot (W_{ZoneAir}-W_{AirWalkIn})$$

$$Q_{WalkInLatentZn}=m_{Water}\cdot \Delta h_{IcetoVapor}\cdot (1-SC{H}_{Defrost,DripDown})$$

$$Q_{WalkInSensInfZn}=Q_{Infiltration}-(m_{Water}\cdot \Delta h_{IcetoVapor})$$

where:

A${}_{door}$ is the area of door facing Zone n (m${}^2$)

Factor${}_{DoorOpen}$ is the value scheduled by user, fraction of time door open during time step

Factor${}_{Flow}$ is the doorway flow factor, = 0.8 if $\Delta T_{Zn}\ge$ 11${}^{\circ }$C; = 1.1 if ΔT$\Delta T_{Zn}$ < = 11${}^{\circ }$C

Factor${}_{Protection}$ is the doorway protection factor, = 0 for no protection; = 0.5 for an air curtain; and 0.9 for a strip curtain

g is the gravitational constant

h${}_{AirWalkIn}$ is the enthalpy of the air within the walk in, = f(T${}_{WalkIn}$,P${}_{Outdoor}$, 90%RH) (J/kg)

h${}_{ZoneAir}$ is the enthalpy of the air in Zone n (J/kg)

H${}_{door}$ is the height of door facing Zone n (m)

Q${}_{FullFlow}$ is the sensible and latent refrigeration load for fully established flow (W)

Q${}_{Infiltration}$ is the average infiltration (sensible and latent) refrigeration load for the time step (W)

Q${}_{WalkInLatentZn}$ is the latent load upon the walk in facing Zone n (W)

Q${}_{WalkInSensInfZn}$ is the sensible load due to infiltration upon the walkin facing Zone n (W)

m${}_{DryAir}$ is the mass of dry air infiltrating into the walk-in (kg/s)

m${}_{Water}$ is the mass of water removed from the infiltrating air (kg/s)

P${}_{Outdoor}$ is the outdoor air pressure (Pa)

SCH${}_{Defrost,DripDown}$ is the value from 0 to 1 indicating whether the system is in the dripdown period

W${}_{AirWalkIn}$ is the humidity ratio of the air within the walk in, = f(T${}_{WalkIn}$,P${}_{Outdoor}$, 90%RH) (kg/kg)

W${}_{ZoneAir}$ is the humidity ratio of Zone n air, kg/kg

$\Delta h_{IcetoVapor}$ is the latent heat absorbed to change ice to vapor (J/kg)

${\rho }_{AirWalkIn}$ is the density of the air within the walk in = f(T${}_{WalkIn}$,P${}_{Outdoor}$, 90%RH) (kg/m${}^3$)

${\rho }_{ZoneAir}$ is the density of air in Zone n (kg/m${}^3$).

The sensible load on the case and the sensible credit to the zone continue throughout the defrost and dripdown periods. However, to be consistent with the treatment of refrigerated cases, there is no latent credit to the zone or latent load upon the cooler during the dripdown period. Latent load and latent credit are both based on reducing the infiltrating vapor to ice. The sensible heat exchange between the walk in and the zone is then the total of the heat transfer through the doors and surfaces and the infiltration sensible load. The latent load upon the walkin is converted to the amount of frost added to the coils during each time step. This accumulating value is used later to determine the load placed upon the walkin during the defrost cycle.

$$Q_{WalkInSensZn}=Q_{WalkInSensInfZn}+Q_{DoorZn}+Q_{surfacesZn}$$

$$Q_{ZoneLatent}=-Q_{WalkInLatentZn}$$

$$Q_{ZoneSens}=-Q_{WalkInSensZn}$$

$$\Delta Fros{t}_{Zn}=\left(m_{Water}\Delta time\right)\cdot (1-SC{H}_{Defrost,DripDown})$$

where:

Q${}_{WalkInSensZn}$ is the total sensible heat exchange between the walkin and Zone n (W)

Q${}_{ZoneLatent}$ is the latent load upon the Zone n (W)

Q${}_{ZoneSens}$ is the sensible load upon Zone n (W)

$\Delta Fros{t}_{Zn}$ is the change in frost inventory (kg)

$\Delta time$ is the length of time step (s).

After the heat exchange with each zone is calculated, the total load on the walkin is calculated:

$$Q_{WalkInLatentTot}=\sum Q_{WalkInLatentZn}$$

$$Q_{WalkInSensT}$$