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Optimization of cooling-dominated hybrid ground-coupled heat pump systems.


Ground-coupled heat pump systems can save up to 50% of the energy that would otherwise be used by conventional heating and cooling systems (EERE 2007). As a result, the number of ground-coupled heat pump systems installed in the U.S. has grown dramatically over the last several decades. However, ground-coupled heat pumps are still a secondary design choice for most applications, in large part due to the high first cost associated with the ground-coupled heat exchanger. In order to allow ground-coupled heat pump technology to capture a larger portion of the heating and cooling market, innovations are required to improve the economics of this technology, particularly for cooling-dominated climates and buildings.

One such innovation is the hybrid ground-coupled heat pump system. Hybrid ground-coupled heat pump systems (HyGCHPs) interface conventional ground-coupled heat pump (GCHP) equipment with supplemental heat rejection or extraction systems. In a cooling-dominated climate (e.g., the southern U.S.), the supplemental heat-rejection device is operated during the cooling season in order to reduce the cooling load on the ground heat exchanger (GHX). The presence of the supplemental heat-rejection device allows the installation of a smaller, less expensive GHX that experiences a more balanced load (i.e., the heat rejection to the ground during the cooling season is more closely matched to the heat extraction during heating season). The more balanced load leads to more efficient heat pump operation by mitigating increases in ground temperature that otherwise occur over time. The benefits of HyGCHP systems in cooling-dominated climates were demonstrated previously on a case-by-case basis either through instrumentation or simulation of installed systems. However, the proper design and control of an HyGCHP system in general is not intuitive due to the interactions between the building load, the components, the climate, and the ground.

This paper presents a systematic and comprehensive design study in which a physics-based TRNSYS model (Klein et al. 2006) of an HyGCHP system is integrated with an optimization engine. The optimization engine varies the system design (i.e., the physical size of the equipment) and the system control strategy (i.e., the algorithm used to control the operation of the equipment) in order to minimize the life-cycle cost (LCC) associated with owning and operating the system. The model utilizes subhourly time steps and simulates twenty years of operation. It is, therefore, capable of resolving the small time-scale effects associated with changes in the building load and control of the equipment, as well as the longer time-scale effects associated with seasonal changes in the climate and changes in the ground temperature that build up over several years due to unbalance between the cooling and heating loads. The simulation/optimization tool is applied to a range of buildings and climates and the results show that an optimally designed HyGCHP system is economically attractive under most conditions. The lifecycle savings (LCS) associated with the lower first cost of the GHX and more efficient operation of the heat pump during its life more than offset the cost of buying and operating the supplemental device in most situations. The characteristics (equipment size and control strategy) of an optimally designed HyGCHP system are examined and used to generate a set of approximate design guidelines that can be applied to a given building and climate to arrive at a near-optimal HyGCHP design.

Hybrid Systems in Literature

The ground heat exchanger model is the critical component in the simulation because it must provide accurate predictions of the behavior of the GHX for short time-scale disturbances associated with changes in its operation over a single day, as well as long time-scale changes associated with the unbalance in the cooling and heating load that occur over a single year. Further, the GHX model must capture the impact of bore-to-bore interactions and the variation in the ground temperature both very near and very far from the bore hole. In order to enable efficient optimization, the GHX model must also be computationally efficient. This project relies on the duct ground heat storage model (DST) of vertical borehole GHXs that was developed at the University of Lund (Hell-strom 1989). Hellstrom's model builds on previous Swedish research in ground heat storage and was implemented in TRNSYS by Pahud et al. (1996). Validations of the model were since done using experimental data, including work by Shonder et al. (1999) and McDowell and Thornton (2008).

Several papers presented the details of actual, installed hybrid systems (Wrobel 2004; Phetteplace and Sullivan 1998). A few studies also used simulation tools to model (Ramamoorthy et al. 2000) and optimize hybrid systems. One example is the optimization of the hybrid ground-coupled system installed in an administrative building at Fort Polk in Louisiana (TESS 2005). The model discussed in this paper is based in part on the model developed for the Fort Polk case study. However, much of the equipment used in the HyGCHP model developed for the Fort Polk case study was of fixed design because the simulation considered a single climate/ building combination. In order to accomplish optimization over a range of buildings and climates, it is necessary to develop much more general models capable of simulating a broad range of designs.

The only general methodology that has been developed for the design of HyGCHP systems is discussed by Kavanaugh (1998) for cooling-dominated climates. One primary premise of Kavanaugh's method is that the GHX in a cooling-dominated hybrid system should be sized to just meet the peak heating load. The results of this project generally agree with that basic premise. Two additional studies in the literature focused on identifying the most optimal control strategies for hybrid ground-coupled systems. A study by Yavuzturk and Spitler (2000) examined several general control strategies applied to hybrid systems in order to identify the optimal choice. The previously mentioned Fort Polk study (TESS 2005) also studied several control strategies and identified the one that resulted in the lowest LCC. These two control studies both conclude that the same general control strategy was optimal; this strategy is used for the simulation presented in this paper, though the specific setpoints used to implement the strategy are modified and optimized for each climate/building combination.


The objective of this project is to identify the optimal equipment and control methodology for specified building/ climate combinations under a set of economic conditions. The effects of changing building loads, ambient conditions, and energy cost throughout a day suggest that an energy simulation with subhourly time resolution is required in order to obtain meaningful results. Additionally, the annual unbalance in the load and its effect on the ground temperature will substantially affect the long-term performance of the system; therefore, a multiyear simulation covering the life of the system is required. TRNSYS was selected as the most appropriate simulation tool to meet all these needs, as well as for the ability to accurately model a GHX. The hybrid system model created for this project integrates several component models according to their energy and mass flows; these components and their interaction are described in more detail below.

Simulation Strategy

The HyGCHP model developed for this project utilizes simplifying assumptions that are necessary in order to allow the consideration of a wide range of equipment sizes, buildings, and climates while remaining computationally efficient--characteristics necessary to accomplish the optimization exercises that are the focus of this project. First, the current hybrid study utilizes building models that are independent of the simulation of the HyGCHP system itself by requiring that the HyGCHP system meet the building load at all times. This methodology of decoupling the building simulation from the heating and cooling equipment was previously adopted and justified in the Fort Polk case study (TESS 2005). The savings in computational time afforded by this assumption are considerable.

Secondly, the hybrid configuration examined in this paper always places the cooling tower upstream of, and in series with, the GHX, as shown in Figure 1. This configuration is not arbitrary. The Fort Polk study (TESS 2005) examined several configurations, as well as different control strategies and supplemental devices for the cooling-dominated administrative building that was being designed, and found that a series configuration always resulted in a lower LCC than a parallel configuration. Based on this observation, the HyGCHP model is always configured with the supplemental device in series with the ground-coupled heat exchanger. However, only the rated amount of fluid is pumped through the cooling tower; the remainder of the flow bypasses the cooling tower. The placement of the tower upstream of the GHX is based on the fact that the cooling tower is more expensive to operate than the GHX. The cooling tower requires the operation of fans that consume more energy than the pumps required to operate the GHX. Therefore, when the tower is operating, it should do so with the largest possible temperature difference between the fluid and the ambient air in order to maximize its performance. It has been observed that in climates with extremely high ground temperature and low wet bulb temperatures (e.g., a very hot and very dry climate), the configuration shown in Figure 1 may not be optimal; in such climates, the GHX should be placed upstream of the cooling tower.


Two studies in the literature have examined the most effective control strategy for the hybrid system shown in Figure 1. Yavuzturk and Spitler (2000) determined the hybrid system control strategy that resulted in the lowest LCC for a cooling-dominated office building. Five different control algorithms were considered and it was found that in both severe (Houston) and moderate (Tulsa) climates, one of these methods resulted in the lowest cost. The difference between the temperature of the fluid upstream of the tower ( Tfl, out ) and the ambient wet bulb temperature is used to control the operation of the cooling tower (i.e., when this temperature difference is greater than some setpoint, the cooling tower is activated). The temperature of the fluid upstream of the ground heat exchanger is then used to control the operation of the GHX; the GHX is activated using a setpoint for cooling and a different setpoint for heating. The Fort Polk study (TESS 2005) also implemented and optimized several different control algorithms and ultimately reached the same conclusion relative to optimal control methodology. This lowest-cost, general control strategy is used in the HyGCHP model presented in this paper. This control sequence is discussed in more detail in the subsequent sections.


Heat Pump. Another simplifying premise of this research is that it is not necessary to specify the exact size and total number of individual heat pumps installed in the system. Rather, the building loads are divided into heating and cooling loads (or core/perimeter loads in some building models); a single heat pump component (which represents the combined performance of many heat pumps) meets the total heating load, and a different heat pump component (also representing many heat pumps) meets the total cooling load. There are therefore only two heat pump component models used to represent the entire building conditioning system, with each component model being scalable so that it can meet the peak load for any building/climate scenario being considered. Further explanation and justification of this strategy is provided in Hackel (2008).

Each scalable heat pump component model (one for heating, one for cooling) simulates a system of fluid-to-air heat pumps. As discussed above, the load on the building (air) side of the heat pump is dictated by an independent building model. On the fluid side, the cooling heat pump model must reject a quantity of energy, [q.sub.tot], to the fluid loop during each timestep (with [q.sub.tot] being the sum of building load and heat pump power consumption). Note that [q.sub.tot] is a function of the time-step duration as well as both the building load and the power consumption of the heat pump. This load is assumed to be met entirely by the HyGCHP fluid loop (i.e., no domestic water heating or other streams are modeled); therefore, the total energy transfer to the loop in a timestep is

[q.sub.tot] = [m.sub.fl][c.sub.p][DELTA]T[[tau].sub.on], (1)

where [m.sub.fl] is the mass flow of the fluid, cp is the specific heat of the fluid, [DELTA]T is the change in fluid temperature from inlet to outlet, and [[tau].sub.on] is the length of time that the heat pump component operates during the time step. The same process is then repeated for the heating loads in the building, using the heating heat pump model. The energy and mass flows are then summed for the heating and cooling units, as they would be in an actual fluid loop.

Although each individual heat pump in the system will operate intermittently (i.e., with varying [[tau].sub.on]), it is not necessary to model the process of turning individual heat pumps on and off during a time step because the individual heat pumps are not sized or discretely modeled for a given building/climate scenario. The operation of many smaller heat pumps turning on and off as needed to supply the load is modeled by varying the fluid flow rate, [m.sub.ft], while maintaining a fixed temperature difference between the inlet and outlet of the heat pump with the value of [[tau].sub.on] set equal to the full time-step duration. Because [DELTA] and [c.sub.p] are not affected by heat pump size, the capacity of the system scales linearly with [m.sub.ft]without regard to the quantity of heat pumps providing that capacity. Additionally, the performance (efficiency) of a heat pump system is found to be unaffected by the quantity or capacity of units in the system (Hackel 2008).

The relationship between heat pump capacity and flow rate provided in Equation 1 is valid regardless of operating temperatures. However, the heat pump capacity and efficiency are functions of the entering GHX fluid and air temperatures; heat pumps operate most efficiently (in heating mode) when absorbing heat from a higher temperature source and (in cooling mode) when rejecting heat to a lower temperature sink. Scaling factors are used in the model to account for this behavior. The cooling capacity scaling factor, [], cool, is defined as the cooling capacity normalized by its value (13.9 Btu/ kW*h) at [] = 90 [degrees] F (32.2 [degrees] C). The cooling capacity scaling function for the heat pump models used to generate Figures 2 through 4 is approximately a linear function of the entering fluid temperature and nearly independent of the heat pump model, according to manufacturer's performance data. The best fit to the data for the cooling capacity scaling function to the fluid inlet temperature is

[F.sub.cap, cool] = [C.sub.1] ([T.sub.fl, in]) + [C.sub.2], (2)

where [C.sub.1] = -0.0058 [degrees][F.sub.-1] (-0.011 [degrees] [C.sub.-1]), [C.sub.2] = 1.52 (1.34 if [T.sub.fl], in is in [degrees] C), and [] is the entering fluid temperature. The cooling efficiency scaling factor, [], is defined as the cooling efficiency normalized by its value at [] = 90[degrees]F (i.e., the value shown in Figure 4). The cooling efficiency scaling function is approximately a linear function of the entering fluid temperature and nearly independent of the heat pump model, according to the manufacturer's performance data. The best fit to the data for the cooling capacity scaling function to the fluid inlet temperature is

[F.sub.eff, cool] = [C.sub.1] ([T.sub.fl, in]) + [C.sub.2], (3)

where [C.sub.1] = -0.0171[degrees][F.sub.-1] (-0.031[degrees][C.sub.-1]), C2 = 2.58 (2.03 if [] is in [degrees]C), and [] is the inlet fluid temperature. Similar curves were generated for heating capacity scaling factor and heating efficiency scaling factor (normalized to a COP of 4.7 at 70[degrees]F) as a function of entering fluid temperature, and these are also used in the model.

Indoor air temperature and humidity also affect the power consumption and capacity of the heat pump for off-design air conditions; the heat pump model adjusts the performance of the unit (based on curve fits to experimental heat pump data) in response to these changes as dictated by user-supplied indoor air conditions.

Ground Heat Exchanger. The ground heat exchanger considered in this analysis is vertical with one U-tube per bore, the most common configuration currently used for commercial/institutional buildings in the U.S. The thermal interaction between the fluid and the ground is simulated using the duct ground heat storage model of a vertical GHX field. This model calculates the transient temperature distribution as the superposition of three solutions: a global temperature solution (at the scale of the entire field), a local solution (at the single borehole scale, accounting for short time-scale effects), and a steady-flux solution (at the single borehole scale, accounting interaction between both scales). The GHX is laid out assuming a cylindrical storage volume, symmetrical about the center axis, with uniform spacing (specified below) between all boreholes of equal depth (see Hellstrom 1989 for more detail).

Dozens of parameters are required in order to specify the GHX model. In this study, values of 300 ft (91.4 m) and 23 ft (7 m) are assumed for drilling depth and spacing, respectively. A ground conductivity of 1.4 Btu/h.ft[degrees]F (2.4 W/m*K) and ground thermal diffusivity of 1.1 [ft.sub.2]/day (0.1 [m.sub.2]/day) are assumed, since ground-coupled systems are more likely to be installed in regions with favorable ground properties. The initial ground temperature is specified based on the geographic location of the scenario considered. The parameters that dictate the overall size of the GHX (i.e., the total bore length, number of bores, etc.) are controlled by the optimizer and varied during the optimization in order to arrive at the most optimal GHX design. An algorithm based on Kavanaugh (1997) is used to lay out the borefield in a manner that assures turbulent flow in the borefield during peak load periods while minimizing pumping power. The piping is assumed to be 1 in. (25 mm) SDR-11 PE pipe, which has an inner diameter of 1.06 in. (27 mm); this diameter is a standard size that is consistent with the most basic installation equipment. The bore diameter is assumed to be 4.5 in. (0.11 m), which leads to a U-tube spacing of 3 in. (0.08 m). The borehole is assumed to be filled with enhanced grout with a thermal conductivity of 0.85 Btu/h*ft*[degrees]F (1.4 W/m*K).

Supplemental Devices. Several devices can be used to provide heat rejection to supplement the GHX for cooling-dominated systems. This study considers both a closed-circuit cooling tower (CCCT) and a dry fluid cooler (DFC). The over-all size of these devices is determined by optimization, so all performance and economic parameters in the model must be scalable with device size.

Heat rejection in a CCCT is accomplished primarily by the evaporation of water that is sprayed on the outside surface of tubes that carry the fluid, and the working fluid never comes into contact with the outside air. The component model used to simulate the CCCT is based on a simulation method developed by Zweifel et al. (1995). The CCCT model assumes that the temperature of the fluid at the outlet is equal to the average temperature of the spray water. This approximation provides reasonable estimates for all closed-circuit cooling towers of the size used in HVAC applications, as shown by Zweifel et al. Design performance and cost data are required to provide baseline model parameters for the CCCT. Cooling tower performance data are taken from manufacturers. Cost data for CCCT and all other equipment are taken from RS Means Mechanical Cost Data Guide (2006).

Heat rejection in a DFC (sometimes referred to as an air fluid cooler) is accomplished by blowing air across tubes through which the working fluid flows; as with the CCCT, the working fluid in a DFC never comes into contact with the outside air. The DFC component model assumes that the fluid cooler device acts as a simple cross-flow heat exchanger (TESS 2005). The total conductance of the heat exchanger is determined from the manufacturer's design specifications, and the performance at all other conditions is predicted using the effectiveness-NTU method.

Both a boiler/tower and GHX-only system configuration are modeled in addition to the hybrid system for each building/climate scenario; these alternative systems are modeled using the same component models and economic assumptions and, therefore, these simulations provide useful information for direct comparison. A boiler component model is required for the boiler/tower simulation. The boiler model assumes a constant 85% efficiency, and the size (capacity) of the boiler is chosen by optimization.

Controller. One general control algorithm was selected for this project based on an examination of the literature. However, in order to implement this control algorithm it is necessary to specify the settings of several control set points. These control set points are varied by the optimizer in order to minimize the LCC; therefore different building/climate scenarios may have very different optimal control sequences even though they use the same general control algorithm. Temperature measurements and flow controls are required in the locations shown in Figure 2 in order to operate the controller.


The controller operates according to the sequence laid out below; this explanation assumes a cooling tower is the supplemental heat-rejection device. A HyGSHP system utilizing a dry fluid cooler is controlled in a similar manner:

1. The controller determines whether net heating is required based on the temperature difference across the heat pump system ([T.sub.fl.sub.out] - []). If heating is required ([T.sub.fl.sub.out] < [, then the fluid is diverted through the GHX whenever the temperature upstream of the GHX ([T.sub.GHX]) falls below a control setpoint temperature, THeat1 (Note that all control set points are implemented with a dead band temperature difference that is set to 2.5[degrees]F (1.4[degrees]C) in this study).

(2.) If cooling is required ([T.sub.fl.sub.out] > []), then the controller follows the remaining steps. The cooling tower is turned on (at low fan speed and flow rate) if the fluid temperature upstream of the tower ([T.sub.fl, out]) is above the ambient wet bulb temperature ([T.sub.wb]) plus some control setpoint temperature difference, [DELTA][T.sub.1].

(3.) If the fluid temperature upstream of the tower is also above some higher control setpoint temperature, [T.sub.Cool1], then the coolin g tower is switched to high fan speed and flow rate.

(4.) If the fluid temperature leaving the cooling tower ([T.sub.GHX]) remains above some setpoint temperature [T.sub.Cool2], then the fluid is diverted through the GHX.

The values of the control setpoints (i.e., [T.sub.Heat1], [DELTA][T.sub.1], [T.sub.Cool1], and [T.sub.Cool2]) are controlled by the optimization algorithm in order to minimize the LCC of the system, therefore the optimal control setpoints are an output of the optimization process. However, the value of these setpoints remain constant during any single simulation.

Pump. A pump is needed in any HyGCHP system in order to circulate the fluid through the fluid loop. In this simulation model, a simple variable speed pump component model represents the characteristics of the pump(s) installed in the system. The pump must operate over a range of speeds because of the changing mass flow rate in the system. The main role of the pump component (in addition to calculating a small addition of pumping waste heat to the fluid), is to calculate pumping power. Power is based on a constant pumping efficiency; for the results presented in this paper, a 60% average overall pump efficiency is assumed. The pressure rise that is required to estimate the pumping power is based on a summation of the pressure drops that are calculated individually across each component in the fluid loop, most of which is caused by pipe friction losses due to flow through the GHX. An algorithm is developed in this study to estimate pipe geometries based on the outputs of the GHX sizing algorithm (Hackel 2008); the pressure drop is calculated according to the borehole furthest from the building.

Economics. In order to perform an optimization, it is necessary to define a figure of merit that will be maximized or minimized. For a building energy system, such as the heat pump systems considered in this project, the LCC associated with owning and operating the equipment over its useful life is the most appropriate figure of merit because the LCC includes the size (i.e., capital cost) and efficiency (i.e., operating costs) of the system equipment. These costs are affected by the time value of money, which depends on both the inflation rate (z) and the required rate of return (used for the discount factor, d). LCC combines these effects into a single number that represents the present value of all costs incurred over the economic life of the system; the economic life is assumed to be equal to the time span of the simulation, which is 20 years in this study.

Equipment first cost is computed based on RS Means Mechanical Cost Data (2006). Maintenance costs are estimated using the RS Means Facilities Maintenance and Repair Cost Data Guide (2002). Other economic parameters, such as discount rate, fuel cost, and GHX cost were selected based on surveys of literature and current market costs. A summary of the key parameters assumed for the parametric study (i.e., quantities that are not optimized, but rather set and used as the basis for an optimal system design) is shown in Table 1. In order to develop guidelines for the design of hybrid ground source heat pump systems, a parametric study was carried out using the HyGCHP model. Simulations were run across a range of building load scenarios that included various climates and building types of interest, as summarized in Table 2 (each building/climate permutation was simulated, resulting in 4 x 6 = 24 scenarios).. Sensitivities to some of these parameters were studied through simulation and are discussed in the results below.
Table 1. Summary of Input Parameters for the Parametric Study

Category        Parameter                      Baseline Value

           Ground conductivity          1.4 Btu/h.ft.[degrees]F (2.4

           Ground diffusivity           1.1 [ft.sup.2]/day (0.1

           Grout conductivity           0.8 Btu/h.ft.[degrees]F (1.4

Bore       Initial ground temperature   Varied according to climate

           Maximum drilling depth       300 ft (91.4 m)

           Borehole diameter            4.5 in. (0.11 m)

           Borehole spacing             22.5 ft (7.0 m)

           Pump efficiency              60%

           Boiler efficiency            85%

Other      Max entering water temp for  95[degrees]F [(35[degrees]
Equipment  heat pump                    C)[degrees]]

           Min entering water temp for  35[degrees]F (1.7 [degrees]C)
           heat pump

           EER of heat pump at ARI      16 Btu/kW*h
           13256-1 conditions

           COP of heat pump at ARI      3.4
           13256-1 conditions

           Life span                    20 years

           Discount rate                8.5%

           Down payment                 30%

           Loan interest rate (20-year  6.0%

           Tax rate                     35%

Economic   Peak electricity rate (10    $0.101/kWh
           a.m.-9 p.m.)

           Off-peak electricity rate    $0.063/kWh

           Electricity demand charge    $6.22/kW, 15 minutes

           Gas price                    $0.99/therm ($9.4/GJ)

           Water price                  $4.0/100 [ft.sup.3]

           Bore field cost              $10/ft ($32.8/m)

Table 2. Climates and Building Types in the Parametric Study

   Type                       Size                   Climates

Nine-month      92,000 [ft.sup.2] (8556 [m.sup.2])  Minneapolis

Retail Store    95,300 [ft.sup.2] (8863 [m.sup.2])  Atlanta

Continuous-use  76,000 [ft.sup.2] (7068 [m.sup.2])  Salt Lake

Office          127,000 [ft.sup.2] (11,811          Seattle

                                                    St. Louis



In order to optimize a HyGCHP system for a building/ climate scenario, the design variables listed below are simultaneously varied by the optimization engine.

* ground heat exchanger length

* cooling tower size

* cooling tower control set points ([DELA][T.sub.1] and [T.sub.Cool1] for high speed)

* GHX control set points ([T.sub.Cool2] for cooling, [T.sub.Heat1] for heating)

The design parameters are similar if a dry fluid cooler is used in place of a closed cycle cooling tower. The optimization was accomplished using the GENOPT software, a general optimization tool shown to be effective for energy simulations (Wetter 2007). Therefore, the optimal design of a HyGCHP system corresponds to the values of the design parameters (in the list above) that result in a minimum LCC for a given scenario. This design is identified by running an initial TRNSYS simulation and calculating a LCC, then allowing GENOPT to change the parameters (using the Hookes-Jeeves algorithm), after which the simulation is run again; this process is repeated hundreds of times until the optimization algorithm is satisfied that a minimum LCC was identified.


In order to develop guidelines for the design of hybrid ground source heat pump systems, a parametric study was carried out using the HyGCHP model. Simulations were run across a range of building load scenarios that included various climates and building types of interest, as summarized in Table 2 (each building/climate permutation was simulated, resulting in 4 x 6 = 24 scenarios).

Three equipment configurations were optimized for each building/climate combination, each with identical heat pump systems and each using the same economic and other assumptions. The equipment configurations include: boiler/tower, GHX-only, and hybrid ground-coupled (with cooling tower). A hybrid ground-coupled system with a dry fluid cooler was also studied for a subset of the building/climate combinations. The hourly building loads were created using an existing building model developed by ASHRAE-sponsored research project TRP-1120; the TRP-1120 project modeled a suite of buildings in order to provide expected hourly building loads for GCHP systems in different buildings and climates (CDH 2000; TESS 2000). The buildings listed in Table 2 were chosen because they were closest to the "normal" values for annual and peak loads identified in the TRP-1120 final report.


All the cases shown in Table 2 were simulated parametrically. The baseline results are summarized in Table 3. Some additional cases were run to determine the model's sensitivity to operating temperature, economics, ground properties, etc.; these results are not shown here, though a discussion of them can be found in Hackel (2008).
Table 3. Results of the Parametric Study with a Cooling Tower as
Supplementary Device--All LCC are for 20 Years and Given in Real
(i.e., Today's) Dollars

                               Costs   Optimal Design Parameters

Building         Climate       LCC,     GHX      Tower  Boiler
Type                          Real $   Length,   Size,  Size,
                                         ft      tons   kBtu/h


Retail        Atlanta         508452   13612.0   215.6    0.0

Retail        Salt Lake City  522373   23985.0   103.8    0.0

Retail        Phoenix         629974    5904.0   449.4    0.0

Retail        St. Louis       539216   22837.0   125.6    0.0

Retail        Seattle         371522   13079.0   121.3    0.0

Retail        Minneap.        504838   22263.0    0.0     0.0

School,       Atlanta         360575   15252.0   157.5    0.0

School,       Salt Lake City  447367   29725.0    3.1     0.0

School,       Phoenix         437491    5904.0   322.5    0.0

School,       St. Louis       418819   24272.0   60.0    0.0

School,       Seattle         307560   19106.0    0.0     0.0

School,       Minneap.        503311   13940.0    0.0     0.0

24-hr Office  Atlanta         562796   11931.0   195.6    0.0

24-hr Office  Salt Lake City  533351   16236.0   133.1    0.0

24-hr Office  Phoenix         660220    5617.0   392.5    0.0

24-hr Office  St. Louis       566215   16810.0   143.1    0.0

24-hr Office  Seattle         442594    9348.0   130.0    0.0

Office        Atlanta         609892   23985.0   178.1    0.0

Office        Salt Lake City  755061   47232.0    3.1     0.0

Office        Phoenix         677239    8487.0   571.9    0.0

Office        St. Louis       738561   43214.0   38.1     0.0

Office        Seattle         487884   23124.0   20.6     0.0


Retail        Atlanta         654396     0.0     333.1  1174.3

Retail        Salt Lake City  572458     0.0     372.5  1311.5

Retail        Phoenix         663154     0.0     525.6  1037.0

Retail        St. Louis       692140     0.0     368.1  1494.5

Retail        Seattle         430461     0.0     302.5  1128.5

Retail        Minneap.        651926     0.0     276.3  1723.3

School,       Atlanta         448391     0.0     363.8  899.8

School,       Salt Lake City  421423     0.0     236.9  1082.8

School,       Phoenix         433065     0.0     333.1  533.8

School,       St. Louis       463924     0.0     381.3  945.5

School,       Seattle         329039     0.0     298.1  579.5

School,       Minneap.        615686     0.0     197.5  6801.5

24-hr Office  Atlanta         683967     0.0     276.3  1082.8

24-hr Office  Salt Lake City  560936     0.0     280.6  1220.0

24-hr Office  Phoenix         662721     0.0     442.5  854.0

24-hr Office  St. Louis       699343     0.0     320.0  1448.8

24-hr Office  Seattle         458399     0.0     254.4  808.2

Office        Atlanta         683069     0.0     446.9  1357.3

Office        Salt Lake City  780900     0.0     302.5  1586.0

Office        Phoenix         721877     0.0     670.0  1220.0

Office        St. Louis       815356     0.0     530.0  1814.8

Office        Seattle         594352     0.0     302.5  1357.3


Retail        Atlanta         967707   97457.0    0.0     0.0

Retail        Salt Lake City  659379   52398.0    0.0     0.0

Retail        Phoenix         2430001  282572.0   0.0     0.0

Retail        St. Louis       744967   64165.0    0.0     0.0

Retail        Seattle         477951   36326.0    0.0     0.0

Retail        Minneap.        504838   22263.0    0.0     0.0

School,       Atlanta         512390   47232.0    0.0     0.0

School,       Salt Lake City  442755   29725.0    0.0     0.0

School,       Phoenix         1268993  146247.0   0.0     0.0

School,       St. Louis       449399   33456.0    0.0     0.0

School,       Seattle         307560   19106.0    0.0     0.0

School,       Minneap.        503311   13940.0    0.0     0.0

24-hr Office  Atlanta         1189983  121278.0   0.0     0.0

24-hr Office  Salt Lake City  807121   67609.0    0.0     0.0

24-hr Office  St. Louis       923776   83968.0    0.0     0.0

24-hr Office  Seattle         682370   55268.0    0.0     0.0

Office        Atlanta         873000   72488.0    0.0     0.0

Office        Salt Lake City  759051   47232.0    0.0     0.0

Office        Phoenix         2349957  266500.0   0.0     0.0

Office        St. Louis       747399   47232.0    0.0     0.0

Office        Seattle         493286   25420.0    0.0     0.0

                    Optimal Design Parameters (IP)

Building       [DELTA]     [T.sub.cool2],  [T.sub.Heat1],
Type          [T.sub.1],    [degrees] F      [degrees] F


Retail           23.2           48.2            55.4

Retail           28.0           61.7            62.2

Retail           22.5           87.4            51.4

Retail           18.6           37.4            70.3

Retail           26.4           59.0            63.5

Retail            0.0           50.5            70.7

School,          19.4           32.0            79.7

School,          57.2           37.4            70.3

School,          22.5           65.8            87.8

School,          16.2           53.6            87.8

School,           0.0           46.4           111.2

School,           0.0           28.9            28.9

24-hr Office     22.5           42.8           109.4

24-hr Office     27.2           67.1            64.9

24-hr Office     22.5           88.7           109.4

24-hr Office     18.6           37.4            62.2

24-hr Office     25.7           64.4           109.4

Office           19.4           57.7            85.1

Office           66.6           56.3            60.8

Office           23.3           84.7           109.4

Office           30.4           53.6            62.2

Office           39.0           55.0            41.9


Retail           25.9           90.5            60.4

Retail           26.7          102.7            77.9

Retail           21.2          117.5            41.5

Retail           24.3           90.5            83.3

Retail           28.2          117.5            42.8

Retail           28.2          117.5            99.5

School,          24.3           90.5            75.2

School,          29.0          100.0            94.1

School,          18.8           98.6            72.5

School,          21.9           97.3            94.1

School,          27.5          117.5            94.1

School,          20.4          117.5            44.2

24-hr Office     26.7           90.5            52.3

24-hr Office     28.2          101.3            46.9

24-hr Office     21.2          106.7            41.5

24-hr Office     26.7           90.5            48.2

24-hr Office     27.5          117.5            40.1

Office           16.4           98.6            77.9

Office           23.5           98.6            87.4

Office           18.0          117.5            44.2

Office           18.0           98.6            87.4

Office           26.7          101.3            64.4


Retail            0.0           68.0            62.6

Retail            0.0           46.4            76.1

Retail            0.0           78.8            68.0

Retail            0.0           46.4            74.8

Retail            0.0           46.4            68.0

Retail            0.0           50.5            70.7

School,           0.0           46.4           111.2

School,           0.0           54.5            70.7

School,           0.0           74.8            84.2

School,           0.0           46.4            89.6

School,           0.0           46.4           111.2

School,           0.0           28.9            28.9

24-hr Office      0.0           66.7            70.7

24-hr Office      0.0           46.4            72.1

24-hr Office      0.0           46.4            77.5

24-hr Office      0.0           61.3            59.9

Office            0.0           69.4            41.0

Office            0.0           58.6            58.6

Office            0.0           76.1            41.0

Office            0.0           46.4            69.4

Office            0.0           54.5           111.2

Optimal Design

The optimal design and cost results were compiled for all equipment configuration and building/climate combinations; more detailed results for each scenario can be found in Hackel (2008). Examination of these results suggest the design guidelines that are discussed in the sections below; these design guidelines should be applied with some caution, as they are based on specific economic and other assumptions summarized in Table 1.

a. GHX Sizing: Size the Ground Heat Exchanger (GHX) So That It Is Just Capable Of Meeting the Peak Heating Load. Figure 3 illustrates the optimal size of the ground heat exchanger (the sum of the entire bore field length) as a function of a peak heating load normalized by a ground temperature term. Each point in Figure 3 represents a different climate/building combination from the parametric study. Notice that the optimal GHX size is, to first order, proportional to the peak heating load, consistent with some design methods for HyGCHP systems that are currently used in the industry (e.g. GCHPCalc; Kavanaugh and Rafferty 1997). GHX size is inversely proportional to the ground temperature term, [[DELTA].sub.ground], which is the difference between the ground temperature and the minimum allowable fluid temperature, which is 35[degrees]F (1.7[degrees]C) in this study (this temperature difference is the main driver for heat transfer in the GHX).


The best fit linear regression to the data shown in Figure 7 is

[L.sub.tot] = [C.sub.1] [q.sub.peak,heat]/[DELTA][T.sub.ground], (4)

where [C.sub.1] = 254 ft*[degrees]F/(kBtu/h), [L.sub.tot] is the GHX length in ft., [q.sub.peak.sub.heat] is in kBtu/h. Equation 4 is equivalent to a GHX that can provide 152 ft/ton of heating at a ground temperature of 55[degrees]F and 87 ft/ton of heating at a ground temperature of 70[degrees]F. The assumed value of the ground conductivity ([k.sub.g]) used to generate these results is 1.4 Btu/ h*ft*[degrees]F (2.4 W/m*K), as listed in Table 1. Sensitivity studies have been carried out on [k.sub.g] (as well as several other parameters in Table 1 and suggest that every 0.1 Btu/ hr*ft*[degrees]F (0.17 W/m*K) decrease in k will result in a 5% increase in the optimal GHX size. In order to develop guidelines for the design of hybrid ground source heat pump systems, a parametric study was carried out using the HyGCHP model. Simulations were run across a range of building load scenarios that included various climates and building types of interest, as summarized in Table 2 (each building/climate permutation was simulated, resulting in 4 x 6 = 24 scenarios). The sensitivity of the optimal design to the economic parameters and operating temperatures is discussed below. See Hackel (2008) for a complete discussion of these studies.

b. Supplemental Device Size: Size the Supplemental Cooling Device Based on the Peak Cooling Load That Is Not Met by the GHX. The rated capacity of the optimally sized closed-circuit cooling tower ([C.sub.CCCT]) is found to be approximately 2.1 x the peak cooling load that cannot be met by the GHX ([q.sub.unmet]). The unmet cooling load is calculated according to Equation 5:


where [C.sub.1] = 3.05 ft/tons*[degrees]F, [q.sub.unmet] is the unmet cooling load (in tons), qpeak cool is the peak cooling load (in tons), and [L.sub.tot] is the total length of the bore field (in ft). The second term in Equation 5, [], is the cooling capacity of the GHX; notice that the cooling capacity is proportional to the length of the GHX (a longer GHX provides more cooling) and inversely proportional to the initial ground temperature (a cooler ground provides more cooling). Based on Equation 5, the optimal size of the cooling tower is

[C.sub.CCCT] = 2.1[q.sub.unmet, cool,] (6)

where [C.sub.CCCT] is the cooling tower capacity (in tons). The factor of 2.1 in Equation 6 suggests that, for the cooling tower characteristics and economic conditions considered in the parametric study, it is economically attractive to oversize the tower (by a factor of 2.1) so that it can be operated almost entirely at its low-speed condition. (The low fan speed assumed in this project is 50%). The setpoint for high-speed operation of the tower, [T.sub.Cooll], was always found to be 5[degrees]F-8[degrees]F (3[degrees]C-4[degrees]C) above the maximum entering heat pump temperature, implying that the tower is only operated at high speed in extreme conditions. If a single-speed tower must be used, then its size should be calculated using Equation 7, which implies that a single-speed cooling tower should only be oversized by 30%.


where Cx = 4.72 ft/tons*[degrees]F.

The optimal cooling tower size can also be estimated based on the unbalance in the building load. Figure 4 illustrates the optimal cooling tower size (normalized by the building size) for each scenario as a function of the ratio of the total annual heating load for the building to the total annual cooling load for the building. Sizing the cooling tower according to Figure 4 should lead to approximately the same result as using Equation 6.


When using a dry fluid cooler rather than a cooling tower as the supplementary device, the optimal sizes follow trends that are similar to those described above.

c. Ground Temperature Change: The Optimal Sizes and Control Setpoints Identified Here Never Balance the Load on the Ground. Balancing the load on the ground was generally not found to be economically optimal. Therefore, the ground temperature always increases over time (for cooling-dominated climates) by an amount that depends on the difference between the total annual heating and cooling loads. The timespan selected for the simulation, therefore, has a significant impact on the results; design guidelines presented here minimize the LCC over 20 years. This fact is demonstrated by an example in the section "Validation of Guidelines, Comparison to Existing Methods" below.

d. The Optimal Design of the System Does not Depend Substantially on the Economic Parameters Used in the Model. Although the LCCs are substantially affected by the economic parameters, the optimal size of the equipment is selected almost entirely based on meeting the specified loads (as discussed above). This result implies that it is rarely economically attractive to purchase a larger piece of equipment (e.g., a GHX that is larger than what is required to meet the peak heating load) in order to improve system efficiency. As a result, the design guidelines presented above for sizing the equipment are valid over a large range of economic parameters. In some sensitivity studies, fuel prices had to be more than doubled in order to affect the optimal equipment sizes.

e. Control Setpoints. The supplemental cooling device should be operated when conditions are favorable; that is, when the fluid temperature entering the device is greater than the ambient wet bulb (dry bulb for dry fluid cooler) + [DELTA][T.sub.1], where

[DELTA][T.sub.1] = 27[degrees]F (15[degrees]C) for a cooling tower if [T.sub.wb.sub.July] < 70[degrees]F (21 [degrees]C); 23[degrees]F (13[degrees]C) for a cooling tower if [T.sub.wb.sub.July] 70[degrees]F to 76[degrees]F (21 [degrees]C to 24[degrees]C); 20 [degrees]F (11 [degrees]C) for a cooling tower if [T.sub.wb.sub.July] > 76[degrees]F (24[degrees]C); 12[degrees]F (6.7[degrees]C) for all dry fluid cooler scenarios, and [T.sub.wb.sub.July] is the ASHRAE 1% design wet bulb temperature for the building's climate in July (ASHRAE 2005). The GHX cooling setpoint ([T.sub.Cool2]) is specified so that the GHX is bypassed only occasionally and generally only in warmer climates. The optimal value of [T.sub.Cool2] increases with more cooling-dominated buildings and should be selected based on the ratio of the peak cooling to peak heating load, as shown in Figure 5.


The GHX heating setpoint ([T.sub.Heat1]) should be set so that the GHX is never bypassed in heating mode; therefore, [T.sub.Heat1] should be set to a high temperature that is never reached in practice.

f. Operating Temperature Sensitivity: The Model Generally Optimizes the GHX to the Smallest Size Possible that Still Meets the Specified Low Temperature Limit; Lower LCC Will Often Result if Lower Minimum Temperatures Are Allowed. The operating temperature limits used in this study are presented in Table 1: the entering fluid temperature is not allowed to go below 35[degrees]F (1.7[degrees]C) or above 95[degrees]F (35[degrees]C) for the base cases shown above. The GHX was generally optimized to just meet the low temperature limit. When these limits were relaxed further, the optimizer tended to select a system that operated at minimum temperatures even lower than 35[degrees]F (1.7[degrees]C). The reduction in GHX first cost (up to 50% in many cases) from choosing a smaller system and operating at temperatures below 35[degrees]F were found to almost always offset the increase costs due to less efficient operation. These lower minimum temperatures should be considered for design if they can be safely tolerated over the life of the equipment.

It should be noted that a propylene glycol solution was modeled in these lower-temperature cases; the increased cost of using antifreeze, both in initial cost and added pumping power, was also more than offset by the decrease in first cost associated with a smaller GHX that is possible with lower minimum temperature.

Validation of Guidelines, Comparison to Existing Methods

Validation was included in the process of building the HyGCHP model. The key components used (GHX, heat pumps, cooling tower) were all independently validated before use by comparison to experimental or manufacturer data. The full HyGCHP model was compared directly to the results from the Fort Polk study upon completion (TESS 2005). Additional qualitative checks were also made for a few hybrid case studies.

Upon completion of the parametric study, the design guidelines that emerged were also critically evaluated. An example here will demonstrate the proper use of these design guidelines and compare the near-optimal design that is consistent with the design guidelines to the true optimal system that is identified by a comprehensive optimization using the HyGCHP simulation/ optimization program. For this demonstration, a typical cooling-dominated building was chosen: a large office building in Atlanta. This particular building has the characteristics summarized in Table 4:
Table 4. Characteristics of the Office Building in Atlanta Used in the
Following Example

      Characteristic                         Value

Building area              127,000 [ft.sup.2] (11,800 [m.sup.2])
Peak cooling load          222 tons (781 kW)
Peak heating load          2413 kBtu/h (707 kW)
Annual cooling load        3683 MMBtu/year (1079 MW*h)
Annual heating load        1905 MMBtu/yr (558 MW*h)
Ground temperature         62.0[degree]F (16.7[degree]C)
July wet bulb temperature  78.6[degree]F (25.9[degree]C)

1. An optimal design begins with equipment configuration. For this building, a hybrid system with a cooling tower was selected. (The next section will show that this is, in fact, the lowest cost option).

2. In order to size the GHX for this system, Figure 3 is used. For this location (with an initial ground temperature of 62[degrees]F (16.7[degrees]C) and the given peak heating load, the resulting GHX size is 23,125 ft (7049 m).

3. Next, the cooling tower is sized using Equation 6. With a total GHX length of [L.sub.tot] = 23,125 ft (7049 m), a peak cooling load of [] = 222 tons (781 kW), and ground temperature [T.sub.ground] = 62[degrees]F (16.7[degrees]C), the rated capacity of the optimally sized cooling tower is 209 tons (735 kW). Figure 4 can also be used to size the cooling tower; the ratio of the annual heating to annual cooling load for this building is 0.52, which suggests a cooling tower size of about 1.5 tons/1000 [ft.sub.2] (57 kW/1000 [m.sub.2]), or about 190 tons (669 kW). A size of 200 tons is chosen as the nearest nominal size (this is an oversized tower; the optimal system operates primarily at half speed).

4. With the equipment configured and sized, the control setpoints are chosen. Because the summer design wet bulb temperature in Atlanta is 78.6[degrees]F (25.9[degrees]C), the optimal value for [DELTA][T.sub.1] is identified as 20[degrees]F (11[degrees]C).

5. [T.sub.Cool2] is chosen to be about 61[degrees]F (16[degrees]C), based on Figure 5.

6. [T.sub.Heat1] is set to 100[degrees]F (38[degrees]C) so that the GHX is never bypassed in heating mode. [T.sub.Cool1] is set to 101[degrees]F (39[degrees]C), which is 5[degrees]-8[degrees]F (3[degrees]-5[degrees]C) above the maximum temperature limits, so that the cooling tower operates primarily at low speed.

The hybrid system for this same building was explicitly optimized using the HyGCHP model. In Table 5, the optimal design values that were selected by the optimizer are compared with the more approximate values selected using the design guidelines, as calculated above. All values computed with the design guidelines are within 10% of the optimal for this scenario.
Table 5. Optimal Design Values Determined with Two Different Methods:
(1) the Designh Calculation Discussed in Section "Validation of
Guidelines, Comparison to Existing Models" and (2) the Optimal Design
Values Determined by the HyGCHP Model

                               Design        HyGCHP     GCHP
                             Guidselines  Optimization  Calc

GHX Size, ft                    23125         23985     23600

Tower Size, tons                 200          178        150

[DELTA] [T.sub.1] ([DELTA]       20           19.4       N/A
[degrees] F)

[T.sub.cool2] ([degrees] F)      61           57.7       N/A

[T.sub.Heat1] ([degrees] F)     Never                    N/A

The results are also compared to the values obtained using the GCHPCalc software discussed by Kavanaugh and Rafferty (1997). This software matches the GHX size identified by this study. However, a direct comparison cannot be made between the tower sizes because GCHPCalc software assumes a single-speed tower and a different control algorithm. The size of the tower identified by GCHPCalc is smaller because there is no low-speed setting assumed for the tower, but there are also differences in how the GHX is utilized for cooling. This example also demonstrates the fact that optimal designs do not necessarily balance the load on the ground. Figure 6 displays the entering fluid temperature for the office example over a twenty-year period. Note the slight increase in temperature.


Cost Comparisons

The parametric study considered and optimized a GHX-only system, a boiler/tower system, and the hybrid ground-coupled system options for each building/climate combination. Therefore, meaningful comparisons can be made between these options based on LCCs.

a. In Most Moderate and Southern Climates, Hybrid Ground-Coupled Systems Have a Lower LCC than Other Options. The LCS of hybrid systems compared to GHX-only systems is proportional to the annual heating/ cooling load imbalance. Figure 7 illustrates the LCS (the difference between the LCCs) associated with using a hybrid system rather than a GHX-only system (these results are normalized by the building size) as a function of the ratio of the total annual heating load to the total annual cooling load for each building/climate scenario. Note that the savings associated with hybridizing a GHX-only system are negligible when the annual load ratio is greater than approximately 0.9. The LCS of a hybrid system relative to a GHX-only system is related to the decrease in the equipment cost associated with a smaller GHX, as well as increased efficiency associated with mitigation of ground temperature change over time. The savings associated with the reduction in the GHX cost alone is $7/[ft.sub.2] of building size ($75/[m.sub.2] of building size) in a climate like Atlanta, and decreases to $3/[ft.sub.2] ($32/[m.sub.2]) in the St. Louis climate.


The LCS associated with using a hybrid system rather than a boiler/tower system is only $1-$2/[ft.sub.2] of building size ($11-$22/[m.sub.2]). The LCS associated with using the hybrid system rather than the boiler/tower system increases with peak heating load and is negligible when the peak heating load is near zero. In this study, the LCC associated with using a dry fluid cooler in place of a closed-circuit cooling tower is essentially identical, although in some warmer climates the LCC was slightly higher with the use of a dry fluid cooler.

b. In Warm, Dry Climates (e.g., Phoenix), Buildings with Low Heating Loads Have Almost the Same LCC for a Hybrid and a Boiler/Tower System. In these climates the heating requirement, and therefore the GHX, is relatively small; the advantage of the GHX over the boiler is therefore minimized. Additionally, the disadvantage of the tower relative to the GHX is minimized by its effectiveness in a dry climate.

c. Unlike the Optimal Design Parameters, the Observed Costs and, therefore, LCS are Sensitive to Economic Parameters. As an example, when fuel inflation is increased to 7.5%, the LCS associated with using a hybrid system rather than a boiler/tower system doubles. The effect of GHX cost on the LCC was also studied. The LCS associated with using a hybrid rather than a GHX-only and a hybrid rather than a boiler tower system areboth shown in Figure 8 as a function of GHX cost. (These results are normalized by building size and represent the average across five random building/climate scenarios.) Notice that increasing the GHX cost tends to significantly improve the savings associated with using a hybrid system, as compared to a GHX-only system, due to the reduction in the GHX size that can be achieved with a hybrid system. However, increasing the GHX costs tends to reduce the savings associated with using a hybrid system as compared to boiler/tower system.



The goal of the project is to systematically and comprehensively optimize a hybrid system in order to minimize life-cycle cost, so that the characteristics of a well-designed hybrid system can be ascertained and studied and the relative advantage of a hybrid system relative to a GHX-only and boiler/tower system can be quantified. These results are meant to assist practicing engineers in selecting and designing HyGCHP systems, and the project has resulted in a powerful simulation/optimization tool as well as a series of more approximate design guidelines that are based on a parametric analysis of a matrix of building/climate combinations.

A HyGCHP model was created using TRNSYS and was set up for cooling-dominated scenarios, as shown in Figure 1. In order to develop design guidelines, parametric studies were carried out using the HyGCHP model, optimizing the system (for lowest LCC) for a number of building/climate permutations. The results from these studies were examined and compiled into a set of general design guidelines. These guidelines refine (but generally agree with) the commonly accepted idea that the GHX in a hybrid system should be sized so that it just meets the peak heating load, and the supplemental device should be sized to meet the remaining cooling load. The guidelines describe the sizing of the supplemental device in more detail and also describe an optimal control strategy. Additionally, observations regarding the effect of the operating temperature, lifespan, parameter sensitivities, and cost are made.


The authors are very grateful to Jeff Thornton for his assistance in understanding and modeling these systems. The support and programming expertise of Diego Arias is also much appreciated. The work described in this paper was supported by ASHRAE through TRP-1384 (with TC 6.8).


C =cost, $

[c.sub.p] = specific heat, Btu/lb*[degrees]F

d = depth, m/discount rate, --

F = scaling factor, --

i = inflation rate, --

k = thermal conductivity, Btu/ft*h*[degrees]F

L = length, ft

m = mass flow rate, lb/s

Q = volume flow rate, ft3/s

q, q = energy transferred, Btu; rate of heat transfer, Btu/h

[tau] = time, s

T = temperature, [degrees]F


cap = capacity

cool = cooling mode

eff = efficiency

fl = fluid (generally water or a glycol solution)

in = an inlet parameter

tot = total

wb = wet bulb temperature


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Scott Hackel is a graduate research assistant and Gregory Nellis and Sanford Klein are professors of mechanical engineering at the University of Wisconsin, Madison, WI.

Scott Hackel

Associate Member ASHRAE

Gregory Nellis, PhD


Sanford Klein, PhD


This paper is based on findings resulting from ASHRAE Research Project RP-1384.
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Author:Hackel, Scott; Nellis, Gregory; Klein, Sanford
Publication:ASHRAE Transactions
Article Type:Report
Geographic Code:1USA
Date:Jan 1, 2009
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