Experimentally validated modeling of a turbo-compression cooling system for power plant waste heat recovery

Accepted Manuscript Experimentally validated modeling of a Turbo-Compression cooling system for power plant waste heat recovery

Shane D. Garland, Jeff Noall, Todd M. Bandhauer PII:

S0360-5442(18)30868-5

DOI:

10.1016/j.energy.2018.05.048

Reference:

EGY 12881

To appear in:

Energy

Received Date:

13 December 2017

Revised Date:

16 April 2018

Accepted Date:

07 May 2018

Please cite this article as: Shane D. Garland, Jeff Noall, Todd M. Bandhauer, Experimentally validated modeling of a Turbo-Compression cooling system for power plant waste heat recovery, Energy (2018), doi: 10.1016/j.energy.2018.05.048

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ACCEPTED MANUSCRIPT

EXPERIMENTALLY VALIDATED MODELING OF A TURBO-COMPRESSION COOLING SYSTEM FOR POWER PLANT WASTE HEAT RECOVERY Shane D. Garland1, Jeff Noall2, Todd M. Bandhauer1* 1Interdisciplinary

Thermal Science Laboratory, Colorado State University, Fort Collins, CO 80524, USA 2Barber-Nichols Inc., Arvada, CO 80002, USA email: [email protected] phone: 970-491-7357 fax: 970-491-3827 Address: Colorado State University Department of Mechanical Engineering 1374 Campus Delivery Fort Collins, CO 80523

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HIGHLIGHTS   

Validation of TCCS model with UA scaling and turbo-compressor efficiency maps COP at off-design conditions predicted to within ±2.0% by the modeling approach Improved system performance predicted for power plant application with R152a

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ABSTRACT Waste heat recovery systems utilize exhaust heat from power generation systems to produce mechanical work, provide cooling, or create high temperature thermal energy. One system that provides a cooling effect is the turbo-compression cooling system, which operates by using low-grade waste heat to vaporize a fluid and spin a turbine in a recuperative Rankine cycle. The turbine power is used to directly drive a compressor in a traditional vapor-compression cycle. This study presents a theoretical modeling approach that uses compressor and turbine efficiency maps and a heat exchanger UA scaling methodology to make performance predictions over a range of ambient temperatures and cooling loads. The results of experimental testing for a 250 kWth TCCS showed good correlation (maximum error of 2.0%) for power and cooling cycle mass flow ranges of 0.35 kg s-1 to 0.5 kg s-1 and 0.65 to 0.85 kg s-1, respectively. The validated modeling approach was used to predict system performance for a Natural Gas Combined Cycle power plant application.

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1. INTRODUCTION Due to thermodynamic limitations and efficiency losses, nearly 70% of all energy produced in the U.S. is rejected as wasted energy [1]. Much of this wasted energy is rejected as low-grade heat in the form of exhaust gas or engine coolant, which emanate from two major contributors: electricity generation and transportation. Although this rejected heat is low temperature, there is still a tremendous amount of energy that can be salvaged by using a waste heat recovery (WHR) system. WHR systems convert the waste thermal energy into alternate forms such as mechanical work, cooling, or high temperature thermal energy. The heat from waste sources is fairly poor and most WHR systems operate at an exhaust temperature range up to 200°C [2]. However, by utilizing energy that is normally wasted, the entire energy ecosystem becomes more efficient, and there is potential to make significant reductions in the amount of CO2 dissipated into the atmosphere. WHR systems that convert heat into mechanical work often suffer from low efficiencies and power outputs due to Carnot limitations caused by the closeness between hot and cold reservoir temperatures. Due to these limitations, fluid selection for Rankine cycles has been studied extensively in an attempt to increase efficiency [3-12]. R245fa is a commonly selected fluid for low temperature waste heat applications (<130°C) with a study by Datla and Brasz finding a maximum efficiency of 14% [12]. Other studies have investigated using a recuperative heat exchanger to improve cycle efficiency. Dian-xun et al. compared multiple fluids in recuperative and non-recuperative cycles and found that, for fluid R601a, the system efficiency increased from 14.2% to 17.7% when adding a recuperator [6]. The efficiency limitations of power generation from waste heat sources has lead

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researchers to analyze and design WHR systems that produce a cooling effect. Some state of the art waste heat driven chillers include adsorption, absorption, organic-Rankine vapor compression (ORVC), and ejector systems. Single and double effect absorptions systems are most prevalent in the commercial market and typically have megawatt scale cooling capacities. Representative single and double effect systems have Coefficient of Performances (COP) of 0.75 and 1.6, respectively, while chilling water from 14°C to 7°C [13]. Adsorption systems are not as prevalent commercially due to their lower cycle efficiencies. However, one study showed an adsorption system had a COP of 0.5 at a 90.6°C waste heat inlet temperature [14]. ORVC systems and ejector systems both have advantages over absorption because they are able to reduce the size and complexity of the systems. Ejector systems, however, suffer from low COPs (between 0.2 and 0.4) due to ejector irreversibilities [15]. ORVC systems can have higher COPs, with a representative system having a COP of 0.58 at a waste heat source of 200°C [16]. One system that uses some of the lessons learned from previous ORVC and Rankine cycle research is a recuperative turbo-compression cooling system (TCCS) that operates with different power cycle and cooling cycle fluids. A basic process flow diagram of the TCCS is shown in Fig. 1. The system absorbs heat at the waste heat boiler of the Rankine cycle and vaporizes a fluid that flows through a turbine. The turbine power is directly transferred to the compressor via a hermetically sealed shaft that is made possible by a magnetic coupling. The compressor operates a vapor-compression system which provides the cooling effect in the evaporator. The hermetic seal between the turbine and compressor allows for two separate fluids on the power and cooling cycles, which maximizes the efficiency of the turbine and compressor simultaneously. There have

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been two previous studies to analyze the performance of the TCCS. One study modeled the TCCS in a full scale application for a 555 MW natural gas power plant and proved the overall heat transfer conductance (UA) of the dry-air heat exchangers could be reduced by 26% [17]. A second study focused on the performance of a TCCS at a 250 kWth cooling scale over a range of ambient conditions. In the study, the authors first determined the baseline performance of the TCCS (including heat exchanger UAs) and then created an off-design performance methodology while assuming the UAs remained constant at all conditions [18]. The present study modifies the offdesign modeling approach by adjusting the UAs based on the changing flow rates and temperatures that accompany the system in off-design conditions. This novel off-design technique allows computational effort to be decreased when investigating a wide range of operational conditions for the TCCS. First, the 250 kWth test facility is described in detail. Next, the modeling methodology is described including the UA scaling technique and turbo-machine efficiency calculation. Finally, the experimental results and modeling predictions are presented, compared, and discussed in detail. 2. TEST FACILITY DESIGN As shown in Fig. 1 and pictorially in Fig. 2, the TCCS test facility has two primary loops, one exhaust gas simulation loop, four condenser cooling towers, and one cooling water simulation loop. The primary loops are the power cycle and cooling cycle which are connected by the magnetically coupled turbo-compressor. The power cycle and cooling cycle fluids are HFE7000 and R134a, respectively. Both fluids were selected for their low toxicity and favorable heat transfer characteristics. The turbine and compressor are both centrifugal machines in which the shafts are connected by a magnetic coupling that allows the fluids to be separated from one another by a

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hermetic barrier can in the turbo-compressor (Fig. 3). This barrier allows magnets connected to the turbine and compressor shafts to transmit power while maintaining a high shaft efficiency (approximately 93%). The shaft bearings on the turbine and compressor are lubricated by liquid refrigerant from their respective cycles to reduce contamination from oil. The nominal operating speed of the unit is 30,000 RPM with a turbine power of 12.4 kW and a compressor power of 11.6 kW. By performing a turbo-machine cordier analysis, both the turbine and compressor performance were determined while they operate at 30,000 RPM. The custom designed heat exchangers are brazed aluminum construction that are either plate-fin or tube-fin. The condensers and waste heat boiler are both tube-fin construction, while the recuperator and cooling cycle evaporator are plate-fin. The exhaust simulation loop circulates hot air through the boilers to add energy to the power cycle. There is one condenser tower for the power cycle, and three for the cooling cycle. The condenser cooling tower fans pull air through the condensers in their respective loops to cool the working fluids. The cooling water simulation loop provides the chilling load for the cooling cycle evaporators and operates with a 30:70 mixture of propylene-gylol:water. The cooling water loop also interacts with an auxiliary boiler system (also 30:70 propylene-glycol:water mixture) to provide a heat source. There are many instruments in the test facility that provide the required data to calculate the work and heat duty of critical components. Absolute and differential pressure transducers were used to measure the pressure at various points, and the temperature was measured using T-Type thermocouples. The mass flow rate is another critical measurement, which is collected with high accuracy coriolis flow meters. The TCCS test facility was operated over multiple test days at an ambient temperature of

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27.5°C, which is higher than the design ambient temperature of 15°C. During the tests, the secondary side flow rates were held constant, with an exhaust mass flow rate of 7.0 kg s-1, power and cooling cycle condenser air mass flow rates of 23.2 kg s-1 and 51.6 kg s-1, respectively, and a cooling water mass flow rate of 10 kg s-1. There were four controlling factors for the tests, including the PC mass flow rate, the CC mass flow rate, the exhaust air inlet temperature, and the cooling water inlet temperature. The power cycle mass flow rate was controlled through a variable frequency drive to adjust the pump speed. The cooling cycle mass flow rate was controlled by adjusting the expansion valve position, which also set the pressure ratio, thus changing the required compressor work and cycle temperatures. The exhaust air and cooling water temperatures were adjusted by increasing the heat input into their respective simulation loops. Changing all of these variables allowed for a wide range of operating conditions at 27.5°C ambient. The performance across all operating conditions was calculated through thermodynamic relationships using data collected from instrumentation to calculate the fluid properties. Because many data points were collected during the tests, it was possible to determine the COP over a power cycle mass flow rate range of 0.35 – 0.5 kg s-1 and a cooling cycle mass flow rate of 0.65 – 0.85 kg s-1. The system was restricted to these mass flow rate ranges because of experimental limitations. At low cooling and power cycle flow rates, the compressor stalled and the system did not provide a cooling load. At high power cycle mass flows, the system was limited by boiler superheating and pump performance. Table 1 shows the relevant instrumentation that was required to determine cycle performance during these tests and the corresponding accuracy. Fig. 1 shows the location of the temperature, pressure, and mass flow rate instrumentation used for each loop to make the COP calculations. The

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accuracies of each of the instruments were used to calculate the uncertainty of the data as shown in Table 6. Further details regarding the test facility construction, equipment, or instrumentation can be found in reference [19]. The data collected during these tests were compared with a system model that utilizes scaled performance methodologies for the turbo-compressor and all of the heat exchangers. This modeling approach is described in the next section. 3. MODEL DESCRIPTION The current study seeks to determine the performance of the TCCS over a range of ambient temperatures and cooling loads and then make comparisons to the experimental data. Although there have been countless studies on thermodynamic systems, very few have modeled these systems at off-design conditions with fixed heat exchanger sizes. The major issue with simulation at off-design conditions is that the heat exchanger sizes are generally fixed, but the conditions within the heat exchangers change. For this reason, complex heat exchanger modeling is required to predict the saturation temperatures and pressures in the heat exchangers. The change in saturation conditions often impacts the efficiency of system turbo-machinery, further increasing modeling complexity. The high degree of complexity has created challenges for some studies to make comparisons with a system model. In one heat activated cooling study, by Wang et. al, an ORVC system was simulated for a military application in which the system produced 5.3 kW of cooling with boiler, condenser, and evaporator temperatures of 200°C, 48.9°C, and 32°C. During testing, however, the conditions at the condenser and evaporator were significantly lower, both being approximately 22°C. This prevented the team from validating their modeling approach [20]. In fact, most studies speculate on off-design system performance but only perform modeling at the

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design conditions. Domanski and McLinden have created a simplified refrigeration system model (Cycle11), which uses fixed heat exchanger sizes and an entering temperature difference to calculate the saturation conditions in the heat exchangers. One issue with the Cycle11 model is the lack of robust compressor modeling that could lead to inaccurate predictions [21]. The modeling approach presented in this study improves upon off-design prediction techniques, such as Cycle11, by utilizing heat exchanger scaling and turbo-compressor efficiency methodologies to predict system performance without complex heat transfer models. This model can be used to make informed decisions on operation in off-design conditions and can help optimize thermodynamic systems. The modeling approach presented in this study employs turbine and compressor efficiency maps [18] and a heat exchanger scaling methodology that accounts for the different operating conditions experienced in the test facility. The heat exchangers and turbo-compressor were both designed for use with cooling cycle fluid R152a, so the baseline thermodynamic calculations are performed using that fluid. However, experiments were conducted with a different cooling cycle fluid (R134a), and, therefore, the off-design modeling approach uses R134a as the working fluid. The first step in the modeling approach is to determine the thermodynamic state points at a baseline design case with ambient conditions of 15°C and a cooling load of 250 kWth. The heat exchanger UAs were calculated at the baseline case (assumptions shown in Table 2) to set the initial size of the system. In the off-design modeling, the baseline UAs were scaled according to the conditions and were used in conjunction with turbine and compressor performance maps to estimate TCCS performance.

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3.1. Assumptions and Baseline Thermodynamic System Calculations The thermodynamic state for the baseline case was determined based on system requirements for application of the TCCS in a power plant. The purpose of the power plant application is to utilize the exhaust flue gases to generate a supplemental cooling effect, thus reducing the size of the dry air cooling system (Fig. 4). A recent report by DOE/NETL for a 555 MW Natural Gas Combined Cycle (NGCC) Case 13, shows flue gas temperatures at 106°C and a cooling water temperature requirement of 16°C when the ambient conditions are 15°C [22]. The TCCS is able to reduce the size of the cooling system because it is driven by waste heat and the condensers can operate at higher saturation temperatures, which makes them more effective and reduces total dry air heat exchange area [17]. To achieve the reduction in cooling load and heat exchange area, the TCCS COP needs to be fairly high, with a target set at 2.1. The performance of the system will be possible due to highly effective heat exchangers and the high efficiency turbomachine. Calculating the thermodynamic states of the TCCS for a baseline design condition at an ambient of 15°C sets the initial UAs of the heat exchangers. These UAs can then be scaled and used with turbine and compressor efficiency maps to estimate performance at any condition. The assumptions for the baseline case, in which the TCCS delivers 250 kWth of cooling at 15°C ambient, are shown in Table 2. The fluids selected for the power and cooling cycles in the baseline case are HFE-7000 and R152a, respectively. The temperature of the chilled water was assumed to enter and exit the liquid-coupled evaporator at 17.15°C and 16°C, respectively, and the waste heat source was assumed to have a temperature of 106°C and flow rate of 31,363 m3 hr-1, which are consistent

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with the scaled version of a NGCC power plant [22]. The two air cooled condensers were assumed to be single pass cross flow heat exchangers, the boiler was two-pass cross-flow, and the recuperator and evaporator were assumed to be counterflow. All of the pressure drops for the heat exchangers were added to approximate realistic system performance, and the pressure drop in each of the lines between components was assumed to be 1 kPa. Because the turbine and compressor operate on the same shaft, the speed of the two are equal, and the transmission efficiency from the turbine to the compressor was assumed to be 93% based on previous estimates. The heat duties of the heat exchangers are calculated from conservation of energy equations, where the inlet and outlet enthalpies are found from property relationships. The efficiencies of the turbine compressor are determined from the definition of isentropic efficiency and are related between each other by a shaft efficiency relationship. The COP of the system is found by taking the cooling load and divided by heat and energy inputs: Q e COP   Qb  Wpump  Waux

(1)

The auxiliary power is a summation of the condenser fan, the waste heat blower, and the chilled water loop pump powers. The state points and heat exchanger heat duties allow for UA calculations as shown in the next subsection. 3.2. Baseline Heat Exchanger UA Calculation Calculating the heat exchanger overall heat transfer conductance (i.e., UA) is a proxy for the size of the heat exchangers. The phase change heat exchangers were split into sections (subcooled, two-phase, or superheated) and the heat duty for each section was found by applying an

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energy balance. The biggest challenge for this method is that the two fluids transfer heat flow in complex paths relative to each other. The three heat exchange styles are shown in Fig 5. The heat exchanger UAs were calculated using the -NTU method presented in Incropera and Dewitt [23]:

UA  NTU  Cmin

(2)

The NTUs are calculated separately for each heat exchanger using correlations based on the style (i.e. cross-flow, counterflow, etc.) and operating regime (i.e. sub-cooled, two-phase, or superheated) of the particular heat exchanger. The cross-flow heat exchangers (condensers and boiler) operate in two different regimes: between dry air and a single phase fluid, and between dry air and a two-phase working fluid. For the two-phase section, the NTU is calculated as follows:

NTU tp   ln 1   tp 

(3)

The NTUs for the single phase regions are determined iteratively by the following equation and assuming both fluids are unmixed:

 NTU 0.22  exp CrNTU 0.78  1     Cr 



 da  1  exp 



(4)

The heat capacity ratio ( Cr ) is defined as the ratio between the minimum and maximum heat capacity ratios as follows: Cr 

Cmin Cmax

(5)

The chiller and recuperator are counter-flow heat exchangers, and employ different correlations relating effectiveness and NTUs. The two-phase regions for the chiller is calculated in

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the same manner as the cross-flow, using Equation 3. The single phase regions, however, are calculated as follows:

  sp for Crsp  1  1   sp  NTU sp    1 ln   sp  1  for Cr  1 sp  Cr  1   Cr  1   sp sp   sp

(6)

The effectiveness for each heat exchanger region is found with the equation below:



Q Cmin  Tin 

(7)

The minimum heat capacity rate (Cmin) is determined by comparing the values mass flow rate multiplied by specific heat for the primary and the secondary fluids.

 Cmin  mCp

(8)

The primary fluid for the boiling and condensing heat exchangers is always the refrigerant, either HFE-7000 or R134a. The secondary fluid for the boiler, chiller, and condensers are exhaust air, 30:70 mixture of propylene-glycol:water, and ambient air, respectively. For the recuperator, the primary flow is the vapor refrigerant and the secondary flow is liquid refrigerant. The secondary side mass flow rate for each fluid section is calculated differently for counterflow vs. cross-flow heat exchangers. For cross-flow heat exchangers (condensers and boiler) the secondary mass flow rate is defined by the frontal area the air is passing through. Each section of the heat exchanger (sub-cooled, two-phase, or superheated) has a fraction of the total air mass flow that is proportional to the heat transfer area required for the heat duty of that section. The heat transfer area depends on the primary side conditions because the primary fluid side heat transfer coefficient for each

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section can change dramatically. For instance, the two-phase heat transfer coefficient is significantly higher (often an order of magnitude) than the single-phase section, so less heat transfer area is required in the two-phase region to obtain the same heat duty. The baseline areas for the cross-flow heat exchangers were known from a proprietary heat exchanger design model. Although the boiler is a two-pass configuration, the area calculation method was assumed to be single pass to simplify the calculation procedure. Therefore, a simple factor is used to determine the secondary mass flow:

m sec  m total Apercent,sec

(9)

Unfortunately, this method cannot be applied to counter-flow exchangers (chiller and recuperator) because the heat transfer area for each section utilizes the same fluid for subsequent sections. For simplicity, the secondary fluid mass flow rate is assumed to rely only upon on heat duty for the counter and cross-counter flow heat exchangers as follows:

 Q  m sec  m total   sec   Qtotal 

(10)

This simplification does not have a major effect on the results because, for the chiller, the twophase region has a large portion of the overall UA, and, for the recuperator, there is only one fluid regime so the changing heat duty has no effect on other regions. Table 3 shows the UAs for each heat exchanger calculated with secondary side flow rates from either equation 2 or 3. The area percentage shown in Table 3 was provided from a proprietary heat exchanger model. 3.3. Off-Design System Methodology Fig. 6 shows a flow chart describing the iterative modeling steps for the off-design

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performance methodology. To predict the fluid conditions for a data point, the power cycle mass flow, cooling cycle mass flow, ambient temperature, exhaust temperature, and cooling water temperature are input in the model along with guesses for the efficiencies and heat exchanger conditions. The ambient air, exhaust air, and cooling water flow rates were held constant because they did not change in the experimental design cases. As described below, instead of a detailed model for each heat exchanger, a scaling methodology is used to predict heat exchanger UA, which are then used in the -NTU equations to determine the new temperatures at each location in the system. The updated temperatures allow the saturation conditions in the heat exchangers to be found, which determines the properties required to predict compressor and turbine performance. In the following two subsections, the heat exchanger scaling and turbocompressor performance methods are described in detail. 3.3.1. Heat Exchanger Performance Scaling When the flow rates and temperatures for the fluids passing through the heat exchangers change, the UA for these components is likely to change. This can be determined from detailed heat exchanger models, but adds considerable computational complexity. Therefore, in the present study, a UA scaling methodology is employed for each heat exchanger to enable simulation over a wide range of conditions. In this method, the temperature assumptions from the baseline case (Table 2) are removed and replaced with scaled heat exchanger UAs that are dependent on the iteratively solved fluid conditions. By inputting the UA, the heat exchangers set the sub-cooling, saturation, and superheating temperatures. Table 4 shows the previous temperature assumption from the basic modeling and the UA replacement used for the off-design modeling. There are nine

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temperature assumptions required to solve the baseline model, and each of these assumptions needs to be replaced by a single UA value. Unfortunately, there are twelve UA sections for the heat exchangers. Therefore, two UAs for the boiler and the two condensers were combined into a single value, and the scaling was applied to the combined UA, while an equation that sums the two UAs is included. The split between the two UAs is determined iteratively using the system state points and scaled heat exchanger calculations. For example, the subcooled and two-phase UAs for the boiler are combined to a single UA. This combined UA allows the boiler saturation temperature to be calculated iteratively, and the subcooled and two-phase UAs are determined by the sum of these two values. The scaling methodology multiplies the baseline component UA by heat transfer coefficient, area, and fluid scaling factors to determine the new UA. First, the primary and secondary side resistances are found for the baseline approach, and the wall resistance and fin efficiencies were neglected because they had negligible effects on the UA change:

UAbase

 1 1    Rprim Rsecon 

  

1

(11)

The secondary side resistance value is found by calculating the secondary side heat transfer coefficient and heat exchange area. For air coupled heat exchangers with louvered fin geometries the heat transfer coefficient has been well characterized, and can be calculated with the correlation presented by Chang and Wang [24]. For the recuperator and chiller, the secondary heat transfer coefficient is calculated using the Dittus-Boelter relationship [25]. The secondary resistance is then calculated by multiplying the heat transfer coefficient by the air side heat transfer area. Calculating

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the secondary resistance allows for calculation of the primary resistance because the baseline UA is known. For any off-design calculation, the primary and secondary resistances are fixed at the baseline and then multiplied by heat transfer, area, and fluid scaling factors calculated from the off-design mass flow rates, temperatures, and pressures. A general form of the equation used to calculate the off-design UA is as follows:

 1 1 UAoff     Rprim f h,prim f A,sec f f Rsecon f h,sec f A,sec f f 

  

1

(12)

The heat transfer scaling factor (fh) is calculated by dividing the heat transfer coefficient of the offdesign case by the heat transfer coefficient of the baseline case. In most cases, the geometric conditions of the heat exchangers are neglected and either a modified heat transfer coefficient or a ratio of the Nusselt numbers is compared:

fh 

hbase Nubase  hoff Nuoff

(13)

The secondary side heat transfer coefficients are calculated using the Chang and Wang correlation for louvered fins (air) or the Dittus-Boeltler correlation (water). The primary side Nusselt numbers are calculated using Dittus-Boeltler [25] for single phase regions, Dobson and Chato [26] for condensing regions, and the Gungor and Winterton [27] for boiling regions. The area scaling factor (fA) is the percentage reduction of heat duty for the off-design design case compared with the baseline case. The heat duty for the particular section is divided by the total heat duty first to obtain the heat duty scaling factor as follows:

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 Q sec,base    Qtotal,base   fQ     Qsec,off    Qtotal,off  

(14)

Unfortunately, scaling the area by the only the heat transfer portion is insufficient because the heat transfer area is dependent on the convection coefficient applied to that heat transfer area. For example, if the heat transfer coefficient is lower than expected on either side, additional crosssectional area and, therefore, secondary fluid mass flow is needed. Therefore, equation 14 would not be adequate to determine the true area of each section because only scaling by the heat duty does not fully account for the change in mass flow rate and therefore heat transfer coefficient through the section. To account for the change in flow through the heat exchanger, the product of the heat duty and heat transfer coefficient scaling factors are multiplied as follows:

f A,sec  fQ f h

(15)

One will notice that in equation 12, the heat transfer factor is multiplied twice, once in the actual factor and once within the area factor. This is necessary to account for the two separate effects is causes: changes in the heat transfer coefficient and the required heat transfer area. The final factor used in the modeling was a fluid factor to account for the difference in maximum possible flow rate between the two cooling cycle fluids. This factor was used because the difference in the enthalpy of vaporization can be significant. For example, using the same chiller heat duty and inlet saturation temperature as the baseline conditions, the flow rate required for R134a in the baseline case is 1.4 kg s-1, versus 0.91 kg s-1 in the R152a design case. The enthalpy of vaporization for R152a is approximately 1.5× an R134a system (Fig. 7); therefore, at

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the same heat duty, the R134a system requires a flow rate 1.5× that of R152a. This difference causes the percentage of the baseline heat transfer area to be less for R134a, which causes the area factor in equation 8 to over-predict performance. As an example, if an R134a system had a cooling cycle mass flow of 0.75 kg s-1, the fraction of baseline mass flow would be 82% based on the value for R152a. This reduces to 53% if the equivalent R134a flow rate is used. The fluid factor seeks to correct this area by finding the percentage difference between the two mass flows compared to their theoretical baselines (R152a: 0.91 kg s-1 and R134a: 1.4 kg s-1).

f f,off 

m off m base,f

(16)

m off m base

(17)

f f,base  ff 

f f,base f f,off

(18)

By calculating the baseline resistances and the scaling factors required, equation 5 is used to determine the new heat exchanger UA under any operating condition. 3.3.2. Turbocompressor Performance To predict the efficiency of the turbine and compressor at any operating condition, compressor and turbine maps (Figs. 8 and 9) were utilized. The x-axis of the maps are relationships between the mass flow rate and the baseline mass flow, and the y-axis is a relationship between the enthalpy change and the baseline enthalpy change. There are several parameters required to calculate the x-axis (corrected mass flow) and yaxis (corrected ideal enthalpy rise) for the compressor and turbine. These parameters relate the

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current design condition to the original design condition and are presented by Mattingly [28]. The pressure ratio between the reference condition and current condition is defined as follows:



Pact Pref

(19)

The actual specific gas constant is found by dividing the universal gas constant by the molecular weight of the fluid. Ract 

Runiv MW

(20)

The actual compressibility factor (Z) is a function of the properties at the inlet of the compressor.

Z act 

Pact,inact,in RunivTact,in

(21)

The actual specific heat ratio is defined as the specific heat at constant pressure divided by the specific heat at constant volume (each evaluated at the inlet with property relationships):

 act 

Cpact Cvact

(22)

The critical velocity for the reference and actual conditions are calculated using the same equation which includes the specific heat ratio, gravitational constant, compressibility factor, specific gas constant, and temperature. Vcr 

2 gZRT  1

(23)

The critical velocity ratio and compressibility factors between reference and actual condition can now be determined as follows:

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V  cr   cr,act  Vcr,ref

  



γ 

2

2     ref  1 

 ref 



(24)  ref  ref 1

 act

(25)

2   act 1    act  1 

 act 

After calculating each parameter, the corrected mass flow rate and ideal enthalpy rise are found using the following equations:

m eq 

m  

heq 

 hideal



(26) (27)

By using equations 12 and 13, the compressor efficiency map is interrogated first to find the predicted speed and efficiency. If the compressor efficiency does not match the original guess, the guess is updated and the cooling cycle state points determined again. Next, the power cycle states are determined. However, the turbine map shows that as the speed lines become vertical, there are infinite possible enthalpy drops for a given mass flow rate. Therefore, the map must be interrogated using the speed and corrected ideal enthalpy. Because they are synchronous, the turbine speed is equal to the compressor speed, and the corrected speed is calculated as follows:

N eq 

22

N



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Using the state points, equation 13, and the equivalent speed, the turbine efficiency and the corrected mass flow rate are determined from the map, and the equivalent mass flow rate is calculated as follows:

m p,t,axis 

m p,t,eq N p,t,eq 10, 000

(29)

Now, equation 12 can be used to calculate the actual power cycle mass flow rate. If either the mass flow or the efficiency do not match the guesses, the turbine efficiency guess is updated and power cycle state points are determined again. After converging, the turbine and compressor power should be matched by the shaft efficiency as follows:

W

shaft  c Wt

(30)

If this is not true, then saturation temperatures and turbo-machine efficiencies should be updated and the entire model is iterated until the turbine map power is equal to the predicted shaft power. After the required turbine power multiplied by the shaft efficiency matches the required compressor power, the overall cycle COP is calculated using equation 1. The following section presents the results of the theoretical modeling compared with the experimental results. 4. RESULTS AND DISCUSSION The test COP as a function of cooling and power cycle mass flow rates are shown in Fig. 10. The plot shows system performance for a range of power and cooling cycle mass flow rates denoted by the COP contour lines. The cooling cycle mass flow rate is set based on the power cycle flow rate and the cooling cycle expansion valve position. Because the turbine directly drives the compressor at

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the same speed, the power transferred through the turbine affects the compressor work, and, therefore, cooling cycle mass flow. For each power cycle flow rate, there is a range of cooling cycle flow rates possible depending on the expansion valve position. A fully closed valve will produce a mass flow rate of zero, while a fully open valve will produce the maximum flow rate available. The upper left region represents the cooling cycle mass flow rate limitation due to the size of the expansion valve, with a less restrictive device allowing the cooling cycle mass flow rate to increase. As shown, the COPs for the system are fairly high compared with other heat activated cooling systems mainly due to the high saturation temperature at the cooling cycle evaporator. The TCCS was designed for a power plant application, in which the cooling water temperature is above the ambient condition [17]. In these applications, the heat from the power plants low pressure steam can be rejected directly to the chiller two-phase fluid, while the TCCS condenser temperature is on average higher than the circulating water in the cooling tower. Although previous studies have shown that the total heat exchanger UA can be reduced with low temperature lift, future studies with higher temperature lifts are planned. A representative evaporator saturation condition during the testing was 32°C which, although significantly less than the waste heat temperature, is high when making direct comparisons to other state-of-the-art heat activated cooling systems. For instance, the maximum theoretical (Carnot) COP for the three reservoir TCCS system was 7.5 with the low, medium, and high temperatures of 27.5°C, 35°C, and 106°C, respectively. In comparison, a representative single effect absorption system had a maximum theoretical COP of 2.35 with low, medium, and high temperatures of 7°C, 29.4°C, and 100.6°C, respectively [29]. Because the maximum theoretical COP of the TCCS is higher, it is expected that the COP is also higher than typical absorption systems.

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As shown in Fig. 10, the COP initially increases, but, at PC flows above 0.4 kg s-1, the COP decreases. This drop is likely caused by the expansion valve size and the varying exhaust gas and cooling water temperatures. The expansion valve size limits the mass flow rate allowed in the cooling cycle. Although the compressor has enough power, the small expansion valve limits the mass flow rate increase. The exhaust and cooling water temperatures also have a significant effect on performance, because they influence the boiler and chiller heat duties. The temperatures of both were adjusted throughout the tests to ensure appropriate amounts of superheated vapor were entering the turbo-compressor. If the degrees of superheating decreased dramatically, liquid slugs could have entered the turbo-compressor, causing damage to the blades. Figs. 11 and 12 show the inlet temperatures of the exhaust gas and cooling water streams. These data show that temperatures vary between tests, and that the exhaust gas temperature increases for higher flow rates. For example, at a PC mass flow of 0.4 kg s-1 the average exhaust temperature is 108°C, but for a mass flow of 0.5 kg s-1 the average is 111°C. This increase causes the boiler heat duty to increase, and, because, the chiller has minimal temperature change, the COP decreases at higher flow rates. These differences in expansion valve size limitation, exhaust inlet temperature, and cooling water inlet temperature were all taken into account during the theoretical modeling by using the same temperatures as seen in the test cases. Table 5 shows a comparison of four representative data points for varying power cycle mass flow and generally with a fully open expansion valve (i.e. maximum cooling cycle mass flow and COP). The cooling cycle evaporator and power cycle boiler heat duties are included because they have a direct influence on the system COP. The saturation conditions of each phase change heat exchanger are included because they provide a proxy for the accuracy of the

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UA scaling method. Table 6 shows the uncertainty in the calculation at a representative data point for the COP, evaporator heat duty, and boiler heat duty as 1.8 ± 0.02, 145 ± 1.3 kW, and 63 ± 1.3 kW, respectively. These uncertainties are consistent with the other data points in the data set that are shown in Fig 10. The uncertainties are so low because the COP largely depends on the heat duties of the boiler and chiller which can be computed accurately. The fluid undergoes a phase change in the boiler and chiller, dramatically increasing the outlet enthalpy compared to the inlet. In addition, the auxiliary power loads have minimal error due to the high accuracy of current transformer instrumentation. Having a low uncertainty in COP provides trust in the results. The first note when examining Table 5 is that the COP predictions are not very close to the experimental case, with the smallest error being 15.3%. Further examination reveals that the cooling cycle evaporator heat duty and auxiliary power loads are close in each case, but the power cycle boiler heat duty is significantly different, which causes a decrease in COP. This difference is most likely due to maldistribution of flow in the exhaust simulation loop during testing. Fig. 13 shows that the outlet temperature of the superheated vapor from the two boiler heat exchangers are not the same, and, differ by up to 15°C. This is likely caused by poor air flow distribution, non-uniform air temperatures, or a combination both of these effects. As a result, the maldistribution causes the model to under-predict the boiler heat duty because the model assumes the full flow rate is being utilized by the heat exchanger. Therefore, an equivalent air flow rate was determined to account for the maldistribution in air flow rate, and is a function of refrigerant flow rate as follows: Vp,b,a  27124m p  12972

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Using this correction, the model shows a significant improvement in prediction accuracy for the boiler heat duty and system COP calculations (Mod. Model in Table 5). For example, the boiler heat duty previously had the largest error of 40%, but was improved significantly to have a maximum error of only 5.6%. This large improvement drove the error in the COP calculation to very low levels. The maximum difference in COP between this modified model and the experimental data is 2.0%. Although the COPs aligned well between the two cases, the saturation temperatures of the heat exchangers did not always agree. The cooling cycle temperatures were fairly close throughout the initial three tests with differences less than 1.8°C, but there were some larger differences during the highest flow rate case, with maximum saturation temperature differences for the chiller and condenser of 3.7°C and 1.6°C, respectively. The power cycle saturation temperatures were predicted less accurately, which indicates the power cycle heat exchanger scaling was less accurate (i.e., maximum temperature differences of 4.5°C and 5.8°C for the boiler and condenser, respectively). The modeling approach was also used to generate a COP map similar to Fig. 10 for a detailed comparison of results. The predicted COP map (Fig. 14) shows similar trends to the experimental modeling approach, with some differences. The region of highest COP for the two maps is slightly different, with the experiment being a small region isolated around power cycle mass flow of 0.4 kg s-1, and the modeling results show an extended region of maximum COP for a power cycle mass flow between 0.4 kg s-1 and 0.44 kg s-1. For the modeling approach, the COP increases in a smooth, linear fashion when the power cycle flow increases beyond 0.45 kg s-1, while the experimental data follows a similar trend the path but not nearly as smooth. One potential use of the validated modeling approach is to predict the performance of the

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currently configured system when operating at the power plant design conditions noted in Table 2. The major difference between the baseline conditions and the currently configured system is that the cooling cycle uses R134a as opposed to the R152a for the power plant application. By analyzing the system with the current configuration, insights can be drawn on future system modifications. As mentioned in Section 3.1, the original performance targets of the system were to achieve a COP of 2.1 with high, medium, and low heat reservoir temperatures of 106°C, 16°C, and 15°C. In addition to operating at substantially different conditions, the evaporator (chiller) UA was substantially lower than originally predicted (i.e., 106 vs. 212 kW K-1). By operating at the design point conditions, it is anticipated that the COP of the system can be made substantially higher if the evaporator UA is increased. Fig. 15 shows the COP as a function of cooling cycle chiller UA for two different fluid cycle options: R134a and R152a. The first points at the left of the figure represent the system operating with the current smaller chiller. As the chiller UA is increased, the performance of both systems increases because there is more heat exchanger area available. However, there is a diminishing effect to this increase because the effectiveness of the heat exchangers approaches its maximum, which limits total chiller heat duty possible and thus the maximum COP for each cycle. For R134a, the maximum COP at the design conditions is 2.12, while for an R152a it is 2.25. These values indicate that R152a has superior fluid properties for this particular temperature range. Future experimental studies will focus on increasing the chiller size and changing the cooling cycle fluid to R152a. 5. CONCLUSIONS The current study validates a theoretical modeling approach with experimental data. The modeling approach used a UA scaling methodology along with turbo-compressor efficiency maps

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to determine TCCS system performance at any design condition. When a maldistribution factor was applied to the exhaust flow rate, the COP was predicted to with ±2.0% by the modeling approach, suggesting that the system scaling methodology is an applicable method for off-design performance prediction. This method can significantly decrease computational effort when investigating a wide range of operational conditions for the TCCS. Furthermore, the modeling approach should not be limited to the TCCS, and could be applied to any thermodynamic system to accurately predict off-design performance with similar styles of heat exchangers (i.e., crossflow and counter-flow). Finally, the approach was applied to the original power plant application to determine the chiller size requirement to meet a desired operation condition. The results of that analysis show that the current R134a system would not meet the COP target of 2.1, and upgrading to R152a would be required. Future work will involve modifying the facility to test at a variety of operational conditions to further validate the theoretical model over a broader range. ACKNOWLEDGMENTS The authors acknowledge the Department of Energy Advanced Research Project Agency-Energy (ARPA-e) for their support under contract DE-AR0000574. The authors also thank Robert Fuller, Jeff Shull, and Kevin Eisemann from Barber-Nichols Inc. and Ranga Sami and Michael Reinke from Modine Manufacturing Co. for their helpful insights and discussions.

NOMENCLATURE A

Area

COP

coefficient of performance

δ

off-design to design pressure ratio

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η

isentropic efficiency

ε

compressibility factor

γ

specific heat ratio

∆ℎ

enthalpy difference

(kW kg-1)

h

heat transfer coefficient

(kW m-2 K-1)

f

factor

𝑚

mass flow rate

(kg s-1)

N

speed

(RPM)

Nu

Nusselt number

𝑄

heat transfer rate

(kW)

R

thermal resistance

(kW K-1)

T

temperature

(°C)

θ

critical velocity ratio

UA

heat exchanger conductance (kW K-1)

𝑉

volumetric flow rate

(m3 hr-1)

𝑊

power

(kW)

Z

Compressibility factor

Subscipts and Supercripts a

air

act

actual

aux

auxiliary

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axis

axis

b

waste heat boiler

base

baseline

c

compressor

cond

condenser

co

cooling cycle

cor

corrected

cr

critical

e

evaporator

eq

equivalent

exh

exhaust

f

fluid

g

glycol

ideal

ideal

in

inlet

HEX heat exchanger h

heat transfer coefficient

liq

liquid

o

outlet

off

off-design

p

power cycle

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percentpercent prim

primary

pump pump Q

heat duty scaling factor

recup recuperator ref

reference

sat

saturated

sc

subcooled region

sec

heat exchanger section

secon secondary sh

superheat region

shaft

shaft

t

turbine

total

total

tp

two-phase region

univ

universal

vap

vapor

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List of Figures Fig 1. Turbo-compression Cooling Process Flow Diagram Fig 2. Overview of the TCCS facility. Fig 3. Turbo-compressor installed into facility. Fig 4. The TCCS is used to provide supplemental cooling system to a dry cooled version of the DOE/NETL Case 13 power plant. Fig 5. Heat exchanger designs for (a) single pass cross-flow (condensers), (b) two-pass crossflow (boiler), and (c) counterflow (recuperator and chiller). Fig 6. Off-design performance methodology flow chart. Fig 7. P-h diagrams for R152a and R134a vapor-compression cycles at the same baseline conditions. Fig 8. Compressor efficiency map Fig 9. Turbine efficiency map Fig 10. Measured system COP contours for various power and cooling cycle mass flow rates at a 27.5°C ambient condition. A representative uncertainty for COP is 1.8 ± 0.02. Fig 11. Variance in exhaust inlet air temperature for mass flow rates used to predict the system COP. Fig 12. Variance in cooling water inlet temperature for mass flow rates used to predict the system COP. Fig 13. Outlet temperature difference for the left and right boilers. Fig 14. Predicted system COP contours for various power and cooling cycle mass flow rates at a 27.5°C ambient condition using the modified modeling approach. Fig 15. Predicted performance of the system operating with cooling cycle fluid R134a and R152a over range of chiller sizes.

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List of Tables Table 1 Instrument range and accuracy for various instruments in the TCCS. Table 2 Component assumptions made for the baseline thermodynamic cycle model. Table 3 Heat exchanger UA calculation results and area percentage for the baseline case (15°C ambient). Table 4 UA-Temperature replacement combinations. Table 5 Experimental data and modeling comparisons for TCCS performance at Tamb = 27.5°C. Table 6. Results and uncertainty for power and cooling cycle flow rates of 0.4 kg s-1 and 0.74 kg s-1, respectively.

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Figures

Fig 1. Turbo-compression Cooling Process Flow Diagram

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Fig 2. Overview of the TCCS facility.

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Fig 3. Turbo-compressor installed into the facility.

Fig 4. The TCCS is used to provide supplemental cooling system to a dry cooled version of the DOE/NETL Case 13 power plant.

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(a)

(b)

(c) Fig 5. Heat exchanger designs for (a) single pass cross-flow (condensers), (b) two-pass cross-flow (boiler), and (c) counterflow (recuperator and chiller).

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Fig 6. Off-design performance methodology flow chart.

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Fig 7. P-h diagrams for R152a and R134a vapor-compression cycles at the same baseline conditions.

Fig 8. Compressor efficiency map

Fig 9. Turbine efficiency map

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Fig 10. Measured system COP contours for various power and cooling cycle mass flow rates at a 27.5°C ambient condition. A representative uncertainty for COP is 1.8 ± 0.02.

Fig 11. Variance in exhaust inlet air temperature for mass flow rates used to predict the system COP.

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Fig 12. Variance in cooling water inlet temperature for mass flow rates used to predict the system COP.

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Fig 13. Outlet temperature difference for the left and right boilers.

Fig 14. Predicted system COP contours for various power and cooling cycle mass flow rates at a 27.5°C ambient condition using the modified modeling approach.

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Fig 15. Predicted performance of the system operating with cooling cycle fluid R134a and R152a over range of chiller sizes.

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Tables Table 1 Instrument range and accuracy for various instruments in the TCCS. Instrument Type Range Accuracy Thermocouple All 1°C Diff. Pressure Transducer All 0.5% FS Pressure Transducer 0-15 PSI 1.5% FS Pressure Transducer 0-15 PSI 0-200 PSI, 1% FS 0-300 PSI Pressure Transducer, 0-200 PSI 1.5% FS 85°C to 125°C assumptions made for the Table 2 Component Pressurethermodynamic Transducer, cycle model. baseline 0-300 PSI 0.25% FS Omega Component Assumption Velocity Waste HeatFlow Boiler Meter, Two0-50 pass cross-flow m s-1 3% FS Flue Loop ΔPb,sc & ΔPsh = 0.2 kPa Velocity Flow Meter, ΔPb,tp = 1.2 kPa-1 0-20 mkPa s 0.2 + 9% MV ΔPp,exh = 0.2 Condenser Cooling Towers Tp,b,sat = 92.6°C Volumetric Flow Meter, Tp,b,sh = 103.5°C-1 ms 1% FS Texh0-6.1 = 106°C Cooling Water 3 -1  Vexh = 31,363 m -1hr Mass Flow Meter 0-7.5 kg s 0.15% MV Chiller Counterflow Power Meter AllkW 1% MV  = 250 (Liquid Coupled) Q e

ΔPe,tp = 19 kPa ΔPe,sh = 1 kPa Te,sat,o = 13.9°C Te,sh = 16.3°C Te,g,in = 17.2°C Te,g,o = 16°C Crossflow ΔPsh & ΔPsc = 0.2 kPa ΔPtp = 1.71 kPa Tcond,sat,o = 23.3°C Tcond,sc = 22.7°C 3 -1 Vcond,a = 135,000 m hr

CC Condenser (Air Cooled)

PC Condenser (Air Cooled)

Crossflow ΔPsh & ΔPsc = 1 kPa ΔPp,cond,tp = 8.8 kPa Tcond,sh = 29.4°C Tcond,sat,o = 23.9°C Tcond,sc = 23.0°C 3 -1 Vcond,a = 39,000 m hr

Recuperator

Counterflow ΔPliq = 1.45 kPa ΔPvap = 4.74 kPa ΔPline = 1 kPa Tamb = 15°C ηt = 80% ηcomp = 80% ηm = 93%

Other inputs Turbo-machine

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Table 3 Heat exchanger UA calculation results and area percentage for the baseline case (15°C ambient). Component

Section

Waste Heat Boiler

UAb,sc UAb,tp UAb,sh UAb UAe,tp UAe,sh UAe UAcond,sc UAcond,tp UAcond,sh UAcond UAcond,sc UAcond,tp UAcond,sh UAcond UArecup

Evaporator (Liquid Coupled) Power Cycle Condenser (Air Cooled) Cooling Cycle Condenser (Air Cooled) Recuperator

Area % for cross-flow HEX 0.15 0.49 0.36 0.07 0.91 0.02 0.11 0.87 0.02 -

UA [kW K-1] 4.14 4.80 1.11 10.1 105.3 1.52 106.8 0.08 10.05 0.03 10.2 0.11 79.4 1.34 80.9 2.53

Table 4 UA-Temperature replacement combinations. Component Waste Heat Boiler Evaporator CC Condenser PC Condenser Recuperator

Temperature assumption

UA replacement

Tb,sat Tb,sh Te,sat,o Te,sh Tcond,sc Tcond,sat,o Tcond,sc Tcond,sat,o Tcond,sh

UAb.sc + UAb,tp UAb,sh UAe,tp UAe,sh UAcond,sc UAcond,tp + UAcond,sh UAcond,sc UAcond,tp + UAcond,sh UArecup

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Table 5 Experimental data and modeling comparisons for TCCS performance at Tamb = 27.5°C. COP

Evap. heat duty [kW]

Test Model Mod. Model

1.74 1.26 1.77

127 123 125

Test Model Mod. Model

1.80 1.38 1.83

145 145 144

Test Model Mod. Model

1.68 1.35 1.70

146 143 142

Test Model Mod. Model

1.76 1.49 1.76

175 141 172

Boiler CC Aux. Chiller heat Condenser Power sat. temp duty sat. temp [kW] [°C] [kW] [°C] PC Mass Flow: 0.35, CC Mass Flow: 0.67 55.7 17.2 33.0 37.3 78.0 19.5 30.8 37.3 52.8 17.5 32.2 36.8 PC Mass Flow: 0.40, CC Mass Flow: 0.74 63.1 17.5 31.8 36.9 84.9 19.8 28.3 36.7 60.7 17.7 30.1 36.3 PC Mass Flow: 0.43, CC Mass Flow: 0.74 69.1 17.8 30.9 37.1 86.4 19.4 27.5 37.3 65.6 17.7 29.1 36.7 PC Mass Flow: 0.52, CC Mass Flow: 0.87 81.7 17.9 32.3 39.2 100 19.3 27.9 38.3 79.1 17.9 28.6 37.6

Table 6 Results and uncertainty for power and cooling cycle flow rates of 0.4 kg s-1 and 0.74 kg s-1, respectively. Parameter Result and Uncertainty COP 1.80 ± 0.02

Q p,b Q

63.1 ± 0.61 kW

Q p,recup Q

17 ± 0.41 kW 145.3 ± 1.3 kW

Q c,cond

148.7 ± 0.56 kW

p,cond

c,e

59.8 ± 0.49 kW

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Boiler sat. temp [°C]

PC Condenser sat. temp [°C]

72.9 75.2 68.4

45.4 41.9 40.6

76.7 79.4 73.3

43.1 39.8 38.0

79.8 80.9 75.9

43.2 39.7 37.7

85.9 87.3 83.2

43.8 42.0 38

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