## Abstract

The design optimization of a diesel exhaust-coupled heat and mass exchanger that drives a 2.71 kW cooling capacity absorption heat pump is presented in this study. Fouling layer thermal resistance and pressure drops from single-tube experiments are used to develop a thermodynamic, heat transfer, and pressure drop model for the exhaust-coupled desorber. A parametric study is performed to select a desorber design that meets system performance while minimizing footprint. Experimental heat duties and pressure drops are within 10% and 3%, respectively, of the model predictions. Thus, large data sets from single-tube experiments with representative geometries are successful in accounting for fouling effects at the component level. Desorber design optimization based on this approach ensures continued heat pump performance after fouling. This study, along with the single-tube experiments, presents a systematic approach to design exhaust-coupled heat exchangers while considering the effects of fouling. These results are applicable for a wide range of waste-heat recovery applications, and this method can be extended to different geometries and operating conditions.

## 1 Introduction

Although strides have been made toward increasing energy production from renewable and non-carbon emitting sources in the last several decades, the energy production from fossil fuels still makes up about 65% of total production in the United States [1]. In addition, approximately two-thirds of the primary energy released in the combustion of fossil fuels, typically for the conversion of thermal-to-mechanical energy, is rejected as waste heat. Rattner and Garimella [2] demonstrated that waste-heat recovery has the potential to reduce US primary energy demand by 12% and CO2 emissions by 13%.

Thermally driven absorption heat pumps can use waste heat to provide cooling or heating. Recent advances in miniaturized heat exchanger technology, which yield greater heat fluxes, have led to the development of absorption heat pumps with cooling capacities ranging from 300 W to 10.5 kW [36]. This enables the use of absorption heat pumps in applications with distributed sources of waste heat from internal combustion engines in vehicle air-conditioning, refrigerated trucking, and small-scale power generation. This requires a heat exchanger that couples the exhaust to the heat pump, either directly or through an intermediate heat transfer fluid. Exhaust gases contain particulate matter and hydrocarbons that have the potential to be deposited on the heat transfer surface, resulting in the buildup of a fouling layer that can reduce heat exchanger performance. Previous work by Aiello et al. [7] quantified heat transfer resistances resulting from fouling layer deposition and investigated underlying fouling mechanisms through single-tube experiments. These findings are used in the present study to guide the design of an exhaust gas coupled desorber for a 2.71 kW cooling capacity ammonia-water absorption heat pump that meets system performance requirements after fouling has occurred.

A review of studies that address the fundamental deposition mechanisms of particulate matter and unburned hydrocarbons in exhaust gas recirculation (EGR) coolers appears in Aiello et al. [7]. Thermophoresis, i.e., particle motion caused by a temperature gradient, has been shown to be the dominant mechanism for particulate matter deposition. This mechanism increases with decreasing coupling fluid temperature, causing an increase in deposit layer thermal resistance and exhaust pressure drop. Hydrocarbon condensation also increases with decreasing coupling fluid temperature. This increases deposition mass; however, liquid hydrocarbons have a much higher thermal conductivity than the porous particulate matter deposit layer. For this reason, conflicting results on the effect of hydrocarbon condensation on deposit layer thermal resistance and exhaust pressure drop have been presented in the literature. Deposit removal mechanisms have also been found to limit fouling layer growth. The primary mechanisms include flow-induced shear and water condensation. Flow-induced shear was found to remove deposit at exhaust flowrates of 42 m s−1 or greater, and water condensation has been shown possible for coupling fluid temperatures below the dew point of approximately 49 °C.

A few researchers have considered the effects of fouling on exhaust-coupled heat exchanger design. Mavridou et al. [8] developed a numerical algorithm to compare the performance of shell-and-tube heat exchangers with smooth, dimpled, or finned circular tubes with that of plate-and-fin heat exchangers with plain fins or metal foam inserts. The algorithm used a value of 1.76 m2 K kW−1 for the fouling resistance on the exhaust side for all the heat exchangers considered. A design and modeling analysis of a heat recovery system for an ammonia-water absorption refrigeration system was performed by Fernández-Seara et al. [9]. The system was designed to extract the waste heat from diesel engine exhaust for onboard trawler chiller fishing vessels and consists of a gas-to-liquid economizer coupled by a synthetic oil to the desorber of the absorption refrigeration plant. The exhaust flowed over the shell side of the economizer at an inlet temperature of 300 °C with synthetic oil on the tube side at a maximum temperature of 190 °C. A critical factor in the sizing of the economizer was the fouling factor on the exhaust side. Fin spacing was limited to 5 mm to prevent blockage, and a fouling heat transfer resistance of 21.23 m2 K kW−1 was implemented. These values were based on the results of Semler et al. [10], who investigated fouling of a finned-tube diesel engine flue gas heat recuperator.

While these studies have considered the fouling resistance in exhaust-coupled heat exchanger design, no investigations that optimize heat exchanger design to minimize additional heat transfer area requirements and pressure drop penalties due to fouling have been reported. Moreover, fouling varies widely based on exhaust temperature, composition, heat exchanger geometry, and coupling fluid temperatures. These factors are not sufficiently considered in the literature when selecting fouling resistance values for heat exchanger design. This could result in exhaust gas coupled heat exchangers that are significantly over or under-sized. The viability of waste-heat recovery systems is strongly dependent on cost-effectiveness and compactness; therefore, accurate sizing of the exhaust-coupled heat exchanger is critical. The use of thermodynamic model-based parameter optimization for designing components in a thermal system has been demonstrated [11,12].

The present study uses fouling results from single-tube experiments with geometries and operating conditions to develop the desorber of a 2.71 kW absorption heat pump. A thermodynamic model is developed, and the design is optimized to limit the effect of fouling by considering fouling thermal resistance and pressure drops at various fluid conditions and heat exchanger geometries.

## 2 Desorber Model Framework

The desorber of an absorption heat pump uses the thermal input to the system to separate the refrigerant vapor from a concentrated solution of the refrigerant in an absorbent. The desorber drives a 2.71 kW ammonia-water absorption heat pump developed by Staedter and Garimella [13] (Fig. 1). A heat transfer and thermodynamic model of the desorber is developed in Engineering Equation Solver (EES) [14] to design a fouled desorber that would still meet performance requirements. Desorber model boundary conditions are obtained from a cycle model developed by Goyal et al. [15]. The inputs are an inlet exhaust temperature of 398.8 °C, exhaust flowrate of 23.5 g s−1, concentrated solution temperature of 137.6 °C, dilute solution temperature of 190.4 °C, and solution pressure of 2889 Pa. The worst-case fouling results from the experiments of Aiello et al. [7] at a variety of exhaust flowrates, henceforth referred to as single-tube experiments, are also used as inputs to the model. In the single-tube experiments, a total of four tube-in-tube heat exchangers were used with exhaust gas flowing in the inner tubes and coolant flowing in the annulus. With these inputs, the model predicted the total heat transfer rate, vapor generation rate, vapor concentration, and the exhaust pressure drop. These parameters are used in the design of the desorber. A segmented modeling approach is used for improved heat transfer performance prediction. The segments are split vertically by desorber trays and horizontally by the two exhaust gas passes, as shown in Fig. 2. The segments are numbered to follow the flow of the exhaust through each desorber column.

Fig. 1
Fig. 1
Close modal
Fig. 2
Fig. 2
Close modal
The inlet exhaust temperature to the first segment is known from the heat pump cycle model, while the inlet exhaust temperature to each subsequent segment is taken as the outlet temperature of the previous segment. The inlet liquid and vapor properties of each segment are also taken to be the outlet properties of the previous segment. Due to the serpentine flow of the vapor and liquid through the desorber, the previous segment depends on the location of the segment. Consider segment three in Fig. 2, the liquid enters from segment four, while vapor enters from segment twelve. The qualities of the liquid and vapor streams entering and exiting each segment are assumed to be zero and unity, respectively. The solution pressure is also assumed to be constant throughout the desorber. With the knowledge of enthalpy or temperature of the upstream segment, the inlet states of liquid and vapor for each segment are defined. The outlet fluid conditions are determined through a mass, species, and energy balance, as shown in the following equations:
$m˙l,in,i+m˙v,in,i=m˙l,out,i+m˙v,out,i$
(1)
$m˙l,in,ixl,in,i+m˙v,in,ixv,in,i=m˙l,out,ixl,out,i+m˙v,out,ixv,out,i$
(2)
$Q˙i=m˙l,out,ihl,out,i+m˙v,out,ihv,out,i−m˙l,in,ihl,in,i−m˙v,in,ihv,in,i$
(3)
A conservative assumption is made to account for the heat and mass transfer resistance between the vapor and liquid. Due to the counter-flow orientation between the liquid and vapor, it is assumed that the outlet vapor temperature is at an average of the inlet vapor temperature and the inlet liquid temperature, as shown in Eq. (4)
$Tv,out,i=(Tv,in,i+Tl,in,i)/2$
(4)
The vapor outlet temperature is used to determine the vapor outlet concentration and enthalpy. The system of equations is closed by employing a heat transfer resistance network to calculate heat transfer in Eq. (3). The heat transfer rate is calculated based on the overall heat transfer conductance and log mean temperature difference between the exhaust and solution, as shown in Eq. (5)
$Q˙i=UAiΔTlm,i$
(5)
The exhaust and solution are in counter-flow in the first pass and co-flow in the second pass, and the log mean temperature difference is determined using the equations for the respective flow direction. The UA in each segment is the inverse of the thermal resistance, which is a combination of the exhaust, fouling layer, wall, and solution resistances as follows, as shown in Eqs. (6) and (7).
$Ri=Rtube,inp,tubes$
(6)
$Rtube,i=Rex,i+Rfoul,i+Rwall,i+Rs,i$
(7)
The exhaust stream convective resistance is dependent on the exhaust heat transfer coefficient, which is predicted using the correlation of Churchill [16]. The fouling resistance is calculated based on the resistivity measured in single-tube experiments, as shown in Eq. (8). Using the resistivity accounts for differences in tube length
$Rfoul,i=R′foul,i/Lseg$
(8)
The wall resistance is calculated based on radial conduction. The resistance of the ammonia-water solution is determined from the boiling heat transfer coefficient of 3000 W m−2 K−1 measured by Delahanty [17] for similar desorber geometries. The thermal resistance, UA, heat transfer rate, and the outlet liquid temperature and concentration for each segment are calculated in this manner. The vapor generation rate and concentration from the desorber column are taken to be the outlet of the final segment for vapor flow (i = nseg/2) which is the seventh segment in Fig. 2. The total heat transfer rate in a column is the sum of the heat transfer in each segment, as shown in Eq. (9):
$Q˙=∑i=1nsegQ˙i$
(9)
The exhaust-side pressure drop is another important parameter for the design of the desorber. The total pressure drop must not exceed the back-pressure limit of the generator. The Kohler 10REOZDC diesel generator used in this study has a back-pressure limit of 12 kPa. Accounting for the pressure drop in the exhaust piping upstream of the desorber, the pressure drop limit was adjusted to be 9.3 kPa. The desorber design is chosen so that the exhaust side pressure drop does not exceed this limit. The exhaust flowrate through each parallel tube in the desorber is assumed to be equal. The major pressure drop in an exhaust tube is calculated for each segment using Eq. (10), with the friction factor determined from Churchill [18] correlation. The major pressure drop for a clean tube is multiplied by the pressure drop ratio from single-tube experiments to predict the pressure drop of a fouled tube. The pressure drop ratio is defined as the ratio of pressure drop after steady-state fouling was achieved to the initial pressure drop with clean tubes.
$ΔPex,maj,i=(ΔPΔPo)fex,iDtube,I58π2m˙ex2Lsegρex,i$
(10)

Calculation of desorber heat duty, vapor generation rate, and pressure drop with this framework provide the basis for desorber design.

## 3 Desorber Design

Desorber performance is optimized by varying the numbers of parallel tubes and tube passes. The number of parallel tubes is varied either by changing the number of tubes in each column or by adding another column in parallel. The number of tube passes through the solution is varied by adding columns in series. A single column has two tube passes; therefore, adding a second column results in four passes, a third in six passes, and so on.

### 3.1 Effect of Geometry.

The effects of changing tubes per pass and the number of passes on desorber heat duty and exhaust pressure drop are analyzed for a desorber without fouling in Fig. 3. As the number of tubes per pass increases, the mass flowrate of exhaust through each tube decreases. This explains the trend of decreasing pressure drop with increasing tubes per pass. Pressure drop is proportional to the square of velocity, which explains the asymptotic approach of pressure drop towards zero as the number of tubes per pass increases and velocity decreases. The heat transfer rate for both the two and four pass cases initially increases with the number of tubes per pass reaches a maximum near 22 tubes per pass, decreases until about 38 tubes per pass, and again begins to increase. This trend is explained by Fig. 4, which shows an exhaust heat transfer coefficient and flow area as a function of the number of tubes per pass. Increasing the number of tubes per pass causes a decrease in gas velocity and Reynolds number, which results in a decrease in the heat transfer coefficient. Gas flow becomes laminar at about 38 tubes per pass, for which the heat transfer coefficient is constant with varying Reynolds number. The exhaust-side heat transfer area increases proportionately with the number of parallel tubes. The exhaust-side surface area and the heat transfer coefficient define the exhaust side thermal resistance, which is the dominant resistance in the desorber. Due to the increasing area and decreasing heat transfer coefficient, the resistance reaches a minimum at about 22 tubes per pass, causing a maximum heat transfer rate. The increasing area is outweighed by the decreasing heat transfer coefficient from about 22 to 38 tubes per pass, causing a decrease in heat transfer rate. As the heat transfer coefficient becomes constant at 38 tubes per pass, the heat transfer rate increases due to increased surface area.

Fig. 3
Fig. 3
Close modal
Fig. 4
Fig. 4
Close modal

The effect of the number of tube passes is also demonstrated in Fig. 3. A comparison is made between a series and parallel configuration of two baseline desorber column designs. This allows for comparison on an equal basis such that the designs have the same total heat transfer area. The series configuration corresponds to four passes of 11 tubes while the parallel configuration corresponds to two passes of 22 tubes. Connecting the two columns in series results in double the exhaust flowrate per tube and double the total tube length as compared with the parallel configuration. This results in an approximately eight-fold increase in exhaust-side pressure drop. The increased flowrate per tube in the series design results in a greater exhaust heat transfer coefficient than in the parallel designs. This causes a reduction in the exhaust thermal resistance and a 25% greater heat transfer rate.

### 3.2 Incorporating Single-Tube Fouling Results.

The 3.8 kW heat duty of the parallel desorber configuration without fouling is used as the target value to be achieved by the fouled desorber. To select the fouled desorber design, the thermal resistance and pressure drop ratio results are used over a range of exhaust flowrates tested in the single-tube experiments Each of the flowrates correspond to a different number of tubes per pass in the desorber design. A parametric study is performed to evaluate six different designs. Designs with fewer tubes per pass require six passes, whereas designs with more tubes per pass require only four passes. The per-tube exhaust flowrate, number of tubes per pass, number of passes, and total tubes for each design are summarized in Table 1.

Table 1

Desorber designs evaluated in parametric study

Desorber designExhaust flowrate per tube (g s−1)Tubes per passNumber of passesTotal number of tubes
12.98648
22.111666
31.714684
41.4176102
51.417468
61.122488
Desorber designExhaust flowrate per tube (g s−1)Tubes per passNumber of passesTotal number of tubes
12.98648
22.111666
31.714684
41.4176102
51.417468
61.122488

Fouling results are input into the model based on the particular flowrate and the tube location in the desorber. For example, the fouling resistance and pressure drop ratio measured in the first tube-in-tube heat exchanger at a flowrate of 2.1 g s−1 are input for the tubes in the first pass of the desorber design with 11 tubes per pass. Similarly, the results from the second tube-in-tube heat exchanger are input for the second pass, and so on. The fouling experiments were either performed with two or four tube-in-tube heat exchangers, which corresponds to two- or four-tube passes. Therefore, fouling measurements are not made for tubes in the final two desorber passes. To account for this, the fouling results of the last tube-in-tube heat exchanger in the experiments are used for the final passes in the desorber model. This is a conservative estimate as it was found that fouling effects were larger in upstream heat exchangers.

The fouling resistances input into the model are a result of 10 h of exhaust exposure, and the fouling resistance had not yet reached a steady-state. The steady-state fouling resistance and pressure drop are predicted by multiplying the 10 h results by the ratio of the 24 h to 10 h results in the experiment performed to steady-state at worst-case conditions. The 24 h to 10 h fouling resistance and pressure drop ratios were 1.5 and 1.6, respectively. Using these factors allowed for a prediction of the steady-state fouling effects based on the 10 h results.

### 3.3 Parametric Design Optimization.

The predicted steady-state desorber heat transfer rate and pressure drop are presented in Fig. 5 for each of the desorber designs investigated. The heat transfer target of 3.8 kW and the pressure drop limit of 9.3 kPa are also shown on the plot. The four designs with 14 or greater tubes per pass have predicted pressure drops less than the limit. Of these designs, the only one that meets the heat transfer requirements has six passes of 17 tubes. However, the six-pass, 14-tube and four-pass, 22-tube designs only fall short of the heat transfer target by about 5%. The total number of tubes for these two designs, 84 and 88 tubes, respectively, is much less than the 102 total tubes in the six-pass, 17-tube design. The additional tubes result in a desorber that is larger and heavier than the other designs. For this reason, the six-pass, 17-tube design is considered less preferable in comparison to the six-pass, 14-tube and four-pass, 22-tube designs. The six-pass, 14-tube (6:14) and four–pass, 22-tube (4:22) designs had very similar predicted heat transfer results, and further examination of the vapor generation rate and purity of the two designs is required. Design 6:14 requires three desorber columns in series, while design 4:22 requires two series columns. Schematics of the two designs with the model predicted inlet and outlet fluid conditions and heat transfer rates are shown in Fig. 6. In this comparison, the dilute solution outlet temperature was specified, and the concentrated solution inlet flowrate was allowed to vary for each column. Numeric values of model inputs are shown in framed labels. Beginning with design 6:14, the heat transfer rate in the first column is greatest and decreases for each subsequent column. The heat transfer rate in the last column is 30% less than that in the first column, which shows the need for having the additional column. As a result of the decreasing heat transfer rate, the concentrated solution inlet flowrate also decreases in each column to maintain the same dilute solution outlet temperature. Similarly, the vapor generation rate decreases with each column, and the vapor temperature increases. Overall, the desorber assembly has a heat transfer rate of 3.65 kW and a vapor generation rate of 1.745 g s−1. The trends for heat transfer rate and vapor generation rate between each column of the four–pass, 22 tube design match that of the six-pass, 14-tube design. The heat transfer rate for the assembly is 3.60 kW, which is slightly less than that of the other design. This also results in a 2% lower vapor generation rate, but these differences were not significant enough to eliminate either design.

Fig. 5
Fig. 5
Close modal
Fig. 6
Fig. 6
Close modal

One concern with a three-column design is the potential for variation of vapor purities and temperature between columns. This is not observed with the present model because the dilute solution outlet temperature was specified for each column. Achieving identical dilute solution temperatures with different heat transfer rates requires a variation of concentrated solution flowrates. In actual heat pump design and operation, a flow control device would be required to tailor the solution flow of each column in this matter, increasing overall cost and complexity. To determine the effect of eliminating the flow control devices, the concentrated solution inlet flowrate to each column is specified to be equal. This represented a case in which a flow balancing header is used to distribute the flow equally. The total flowrate to the desorber assembly is taken to be the total predicted flowrate of the model while specifying a dilute solution temperature. The results of specifying concentrated solution flowrate are shown in Fig. 7.

Fig. 7
Fig. 7
Close modal

While the combined dilute solution outlet temperature of both desorber assemblies is still 190 °C, the dilute solution outlet temperature of each column ranges from 178 to 204 °C for design 6:14 and from 180 to 200 °C for design 4:22. This causes a greater variation in vapor outlet temperature and a slightly lower vapor concentration as compared to the previous model. The lower purity is more than compensated for by a greater vapor generation rate such that the total amount of ammonia generated is greater for the equal solution flowrate case. The overall heat transfer rates are also slightly greater for this case because the temperature difference between the exhaust and coolant is greater in the latter columns. While having three columns instead of two produces slightly greater variation in vapor concentration between each column, the differences are not large enough to cause concern for system operation.

### 3.4 Desorber Design Selection.

In comparing both designs and examining differences in heat transfer rate, vapor generation rates, and vapor concentrations, neither design provided a significant advantage over the other to justify a selection based on these criteria. A three-dimensional computer-aided design model was developed to determine the size and weight of each design. For the purposes of validating the fouling results in this study, simulation desorbers were designed with a single-phase inlet and outlet. The simulation desorbers contain identical exhaust side geometry without detailed solution side fin-tray design required for liquid–vapor interaction. Given that the dominant thermal resistance is on the exhaust gas side, single-phase simulation of the solution side allowed for more accurate determination of fouling resistances of each column and more flexible experimental operation.

The exhaust tubes are 254.1 mm in length, 12.7 mm in outer diameter, and have a wall thickness of 0.9 mm. The tubes for Design 6:14 are contained in a stainless steel pipe with 144 mm outside diameter (OD) and a wall thickness of 6 mm, while the tubes for Design 4:22 are contained in a 168 mm OD stainless steel pipe with a wall thickness of 11 mm. The working fluid pressure requires a greater wall thickness for the larger shell diameter. Baffles are installed in the shell to improve tube stability, promote the serpentine flow of the coolant, and increase coolant heat transfer coefficient. The tubes are joined to the top and bottom of the outer shell with a 6.3 mm thick plate. A pipe cap is placed on the top plate to serve as the exhaust header. The size, weight, and total heat transfer area of the two designs are compared in Table 2. The footprint and weight of Design 6:14 are much less than that for Design 4:22, with a minimal decrease in the heat transfer area. Therefore, the six-pass, 22 tube design is selected as the most desirable for meeting system performance requirements and limiting the component size and weight for incorporation into a heat pump. This design is fabricated for testing and validation of fouling results and heat transfer performance.

Table 2

Comparison of the physical characteristics of the simulation desorber designs

Desorber designFootprint (m2)Heat transfer area (m2)Weight (kg)
Six-pass, 14 tubes0.0210.80922.7
four-pass, 22 tubes0.0450.84738.5
Percent difference−54%−5%−41%
Desorber designFootprint (m2)Heat transfer area (m2)Weight (kg)
Six-pass, 14 tubes0.0210.80922.7
four-pass, 22 tubes0.0450.84738.5
Percent difference−54%−5%−41%

The fabricated simulation desorber column is shown in Fig. 8. The coolant inlet and outlet are placed in a similar location as the concentrated solution inlet and dilute solution outlet of the actual desorber to create similar temperature profiles. The bottom view of the desorber shows the placement of the tubes within the shell. The tubes are spaced to account for desorber internal tray geometries not included in the simulation desorber. The three-simulation desorber columns are sealed to an exhaust header. The header routes the exhaust through each pass of the entire assembly and contains the ports for exhaust pressure and temperature measurement. The subassemblies of the simulation desorber columns and the header are shown in Fig. 9.

Fig. 8
Fig. 8
Close modal
Fig. 9
Fig. 9
Close modal

## 4 Data Analysis

The heat transfer rate from the exhaust in each column is calculated based on the exhaust specific heat, exhaust mass flowrate, and the inlet and outlet exhaust temperature, as follows:
$Q˙ex,i=m˙excp,ex,i(Tex,i−Tex,i+1)$
(11)
The subscript i specifies the column number. The specific heat is calculated based on the average exhaust temperature and composition. The total desorber heat transfer rate from the exhaust is the sum of the heat transfer in each column. The total heat transfer rate to the coolant in the desorber assembly is calculated based on the total coolant flowrate, specific heat, and the inlet and outlet mixture temperatures of the entire desorber assembly, as shown in Eq. (12).
$Q˙c=m˙ccp,c(Tc,out−Tc,in)$
(12)

Total exhaust and coolant heat transfer rate measurements are compared to ensure accurate heat transfer rate measurement.

The total thermal resistance in each column is calculated using the ɛNTU method for a shell-and-tube heat exchanger as presented by Bergman et al. [19]. The effectiveness of each column is defined as the ratio of the heat transfer rate to the maximum heat transfer rate in Eq. (13). The maximum heat transfer rate is calculated based on the exhaust inlet temperature, coolant inlet temperature, and the minimum heat capacitance rate of the two fluids. In this case, the exhaust has the minimum heat capacitance rate and is used to calculate the maximum heat transfer rate in Eq. (14).
$εi=Q˙c,iQ˙max,i$
(13)
$Q˙max,i=m˙excp,ex,i(Tex,in,i−Tc,in,i)$
(14)
The number of transfer units (NTU) for a shell-and-tube heat exchanger with a single shell pass and any even number of tube passes is dependent on the ratio of the heat capacitance rates, Cr, and the heat exchanger effectiveness. The relationship presented by Bergman et al. [19] is shown in Eqs. (15) and (16).
$Ei=2/εi−(1+Cr,i)(1+Cr,i2)1/2$
(15)
$NTUi=−(1+Cr,i2)−1/2lnEi−1Ei+1$
(16)
NTU is defined as the ratio of the overall heat transfer conductance to the minimum heat capacitance ratio, and the UA for each column is calculated with Eq. (17). The thermal resistance of each column is the inverse of the overall heat transfer conductance, as shown in Eq. (18).
$UAi=m˙excp,ex,iNTUi$
(17)
$Ri=1/UAi$
(18)
Assuming that the resistance through each tube is equal, the total resistance of all of the tubes is represented by Eq. (19).
$Ri=Rtube,i/np,tubes$
(19)
The resistance from the exhaust to the coolant for each individual tube is a series combination of the exhaust convective resistance, fouling resistance, wall resistance, and the coolant resistance, as follows:
$Rtube,i=Rex,i+Rfoul,i+Rwall,i+Rc,i$
(20)

The coolant heat transfer coefficient is calculated using the method of Kern [20], who developed a correlation for shell-and-tube heat exchangers with a baffle cut of 25%. The wall resistance is calculated for radial conduction through a hollow cylinder, and the exhaust convective resistance is calculated using the correlation of Churchill [16].

The effect of fouling on pressure drop for each column is also analyzed. Pressure drops between the inlet and outlet header of each column in the desorber experiments are measured. The ratio of the friction factor to the diameter of the fouling layer to the fifth power is calculated from Eq. (21) and is used to determine the pressure drop ratio, in Eq. (22).
$ΔPex,i=fiDfoul,i58π2m˙ex,pt2Ltubeρex,i$
(21)
$ΔPex,iΔPex,o,i=fi/Dfoul,i5fo,i/Dtube,I5$
(22)

The friction factor of a clean tube is determined from the Churchill [18] correlation.

## 5 Experiments

### 5.1 Experimental Facility and Procedure.

The desorber fouling experiment is performed at the worst-case fouling conditions determined from the single-tube experiments, corresponding to the lowest coolant temperature, the diesel generator operating at full load, and simultaneous start-up of the generator and heat pump. The target exhaust flowrate is 23.5 g s−1. The average conditions of the experiment throughout its duration are summarized in Table 3. The generator load and coolant temperatures in the experiment match the target values well, but the exhaust flowrate is 12% less than the target. The average conditions of the experiment are used in the desorber model to compare model predictions and experimental results.

Table 3

Summary of conditions in desorber fouling experiment

ConditionTarget valueExperimental value
Exhaust flowrate (g s−1)23.520.6
Exhaust inlet temperature (°C)398.8420.3
Coolant inlet temperature (°C)95.394.9
Coolant outlet temperature (°C)160.4158.6
ConditionTarget valueExperimental value
Exhaust flowrate (g s−1)23.520.6
Exhaust inlet temperature (°C)398.8420.3
Coolant inlet temperature (°C)95.394.9
Coolant outlet temperature (°C)160.4158.6

A Kohler 10REOZDC 10 kW diesel generator is used to produce the exhaust for the experiments. A Scotcher Model 627 0–10.8 kW adjustable load bank is used to control generator power output. Coolant temperature measurements are made at the inlet and outlet of each heat exchanger with Omega T-type thermocouples, and the flowrate through each heat exchanger is measured using Flow Technology FTO-1 turbine flowmeters. Temperatures of the exhaust stream are also measured at the inlet and outlet of each heat exchanger with Omega J-type thermocouples. The exhaust flowrate through the heat exchangers is measured using a Coin wedge meter and a Rosemount 3051S differential pressure transducer. These measurements allow the heat transfer rate to be calculated for both the exhaust and coolant in each heat exchanger. Additional details of the facility can be found in Aiello et al. [7].

In the experiment, the desorber assembly is exposed to exhaust continuously until a fouling steady-state is achieved. The fouling resistance of each column (Fig. 10) grows quickly initially and begins to level off with time. The fouling resistance reaches a steady-state, which is defined as a less than 2% change for two consecutive hours, after 27 h of exhaust exposure. This is similar to the 23 and 24 h it took to reach a steady-state in single-tube experiments at worst case and design conditions, respectively. Comparing the differences between individual columns, the steady-state fouling resistance of the first and second columns is approximately equal, while that of the third column is noticeably lower. The change in pressure drop throughout the experiment provides some insight into this phenomenon.

Fig. 10
Fig. 10
Close modal

### 5.2 Experimental Results.

The pressure drop ratio results shown in Fig. 11 follow the same trends as the fouling resistance. At steady-state, the pressure drop ratio of the first column is greater than that of the second column, which is in turn greater than the pressure drop ratio of the third column. This is different from the fouling resistance values, which are approximately the same for the first and second columns. A similar trend was observed in single-tube experiments for the second and third tube-in-tube heat exchanger, which had very similar fouling resistances but the pressure drop of the third tube-in-tube heat exchanger was less than that of the second. This was found to be due to the difference in thickness and thermal conductivities of the two fouling layers. In the second heat exchanger, the fouling layer was thicker and more conductive, but that of the third heat exchanger was thinner and less conductive. The larger diameter of the third heat exchanger resulted in a lower pressure drop, but the lower conductivity caused greater fouling resistance. A similar trend most probably caused this in the first and second columns in the present desorber experiment.

Fig. 11
Fig. 11
Close modal

Photographs of the bottom plate of each desorber column after the 27 h of exhaust exposure are compared with an image of a clean bottom plate in Fig. 12. A soot layer covered the portions of the bottom plate exposed to the exhaust and the inside surface of the exhaust tubes. A few tubes in the center of the third column do appear to have fouled more than the others, but this is due to a gasket material that extended over a portion of the tube inlet. The remainder of the tubes appears to have fouled uniformly, which suggests the equal distribution of exhaust flow between the tubes in each column. The fouling resistance and pressure drop results do suggest differences in fouling layer thickness between the columns; however, the fouling layer thickness of the first and fourth heat exchanger in the single-tube experiment only differed by 360 µm (∼3%). This would be difficult to observe without a magnified image. The comparison of any of the fouled columns with the clean column shows an 8–10% reduction in the exhaust tube diameter and illustrates the importance of accounting for fouling in the design of the desorber.

Fig. 12
Fig. 12
Close modal

## 6 Discussion

To evaluate the ability of the single-tube experiments to predict the fouling resistance in the desorber, a direct comparison is made between the measured steady-state fouling resistances. The fouling resistance in the desorber experiments is calculated for the inlet and outlet pass of each column, and the length of the tube used to calculate the resistance in the desorber experiments is about twice the length of each tube-in-tube heat exchanger. To compare the fouling resistances from the two experiments on an equal basis, the resistivity is calculated using Eqs. (23) and (24) for the single-tube and desorber experiments, respectively:
$Rfoul′=RfoulLannulus$
(23)
$Rfoul′=Rfoul(2Ltube)$
(24)

The data analysis of the desorber experiments provides one fouling resistance for each column, but the single-tube experiment provided fouling resistances for both the inlet and outlet tube in each column. Therefore, the fouling resistance per unit length for both the first and second tube-in-tube heat exchangers is compared with the fouling resistance in the first column, and the fouling resistance per unit length for the third and fourth tube-in-tube heat exchangers is compared with the fouling resistance in the second column. The fouling resistance in the third column does not have a direct comparison to the single-tube experiments as this would have required six tube-in-tube heat exchangers.

The final fouling resistance of the desorber is generally greater than that of the tube-in-tube heat exchangers, as shown in Fig. 13. The results of the two experiments show the best agreement for the first column, with the fouling resistance of both the first and second heat exchanger of the single-tube experiments falling within the uncertainty of the fouling resistance of the first column. The fouling resistance in the second and third columns is greater than that in the third and fourth heat exchangers.

Fig. 13
Fig. 13
Close modal

A potential reason for the greater fouling resistance is the lower exhaust mass flowrate per tube in the desorber experiment than in the single-tube experiment. Greater exhaust flowrates result in greater velocities, which were found to have a significant effect on the steadying of fouling layer growth in the single-tube experiments. If fouling reaches a steady-state because of a balance between reduced thermophoretic deposition and removal due to flow-induced shear, steady-state would not have been reached until the exhaust velocity reaches the threshold for deposit removal. At a lower mass flowrate, more fouling was required to reach the threshold velocity as the inner diameter of the tube must be smaller to achieve the same velocity. This could be the reason for both greater fouling resistance and the additional time required to reach a steady-state in the desorber experiment.

The pressure drop ratios of the first and second column are slightly greater than those for the corresponding heat exchangers of single-tube experiments, as shown in Fig. 14. The pressure drop in the third column is significantly less than that in the second column, which is used to predict the pressure drop in the third column for the desorber model. This should result in less pressure drop than the model prediction for the third column. In general, the pressure drop ratio results between the two experiments show better agreement than the fouling resistance results.

Fig. 14
Fig. 14
Close modal

For direct comparison between the model predictions and the measured performance of the desorber, the exhaust inlet temperature, coolant temperatures, and exhaust flowrate from the desorber experiment are used as inputs to the model. The single-tube fouling results at worst-case conditions are used in the model to obtain values for heat transfer and pressure drop performance of the desorber. The measured heat transfer rates in the experiment are compared with the target heat transfer rates predicted by the model in Fig. 15. The heat transfer rates in the first column are approximately equal, while the measured heat transfer rates of the second and third columns are lower than the model predictions. This trend is attributed to the greater fouling resistance of the second and third columns in the desorber experiments than in the single-tube experiments. The total heat transfer rate of the desorber is 9.6% less than the target heat transfer rate predicted by the model.

Fig. 15
Fig. 15
Close modal

It is observed from Fig. 16 that the measured and predicted pressure drops are about equal in the first column, the measured pressure drop is slightly greater in the second column, and the pressure drop in the third column is less than predicted. The greater difference between the model and the experiments for the third column is due to the use of the fourth tube-in-tube heat exchanger pressure drop ratio in the model, which has been found to be greater than the pressure drop ratio in the third column. The total exhaust pressure drop is 4.7 kPa, which is 2.6% greater than the predicted value. This pressure drop value cannot be compared directly to the back-pressure limit of the generator because it is at a lower exhaust flowrate. The model predicted pressure drop at the design exhaust flowrate is 8.3 kPa. A 2.6% increase results in a pressure drop of 8.5 kPa, which is less than the back-pressure limit of 9.3 kPa.

Fig. 16
Fig. 16
Close modal

In this study, fouling due to exhaust is minimized by optimizing the heat exchanger geometry and configuration. The use of surface coatings and exhaust emission treatment devices, such as diesel particulate filters, should be investigated in the future for reducing fouling in exhaust-coupled heat exchangers.

## 7 Conclusion

A heat transfer, thermodynamic, and pressure drop model of the desorber in a 2.71 kW cooling capacity absorption heat pump is developed to predict component performance under the influence of diesel engine exhaust fouling. A parametric study is performed varying desorber geometry and utilizing fouling thermal resistance and pressure drop results obtained from single-tube experiments at representative conditions. Parametric study results provide a desorber design that minimizes additional size and weight requirements to maintain system performance despite the effects of fouling. The results from the desorber experiments are within 10% of model predictions, demonstrating the ability of representative single-tube experiments to simulate full component fouling. The importance of choosing appropriate fouling resistance values, which are highly dependent on the operating conditions, geometry, etc., is highlighted. The optimized desorber design ensures consistent heat pump performance for direct-coupled waste-heat recovery applications under the influence of a variety of engine exhaust streams.

## Acknowledgment

The authors acknowledge the financial support for this research through Advanced Research Projects Agency (ARPA-E), Department of Energy, USA Award No. DE-AR0000370

## Conflict of Interest

There are no conflicts of interest.

## Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request. The authors attest that all data for this study are included in the paper.

## Nomenclature

• f =

Darcy friction factor

•
• h =

heat transfer coefficient, W m−1 K−1

•
• k =

thermal conductivity, W m−1 K−1

•
• x =

concentration by mass

•
• A =

area, m2

•
• D =

diameter, m

•
• L =

length, m

•
• P =

pressure, Pa

•
• R =

thermal resistance, K W−1

•
• T =

temperature, °C

•
• V =

velocity

•
• $m˙$ =

mass flowrate, kg s−1

•
• $Q˙$ =

heat transfer rate, W

•
• R′ =

resistivity, K W−1 m−1

•
• cp =

specific heat, J kg−1 K−1

•
• Nu =

Nusselt number

•
• NTU =

number of transfer units, K−1

•
• $Pr$ =

Prandtl number

•
• $Re$ =

Reynolds number

•
• UA =

overall thermal conductance, W K−1

### Greek Symbols

• Δ =

Differential

•
• μ =

dynamic viscosity, kg m−1 s−1

•
• ρ =

density, kg m−3

### Subscripts

• c =

coolant

•
• cs =

concentrated solution

•
• des =

desorber

•
• ds =

dilute solution

•
• ex =

exhaust

•
• foul =

fouling

•
• i =

segment number

•
• in =

In

•
• IT =

inner tube

•
• l =

liquid

•
• L =

length

•
• lm =

log mean

•
• O =

outer

•
• OT =

outer tube

•
• out =

out

•
• pt =

per tube

•

•
• s =

solution

•
• v =

vapor

## References

1.
US EIA
,
2020
, “
Annual Energy Outlook 2020
,”
US Energy Information Administration
,
Washington, DC
.
2.
Rattner
,
A. S.
, and
Garimella
,
S.
,
2011
, “
Energy Harvesting, Reuse and Upgrade to Reduce Primary Energy Usage in the USA
,”
Energy
,
36
(
10
), pp.
6172
6183
. 10.1016/j.energy.2011.07.047
3.
Determan
,
M. D.
, and
Garimella
,
S.
,
2012
, “
Design, Fabrication, and Experimental Demonstration of a Microscale Monolithic Modular Absorption Heat Pump
,”
Appl. Therm. Eng.
,
47
, pp.
119
125
. 10.1016/j.applthermaleng.2011.10.043
4.
Garimella
,
S.
,
Keinath
,
C. M.
,
Delahanty
,
J. C.
,
Hoysall
,
D. C.
,
Staedter
,
M. A.
,
Goyal
,
A.
, and
Garrabrant
,
M. A.
,
2016
, “
Development and Demonstration of a Compact Ammonia–Water Absorption Heat Pump Prototype With Microscale Features for Space-Conditioning Applications
,”
Appl. Therm. Eng.
,
102
, pp.
557
564
. 10.1016/j.applthermaleng.2016.03.169
5.
Staedter
,
M. A.
, and
Garimella
,
S.
,
2018
, “
Development of a Micro-Scale Heat Exchanger Based, Residential Capacity Ammonia–Water Absorption Chiller
,”
Int. J. Refrig.
,
89
, pp.
93
103
. 10.1016/j.ijrefrig.2018.02.016
6.
Kini
,
G.
,
Chandrasekaran
,
S.
,
Tambasco
,
M.
, and
Garimella
,
S.
,
2020
, “
A Residential Absorption Chiller for High Ambient Temperatures
,”
Int. J. Refrig.
,
120
, pp.
31
38
. 10.1016/j.ijrefrig.2020.08.022
7.
Aiello
,
V. C.
,
Kini
,
G.
,
Staedter
,
M. A.
, and
Garimella
,
S.
,
2020
, “
Investigation of Fouling Mechanisms for Diesel Engine Exhaust Heat Recovery
,”
Appl. Therm. Eng.
,
181
, p.
115973
. 10.1016/j.applthermaleng.2020.115973
8.
Mavridou
,
S.
,
Mavropoulos
,
G. C.
,
Bouris
,
D.
,
Hountalas
,
D. T.
, and
Bergeles
,
G.
,
2010
, “
Comparative Design Study of a Diesel Exhaust gas Heat Exchanger for Truck Applications With Conventional and State of the art Heat Transfer Enhancements
,”
Appl. Therm. Eng.
,
30
(
8
), pp.
935
947
. 10.1016/j.applthermaleng.2010.01.003
9.
Fernández-Seara
,
J.
,
Vales
,
A.
, and
Vázquez
,
M.
,
1998
, “
Heat Recovery System to Power an Onboard NH3-H2O Absorption Refrigeration Plant in Trawler Chiller Fishing Vessels
,”
Appl. Therm. Eng.
,
18
(
12
), pp.
1189
1205
. 10.1016/S1359-4311(98)00001-5
10.
Semler
,
T.
,
Bogue
,
J.
,
Henslee
,
S.
, and
Casper
,
L.
,
1982
,
Fouling of a Finned-Tube Diesel-Flue-gas Heat Recuperator
,
Idaho National Engineering Lab.
,
Idaho Falls (USA)
;
Honeywell, Inc., Plymouth, MN (USA)
.
11.
Xiong
,
Q.
,
Yeganeh
,
M. M.
,
Yaghoubi
,
E.
,
,
A.
,
Doranehgard
,
M. H.
, and
Hong
,
K.
,
2018
, “
Parametric Investigation on Biomass Gasification in a Fluidized Bed Gasifier and Conceptual Design of Gasifier
,”
Chem. Eng. Process.
,
127
, pp.
271
291
. 10.1016/j.cep.2018.04.003
12.
Maghsoudi
,
P.
,
,
S.
,
Xiong
,
Q.
, and
,
M.
,
2019
, “
A Multi-Factor Methodology for Evaluation and Optimization of Plate-Fin Recuperators for Micro Gas Turbine Applications Considering Payback Period as Universal Objective Function
,”
Int. J. Numer. Methods Heat Fluid Flow
,
30
(
5
), pp.
2411
2438
. 10.1108/HFF-04-2019-0333
13.
Staedter
,
M. A.
, and
Garimella
,
S.
,
2018
, “
Direct-Coupled Desorption for Small Capacity Ammonia-Water Absorption Systems
,”
Int. J. Heat Mass Transfer
,
127
, pp.
196
205
. 10.1016/j.ijheatmasstransfer.2018.06.118
14.
Klein
,
S.
,
2016
, “
Engineering equation solver
,”
F-Chart Software
,
,
1
.
15.
Goyal
,
A.
,
Staedter
,
M. A.
,
Hoysall
,
D. C.
,
Ponkala
,
M. J.
, and
Garimella
,
S.
,
2017
, “
Experimental Evaluation of a Small-Capacity, Waste-Heat Driven Ammonia-Water Absorption Chiller
,”
Int. J. Refrig.
,
79
, pp.
89
100
. 10.1016/j.ijrefrig.2017.04.006
16.
Churchill
,
S. W.
,
1977
, “
Comprehensive Correlating Equations for Heat, Mass and Momentum Transfer in Fully Developed Flow in Smooth Tubes
,”
Ind. Eng. Chem. Fundam.
,
16
(
1
), pp.
109
116
. 10.1021/i160061a021
17.
Delahanty
,
J. C.
,
2015
, “
Desorption of Ammonia-Water Mixtures in Microscale Geometries for Miniaturized Absorption Systems
”.
18.
Churchill
,
S. W.
,
1977
, “
Friction-Factor Equation Spans all Fluid-Flow Regimes
,”
Chem. Eng.
,
84
(
24
), pp.
91
92
.
19.
Bergman
,
T. L.
,
Incropera
,
F. P.
, and
Lavine
,
A. S.
,
2011
,
Fundamentals of Heat and Mass Transfer
,
John Wiley & Sons
,
Hoboken, NJ
.
20.
Kern
,
D. Q.
,
1950
,
Process Heat Transfer
,
Tata McGraw-Hill Education
,
New Delhi, India
.