ANALYSIS AND OPTIMIZATION OF VAPOR ABSORPTION GENERATOR-HEAT EXCHANGER USING KERN METHOD AND CFD

The growing demand for new and eco-friendly energy resources has raised the need of sustainable sources or renewable energy for use in present era. A vapor absorption refrigeration system (VARS or VAS) is a closed loop refrigeration system which requires low heat for its functioning and, it is therefore, considered an eco-friendly solution. Since, generator is the main component of VAS which can significantly influence the efficacy of overall system, the current paper involves modeling and thermal analysis of generator using Computational Fluid Dynamics (CFD). The objective of this study is to optimize the heat transfer by changing baffle spacing of generator heat exchanger, running on a single effect LiBr/ water absorption cycle. For this purpose, hot water driven generator of 1ton capacity is taken. The simulation results of CFD were validated by comparing them with theoretical results. The overall design estimation and design technique that follows Birmingham Wire Gauge (BWG) and Tubular Exchangers Manufacturers Association (TEMA) standard are considered in this study. It was found from the analysis that the design model with smallest baffle spacing has the highest heat transfer coefficient. On reducing the baffle spacing from 137mm to 101mm, an increment of 48% in overall heat transfer coefficient was observed. Likewise, an increase in velocity by 36% and drop in static pressure by 27% were seen. Similar trend was observed in the theoretical results.

working fluid. It was identified that the thermal performance of the system improved but, with rise in the pressure drop value [21]. It was established through experimental studies on boiling mechanism of a disc copper made heater at different heat flux, mass concentration of nano-fluids and sub-cooling temperatures. The study proved that heat transfer coefficient of Titana nano-fluids are comparatively better than that of the base fluid. Sarafraz et al. [22] obtained that in attendance of surfactant, higher pool boiling heat transfer coefficient was improved. According to their report, the smoothness of surface is powerfully controlled by nanofluid concentration due to deposition of nanofluids on the heating division. Robert et al. [23] found this article were in good approval with other literature review which offer development using nanofluids with changes in the surface play in pool boiling the most imperative part in defining whether enhancement is realized.
In current study though nanofluid has not been used in this system in order to avoid chemical reaction due to using LiBr/H2O. Practical problem typical to lithium-bromide water-based VAS is phase changing (steam generation). As we know the system is closed loop and is completely independent of the external heat sources. To minimize the external heat supplied or energy consumption, the efficiency of the system should be improved to achieve phase changing. This is done by increase the heat transfer in generator, whereas, pressure and temperature have to be maintained at certain level.
Since, generator is the main component of VAS which can significantly influence the efficacy of overall system, the current paper involves modeling and thermal analysis of generator using Computational Fluid Dynamics (CFD) wherein a single effect LiBr/water absorption cycle has been considered. The objective of this study is to optimize the heat transfer by changing baffle spacing of generator heat exchanger. For this, hot water driven generator of 1ton capacity is taken. The theoretical results were obtained using Kern method and they were compared with the simulation results of CFD. The heat exchanger comprising of single shell and double tube in vertical disposition, with 25% baffles cut were taken with varying baffle spacing as: 139mm, 127mm, 110mm and 101mm. The overall designing estimation and design technique that follows Birmingham Wire Gauge (BWG) and Tubular Exchangers Manufacturers Association (TEMA) standard are considered in this study. This paper has been organized into the following four major sections: Section 1 describes briefly about the Vapor Absorption System and its functioning. Section 2 contains the design methodology adopted in this work. Section 3 shows the results obtained from the theoretical and the simulation methods, followed by comparison between the two. Finally, section 4 provides the conclusion of the current study.

DESIGN METHODOLOGY Heat transfer in generator of VAS
The generator heat exchanger of single effect LiBr/H2O absorption refrigeration system comprises of a shelland-tube heat exchanger. The generator is in vertical orientation with an inlet, two outlets, an inner and outer shell. The strong solution enters into the inner shell directly from the inlet at the top of generator, and then moves between the baffle plates around the tubes and get heated up via absorption of heat from hot fluid which passes in tubes. When the solution reach at the bottom, the water vaporizes. The inner shell opens to outer shell at the bottom. The weak solution is discharged from the generator at the bottom outlet and from there it is returned back to the absorber, where it becomes ready to absorb fresh refrigerant. When the steam passes between the inner and outer shell, it absorbs more heat until discharge from outlet at the top of generator and passes to the condenser. By adding the outer shell, we can allow the steam to rise upward to discharge from the top, without restriction to the solution to pass in the opposite direction. In this way, the refrigerant keeps on repeatedly moving inside the cycle. In this section all the fundamental equations related to the modeling of generator of VAS have been provided. For cooling of chiller generator lithium bromide water system 4.6 kW/TR of heat is supplied [24]. The mass flow rate (ṁ ℎ ) of the hot fluid (water) can be obtained from heat transfer rate ( ) using overall energy balance equation [25]: where, ℎ, and ℎ, represents temperature of hot fluid at inlet and outlet, respectively, and ,ℎ is the specific heat of hot fluid at constant pressure.
The temperature ( , ) of the cold fluid at outlet (solution of LiBr -Water) can therefore be obtained using Eq. (2) [25]: where, , represents temperature of cold fluid at inlet, , is the specific heat of cold fluid at constant pressure, flowing with mass flow rate (ṁ ).

Kern Method:
The heat transfer area ( ) can be determined from Eq. (3) [26]: where, is the total area of hot fluid-side or cold fluid-side for heat transfer, is the average overall heat transfer coefficient and ∆ is a function of hot and cold fluid temperature at input and output, respectively symbolized as: ℎ, , ℎ,0 , , , , . The LMTD (Log Mean Temperature Difference) method is a convenient way for finding the size of a heat exchanger (generator in our case), for a given value of input and output temperatures of the hot (water) and cold (LiBr/H2O) fluids, and can be calculated using Eq. (4) [25,26]: For multi-pass, crossflow the correction factor (FT) of heat exchanger is used to rectify the log mean temperature difference. Reference [24] can be referred for values of one shell and two or more tube passes). The value of overall heat transfer coefficient ( ) of 250 w/m 2 K is taken to begin the design calculation for the lithium bromide water solution and hot water for generator heat exchanger. The approximate range of the overall heat transfer coefficient depends upon temperature difference between the fluids, and it can be found out from reference [25]. The number of tubes ( ) required for heat transfer can be calculated using following Eq. (5) [26]: where, and are the outside diameter and length of tube.
The overall heat transfer coefficient , is dependent upon the physical properties of the fluid and its physical state. The expression for , is given by Eq. (6): The convective heat transfer coefficient, hi and hₒ at the tube side and the shell side, respectively, can be calculated using Eq. (9) and Eq. (12) [26,27].
Next, the Reynold's number for the hot water flowing through the tube is calculated using Eq. (7) [25]: The empirical relation for the local Nusselt number, in case of fully developed (hydrodynamically and thermally) turbulent flow in case of a smooth circular tube, is given by Dittus-Boelter equation [27], as follow: Hence, the convective heat transfer coefficient ℎ at the tube side can be expressed as [25]: The Reynold's number for LiBr-water solution flowing through shell, is calculated using Eq. (10) [26]: where the equivalent diameter, for the shell side with square pitch , is obtained by Eq. (11) [26,27]: The convective heat transfer coefficient ℎ at the shell side is calculated from Colburn factor ( ), obtained from curve of shell side heat transfer for bundles with 25% cut segmental baffles at calculated value of Reynold's number ( ). The relationship between ℎ and is expressed in Eq. (12) [26,27]: The clean overall heat transfer coefficient can be determined from Eq. (13) [28]: Therefore, the calculation of overall heat transfer coefficient is within the design criteria, viz.
Due to flow of the fluid through a generator, the pressure drops in downstream except for the cases with decreasing fluid velocity, wherein the pressure rises in the downstream side. The tube-side pressure drop can be calculated from Eq. (15) [28]: The additional pressure drop due to change in the direction of the tube is calculated using Eq. (16) [28]: The total pressure drop of tube-side is the sum of pressure drop due to friction during flow and that due to change in direction: The shell-side pressure drop for fluid flow across the tube bundles (frictional loss) is calculated using Eq.(18) [28]: For overdesign calculation of extra surface area beyond what is required for compensation of fouling, a typical value of 10% or less is considered acceptable [27,28].

Baffle Spacing and Baffle Cut
The baffle spacing ( ) is the center-to-center distance between adjacent baffles, as shown in Figure 1. The baffle spacing is one of the most critical geometric parameters that affects both the pressure drop and the heat transfer characteristics of shell side model. By changing the baffle spacing, the mass velocity and the counter flow area of the shell side fluid is changed which ultimately changes the heat transfer. For smaller baffle distance, the flow area is smaller, and the fluid velocity is higher. The high flow velocity means there is slight increase in the frictional pressure drop along with the heat transfer coefficient. Although, the heat transfer coefficient is increased when the baffle distance is reduced, the TEMA has set a standard for its lower limit to be 0.2 to 1 times of the inside shell diameter ( ). Similarly, when the baffle distance is high, the heat transfer coefficient is low. Moreover, higher baffle distance also give rise to longitudinal flow which is considered less efficient compared to cross flow. This also leads to lesser unsupported tube length which makes the design less strong and more prone to failure due to buckling and vibration. Hence, TEMA has set the standard for maximum baffle spacing for mechanical considerations. In generator heat exchanger model, the baffle spacing therefore should be chosen so that it may ensure sufficient support to the tubes within the shell, besides, achieving the highest possible amount of the heat transfer rate within prescribed pressure drop limit. The baffle cut from 15% to 45% is generally used, but 20 to 25% provides perfect heat transfer with a slight pressure drop resulting due to frictional losses. This is because, in case of small cut for segmental plates (baffles), the shell side fluid flow turbulence is high which results in high fluid velocity and consequently increases the heat transfer coefficient. Contrary to this, in case of large baffle cut, the velocity is low and hence the heat transfer coefficient is also low [5]. In the current study, a baffle cut of 25% has been taken for four different baffle spacings, from 40% to 55% of the inside shell diameter specifically as: 139mm, 127mm, 110mm and 101mm.

3D MODELING
The 3-D model of the generator was first created in Solid Works, as shown in figure 2. Figure 2a and Figure  2b shows full and cut section of one of the generator models, respectively. The inlet and outlet for LiBr water solution as well the hot water can be seen in Figure 2a. The cut section presented in Figure 2b displays the disposition of the tubes and baffles inside the shell of the generator heat exchanger.  Figure 3 shows the drawings of all the four models with major geometrical dimensions, considered in the current study for analysis of generator heat exchanger.

CFD AND THEORETICAL ANALYSIS Theoretical Analysis
The Table 1 and Table 2 shows the modeling data for working fluid and properties of lithium bromide/ water solution, used in the current study as the working fluid, required for theoretical calculation for tube side. The system of equations presented previous section were solved for the above parameter settings and the properties of fluid given in Table 3.
The summary of the results so obtained have been presented in Table 4. As per the values obtained for convective as well as the overall heat transfer coefficient of different models, model D with the smallest baffle spacing shows the best heat transfer characteristics.   Figure 4 shows the summary results for different baffle spacing corresponding to different generator models namely A, B, C and D considered in the current work. Figures 4 (a), (b) and (c) shows a comparative view of the shell side pressure drop, heat transfer coefficient and Reynold's number, respectively, for different baffle spacing. Figure 4(a) shows the effect of baffle distance on shell side pressure drop, wherein it can be seen that by increasing the baffle distance the shell side pressure drop is reduced. The highest and the lowest values of shell side pressure drop are 0.076 Psi and 0.058 Psi, corresponding to Model D and Model A, respectively. The decrease in pressure drop due to increasing baffle distance is because of smaller shell fluid mass velocity. A decrease of about 36% in shell fluid mass velocity is observed on increasing the baffle space from 101mm to 139mm and this amount is sufficient to decreases shell side pressure drop by 31%. Figure 4(b) shows the relationship of baffle distance and shell region fluid heat transfer coefficient, wherein the high and low values of shell side heat transfer coefficient are 1022 W/m 2 K and 864 W/m 2 K, corresponding to Model D and Model A, respectively. It is apparent from here that with increasing baffle space the heat transfer coefficient decreases, and this is because the increase in baffle spacing causes unsteady shell side fluid flow. Figure 4(c) shows the percentage of Reynolds number increase for different generator models. An increase of 36.7% in Reynolds number percentage is observed as we move from model A to D due to which the heat transfer is also highest in model D (because of higher turbulence).

CFD Analysis Geometry
The Generator was made like a shell-tube heat exchanger on solid works and then exported in IGS file into ANSYS Fluent. In workbench stage there are some processers it was generated like united, merge and fill the surfaces inside, outside the tubes and shell domain, then finally named cell zone selection that will help for selection the special materials for every domain. 25% baffle cut was taken in the current study. Baffles spacing of 139mm, 127mm, 110mm and 101mm for model A, B, C and D, respectively, in order to study its influence on the heat transfer rate. In order to reduce the computational time, only smaller number of tubes have been taken in the analysis part and the cover shell have been removed, ensuring that these inclusions does not affect the final analysis results. Although simulation time depends mainly on computational method and the configuration of computational hardware, the time taken in our case (double precision and 2 processes method, core i7, 200 iteration) was roughly 25minute. Figure 5 shows the geometry of the tube-shell assembly of Model C of the generator, imported in ANSYS Fluid.

Meshing
Meshing is an integral part of the computer aided engineering simulation process. The mesh affects the accuracy, convergence and speed of the solution result and meshing should be done properly on the surface and edges, as per the geometry details and solution convergence. If the geometry has high number of element it will give (a) (b) more accuracy result and it can show very clear on the surface. Figure 6 shows the meshed model of generator in the ANSYS workbench, obtained using double precision and 2 processes method. The number of elements used in this meshing for different models, is shown in Table 5. In this process face meshing and edge sizing of meshing is done to analyze the process.

CFD Results
The CFD model (ANSYS Fluent 16) was initially used to verify the performance of generator heat exchanger. The analysis setup based on four cell zone condition, tubes and shell solid material (copper and steel), and cold fluid (LiBr/H2O) solution and hot fluid (water) ,this analysis done in double precision for more accuracy, under vacuum pressure the theoretical results of Table 1 and Table 2 were used as input data in boundary condition for setup stage, standard initialization method option used in solution monitors and computed from all zone condition, 100 number of iteration was taken for run calculation in CFD analysis. The baffle spacing of the different models, namely Model A, Model B, Model C, and Model D were taken as 139mm, 127mm, 110mm and 101mm, respectively. With different baffle spacing the models are supposed to have different flow velocity between the baffles in shell, thereby yielding different heat transfer rate. Figure 7 for Model A, Figure 8 for Model B, Figure 9 for Model C and Figure 10   It is inferential from the figures that with decrease in the baffle distance, the wall heat transfer coefficient increases (as visible from increasing trend Model A to Model D). The lowest value of heat transfer coefficient, possessed by Model A is 2771 W/m 2 k whereas the highest value, possessed by Model D is 4100 W/m 2 k which is 48% higher than that of Model A. Similarly, the stream velocity has increased by about 36% from Model A to Model D, due to decreasing baffle spacing. The static pressure has decreased by 27% from Model A to Model D. This is because of frictional losses, however it has consequently improved the heat transfer coefficient due to increased static temperature in LiBr/H2O fluid to the required temperature of 90 o C (outlet of cold fluid). Among all the four models, Model D shows the best result as per the CFD analysis. Figure 11 shows the temperature gradient at the entry and exit of the generator model D. Figure 11(a) shows entry of LiBr/H2O solution in the shell and exit of hot water inside the tube. Figure 11(b) shows entry of hot water and exit of LiBr/H2O solution. It can be seen that at the entry, the LiBr/H2O solution in the shell domain has around temperature 313K at input boundary condition as (VAS) cycle design which is sufficient to generate vapors. However, as the heat is exchanged between hot water and LiBr/H2O downstream the tubes, the LiBr/H2O becomes sufficiently hot with average temperature of 363 K.     The simulation results obtained using CFD analysis, were validate by comparing their values with theoretical results (obtained using Kern method). Though these values do not match closely, the trend of the variation is same in both the cases, which is sufficient to indicate the optimal design parameters.  Table 7 shows the validation of simulated temperature values of different models with theoretical results. The variation corresponding to Model D is 4.7 % at outlet of cold fluid (lithium bromide water solution). This deviation may be due to difference in the velocity magnitude incurred by variation in baffle spacing used in actual simulation. Figure 15 below shows a simpler view of the validation presented in Table 7, above.

CONCLUSION
In tube-shell type generator heat exchanger, reducing the baffle spacing increases the heat transfer coefficient. The lower limit for the baffle spacing has been set by the TEMA Standards in the range, 0.2 to 1 times of the inside shell diameter. Contrarily, if the baffle spacing is large, the heat transfer coefficient is small. Moreover, large baffle spacing promotes longitudinal fluid flow which is considered less efficient compared to cross flow. This also leads to lesser unsupported tube length which makes the design less strong and more prone to failure due to buckling and vibration.
In this study we presented a detailed description of optimizing the generator heat exchanger of absorption system (VAS) using CFD simulation. Lithium bromide/water was taken as an absorbent-refrigerant pair. The effects of variable baffle distance of the generator heat exchanger on wall heat transfer coefficient, Reynolds number and static pressure have been analyzed, corresponding to four models. It was found that the model with the smallest baffle distance has the highest wall heat transfer coefficient which is attributed to high turbulence acting in the small spacing of the heat exchanger. By reducing the baffle space from 137mm to 101mm, an increase in the wall heat transfer coefficient of 48% was observed. Likewise, an increase in velocity by 36% and drop in static pressure by 27% were seen. Similar trend was observed in the theoretical results; however, the theoretical values differ from CFD results. This is because the theoretical calculations are based on normal pressure of LiBr-H2O solution, while, the CFD results are based on four cell zone condition, tubes and shell solid material (copper and steel), and cold fluid (LiBr/H2O) solution and hot fluid (water). The CFD analysis was done using double precision and 2 processes method under vacuum pressure which represents the actual working condition (to create vapor at low boiling point) and hence, provides more accurate results.