3D CFD fluid flow and thermal analyses of a new design of plate heat exchanger

Abstract The paper presents a Computational Fluid Dynamics (CFD) numerical study for a new design of a plate heat exchanger with two different flow patterns. The impact of geometric characteristics of the two studied geometries of exchanger plates on the intensification process of heat transfer was considered. The velocity, temperature and pressure distributions along the heat exchanger were examined. The CFD results were validated against experimental data and a good agreement was achieved. The results revealed that geometrical arrangement of the plates strongly influence the fluid flow. An increase in the Reynolds number led to lowering the friction factor value and increasing the pressure drop. The configuration II of the plate heat exchanger resulted in lower outlet hot fluid temperature in comparison with the configuration I, which means improvement of heat transfer.


INTRODUCTION
Plate heat exchangers have been frequently studied 1, 2 due to their broad application in a wide range of industries including air conditioning and heat pump coils, steam power boilers, home heating convectors as well as wasteheat recovery 3 . Advances affecting the performance of plate heat exchangers were summarized by Abu-Khader 4 . In the review 4 , the selected issues such as thermal and hydrodynamic characteristics, two-phase fl ows as well as fouling and corrosion were discussed. Main research efforts were made to develop advanced compact plate heat exchangers that can effectively exchange heat between two fl uid streams having a low temperature difference.
In order to increase the effectiveness of plate heat exchangers, a multi-pass design of several manifold microchannel segments was proposed by Arie et al. 5 . The short fl ow path through the microchannels maintain the fl ow in the developing regime and ensure better heat transfer than in that of fully developed fl ow as well as reduced pressure drop. To estimate the optimum performance of the heat exchanger, a hybrid computational method was developed based on solution of full 3D Navier-Stokes and energy equations in a microchannel segment of the heat exchanger in combination with 1D momentum and mass balance equations in manifolds. Another solution was presented by Goodarzi and Nouri 6 . They showed that a double pass arrangement cools the channel walls down more symmetrically, in comparison to the simple pass arrangement, with better uniformity in wall temperature distribution. The uniformity index increases by 16.7% compared to the original heat exchanger. However, power consumption for handling the coolant fl ow increases in comparison to the original solution. In addition, they noticed that sinusoidal separating plate increased heat transfer performance compared to the fl at one. Wavy plates instead of usual fl at plate for channels' walls were also recognized as better solution by Kim et al. 7 . A 2D fi ve way fi n with corrugation angle 20 o was used as the geometry for simulation and the cross-cut was applied at the third wave. The results showed that the heat performance of optimized cross cut wavy fi n was enhanced by a maximum of 23.81% more than for a typical wavy fi n. The pressure drop also increased up to 7.04% in optimized case. Finned and wavy walls generate secondary fl ows along the fl ow direction which increase the local convective heat transfer coeffi cient.
Taking into account that the convective heat transfer coeffi cient depends on fl ow pattern through the channel, the only way for increasing its value is to change the fl ow pattern within the internal channel space 6 . Therefore, the effect of fl uid fl ow nonuniformity on heat exchanger effi ciency is of fi rst order importance and has decisive impact on their effi ciency due to maldistribution of interior temperature. According to Yaici et al. 8 two main types of the fl ow nonuniformity can be distinguished: gross maldistribution and passage-to-passage maldistribution. The fi rst type is associated with improper heat exchanger entrance confi guration, such as poor design of header and distributor confi guration. The second type of passage-to-passage fl ow maldistribution occurs in a highly compact heat exchanger caused by various manufacturing tolerances.
Yaici et al. 8 studied a variety of inlet air fl ow distributions on in-line and staggered plate-fi n-and-tube heat exchangers in order to estimate their effects on system performance including Reynolds number, Prandtl number, geometrical parameters of the heat exchanger, tube arrangement and different working fl uids. Their results indicated that either up to 50% improvement or deterioration in the Colburn factor and the friction factor were found compared to the baseline case of a heat exchanger with uniform inlet velocity profi le. It was confi rmed that the tube arrangement plays a critical role in the heat transfer and pressure drop characteristics. In staggered arrangements, there was better fl ow mixing due to staggered tube layouts and higher heat transfer. In addition, it was shown that the inlet air fl ow distribution has a signifi cant impact on the fl uid fl ow and heat transfer characteristics and the thermo-hydraulic performance. The pressure drop decreased monotonically along the heat exchanger, however, its value increased with the inlet velocity of the air fl owing into the heat exchanger. The authors 8 concluded that the inlet airfl ow distribution can be used as a mechanism to enhance the local heat rate. A similar study was carried out by Vafajoo et al. 9 for fl ue gas-air Chevron type plate heat exchangers. A higher angle of the Chevron type plates resulted in 18% enhancement in the output air temperature and an increase of 63% in the gas pressure drop in comparison with the plate heat exchanger.
Most of the research on heat exchangers has been carried out experimentally or analytically due to their complexity. A variety of techniques of enhancing heat transfer in plate heat exchangers was presented by Shah and Sekulic 10 based on the method of Logarithmic Mean Temperature Difference (LMTD) or the exchanger effectiveness ε -Number of Transfer Units NTU (ε-NTU). Using those methods, Wakui and Yokoyama 11 developed a steady-state model of a shell and tube heat exchanger for performance monitoring based on an online model. With improving capabilities of commercial CFD codes and cost of computing power, numerical investigations of fl ow maldistribution effects on heat exchanger performance became more common. For example, Tao et al. 12 simulated a multistage heat exchanger with plain fi ns and slit fi ns. The better heat transfer conditions in the slit fi n heat exchanger were attributed to better synergy between the velocity and temperature gradients. A detailed analysis of the velocity distribution in a corrugation plate heat exchanger was given by Luan et al. 13 . It was noticed that the longitudinal corrugation in compound corrugation plate was inducing cross mixing of the working fl uid and thus enhancing turbulence and also heat transfer between the fl uid and the plate. Numerical simulations and experiments showed that the fl ow resistance of working fl uid in the corrugation plate heat exchanger was decreased more than 50% in comparison to the traditional Chevron type one and hence the problem of fl ow path blockage can be effectively avoided. More recently, Giurgiu et al. 14 performed fl ow analysis through mini channels in plate heat exchangers. The analysed mini channels had the inclination angles from 30 o to 60 o . Both the experimental and CFD results showed that the best heat transfer conditions were obtained for the plate heat exchanger with inclination angle of 60 o . In addition, it was noticed that the geometry of the plates signifi cantly affects the fl uid fl ows through channels formed between the plates and highlights the performance of thermodynamic characteristics of these devices. The use of manifolding of microchannels for performance enhancement of plate heat exchangers in a counter fl ow confi guration was studied also by Andhare et al. 15 . The heat transfer coeffi cient obtained in the numerical simulations was found to be approximately 16% higher than that in the experimental fi ndings. The deviation between numerical and experimental values was explained due to the variability of the microchannels. The heat exchanger was made of nickel, which is quite diffi cult to machine and it can lead to variability in microchannel dimensions. Another signifi cant observation was that the introduction of the fl uid into a developing fl ow region enhanced the performance of the heat exchanger. The contour plots of the velocity obtained from the numerical study showed higher local fl ow velocities near the base of the microchannel. This effect was explained by turning of the fl ow from manifold to microchannel and back to the manifold in a very short fl ow length.
The need of investigation of the effect of corrugated fl at plate heat exchanger with and without baffl es on the thermal-hydraulic characteristics, including effi ciency of heat transfer and fl ow resistance in heat exchanger, was recognized by Rios-Iribe et al. 16 . The impact of plates number and distance between plates on the heat transfer and the friction factor were studied over a wide Reynolds number range in the case of non-Newtonian fl uids fl owing through the plate heat exchangers. It was found that for all investigated Reynolds numbers in the heat exchanger with two plates, the CFD results correctly fi tted an empirical correlation of the friction factor. The variation of heat transfer was presented as a function of the pumping power. It was found that at high fl ow rate, an increase in the number of used plates lowered the ratio between the heat transfer and the pumping power. Other aspects were considered by Dvorak and Vit 17 , who focused on an effect of material thickness on pressure loss and effectiveness of a counter fl ow plate heat exchanger. The authors demonstrated that the low material thickness, of only 5% of the plate pitch, was crucial in creating the most effective recuperative air to air heat exchanger with high effectiveness and low pressure loss, while the properties of the material itself were unimportant. The CFD results for effectiveness corresponded well with the measured ones, while the results for pressure loss differed signifi cantly and underestimated the measured pressure drop by 19-75% in a wide Reynolds number range. The high difference in pressure loss was explained by not taking into account in simulations the plate parameters, such as plate roughness, plate deformation or differences between the shapes of the numerical and real plates of the heat exchangers.
Most of the reviewed papers clearly indicated that non--uniform fl uid fl ow at the infl ow to the narrow passage formed between the fi ns as well as the thermal contact resistance between the fi n and tube/plate can strongly infl uence the heat transfer process inside plate heat exchangers. Thus, in the case of those exchangers, where fl uid fl ow through parallel fl at plates is characterized by the formation of large dead fl ow zones, supporting the reliability of the computation seems to be particularly useful. The CFD codes allow predicting how these undesirable thermal-hydraulic characteristics can be reduced and hence lead to an increase in the pressure drop and the heat transfer. The presented results 8, 14-17 showed that 3D CFD simulations can provide an effective tool for engineering analysis since various design options and a wide variety of physical conditions can be examined without constructing expensive test rigs or large scale prototypes. Thus an optimal design of the plate heat exchanger can be determined at a relatively low cost.
Therefore, the aim of the study was to examine the infl uence of geometrical parameters of the heat exchanger plates on heat transfer conditions by means of the CFD modelling. With this aim, the plate heat exchangers of two different fl ow patterns were studied and the CFD results were compared with an existing experimental data for the original geometry of the plate heat exchanger.

NUMERICAL APPROACH
The scheme of a plate heat exchanger with two different confi gurations I and II, for which computations of velocity, pressure and temperature were conducted, is shown in Figure 1. The plate heat exchanger is used for cooling the cathode off gas leaving a developed hybrid power generation system based on Solid Oxide Fuel Cells. To simplify the computational case, the cathode off gas was represented by air fl ow with the same mass fl ow rate and temperature values as the cathode off gas in a real system. The cathode off gas was marked as hot fl ow and it was cooled by air (cold fl ow). The complete plate heat exchanger was 95 mm wide, 210 mm long and 33 mm thick. The total number of plates was equal to 18 resulting in 9 and 8 channels for cold and hot fl ows, respectively. The plate fi ns and walls were made of stainless steel with the thermal conductivity of k = 16.27 W/mK. The fi ns of the hot and cold fl ows in the plate heat exchanger confi guration I were J-shaped, while for the confi guration II the fi ns for the hot fl ow were straight and for the cold fl uid fl ow they were S-shaped. Relevant 3D geometrical models of plate heat exchanger were built in the CFD commercial software ANSYS Workbench.
the turbulent fl ows through the plate heat exchanger the RNG k-epsilon model was used with standard values of model constants. The behaviour of this model near the wall was corrected by incorporating the standard wall functions. The working fl uids were assumed Newtonian, incompressible with piecewise linear temperature profi le properties presented in Table 1.
The counter fl ow of the fl owing streams was considered. Thirteen cases for both confi gurations of the plate heat exchanger were simulated using different boundary conditions. The mass fl ow rates, N, and temperatures, T, of the inlet cold and hot streams were set fi xed to the values shown in Table 2. Turbulence intensity was set at  The following assumptions were considered in the developed approach: the working fl uid was air for both cold and hot fl ows within the turbulent regime. To simulate 5% what was acceptable given the suffi cient entry length provision. Zero velocity with no slip shear condition was applied to the fl ow in the boundary layer at walls.
Since the study was assumed for stationary conditions, the Navier-Stokes and energy equations in three dimensional form 18 were used to solve for the steady state hydrodynamics and thermal fi elds in the plate heat exchanger. The hot fl uid fl ow was treated as a non-participating media in radiation 22 . The governing equations are presented in Table 3.
where: δ k is constant in Equation (4), C 1ε , C 2ε , δ ε are adjustable constants in Equation (5), while C μ is the constant in Equation (7) 18 . The stress tensor,  , turbulent viscosity, t  , RNG additional term, R  , as well as ratio of the mean fl ow to turbulent time scale are given by Equations (6) -(9), respectively: Turbulent viscosity: RNG additional term: Ratio of the mean flow to turbulent time scale: The RNG k- model delivers a better response to the instantaneously changing fl ow with the additional term, R  , in comparison to the standard k- model 23 .
The modeling was conducted using the commercial CFD code ANSYS Fluent 15.0. The governing equations Table 1. Material properties of the working fl uid Table 2. Boundary conditions for the hot and cold fl uids in the plate heat exchanger Table 3. The governing equations velocity increase due to the fl uid inertia inducing the reverse fl uid fl ow in areas between plates and heat exchanger walls.
The accuracy of numerical predictions was evaluated based on the standard deviation between the measurement and model results of pressure drop for each considered case as a function of the plates shape (confi gurations I and II). Figure 6 presents the impact of the fl ow regime and heat exchanger confi guration on the pressure drop.
A signifi cant deviation of 40% between the predicted and measured values of pressure drop was noticed at the operating mass fl ow rates for both hot and cold fl uid fl ows in the plate heat exchanger confi guration I. For the confi guration II, however, these differences were lower and the mean standard deviations of 12% and 32% were noticed for the hot and cold fl uid fl ow, respectively. It should be mentioned that the calculated pressure drop using the CFD model for the hot fl uid fl ow was overestimated, while that for the cold fl uid was underestimated in both confi gurations. Figures 7 and 8 show the contours of local pressure for both fl uids: hot and cold and the two heat exchanger confi gurations.
The pressure decreases monotonically along the heat exchanger in both fl uid zones as expected. However, it should be underlined a strong effect of the plates arrangement on the pressure distribution. In the pressure distributions presented in Figures 7 and 8, high pressure spots can be noticed for both fl uids resulted from the fl ow interactions with these vertical plates. The presence of those plates causes fl uid fl uctuations. Thus, the ve-were discretized by the Finite Volume Method, the pressure-velocity coupling was implemented by SIMPLE algorithm, while the convection terms were discretized by Second Order Upwind, and the First Order Upwind scheme was selected for the kinetic energy and its dissipation rate. The fi rst step was to determine the pseudo-laminar fl ow fi elds with the turbulence model turned off, then the turbulence model was activated in the computations to simulate the turbulent velocity fi elds and fi nally the energy equation was solved. The iterations were carried out as long as the standardized sum of residuals fell below 1 . 10 -4 and the residual plots showed a plateau for at least 100 last iterations.
The CFD model was validated by quantitative comparison to the experimental results obtained from the industrial project partner -sunfi re 19 . In addition, the Fanning friction factor, f, was calculated as follows (Eq. (10)) 20, 21 : in which P  is the pressure drop equal to the difference between the inlet and outlet, where L and D h are the length and hydraulic diameter of the channel, respectively.
For fully developed turbulent fl ows (2000<Re<25000) the Fanning friction factor for heat exchanger was given in Eq. (11) by 13 and used for comparison with the simulation results.

RESULTS AND DISCUSSION
The plots of the friction factor as the function of the Reynolds number in the heat exchanger with the two-plate confi gurations is shown in Figure 3. For both confi gurations of the heat exchanger a good agreement can be seen between the calculated friction factor and the experimental values as well as the theoretical relationship (11) over the Reynolds number range of 4500-10106 [-]. However, the friction factor tends to be strongly dependent on the geometrical shape of the heat exchanger. At the inlet area, a constant fl ow is defi ned by the geometrical shape of the tubular manifold. Then the fl ow gets into the main area of the heat exchanger and it is divided into two parts. In addition, plates arrangement in the confi guration I for both hot and cold fl uid channels cause the fl ow changes its direction by 90 o , inducing secondary fl ows that produce dead fl ow zones in the curvature of the channel visible in Figures  4a and 5a at the upper left corners at a lower fl ow rate (Re = 1528). However, at a higher fl ow rate the fl ow tends to limit dead fl ow zones as showed in Figures 4b  and 5b for two cases of Table 2. Clear dead fl ow areas to occur in the cold fl uid zone (Fig. 5b upper part) and it seems that S-shaped plates strengthen this phenomenon independently of the fl ow rate studied.
In addition, for the second confi guration of the plate heat exchanger, the velocity fi eld for the cold fl uid zone strongly depends on the geometrical arrangement of the plates and at high Reynolds number the dynamic losses are greater (Fig. 5b) than those observed in the confi guration I (Fig. 4b) at the same Reynolds number, Re = 10 105. Dead fl ow zones decrease when the inlet   arrangement. It seems, on the one side, that the applied fl uid fl ow division allows to improve mixing and in consequence leads to an increase of the heat transfer. On the other side, local hot spots can be observed, which can cause material problems and should be avoided due to safety reasons. Analysis of the simulated temperatures at the outlets from the heat exchanger (confi guration I) revealed that a quite good agreement was obtained between the CFD results and the measured ones by 19 , as it can be seen from Figure 11. The maximum deviation between the simulation and experimental values of temperature for hot fl uid was equal to 17%, while for the cold fl uid it was 13%. Therefore, it can be assumed the CFD temperature distributions of confi guration I were close to the real ones. As indicated in Figure 11 for the second confi guration of the plate heat exchanger, the agreement between the CFD and experimental results was even better. The maximum deviation between simulation and experimental values was equal to 15% and 12% for the cold and hot fl uids, respectively. In addition, it should be underlined that application of the second confi guration of the plate heat exchanger allows decreasing the hot fl uid temperature at the outlet in the operating fl uid fl ow rate and results in heat transfer enhancement.

CONCLUSIONS
Comparison of two heat exchanger confi gurations with different plates' arrangement showed that the second confi guration allows to obtain lower outlet temperature for the hot fl uid fl ow. In all considered CFD cases, an increased Reynolds number caused a decrease of the friction factor and increase in the pressure drop. A higher pressure drop for the hot fl uid of 26% was noticed for the confi guration I of the plate heat exchanger in com- parison to confi guration II, indicating higher turbulence intensity. However, it seems that the critical impact on the heat transfer effi ciency in the plate heat exchanger has the cold fl uid distributions. The pressure drop for the cold fl uid was higher of about 13% in confi guration II than in I. Thus, the CFD results showed a signifi cant importance of fl uid fl ow nonuniformity on the heat exchanger effi ciency. Moreover, the present study with respect to fl ow maldistribution (dead fl uid zones), demonstrates that 3D CFD simulations are a useful tool for analyzing, designing and optimizing heat exchanger design. The results of this study can be also helpful in further optimization of heat exchanger confi guration in order to minimize fl ow maldistribution.