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Effects of smooth longitudinal passages and port configuration on the flow and thermal fields in a plate heat exchanger
Applied Thermal Engineering 31 (2011) 4113e4124
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Effects of smooth longitudinal passages and port configuration on the flow and thermal fields in a plate heat exchanger Iulian Gherasim a, Nicolas Galanis a, Cong Tam Nguyen b, * a b
Mechanical Engineering, Université de Sherbrooke, Sherbrooke, QC, Canada J1K 2R1 Mechanical Engineering, Université de Moncton, Moncton, NB, Canada E1A 3E9
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 June 2011 Accepted 16 August 2011 Available online 23 August 2011
Numerical results for heat transfer with laminar or turbulent flow in a two-channel PHE are presented. The temperature, heat flux and mass flow distributions are analyzed in the case of two fluid combinations: water/water and water/engine oil. These results show that, in the case of water/engine oil, both the thermal field and the mass flow distribution are more uniform compared to the water/water case. A comparison between the original geometry and the geometry with obstructed longitudinal channels shows that the presence of these passages decreases the heat transfer rate and the friction factor. The calculated performances of the side-flow and diagonal-flow configurations differ only slightly. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Plate heat exchanger Temperature distribution Flow distribution Smooth longitudinal passages Port configuration CFD Laminar flow Turbulent flow
1. Introduction Plate heat exchangers (PHE) are widely used in many applications (food, oil, chemical and paper industries, HVAC, heat recovery, refrigeration, etc.) because of their small size and weight, the ease of cleaning as well as their superior thermal performance compared to other types of heat exchangers. Due to the corrugations, which induce secondary flows, boundary layer separation and turbulence at relatively low Re numbers, they are well suited to low Reynolds number flows encountered when using viscous liquids such as engine oil [1,2]. For a detailed synthesis of the applications of the PHEs see for example [3]. Several experimental and numerical studies have therefore been recently conducted in order to predict the flow and temperature distribution in PHEs. Many of the latter use simplifying assumptions. Lozano et al. [4] analyzed the flow distribution inside one channel of a PHE for the automotive industry, without considering the heat transfer. They created and validated a 3D model which consists of a single channel. Their analysis concluded that the flow was not uniform and preferentially moved along the lateral extremes of the plates. Kanaris et al. [5] studied the flow and heat
* Corresponding author. Tel.: þ1 506 858 4347; fax: þ1 506 858 4082. E-mail address: [email protected] (C. T. Nguyen). 1359-4311/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2011.08.025
transfer in a PHE. They used a 3D model which includes two complete channels and validated it against experimental and literature data. A similar model was used by Tsai et al. [6] in order to investigate the hydrodynamic characteristics and distribution of flow inside a PHE with no heat transfer involved. Their CFD models use the real geometry of the plates, including the entire entrance and distribution zones. Jain et al. [7] considered a 3D turbulent model with a complete cold channel and two halves of the adjacent hot channels. This model uses more realistic hydrodynamic and thermal boundary conditions; the two halves of the hot channels on either side have flat periodic boundaries. As a result, they were able to validate their model on a PHE with 13 channels. Hur et al. [8] created a similar model in order to study the heat transfer in a PHE. Although the chevron angle is the same with the one in the present study (4 ¼ 60 ) and the Reynolds number varied between 249 and 1018, they used only the laminar model for all the simulations. Galeazzo et al. [9] have modeled in three dimensions an industrial PHE with four channels. However, this PHE was a nonchevron type with five smooth plates. The authors have investigated parallel and series flow arrangements and validated it with experimental data. In their experimental work Okada et al. [10] analyzed the temperature distribution on the first and last plates of a two-channels PHE of non-chevron type. They
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Nomenclature dA C1,C2 Cp DH f g Gk,Gb
hm k, kt L Nu p Re Sk, Sε T Tm
elementary surface, m2 constants specific heat, J kg1 K1 channel hydraulic diameter, m Darcy friction factor,f ¼ 2 ΔP DH/(rm L u2m) gravitational acceleration, m s2 rates of turbulence kinetic energy generation due to mean velocity gradients and to buoyancy respectively, J m3 average heat transfer coefficient, W m2 K1 thermal conductivity, turbulent thermal conductivity, W m1 K1 length of the channel, m Nusselt number, Nu ¼ hm DH/km pressure, Pa channel flow Reynolds number, Re ¼ um DH rm/mm user-defined source terms temperature, K average temperature in a channel, K
compared the temperature distributions for diagonal and sideflow channels, and also for upwards and downwards flow of the cold and hot fluids. To our knowledge, this is the only article with such results. Han et al. [11] in their numerical and experimental study, described the temperature and pressure distribution on a chevron corrugated PHE with five plates (four channels). By analyzing the temperature distribution and the streamlines, the authors noticed that the flow prefers to flow to the port side. They validated the numerical results, finding similar experimental and
ui ; ui um xi X, Y, Z YM
i-axis velocity component and time-averaged value, m s1 mean velocity of the fluid in a channel, m s1 i-axis coordinates contribution of the fluctuating dilatation to the dissipation rate (for compressible flows)
Greek letters ΔP pressure loss between inlet and outlet of a channel, Pa ε turbulence kinetic energy dissipation rate, J kg1 k turbulence kinetic energy, J kg1 s1 y, yt kinematic viscosity, turbulent kinematic viscosity, m2 s1 m, mt dynamic viscosity, turbulent dynamic viscosity, Pa s r density, kg m3 sk,sε constants Subscripts b refers to bulk temperature m refers to the average value in the channel, with properties evaluated at Tm numerical results in terms of outlet temperatures and pressure drops. In our previous experimental [12] and numerical [13,14] articles the hydrodynamic and thermal fields in a two-channel chevron PHE were analyzed for water flow in both channels. The CFD model was satisfactorily validated for both laminar e using the laminar model e and turbulent conditions [13] e using two-equation turbulent models e by comparing the numerical and experimental temperature distributions on the PHE’s exterior plates, the friction factor and the Nusselt number for each channel, as well as
Fig. 1. (a) View of the model with 2 channels; (b) a detail of the fluid volume; (c) main dimensions in mm; (d) the coordinate system with positions of inlets and outlets; (e) Crosssections of the channel at three positions.
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the outlet temperatures of the two streams. For the turbulent flow regime, the Realizable keε model with non-equilibrium wall functions was found to give the closest results with respect to the experimental data. This CFD model is used in the present study which aims to analyze in more depth the flow, temperature and heat flux distribution inside a PHE, by considering both flow and heat transfer. This CFD model includes the complete geometry of the channels and possesses more complex distribution zones than other studies. The side port and diagonal port PHEs are also compared in terms of their hydraulic and heat transfer performance. The results for two fluid combinations (water/water and water/engine oil) are analyzed and compared. This study also aims to assess the influence of the smooth longitudinal straight passages (which is a particularity of the present PHE) on the overall thermal and hydraulic performances of the PHE. A comparison between the side-flow and diagonal-flow configurations in terms of heat transfer and pressure loss is also presented. The paper is organized in two main sections. In Section 2 details regarding the numerical modeling (geometry considered, governing equations and boundary conditions) are presented. In Section 3 numerical results obtained for the flow and thermal fields are shown and discussed, with emphasis on the effect due to the presence of smooth longitudinal passages as well as that of the port configuration. The paper terminates with the conclusion that summarizes the main findings. 2. Numerical modeling The calculation domain, which consists of a two-channel PHE tested in our experimental study, consists of three plates and two fluid passages (Fig. 1a, b) confined between the plates. It reproduces with fidelity the geometry of the physical system, including all geometrical details of the fluid entrance/exit regions and of the central chevron zones. The three solid plates are considered as surfaces with virtual thicknesses which possess three-dimensional heat conduction capability. The plates have a herringbone pattern with trapezoidal shape corrugations; the gap between them, b, is 2.5 mm. Fig. 1c and d show, respectively, the main plate dimensions and the adopted coordinate system. Fig. 1e shows three particular cross-sections normal to the X-axis. It is worth noting that the plates do not touch each other at X ¼ 0. The X coordinates of the other two cross-sections were especially chosen so that the contact points between the plates can be visible. Complete details regarding the modeling of the geometry considered in this study are also available in Refs. [12e14]. The flow in the PHE is countercurrent. For the numerical model, the coordinate system is chosen so that the length, width and height of the channels are aligned with the X, Z and Y axis respectively (Fig. 1d). The inlet and exit ports for each fluid are located on the same side (side-flow PHE) with the two inlets on opposite sides, at the extremities of one of the plate’s diagonals. At the sides of the plates (Zmin and Zmax) there are areas free of
Fig. 2. Flow structure: (a) Velocity vectors and (b) streamlines, colored by temperature of the hot fluid, Re ¼ 475; (c) Streamlines of the hot fluid, Re ¼ 1565.
corrugations, which form two smooth passages that run over their entire length. As observed in our previous paper [13] and also by Lozano et al. [4] for a PHE with similar construction, the fluid preferentially flows within these longitudinal passages because of reduced friction therein. The problem under consideration is a steady-state fluid flow and heat transfer one. All the properties of the fluids used in this study
Table 1 Main parameters of the simulations. Water/water series
Water/oil series
Simulation no.
Vin (m/s)
Mean channels velocity (m/s)
Channels volumetric flow rate (m3/s)
Rec
Reh
Rec
Reh
1 2 3 4 5 6
0.1 0.2 0.3 0.4 0.5 0.6
4.386∙102 8.773∙102 1.316∙101 1.755∙101 2.193∙101 2.632∙101
1.89177∙105 3.78354∙105 5.67531∙105 7.56708∙105 9.45885∙105 1.13506∙104
316 579 832 1080 1325 1568
475 1012 1565 2123 2685 3239
249 480 705 929 1152 1375
3.5 8.0 13.1 18.3 23.7 29.2
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(water and engine oil) are considered to be temperature dependent. The corresponding data was taken from [15] and [16] for water and engine oil respectively and implemented in the numerical code as piecewise-linear functions of temperature. Gravity forces are neglected. Therefore the hydrodynamic and thermal fields are coupled but the effects of buoyancy are not taken into account. Simulations were carried out for both the laminar and turbulent regimes. In this study we have used the laminar numerical model for flows with Reynolds numbers less than 400 and the Realizable keε model [17] with non-equilibrium wall functions for Reynolds numbers higher than 400. These choices were justified in our previous numerical study [13] and were the results of a detailed analysis and comparison between experimental and numerical data. The governing equations for the laminar numerical model are as follows [18]:
vðr$ui Þ vxi
¼ 0
(1)
vðr$ui Þ vp v vu m$ i ¼ r$gi þ uj $ vxj vxj vxi vxj vðr$CP $TÞ v vT k$ ¼ uj $ vxj vxj vxj
! (2)
! (3)
For the steady-state turbulent flow of an incompressible fluid the equations of continuity, momentum and energy are [18]:
vðr$ul Þ ¼ 0 vxi
(4)
vðr$ul Þ vp v vu ðm þ mt Þ$ l uj $ ¼ þ vxj vxi vxj vxj
! (5)
vðr$TÞ v vT Cp $uj $ ðk þ kt Þ$ ¼ vxj vxj vxj
! (6)
The equations for the kinetic turbulent energy and the rate of dissipation of the turbulence kinetic energy corresponding to the Realizable k-ε model are [19]:
# " mt vk vðr$kÞ v $ þ Gk þ Gb r$ε YM þ Sk uj $ ¼ $ mþ sk vxj vxj vxj
(7)
# " mt vε vðr$εÞ v ε2 pffiffiffiffiffiffiffi uj $ $ þ r$C1 $Sε þ Gb r$C1 $ ¼ $ mþ sε vxj vxj vxj k þ v$ε (8) The equation for the steady-state heat conduction with constant thermal conductivity in the solid walls is as follows [18]:
v2 T ¼ 0 vx2i
(9)
The significance of the various terms in Eqs. (1)e(9) is given in the Nomenclature. The domain was discretized using a tetrahedral mesh generation algorithm. The resulting mesh, chosen as a result of a grid sensitivity analysis, detailed in our previous work [13], contains 9.63∙106 elements and 1.78∙106 nodes. A commercial code [19], based on the finite volume method [20,21], was used to solve the set of partial differential governing equations in order to determine the flow and heat transfer in the PHE. As a consequence of using a tetrahedral mesh, and in order to minimize the numerical diffusion while solving the momentum and energy equations, each simulation was first carried out using the first-order discretization scheme for a few hundred iterations, followed by the second-order one until the final convergence. The PRESTO! discretization method
Fig. 3. Temperature field on the middle plate for: (a) water/water; (b) water/engine oil.
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Fig. 4. Fluid temperature variation with Z for cold and hot fluids.
was used for the calculation of the cell-face pressure and the SIMPLE algorithm was used for the treatment of velocity e pressure coupling. The calculations were carried out on an eight parallelprocessors station.
As convergence indicators, the residuals resulting from the integration of the conservation Eqs (1)e(9) over the finite control volumes were monitored. For all the simulations performed in this study, a converged solution was usually achieved
Fig. 5. Fluid temperature variation with X for cold and hot fluids.
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Fig. 6. Variation of hot fluid mass flow rate per unit area with Z at X ¼ 0 for: (a) Vin ¼ 0.1 m/s; (b) Vin ¼ 0.6 m/s.
with normalized residuals as low as 103 or less for the continuity, momentum and turbulent quantities equations and 106 or less for the energy equation. The mass balance for each stream and the balance of the heat quantity exchanged between the fluids were checked and differences of less than 0.6% were observed. At the two inlets, the velocity and the temperature of the fluids were specified. It was assumed that the velocity is uniformly distributed and the direction of the inlet velocity is normal to the curved inlet surface (see Fig. 1a and b). Turbulence intensity and hydraulic diameter were used to specify the turbulence boundary conditions at the inlets and outlets. The value of the turbulence intensity for all simulations was estimated from the following correlation [19]:
I ¼ 0:16Re1=8
(10)
For the two outlets, the pressure outlet condition was used. The backflow temperature was set equal to the average temperature of the two fluids at the inlets. 3. Results and discussion 3.1. Description of the simulated cases Two series of six simulations each are analyzed, the first one with water in the cold and hot channels and the second one with water and engine oil in the cold and hot channels respectively. The main parameters of the two series are presented in Table 1. For each simulation we used the same volumetric flow rate at the two inlets i.e. an identical mean inlet velocity for both channels. In order to calculate the Reynolds numbers for each fluid the properties were evaluated at the average temperature in the channel, i.e. the arithmetic mean of the inlet and outlet temperatures. For all simulations, the inlet fluid temperatures are fixed at 20 C and 80 C for the cold and hot side respectively.
It is worth noting that graphics representing the central plate in the next subsections are presented with respect to the axis system (see Fig. 1d); note that the Z-axis points to right and the X-axis points to the top of the plate. 3.2. Analysis of the flow structure Fig. 2a shows the zigzag flow pattern obtained in the central region of the hot channel for simulation No. 1 of the water/water series. The streamlines colored by temperature for the same simulation can be observed in Fig. 2b; it can be noticed that the flow is mainly aligned with the length of the channel, which is similar to that observed by others (see for example references [2e4]). It is interesting to observe that the flow is highly threedimensional. Thus, there are currents of fluid that follow the plate furrows; and where these currents intersect the flow becomes rotational or swirling. Fluid particles exhibit complex threedimensional and helical trajectories as seen in Fig. 2c which shows an isometric view of the flow structure for the hot fluid (water/water series) for simulation No. 3 (Reh ¼ 1565). 3.3. Structure of the thermal field Fig. 3a and b show the temperature distributions on the middle plate for the water/water simulations and for the water/engine oil simulations respectively. The white spots on the plate surface Table 2 Mass flow rate of the side streams as a percentage of the total mass flow rate. Vin
Percentage Water/water series Hot fluid: water
0.1 0.6
Water/engine oil series Hot fluid: engine oil
Left stream
Right stream
Total
Left stream
Right stream
Total
11.7 13.8
13.9 14.3
25.6 28.1
3.2 4.9
7.0 6.7
10.2 11.6
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indicate that these areas do not appear on the graphic as they belong to another boundary entity. For the water/water cases we can notice that the temperature distribution is more symmetrical with respect to X-axis (along the length of the plate), for the last four simulations (Vin from 0.3 to
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0.6 m/s). We can also see that, for small Reynolds numbers, the temperature distribution is clearly affected by the presence of the inlets. Thus, for the first simulation, Rec ¼ 316 and Reh ¼ 475, the cold zone is longer on the left side and the hot zone is longer on the right side, where the cold and the hot inlets are respectively
Fig. 7. Spatial variation of heat flux through the middle plate for Vin ¼ 0.3 m/s: (a) water/water; (b) water/engine oil; (c) detail of the figure for water/engine oil.
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Average heat flux (W/m2)
0.1 0.2 0.3 0.4 0.5 0.6
44,413 66,875 85,592 103,754 120,822 137,613
Table 4 Average heat fluxes for the water/engine oil simulations. Vin (m/s)
Average heat flux (W/m2)
0.1 0.2 0.3 0.4 0.5 0.6
14,777 21,644 25,545 28,652 31,229 33,434
positioned. As the inlet fluid velocities increase, the influence of the position of the inlets becomes less important. However, the temperature distribution is clearly not uniform along the width (Z-axis) of the plates, even for cases with higher Reynolds numbers. In the case of the engine oil (Fig. 3b), the temperature distribution is more uniform and the influence of the inlets is less important than in the case of a water/water PHE. The same symmetry with respect to the X-axis as in the case of Fig. 3a can be observed. In order to better visualize and to analyze more easily the temperature field we present temperature profiles along the Z-axis (Fig. 4) and along the X-axis (Fig. 5) for the Vin ¼ 0.3 m/s cases of the water/water and water/engine oil series. It is worth noting that the temperature shown at each Z or X coordinate in Figs. 4 and 5 is, in fact, a mass-weighted average of the fluid temperature computed along the Y axis (i.e. through the depth of the fluid volume between the plates) using the following equation:
P Tb;y ¼
y ðT$u$r$dAÞ P y ðu$r$dAÞ
(11)
In all these figures the fluctuations of fluid temperature indicate the effect due to the variation of the channel height (i.e. the thickness of the fluid volume) with the (X, Z) position.
As we can notice from these figures, the temperature profiles are very steep at the extremities of the channels where the straight smooth longitudinal passages are situated. For the water/water series we can clearly notice the negative influence of the peripheral fluid streams. Thus, at the extreme values of the Z-coordinate the cold fluid temperature is lower, and the hot fluid temperature is higher, compared to that in the central region of the channel. For the water/engine oil series we can observe that the peripheral fluid streams have a rather positive influence, especially in the case of the oil for which, at the extreme values of Z-coordinate, the fluid temperature is lower than in the central region of the channel. This can be explained by analyzing the Prandtl number of the two fluids for the considered temperature range; its value is between approximately 2.2 and 7 for the water but is much higher for the engine oil (between approximately 361 and 9297). Consequently, the convective heat transfer is more important in the case of engine oil. The peaks and valleys in these figures indicate the existence of local minimum and maximum values of the mass flow rate per unit area (see Fig. 6). They are due to the fact that the distance between the plates varies with the Z-position and it can be zero where they touch each other. Also, the heat exchange is more important near the “points” of contact between the plates (which are actually small parallelograms) because it takes place directly by conduction through the metal plates. The difference in Prandtl numbers also causes these “fluctuations” to be much higher in the case of engine oil. One can also notice that the heat transfer is weaker for the oil e for example in Fig. 4 we observe that the increase in temperature from one cross-section to the next is low and the temperatures at the three sections overlap at some points. We can also notice the influence of the inlets. In Fig. 4 we can observe that all curves exhibit a slight slope: the cold fluid is colder toward the left side which is the cold fluid entrance side, while the hot fluid is hotter toward the right side where the hot inlet is positioned. Fig. 5 shows the temperature profiles for three lines parallel to the X-axis at different Z-coordinates. In these figures we can clearly notice the non-uniformity of the fluid temperature field in the Z-direction for a given cross-section. This behavior which is contrary to some previous observations e see for example [5,8] e is a direct consequence of the non-uniform distribution of the flow within the channels, as discussed in Section 3.4. As in the case of Fig. 4, the peaks and valleys are much higher in the case of engine oil for the reasons presented above. From all these figures we can conclude that the temperature field exhibits a 3D complex distribution; it is not uniform either
Fig. 8. The PHE without the straight smooth longitudinal passages.
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along the Z or Y-axis, contrary to statements made in some other articles (see for example [5]). One source of these differences can be the fact that our data was obtained with a side port configuration PHE while the study of Kanaris et al. [5] was performed by using a diagonal port configuration. The absence of the straight smooth longitudinal passages in their case could be another cause of the uniformity of the thermal field. 3.4. Analysis of the flow distribution In order to visualize the distribution of the flow across the width of the channels, we show in this subsection the mass flow rate per unit area as a function of Z over the X ¼ 0 cross-section of the channels for different inlet velocities and fluids. The procedure of computing such a local mass flow rate is as follows: first, we divide a given cross-section of the channel perpendicular to the X-axis into many sub-surfaces of width DZ and perform the integration of the X-axis velocity component for each of these sub-surfaces; the result is then normalized with respect to the corresponding surface area:
P Mass flow rate per unit area ¼
y ðux $r$dAÞ
P
y
ðdAÞ
The flow distributions for the hot fluid in the first and the sixth cases of the water/water and water/engine oil simulation series are presented in Fig. 6a and b. We have presented only the hot fluids because the flow distribution for the water is similar for all simulations, and therefore, these figures are representative. One can notice the peaks and valleys in these figures which can be explained by the fact that the height of a channel varies with Z and X and it can be zero where the plates touch each other. We can also notice
Fig. 10. Comparison of the temperature field for two configurations: original (left) and without longitudinal passages (right).
that there are regions where the mass flow rate has the opposite sign; this means that in those regions the flow is complex and some currents of fluid may have an opposite direction with respect to the main flow direction. It is worth recalling that for the particular X ¼ 0 cross-section, there are no contact points between the plates (see again Fig. 1e). In all figures, one can observe that the mass flow rate that passes within the two straight smooth longitudinal passages is considerably higher than that in other regions of the channel. Globally, in the case of water, we can observe that the highest values (maximum or minimum depending upon the fluid direction) of the mass flow rate are nearly 5.3e7.2 times the average value on the rest of the section. In the case of oil, the mass flow distribution is more uniform: the highest values of the mass flow rate are from 3.4 to 3.7 times the average value of the rest of the section. It is interesting to notice that for the water/water cases the mass flow rate through the smooth longitudinal channels represents 25.6%e28.1% of the total (see Table 2). For the engine oil, the value is lower e up to 11.6%. These streams have an important effect on the heat exchanger efficiency, as discussed later in Section 3.6. 3.5. Analysis of the heat flux distribution Fig. 7a and b present the heat flux through the middle plate for the water/water and water/engine oil series respectively, all cases with Vin ¼ 0.3 m/s Fig. 7c shows a detail of Fig. 7b, a portion of the central chevron zone of the plate. We can observe that in both cases the heat flux is fairly uniform over most of the plate. The maximum values occur on a few very small areas, around “points” of contact between the plates (which are actually small parallelograms). In
Fig. 9. Comparison of the mass flow rate/unit area distributions at X ¼ 0 for water/oil and Vin ¼ 0.6 m/s: (a) cold channel and (b) hot channel.
Fig. 11. Nusselt number comparison.
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Fig. 12. Friction factor comparison.
these areas, the heat exchange is important because it takes place directly by conduction through the metal plates. Also, in the case of the water/water series the heat flux is generally more important along the two straight smooth longitudinal passages where the fastest fluid streams are present (see Fig. 6). Tables 3 and 4 present the average heat fluxes for the cases under consideration. This quantity increases monotonically with the inlet velocity but the rate of increase diminishes as Vin increases. It is also noted that the average heat flux is three to four times higher in the case of water/ water. It may be noted in Fig. 7c the appearance of “peacock tail” of the distribution of heat flux on the area of the corrugated plate. It is important to note that the heat transferred across the two entrance/exit regions of the middle plate is between 19.5% and 23.0% of the corresponding total for each of the twelve cases under investigation (see Table 1). This result shows that these regions are very important for the calculation of the PHE thermal performance and must be included in heat transfer simulations. Furthermore, since these regions represent 21% of the total heat transfer area of the plate it follows that their contribution to heat transfer is equivalent to that of the central chevron zone. 3.6. Performance of the PHE without the longitudinal streams The results presented in the previous paragraphs suggest that the presence of the straight smooth longitudinal passages causes a deterioration of the thermal performance accompanied by a beneficial decrease of the pressure loss. In order to verify this hypothesis a modified geometrical configuration which does not contain the straight smooth longitudinal passages was considered
(see Fig. 8). In a real PHE it is possible to eliminate these passages by using straight gaskets to completely fill the grooves. Various simulations were performed with this new configuration in order to analyze qualitatively and quantitatively its behavior. First, simulations were performed for the conditions in Table 1. Fig. 9a and b compare the mass flow rate distributions for the sixth case in the water/engine oil series which is representative of the behavior for all cases. In each figure we plot the curve obtained for the original geometry with the straight smooth longitudinal passages and that obtained by obstructing these passages. By consequence, the curves for the original geometry are the same as those presented in Fig. 6. For the new geometry, we obviously notice the absence of the fluid streams near the left and right edges of the plate. The peaks and valleys of the profiles occur at the same positions reflecting the presence of the obstructions and channels caused by the chevrons. For the cold fluid (Fig. 9a) the maximum (upward) flow is everywhere higher in the new geometry. The minimum values in the new geometry are lower than in the original one. In fact, the results for the new geometry suggest that flow reversal may be present in this case. For the hot fluid (Fig. 9b) the maximum (downward) flow is everywhere higher in the new geometry. The minimum values are sometimes positive suggesting that flow reversal may also occur in the hot fluid. Fig. 10 presents the comparison between the distributions of temperature on the middle plate for the case water/water with Vin ¼ 0.1 m/s for the original geometry and the geometry with longitudinal passages obstructed. It is noted that the temperature distributions are similar in the area of the plate common for these images. The same similarity was observed by analyzing all the results and therefore these cases are not presented here. Since these results do not give clear indications regarding the influence of the straight smooth longitudinal passages on the PHE performance we have compared the numerical predictions of the Nusselt number and friction factor for the PHEs with and without these longitudinal passages. In order to obtain the Nusselt number another set of 11 simulations was performed with water in both channels of the PHE. The cold fluid flow rate was maintained constant and the cold fluid Reynolds number was around 800. The hot side Reynolds number was varied between 400 and 1400 by changing the corresponding flow rate. These simulations are based on our previous numerical data [13]. For the friction factor, the simulations were performed considering isothermal conditions with water at 25 C and the related constant properties. This approach was often adopted (see in particular [2,22]).
Fig. 13. The 3D model of the diagonal-flow PHE e view of a fluid zone.
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Fig. 14. Comparison between the flow distributions for the side-flow and diagonalflow configurations.
The results are presented in Figs. 11 and 12 respectively. The obstruction of the straight smooth longitudinal passages causes an increase of both the Nusselt number and the friction factor. The average increase is 12.4% (between 9.2 and 15.7%) for the Nusselt number and 19.5% (between 14.5 and 21.2%) for the friction factor. This improvement in terms of heat transfer suggests that is possible to decrease the size of the PHE for the same heat transfer rate at the cost of a larger pressure drop, which can be translated by a larger pumping power requirement. 3.7. Influence of port arrangement on the performance of the PHE The port arrangement can result in side-flow or diagonal-flow PHEs. The fact that the port arrangement can influence the thermal and hydraulic performance of PHEs is mentioned in some works [15,23]. Gut and Pinto [24,25] mentioned that the influence of the port arrangement over the convective coefficients and friction factor is unknown. All the above mentioned sources cited the work of Okada et al. [10] in which a comparison of temperature profiles for Reynolds number of approximately 4000 in a PHE of nonchevron type was performed. This comparison has shown that there is no significant difference between the two arrangements. In order to compare the two port arrangements, another model was built. This model was obtained by modifying the one presented in Section 2. For each fluid, one of the distribution zones, including the corresponding inlet or outlet, has been mirrored about the Xaxis (Fig. 13). Simulations were then performed for this new geometry, the two fluid combinations (water/water and water/oil) and the conditions specified in Table 1. The comparison of flow distribution shows some small hydrodynamic differences between the two port configurations. In Fig. 14
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the results for the hot fluid from the first simulation of the water/ engine oil series are shown. It can be noticed that the fluid is better distributed in the case of the diagonal-flow configuration; the peak close to Zmax is less pronounced and generally there is more symmetry than in the case of the side-flow configuration. Fig. 15 shows the temperature distributions on the middle plate for the water/water simulations with Vin ¼ 0.1 m/s. In the left and the right side of this figure are represented the result for the sideflow and the diagonal-flow PHE respectively. One can notice that the temperature distribution is more symmetrical with respect to the X-axis (along the length of the plate) for the diagonal-flow case. As the inlet fluid velocities increase the influence of the port arrangement becomes less important. Therefore, these cases are not presented here. The results also show that there are small differences in heat transfer between the two types of port arrangements. The Nusselt number is higher for the diagonal port than for the side port type: the enhancement is estimated to be 1.7% in average (it varies between 1.3% and 2.4%) for the water/water series, and 1.6% in average (varying between 0.9% and 3.2%) for the water/oil series. The differences in terms of friction factor are insignificant; for all simulations, the differences are lower than 0.4% between the two port arrangements. 4. Conclusion This paper presented results from numerical simulations of the flow and heat transfer in a two-channel side-flow PHE. The temperature, heat flux and mass flow distribution were analyzed in the case of two fluid combinations: water/water and water/engine oil. The temperature field was found to be non-uniform and to depend strongly on the fluid combination: it appears to be more uniform in the case of the water/engine oil case. The flow in the channels presents two streams of higher velocity near the lateral sides of the PHE, regions where straight smooth passages parallel to the X-axis are present. The relative importance of these streams varies with the flow rate and with the fluid used; it is less prominent in the case of oil, for which the mass flow distribution is more uniform. A comparison with the results obtained with obstructed longitudinal passages shows that their presence decreases both the heat transfer rate and the friction factor. The side-flow and diagonal-flow PHE configurations have also been compared and a small improvement in the heat transfer rate was observed when using the diagonal-flow configuration, especially at small flow rates. Acknowledgements This project is part of the R&D program of the NSERC Chair in Industrial Energy Efficiency established in 2006 at Université de Sherbrooke. The authors acknowledge the support of the Natural Sciences & Engineering Research Council of Canada, Hydro Québec, Rio Tinto Alcan and Canmet-Energy Research Center. References
Fig. 15. Temperature field on the middle plate for: the side-flow PHE (left) and the diagonal-flow PHE (right).
[1] M.F. Edwards, Heat transfer in plate heat exchangers at low Reynolds numbers. in: S. Kakac, R.K. Shah, A.E. Bergles (Eds.), Low Reynolds Number Flow Heat Exchangers. Hemisphere Publishing Corporation, 1983 (Chapter 7). [2] A. Muley, R.M. Manglik, Investigation of enhanced heat transfer in low Reynolds number flows in a plate heat exchanger, Proceedings of the ASME, Heat Transfer Division 3 (1998) 295e302. [3] L. Wang, B. Sundén, R.M. Manglik, Plate heat exchangers e design, applications and performance. Wit Press, 2007. [4] A. Lozano, F. Barreras, N. Fueyo, S. Santodomingo, The flow in an oil/water plate heat exchanger for the automotive industry, Applied Thermal Engineering 28 (10) (2008) 1109e1117.
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[5] A.G. Kanaris, A.A. Mouza, S.V. Paras, Flow and heat transfer prediction in a corrugated plate heat exchanger using a CFD code, Chemical Engineering & Technology 29 (8) (2006) 923e930. [6] Y.C. Tsai, F.B. Liu, P.T. Shen, Investigations of the pressure drop and flow distribution in a chevron-type plate heat exchanger, International Communications in Heat and Mass Transfer 36 (2009) 574e578. [7] S. Jain, A. Joshi, P.K. Bansal, A new approach to numerical simulation of small sized plate heat exchangers with chevron plates, Journal of Heat Transfer 129 (2007) 291e297. [8] N. Hur, M. Lee, B.H. Kang, C.S. Won, Numerical analysis of heat transfer in a plate heat exchanger, Progress in Computational Fluid Dynamics 8 (7/8) (2008) 406e412. [9] F.C.C. Galeazzo, R.Y. Miura, J.A.W. Gut, C.C. Tadini, Experimental and numerical heat transfer in a plate heat exchanger, Chemical Engineering Science 61 (2006) 7133e7138. [10] K. Okada, M. Ono, T. Tomimura, T. Okuma, H. Konno, S. Ohtani, Temperature distribution in plate type heat exchangers, Kagaku Kogaku 34 (1) (1970) 93e95 (in Japanese). [11] X.H. Han, L.Q. Cui, S.J. Chen, G.M. Chen, Q. Wang, A numerical and experimental study of chevron, corrugated-plate heat exchangers, International Communications in Heat and Mass Transfer 37 (2010) 1008e1014. [12] I. Gherasim, M. Taws, N. Galanis, C.T. Nguyen, Heat transfer and fluid flow in a plate heat exchanger. Part I e Experimental investigation, International Journal of Thermal Sciences 50 (2011) 1492e1498. [13] I. Gherasim, N. Galanis, C.T. Nguyen, Heat transfer and fluid flow in a plate heat exchanger. Part II e Assessment of laminar and two equation turbulent models, International Journal of Thermal Sciences 50 (2011) 1499e1511.
[14] Gherasim I, Galanis N, Nguyen C.T. Numerical investigation of heat transfer for laminar and turbulent flow in a plate heat exchanger. In: Proc. 14th International Heat Transfer Conference. Washington D.C., USA, Paper No. IHTC1422378; 2010. p. 10. [15] American Society of Heating and Refrigerating. ASHRAE Handbook of Fundamentals; 2005. [16] F.P. Incropera, D.P. DeWitt Appendix A, Fundamentals of heat and mass transfer John Wiley and Sons, 2006. [17] T.H. Shih, W.W. Liou, A. Shabbir, Z. Yang, J. Zhu, A new k-ε eddy-viscosity model for High Reynolds number turbulent flows e model development and validation, Computers and Fluids 24 (3) (1995) 227e238. [18] W.J. Minkowycz, E.M. Sparrow, J.Y. Murthy, Handbook of Numerical Heat Transfer Wiley, 2006. [19] Fluent Inc. FLUENT 6.3 User’s Manual; 2006. [20] H.K. Versteeg, W. Malalasekera, Introduction to computational fluid dynamics: the finite volume method. Pearson/Prentice-Hall, 1995. [21] S.V. Patankar, Numerical heat transfer and fluid flow. Hemisphere Inc., McGraw-Hill, New York, USA, 1980. [22] Heavner H, Kumar RL, Wanniarachchci AS. Performance of an industrial plate heat exchanger: Effect of chevron angle. In: Proceedings of the 29th National Heat Transfer Conference. Atlanta, GA, 89: 262e267. [23] A. Cooper, J.D. Usher, USA Section 3.7 e Plate heat exchangers, in: Heat Exchanger Design Handbook, vol. 3. Hemisphere, Washington, 1983. [24] J.A. Gut, J.M. Pinto, Modeling of plate heat exchangers with generalized configuration, International Journal of Heat and Mass Transfer 46 (2003) 2571e2585. [25] J.A. Gut, J.M. Pinto, Optimal configuration design for plate heat exchangers, International Journal of Heat and Mass Transfer 47 (2004) 4833e4848.
Contents lists available at SciVerse ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Effects of smooth longitudinal passages and port configuration on the flow and thermal fields in a plate heat exchanger Iulian Gherasim a, Nicolas Galanis a, Cong Tam Nguyen b, * a b
Mechanical Engineering, Université de Sherbrooke, Sherbrooke, QC, Canada J1K 2R1 Mechanical Engineering, Université de Moncton, Moncton, NB, Canada E1A 3E9
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 June 2011 Accepted 16 August 2011 Available online 23 August 2011
Numerical results for heat transfer with laminar or turbulent flow in a two-channel PHE are presented. The temperature, heat flux and mass flow distributions are analyzed in the case of two fluid combinations: water/water and water/engine oil. These results show that, in the case of water/engine oil, both the thermal field and the mass flow distribution are more uniform compared to the water/water case. A comparison between the original geometry and the geometry with obstructed longitudinal channels shows that the presence of these passages decreases the heat transfer rate and the friction factor. The calculated performances of the side-flow and diagonal-flow configurations differ only slightly. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Plate heat exchanger Temperature distribution Flow distribution Smooth longitudinal passages Port configuration CFD Laminar flow Turbulent flow
1. Introduction Plate heat exchangers (PHE) are widely used in many applications (food, oil, chemical and paper industries, HVAC, heat recovery, refrigeration, etc.) because of their small size and weight, the ease of cleaning as well as their superior thermal performance compared to other types of heat exchangers. Due to the corrugations, which induce secondary flows, boundary layer separation and turbulence at relatively low Re numbers, they are well suited to low Reynolds number flows encountered when using viscous liquids such as engine oil [1,2]. For a detailed synthesis of the applications of the PHEs see for example [3]. Several experimental and numerical studies have therefore been recently conducted in order to predict the flow and temperature distribution in PHEs. Many of the latter use simplifying assumptions. Lozano et al. [4] analyzed the flow distribution inside one channel of a PHE for the automotive industry, without considering the heat transfer. They created and validated a 3D model which consists of a single channel. Their analysis concluded that the flow was not uniform and preferentially moved along the lateral extremes of the plates. Kanaris et al. [5] studied the flow and heat
* Corresponding author. Tel.: þ1 506 858 4347; fax: þ1 506 858 4082. E-mail address: [email protected] (C. T. Nguyen). 1359-4311/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2011.08.025
transfer in a PHE. They used a 3D model which includes two complete channels and validated it against experimental and literature data. A similar model was used by Tsai et al. [6] in order to investigate the hydrodynamic characteristics and distribution of flow inside a PHE with no heat transfer involved. Their CFD models use the real geometry of the plates, including the entire entrance and distribution zones. Jain et al. [7] considered a 3D turbulent model with a complete cold channel and two halves of the adjacent hot channels. This model uses more realistic hydrodynamic and thermal boundary conditions; the two halves of the hot channels on either side have flat periodic boundaries. As a result, they were able to validate their model on a PHE with 13 channels. Hur et al. [8] created a similar model in order to study the heat transfer in a PHE. Although the chevron angle is the same with the one in the present study (4 ¼ 60 ) and the Reynolds number varied between 249 and 1018, they used only the laminar model for all the simulations. Galeazzo et al. [9] have modeled in three dimensions an industrial PHE with four channels. However, this PHE was a nonchevron type with five smooth plates. The authors have investigated parallel and series flow arrangements and validated it with experimental data. In their experimental work Okada et al. [10] analyzed the temperature distribution on the first and last plates of a two-channels PHE of non-chevron type. They
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Nomenclature dA C1,C2 Cp DH f g Gk,Gb
hm k, kt L Nu p Re Sk, Sε T Tm
elementary surface, m2 constants specific heat, J kg1 K1 channel hydraulic diameter, m Darcy friction factor,f ¼ 2 ΔP DH/(rm L u2m) gravitational acceleration, m s2 rates of turbulence kinetic energy generation due to mean velocity gradients and to buoyancy respectively, J m3 average heat transfer coefficient, W m2 K1 thermal conductivity, turbulent thermal conductivity, W m1 K1 length of the channel, m Nusselt number, Nu ¼ hm DH/km pressure, Pa channel flow Reynolds number, Re ¼ um DH rm/mm user-defined source terms temperature, K average temperature in a channel, K
compared the temperature distributions for diagonal and sideflow channels, and also for upwards and downwards flow of the cold and hot fluids. To our knowledge, this is the only article with such results. Han et al. [11] in their numerical and experimental study, described the temperature and pressure distribution on a chevron corrugated PHE with five plates (four channels). By analyzing the temperature distribution and the streamlines, the authors noticed that the flow prefers to flow to the port side. They validated the numerical results, finding similar experimental and
ui ; ui um xi X, Y, Z YM
i-axis velocity component and time-averaged value, m s1 mean velocity of the fluid in a channel, m s1 i-axis coordinates contribution of the fluctuating dilatation to the dissipation rate (for compressible flows)
Greek letters ΔP pressure loss between inlet and outlet of a channel, Pa ε turbulence kinetic energy dissipation rate, J kg1 k turbulence kinetic energy, J kg1 s1 y, yt kinematic viscosity, turbulent kinematic viscosity, m2 s1 m, mt dynamic viscosity, turbulent dynamic viscosity, Pa s r density, kg m3 sk,sε constants Subscripts b refers to bulk temperature m refers to the average value in the channel, with properties evaluated at Tm numerical results in terms of outlet temperatures and pressure drops. In our previous experimental [12] and numerical [13,14] articles the hydrodynamic and thermal fields in a two-channel chevron PHE were analyzed for water flow in both channels. The CFD model was satisfactorily validated for both laminar e using the laminar model e and turbulent conditions [13] e using two-equation turbulent models e by comparing the numerical and experimental temperature distributions on the PHE’s exterior plates, the friction factor and the Nusselt number for each channel, as well as
Fig. 1. (a) View of the model with 2 channels; (b) a detail of the fluid volume; (c) main dimensions in mm; (d) the coordinate system with positions of inlets and outlets; (e) Crosssections of the channel at three positions.
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the outlet temperatures of the two streams. For the turbulent flow regime, the Realizable keε model with non-equilibrium wall functions was found to give the closest results with respect to the experimental data. This CFD model is used in the present study which aims to analyze in more depth the flow, temperature and heat flux distribution inside a PHE, by considering both flow and heat transfer. This CFD model includes the complete geometry of the channels and possesses more complex distribution zones than other studies. The side port and diagonal port PHEs are also compared in terms of their hydraulic and heat transfer performance. The results for two fluid combinations (water/water and water/engine oil) are analyzed and compared. This study also aims to assess the influence of the smooth longitudinal straight passages (which is a particularity of the present PHE) on the overall thermal and hydraulic performances of the PHE. A comparison between the side-flow and diagonal-flow configurations in terms of heat transfer and pressure loss is also presented. The paper is organized in two main sections. In Section 2 details regarding the numerical modeling (geometry considered, governing equations and boundary conditions) are presented. In Section 3 numerical results obtained for the flow and thermal fields are shown and discussed, with emphasis on the effect due to the presence of smooth longitudinal passages as well as that of the port configuration. The paper terminates with the conclusion that summarizes the main findings. 2. Numerical modeling The calculation domain, which consists of a two-channel PHE tested in our experimental study, consists of three plates and two fluid passages (Fig. 1a, b) confined between the plates. It reproduces with fidelity the geometry of the physical system, including all geometrical details of the fluid entrance/exit regions and of the central chevron zones. The three solid plates are considered as surfaces with virtual thicknesses which possess three-dimensional heat conduction capability. The plates have a herringbone pattern with trapezoidal shape corrugations; the gap between them, b, is 2.5 mm. Fig. 1c and d show, respectively, the main plate dimensions and the adopted coordinate system. Fig. 1e shows three particular cross-sections normal to the X-axis. It is worth noting that the plates do not touch each other at X ¼ 0. The X coordinates of the other two cross-sections were especially chosen so that the contact points between the plates can be visible. Complete details regarding the modeling of the geometry considered in this study are also available in Refs. [12e14]. The flow in the PHE is countercurrent. For the numerical model, the coordinate system is chosen so that the length, width and height of the channels are aligned with the X, Z and Y axis respectively (Fig. 1d). The inlet and exit ports for each fluid are located on the same side (side-flow PHE) with the two inlets on opposite sides, at the extremities of one of the plate’s diagonals. At the sides of the plates (Zmin and Zmax) there are areas free of
Fig. 2. Flow structure: (a) Velocity vectors and (b) streamlines, colored by temperature of the hot fluid, Re ¼ 475; (c) Streamlines of the hot fluid, Re ¼ 1565.
corrugations, which form two smooth passages that run over their entire length. As observed in our previous paper [13] and also by Lozano et al. [4] for a PHE with similar construction, the fluid preferentially flows within these longitudinal passages because of reduced friction therein. The problem under consideration is a steady-state fluid flow and heat transfer one. All the properties of the fluids used in this study
Table 1 Main parameters of the simulations. Water/water series
Water/oil series
Simulation no.
Vin (m/s)
Mean channels velocity (m/s)
Channels volumetric flow rate (m3/s)
Rec
Reh
Rec
Reh
1 2 3 4 5 6
0.1 0.2 0.3 0.4 0.5 0.6
4.386∙102 8.773∙102 1.316∙101 1.755∙101 2.193∙101 2.632∙101
1.89177∙105 3.78354∙105 5.67531∙105 7.56708∙105 9.45885∙105 1.13506∙104
316 579 832 1080 1325 1568
475 1012 1565 2123 2685 3239
249 480 705 929 1152 1375
3.5 8.0 13.1 18.3 23.7 29.2
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(water and engine oil) are considered to be temperature dependent. The corresponding data was taken from [15] and [16] for water and engine oil respectively and implemented in the numerical code as piecewise-linear functions of temperature. Gravity forces are neglected. Therefore the hydrodynamic and thermal fields are coupled but the effects of buoyancy are not taken into account. Simulations were carried out for both the laminar and turbulent regimes. In this study we have used the laminar numerical model for flows with Reynolds numbers less than 400 and the Realizable keε model [17] with non-equilibrium wall functions for Reynolds numbers higher than 400. These choices were justified in our previous numerical study [13] and were the results of a detailed analysis and comparison between experimental and numerical data. The governing equations for the laminar numerical model are as follows [18]:
vðr$ui Þ vxi
¼ 0
(1)
vðr$ui Þ vp v vu m$ i ¼ r$gi þ uj $ vxj vxj vxi vxj vðr$CP $TÞ v vT k$ ¼ uj $ vxj vxj vxj
! (2)
! (3)
For the steady-state turbulent flow of an incompressible fluid the equations of continuity, momentum and energy are [18]:
vðr$ul Þ ¼ 0 vxi
(4)
vðr$ul Þ vp v vu ðm þ mt Þ$ l uj $ ¼ þ vxj vxi vxj vxj
! (5)
vðr$TÞ v vT Cp $uj $ ðk þ kt Þ$ ¼ vxj vxj vxj
! (6)
The equations for the kinetic turbulent energy and the rate of dissipation of the turbulence kinetic energy corresponding to the Realizable k-ε model are [19]:
# " mt vk vðr$kÞ v $ þ Gk þ Gb r$ε YM þ Sk uj $ ¼ $ mþ sk vxj vxj vxj
(7)
# " mt vε vðr$εÞ v ε2 pffiffiffiffiffiffiffi uj $ $ þ r$C1 $Sε þ Gb r$C1 $ ¼ $ mþ sε vxj vxj vxj k þ v$ε (8) The equation for the steady-state heat conduction with constant thermal conductivity in the solid walls is as follows [18]:
v2 T ¼ 0 vx2i
(9)
The significance of the various terms in Eqs. (1)e(9) is given in the Nomenclature. The domain was discretized using a tetrahedral mesh generation algorithm. The resulting mesh, chosen as a result of a grid sensitivity analysis, detailed in our previous work [13], contains 9.63∙106 elements and 1.78∙106 nodes. A commercial code [19], based on the finite volume method [20,21], was used to solve the set of partial differential governing equations in order to determine the flow and heat transfer in the PHE. As a consequence of using a tetrahedral mesh, and in order to minimize the numerical diffusion while solving the momentum and energy equations, each simulation was first carried out using the first-order discretization scheme for a few hundred iterations, followed by the second-order one until the final convergence. The PRESTO! discretization method
Fig. 3. Temperature field on the middle plate for: (a) water/water; (b) water/engine oil.
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Fig. 4. Fluid temperature variation with Z for cold and hot fluids.
was used for the calculation of the cell-face pressure and the SIMPLE algorithm was used for the treatment of velocity e pressure coupling. The calculations were carried out on an eight parallelprocessors station.
As convergence indicators, the residuals resulting from the integration of the conservation Eqs (1)e(9) over the finite control volumes were monitored. For all the simulations performed in this study, a converged solution was usually achieved
Fig. 5. Fluid temperature variation with X for cold and hot fluids.
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Fig. 6. Variation of hot fluid mass flow rate per unit area with Z at X ¼ 0 for: (a) Vin ¼ 0.1 m/s; (b) Vin ¼ 0.6 m/s.
with normalized residuals as low as 103 or less for the continuity, momentum and turbulent quantities equations and 106 or less for the energy equation. The mass balance for each stream and the balance of the heat quantity exchanged between the fluids were checked and differences of less than 0.6% were observed. At the two inlets, the velocity and the temperature of the fluids were specified. It was assumed that the velocity is uniformly distributed and the direction of the inlet velocity is normal to the curved inlet surface (see Fig. 1a and b). Turbulence intensity and hydraulic diameter were used to specify the turbulence boundary conditions at the inlets and outlets. The value of the turbulence intensity for all simulations was estimated from the following correlation [19]:
I ¼ 0:16Re1=8
(10)
For the two outlets, the pressure outlet condition was used. The backflow temperature was set equal to the average temperature of the two fluids at the inlets. 3. Results and discussion 3.1. Description of the simulated cases Two series of six simulations each are analyzed, the first one with water in the cold and hot channels and the second one with water and engine oil in the cold and hot channels respectively. The main parameters of the two series are presented in Table 1. For each simulation we used the same volumetric flow rate at the two inlets i.e. an identical mean inlet velocity for both channels. In order to calculate the Reynolds numbers for each fluid the properties were evaluated at the average temperature in the channel, i.e. the arithmetic mean of the inlet and outlet temperatures. For all simulations, the inlet fluid temperatures are fixed at 20 C and 80 C for the cold and hot side respectively.
It is worth noting that graphics representing the central plate in the next subsections are presented with respect to the axis system (see Fig. 1d); note that the Z-axis points to right and the X-axis points to the top of the plate. 3.2. Analysis of the flow structure Fig. 2a shows the zigzag flow pattern obtained in the central region of the hot channel for simulation No. 1 of the water/water series. The streamlines colored by temperature for the same simulation can be observed in Fig. 2b; it can be noticed that the flow is mainly aligned with the length of the channel, which is similar to that observed by others (see for example references [2e4]). It is interesting to observe that the flow is highly threedimensional. Thus, there are currents of fluid that follow the plate furrows; and where these currents intersect the flow becomes rotational or swirling. Fluid particles exhibit complex threedimensional and helical trajectories as seen in Fig. 2c which shows an isometric view of the flow structure for the hot fluid (water/water series) for simulation No. 3 (Reh ¼ 1565). 3.3. Structure of the thermal field Fig. 3a and b show the temperature distributions on the middle plate for the water/water simulations and for the water/engine oil simulations respectively. The white spots on the plate surface Table 2 Mass flow rate of the side streams as a percentage of the total mass flow rate. Vin
Percentage Water/water series Hot fluid: water
0.1 0.6
Water/engine oil series Hot fluid: engine oil
Left stream
Right stream
Total
Left stream
Right stream
Total
11.7 13.8
13.9 14.3
25.6 28.1
3.2 4.9
7.0 6.7
10.2 11.6
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indicate that these areas do not appear on the graphic as they belong to another boundary entity. For the water/water cases we can notice that the temperature distribution is more symmetrical with respect to X-axis (along the length of the plate), for the last four simulations (Vin from 0.3 to
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0.6 m/s). We can also see that, for small Reynolds numbers, the temperature distribution is clearly affected by the presence of the inlets. Thus, for the first simulation, Rec ¼ 316 and Reh ¼ 475, the cold zone is longer on the left side and the hot zone is longer on the right side, where the cold and the hot inlets are respectively
Fig. 7. Spatial variation of heat flux through the middle plate for Vin ¼ 0.3 m/s: (a) water/water; (b) water/engine oil; (c) detail of the figure for water/engine oil.
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Average heat flux (W/m2)
0.1 0.2 0.3 0.4 0.5 0.6
44,413 66,875 85,592 103,754 120,822 137,613
Table 4 Average heat fluxes for the water/engine oil simulations. Vin (m/s)
Average heat flux (W/m2)
0.1 0.2 0.3 0.4 0.5 0.6
14,777 21,644 25,545 28,652 31,229 33,434
positioned. As the inlet fluid velocities increase, the influence of the position of the inlets becomes less important. However, the temperature distribution is clearly not uniform along the width (Z-axis) of the plates, even for cases with higher Reynolds numbers. In the case of the engine oil (Fig. 3b), the temperature distribution is more uniform and the influence of the inlets is less important than in the case of a water/water PHE. The same symmetry with respect to the X-axis as in the case of Fig. 3a can be observed. In order to better visualize and to analyze more easily the temperature field we present temperature profiles along the Z-axis (Fig. 4) and along the X-axis (Fig. 5) for the Vin ¼ 0.3 m/s cases of the water/water and water/engine oil series. It is worth noting that the temperature shown at each Z or X coordinate in Figs. 4 and 5 is, in fact, a mass-weighted average of the fluid temperature computed along the Y axis (i.e. through the depth of the fluid volume between the plates) using the following equation:
P Tb;y ¼
y ðT$u$r$dAÞ P y ðu$r$dAÞ
(11)
In all these figures the fluctuations of fluid temperature indicate the effect due to the variation of the channel height (i.e. the thickness of the fluid volume) with the (X, Z) position.
As we can notice from these figures, the temperature profiles are very steep at the extremities of the channels where the straight smooth longitudinal passages are situated. For the water/water series we can clearly notice the negative influence of the peripheral fluid streams. Thus, at the extreme values of the Z-coordinate the cold fluid temperature is lower, and the hot fluid temperature is higher, compared to that in the central region of the channel. For the water/engine oil series we can observe that the peripheral fluid streams have a rather positive influence, especially in the case of the oil for which, at the extreme values of Z-coordinate, the fluid temperature is lower than in the central region of the channel. This can be explained by analyzing the Prandtl number of the two fluids for the considered temperature range; its value is between approximately 2.2 and 7 for the water but is much higher for the engine oil (between approximately 361 and 9297). Consequently, the convective heat transfer is more important in the case of engine oil. The peaks and valleys in these figures indicate the existence of local minimum and maximum values of the mass flow rate per unit area (see Fig. 6). They are due to the fact that the distance between the plates varies with the Z-position and it can be zero where they touch each other. Also, the heat exchange is more important near the “points” of contact between the plates (which are actually small parallelograms) because it takes place directly by conduction through the metal plates. The difference in Prandtl numbers also causes these “fluctuations” to be much higher in the case of engine oil. One can also notice that the heat transfer is weaker for the oil e for example in Fig. 4 we observe that the increase in temperature from one cross-section to the next is low and the temperatures at the three sections overlap at some points. We can also notice the influence of the inlets. In Fig. 4 we can observe that all curves exhibit a slight slope: the cold fluid is colder toward the left side which is the cold fluid entrance side, while the hot fluid is hotter toward the right side where the hot inlet is positioned. Fig. 5 shows the temperature profiles for three lines parallel to the X-axis at different Z-coordinates. In these figures we can clearly notice the non-uniformity of the fluid temperature field in the Z-direction for a given cross-section. This behavior which is contrary to some previous observations e see for example [5,8] e is a direct consequence of the non-uniform distribution of the flow within the channels, as discussed in Section 3.4. As in the case of Fig. 4, the peaks and valleys are much higher in the case of engine oil for the reasons presented above. From all these figures we can conclude that the temperature field exhibits a 3D complex distribution; it is not uniform either
Fig. 8. The PHE without the straight smooth longitudinal passages.
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along the Z or Y-axis, contrary to statements made in some other articles (see for example [5]). One source of these differences can be the fact that our data was obtained with a side port configuration PHE while the study of Kanaris et al. [5] was performed by using a diagonal port configuration. The absence of the straight smooth longitudinal passages in their case could be another cause of the uniformity of the thermal field. 3.4. Analysis of the flow distribution In order to visualize the distribution of the flow across the width of the channels, we show in this subsection the mass flow rate per unit area as a function of Z over the X ¼ 0 cross-section of the channels for different inlet velocities and fluids. The procedure of computing such a local mass flow rate is as follows: first, we divide a given cross-section of the channel perpendicular to the X-axis into many sub-surfaces of width DZ and perform the integration of the X-axis velocity component for each of these sub-surfaces; the result is then normalized with respect to the corresponding surface area:
P Mass flow rate per unit area ¼
y ðux $r$dAÞ
P
y
ðdAÞ
The flow distributions for the hot fluid in the first and the sixth cases of the water/water and water/engine oil simulation series are presented in Fig. 6a and b. We have presented only the hot fluids because the flow distribution for the water is similar for all simulations, and therefore, these figures are representative. One can notice the peaks and valleys in these figures which can be explained by the fact that the height of a channel varies with Z and X and it can be zero where the plates touch each other. We can also notice
Fig. 10. Comparison of the temperature field for two configurations: original (left) and without longitudinal passages (right).
that there are regions where the mass flow rate has the opposite sign; this means that in those regions the flow is complex and some currents of fluid may have an opposite direction with respect to the main flow direction. It is worth recalling that for the particular X ¼ 0 cross-section, there are no contact points between the plates (see again Fig. 1e). In all figures, one can observe that the mass flow rate that passes within the two straight smooth longitudinal passages is considerably higher than that in other regions of the channel. Globally, in the case of water, we can observe that the highest values (maximum or minimum depending upon the fluid direction) of the mass flow rate are nearly 5.3e7.2 times the average value on the rest of the section. In the case of oil, the mass flow distribution is more uniform: the highest values of the mass flow rate are from 3.4 to 3.7 times the average value of the rest of the section. It is interesting to notice that for the water/water cases the mass flow rate through the smooth longitudinal channels represents 25.6%e28.1% of the total (see Table 2). For the engine oil, the value is lower e up to 11.6%. These streams have an important effect on the heat exchanger efficiency, as discussed later in Section 3.6. 3.5. Analysis of the heat flux distribution Fig. 7a and b present the heat flux through the middle plate for the water/water and water/engine oil series respectively, all cases with Vin ¼ 0.3 m/s Fig. 7c shows a detail of Fig. 7b, a portion of the central chevron zone of the plate. We can observe that in both cases the heat flux is fairly uniform over most of the plate. The maximum values occur on a few very small areas, around “points” of contact between the plates (which are actually small parallelograms). In
Fig. 9. Comparison of the mass flow rate/unit area distributions at X ¼ 0 for water/oil and Vin ¼ 0.6 m/s: (a) cold channel and (b) hot channel.
Fig. 11. Nusselt number comparison.
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Fig. 12. Friction factor comparison.
these areas, the heat exchange is important because it takes place directly by conduction through the metal plates. Also, in the case of the water/water series the heat flux is generally more important along the two straight smooth longitudinal passages where the fastest fluid streams are present (see Fig. 6). Tables 3 and 4 present the average heat fluxes for the cases under consideration. This quantity increases monotonically with the inlet velocity but the rate of increase diminishes as Vin increases. It is also noted that the average heat flux is three to four times higher in the case of water/ water. It may be noted in Fig. 7c the appearance of “peacock tail” of the distribution of heat flux on the area of the corrugated plate. It is important to note that the heat transferred across the two entrance/exit regions of the middle plate is between 19.5% and 23.0% of the corresponding total for each of the twelve cases under investigation (see Table 1). This result shows that these regions are very important for the calculation of the PHE thermal performance and must be included in heat transfer simulations. Furthermore, since these regions represent 21% of the total heat transfer area of the plate it follows that their contribution to heat transfer is equivalent to that of the central chevron zone. 3.6. Performance of the PHE without the longitudinal streams The results presented in the previous paragraphs suggest that the presence of the straight smooth longitudinal passages causes a deterioration of the thermal performance accompanied by a beneficial decrease of the pressure loss. In order to verify this hypothesis a modified geometrical configuration which does not contain the straight smooth longitudinal passages was considered
(see Fig. 8). In a real PHE it is possible to eliminate these passages by using straight gaskets to completely fill the grooves. Various simulations were performed with this new configuration in order to analyze qualitatively and quantitatively its behavior. First, simulations were performed for the conditions in Table 1. Fig. 9a and b compare the mass flow rate distributions for the sixth case in the water/engine oil series which is representative of the behavior for all cases. In each figure we plot the curve obtained for the original geometry with the straight smooth longitudinal passages and that obtained by obstructing these passages. By consequence, the curves for the original geometry are the same as those presented in Fig. 6. For the new geometry, we obviously notice the absence of the fluid streams near the left and right edges of the plate. The peaks and valleys of the profiles occur at the same positions reflecting the presence of the obstructions and channels caused by the chevrons. For the cold fluid (Fig. 9a) the maximum (upward) flow is everywhere higher in the new geometry. The minimum values in the new geometry are lower than in the original one. In fact, the results for the new geometry suggest that flow reversal may be present in this case. For the hot fluid (Fig. 9b) the maximum (downward) flow is everywhere higher in the new geometry. The minimum values are sometimes positive suggesting that flow reversal may also occur in the hot fluid. Fig. 10 presents the comparison between the distributions of temperature on the middle plate for the case water/water with Vin ¼ 0.1 m/s for the original geometry and the geometry with longitudinal passages obstructed. It is noted that the temperature distributions are similar in the area of the plate common for these images. The same similarity was observed by analyzing all the results and therefore these cases are not presented here. Since these results do not give clear indications regarding the influence of the straight smooth longitudinal passages on the PHE performance we have compared the numerical predictions of the Nusselt number and friction factor for the PHEs with and without these longitudinal passages. In order to obtain the Nusselt number another set of 11 simulations was performed with water in both channels of the PHE. The cold fluid flow rate was maintained constant and the cold fluid Reynolds number was around 800. The hot side Reynolds number was varied between 400 and 1400 by changing the corresponding flow rate. These simulations are based on our previous numerical data [13]. For the friction factor, the simulations were performed considering isothermal conditions with water at 25 C and the related constant properties. This approach was often adopted (see in particular [2,22]).
Fig. 13. The 3D model of the diagonal-flow PHE e view of a fluid zone.
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Fig. 14. Comparison between the flow distributions for the side-flow and diagonalflow configurations.
The results are presented in Figs. 11 and 12 respectively. The obstruction of the straight smooth longitudinal passages causes an increase of both the Nusselt number and the friction factor. The average increase is 12.4% (between 9.2 and 15.7%) for the Nusselt number and 19.5% (between 14.5 and 21.2%) for the friction factor. This improvement in terms of heat transfer suggests that is possible to decrease the size of the PHE for the same heat transfer rate at the cost of a larger pressure drop, which can be translated by a larger pumping power requirement. 3.7. Influence of port arrangement on the performance of the PHE The port arrangement can result in side-flow or diagonal-flow PHEs. The fact that the port arrangement can influence the thermal and hydraulic performance of PHEs is mentioned in some works [15,23]. Gut and Pinto [24,25] mentioned that the influence of the port arrangement over the convective coefficients and friction factor is unknown. All the above mentioned sources cited the work of Okada et al. [10] in which a comparison of temperature profiles for Reynolds number of approximately 4000 in a PHE of nonchevron type was performed. This comparison has shown that there is no significant difference between the two arrangements. In order to compare the two port arrangements, another model was built. This model was obtained by modifying the one presented in Section 2. For each fluid, one of the distribution zones, including the corresponding inlet or outlet, has been mirrored about the Xaxis (Fig. 13). Simulations were then performed for this new geometry, the two fluid combinations (water/water and water/oil) and the conditions specified in Table 1. The comparison of flow distribution shows some small hydrodynamic differences between the two port configurations. In Fig. 14
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the results for the hot fluid from the first simulation of the water/ engine oil series are shown. It can be noticed that the fluid is better distributed in the case of the diagonal-flow configuration; the peak close to Zmax is less pronounced and generally there is more symmetry than in the case of the side-flow configuration. Fig. 15 shows the temperature distributions on the middle plate for the water/water simulations with Vin ¼ 0.1 m/s. In the left and the right side of this figure are represented the result for the sideflow and the diagonal-flow PHE respectively. One can notice that the temperature distribution is more symmetrical with respect to the X-axis (along the length of the plate) for the diagonal-flow case. As the inlet fluid velocities increase the influence of the port arrangement becomes less important. Therefore, these cases are not presented here. The results also show that there are small differences in heat transfer between the two types of port arrangements. The Nusselt number is higher for the diagonal port than for the side port type: the enhancement is estimated to be 1.7% in average (it varies between 1.3% and 2.4%) for the water/water series, and 1.6% in average (varying between 0.9% and 3.2%) for the water/oil series. The differences in terms of friction factor are insignificant; for all simulations, the differences are lower than 0.4% between the two port arrangements. 4. Conclusion This paper presented results from numerical simulations of the flow and heat transfer in a two-channel side-flow PHE. The temperature, heat flux and mass flow distribution were analyzed in the case of two fluid combinations: water/water and water/engine oil. The temperature field was found to be non-uniform and to depend strongly on the fluid combination: it appears to be more uniform in the case of the water/engine oil case. The flow in the channels presents two streams of higher velocity near the lateral sides of the PHE, regions where straight smooth passages parallel to the X-axis are present. The relative importance of these streams varies with the flow rate and with the fluid used; it is less prominent in the case of oil, for which the mass flow distribution is more uniform. A comparison with the results obtained with obstructed longitudinal passages shows that their presence decreases both the heat transfer rate and the friction factor. The side-flow and diagonal-flow PHE configurations have also been compared and a small improvement in the heat transfer rate was observed when using the diagonal-flow configuration, especially at small flow rates. Acknowledgements This project is part of the R&D program of the NSERC Chair in Industrial Energy Efficiency established in 2006 at Université de Sherbrooke. The authors acknowledge the support of the Natural Sciences & Engineering Research Council of Canada, Hydro Québec, Rio Tinto Alcan and Canmet-Energy Research Center. References
Fig. 15. Temperature field on the middle plate for: the side-flow PHE (left) and the diagonal-flow PHE (right).
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