Performance and flow distribution of the plate heat exchanger with supercritical fluid of carbon dio

Abstract

Keywords: Supercritical fluid; plate heat exchanger; carbon dioxide; flow distribution

Introduction

The plate heat exchangers feature compact size and high heat transfer performance, and is regarded to be more advantageous than its counterpart – shell-and-tube heat exchangers. Hence they are rapidly used to replace the traditional shell-and-tube heat exchangers in many industrial applications such as dairy, food processing, paper/pulp, heating, ventilating, and other related industry [1]. Appreciable experimental studies for single-phase flow in plate heat exchangers had been reported. For example, Khan et al. [2] had mentioned tens of experimental studies in association with single phase fluid. Yet Han et al. [3] also summarized more than fifteen numerical studies concerning plate heat exchangers applicable for single-phase fluid. However, the foregoing studies, either experimental or numerical, mainly stressed on the performance of single-phase fluids like water or air. The development of high-performance heat pump water heaters using natural working fluids had received a lot attention recently as far as energy conservation and greenhouse gas reduction is concerned [4]. Among the existing natural refrigerants, carbon dioxide (CO2) is especially prominent for its outstanding features like nonflammable, nontoxic, no known carcinogenic, and free from mutagenic. Moreover, using CO2 in refrigerating systems can be regarded as an alternative form of

Bassiouny and Martin [15] presented a model to investigate the flow distribution of the plate heat exchangers. Meanwhile, the control volume for intake and exhaust conduit is also studied in this paper, it is assumed that the ratio of average velocity  is known and the friction loss of inlet is also negligible. In realistic cases, however, the value of  will change subject to different locations of intake and exhaust conduit. Rao et al. [16] proposed a one-dimensional model for predicting the heat transfer and flow distribution of a plate heat exchanger. However, until now, there is no model available for predicting the heat transfer characteristics of the trans-critical CO2 in a plate heat exchanger, it is therefore the objective of this study to account for the drastic property change of CO2 in a

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plate gas cooler. Note that the significant change of physical property, especially heat capacity, may impose appreciable influence on the heat transfer performance. This can be made clear from Yu et al. [17, 18] who numerically and experimentally examined the transcritical heat transfer phenomenon of a tube-in-tube heat exchanger, and a local maximum is reported. Hence, it would be interested to study this phenomenon in the plate heat exchanger. Moreover, the plate heat exchangers normally consists many plates where maldistribution within the plates may occur and impair the heat transfer performance accordingly. Therefore, it is quite imperative to investigate the flow distribution and the associated heat transfer performance of the CO2 plate heat exchangers.

Balanced Equations Equations used in this research is based on the formulation of a U-type PHE by Bassiouny and Martin [15]. Although the basic formulation by Bassiouny and Martin can well apply to most of the working fluids, it may not totally fit into the present supercritical CO2 plate heat exchanger. Some minor corrections are modified as described in the following. Taking cold side for example, the control volume of the grid node is shown in Fig. 2. Yet the corresponding momentum and mass balance equation can be written as in the following.

(a) Schematic of the configuration for cold side (b) Grid node for exhaust manifold

(b) Schematic of the configuration for hot side Fig. 1 Numerical modeling for the water-CO2 plate heat exchanger. (c) Grid node in channel Fig. 2 Schematic for the control volume used for simulation in the intake, exhaust, and plate channels.

Numerical Modeling And Calculation

The simulation considers a one-dimensional flow for water or CO2 alongside the plate. The plate heat exchanger is of Utype configuration, i.e. the inlet and outlet for water or CO2 are located at the first plate. Heat lost from the plate heat exchanger to the ambient is negligible and the effect of gravity is also neglected. As depicted in Fig. 1(a), the plate heat exchanger is consisted of cold plate (water side) and hot plate (CO2) and the layout configuration of plate heat exchanger can be usually simplified with two manifolds (one inlet dividing manifold and an outlet combining manifold) and the heat transfer takes places only at the flow passages rather than at the manifolds. Because of the reverse flow direction, the hot side inlet (CO2 side) shown in Figure 1(b) is designated at the upper left whereas the lower right represents its outlet.

Equations: (1) Intake manifold: (i) Mass balance conservation  in AVin   Ac ui ,1   in i

(2) Exhaust manifold: (i) Mass conservation out AVouti   Acui , N  outi 1 AVouti 1

(ii) Momentum conservation 2 2 Pouti 1 A  Pouti A   AVout   AVout  Kc  AVo2uti 1 (4) i i 1 (3) Channels: (i) Mass conservation 145

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i , j Ac ui , j  i , j 1 Ac ui , j 1  0 (5) (ii) Momentum conservation Pi , j Ac  Pi , j 1 Ac   w Pl   Ac ui2, j   Ac ui2, j 1  0 (6) Where u2

For the sake of simplicity, the terminologies of the symbol are described in the nomenclature. Besides, the turning loss into (or out of) plate channels should be taken into consideration. Pini A  Pchi ,1 Ac  1  Ct  i ,1 Aui2,1  0 (8)

For the energy balance equation, heat transfer in the manifolds is neglected. The corresponding equations are shown in the following [16]: For cold side:

Fig. 3 Flow chart of the plate heat exchanger simulation program.

Results And Discussion

The proposed model is first compared with some existing data for validation. Fig. 4 is the comparison for the variation of the pressure drop and velocity distribution (in terms of

) between the predictive result and experimental data [20]. The inlet conditions and plate number is the same as those of [20]. Basically, the simulation is in line with the experimental data. Also, the calculation indicates that an appreciable falloff of pressure drop alongside the manifold. The results imply that there will be an uneven flow distribution alongside the plate. Apparently, the flowrate will decrease from the inlet toward the downstream due to detectable drop of pressure drop alongside the plate number. Fig. 4(a) and 4(b) is the comparison of the channel velocity between the predictive result and the experimental data from Rao et al. [20]. For the temperature distribution alongside the plate, comparison is also made with the simulation by Gherasim et al. [21] as shown in Fig. 4(c). Note that Gherasim et al. [21] performed a numerical simulation for plate heat exchanger using hot water and cold water. The current calculations are made with the same plate geometry and inlet conditions. Calculated results are shown in Fig. 4(c). Again, the prediction in this research also accord with the temperature distribution (dimensionless temperature) of Gherasim et al. [21]. The variation of the outlet temperature amid this study and theirs are within 1.5 C (about 3%). Note that the detailed geometry and the correlations for the plate heat exchangers are given in Table 1.

Where LMTD is the log mean temperature difference. Mathematical formulation In the simulation, the plate channel is first discretized into some tiny nodes and the foregoing mass, momentum, and energy equations in each node can be summarized in a matrix to form a system of nonlinear equations. The system nonlinear equations are then solved by Newton method along with Newton downhill algorithm for quicker convergence. Before the program starts, a curve fitting on thermal properties of water and CO2 [12] should be made. Besides, the loss coefficients (such as KL and Kc from Eqs. (2) and (4) subject to different configurations and flowrates are taken from reference [19]. Detailed flow chart depicting the solution algorithm for the plate heat exchanger is given in Fig. 3.

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Table 1 Geometry of the plate heat exchanger tested by Gherasim et al. [21] Geometry and inlet conditions for the plate heat exchanger Number of plates in cold 10 side (n) Number of plates in hot 9 side Plate spacing (mm) 2.9 Plate thickness (mm) 0.8 Height of plate (mm) 600 Width of plate (mm) 218 Inlet manifold diameter 70 (mm) Characteristics 5.8 dimension of plate channel (mm) Heat capacity ratio (C*) 1 Both Water to water conditions at the inlet Inlet cold water velocity 0.535 (m/s) Inlet hot water velocity 0.522 (m/s) Inlet cold water 353 temperature (K) Inlet cold water 303 temperature (K) Correlation used for estimation of pressure drops and heat transfer [20] Friction Factor f  1.441  Re 0.206 correlation Nusselt Number Nu  0.3  Re0.663  Pr 0.333  (  / m )0.17 correlation

(a) Comparison for pressure distribution with experimental data from Rao et al. [20]

The foregoing results are applicable for water to water plate heat exchanger. For the present CO2-water gas cooler, Fig. 5 indicates the effect of the Reynolds number on the maldistribution of the flow under the isothermal state for water side. The plate numbers are 10 and 40, respectively. As shown in the figure, the flow mal-distribution increases with the rise of the Reynolds number. The results indicate that a higher inlet velocity leads to a severe mal-distribution alongside the plate. For an inlet Reynolds number of 100,000, the first plate may possess 21% higher mass flowrate than that in the last plate for n = 10. The higher mass flowrate near the entrance is mainly associated with larger pressure difference between the inlet and outlet conduit based on the calculated results. It is interesting to know that the mal-distribution becomes more and more pronounced when the number of plates increases further. In fact, difference in the mass flowrate between the first and last plate may exceed over seven times for an inlet Reynolds number of 100,000 when n = 40. The foregoing velocity distribution for water side is made under isothermal condition. For the simulation of the CO2-water gas cooler, until now, there were no heat transfer and friction correlation applicable for the supercritical CO2. Hence the dimensionless correlation applicable for water shown in Table 1 from [20] is presumed valid and is used throughout this study.

(b) Comparison for velocity distribution from Rao et al. [20] 1.0 Hot Channel - Gherasim et al. Cold Channel- Gherasim et al. Hot Channel - present research Cold Channel- present research

z (c) Comparison for temperature distribution alongside the plate with field Gherasim et al. [21]. Fig. 4 Comparisons with the present predictive results with other researchers. 147

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Additionally, the plate geometry is the same as shown in Table

1. However, the local gigantic change of properties of CO2 is

taken into account in the calculation alongside the plate when using the correlation during iterations. This is especially important for CO2. With imposing heat exchange between water and CO2, the corresponding velocity distributions for water side and CO2 side (the inlet water flowrate is 2 kg/s at 283 K and the inlet CO2 flowrate is 6.15 kg/s at 370 K, and pressure is 8 MPa) subject to different values of C* ( CCO / CH O ) is shown in Fig. 2

6. For water, imposing heat exchange poses only a slight effect

on the flow distribution at the first and last plate. This is because a significant difference in heat transfer rate occurring at these two plates since one side of the plate is insulated. Hence the effective viscosity increases and consequently a lower water velocity prevails. Yet the last plate experiences an even pronounced drop of velocity due to a larger temperature difference. For the rest of the plates of the cold water side, the flow distribution is analogous to those without heat transfer (Fig. 5). The results suggest that imposing heat transfer casts very minor influence on the water side velocity distribution. This is applicable for C* ranging from 0.1 to 1.

Re500 =0.003425 Re1000 =0.003776 Re2000 =0.004161 Re5000 =0.004729 Re10000 =0.005208 Re100000 =0.007151 average

(b) CO2 Fig. 6 Velocity distributions of each plate for the water and CO2.

The distribution of dimensionless velocity on CO2 side is given in Fig. 6(b). However, it is clear from the figure that the distribution of CO2 differs significantly from that of water. As appeared in Fig. 6(a), the water velocity distribution shows a consistent decline alongside the plate (except the first one due to considerable heat transfer difference). For CO2 plate and C* = 1, it is found that the flow distribution is rather uniform, yet some mal-distribution emerges when C* is decreased. The flow distribution is actually associated with the pressure difference at the intake and outlet manifold. Based on the calculated results, it appears that the pressure difference between the intake and exhaust manifold is quite even alongside the manifold direction. In this regard, one can see the flow distribution is quite uniform for C* = 1. With C* being decreased to 0.1, the velocity difference is only around 6%. One of the explanations of the more uniform distribution of the CO2 channels is for being operated at a very extremely high pressure. The results imply that the frictional pressure drop across the plate channel is much lower than the corresponding system pressure, thereby a better uniformity of the CO2 is achieved. As C* is reduced, it appears

Re500 =0.010486 Re1000 =0.0112899 Re2000 =0.012133 Re5000 =0.013303 Re10000 =0.014236 Re100000 =0.017561 average

(b) n = 40 Fig. 5 Effects of Reynolds number on velocity distribution for water under isothermal state. 148

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that the CO2 may pass through the pseudo-critical temperature, leading to an appreciable change of properties such as heat capacity, density, and the like. As a consequence, the drastic change of property leads to change of heat transfer performance and its interaction with the water side leads to a comparatively uneven flow distribution as compared to that of C* = 1. Note that at C* = 1, the exit temperature of CO2 is around 330 K which is still above the pseudo-critical temperature. Hence the property change is much small and accordingly its influence on velocity is relatively small.

slightly increased with the change of location along the plate but followed by a slight decline. Conversely, the heat flux of 8 MPa shows a noticeable increase after x/L > 0.5 which is different from the other two cases.

Fig. 7 represents different results of heat transfer rate with different values of C* (case 1 for 0.1, case 2 for 0.25, case 3 for 0.5, case 4 for 0.75 and case 5 for 1). The heat transfer rate rises with the C*. By comparison between C* = 0.1 (denote case 1 in Fig. 7) and C* = 0.5 (case 3), we can find that the flow rate of CO2 has risen fivefold while the heat transfer rate has increased nearly threefold. The significant rise of heat transfer rate suggests that the control resistance falls in the CO2 side. Moreover, the heat transfer performance is considerably improved for the operation may pass through the pseudo-critical point. (a) C* = 1

Fig. 7 Heat transfer rate distribution with different values of C*.

The effect of inlet pressure of CO2 on the total heat transfer rate for an inlet C* =1 and C* = 0.002 are depicted in Fig. 8. Basically the heat transfer rate rises with the rise of inlet pressure. For C* = 1 as shown Fig. 8(a), one can see that the total heat transfer rate increases with the rise of inlet pressure. This is somewhat expected for the effective heat capacity alongside the plate for a larger system pressure like P = 12 MPa is higher than that of P = 10 MPa as shown in Fig. 10(a). Basically, the outlet temperature of CO2 is higher than the corresponding pseudo-critical temperature. In this sense, there is no significant change of heat capacity and the heat transfer coefficient. As a consequence, one can expect a moderate increase of heat transfer rate with the rise of system pressure. Thus, for C* = 0.002 as shown in Fig. 8(b), one can see that the heat transfer rate of 12MPa is expected higher than that of 10MPa. As shown in Fig. 9, however, the heat flux of 12MPa is

(b) C* = 0.002 Fig. 8 Heat transfer rate for each CO2 plate.

Basically, the phenomenon is associated with the transcritical phenomenon of CO2. Note that the heat capacity of CO2 will undergo a tremendous increase when the temperature is near the pseudo critical temperature. Yet this phenomenon becomes more pronounced when the system pressure is close to the critical pressure. In this regard, it is expected that the pseudo-critical temperature may occur somewhere in the plate channel when C* is reduced, see Fig. 10 for the heat capacity variation subject to various system pressure. Therefore, a gigantic rise of heat capacity as shown in Fig. 10(b) is encountered. Note that the abscissa in Fig. 10 represents the 149

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location along the plate (A total of 10 grids are used in each plate for this simulation). On the other hand the sharp rise of heat capacity will follow by a sharp decline. Hence the substantial rise of heat capacity does not ensure an effective rise of average heat capacity. If the average heat capacity in the plate is higher than the average value at a high pressure such as in Fig. 10(b), one would expect an appreciable heat flux recovery at P = 10 MPa at some specific position within the plate. In the meantime, despite a sharp rise of heat capacity also emerges for P = 8 MPa, but again a sharp decline is also encountered when CO2 flow is passing through the pseudocritical point where the corresponding average heat capacity may be still lower than that of higher pressure, thereby a lower heat transfer rate prevails. The corresponding heat capacity for C* = 1 for P = 8MPa, 10 MPa and 12 MPa is shown in Fig. 10(a). As seen in the figure, the CO2 flow did not pass through the pseudo-critical point, and as a result a continuous rise of heat transfer rate vs. system pressure is shown.

(b)C* =0.002 Fig. 10 Heat capacity of CO2 alongside the plate channel for P = 10 MPa and 12 MPa.

Conclusions

In this study, a plate heat exchanger model capable of handling supercritical like CO2 had been proposed. The plate heat exchanger is of U-type configuration, the plate spacing is

1. The proposed model was first compared with some existing

water to water plate heat exchanger data. Generally, the predicted water flow distributions are in line with the experimental data. Yet the simulation results of temperature distribution alongside the plate also agree excellently with other predicted model.

Fig. 9 Heat flux of CO2 alongside the plate channel for P = 10 MPa and 12 MPa C=0.002. 1800 1600 1400

2. For the plate heat exchanger in the water side, it is found that

a detectable mal-distribution is found in associated with the inlet flowrate at the manifold. Basically, larger mal-distribution is encountered when the inlet flowrate is increased. In addition, the mal-distribution also increases with the rise of plate number. In the worst case, a seven-fold difference can be encountered between the first and last plate. Normally the largest flowrate occurs at the first plate. However, with imposing heat transfer, the flow rate at the first plate may be slight reduced due to the uneven heat transfer rate at the first plate.

3. The simulation indicates that the inlet temperature of water

casts negligible influence on the water flowrate distribution. This is because the density variation for water is quite small 150

Keynote Speech-Conference Extended Research Paper – JTEN – 2014-24 Qi, P.C., He, Y.L., Wang, X.L., Meng, X.Z., “Experimental investigation of the optimal heat rejection pressure for a transcritical CO2 heat pump water heater,” Applied Thermal Engineering, 56, pp. 120-125, (2013). [10] Dittus, F.W., Boelter, L.M.K., “Heat transfer in automobile radiators of the tubular type,” Univ. Calif. Publ. Eng., 2(13), pp. 443-46, (1930). [11] Gnielinski, V., “New equations for heat and mass transfer in turbulent pipe and channel flow,” International Chemical Engineering, 16, pp. 359-368 (1976). [12] McLinden, M. Klein, S.A., Lemmon, E.W., Peskin, A.P., “Ther odyna ic and Transport properties of Refrigerants and Refrigerant Mixtures-REFPROP,” Version 8.0, National Institute of Standards and Technology, USA, (1998). [13] Yoon, S.H. , Kim, J.H., Hwang, Y.W., Kim, M.S., Min, K., Kim, Y., “Heat transfer and pressure drop characteristics during the in-tube cooling process of carbon dioxide in the supercritical region,” International Journal of Refrigeration, 26, pp. 857-864, (2003). [14] Son, C.H., Park, S.J., “An experimental study on heat transfer and pressure drop characteristics of carbon dioxide during gas cooling process in a horizontal tube,” International Journal of Refrigeration, 29, pp. 539-546, (2005). [15] Bassiouny, M K., Martin, H., “Flow distribution and pressure drop in plate heat exchangers-I,” Chemical Engineering Science, 39(4), pp. 693-700, (1984). [16] Rao, B.P., Kumar, P.K., Das, S.K., “Effect of flow distribution to the channels on the thermal performance of a plate heat exchanger,” Chemical Engineering and Processing, 41, pp. 4958, (2002). [17] Yu, P.Y., Lin, K.H., Lin, W.K., Wang, C.C., “Perfor ance of a tube-in-tube CO2 gas cooler,” Int. J. of Refrigeration, 35, pp. 2033-2038 (2012). [18] Yu, P.Y., Lin W.K., Wang, C.C., “Perfor ance evaluation of a tube-in-tube CO2 gas cooler used in a heat pump water heater,” Experimental Thermal and Fluid Science, 54, pp. 304-312, (2014). [19] Idelchik, I.E., “Handbook of Hydraulic Resistance,” pp. 413-501, 3rd Edition, New York, (1994). [20] Rao, B.P., Sunden, B., Das, S.K., “An experimental investigation of the port flow maldistribution in small and large plate package heat exchangers,” Applied Thermal Engineering, 26, pp. 1919-1926, (2006). [21] Gherasim, I., Galanis, N., Nguyen, C.T., “Effects of dissipation and temperature-dependent viscosity on the performance of plate heat exchangers,” Applied Thermal Engineering, 29, pp. 31323139, (2009). [9]

with the temperature. By contrast, it is found that the inlet temperature difference for the CO2 side may raise significant change of thermodynamics and transport property of CO2, and result in a great difference in flow distribution. For the water side, it is found that the flowrate normally declines alongside the manifold. However, the flowrate distribution of CO2 is rather uniform due to its much higher system pressure. However, the flow distribution of CO2 also depends on C*, smaller C* may reverse the flow distribution to increasing trend rather commonly observed decreasing trend despite the variation from plate to plate is still quite small.

Acknowledgments

The financial support from the Ministry of Science and Technology, Taiwan is highly appreciated.

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