International Communications in Heat and Mass Transfer

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1 International Communications in Heat and Mass Transfer 38 (2011) Contents lists available at ScienceDirect International Communications in Heat and Mass Transfer journal homepage: Numerical studies on flow and heat transfer in membrane helical-coil heat exchanger and membrane serpentine-tube heat exchanger Zhenxing Zhao, Xiangyu Wang, Defu Che, Zidong Cao State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an , China article info abstract Available online 14 July 2011 Keywords: Flow and heat transfer Membrane helical-coil heat exchanger Syngas Tangential velocity The flow and heat transfer characteristics of synthesis gas (syngas) in membrane helical-coil heat exchanger and membrane serpentine-tube heat exchanger under different operating pressures, inlet velocities and pitches are investigated numerically. The three-dimensional governing equations for mass, momentum and heat transfer are solved using a control volume finite difference method. The realizable k-ε model is adopted to simulate the turbulent flow and heat transfer in heat exchangers. There flows syngas in the channels consisting of the membrane helical coils or membrane serpentine tubes, where the operating pressure varies from 0.5 to 3.0 MPa. The numerically obtained heat transfer coefficients for heat exchangers are in good agreement with experimental values. The results show that the syngas tangential flow in the channel consisting of membrane helical coils is significant to the heat transfer enhancement to lead to the higher average heat transfer coefficient of membrane helical-coil heat exchanger compared to membrane serpentine-tube heat exchanger. The syngas tangential velocity in the membrane helical-coil heat exchanger increases along the axial direction, and it is independent of the gas pressure, increasing with the axial velocity and axial pitch rise and decreasing with the radial pitch rise Elsevier Ltd. All rights reserved. 1. Introduction Helical coils have been widely used in heat transfer applications, for example, heat recovery systems, chemical reactors, power generation, etc. Recently, the membrane helical-coil heat exchanger is used for the waste heat recovery system in integrated gasification combined cycle (IGCC) system due to its high overall heat transfer coefficient and compact configuration. There is a considerable amount of work reported on the flow and heat transfer of fluid inside helically coiled tubes. A review on heat transfer and friction coefficient correlations in helical or curved ducts was presented by Vashisth et al. [1]. The experimental studies on residence time distribution in helical coils for single phase laminar flow with different cross-sectional geometrics and flow situations have been reported by Saxena and Nigam [2]. Guo et al. [3] have developed correlations for estimation of Nusselt number for steady state and pulsating turbulent flow in helical coils. However, this correlation does not include coil parameters (such as curvature ratio) and is applicable only to their setup. Lin [4] applied the k-ε model to study the developing turbulent heat transfer in helical coil of definite pitch for a constant wall temperature case. Kumar [5] used Communicated by P. Cheng and W.Q. Tao. Corresponding author. addresses: zhao.zhenxing@stu.xjtu.edu.cn (Z. Zhao), wang.xy@stu.xjtu.edu.cn (X. Wang), dfche@mail.xjtu.edu.cn (D. Che), pro_cao@163.com (Z. Cao). the renormalization group (RNG) k-ε model to model the turbulent flow and heat transfer in the tube-in-tube helically coiled heat exchanger and developed the new empirical correlations for hydrodynamic and heattransfer predictions in the outer tube of this heat exchanger. In addition, considerable investigations on the flow and heat transfer of the flow across tube banks and finned tubes by means of either experiments or numerical computations have been carried out. Beale [6] conducted a detailed numerical study on fluid flow and heat transfer in tube banks and obtained a potential flow solution. Later Beale and Spalding [7] extended the previous work for laminar fullydeveloped cross flow and heat transfer in tube-bank heat exchangers and obtained a wide range of results for inline square, rotated square and equilateral triangle configurations. A series of investigations of the herringbone wavy fin patterns based on commercially available samples was conducted by Wang et al. [8,9]. The effects of fin spacing, number of tube rows, wave height, and edge corrugation were systematically examined. They presented the correlations applicable to larger diameter tubes and smaller diameter tubes. Paul et al. [10] used PIV (Particle Image Velocimetry) method to conduct detailed velocity measurements in turbulent flow in the staggered tube bundle at different Reynolds numbers. Most of these above-mentioned investigations were concerned with helically coiled tubes, characterized by curvature for the interior flow and circular cylinders and finned tubes for the external flow. For membrane helical-coil heat exchanger in IGCC, the flow and heat transfer characteristics of syngas flow outside membrane helical coils are very important. However, to the best of our knowledge, few /$ see front matter 2011 Elsevier Ltd. All rights reserved. doi: /j.icheatmasstransfer

2 1190 Z. Zhao et al. / International Communications in Heat and Mass Transfer 38 (2011) Nomenclature A f the outer surface area (m 2 ) d external diameter of helically coiled tube ( mm) D diameter of the inner helical coil (mm) h t surface heat transfer coefficient (W/m 2 K) I turbulence intensity (%) L length of the heat exchanger (mm) M molecular weight (g/mol) n iterations Nu Nusselt number P gas pressure (MPa) Q rate of heat transfer (W) Re Reynolds number s 1 radial pitch (mm) s 2 axial pitch (mm) T temperature (K) t m logarithmic temperature difference (K) u velocity (m/s) V volume (cm 3 /mol) W width of the heat exchanger (mm) x spatial position (mm) Greek letters ε turbulent energy dissipation k turbulent kinetic energy ρ density of fluid (kg/m 3 ) μ dynamic viscosity (kg/m s) σ collision diameter (0.1 nm) σ k diffusion Prandtl number for k σ ε turbulent Prandtl number for ε Ω collision integral Subscripts 0 inlet conditions c critical state m mixture out outlet conditions t tangential w wall condition related studies have been reported in the literature. The present authors have carried out the experimental investigations on the heat transfer characteristics of membrane helical coils [11,12]. The experimental results show that the average heat transfer coefficient of the membrane helical coil outer surface is higher than that of the membrane serpentine tube under the same conditions. However, the heat transfer enhancement mechanism has not been understood. The objective of this paper is to numerically study the heat transfer and flow in the heat exchangers consisting of the membrane helical coils and membrane serpentine tubes in order to elucidate the mechanism of heat transfer enhancement for membrane helical coils. 2. Description of heat exchangers The studied heat exchangers consist of three membrane helical coils or membrane serpentine tubes. Fig. 1a shows the geometrical configuration of membrane helical coil, and the geometry considered for membrane helical-coil heat exchanger is illustrated in Fig. 1b. The coiled tube has a diameter of d, and is coiled at a diameter D. The distance between the two turns (axial pitch) is expressed by s 2, and the distance between the two coils (radial pitch) is expressed by s 1. The heat exchanger had a length of L. Fig. 1c illustrates the investigated membrane serpentine-tube heat exchanger. Similarly, serpentine tube has a diameter of d, a length of L (x-direction) and a width of W (z-direction). The axial pitch is expressed by s 2, and the radial pitch is expressed by s 1. For membrane helical-coil heat exchanger and membrane serpentine-tube heat exchanger, the hot syngas flows outside the coils and tubes, respectively Mathematical formulation In the present study, the flow is considered to be steady, and CO and H 2 are mixed at a molar ratio of 2:1 to simulate the syngas. The pressure variations in heat exchangers are so small and Mach number of syngas is so low that the syngas flow can be considered to be incompressible ideal gas, which is similar to the previous work [13], The viscosities of each pure gas and syngas were calculated using Chung's law in Eq. (1), and the other detailed equations used for this calculation can be seen in ref. [14]. μ =40:785 F c ðmtþ 0:5 and μ V 2 = 3 m = 26:69F cm ðm m TÞ 0:5 c Ω v σ m Ω v Heat conductivity and specific heat were calculated by the fifth order polynomials of temperature, the thermal parameters (except viscosity) of syngas were calculated using the mass-weighted mixing law. At the inlet, syngas with temperature T 0 enters the heat exchanger at the velocity of u 0. Turbulent flow and heat transfer develop simultaneously downstream in the heat exchanger. The flow is assumed to be steady. For the turbulent flow and heat transfer simulation, the realizable k-ε model is used in this study because the performance of the realizable k-ε model has been found to be substantially better than that of the standard k-ε model for channel and boundary layer flows, and separated flows. In this simulation, the governing equations are N-S equations of which form are well known and not given in this paper. The two-layer based non-equilibrium wall function [5] was used for the near-wall treatment in the given geometry. This function is recommended for complex flows because of the capability to partly account for the effects of pressure gradients and departure from equilibrium. In addition, the constant wall temperature condition is widely used and validated by the classical models [4], so no slip and isothermal wall boundary conditions are applied on the coils and tubes wall. The uniform profiles at the inlet boundary condition and the diffusion fluxes at the outlet are as follows: u i = u 0 ; T = T 0 ; k = k 0 ; ε = ε 0 ð n u i ; p; T; k; εþ =0: ð3þ 2.2. Numerical computation Three-dimensional numerical simulations of flow and heat transfer in heat exchangers are obtained using a finite volume based commercial CFD package (FLUENT 6.3). The SIMPLEC algorithm was used to resolve the coupling between velocity and pressure. The convection terms and diffusion terms in the governing equations were modeled with the bounded second-order upwind scheme. The unstructured grid system is used in 3-D computational domain. Fig. 2 depicts the local grid topology on membrane helical ð1þ ð2þ

3 Z. Zhao et al. / International Communications in Heat and Mass Transfer 38 (2011) Fig. 1. Geometry for membrane helical coil (a), Membrane helical-coil heat exchanger (b) and membrane serpentine-tube heat exchanger (c). coil. As shown in Fig. 2, y + adaptive grid refinement is used in this simulation. In the present study, the y + on the wall was taken in the range of In order to obtain the satisfactory solutions for membrane helical-coil heat exchanger, the grid independence is carried out by different computational grid consisting of 650,000, 900,000, 1,350,000, and 1,750,000 volumes. The grid independence test indicated that the amount of grid of 1,350,000 ensures a satisfactory and converged solution. This is verified by the fact that the difference of outlet syngas temperature and heat transfer rate is within 0.5% between grid of 1,350,000 and grid of 1,750,000. At the inlet, the syngas with temperature T 0 (873 K) enters heat exchangers. The wall temperature of membrane coils and tubes are assumed to be uniform, T w (313 K). Geometry and flow parameters for heat exchangers are given in Table 1. The numerical computation is considered to be convergent when the residual summed over all the computational nodes at the nth iteration is no more than Calculation of heat transfer coefficient The surface heat-transfer coefficient, h t, was calculated from the inlet and outlet temperature data and the flow rates, using the following equation: h t = Q A f Δt m ð4þ Table 1 Geometrical and flow parameters for heat exchangers. Case s 1 /d s 2 /d L/d W/d D (mm) d (mm) u 0 (m/s) P (MPa) Fig. 2. The local grid on membrane helical coil. Case Case Case Case Case

4 1192 Z. Zhao et al. / International Communications in Heat and Mass Transfer 38 (2011) where Δt m is the logarithmic temperature difference. The surface heat transfer rates were based on the outer surface area, A f, of the membrane helical coil or membrane serpentine tube. The Δt m was calculated based on the syngas inlet temperature, T 0, the syngas outlet temperature, T out, and the wall temperature, T w. Δt m = T 0 T out ln½ðt 0 T w Þ= ðt out T w ÞŠ ð5þ 3. Results and discussion 3.1. Model validation In order to verify the present numerical work, the model validation is conducted at first. Experiments have been carried out to study the heat transfer of the membrane helical-coil heat exchanger. The heat exchanger used for the experiments has the same geometrical parameters as Case 1 or Case 5 listed in Table 1. The gas mixture (molar ratio N 2 : He=2:1) serves as the working fluid. The gas pressure varies from 0.5 MPa to 3.0 MPa, and gas inlet velocity varies from 1.5 m/s to 3.0 m/s. The uncertainties of the average Nusselt number and Rayleigh number were less than 4.2% and 3.4%, respectively. The heat transfer correlation of the membrane helical-coil heat exchanger is obtained. Fig. 3a shows the comparison between the present numerical values and the predicted results by the experimental heat transfer correlation at s 1 /d=1.6 for membrane helical-coil heat exchanger under the operating pressures from 0.5 MPa to 3.0 MPa. It can be seen that the maximum deviation between the simulated prediction and experimental correlation prediction is less than 5%. Therefore, the simulation results are in a good agreement with the predicted results by experimental correlation Heat transfer coefficient Fig. 3b and c show the numerically obtained average heat transfer coefficients, h t, of the inner coil, the intermediate coil, the outer coil and the heat exchangers at s 1 /d=1.6 and s 1 /d=2.0. From the figures it can be observed that h t increases with the increase of the operation pressure under the same inlet syngas velocity. It demonstrates that higher operation pressure can improve heat transfer, which is attributed to the difference in syngas mass flow rate Tangential velocity It is shown in Fig. 3bthath t of membrane helical-coil heat exchanger is higher than that of membrane serpentine-tube heat exchanger under the same heat transfer condition, which is consistent with the experimental results [11]. To clarify the mechanism of this phenomenon, the effects of flow field within both heat exchangers on heat transfer were considered by numerical methods. Fig. 4 shows the syngas tangential velocity, u t, distribution with different cross sections for Case1 and Case 3 with the same operation pressure (3.0 MPa), respectively. From the figures, u t in the annular channel consisting of membrane helical coils is significantly higher than that in the membrane serpentine-tube parallel channel, while u t in the parallel channel almost approaches zero. In addition, u t in the membrane helical-coil heat exchanger increases along the axial direction, whereas u t in the membrane serpentine-tube heat exchanger is independent of the axial direction. In this simulation, the syngas density is mainly influenced by the syngas temperature due to the small pressure variations in heat exchangers. As the syngas temperature decreases along the axial direction, its density increases by about 30% accordingly. Because the syngas tangential flow is near the membrane helical coils, the drop of the tangential flow temperature is faster than that of the main flow temperature; thus it leads to the pressure difference between the main Fig. 3. Nusselt number as function of Reynolds number (a) and heat transfer coefficients versus operating pressure: (b) Case 1 and Case 3; (c) Case 2 and Case 4. flow and the tangential flow. Therefore, the syngas of the main flow may enter the tangential flow continuously, resulting in the velocity rise of the tangential flow. For the membrane helical-coil heat exchanger, there is a helical groove in the annular channel, and thus makes fluid near the wall generate revolving flow which can promote disturbance of the thermal boundary layer and reduce the thermal boundary layer resistance [15]. As shown in Fig.4, the maximum tangential velocity in membrane helical-coil heat exchanger is up to 2.3 m/s, valuing about

5 Z. Zhao et al. / International Communications in Heat and Mass Transfer 38 (2011) Fig. 4. Tangential velocity distribution for membrane helical-coil heat exchanger (a) and membrane serpentine-tube heat exchanger (b). 30% of the axial average velocity. Therefore, the tangential flow plays an important role in heat transfer. In addition, u t peaks at the membrane. The tangential flow can increase the flow velocity and turbulence intensity in the wake region of coil, thus, the local heat transfer coefficients on the membrane helical coil are enhanced. Moreover, the tangential flow cannot only improve heat transfer condition of the wake region, but also decrease the influence of wake region on downstream coil so as to enhance heat transfer of helically coiled tube. So, the tangential flow is of great importance upon heat transfer enhancement for the membrane helical coil Effects of operating pressure and inlet velocity on tangential velocity The tangential velocity distributions at x=100 in Case 1 with different working pressures, i.e.0.5 MPa, 2.0 MPa and 3.0 MPa, are shown in Fig.5a. From the figures it can be observed that u t in annular channel is independent of the increase of the operation pressure, which demonstrates that higher operation pressure cannot change the velocity field in heat exchanger but can improve heat transfer due to the increase of the syngas mass flow rate. Calculations for the heat transfer and flow of the membrane helical-coil heat exchanger for different syngas inlet velocity were performed. Fig. 5b shows the tangential velocity distribution at x=100 mm under the syngas pressure of 3.0 MPa for the different syngas inlet velocity. It is found that u t increases with the inlet velocity (axial velocity) rise under the same radial pitch. The flow resistance in the channel is proportional to the square of syngas velocity, and the axial flow resistance in channel increases with the syngas axial velocity rise, thus, there is more syngas tangentially flow through the helical groove in the channel. Obviously, the higher the tangential velocity is, the more remarkable the heat transfer enhancement grows, which can explain the experimental results [12] that the average heat transfer coefficient of membrane helical coil increases faster than that of the membrane serpentine tube with the increase of inlet velocity Effects of radial pitch and axial pitch on tangential velocity Fig. 5c shows the tangential velocity distribution for the different radial pitch and axial pitch for membrane helical-coil heat exchanger under the syngas pressure of 3.0 MPa. As shown in Fig. 5c, u t increases with the decrease of radial pitch or the increase of axial pitch. The radial pitch rise reduces the axial flow resistance, leading to the reduction in the tangential flow accordingly. The heat transfer enhancement reduces with the decrease of the syngas tangential flow due to the radial pitch rise, thus, Fig. 3b and c revealed that the heat transfer coefficient difference between membrane serpentine tube and membrane helical coil at s 1 /d=1.6 is greater than that at s 1 /d=2.0 for the same inlet velocity. The axial pitch rise not only brings higher axial flow resistance, but also decreases the tangential flow resistance, leading to the increase in the tangential velocity of syngas. A bigger axial pitch can enhance the heat transfer on the membrane surface. However, because the increase of the axial pitch may lower the compactness of the whole heat exchanger, the smaller axial pitch (s 2 /d 2.5) is usually adopted in engineering practice, which also can lead to the reduction of pressure loss. 4. Conclusions Fig. 5. Tangential velocity distribution. Numerical studies on the flow and heat transfer characteristics of the high-pressure syngas in the heat exchangers consisting of membrane helical coils and membrane serpentine tubes were performed under various operating pressures, inlet velocities and pitches. The numerically obtained heat transfer coefficients for heat exchangers were verified by experimental data. The major findings are summarized as follows: (1) The gas tangential flow in membrane helical-coil heat exchanger is significant to heat transfer enhancement, thus, the average heat transfer coefficient of membrane helical-coil heat exchanger is higher than that of membrane serpentinetube heat exchanger under the same conditions. (2) The syngas tangential velocity in the membrane helical-coil heat exchanger increases along the axial direction. The syngas tangential velocity in the membrane serpentine-tube heat exchanger is independent of the axial direction and approaches zero.

6 1194 Z. Zhao et al. / International Communications in Heat and Mass Transfer 38 (2011) (3) Operation pressure do not exert any influence on the velocity field in heat exchangers, however high pressure can improve heat transfer through the increase of the syngas mass flow rate. (4) The syngas tangential velocity in membrane helical-coil heat exchanger is independent of the gas pressure, increasing with the axial velocity and axial pitch rise and decreasing with the radial pitch rise. References [1] S. Vashisth, V. Kumar, K.D.P. Nigam, A review on the potential applications of curved geometries in process industry, Industrial & Engineering Chemistry Research 47 (10) (2008) [2] A.K. Saxena, K. Nigam, Effect of coil pitch and cross-sectional ellipticity on RTD for diffusion-free laminar flow in coiled tubes, Chemical Engineering Communications 23 (4) (1983) [3] L. Guo, X. Chen, Z. Feng, B. Bai, Transient convective heat transfer in a helical coiled tube with pulsatile fully developed turbulent flow, International Journal of Heat and Mass Transfer 41 (19) (1998) [4] C. Lin, M. Ebadian, Developing turbulent convective heat transfer in helical pipes, International Journal of Heat and Mass Transfer 40 (16) (1997) [5] V. Kumar, B. Faizee, M. Mridha, K. Nigam, Numerical studies of a tube-in-tube helically coiled heat exchanger, Chemical Engineering and Processing: Process Intensification 47 (12) (2008) [6] S. Beale, Fluid flow and heat transfer in tube banks, Imperial College, London, [7] S. Beale, D. Spalding, Numerical study of fluid flow and heat transfer in tube banks with stream-wise periodic boundary conditions, Transactions of the CSME 22 (4A) (1998) [8] C. Wang, W. Fu, C. Chang, Heat transfer and friction characteristics of typical wavy fin-and-tube heat exchangers, Experimental Thermal and Fluid Science 14 (2) (1997) [9] C. Wang, Investigation of wavy fin-and-tube heat exchangers: a contribution to databank, Experimental Heat Transfer 12 (1) (1999) [10] S. Paul, M. Tachie, S. Ormiston, Experimental study of turbulent cross-flow in a staggered tube bundle using particle image velocimetry, International Journal of Heat and Fluid Flow 28 (3) (2007) [11] Z. Yang, Z. Zhao, Q. Guo, Convective heat transfer characteristics of high-pressure gas in annular channel heat exchanger with membrane spiral tubes, Journal of Xi'an Jiaotong University 44 (11) (2010) [12] Z. Zhao, Z. Yang, H. Liu, Heat transfer characteristics of different heat transfer structures in gasification convective syngas cooler, Journal of Xi'an Jiaotong University 45 (01) (2011) [13] A. Safwat Wilson, M. Khalil Bassiouny, Modeling of heat transfer for flow across tube banks* 1, Chemical Engineering and Processing 39 (1) (2000) [14] T. Chung, L. Lee, K. Starling, Applications of kinetic gas theories and multiparameter correlation for prediction of dilute gas viscosity and thermal conductivity, Industrial & Engineering Chemistry Fundamentals 23 (1) (1984) [15] M. Yilmaz, Ö. Çomakli, S. Yapici, Enhancement of heat transfer by turbulent decaying swirl flow, Energy Conversion and Management 40 (13) (1999)