Semiporous Media Approach for Numerical Simulation of Flow through Large-Scale Sparse Tubular Heat Exchangers

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Semiporous Media Approach forNumerical Simulation of Flow throughLarge-Scale Sparse Tubular HeatExchangersYu-Ling Shi , Jun-Jie Ji a & Chun-Lu Zhang ba China R&D Center, Carrier Corporation , Shanghai, Chinab College of Mechanical Engineering, Tongji University ,ShanghaiPublished online: 22 Feb 2011.

To cite this article: Yu-Ling Shi , Jun-Jie Ji & Chun-Lu Zhang (2010) Semiporous Media Approachfor Numerical Simulation of Flow through Large-Scale Sparse Tubular Heat Exchangers, HVAC&RResearch, 16:5, 617-628

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VOLUME 16, NUMBER 5 HVAC&R RESEARCH SEPTEMBER 2010

617

Semiporous Media Approach for Numerical Simulation of Flow

through Large-Scale Sparse Tubular Heat Exchangers

Yu-Ling Shi, PhD Jun-Jie Ji, PhD Chun-Lu Zhang, PhD

Received March 14, 2010; accepted June 1, 2010

Steady-state, three-dimensional numerical simulations for airflow through large-scale sparse tubular heat exchangers are performed using Fluent (2006). A new porous media approach, semiporous media, is developed to simplify the computational fluid dynamics (CFD) modeling. In this approach, the tube bundle is simplified to a porous media zone that has half real tubes on both sides of it. Three CFD approaches, the real tube one, the semiporous media one, and the conventional porous media one, are compared in the predictions of the tubular heat exchanger airflow distributions. The comparison shows that the semiporous media approach predicts air-flow distribution similar to the real tube distributions, reduces computational cost significantly, and can be easily implemented. The heat exchanger pressure drops predicted by the semiporous media approach are compared with the experimental data for eight designs. The results show that this new approach gives reasonable agreement with the experiments.

INTRODUCTION

Large-scale sparse tubular heat exchangers are widely used in air-conditioning (e.g., gas heat-ers) and other industries. Figure 1 shows the typical large-scale sparse tubular heat exchanger used as the gas-heating unit of an air-conditioning system. A typical heat exchanger box size is about 1.2 × 1.7 × 2.4 m (47.2 × 66.9 × 94.5 in.). There are four U-shaped tube bundles inside the air box. Each tube bundle consists of seven tubes, which are about 3.3 m (129.9 in.) long with dimples on the tube surface to improve heat transfer. Cold air enters the air room from the top left corner blown by a centrifugal fan and goes through the heat exchanger, then flows out the air room from the bottom. Natural gas combusts and flows inside the tubes. The design of this kind of heat exchanger requires balancing the thermal behavior and the pressure drop. This paper focuses on the study of the airflow and pressure drop predictions for this kind of large-scale sparse heat exchangers using a semiporous media approach using Fluent (2006).

Experimentation is still the main approach for the tubular heat exchanger design due to the complexity of its flow and heat transfer behaviors (Halle et al. 1984; Roetzel and Lee 1993; Gentry 1990). However, experimental testing is usually expensive, and flow visualization in heat exchangers is difficult to perform. Well-validated computer models using genetic algo-rithms can provide convenient and economical assistance in heat exchanger design (Reppich and Kohoutek 1994; Cornelissen and Hirs 1999; Hofman 2000; Resat et al. 2006). With recent developments of numerous powerful computational fluid dynamics (CFD) programs, commer-cial CFD programs have been proven to be useful tools in numerical simulations of complex fluid flow problems. But most of the research was for small-size tubular heat exchangers or

Yu-Ling Shi is a staff engineer and Jun-Jie Ji is a senior engineer at China R&D Center, Carrier Corporation, Shanghai, China. Chun-Lu Zhang is a professor in the College of Mechanical Engineering, Tongji University, Shanghai.

© 2010 American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in HVAC&R Research (Vol. 16, Issue 5, September 2010). For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAE's prior written permission.

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applied periodic boundary conditions (Lei et al. 2008; Dong et al. 2008). With the development of CFD, the distributed flow resistance approach was developed, in which the internal structure is regarded as a porous media with different resistance coefficients for different computational grids. Studies on the distributed flow resistance porous media CFD approach for shell-and-tube heat exchanger modeling have been conducted for decades. Patankar and Spalding (1974) were the first ones to simulate the shell-side pressure drop using this type of porous media method. The complex geometry of the flow field was thus simplified to regular grids. Sha et al. (1982) developed a multidimensional model to predict the shell-side flow in steam generators based on the same method used to study blockage effects. In addition, they added the concept of surface permeability so as to consider the resistance anisotropy. Zhang et al. (1991) analyzed the flow and heat transfer in several types of steam surface condensers using the distributed flow resis-tance porous media approach. Stevanovic et al. (2001) also carried out CFD modeling using this porous media approach to calculate and optimize the shell-and-tube heat exchangers according to the predicted flow and pressure drop. He et al. (2005) used this method to design novel effi-cient heat exchangers. They conducted a numerical investigation of three different heat exchangers (vertical baffles, helical baffles, and finned-tube banks) based on the distributed resistance concept.

However, there is little CFD modeling of large-scale sparse tubular heat exchangers. For the large-scale sparse tubular heat exchanger, the full-size real tube CFD model is too difficult and expensive to create and the conventional porous media model is not applicable due to the non-uniform flow resistance distribution of the sparse tube bundle. This paper introduces the semipo-rous media approach suitable for large-scale sparse tubular heat exchanger airflow and pressure drop predictions.

Figure 1. Typical large-scale sparse tubular heat exchanger.


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VOLUME 16, NUMBER 5, SEPTEMBER 2010 619

NUMERICAL APPROACH

Governing Equations

The CFD software Fluent version 6.3 (Fluent 2006) is used for the tubular heat exchanger numerical modeling. The governing equations for continuity and momentum in tensor form for the computation domain can be expressed as follows:

(1)

(2)

In the simulations, fluid flow is fully turbulent and incompressible. The standard k-ε turbu-lence model, with default coefficients, in Fluent is used for the turbulence flow modeling. Heat transfer is not covered in this study.

The porous media method adds an additional loss term Si into the momentum equation to account for the flow resistance. The porous media flow resistance definition will be introduced later.

Porous Media Zone Definition

To enhance heat transfer, dimple tubes are frequently used in gas-fired tubular heat exchang-ers. Each U-shaped tube consists of a round section and a dimple section. Therefore, different porous media zones are defined to represent the round tube section and the dimple tube section. The flow resistance of the large-scale sparse tubular heat exchanger is generally nonuniform and anisotropic. The flow resistance on both sides of the tube bundle is lower than that in the middle of the tube bundle because the distance from tube bundle side tubes to the heat exchanger box is bigger than the gap between tubes. To deal with the nonuniform flow resistance effect, the porous media zone with half real tubes on both sides of the porous media zone is applied (see Figure 2). This is termed the semiporous media approach.

Boundary Conditions

Heat Exchanger Inlet. The air is blown through the heat exchanger by a centrifugal fan. To include the fan/heat exchanger interaction, the fan velocity profiles (Vx, Vy, and Vz) and turbu-lence profiles (k and ε) are attached at the gas-fired tubular heat exchanger inlet. The fan veloc-ity and turbulence profiles are from a separate CFD model of the fan.

∂ ρuj( )∂xj---------------- 0=

∂∂xj------- ρuiuj( ) ∂

∂xj------- μeff

∂ui

∂xj-------⎝ ⎠

⎛ ⎞– ∂P∂xi-------–

∂∂xj------- μeff

∂uj

∂xi-------⎝ ⎠⎛ ⎞ 2

3--- ρk μeff

uk

xk-----+⎝ ⎠

⎛ ⎞ δij– Si+ +=

Figure 2. Semiporous media simplification.


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Flow Resistance Definition in Porous Media Zone. For the tubular heat exchanger studied in this work, the flow resistance is anisotropic; therefore, the flow resistance coefficients are defined in three directions, Rm; Rs1, and Rs2, as shown in Figure 3.

Generally, the tube bundle flow resistance coefficients can be determined from direct mea-surement, published literature, or CFD prediction. Direct measurement and published data are highly recommended for tube bundle flow resistance coefficient estimation, but these two approaches are not applicable for this work because there are no tube bundle prototypes for flow resistance measurement. Moreover, the published flow resistance data are not suitable for the dimple tube bundle. Therefore, CFD modeling is used to predict the tube bundle flow resistance coefficients. First, CFD prediction on the published tube bundle (Incropera and DeWitt 2002; Rohsenow et al. 1998; Hua and Yang 1985), which has similar Reynolds number and geometry parameters as the round tube bundle in this work, is conducted to develop a reliable CFD approach for the tube bundle flow resistance prediction. The tube bundle flow resistance com-parison between the published data and predicted values shows that the flow resistance predic-tion deviation is less than 5%. Table 1 summarizes the grid density and turbulence model recommended from the CFD predictions.

CFD simulations using the grid density and turbulence model recommended in Table 1 are carried out to predict the flow resistance coefficients for the tube bundles used in this work. For each tube bundle, the flow resistance coefficients of Rm and Rs2 are predicted individually. The Rs1 is simply assumed to be the same as the main flow resistance coefficient, Rm. To save CFD modeling costs, the periodic and symmetry boundary conditions are used in the simulation. The

Table 1. Recommended CFD Options for Tube Bundle Flow Resistance Prediction

Turbulence Model Shear Stress Transport (SST) k-ω

Tube wall Y+ 1

Boundary layer growth rate 1.25

Boundary layer number 15

Figure 3. Tube bundle flow resistance definition in three directions.


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correlations between the pressure drop, ΔP, through the tube bundle and the air incoming veloc-ity, V, are plotted to create a trend line:

(3)

Then,

, (4)

where D is viscous resistance, C is inertial resistance, μ is the viscosity, ρ is the air density, and L is the thickness of the porous media zone. The constants, D and C, with their correspond-ing directions, are defined in the Fluent porous media setting to calculate the tube bundle pres-sure drop.

RESULTS AND DISCUSSION

Comparison of Different CFD Approaches

The airflow distribution predictions are compared among the real tube CFD model, the con-ventional porous media model, and the semiporous media model for a tubular heat exchanger shown in Figure 4. The comparison of the air velocity distribution on a cross-sectional surface is shown in Figure 5. It can be noted that the airflow distribution predicted by the semiporous media model is similar to that predicted by the real tube model. If there are not the two half tubes attached to both sides of the porous media zone, the predicted bypass flow is weak compared to that predicted by the real tube model. The heat exchanger pressure drop prediction deviation between the real tube model and semiporous media model is about –7% for this case.

Figure 6 shows the mesh of the real tube CFD model. Boundary layers are attached on the tube wall and the tube wall Y+ is about 54. The total grid number of the heat exchanger is about 5 M (million). The grid sensitivity study of a single-tube duct flow recommends the near-wall function “enhanced wall treatment” with Y+ = 1 near-wall mesh for flow and pressure drop prediction. But for the large-scale tubular heat exchanger, even for the mesh density that Y+ is equal to 54, the total grid numbers are already more than 5 M and a parallel simulation on two workstations is required. For the fine mesh, Y+ = 1, the total grid number for the heat exchangers with three tube

ΔP aV2 bV+=

D b μL( )⁄= and C 2a ρL( )⁄=

Figure 4. Three CFD modeling approaches.


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bundles will be more than 10 M. By contrast, the semiporous media approach can save a great amount of grid numbers. The hexahedral finite volume elements are generated in the porous media zone to simulate the tube bundle flow resistance. As a result, the grid number for each tube bundle element is less than 400 K (thousand) and the total grid numbers of the gas heater heat exchanger are about 2 M in this work.

As mentioned in the introduction, besides the semiporous media approach and conventional porous media approach, there have been many works applied to the distributed flow resistance porous media approach using user-defined function (UDF)—we term this the UDF-porous media approach. Table 2 compares the advantages and disadvantages of the real tube model, UDF-porous media model, conventional porous media model, and semiporous media model for the tubular heat exchanger flow and pressure drop prediction. From this table, it can be noted that the real tube model has high accuracy and wide application scope, but at the same time it

Figure 5. Velocity distribution prediction comparison.

Figure 6. Mesh of real tube CFD model.


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also has very high computational and implementation costs, as generally the real tube model requires very fine mesh and has to be simulated in parallel. The other approaches have lower computational costs than the real tube model because porous media approaches simplify the tube bundles to porous media zones so that tube surface fine mesh and boundary layer mesh are not required. As a result, the total grid number is greatly reduced, as is the computational cost. The conventional porous media model is easily implemented and has low computation cost, but it also has low accuracy and limited application scope. In contrast, the UDF-porous media and semiporous media approaches both have accuracy and application scope similar to the real tube model, while the semiporous media model is easier to implement and has lower computational cost than the UDF-porous media model because the UDF-porous media approach requires developing code and calculating the distributed flow resistance coefficients on each grid. There-fore, the semiporous media approach is an efficient and economic approach to predict the sparse tubular heat exchanger performance without extensive code development time.

Semiporous Media Model ValidationThe heat exchanger air-side pressure drop predicted by the semiporous media model is com-

pared to test data for eight designs, shown in Figure 7. Design 1 has three tube bundles, and designs 2–8 have four tube bundles. Designs 3–8 have different baffles installed to adjust the airflow distribution. The air was blown by a centrifugal fan and the airflow rate was measured by a nozzle flow chamber, which was connected to the heat exchanger downstream duct. Pres-sure drop through the heat exchanger was measured by capacitive-type pressure sensors. The uncertainty of capacitive-type pressure sensors is ±1%. Typically, the experimental uncertainty of the air mass flow rate measurement was 3%. The atmospheric pressure was monitored by a barometer of column of mercury with a smallest scale division of 0.1 mm (0.00394 in.). The ambient temperature was sensed by thermal couples of ±0.2°C (0.11°F) uncertainty.

To obtain the pressure drop of the tubular heat exchanger, four capacitive pressure taps were placed to measure the heat exchanger upstream and downstream static pressure. Their detailed locations are given in Figure 8. Pressure taps 1 and 2 on the side wall and roof wall were for the heat exchanger upstream static pressure measurement, while pressure taps 3 and 4 on the wall

Table 2. Comparisons of Different CFD Approaches

Real Tube Model

UDF-Porous Media Model

Conventional Porous Media

Model

Semiporous Media Model

AccuracyΔP deviation less than –20% using

5 M grids

No study of this approach found on sparse tubular heat

exchangers

ΔP deviation about –37% using 1–2 M grids

ΔP deviation is less than –13% using 2

M grids

ApplicabilityBoth sparse and

dense tubular heat exchangers

Both sparse and dense tubular heat

exchangers

Dense tubular heat exchangers

Both sparse and dense tubular heat

exchangers

Computational cost

10 M grids 1–2 M grids 1–2 M grids 2 M grids

Implementation cost

Fine tube surface mesh, BL mesh,

Y+ = 1, 10 layers BL

UDF coding, does not require fine

tube surface mesh or BL mesh

Does not require extensive coding, fine tube surface

mesh, or BL mesh

Does not require extensive coding, fine tube surface

mesh, or BL mesh


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near the heat exchanger outlet duct were for the heat exchanger downstream static pressure mea-surement. The heat exchanger static pressure drop is estimated by the following equations:

(5)

(6)

(7)

Figures 9 and 10 show the heat exchanger pressure drop comparisons between the CFD pre-diction and measurement for ΔPs1 and ΔPs2, respectively. The detailed numbers are summarized in Table 3. It can be seen that the prediction deviations of heat exchanger air-side pressure drop are less than ±13%. And for most of the cases compared, the pressure drop prediction deviations are less than ±10%. The above comparison shows that the semiporous CFD model is capable for the pressure drop prediction of the large-scale sparse tubular heat exchanger design and optimi-zation.

Figure 7. Designs for semiporous media model validation.

Figure 8. Positions of static pressure sensors.

ΔPs1 Psdisch earg Ps1–=

ΔPs2 Psdisch earg Ps2–=

Psdisch earg12--- Ps3 Ps4+( )=


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CONCLUSIONThe semiporous media model, which keeps half real tubes on both sides of a porous media

zone, is developed for large-scale sparse tubular heat exchanger airflow and pressure drop pre-dictions. Comparison of the real tube model, UDF-porous media model, conventional porous media model, and semiporous media model shows that the semiporous media model agrees well with the real tube model, predicts clearer and more accurate flow distribution than the conven-tional porous media model, reduces computational costs greatly, and is easier to implement than the UDF-porous media model. The semiporous media model is applied for eight heat exchanger designs. The predicted pressure drop agrees reasonably well with the experiment data. The semi-porous media model is an alternative way to replace expensive and tedious laboratory and pilot-scale studies for gas heater concept design.

NOMENCLATURE

a = coefficient in the polynomial fit b = coefficient in the polynomial fitBL = boundary layerC = inertial resistance factor, m–1 (in.–1)

D = viscous resistance factor, m–2 (in.–2)

k = turbulent kinetic energy, J⋅kg–1 (Btu⋅lb–1)

Figure 9. Pressure drop comparison between CFD results and experimental data for ∆Ps1.


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Rm = flow resistance in mean flow direc-tion

Rs1, Rs2 = flow resistance in side directionsS = source term

u, U, V = velocity, m⋅s–1 (in.⋅s–1)Y+ = parameter in wall function treat-

ment, dimensionless

Greek Symbolsδ = kronecker deltaε = dissipation rate of k, m2⋅s–3

(in.2⋅s–3)

μ, μeff = viscosity, effective viscosity, Pa·s (in. wg·s)

ρ = density, kg⋅m–3 (lb⋅ft–3)ω = specific dissipation rate, s–1

Subscriptsi, j, k = Cartesian components x, y, z = Cartesian components

REFERENCESCornelissen, R.L., and G.G. Hirs. 1999. Thermodynamic optimization of a heat exchanger. Int. J. Heat

Mass Transfer 42:951–59.Dong, Q.W., Y.Q. Wang, and M.S. Liu. 2008. Numerical and experimental investigation of shellside char-

acteristics for ROB baffle heat exchanger. Appl. Therm. Eng. 63:651–60.

Figure 10. Pressure drop comparison between CFD results and experimental data for ∆Ps2.


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Fluent. 2006. Fluent 6.3 User's Guide. Lebanon, NH: Fluent, Inc.

Gentry, C.C. 1990. ROD baffle heat exchanger technology. Chem. Eng. Proc. 86(7):48–57.

Halle, H., J.M. Cheoweth, and M.W. Wambsganss. 1984. Shell side water flow pressure drop distribution measurements in an industrial-sized test heat exchanger: A reappraisal of shell side tube flow in heat exchangers. Proceedings of 22nd Heat Transfer Conference and Exhibition, ASME HTD, pp. 37–48.

He, Y.L., W.Q. Tao, and B. Deng. 2005. Numerical simulation and experimental study of flow and heat transfer characteristics of shell side fluid in shell-and-tube heat exchangers. Proceedings of Fifth Inter-national Conference on Enhanced, Compact and Ultra-Compact Heat Exchangers: Science, Engineer-ing and Technology, pp. 29–42.

Hofman, A. 2000. Theoretical solution for the cross-• ow heat exchanger. Heat Mass Transfer 36:127–33.

Hua, S.Z., and X.N. Yang. 1985. Flow Resistance Handbook (in Chinese). Beijing: National Defense Industry Press.

Incropera, F.P., and D.P. DeWitt. 2002. Fundamentals of Heat and Mass Transfer, 5th ed. NY: John Wiley & Sons.

Lei, Y.G., Y.L. He, P. Chu, and R. Li. 2008. Design and optimization of heat exchangers with helical baf-fles. Chem. Eng. Sci. 63:4386–96.

Table 3. Comparison of Measured and CFD Predicted Pressure Drops

Concepts∆P test (Pa) ∆P CFD (Pa) Deviation

∆Ps1 ∆Ps2 ∆Ps1 ∆Ps2 ∆Ps1 ∆Ps2

Design 1 216.7 229.2 199.3 204.3 –8.0% –10.9%

Design 2 249.1 276.5 251.6 249.1 1.0% –9.9%

Design 3 293.9 326.3 303.9 301.4 3.4% –7.6%

Design 4 288.9 316.3 323.8 321.3 12.1% 1.6%

Design 5 291.4 316.3 321.3 318.8 10.3% 0.8%

Design 6 288.9 318.8 298.9 296.4 3.4% –7.0%

Design 7 311.4 341.3 331.3 328.8 6.4% –3.6%

Design 8 323.8 351.2 358.7 358.7 10.8% 2.1%

Concepts∆P test (in. wg) ∆P CFD (in. wg) Deviation

∆Ps1 ∆Ps2 ∆Ps1 ∆Ps2 ∆Ps1 ∆Ps2

Design 1 0.87 0.92 0.80 0.82 –8.0% –10.9%

Design 2 1.00 1.11 1.01 1.00 1.0% –9.9%

Design 3 1.18 1.31 1.22 1.21 3.4% –7.6%

Design 4 1.16 1.27 1.30 1.29 12.1% 1.6%

Design 5 1.17 1.27 1.29 1.28 10.3% 0.8%

Design 6 1.16 1.28 1.20 1.19 3.4% –7.0%

Design 7 1.25 1.37 1.33 1.32 6.4% –3.6%

Design 8 1.30 1.41 1.44 1.44 10.8% 2.1%


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Patankar, S.V., and D.B. Spalding. 1974. A calculation procedure for the transient and steady-state behav-ior of shell-and-tube heat exchangers, pp. 155–76. In: Heat Transfer Design and Theory Sourcebook. Washington: Afgan and Schlunder.

Reppich, M., and J. Kohoutek. 1994. Optimal design of shell-and-tube heat exchangers. Comput. Chem. Eng. 18:S295–S299.

Resat, S., K. Onder, and R. Marcus. 2006. A new design approach for shell-and-tube heat exchangers using genetic algorithms from economic point of view. Chem. Eng. and Proc. 45:268–75.

Roetzel, W., and D. Lee. 1993. Experimental investigation of leakage in shell-and-tube heat exchangers with segmental baffles. Int. J. Heat Mass Transfer. 36(15):3765–71.

Rohsenow, W.M., J.P. Hartnett, and Y.I. Cho. 1998. Handbook of Heat Transfer, 3d ed. NY: McGraw-Hill.

Sha, W.T., C.I. Yang, and T.T. Kao. 1982. Multidimensional numerical modeling of heat exchangers. ASME J. Heat Transfer 104:417–25.

Stevanovic, Z., G. Ilic, and N. Radojkoyic. 2001. Design of shell-and-tube heat exchangers by using CFD technique—Part one: Thermo-hydraulic calculation. Facta Universitatis Series: Mechanical Engineer-ing. 1(8):1091–1105.

Zhang, C., A.C.M. Sousa, and J.E.S. Venart. 1991. Numerical simulation of different types of steam sur-face condensers. J. Energy Resources Technology 113(2):63–70.


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Semiporous Media Approach for Numerical Simulation of Flow through Large-Scale Sparse Tubular Heat Exchangers