0
Research Papers: Techniques and Procedures

Numerical Simulation of Heat Transfer Process of Viscoelastic Fluid Flow at High Weissenberg Number by Log-Conformation Reformulation

[+] Author and Article Information
Hong-Na Zhang

School of Energy Science and Engineering,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: zhanghn@hit.edu.cn

Dong-Yang Li

School of Energy Science and Engineering,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: lidongyang@hit.edu.cn

Xiao-Bin Li

Mem. ASME
School of Energy Science and Engineering,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: lixb@hit.edu.cn

Wei-Hua Cai

Mem. ASME
School of Energy Science and Engineering,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: caiwh@hit.edu.cn

Feng-Chen Li

Mem. ASME
School of Energy Science and Engineering,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: lifch@hit.edu.cn

1Both authors contributed equally to the paper.

2Corresponding authors.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received November 28, 2016; final manuscript received March 9, 2017; published online June 28, 2017. Assoc. Editor: Mark F. Tachie.

J. Fluids Eng 139(9), 091402 (Jun 28, 2017) (12 pages) Paper No: FE-16-1777; doi: 10.1115/1.4036592 History: Received November 28, 2016; Revised March 09, 2017

Viscoelastic fluids are now becoming promising candidates of microheat exchangers’ working medium due to the occurrence of elastic instability and turbulence at microscale. This paper developed a sound solver for the heat transfer process of viscoelastic fluid flow at high Wi, and this solver can be used to design the multiple heat exchangers with viscoelastic fluids as working medium. The solver validation was conducted by simulating four fundamental benchmarks to assure the reliability of the established solver. After that, the solver was adopted to study the heat transfer process of viscoelastic fluid flow in a curvilinear channel, where apparent heat transfer enhancement (HTE) by viscoelastic fluid was achieved. The observed heat transfer enhancement was attributed to the occurrence of elastic turbulence which continuously mix the hot and cold fluids by the twisting and wiggling flow motions.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Andhare, R. S. , Shooshtari, A. , Dessiatoun, S. V. , and Ohadi, M. M. , 2016, “ Heat Transfer and Pressure Drop Characteristics of a Flat Plate Manifold Microchannel Heat Exchanger in Counter Flow Configuration,” Appl. Therm. Eng., 96, pp. 178–189. [CrossRef]
Dang, M. , Hassan, I. , and Kim, S. I. , 2008, “ Numerically Investigating the Effects of Cross-Links in Scaled Microchannel Heat Sinks,” ASME J. Fluids Eng., 130(12), p. 121103. [CrossRef]
Mohammadi, M. , Jovanovic, G. N. , and Sharp, K. V. , 2013, “ Numerical Study of Flow Uniformity and Pressure Characteristics Within a Microchannel Array With Triangular Manifolds,” Comput. Chem. Eng., 52(10), pp. 134–144. [CrossRef]
Ryu, J. H. , Choi, D. H. , and Kim, S. J. , 2003, “ Three-Dimensional Numerical Optimization of a Manifold Microchannel Heat Sink,” Int. J. Heat Mass Transfer, 46(9), pp. 1553–1562. [CrossRef]
Shen, S. , Xu, J. L. , Zhou, J. J. , and Chen, Y. , 2006, “ Flow and Heat Transfer in Microchannels With Rough Wall Surface,” Energy Convers. Manage., 47(11–12), pp. 1311–1325. [CrossRef]
Tuckerman, D. B. , and Pease, R. F. W. , 1981, “ High-Performance Heat Sinking for VLSI,” IEEE Electron. Device Lett., 2(5), pp. 126–129. [CrossRef]
Xia, G. , Chai, L. , Wang, H. , Zhou, M. , and Cui, Z. , 2011, “ Optimum Thermal Design of Microchannel Heat Sink With Triangular Reentrant Cavities,” Appl. Therm. Eng., 31(6–7), pp. 1208–1219. [CrossRef]
Xie, G. , Shen, H. , and Wang, C.-C. , 2015, “ Parametric Study on Thermal Performance of Microchannel Heat Sinks With Internal Vertical Y-Shaped Bifurcations,” Int. J. Heat Mass Transfer, 90, pp. 948–958. [CrossRef]
Xie, G. , Zhang, F. , Sundén, B. , and Zhang, W. H. , 2014, “ Constructal Design and Thermal Analysis of Microchannel Heat Sinks With Multistage Bifurcations in Single-Phase Liquid Flow,” Appl. Therm. Eng., 62(2), pp. 791–802. [CrossRef]
Xu, J. L. , Gan, Y. H. , Zhang, D. C. , and Li, X. H. , 2005, “ Microscale Heat Transfer Enhancement Using Thermal Boundary Layer Redeveloping Concept,” Int. J. Heat Mass Transfer, 48(9), pp. 1662–1674. [CrossRef]
Ammar, H. , Ould el Moctar, A. , Garnier, B. , and Peerhossaini, H. , 2014, “ Flow Pulsation and Geometry Effects on Mixing of Two Miscible Fluids in Microchannels,” ASME J. Fluids Eng., 136(12), p. 121101. [CrossRef]
Nishimura, T. , Morega, A. M. , and Kunitsugu, K. , 1997, “ Vortex Structure and Fluid Mixing in Pulsatile Flow Through Periodically Grooved Channels at Low Reynolds Numbers,” JSME Int. J., 40(3), pp. 377–385. [CrossRef]
Nishimura, T. , Oka, N. , Yoshinaka, Y. , and Kunitsugu, K. , 2000, “ Influence of Imposed Oscillatory Frequency on Mass Transfer Enhancement of Grooved Channels for Pulsatile Flow,” Int. J. Heat Mass Transfer, 43(13), pp. 2365–2374. [CrossRef]
Bird, R. B. , 1987, Dynamics of Polymeric Liquids, Wiley, New York.
Groisman, A. , and Steinberg, V. , 2000, “ Elastic Turbulence in a Polymer Solution Flow,” Nature, 405, pp. 53–55. [CrossRef] [PubMed]
Hung, T.-C. , Yan, W.-M. , Wang, X.-D. , and Chang, C.-Y. , 2012, “ Heat Transfer Enhancement in Microchannel Heat Sinks Using Nanofluids,” Int. J. Heat Mass Transfer, 55(9–10), pp. 2559–2570. [CrossRef]
Ibrahim, W. , and Shanker, B. , 2012, “ Boundary-Layer Flow and Heat Transfer of Nanofluid Over a Vertical Plate With Convective Surface Boundary Condition,” ASME J. Fluids Eng., 134(8), p. 081203. [CrossRef]
Kiyasatfar, M. , and Pourmahmoud, N. , 2016, “ Laminar MHD Flow and Heat Transfer of Power-Law Fluids in Square Microchannels,” Int. J. Therm. Sci., 99, pp. 26–35. [CrossRef]
Li, S.-N. , Zhang, H.-N. , Li, X.-B. , Li, Q. , Li, F.-C. , Qian, S. , and Sang, W. J. , 2016, “ Numerical Study on the Heat Transfer Performance of Non-Newtonian Fluid Flow in a Manifold Microchannel Heat Sink,” Appl. Therm. Eng., 115, pp. 1213–1225.
Nejat, A. , Mirzakhalili, E. , Aliakbari, A. , Niasar, M. S. F. , and Vahidkhah, K. , 2012, “ Non-Newtonian Power-Law Fluid Flow and Heat Transfer Computation Across a Pair of Confined Elliptical Cylinders in the Line Array,” J. Non-Newtonian Fluid Mech., 171–172, pp. 67–82. [CrossRef]
Pimenta, T. A. , and Campos, J. B. L. M. , 2013, “ Heat Transfer Coefficients From Newtonian and Non-Newtonian Fluids Flowing in Laminar Regime in a Helical Coil,” Int. J. Heat Mass Transfer, 58(1–2), pp. 676–690. [CrossRef]
Chein, R. , and Huang, G. , 2005, “ Analysis of Microchannel Heat Sink Performance Using Nanofluids,” Appl. Therm. Eng., 25(17–18), pp. 3104–3114. [CrossRef]
Li, J. , Sheeran, P. S. , and Kleinstreuer, C. , 2011, “ Analysis of Multi-Layer Immiscible Fluid Flow in a Microchannel,” ASME J. Fluids Eng., 133(11), p. 111202. [CrossRef]
Groisman, A. , and Steinberg, V. , 2004, “ Elastic Turbulence in Curvilinear Flows of Polymer Solutions,” New J. Phys., 6(1), p. 29. [CrossRef]
Burghelea, T. , Segre, E. , and Steinberg, V. , 2007, “ Elastic Turbulence in von Karman Swirling Flow Between Two Disks,” Phys. Fluids, 19(5), p. 053104. [CrossRef]
Li, F.-C. , Kinoshita, H. , Li, X.-B. , Oishi, M. , Fujii, T. , and Oshima, M. , 2010, “ Creation of Very-Low-Reynolds-Number Chaotic Fluid Motions in Microchannels Using Viscoelastic Surfactant Solution,” Exp. Therm. Fluid Sci., 34(1), pp. 20–27. [CrossRef]
Li, F.-C. , Zhang, H.-N. , Cao, Y. , Tomoaki, K. , Haruyuki, K. , and Marie, O. , 2012, “ A Purely Elastic Instability and Mixing Enhancement in a 3D Curvilinear Channel Flow,” Chin. Phys. Lett., 29(9), p. 094704. [CrossRef]
Zhang, H.-N. , Li, F.-C. , Cao, Y. , Tomoaki, K. , and Yu, B. , 2013, “ Direct Numerical Simulation of Elastic Turbulence and Its Mixing-Enhancement Effect in a Straight Channel Flow,” Chin. Phys. B, 22(2), p. 024703. [CrossRef]
Zhang, H.-N. , Li, F.-C. , Li, X.-B. , Li, D.-Y. , Cai, W.-H. , and Yu, B. , 2016, “ Characteristics and Generation of Elastic Turbulence in a Three-Dimensional Parallel Plate Channel Using Direct Numerical Simulation,” Chin. Phys. B, 25(9), p. 094701. [CrossRef]
Li, X.-B. , Oishi, M. , Matsuo, T. , Oshima, M. , and Li, F.-C. , 2016, “ Measurement of Viscoelastic Fluid Flow in the Curved Microchannel Using Digital Holographic Microscope and Polarized Camera,” ASME J. Fluids Eng., 138(9), p. 091401. [CrossRef]
Li, D.-Y. , Li, X.-B. , Zhang, H.-N. , Li, F.-C. , Qian, S.-Z. , and Joo, S. W. , 2016, “ Measuring Heat Transfer Performance of Viscoelastic Fluid Flow in Curved Microchannel Using Ti–Pt Film Temperature Sensor,” Exp. Therm. Fluid Sci., 77, pp. 226–233. [CrossRef]
Burghelea, T. , Segre, E. , Bar-Joseph, I. , Groisman, A. , and Steinberg, V. , 2004, “ Chaotic Flow and Efficient Mixing in a Microchannel With a Polymer Solution,” Phys. Rev., E, 69(6 Pt. 2), p. 066305. [CrossRef]
Groisman, A. , and Steinberg, V. , 2001, “ Efficient Mixing at Low Reynolds Numbers Using Polymer Additives,” Nature, 410(6831), pp. 905–908. [CrossRef] [PubMed]
Jun, Y. , and Steinberg, V. , 2010, “ Mixing of Passive Tracers in the Decay Batchelor Regime of a Channel Flow,” Phys. Fluids, 22(12), p. 123101. [CrossRef]
Li, X.-B. , Zhang, H.-N. , Cao, Y. , Oshima, M. , and Li, F.-C. , 2015, “ Motion of Passive Scalar by Elasticity-Induced Instability in Curved Microchannel,” Adv. Mech. Eng., 6, p. 734175. [CrossRef]
Keunings, R. , 1986, “ On the High Weissenberg Number Problem,” J. Non-Newtonian Fluid Mech., 20, pp. 209–226. [CrossRef]
Guénette, R. , and Fortin, M. , 1995, “ A New Mixed Finite Element Method for Computing Viscoelastic Flows,” J. Non-Newtonian Fluid Mech., 60(1), pp. 27–52. [CrossRef]
Vaithianathan, T. , and Collins, L. R. , 2003, “ Numerical Approach to Simulating Turbulent Flow of a Viscoelastic Polymer Solution,” J. Comput. Phys., 187(1), pp. 1–21. [CrossRef]
Fattal, R. , and Kupferman, R. , 2004, “ Constitutive Laws for the Matrix-Logarithm of the Conformation Tensor,” J. Non-Newtonian Fluid Mech., 123(2–3), pp. 281–285. [CrossRef]
Afonso, A. , Oliveira, P. J. , Pinho, F. T. , and Alves, M. A. , 2009, “ The Log-Conformation Tensor Approach in the Finite-Volume Method Framework,” J. Non-Newtonian Fluid Mech., 157(1–2), pp. 55–65. [CrossRef]
Favero, J. L. , Secchi, A. R. , Cardozo, N. S. M. , and Jasak, H. , 2010, “ Viscoelastic Flow Analysis Using the Software OpenFOAM and Differential Constitutive Equations,” J. Non-Newtonian Fluid Mech., 165(23–24), pp. 1625–1636. [CrossRef]
Habla, F. , Tan, M. W. , Haßlberger, J. , and Hinrichsen, O. , 2014, “ Numerical Simulation of the Viscoelastic Flow in a Three-Dimensional Lid-Driven Cavity Using the Log-Conformation Reformulation in OpenFOAM®,” J. Non-Newtonian Fluid Mech., 212, pp. 47–62. [CrossRef]
Jensen, K. E. , Szabo, P. , and Okkels, F. , 2015, “ Implementation of the Log-Conformation Formulation for Two-Dimensional Viscoelastic Flow,” Comput. Sci., 223, pp. 209–220. https://arxiv.org/abs/1508.01041
Fattal, R. , and Kupferman, R. , 2005, “ Time-Dependent Simulation of Viscoelastic Flows at High Weissenberg Number Using the Log-Conformation Representation,” J. Non-Newtonian Fluid Mech., 126(1), pp. 23–37. [CrossRef]
Comminal, R. , Spangenberg, J. , and Hattel, J. H. , 2015, “ Robust Simulations of Viscoelastic Flows at High Weissenberg Numbers With the Streamfunction/Log-Conformation Formulation,” J. Non-Newtonian Fluid Mech., 223, pp. 37–61. [CrossRef]
Incropera, F. P. , and Dewitt, D. P. , 1996, Fundamental of Heat and Mass Transfer, Wiley, New York.
Knechtges, P. , 2015, “ The Fully-Implicit Log-Conformation Formulation and Its Application to Three-Dimensional Flows,” J. Non-Newtonian Fluid Mech., 223, pp. 209–220. [CrossRef]
Cruz, F. A. , Poole, R. J. , Afonso, A. M. , Pinho, F. T. , Oliveira, P. J. , and Alves, M. A. , 2014, “ A New Viscoelastic Benchmark Flow: Stationary Bifurcation in a Cross-Slot,” J. Non-Newtonian Fluid Mech., 214, pp. 57–68. [CrossRef]
Miranda, A. I. P. , and Oliveira, P. J. , 2010, “ Start-Up Times in Viscoelastic Channel and Pipe Flows,” Korea-Australia Rheol. J., 22(1), pp. 65–73. http://webx.ubi.pt/~pjpo/ri62.pdf
Abed, W. M. , Whalley, R. D. , Dennis, D. J. C. , and Poole, R. J. , 2016, “ Experimental Investigation of the Impact of Elastic Turbulence on Heat Transfer in a Serpentine Channel,” J. Non-Newton. Fluid Mech., 231, pp. 68–78. [CrossRef]
Li, D.-Y. , Zhang, H. , Cheng, J.-P. , Li, X.-B. , Li, F. C. , Qian, S. , and Joo, S. W. , 2017, “ Numerical Simulation of Heat Transfer Enhancement by Elastic Turbulence in a Curvy Channel,” Microfluid. Nanofluid., 21, p. 25.
Kraichnan, R. H. , 1968, “ Small-Scale Structure of a Scalar Field Convected by Turbulence,” Phys. Fluids, 11(5), pp. 945–953. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Flowchart of the numerical procedures

Grahic Jump Location
Fig. 2

Schematic of sphere sedimentation in a tube

Grahic Jump Location
Fig. 3

(a) Schematic of cross slot geometry, (b) contour of velocity magnitude, and (c) contour of the trace of the conformation tensor together with streamline

Grahic Jump Location
Fig. 4

(a) Schematic of startup of Poiseuille flow; and comparison between the numerical results and analytical solution at (b) E = 10; (c) E = 50 for Oldroyd-B fluid with β = 0.01, U0 is centerline velocity, and t is the dimensionless time

Grahic Jump Location
Fig. 5

Schematic of (a) the computational domain and (b) the mesh of 3D serpentine microchannel. The origin of the coordinate system for this channel is its center point. (Reprinted with permission from Li et al. [51]. Copyright 2017 by Springer.)

Grahic Jump Location
Fig. 6

Temporal evolutions of (a) the streamwise velocity component U, (b) the radial velocity component −V, (c) the dimensionless temperature, at the monitoring point (the center point of the channel) at various Wi, and (d) spectrum of fluctuations of radial velocity component and dimensionless temperature at the monitoring points at Wi = 5

Grahic Jump Location
Fig. 7

Time-averaged streamwise velocity component U in the y–z midplane at x = 0 for different Wi: (a) Wi = 0, (b) Wi = 1, (c)Wi = 2, (d) Wi = 5, and (e) Wi = 10

Grahic Jump Location
Fig. 8

Time-averaged heat transfer performance of viscoelastic fluid flow at various Wi

Grahic Jump Location
Fig. 9

Distributions of dimensionless temperature and tr(C) in the horizontal plane (x–y midplane at z = 0) and vertical plane (y–z midplane at x = 0) for Newtonian fluid flow (Wi = 0) and viscoelastic fluid flow (Wi = 10)

Grahic Jump Location
Fig. 10

Numerical results in the horizontal centerline of center cross section for five sets of mesh resolution: (a) time-averaged dimensionless velocity profiles and (b) time-averaged dimensionless temperature profiles, at Re = 1, Pr = 1000, Wi = 20, and β = 0.2. (Reprinted with permission from Li et al. [51]. Copyright 2017 by Springer.)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In