CHEN Sheng. Effect of Richardson Number on Entropy Generation Over a Backward Facing Step[J]. Applied Mathematics and Mechanics, 2012, 33(11): 1330-1339. doi: 10.3879/j.issn.1000-0887.2012.11.008
Citation: CHEN Sheng. Effect of Richardson Number on Entropy Generation Over a Backward Facing Step[J]. Applied Mathematics and Mechanics, 2012, 33(11): 1330-1339. doi: 10.3879/j.issn.1000-0887.2012.11.008

Effect of Richardson Number on Entropy Generation Over a Backward Facing Step

doi: 10.3879/j.issn.1000-0887.2012.11.008
  • Received Date: 2011-11-17
  • Rev Recd Date: 2012-05-05
  • Publish Date: 2012-11-15
  • Flow over a backward facing step (BFS) has been taken as a useful prototype to investigate characteristics of separated flow with heat transfer. However, to date the study on the effect of Richardson number on entropy generation over BFS is absent yet although the flow pattern and heat transfer characteristic both would receive significant influence caused by variation of Richardson number in many practical applications, for example in microelectromechanical systems and aerocrafts. The effect of Richardson number on entropy generation in BFS flow was reported for the first time. Results of entropy generation analysis was obtained by numerically solving the entropy generation equation. The values of velocity and temperature, which were the inputs of the entropy generation equation, were obtained by the lattice Boltzmann method.It is found that the distributions of local entropy generation number and Bejan number are significantly influenced by the variation of Richardson number. The total entropy generation number is a monotonic decreasing function of Richardson number whereas the average Bejan number is a monotonic increasing function of Richardson number.
  • loading
  • [1]
    Leone Jr J M. Open boundary condition symposium benchmark solution: stratified flow over a backward-facing step[J]. International Journal for Numerical Methods in Fluids, 1990, 11(7): 969-984.
    [2]
    Armaly B F, Durst F, Pereira J C F, Schonung B. Experimental and theoretical investigation of backward-facing step flow[J]. Journal of Fluid Mechanics, 1983, 127: 473-496.
    [3]
    Le H, Moin P, Kim J. Direct numerical simulation of turbulent flow over a backward-facing step[J]. Journal of Fluid Mechanics, 1997, 330: 349-374.
    [4]
    Ramsak M, Skerget L, Hribersek M, Zunic Z. A multidomain boundary element method for unsteady laminar flow using stream function vorticity equations[J]. Engineering Analysis With Boundary Elements, 2005, 29(1): 1-14.
    [5]
    Calle J L D, Devloo P R B, Gomes S M. Stabilized discontinuous Galerkin method for hyperbolic equations[J]. Computer Methods in Applied Mechanics and Engineering, 2005, 194(17): 1861-1874.
    [6]
    Creuse E, Giovannini A, Mortazavi I. Vortex simulation of active control strategies for transitional backward-facing step flows[J]. Computers and Fluids, 2009, 38(7): 1348-1360.
    [7]
    Abu-Mulaweh H I. A review of research on laminar mixed convection flow over backward- and forward-facing steps[J]. International Journal of Thermal Sciences, 2003, 42(9): 897-909.
    [8]
    Ho C, Tai Y. Micro-electro-mechanical-systems (MEMS) and fluid flows[J]. Annual Review of Fluid Mechanics, 1998, 30: 579-612.
    [9]
    Karniadakis G E, Beskok A. Micro Flows Fundamentals and Simulation[M]. New York: Springer-Verlag, 2002: 55-70.
    [10]
    Bejan A. Entropy Generation Through Heat and Fluid Flow[M]. 2nd ed. New York: Wiley Interscience, 1994: 200-210.
    [11]
    Abu-Nada E. Investigation of entropy generation over a backward facing step under bleeding conditions[J]. Energy Conversion and Management, 2008, 49(11): 3237-3242.
    [12]
    Abu-Nada E. Numerical prediction of entropy generation in separated flows[J]. Entropy, 2005, 7(4): 234-252.
    [13]
    Abu-Nada E. Entropy generation due to heat and fluid flow in backward facing step flow with various expansion ratios[J]. International Journal of Energy, 2006, 3(4): 419-435.
    [14]
    Chen S, Liu Z, Shi B, Zheng C G. Computation of gas-solid flows by finite difference Boltzmann equation[J]. Applied Mathematics and Computation, 2006, 173(1): 33-49.
    [15]
    Chen S, Shi B, Liu Z, He Z, Guo Z L, Zheng C G. Lattice-Boltzmann simulation of particle-laden flow over a backward-facing step[J]. Chinese Physics, 2004, 13(10): 1657-1664.
    [16]
    Qian Y, D’Humières D, Lallemand P. Lattice BGK models for Navier-Stokes equation[J]. Europhysics Letters, 1992, 17: 479-484.
    [17]
    Benzi R, Succi S, Vergassola M. The lattice Boltzmann equation: theory and applications[J]. Physics Report, 1992, 222(3): 145-197.
    [18]
    Chen S, Doolen G D. Lattice Boltzmann method for fluid flows[J]. Annual Review of Fluid Mechanics, 1998, 30: 329-364.
    [19]
    Succi S. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond[M]. Oxford: Oxford University Press, 2001: 10-52.
    [20]
    Chen S, Krafczyk M. Entropy generation in turbulent natural convection due to internal heat generation[J]. International Journal of Thermal Sciences, 2009, 48(10): 1978-1987.
    [21]
    Lioua K, Oztop H F, Borjini M N, Al-Salemc K. Second law analysis in a three dimensional lid-driven cavity[J]. International Communications in Heat and Mass Transfer, 2011, 38(10): 1376-1383.
    [22]
    Kuo L S, Chen P H. Numerical implementation of thermal boundary conditions in the lattice Boltzmann method[J]. International Journal of Heat and Mass Transfer, 2009, 52(1/2): 529-532.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1548) PDF downloads(865) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return