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Direct-Forcing Immersed Boundary Method for Mixed Heat Transfer

Part of: Coupling of solid mechanics with other effects Partial differential equations, initial value and time-dependent initial-boundary value problems Incompressible viscous fluids

Published online by Cambridge University Press:  15 October 2015

Ming-Jyh Chern ,
Dedy Zulhidayat Noor ,
Ching-Biao Liao  and
Tzyy-Leng Horng
Ming-Jyh Chern
Affiliation:
Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan
Dedy Zulhidayat Noor
Affiliation:
Department of Mechanical Engineering, Institut Teknologi Sepuluh Nopember Sukolilo, Surabaya, Indonesia
Ching-Biao Liao
Affiliation:
Department of Water Resources Engineering and Conservation, Feng Chia University, Taichung, Taiwan
Tzyy-Leng Horng*
Affiliation:
Department of Applied Mathematics, Feng Chia University, Taichung, Taiwan
*
*Corresponding author. Email address: tlhorng123@gmail.com (T.-L. Horng)
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Abstract

A direct-forcing immersed boundary method (DFIB) with both virtual force and heat source is developed here to solve Navier-Stokes and the associated energy transport equations to study some thermal flow problems caused by a moving rigid solid object within. The key point of this novel numerical method is that the solid object, stationary or moving, is first treated as fluid governed by Navier-Stokes equations for velocity and pressure, and by energy transport equation for temperature in every time step. An additional virtual force term is then introduced on the right hand side of momentum equations in the solid object region to make it act exactly as if it were a solid rigid body immersed in the fluid. Likewise, an additional virtual heat source term is applied to the right hand side of energy equation at the solid object region to maintain the solid object at the prescribed temperature all the time. The current method was validated by some benchmark forced and natural convection problems such as a uniform flow past a heated circular cylinder, and a heated circular cylinder inside a square enclosure. We further demonstrated this method by studying a mixed convection problem involving a heated circular cylinder moving inside a square enclosure. Our current method avoids the otherwise requested dynamic grid generation in traditional method and shows great efficiency in the computation of thermal and flow fields caused by fluid-structure interaction.

Keywords

Direct-forcing immersed boundary methodfluid-structure interactionmixed convection

MSC classification

Secondary: 74F10: Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 65M06: Finite difference methods 76D05: Navier-Stokes equations
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 4 , October 2015 , pp. 1072 - 1094
Copyright
Copyright © Global-Science Press 2015 

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References

[1]Hirt, C. W., Amsden, A. A. and Cook, J. L., An arbitrary Lagrangian-Eulerian computing method for all flow speeds, J. Comput. Phys., 4 (1974), 227–253.Google Scholar
[2]Bailey, D., Berndt, M., Kucharik, M. and Shashkov, M., Reduced-dissipation remapping of velocity in staggered arbitrary Lagrangian-Eulerian methods, J. Comput. Appl. Math. 233 (2010), 3148–3156.Google Scholar
[3]Kucharik, M., Liska, R., Shashkov, M., Conservative Remapping and ALE Methods for Plasma Physics, in Proceedings of HYP 2004, Tenth International Conference on Hyperbolic Problems: Theory, Numerics, Applications, Yokohama Publisher, Japan, 2006.Google Scholar
[4]Benson, D. J., Computational methods in Lagrangian and Eulerian hydrocodes, Comput. Method Appl. M., 99 (1992), 235–394.Google Scholar
[5]Kjellgren, P. and Hyvarinen, J., An arbitrary Lagrangian-Eulerian finite element method. Comput. Mech., 21 (1998), 81–90.Google Scholar
[6]Peery, J. S. and Carrol, D. E., Multi-material ALE methods in unstructured grids, Comput. Method Appl. M., 187 (2000), 591–619.Google Scholar
[7]Peskin, C. S., Flow patterns around heart valve: A numerical method, J. Comput. Phys., 10 (1972), 252–271.Google Scholar
[8]Goldstein, D., Handler, R. and Sirovich, L., Modeling and no-slip flow boundary with an external force field, J. Comput. Phys., 105 (1993), 354–366.Google Scholar
[9]Saiki, E. M. and Biringen, S., Numerical simulation of a cylinder in uniform flow: Application of a virtual boundary method, J. Comput. Phys., 123 (1996), 450–365.Google Scholar
[10]Lai, M. C. and Peskin, C. S., An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J. Comput. Phys., 160 (2000), 705–719.Google Scholar
[11]Su, S. W., Lai, M. C. and Lin, C. A., An immersed boundary technique for simulating complex flows with rigid boundary, Comput. Fluids, 36 (2007), 313–324.Google Scholar
[12]Mohd-Yusof, J., Interaction of massive particles with turbulence, PhD. Dissertation, Dept. of Mechanical and Aerospace Engineering, Cornell University, USA, 1996.Google Scholar
[13]Ye, T., Mittal, R., Udaykumar, H. S. and Shyy, W., An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries, J. Comput. Phys., 156 (1999), 209–240.Google Scholar
[14]Fadlun, E. A., Verzicco, R., Orlandi, P. and Mohd-Yusof, J., Combined immersed-boundary finite-difference method for three dimensional complex flow simulations, J. Comput. Phys., 161 (2000), 35–60.CrossRefGoogle Scholar
[15]Tseng, Y. H. and Ferziger, J. H., A ghost-cell immersed boundary method for flow in complex geometry, J. Comput. Phys., 192 (2003), 593–623.CrossRefGoogle Scholar
[16]Zhang, N. and Zheng, Z. C., An improved direct-forcing immersed-boundary method for finite difference applications, J. Comput. Phys., 221 (2007), 250–268.Google Scholar
[17]Noor, D. Z., Chern, M. J. and Horng, T. L., An immersed boundary method to solve fluid-solid interaction problems, Comput. Mech., 44 (2009), 447–453.Google Scholar
[18]Chern, M. J., Hsu, W. C. and Horng, T. L., Numerical prediction of hydrodynamic loading on circular cylinder array in oscillatory flow using direct-forcing immersed boundary method, J. Appl. Math., (2012), Article ID 505916.CrossRefGoogle Scholar
[19]Chern, M. J., Shiu, W. C. and Horng, T. L., Immersed boundary modeling for interaction of oscillatory flow with cylinder array under effects of flow direction and cylinder arrangement, J. Fluid Struct., 43 (2013), 325–346.Google Scholar
[20]Chern, M. J., Kuan, Y. H., Nugroho, G., Lu, G. T. and Horng, T. L., Direct-forcing immersed boundary modeling of vortex-induced vibration of a circular cylinder, J. Wind Eng. Ind. Aerod., 134 (2014), 109–121.Google Scholar
[21]Paravento, F., Pourquie, M. J., Boersma, B. J., An immersed boundary method for complex flow and heat transfer, Flow Turbul. Combust., 80 (2007), 187–206.Google Scholar
[22]Vega, A. P., Pacheco, J. R. and Rodic, T., A general scheme for the boundary conditions in convective and diffusive heat transfer with immersed boundary methods, J. Heat Transf., 129 (2007), 1506–1516.CrossRefGoogle Scholar
[23]Pan, D., An immersed boundary method on unstructured Cartesian meshes for incompressible flows with heat transfer, Numer. Heat Tr. B-Fund., 49 (2006), 277–297.Google Scholar
[24]Dhole, S. D., Chhabra, R. P. and Eswaran, V., A numerical study on the forced convection heat transfer from an isothermal and isoflux sphere in the steady symmetric flow regime, Int. J. Heat Mass Tran., 49 (2006), 984–994.Google Scholar
[25]Kuyper, R. A., der Meer, T. H. van, Hoogendoorn, C. J. and Henkes, R. A. W. M., Numerical study of laminar and turbulent natural convection in an inclined square cavity, Int. J. Heat Mass Tran., 36 (1993), 2899–2911.Google Scholar
[26]Kim, J., Kim, D. and Choi, H., An immersed-boundary finite-volume method for simulations of flow in complex geometries, J. Comput. Phys., 171 (2001), 132–150.Google Scholar
[27]Eckert, E. R. G. and Soehngen, E., Distribution of heat transfer coefficients around circular cylinder in cross flow at Reynolds number from 20 to 500, Trans. ASME, 74 (1952), 343347.Google Scholar
[28]Dias, A. and Majumdar, S., Numerical computation of flow around a circular cylinder, Technical Report, PS II Report, BITS Pilani, India, 2002.Google Scholar
[29]Moukalled, F. and Acharya, S., Natural convection in the annulus between concentric horizontal circular and square cylinder, J. Thermophys. Heat Tr., 10 (1996), 524–531.Google Scholar
[30]Shu, C., Xue, H., Zhu, Y. D., Numerical study of natural convection in an eccentric annulus between a square outer cylinder and a circular inner cylinder using DQ method, Int. J. Heat Mass Tran., 44 (2001), 3321–3333.Google Scholar
[31]Sadat, H. and Couturier, S., Performance and accuracy of a meshless method for laminar natural convection, Numer. Heat Tr. B-Fund., 37 (2000), 455–467.Google Scholar
[32]Tritton, D. J., Experiments on the flow past a circular cylinder at low Reynolds number, J. Fluid Mech., 6 (1959), 547–567.Google Scholar
[33]Borthwick, A. G. L., Comparison between two finite difference schemes for computing the flow around a cylinder, Int. J. Numer. Methods Fluids, 6 (1986), 275–290.Google Scholar
[34]Sheard, G. J., Hourigan, K. and Thompson, M. C., Computations of the drag coefficients for low-Reynolds-number flow past rings, J. Fluid Mech., 526 (2005), 257–275.Google Scholar
[35]Dennis, S. C. R. and Chang, G. Z., Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100, J. Fluid Mech., 42 (1970), 471–489.Google Scholar
[36]Lange, C. F., Durst, F. and Breuer, M., Momentum and heat transfer from cylinders in laminar crossflow at 10-4 ≤Re≤200, Int. J. Heat Mass Tran., 41 (1998), 3409–3430.CrossRefGoogle Scholar
[37]Soares, A. A., Ferreira, J. M. and Chhabra, R. P., Flow and forced convection heat transfer in crossflow of non-Newtonian fluids over a circular cylinder, Industrial & Engineering Chemistry Research, 44 (2005), 5815–5827.Google Scholar
[38]Fornberg, B., Anumerical studyof steady viscous flow past acircular cylinder, J. Fluid Mech., 98 (1980), 819–855.Google Scholar
[39]Li, Z. and Lai, M. C., The immersed interface method for the NavierStokes equations with singular forces, J. Comput. Phys., 171 (2001), 822–842.CrossRefGoogle Scholar