Simulation of conjugate heat transfer in the microchannel system by means of the hybrid method

S. A. Filimonov ; A. A. Dekterev ; A. V. Sentyabov ; A. V. Minakov

Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 3, pp. 86-97.

Résumé

A hybrid method of calculation of fluid dynamics and heat transfer in complex hydraulic systems is proposed. The method is based on both hydraulic network models and CFD models. Validation of the hybrid method was performed by calculations of the fluid dynamics and heat transfer in microchannels. Test calculations have showed high computational efficiency of the method.

Détail

Keywords: numerical modeling, hydraulic network models, hybrid method, conjugate heat transfer.
Mots-clés : CFD, microchannels

Bibliographie

[1] Merenkov A. P., Khasilev V. Ya., Teoriya gidravlicheskikh tsepei, Nauka, M., 1985

[2] Novitskii N. N., Sennova E. V., Sukharev M. G. i dr., Gidravlicheskie tsepi. Razvitie teorii i prilozheniya, Nauka, Novosibirsk, 2000

[3] Twigt D. J., De Goede E. D., Zijl F., Schwanenberg D., Chiu A. Y. W., “Coupled 1D-3D hydrodynamic modelling, with application to the Pearl River Delta”, Ocean Dynamics, 59 (2009), 1077–1093 | DOI

[4] Zhang W., Lyu S., Zhu Yu., Chen X., “A coupled model of the 1D river network and 3D estuary based on hydrodynamics and suspended sediment simulatio”, J. Appl. Math., 2014 (2014), ID 798579, 13 pp. | DOI

[5] D'Angelo C., Quarteroni A., On the coupling of 1D and 3D diffusion-reaction equations. Applications to tissue perfusion problems, MOX-Report No. 28/2008

[6] Fernandez-Nietoa E. D., Marinb J., Monnierc J., “Coupling superposed 1D and 2D shallowwater models: Source terms in finite volume schemes”, Computers Fluids, 39 (2010), 1070–1082 | DOI | MR

[7] Formaggia L., Nobile F., Quarteroni A., Veneziani A., “Multiscale modelling of the circulatory system: a preliminary analysis”, Computing and Visualization in Sci., 2:2–3 (1999), 75–83 | DOI | Zbl

[8] Harvey H. et al., “A hybrid 1D and 3D approach to hemo dynamics modelling for a patientspecific cerebral vasculature and aneurysm”, Lecture Notes in Computer Science, 5762, 2009, 323–330 | DOI

[9] Astrakhantseva E. V., Gidaspov V. Yu., Reviznikov D. L., “Matematicheskoe modelirovanie gemodinamiki krupnykh krovenosnykh sosudov”, Mat. modelirovanie, 17:8 (2005), 61–80 | Zbl

[10] Voevodin A. F., Nikiforovskaya V. S., “Chislennoe modelirovanie neustanovivshikhsya gidrotermicheskikh protsessov v vodnykh ob'ektakh”, Mezhdunar. konf. “Sovremennye prolemy prikladnoi matematiki i mekhaniki: teoriya, eksperiment i praktika”, posvyasch. 90-letiyu so dnya rozhdeniya akad. N. N. Yanenko, Novosibirsk, 2011, 16

[11] Dobroserdova T. K., Chislennoe modelirovanie krovotoka pri nalichii sosudistykh implantatov ili patologii, Dis. $\dots$ kand. fiz.-mat. nauk, M., 2013

[12] Alastruey J., Parker K. H., Peirò J., Sherwin S. J., “Lumped parameter outflow models for 1D blood flow simulations: Effect on pulse waves and parameter estimation”, Comm. Computat. Phy., 4:2 (2008), 317–336 | MR

[13] Fadeev S. I., Kostsov E. G., Pimanov D. O., “Chislennoe issledovanie matematicheskikh modelei mikroelektromekhanicheskikh rezonatorov raznogo tipa”, Sib. zhurn. industr. matematiki, 17:4 (2014), 120–135

[14] Rudyak V. Ya., Minakov A. V., Gavrilov A. A., Dekterev A. A., “Application of new numerical algorithm for solving the Navier–Stokes equations for modelling the work of a viscometer of the physical pendulum type”, Thermophysics and Aeromechanics, 15 (2008), 333–345 | DOI

[15] Rudyak V. Ya., Minakov A. V., Gavrilov A. A., Dekterev A. A., “Modelling of flows in micromixers”, Thermophysics and Aeromechanics, 17 (2010), 565–576 | DOI

[16] Rudyak V. Ya., Minakov A. V., Gavrilov A. A., Dekterev A. A., “Mixing in a T-shaped micromixer at moderate Reynolds numbers”, Thermophysics and Aeromechanics, 19 (2012), 385–395 | DOI

[17] Minakov A., Rudyak V., Dekterev A., Gavrilov A., “Investigation of slip boundary conditions in the T-shaped microchannel”, Internat. J. Heat and Fluid Flow, 43 (2013), 161–169 | DOI

[18] Gavrilov A. A., Minakov A. V., Dekterev A. A., Rudyak V. Ya., “Chislennyi algoritm dlya modelirovaniya laminarnykh techenii v koltsevom kanale s ekstsentrisitetom”, Sib. zhurn. industr. matematiki, 13:4 (2010), 3–14 | MR | Zbl

[19] Minakov A. V., “Chislennyi algoritm resheniya zadach gidrodinamiki c podvizhnymi granitsami i ego testirovanie”, Zhurn. vychisl. matematiki i mat. fiziki, 54:10 (2014), 1618–1629 | DOI | MR

[20] Dekterev A. A., Gavrilov A. A., Minakov A. V., “Sovremennye vozmozhnosti SFD koda SigmaFlow dlya resheniya teplofizicheskikh zadach”, Sovremennaya nauka: issledovaniya, idei, rezultaty, tekhnologii, 4:2 (2010), 117–122

[21] Gavrilov A. A., Minakov A. V., Dekterev A. A, Rudyak V. Ya., “Chislennyi algoritm dlya modelirovaniya laminarnykh techenii v koltsevom kanale s ekstsentrisitetom”, Sib. zhurn. industr. matematiki, 13:4 (2010), 3–14 | MR | Zbl

[22] Novitskii N. N., Sukharev M. G., Sardanashvili S. A. i dr., “Gibridnyi podkhod dlya resheniya zadach TGTs, soderzhaschikh prostranstvennye elementy”, Truboprovodnye sistemy energetiki: matematicheskoe i kompyuternoe modelirovanie, ISEM SO RAN, Irkutsk, 2014, 46–55

[23] Filimonov S. A., Dekterev A. A., Boikov D. V., “Chislennoe modelirovanie kozhukhotrubchatogo teploobmennika s pomoschyu gibridnogo algoritma”, Teplovye protsessy v tekhnike, 6:8 (2014), 343–348

[24] Patankar C., Chislennye metody resheniya zadach teploobmena i dinamiki zhidkosti, Energoatomizdat, M., 1984

[25] Wang X.-Q., Mujumdar A. S., Yap C., “Thermal characteristics of tree-shaped microchannel nets for cooling of a rectangular heat sink”, Intern. J. Thermal Sci., 45 (2006), 1103–1112 | DOI

[26] Khandekar S., Agarwal G., Moharana M. K., “Thermo-hydrodynamics of developing flow in a rectangular mini-channel array”, Proc. 20 National and 9 International ISHMT–ASME Heat and Mass Transfer Conf., Bombay, 2010, 1342–1349

[27] Lobasov A. S., Minakov A. V., Dekterev A. A., “Modelirovanie gidrodinamiki i konvektivnogo teploobmena v mikrokanalakh”, Vychisl. mekhanika sploshnykh sred, 5:4 (2012), 481–488