The concept of a quasi-micropolar fluid model

Szubartowski, D.; Ganczarski, A.

Artykuł - szczegóły

Tytuł artykułu

The concept of a quasi-micropolar fluid model

Autorzy

Szubartowski D. , Ganczarski A.

Wybrane pełne teksty z tego czasopisma

http://repozytorium.biblos.pk.edu.pl/resources/35439

Identyfikatory

Warianty tytułu

Quasi-mikropolarny model cieczy

Języki publikacji

Abstrakty

This paper presents a micropolar fluid model that direct applies Cosserat’s continuum to hydrodynamics. The corresponding system of equations describing isotropic micropolar fluid is obtained by assuming lack of symmetry of the Cauchy stress tensor and taking into account the conservation of angular momentum. This turns out to be an extension of the NavierStokes fluid but containing turbulent effect built in.

W artykule przedstawiono mikropolarny model cieczy stanowiący bezpośrednie zastosowanie kontinuum Cosseratów w hydromechanice. Zakładając brak symetrii tensora naprężenia Cauchy’ego oraz uwzględniając zasadę zachowania momentu pędu otrzymano układ równań opisujący izotropową ciecz mikropolarną. Układ równań jest uogólnieniem równań NavieraStokesa poprzez uwzględnienie efektu turbulentnego.

Słowa kluczowe

micropolar fluid turbulent effect

ciecz mikropolarna efekt turbulentny

Wydawca

Wydawnictwo Politechniki Krakowskiej im. Tadeusza Kościuszki

Czasopismo

Czasopismo Techniczne. Mechanika

Rocznik

2016

Tom

Y. 113, iss. 1-M

Strony

224--230

Opis fizyczny

Bibliogr. 47 poz., wz., wykr.

Twórcy

autor

Szubartowski D.

Institute of Applied Mechanics, Faculty of Mechanical Engineering, Cracow University of Technology

autor

Ganczarski A.

Institute of Applied Mechanics, Faculty of Mechanical Engineering, Cracow University of Technology

Bibliografia

[1] Altenbach H., Eremeyev V.A., Generalized Continua – from the Theory to Engineering Applications, CISM Int. Centre for Mech. Sci. 541, 2013.
[2] Areo E.L., Bulygin A.N., Kuvshinskii E.V., Asymmetric hydromechanics, J. Appl. Math. Mech., 29(2), 1965, 333-346.
[3] Areo E.L., Kuvshinskii E.V., Continuum theory of asymmetric elasticity. Equilibrium of an isotropic body (in Russian), Fizika Tverdogo Tela, 6, 1964, 2689-2699.
[4] Areo E.L., Kuvshinskii E.V., Fundamental equations of the theory of elastic media with rotationally interacting particles, Sov. Phys. Solid State, 2(7), 1961, 1272-1281.
[5] Besdo D., Ein Beitrag zur nichtlinearen Theorie des Cosserat-Kontinuums, Acta Mechanica, 20(1-2), 1974, 105-131.
[6] Bogy D.B., Sternberg E., The effect of couple-stresses on the corner singularity due to an asymmetric shear loading, Int. J. solid Structures, 4(2), 1968.
[7] Cosserat E., Cosserat F., Sur la théorie de l’elasticité, Ann. Toulouse, 10, 1896, 1-116.
[8] Cosserat E., Cosserat F., Théorie des corps déformables, Hermann, Paris 1909.
[9] Eremeyev V.A., Zubov L.M., Principles of Viscoelastic Micropolar Fluid Mechanics (in Russian), SSC of RASci Publishers, Rostov on Don 2009.
[10] Eremeyev V.A., Zubov L.M., The theory of elastic and viscoelastic micropolar liquids, J. Appl. Math. Mech., 63(5), 1999, 755-767.
[11] Eringen A.C., A unified continuum theory of electrodynamics of liquid crystals, Int. J. Eng. Sci., 35(12-13), 1997, 1137-1157.
[12] Eringen A.C., A unified continuum theory of electrodynamics of polymeric liquid crystals, Int. J. Eng. Sci., 38(9-10), 2000, 959-987.
[13] Eringen A.C., A unified continuum theory of liquid crystals, ARI Int. J. Phys. Eng. Sci., 73-84(2), 1997, 369-374.
[14] Eringen A.C., Kafadar C.B., Polar field theories, in Continuum Physics, vol. IV, ed. Eringen A.C., Academic Press, New York, 1-75, 1976.
[15] Eringen A.C., Linear theory of micropolar elasticity, J. Math. Mech., 15(6), 1966, 909-923.
[16] Eringen A.C., Linear theory of micropolar viscoelasticity, Int. J. Eng. Sci., 5(2), 1967, 191-204.
[17] Eringen A.C., Theory of micropolar fluids, J. Math. Mech., 16(1), 1966, 1-18.
[18] Green A.E., Rivlin R.S., Multipolar continuum mechanics, Arch. Ration. Mech. Anal., 17(2), 1964, 113-147.
[19] Grioli G., Contributo per una formulazione di tipo integrale della meccanica dei continui di Cosserat, Annali di Matematica Pura ed Applicata, 111(1), 1976, 389-417.
[20] Grioli G., Elasticita asimmetria, Annali di Matematica Pura ed Applicata, 50(1), 1960, 389-417.
[21] Günther W., Zur Statik und Kinematik des Cosseratschen Kontinuums, Abhandlungen der Braunschweigschen Wissenschaftlischen Gesellschaft, Göttingen, 10, 1958, 196-213.
[22] Hammel G., Elementare Mechanik, Leipzig, Berlin 1912.
[23] Ieşan D., On the linear theory of micropolar elasticity, Int. J. Eng. Sci., 7(12), 1969, 1213-1220.
[24] Kafadar C.B., Eringen A.C., Micropolar media – I. The classical theory, Int. J. Eng. Sci., 9(3), 1964, 271-305.
[25] Koiter W.T., Couple-stresses in the theory of elasticity, Pt I-II, Proc. Koninkl. Neterland. Akad. Wetensh., B67, 1964, 17-44.
[26] Łukaszewicz G., MicropolarFluids: Theory and Applications, Birkhäuser, Basel 1999.
[27] Migoun N.P., Prokhorenko P.P., Hydrodynamics and Heat Transfer in Gradient Flows of Microstructured Fluids (in Russian), Nauka i Technika, Minsk 1984.
[28] Mindlin R.D., Tiersten H.F., Effects of couple-stresses in linear elasticity, Arch. Ration. Mech. Anal., 11, 1962, 415-448.
[29] Muki R., Sternberg E., The influence of couple-stresses on singular stress concentrations in elastic solids, ZAMP, 16(5), 1965.
[30] Nowacki W., Theory of non-symmetric elasticity, IPPT PAN, PWN, Warsaw 1981.
[31] Ostoja-Starzewski M., Second law violations, continuum mechanics, and permeability, Continuum Mech. Thermodyn. DOI 10.1007/s00161-015-0451-4, 2015.
[32] Pal’mov V.A., Fundamental equations of the theory of asymmetric elasticity, J. Appl. Mech. Math., 28(3), 1964, 496-505.
[33] Reissner E., A further note on the equations of finite-strain force and moment stress elasticity. ZAMP, 38, 1987, 665-673.
[34] Reissner E., Note on the equations of finite-strain force and moment stress elasticity, Stud. Appl. Math., 54, 1975, 1-8.
[35] Reissner E., On kinematics and statics of finite-strain force and moment stress elasticity, Stud. Appl. Math., 52, 1973, 93-101.
[36] Resensweig R.E., Magnetic fluids, Ann. Rev. Fluid Mech., 19, 1987, 437-461.
[37] Sawin G.N., Stress distributions around holes (in Russian), Naukova Dumka, Kiev 1968.
[38] Schaefer H., Das Cosserat-Kontinuum, ZAMM, 47(8), 1967, 485-498.
[39] Stojanovic R., Mechanics of Polar Continua: Theory and Applications, CISM Courses and Lectures, vol. 2, Springer Wien 1969.
[40] Stojanovic R., Nonlinear micropolar elasticity, in Micropolar Elasticity, vol. 151, ed. Nowacki W. and Olszak W., Springer Wien, 1974, 73-103.
[41] Stojanovic R., Recent Developments in the Theory of Polar Continua, CISM Courses and Lectures, vol. 27, Springer Wien 1969.
[42] Toupin R.A., Elastic materials with couple-stress, Arch. Ratin. Mech. Anal., 11, 1962, 385-414.
[43] Toupin R.A., Theories of elasticity with couple-stress, Arch. Ration. Mech. Anal., 17, 1964, 85-112.
[44] Truesdell C., Noll W., The nonlinear field theories of mechanics, in Handbook der Physik, vol. III/3, ed. Flügge S., Springer, Berlin 1987.
[45] Truesdell C., Toupin R., The classical field theories, in Handbook der Physik, vol. III/1, ed. Flügge S., Springer, Berlin 1960.
[46] Voigt W., Theoretishe Studien über die Elastizitätsverhältnisse der Kristalle, Abh. Ges. Wiss. Göttingen, Bd. 34, 1887.
[47] Zubov L.M., Eremeyev V.A., Equations of elastic and viscoelastic micropolar fluid, Doklady Phys., 14(2), 1996, 598-601.

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Bibliografia

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