Alternative constitutive relation for momentum transport of extended Navier-Stokes equations

doi:10.1088/1674-1056/abb3e5

中国物理B ›› 2020, Vol. 29 ›› Issue (12): 124701-.doi: 10.1088/1674-1056/abb3e5

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

收稿日期:2020-05-01 修回日期:2020-06-28 接受日期:2020-09-01 出版日期:2020-12-01 发布日期:2020-11-19

Alternative constitutive relation for momentum transport of extended Navier-Stokes equations

Guo-Feng Han(韩国锋)¹, Xiao-Li Liu(刘晓丽)^2,†, Jin Huang(黄进)², Kumar Nawnit², and Liang Sun(孙亮)³

¹ Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China; ² State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China; ³ PetroChina Research Institute of Petroleum Exploration & Development, Beijing 100083, China

Received:2020-05-01 Revised:2020-06-28 Accepted:2020-09-01 Online:2020-12-01 Published:2020-11-19
Contact: ^†Corresponding author. E-mail: xiaoli.liu@tsinghua.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China-Outstanding Youth Foundation (Grant No. 51522903), the National Natural Science Foundation of China (Grant Nos. 11602276 and 51479094), and the Fund from the Key Laboratory for Mechanics in Fluid Solid Coupling Systems of the Chinese Academy of Sciences.

摘要/Abstract

Abstract: The classical Navier-Stokes equation (NSE) is the fundamental partial differential equation that describes the flow of fluids, but in certain cases, like high local density and temperature gradient, it is inconsistent with the experimental results. Some extended Navier-Stokes equations with diffusion terms taken into consideration have been proposed. However, a consensus conclusion on the specific expression of the additional diffusion term has not been reached in the academic circle. The models adopt the form of the generalized Newtonian constitutive relation by substituting the convection velocity with a new term, or by using some analogy. In this study, a new constitutive relation for momentum transport and a momentum balance equation are obtained based on the molecular kinetic theory. The new constitutive relation preserves the symmetry of the deviation stress, and the momentum balance equation satisfies Galilean invariance. The results show that for Poiseuille flow in a circular micro-tube, self-diffusion in micro-flow needs considering even if the local density gradient is very low.

Key words: extended Navier-Stokes equation, constitutive relation, momentum transport, mass diffusion

中图分类号: (Navier-Stokes equations)

47.10.ad

47.10.ab (Conservation laws and constitutive relations) 91.65.My (Fluid flow)

. [J]. 中国物理B, 2020, 29(12): 124701-.

Guo-Feng Han(韩国锋), Xiao-Li Liu(刘晓丽), Jin Huang(黄进), Kumar Nawnit, and Liang Sun(孙亮). Alternative constitutive relation for momentum transport of extended Navier-Stokes equations[J]. Chin. Phys. B, 2020, 29(12): 124701-.

参考文献

[1] Brenner H Physica A 349 11 DOI: 10.1016/j.physa.2004.10.0332005
[2] Brenner H Physica A 349 60 DOI: 10.1016/j.physa.2004.10.0342005
[3] Brenner H Physica A 370 190 DOI: 10.1016/j.physa.2006.03.0662006
[4] Brenner H Physica A 388 3391 DOI: 10.1016/j.physa.2009.04.0292009
[5] Brenner H Physica A 389 4026 DOI: 10.1016/j.physa.2010.06.0102010
[6] Brenner H Int. J. Eng. Sci. 54 67 DOI: 10.1016/j.ijengsci.2012.01.0062012
[7] Oettinger H C2005 Beyond Equilibrium Thermodynamics (New Jersey: Wiley and Sons) pp. 51-63
[8] Chakraborty S and Durst F Phys. Fluids 19 088104 DOI: 10.1063/1.27595312007
[9] Dadzie S K, Reese J M and McInnes C R Physica A 387 6079 DOI: 10.1016/j.physa.2008.07.0092008
[10] Dadzie S K and Reese J M Phys. Lett. A 376 967 DOI: 10.1016/j.physleta.2012.01.0042012
[11] Dadzie S K Phys. Lett. A 376 3223 DOI: 10.1016/j.physleta.2012.09.0512012
[12] Abramov R V Physica A 484 532 DOI: 10.1016/j.physa.2017.04.1492017
[13] Sambasivam R Extended Navier-Stokes equations: derivations and applications to fluid flow problems, Ph. D. Dissertation(Erlangen: University of Erlangen) pp. 18-38 https://opus4.kobv.de/opus4-fau/frontdoor/index/index/docId/3064.2013
[14] Kennard E H1938 Kinetic theory of gases: with an introduction to statistical mechanics (New York and London: McGraw-Hill Book Company) p. 140
[15] Reddy M H L, Dadzie S K, Ocone R, Borg M K and Reese J M J. Phys. Commun. 3 105009 DOI: 10.1088/2399-6528/ab4b862019
[16] Dadzie S K and Reese J M Phys. Rev. E 85 041202 DOI: 10.1103/PhysRevE.85.0412022012
[17] ttinger H C, Struchtrup H and Liu M Phys. Rev. E 80 056303 DOI: 10.1103/PhysRevE.80.0563032009
[18] Han G F, Liu X L, Huang J, Nawnit K and Sun L Phys. Fluids 32 022001 DOI: 10.1063/1.51395012020
[19] Chapman S and Cowling T G1970 The mathematical theory of non-uniform gases, 3rd edn. (Cambridge: Cambridge University Press) pp. 110-131
[20] Stamatiou A, Dadzie S K and Reddy M H L J. Phys. Commun. 3 125012 DOI: 10.1088/2399-6528/ab5f9e2019
[21] Greenshields C J and Reese J M J. Fluid Mech. 580 407 DOI: 10.1017/S00221120070055752007
[22] Lv Q, Liu X, Wang E and Wang S Phys. Rev. E 88 013007 DOI: 10.1103/PhysRevE.88.0130072013
[23] Lv Q, Wang E, Liu X and Wang S Microfluid Nanofluid 16 841 DOI: 10.1007/s10404-014-1332-z2014

Alternative constitutive relation for momentum transport of extended Navier-Stokes equations

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	. [J]. 中国物理B, 2021, 30(4): 44601-.
[2]	王成, 吴易烜, 黄金, 韩文虎, 宋清官. Effect of transversal concentration gradient on H₂-O₂ cellular detonation[J]. 中国物理B, 2020, 29(6): 60503-060503.
[3]	唐怡闻, 李志兵. Opto propeller effect on Micro-Rotors with different handedness[J]. 中国物理B, 2019, 28(8): 84702-084702.
[4]	赵书霞, 丰曌. Gas flow characteristics of argon inductively coupled plasma and advections of plasma species under incompressible and compressible flows[J]. 中国物理B, 2018, 27(12): 124701-124701.
[5]	Z. Asghar, N. Ali. Slip effects on streamline topologies and their bifurcations for peristaltic flows of a viscous fluid[J]. 中国物理B, 2014, 23(6): 64701-064701.
[6]	Sadegh Khalili, Saeed Dinarvand, Reza Hosseini, Hossein Tamim, Ioan Pop. Unsteady MHD flow and heat transfer near stagnation point over a stretching/shrinking sheet in porous medium filled with a nanofluid[J]. 中国物理B, 2014, 23(4): 48203-048203.
[7]	Imtiaz Ahmad, 卢志明, 刘宇陆. Longitudinal and transverse structure functions in decaying nearly homogeneous and isotropic turbulence[J]. Chin. Phys. B, 2014, 23(1): 14701-014701.
[8]	Ahmed M. Megahed. Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity[J]. 中国物理B, 2013, 22(9): 94701-094701.
[9]	冉政, 许宇鹏. Entropy and weak solutions in the lattice Bhatnagar–Gross–Krook model[J]. 中国物理B, 2011, 20(11): 114702-114702.
[10]	汪小卫, 蔡国飙, 金平. Scaling of the flow field in a combustion chamber with agas--gas injector[J]. 中国物理B, 2010, 19(1): 19401-019401.
[11]	燕秀林, 冉政. Single point velocity distributions in homogeneous isotropic turbulence[J]. 中国物理B, 2009, 18(10): 4360-4365.
[12]	冉政. Thermal equation of state for lattice Boltzmann gases[J]. 中国物理B, 2009, 18(6): 2159-2167.
[13]	姜洪源, 任玉坤, 敖宏瑞, AntonioRamos. Electrohydromechanical analysis based on conductivity gradient in microchannel[J]. 中国物理B, 2008, 17(12): 4541-4546.
[14]	周军, 蔡力, 周凤岐. A hybrid scheme for computing incompressible two-phase flows[J]. 中国物理B, 2008, 17(5): 1535-1544.
[15]	邹立勇, 柏劲松, 李步阳, 谭多望, 李平, 刘仓理. Vertical rotation effect on turbulence characteristics in an open channel flow[J]. 中国物理B, 2008, 17(3): 1034-1040.