| ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS |
Prev
Next
|
|
|
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 |
|
|
|
|
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.
|
Received: 01 May 2020
Revised: 28 June 2020
Accepted manuscript online: 01 September 2020
|
|
PACS:
|
47.10.ad
|
(Navier-Stokes equations)
|
| |
47.10.ab
|
(Conservation laws and constitutive relations)
|
| |
91.65.My
|
(Fluid flow)
|
|
| Fund: 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. |
|
Corresponding Authors:
†Corresponding author. E-mail: xiaoli.liu@tsinghua.edu.cn
|
Cite this article:
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 2020 Chin. Phys. B 29 124701
|
[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 |
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
