Reynolds Analogy Coefficient in the Longitudinal Cylindrical Couette Problem: from the Continuous Medium to Free Molecular Flow-Reference-Cited by-同舟云学术

Reynolds Analogy Coefficient in the Longitudinal Cylindrical Couette Problem: from the Continuous Medium to Free Molecular Flow

Published:2023-02-01 Issue:2 Volume:63 Page:317-326
ISSN:0044-4669
Container-title:Журнал вычислительной математики и математической физики
language:
Short-container-title:Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki

Author:

Abramov A. A.¹,Aleksandrov V. Yu.¹,Butkovskii A. V.¹

Affiliation:

1. Central Aerohydrodynamic Institute

Abstract

The gas Couette flow for a cylindrical geometry of bounding surfaces that move in the longitudinal direction relative to their symmetry axis is considered. For a monoatomic gas, the relation between the shear stress and the energy flux transferred to the longitudinal-flow surface (Reynolds analogy) is studied. In the case of continuous medium and free molecular flow regimes, simple explicit analytical expressions for the Reynolds analogy coefficient are obtained, which depend only on the Eckert number and are independent of the ratio of the cylinder radii. The transitional regime for various values of the Knudsen number is studied using the direct simulation Monte Carlo (DSMC) method. It is shown that, in this case, the Reynolds analogy coefficient at a fixed ratio of the radii and the Knudsen number depends on the relative velocity and temperatures of the surfaces mainly through the Eckert number. A relationship between the linear energy fluxes transferred to the cylindrical surfaces is found.

Publisher

The Russian Academy of Sciences

Reference17 articles.

1. Liepmann H.W., Roshko A. Elements of Gasdynamics. New York: Willey, 1957. Перевод Липман Г.В., Рожко А. Элементы газовой динамики. М.: Иностр. лит., 1960.

2. Illingworth C.R. Some solutions of the equations of flow of a viscous compressible fluid // Math. Proc. of the Cambridge Philosophical Society. 1950. V. 46. P. 469.

3. Perlmutter M. Analysis of Couette flow and heat transfer between parallel plates enclosing rarefied gas by Monte Carlo // Proc. of 5th Internat. Symposium on Rarefied Gas Dynamics, edited by C. L. Brundin. New York: -Academic Press, 1967. V. 1. P. 455.

4. Sharipov F., Kalempa D. Oscillatory Couette flow at arbitrary oscillation frequency over the whole range of the Knudsen number // Microfluid Nanofluid. 2008. V. 4. P. 363.

5. Roy S., Chakraborty S. Near-wall effects in micro scale Couette flow and heat transfer in the Maxwell-slip regimes // Microfluid and Nanofluid. 2007. V. 3. P. 437.