Physics-informed neural networks for rarefied-gas dynamics: Thermal creep flow in the Bhatnagar–Gross–Krook approximation

2021 ◽  
Vol 33 (4) ◽  
pp. 047110
Author(s):  
Mario De Florio ◽  
Enrico Schiassi ◽  
Barry D. Ganapol ◽  
Roberto Furfaro
Keyword(s):  
Neural Networks ◽  
Gas Dynamics ◽  
Rarefied Gas ◽  
Rarefied Gas Dynamics ◽  
Thermal Creep ◽  
Creep Flow ◽  
Thermal Creep Flow

Axisymmetric thermal-creep flow of a slightly rarefied gas induced around two unequal spheres

1984 ◽  
Vol 144 ◽  
pp. 103-121 ◽  
Author(s):  
Yoshimoto Onishi
Keyword(s):  
Reynolds Number ◽  
Temperature Gradient ◽  
Rarefied Gas ◽  
Low Reynolds Number ◽  
Thermal Creep ◽  
Creep Flow ◽  
Low Reynolds ◽  
Thermal Creep Flow ◽  
Slightly Rarefied Gas ◽  
Thermal Conductivities

A thermal-creep flow of a slightly rarefied gas induced axisymmetrically around two unequal spheres is studied on the basis of kinetic theory. The spheres, whose thermal conductivities are assumed to be identical with that of the gas, for simplicity, are placed in an infinite expanse of the gas at rest with a uniform temperature gradient at a far distance. Owing to the poor thermal conductivities of the spheres, a tangential temperature gradient is established on the surfaces, and this causes a thermal-creep flow in its direction. Consequently, the spheres experience forces in the opposite direction.The flow considered here is a low-Reynolds-number flow in the ordinary fluid-dynamic sense (except for the Knudsen layer), and the solution is obtained in terms of bispherical coordinates, with respect to which the system of equations of Stokes type is well developed. The velocity field around the spheres and the forces acting on them are given explicitly. The results show the interesting feature that the smaller sphere experiences the minimum force at a value of the separation distance that depends on the radius ratio. This is in contrast with the case of the axisymmetric motion of two spheres treated by Stimson & Jeffery (1926) in ordinary fluid dynamics at low Reynolds number.The ultimate velocities that the spheres would have under the action of the present thermal force when they are freely suspended are also obtained by utilizing the results for the forces of axisymmetric translational problems of two spheres at low Reynolds number. For a given temperature gradient in the gas, both spheres acquire larger velocities than those they would have if they were alone, and the smaller sphere tends to move faster than the larger one in the direction opposite to the temperature gradient.Also presented, for completeness, are the results for the sphere–plane case and for the case of eccentric spheres, the solutions for which are derived as special cases of the preceding problem of two unequal spheres.

THE CONTRIBUTION OF THE BHATNAGAR–GROSS–KROOK MODEL TO THE DEVELOPMENT OF RAREFIED GAS DYNAMICS IN THE EARLY YEARS OF THE SPACE AGE

2013 ◽  
Vol 25 (01) ◽  
pp. 1340025
Author(s):  
RODDAM NARASIMHA
Keyword(s):  
Boltzmann Equation ◽  
Gas Dynamics ◽  
Rarefied Gas ◽  
Rarefied Gas Dynamics ◽  
Early Years ◽  
Plane Shock ◽  
Bgk Model ◽  
The Boltzmann Equation ◽  
Nonequilibrium Flows ◽  
Space Age

The advent of the space age in 1957 was accompanied by a sudden surge of interest in rarefied gas dynamics (RGD). The well-known difficulties associated with solving the Boltzmann equation that governs RGD made progress slow but the Bhatnagar–Gross–Krook (BGK) model, proposed three years before Sputnik, turned out to have been an uncannily timely, attractive and fruitful option, both for gaining insights into the Boltzmann equation and for estimating various technologically useful flow parameters. This paper gives a view of how BGK contributed to the growth of RGD during the first decade of the space age. Early efforts intended to probe the limits of the BGK model showed that, in and near both the continuum Euler limit and the collisionless Knudsen limit, BGK could provide useful answers. Attempts were therefore made to tackle more ambitious nonlinear nonequilibrium problems. The most challenging of these was the structure of a plane shock wave. The first exact numerical solutions of the BGK equation for the shock appeared during 1962 to 1964, and yielded deep insights into the character of transitional nonequilibrium flows that had resisted all attempts at solution through the Boltzmann equation. In particular, a BGK weak shock was found to be amenable to an asymptotic analysis. The results highlighted the importance of accounting separately for fast-molecule dynamics, most strikingly manifested as tails in the distribution function, both in velocity and in physical space — tails are strange versions or combinations of collisionless and collision-generated flows. However, by the mid-1960s Monte-Carlo methods of solving the full Boltzmann equation were getting to be mature and reliable and interest in the BGK waned in the following years. Interestingly, it has seen a minor revival in recent years as a tool for developing more effective algorithms in continuum computational fluid dynamics, but the insights derived from the BGK for strongly nonequilibrium flows should be of lasting value.

Sign in / Sign up

Export Citation Format

Share Document