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Similarity of ideal gas flow at different scales

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Abstract

The similarity of ideal gas flow at different scales is investigated analytically and numerically. With the compressible and rarefied effects considered, two dimensionless parameters, Mach number and Knudsen number, are proposed as the similarity criterions, because the Reynolds number can be expressed by the Mach number and the Knudsen number of ideal gases. A DSMC method is used to simulate flows at different scales with the same Ma and Kn, including subsonic channel flows and the supersonic flows over a hot plate. Comparisons between the results of different scales show that the normalized fields of macroscopic quantities are the same. This confirms the similarity. Especially, the results indicate that the micro flow are similar to the rarefied flow of ideal gas, which suggests that many transformations are available from the existing rarefied flow results to the micro flow.

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Abbreviations

a :

sound speed

P :

pressure

c m :

most probable molecular speed

Re :

Reynolds number

d :

molecular diameter

T :

overall temperature

H :

height of the computer domain

T g :

gas temperature on wall surfaces

k :

Boltamann constant

Kn :

Knudsen number

T u :

translational temperature

Kn local :

local Knudsen number

T rot :

rotational temperature

L :

characteristic

length:

length of the computed domain

T ∞ :

treestream temperature

m :

molecular mass

T w :

wall temperature of cylinder

Ma :

Mach number

\(\bar v_m \) :

molecular mean velocity

n :

number density

v :

molecular velocity

γ:

specific heat rate

μ:

dynamic viscosity

λ:

mean free path

ν:

kinetic viscosity

ρ:

density

ɛrot :

rotational energy

ζ:

number of internal degree of freedom

σT :

total collision cross-section

Δt :

time step

ɛtr :

translational energy

Δx :

size of a cell

∞:

freestream

tr:

translational mole

w:

wall surfaces

rot:

rotational mode

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Authors and Affiliations

  1. Department of Engineering Mechanics, Tsinghua University, 100084, Beijing, China

    Wang Moran & Li Zhixin

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  1. Wang Moran
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  2. Li Zhixin
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Correspondence to Wang Moran.

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Wang, M., Li, Z. Similarity of ideal gas flow at different scales. Sci. China Ser. E-Technol. Sci. 46, 661–670 (2003). https://doi.org/10.1360/02ye0072

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