Solution of the Boltzmann Equations for Strong Shock Waves by the Two-Fluid Model

Journal Article · Sun Apr 01 04:00:00 EST 1962 · Physics of Fluids (U.S.)

DOI:https://doi.org/10.1063/1.1706628· OSTI ID:4790438

Glansdorff, P

The structure of a plane shock wave is studied by an extension to the gas dynamics of the two-fluid model already introduced in the superfluidity theory. The classical form is used for the linearization of two Boltzmann equations, and restricted to the first approximation. This is different from Mott-Smith's solutions which cannot be derived by linearization from a single Boltzmann equation, and as a result has to be introduced arbitrarily. Six equations of change for conservative quantities (mass, momentum, energy) are obtained which makes possible the solution of the wave problem without having to introduce other equations of change. Calculations are made using the elastic-sphere model. Comparison with observations made on argon gives very satisfactory results. The solutions tend asymptotically to a stationary solution corresponding to a Mach number equal to infinity, and to a shock wave thickness 11.4 times the mean free path ahead of the shock for all monatomic gases. This establishes the possibility of coexistence of two fluids in nonequilibrium, even thermal, in shock waves with large gradients.

• Research Organization: Universite Libre, Brussels
• Sponsoring Organization: USDOE
• NSA Number: NSA-16-016852
• OSTI ID: 4790438
• Journal Information: Physics of Fluids (U.S.), Journal Name: Physics of Fluids (U.S.) Vol. Vol: 5; ISSN PFLDA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ARGON
ATOMS
BOLTZMANN EQUATION
CRYOGENICS
DIFFERENTIAL EQUATIONS
DIFFUSION LENGTH
ENERGY
FLUIDS
GASES
MASS
MATHEMATICS
MEAN FREE PATH
MOCKUP
MOMENTUM
PHYSICS
PRESSURE
SHOCK WAVES
SPHERES
SUPERFLUIDITY
THERMODYNAMICS
THICKNESS
VELOCITY
VISCOSITY