Felix Sharipov

Data on Internal Rarefied Gas Flows

The present review, containing 178 references, is dedicated to one of the largest and most important branches of the rarefied gas dynamics, namely internal flows. A critical analysis of the corresponding numerical data and analytical results available in the literature was made. The most reliable data were selected and tabulated. The review will be useful as a reference for mathematicians, physicists and aerodynamicists interested in rarefied gas flows. In this paper the complete ranges of the main parameters, determining rarefied gas flows through a capillary, are covered. The capillary length varies from zero, when the capillary degenerates into a thin orifice, to infinity when the end effects can be neglected. The Knudsen number, characterizing the gas rarefaction, varies from zero when the gas is considered as a continuous medium to infinity when the intermolecular collisions can be discounted. The pressure and temperature drops on the capillary ends vary from the small values when the linear theory i...

Rarefied gas flow through a long rectangular channel

The mass flow rate of a rarefied gas through a long channel with a rectangular cross section has been calculated based on the model kinetic equation for the whole range of the Knudsen number and in the wide range of the height-to-width ratio. First, the reduced flow rate through a cross section has been calculated as a function of the local rarefaction parameter assuming the pressure gradient to be small. A criterion of the lateral wall influence on the flow rate has been given. Then, the mass flow rate has been calculated as a function of the rarefaction parameters on the channel ends. The last result is obtained for any pressure ratio even if the flow varies along the channel from the hydrodynamic regime to the free molecular one.

Application of the Cercignani–Lampis scattering kernel to calculations of rarefied gas flows. II. Slip and jump coefficients

Abstract The Cercignani–Lampis scattering kernel of the gas–surface interaction is applied to numerical calculations of the viscous slip coefficient, the thermal slip coefficient and the temperature jump coefficient. The S model of the Boltzmann equation is numerically solved by the discrete velocity method. The calculations have been carried out in the wide ranges of the accommodation coefficients of momentum and energy. Comparing the present results with experimental data on the viscous slip coefficient the values of the accommodation coefficients are calculated for some gases and glass surface.

Data on the Velocity Slip and Temperature Jump on a Gas-Solid Interface

The present review is dedicated to the velocity slip and temperature jump coefficients applied to modeling of gas flows. Such coefficients are used when a moderate gas rarefaction must be taken into account. In this case, calculations of gas flows can be performed on the basis of continuum mechanics equations applying the velocity slip and temperature jump boundary conditions. Thus, the velocity slip and temperature jump coefficients have the same importance in gas dynamics as the transport coefficients such as viscosity, thermal conductivity, and diffusion coefficients. A critical analysis of theoretical and experimental data on the slip and jump coefficients available in the open literature is presented in an accessible form so that it can be easily understandable for nonspecialists in rarefied gas dynamics. The most reliable results are selected and tabulated. The results cover a single gas with the complete and noncomplete accommodation on a solid surface, gaseous mixtures, and polyatomic gases. Many ...

Non-isothermal gas flow through rectangular microchannels

The mass flow rate of a rarefied gas through a long rectangular channel caused by both pressure and temperature differences was calculated applying the S-model kinetic equation. The calculations have been carried out over wide ranges of the four parameters that determine the solution of the problem: the gas rarefaction, the height-to-width ratio of the channel, the pressure ratio on the channel ends and the analogous temperature ratio. First, the Poiseuille flow and the thermal creep were calculated, separately, as functions of the local rarefaction parameter, assuming the pressure and the temperature gradients to be small. The lateral-wall influence on the flow rates was analyzed. The total mass flow rate for the temperature ratio equal to 3.8 and for two values of the pressure ratio (1 and 100) was calculated. The corresponding numerical program is available at the site: fisica.ufpr.br/sharipov.

Velocity slip and temperature jump coefficients for gaseous mixtures. I. Viscous slip coefficient

The viscous slip coefficient was calculated for binary gaseous mixtures on the basis of the McCormack kinetic model of the Boltzmann equation, which was solved by the discrete velocity method. The calculations were carried out for the three mixtures of noble gases: neon–argon, helium–argon, and helium–xenon. It was showed that for the mixture of helium and xenon, which has a large ration of the molecular masses, the slip coefficient significantly differs from that for a single gas. A comparison of the present results with those obtained by the moment method applied to the Boltzmann equation showed that the McCormack model equation provides reliable results with modest computational efforts. An example of application of the viscous slip coefficient was given.

Rarefied gas flow through a long tube at any temperature ratio

The mass flow rate of a rarefied gas through a long capillary caused by small pressure and temperature gradients has been calculated based on the s‐model for the diffuse specular gas‐surface interaction in the range of the rarefaction parameter from 0.005 to 50. A simple method of calculation of the thermomolecular pressure effect and the thermal creep caused by a large temperature ratio have been elaborated. Numerical calculations of both phenomena for the temperature ratio T2/T1=3.8—usually realized in experiments—have been carried out. It has been determined that the nonlinear thermomolecular pressure effect does not depend on the temperature distribution along the capillary. The nonlinear thermal creep has been calculated for two different temperature distributions along the capillary. A dependence of the creep on the temperature distribution has been found. It has been shown that the application of the linear theory based on the average rarefaction parameter to the gas flow at a large temperature rat...

Rarefied gas flow through short tubes into vacuum

A rarefied gas flow into vacuum through a tube of finite length is investigated over the whole range of gas rarefaction by the direct simulation Monte Carlo method. The nonequilibrium effects at the inlet and outlet of the tube have been considered by including in the computational domain large volumes of the upstream and downstream reservoirs. Results for the dimensionless flow rate and for the flow field are presented for a wide range of the gas rarefaction and for various values of the length to radius ratio in the range from 0 to 10. The influence of the gas-surface interaction model, as well as the effect of the intermolecular potential model on the gas flow, is examined. A good agreement has been obtained between the present numerical results and the corresponding experimental ones available in the literature.A rarefied gas flow into vacuum through a tube of finite length is investigated over the whole range of gas rarefaction by the direct simulation Monte Carlo method. The nonequilibrium effects at the inlet and outlet of the tube have been considered by including in the computational domain large volumes of the upstream and downstream reservoirs. Results for the dimensionless flow rate and for the flow field are presented for a wide range of the gas rarefaction and for various values of the length to radius ratio in the range from 0 to 10. The influence of the gas-surface interaction model, as well as the effect of the intermolecular potential model on the gas flow, is examined. A good agreement has been obtained between the present numerical results and the corresponding experimental ones available in the literature.

Gaseous mixture flow through a long tube at arbitrary Knudsen numbers

The mass flow, heat flux, and diffusion flux of rarefied gas mixture through a tube caused by gradients of pressure, temperature, and concentration were calculated over a wide range of the Knudsen number on the basis of the kinetic equation. The thermodynamic fluxes are presented in the form that allows us to prove the Onsager relations and then to reduce the number of kinetic coefficients determining the solution down to six. The numerical values of the kinetic coefficients are tabulated and the velocity profiles are given in figures.

Application of the Cercignani-Lampis scattering kernel to calculations of rarefied gas flows. I. Plane flow between two parallel plates

Abstract The Cercignani–Lampis scattering kernel of the gas-surface interaction was applied to numerical calculations of the plane Poiseuille flow, thermal creep, mechanocaloric flux and heat flux. The S model of the Boltzmann equation was numerically solved by the discrete velocity method. The calculations have been carried out in wide ranges of the rarefaction parameter and of the accommodation coefficients of momentum and energy. Comparing the present results with experimental data the value of the accommodation coefficients can be calculated.