Numerical solution of the variational Rayleigh problem of gas lubrication theory

The three-dimensional variational problem of the optimization of the microgeometry of a gas-lubricated bearing with respect to the maximum lift criterion is considered. The pressure field in the gas film is determined using the Dirichlet boundary-value problem for the gas lubrication Reynolds equation. The results of the numerical solution of the variational problem based on the consideration of the first variation of a functional are presented. The calculation results are presented for a wide range of the problem parameters.St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 31–38, November–December, 1995.     

Numerical solution of axisymmetric multi-species compressible gas flow: towards improved circuit breaker simulation

Nozzle wall ablation caused by high-temperature electrical arcs is studied in the context of high voltage SF₆ circuit breakers. The gases generated by the ablation mix with insulating gas, thereby modifying the thermodynamics and chemistry of the problem. To simulate these phenomena, an axisymmetric Euler equations model for multi-species flow at local thermodynamic equilibrium has been developed. The governing equations are solved using a finite-volume method based on Roe's flux-splitting scheme and a new procedure is proposed to obtain the mean values used in Roe's matrix involving multi-species. The change in the gas composition due to dissociation, ionisation and recombinations are taken into account by a dynamic coupling to a thermodynamic database. The formulation is appropriate for general equations of state. The scheme has been verified by comparisons with the analytical solution of a classic shock-tube problem. An experimental validation is presented involving the simulation of shock interactions with helium cylinders and bubbles in air. The scheme is also compared to experimental ablation results, as well as a previous version of the code. The model is then applied to a well controlled experimental arrangement with an arc inside a small Teflon^® tube. Finally, a simulation with a model circuit breaker completes the study.     

Numerical solution of two-dimensional problem of gas flow from a chamber with flat walls

A study is made of the classical problem of steady flow of ideal gas from an infinite two-dimensional chamber with straight wall generator making angle _w with the symmetry plane of the flow. Specification of _w, the pressure ratio _a-P_a/P_o (P_o is the stagnation pressure of the gas in the chamber, P is the pressure in the ambient medium), and the specific-heat ratio completely determines the flow of gas from the chamber.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 177–181, July–August, 1988.I thank A. N. Kraiko for his interest in the work and helpful discussions of the results.     

Numerical solution of one problem in the spherical-radial filtration of a gas

The article discusses the solution of the problem of the influx of gas into the closed cylinder of a stratum probe on a well-logged cable, for a centrally symmetrical model of the filtration flow. The solution is obtained by the method of finite differences.     

Numerical analysis of axisymmetric and planar sudden expansion flows for laminar regime

In this study, the Navier–Stokes equations are solved numerically for axisymmetric and planar sudden expansion flows. The flow is considered laminar and steady state, and the fluid is incompressible. Finite difference equations are obtained using a control volume method in a non‐staggered grid arrangement, and solved by line‐by‐line TDMA technique using the SIMPLEM (SIMPLEM‐Modified) algorithm. Calculations are performed for higher expansion ratios, β, ranging from 1.5 to 10 and Reynolds numbers from 0.1 to 500. Results are presented in terms of streamlines, relative eddy intensity, location of the eddy center, and the eddy reattachment length depending on Re number and β values for both axisymmetric and planar sudden expansions. It is aimed to provide a picture of the effects of high values of expansion ratio and Reynolds number on the sudden expansion flow. As a result, it is found that the flow characteristics keep their structure for both higher expansion ratios and higher Reynolds numbers. Further, correlations were developed for the nondimensional eddy reattachment length, location of the eddy center and the relative eddy intensity, which have agreeable results to the computed results available from the literature. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical solution of axisymmetric cavity flows using the boundary element method

This paper presents a formulation of the boundary element method (BEM) for solution of axisymmetric cavity flow problems. The governing equation is written in terms of Stokes' stream function, requiring a new fundamental solution to be found. The iterative procedure for adjusting the free-surface position is similar to that used for planar cavity flows. Numerical results are compared with finite difference and finite element solutions, showing the robustness of the BEM model.     

Numerical investigation of “lateral” interaction with an obstacle of an axisymmetric jet exhausting into vacuum

The problem of the interaction of a strongly underexpanded axisymmetric jet with an obstacle for which the normal to the surface makes an angle near /2 with the jet axis is rather laborious for numerical solution due to the high disequilibrium of the gas-dynamic parameters in the peripheral part of the jet and the three-dimensional nature of the flow in the interaction region. Therefore, the results at present available have mainly been obtained experimentally [1, 2]. Among the theoretical studies made in this direction, it is necessary to mention Ivanov and Nazarov's [3], which gives the results of numerical investigation of lateral interaction of a jet with obstacles of various shapes in the case of weakly underexpanded jets when the flow in the interaction region is everywhere supersonic. In the present paper, a study is made of the case when a jet exhausts into vacuum and in front of the obstacle there is a detached shock wave, behind which there is mixed subsonic and supersonic three-dimensional flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 49–54, November–December, 1982.We thank V. I. Uskov for assistance in the present work.     

An elasticity solution for axisymmetric problem of finite circular cylinder

In this paper,the complete double-series in the closed region expressing the double-variable functions and their partial derivatives are derived by the H-transformation and Stockes’transformation.Using the double-series,a series solution for the axisymmetric boundary value problem of the elastic circular cylinder with finite length is presented.In a numerical example,the cylinder subjected to the axisymmetric tra(?)s with various loaded regions is investigated and the distributions of the displacements and stresses are obtained.It is possible to solve the axisymmetric boundary value problems in the cylinderical coordinates for other scientific fields by use of the method presented in this paper.     

A general solution and the application of space axisymmetric problem in piezoelectric material

ＡＧＥＮＥＲＡＬＳＯＬＵＴＩＯＮＡＮＤＴＨＥＡＰＰＬＩＣＡＴＩＯＮＯＦＳＰＡＣＥＡＸＩＳＹＭＭＥＴＲＩＣＰＲＯＢＬＥＭＩＮＰＩＥＺＯＥＬＥＣＴＲＩＣＭＡＴＥＲＩＡＬＷａｎｇＺｉ－ｋｕｎｇ（王子昆）ＣｈｅｎＧｅｎｇ－ｃｈａｏ（陈庚超）（ＸｉａｎＪｉａｏ...     

Self-similar solution to a problem of axisymmetric motion of gas through a porous medium in the case of a quadratic law of resistance

The results of solution of the self-similar problem of planar flow of gas through a porous medium in the case of a quadratic law of resistance [1] are generalized to the case of axisymmetric motion. The equation in similarity variables for the velocity of isothermal gas flow is reduced to an equation having cylindrical functions as solution. Analytic dependences of the pressure and the gas velocity on the coordinate and time are obtained for a given flow rate of the gas at the coordinate origin and for zero Initial gas pressure in the porous medium.Translated from Izvestlya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 4, pp. 168–171, July–August, 1982.     

A general solution of the axisymmetric contact problem for biphasic cartilage layers

A unilateral axisymmetric contact problem for articular cartilage layers is considered. The articular cartilages bonded to subchondral bones are modeled as biphasic materials consisting of a solid phase and a fluid phase. It is assumed that the subchondral bones are rigid and shaped like bodies of revolution with arbitrary convex profiles. The obtained closed-form analytical solution is valid over time periods compared with the typical diffusion time and can be used for increasing loading.     

Nonuniqueness of the solution of the problem of viscous interaction on an axisymmetric body

The article discusses solutions of the equations of the hypersonic boundary layer on an axisymmetric offset slender body (with a power exponent equal to 3/4), taking account of interactions with a nonviscous flow. It is shown that, in this case, the equations of the boundary layer have solutions differing from the self-similar solution corresponding to flow around a semi-infinite body. The solutions obtained are analogous to solutions for a strong interaction on a plate with slipping and triangular vanes [1–4], but are obtained over a wide range of values of the parameter of viscous interaction. An asymptotic solution is given to the problem with the approach to zero of the interaction parameter.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 41–47, September–October, 1973.The authors thank V. V. Mikhailova for discussion of the work and useful advice.     

Analytical solution in the problem of constructing axisymmetric noses with minimum wave drag

An analytical procedure for determining the axisymmetric nose shapes that ensure minimum wave drag is developed. The solution is constructed as an improving variation on the conical shape. The target function is built up in an approximate form on the basis of the assumption that the relationship between the geometric and gasdynamic parameters is local in nature. It is shown that the optimal bodies are truncated power-law bodies with an exponent equal to 2/3. The bodies thus obtained are compared with those constructed in accordance with an exact formulation of the problem.     

Numerical solution of Cauchy problems in linear elasticity in axisymmetric situations

An iterative method for solving axisymmetric Cauchy problems in linear elasticity is presented. This kind of problem consists in recovering missing displacements and forces data on one part of a domain boundary from the knowledge of overspecified displacements and forces data on another part of this boundary. Numerical simulations using the finite element method highlight the algorithm’s efficiency, accuracy and robustness to noisy data as well as its ability to deblur noisy data. An application of the inverse technique to the identification of a friction coefficient is also presented.     

Numerical analysis of supersonic viscous gas flow past axisymmetric nonpointed bodies

Supersonic viscous homogeneous gas flow past axisymmetric smooth nonpointed bodies is analyzed numerically for widely varying Mach and Reynolds numbers and flow geometry. The initial equations of a viscous shock layer are solved by the stabilization method. The effect of the determining parameters on the flow character and the heat transfer distribution along the surface is analyzed. The accuracy and domain of applicability of several approximate approaches to the solution of the problem are estimated. Tomsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 107–117, January–February, 1999. This research was carried out with financial support from the Russian Foundation for Basic Research (project No. 98-01-00298).