Dependence of slip coefficients on the nature of the interaction between gas molecules and a wall

A method of solution of the boundary-value problems of kinetic gas theory is developed, making it possible to use the boundary conditions in the most general form. The generalized Maxwell boundary condition that takes into account the dependence of the accommodation coefficient on the angle of incidence of gas molecules is considered as an example.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 149–152, September–October, 1986.     

Poiseuille flow and thermal creep in a capillary tube on the basis of the kinetic R-model

Flow of a diatomic rarefied gas in a capillary tube of infinite length and an arbitrary cross-section under a given small pressure gradient (Poiseuille flow) or a small temperature gradient (thermal creep) is studied on the basis of a kinetic model that takes account for the rotational degrees of freedom of molecules (R-model). Numerical investigation is carried out for flows between parallel flat plates and in a circular capillary tube at the gas parameters corresponding to nitrogen. The main calculated quantity is the gas flow rate through a tube cross-section. The results are compared with the corresponding data obtained on the basis of the S-model.     

A boundary model for the thermal creep problem

A new integral boundary condition model for determining the particle velocity distribution function in a Knudsen layer, which makes it possible to improve the accuracy of the moment approximations, is proposed. The results for various models are compared with the exact numerical solution of the problem.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 160–163, November–December, 1993.This research was made possible by financial support from the Exploratory Research Program, US EPA and by a Fulbright grant for Professor I. N. Ivchenko.     

Mixed convection boundary layer flow near stagnation-point on vertical surface with slip

This paper considers the steady mixed convection boundary layer flow of a viscous and incompressible fluid near the stagnation-point on a vertical surface with the slip effect at the boundary. The temperature of the sheet and the velocity of the external flow are assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations are first transformed into a system of ordinary differential equations, which are then solved numerically by a shooting method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. The results indicate that for the opposing flow, the dual solutions exist in a certain range of the buoyancy parameter, while for the assisting flow, the solution is unique. In general, the velocity slip increases the heat transfer rate at the surface, while the thermal slip decreases it.     

Diffusion and thermal slip of a binary gas mixture

Let us note that the phenomenon of diffusion slip at a constant gas-mixture temperature has been considered in [1], for example, and thermal slip for a single-component gas in [2]. The slip velocity of a binary gas mixture has been calculated in a field of the temperature gradient and of the partial pressure gradients. The kinetic equation is solved by an approximate method based on physical considerations. A formula has been obtained analytically for the slip velocity for arbitrary accommodation coefficients as well as for arbitrary gas concentrations and arbitrary molecule masses. The results agree to 1% accuracy with the numerical computations of other authors.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 51–55, July–August, 1970.     

Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition

This paper presents heat transfer process in a two-dimensional steady hydromagnetic convective flow of an electrically conducting fluid over a flat plate with partial slip at the surface of the boundary subjected to the convective surface heat flux at the boundary. The analysis accounts for both temperature-dependent viscosity and temperature dependent thermal conductivity. The local similarity equations are derived and solved numerically using the Nachtsheim-Swigert iteration procedure. Results for the dimensionless velocity, temperature and ambient Prandtl number within the boundary layer are displayed graphically delineating the effect of various parameters characterizing the flow. The results show that momentum boundary layer thickness significantly depends on the surface convection parameter, Hartmann number and on the sign of the variable viscosity parameter. The results also show that plate surface temperature is higher when there is no slip at the plate compared to its presence. For both slip and no-slip cases surface temperature of the plate can be controlled by controlling the strength of the applied magnetic field. In modelling the thermal boundary layer flow with variable viscosity and variable thermal conductivity, the Prandtl number must be treated as a variable irrespective of flow conditions whether there is slip or no-slip at the boundary to obtain realistic results.     

Boundary conditions of gas dynamic slip on a rough surface

The phenomenon of gas dynamic slip associated with the flow of a monatomic, slightly rarefied gas over a rough surface is investigated. It is assumed that the characteristic dimensions of the roughness are comparable with the molecular mean free path. It is shown that if there is anisotropy of the surface shape the relation between the slip velocity and the friction stress vector becomes tensorial. In this case for almost any orientation of the gas dynamic flow the so-called cross slip effect is observed. The symmetry of the slip coefficient matrix is proved for fairly general assumptions concerning the type of roughness, the law of reflection of molecules from the surface, and the law of intermolecular interaction. The components of the slip coefficient matrix are calculated by a variational method for a corrugated model of the roughness.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 180–184, January–February, 1987.     

Unsteady-state slip of a gas near an infinite plane with diffusion-mirror reflection of molecules

Journal of Applied Mechanics and Technical Physics - On the basis of a “two-point” approximation for the distribution function, an approximate analytical solution is obtained to the...     

Perturbation solutions of weakly compressible Newtonian Poiseuille flows with Navier slip at the wall

We consider both the planar and axisymmetric steady, laminar Poiseuille flows of a weakly compressible Newtonian fluid assuming that slip occurs along the wall following Navier’s slip equation and that the density obeys a linear equation of state. A perturbation analysis is performed in terms of the primary flow variables using the dimensionless isothermal compressibility as the perturbation parameter. Solutions up to the second order are derived and compared with available analytical results. The combined effects of slip, compressibility, and inertia are discussed with emphasis on the required pressure drop and the average Darcy friction factor.     

基于二阶滑移边界的螺旋槽干气密封泄漏量计算与分析

为解决螺旋槽干气密封流场计算中一阶线性滑移边界条件下得到的泄漏量与实验结果之间存在较大误差的问题,在一阶线性滑移边界条件的基础上,推导出二阶非线性滑移边界条件下的修正的广义雷诺方程,应用迭代法、PH 线性化方法等求解非线性雷诺方程,获得了气膜压力、流速、泄漏量的近似解.利用Maple程序计算了工程实例中不同转速和不同压力情况下的泄漏量,并与一阶线性滑移边界条件下的泄漏量和实验数值进行比较.结果表明:在工程实例中,压力相同时,泄漏量随转速的增大而增大,一、二阶最大相对误差分别为14.4%、5.4%;转速相同时,泄漏量随压力的增大而增大,一、二阶最大相对误差分别为33.3%、13.3%.本文未考虑干气密封内部的振动情况,因此一、二阶理论计算值小于实际测试值.二阶非线性滑移边界条件下的泄漏量值比一阶线性滑移边界条件下的泄漏量值更加接近实验数值,特别是在工程实例中转速、压力较低的工况下更加明显.     

A nonlinear creep model based on the concept of slip

Relations between the creep strain and the stress are obtained for a complex stress state on basis of the hypothesis that the tangent strain components depend, in a certain slip system, only on the history of variation of the corresponding shear stress component. It is assumed that the slip system orientation is chaotically distributed over all directions and the total strain of the polycrystal is considered as the sum of contributions of all slips. This permits describing the creep strains in an arbitrary stress state by using a common operator defining the dislocation slip in a certain slip system. The model can be used for arbitrary creep operators. Computational results are analyzed and compared with experimental data obtained by other authors.     

Couette flow with slip and jump boundary conditions

The steady plane Couette flow is analyzed within the framework of the five field equations of mass, momentum and energy for a Newtonian viscous heat conducting ideal gas in which slip and jump boundary conditions are considered. The results obtained are compared with those that follow from the direct simulation Monte Carlo method. Received July 10, 2000     

Dependence between the shock and the separation bubble in a shock wave boundary layer interaction

We present experimental results obtained in a turbulent boundary layer at a Mach number of 2.3 impinged by an oblique shock wave. Strong unsteadiness is developed in the interaction, involving several frequency ranges which can extend over two orders of magnitude. In this paper, attention is focused on the links between the low-frequency shock motions and the separation bubble, in particular phase relationships are evaluated. An interpretation based on a simple scheme of the streamwise evolution of the instantaneous pressure is proposed. As it is mainly based on the pressure signal properties inside the region of the shock oscillation, it may be expected that it will still be relevant for different configurations of shock-induced separation as compression ramp, blunt bodies, or over expanded nozzles.     

Numerical simulation of the transition from adhesion to slip with friction in generalized Newtonian Poiseuille flow

The axisymmetric Poiseuille flow of a purely viscous generalized Newtonian fluid under rate of flow controlled conditions is studied with a change in the boundary conditions at a transition point from an adhesive to a slip condition with friction at the wall. The friction law used originates from an experimental study by (J.M. Piau and N. El Kissi, J. Non-Newtonian Fluid Mech. 54 (1994) 121–142) using a capillary made of steel and a silicone fluid, and is based also on a molecular dynamics theory by (Yu. B. Chernyak, A.I. Leonov, Wear, 108 (1986) 105–138). It gives a non-linear multivalued dependance of the wall shear stress to the velocity at the wall. Moreover, wall shear stress values may become smaller than values obtained when adhesion prevails in the capillary. The shear stress must over-step some limiting stress level to trigger the wall slip. After checking slip boundary condition implementation for the case of Poiseuille flow with slip along the entire wall, the convergence and the validity of the computation was studied. Important morphologic changes of the flow field and the stress field appear around the transition point from adhesion to slip boundary condition. Slip at the wall allows the principal stress difference to be drastically reduced, except in the vicinity of the transition point where this difference is maximum. A peak in shear stress located upstream of the transition, and a peak in elongational stress located downstream of the transition, are observed at the wall. Fully developed near plug-like flows are obtained within about 1D only downstream of the transition point. It is concluded that the effect of slip on extrudates distorsion should appear clearly even when the exit slippery zone is reduced to 1D.     

Theory of the interaction of a shock wave with a boundary layer on a moving surface

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 8–14, September–October, 1990.     

MHD flow and heat transfer over a stretching surface with variable thermal conductivity and partial slip

In this paper we analyze the flow and heat transfer of an MHD fluid over an impermeable stretching surface with variable thermal conductivity and non-uniform heat source/sink in the presence of partial slip. The governing partial differential equations of the problem are reduced to nonlinear ordinary differential equations by using a similarity transformation. The temperature boundary conditions are assumed to be linear functions of the distance from the origin. Analytical solutions of the energy equations for Prescribed Surface Temperature (PST) and Prescribed Heat Flux (PHF) cases are obtained in terms of a hypergeometric function, without applying the boundary-layer approximation. The effects of the governing parameters on the flow and heat transfer fields are presented through tables and graphs, and they are discussed. Furthermore, the obtained numerical results for the skin friction, wall-temperature gradient and wall temperature are analyzed and compared with the available results in the literature for special cases.