Measurement of velocity and concentration in a stream of a helium‐air mixture by hot‐wire/film anemometry

A method for simultaneous measurement of instantaneous velocity and concentration values in a stream of the air/helium mixture was suggested. The method applies the hot‐element anemometry principles using dual sensor.     

Viscous linear instability of a sheared liquid-gas interface - Effect of a velocity deficit near the interface

The initial state of liquid atomization by a fast gas stream is considered by viscous linear spatial stability analysis for parallel two-fluid flow. The unbounded basic velocity profile is characterized by different asymptotic velocities and a velocity deficit near the interface. We examine the influence of the velocity deficit on the spatial growth rates of two competing modes originating from the Kelvin-Helmholtz and viscosity contrast mechanisms. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Creeping flow of a second grade fluid in a corner

A variant of Taylor’s (1962) [23] scraper problem, in which, the lower plate rotates is considered. The non-linear partial differential equations governing the flow of a second grade fluid are modeled and solved by using the domain perturbation technique considering the angular velocity of the rotating plate as a small parameter. Also the rheology of the second grade fluid is examined by depicting the profiles of the velocity, stream function, pressure and stress fields.     

Spatial Instability Of Two-Phase Mixing Layers

The initial stage of liquid atomization by a fast gas stream is considered by means of spatial stability analysis of two–phase shear layers. We solve the viscous linear stability problem for parallel flow modelled by error–function profiles. The unstable modes known from temporal theory are recovered in the convectively unstable case for fluid properties close to the air/water system. The most unstable wavelength depends only weakly on the absolute velocity relative to the laboratory system. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On unsteady MHD flow near an infinite flat wall

The flow of an electrically conducting incompressible viscous fluid near an infinite flat wall in the presence of a magnetic field when the free stream velocity is to be expressed in power series of √ t is considered. The effect of the magnetic field strength on the velocity field induced magnetic field and skin friction is analyzed for two particular cases of the free stream velocity.     

A moving-wall boundary layer flow of a slightly rarefied gas free stream over a moving flat plate

In the current work, the boundary layer flow of a slightly rarefied gas free stream over a moving flat plate is presented and solved numerically. The first-order slip boundary condition is adopted in the derivation. The dimensionless velocity and shear stress profiles are plotted and discussed. A theoretical derivation of the estimated solution domain is developed, which will give a very close estimation to the exact solution domain obtained numerically. The influences of velocity slip at the wall on the velocity and shear stress are also addressed.     

旋转流体中圆球沿旋转轴运动产生的扰动

本文用线化理论分析了整体旋转的理想流体中有一个圆球沿旋转轴作匀速运动时流体的扰动,基于旋轴对称流动的假设导出了决定运动稳定性的扰动压力方程和扰动流函数方程.用简正模法分析了扰动流函数方程,得出了非平凡中性扰动的波数与波速必须满足的约束条件,并求出了扰动的精确表达式.文中得出结论,中性扰动共有三种可能的形式.     

Mass transfer from a vertical flat plate due to natural convection with a constant counterflow

This paper first examines the mass transfer from a vertical flat surface of a soluble material due to natural convection. A perturbation term is then introduced into the stream function to model the introduction of a constant counterflow. The effect this counterflow has on both the overall mass transfer and the overall velocity profile is studied in detail.     

On perturbations associated with the creation of lift acting on a body in a transonic stream of a dissipative gas PMM vol. 31, no. 6, 1967, pp. 1035–1049

The flow pattern of a viscous imcompressible fluid past a finite body is well known; an approximate solution of the related problem can, for example, be found in the book by Landau and Lifshits [1]. Finn [2] made a rigorous and exhaustive study of plane-parallel flows. No fundamental difficulties arise in passing from the motion of an incompressible fluid to a transonic flow of a compressible gas, however the velocity field is different, when the velocity of particles becomes critical at infinity.

The pattern of a sonic flow past a body of circular cross-section was investigated in paper [3]. This paper deals with perturbations associated with the creation of lift acting on an arbitrary body in a three-dimensional flow. When solving this problem it is necessary to consider not only the external stream, but also the laminar vortex trail because of the velocity vector transverse components becoming infinitely great, if functions defining these are formally extended into the trail area. This difficulty arises in investigations of three-dimensional flows only. The solution defining perturbation damping in an axisymmetric sonic stream of a dissipative gas has in its first approximation one singular point only, and does not contain any other singularities along the axis of symmetry [3].

The external stream pattern is essentially formed by the action of normal viscous stresses and the longitudinal component of the heat flux vector, while the distribution of gas parameters in the laminar trail is defined by tangential stresses. The conjunction of solutions valid for each of these areas makes the closure of the problem, and the determination of all necessary parameters possible.     

蠕动流中圆球阻力系数的入口效应

本文研究了圆球在半无穷长圆管入口处的蠕动流。得到了速度分布,压力分布和流函数的无穷级数形式的分析解.采用配置法将无穷级数截断并确定出级数中各项系数.求出了均匀入口流绕静止圆球以及圆球以瞬时速度在管内静止流体中运动这两种情形下圆球的阻力系数以及圆球表面上的应力分布.结果表明,当圆球在入口处运动时会遭受到较无穷圆管内为大的阻力.本文还对配置法的收敛性进行了数值实验.试验证明,该法具有好的收敛性.     

圆截面螺旋管道内非定常流动研究

以血液流动为背景,利用双参数摄动法研究了圆截面螺旋管内低频振荡流动,得到问题的二阶摄动解,分析了轴向速度、二次流、壁面剪应力在不同时刻的特点及随时间和Womersley数的变化情况。研究表明:挠率对圆截面曲线管道内低频振荡流动的影响不可忽略,尤其是轴向压力梯度绝对值很小时,挠率将对二次流动结构起主要影响作用。流函数的剧烈变化只发生在正、负数值发生转变的很小的时间段内,大部分时间段内变化平缓。壁面剪应力随θ的变化也很大。     

Non-linear peristaltic flow of a non-Newtonian fluid under effect of a magnetic field in a planar channel

This paper is devoted to the study of peristaltic flow of a fourth grade fluid in a channel under the considerations of long wavelength and low-Reynolds number. The flow is examined in a wave frame of reference moving with velocity of the wave. The analytic solution has been obtained in the form of a stream function from which the axial velocity and axial pressure gradient have been derived. The results for the pressure rise and frictional force per wavelength have also been computed numerically. The computational results indicate that the pressure rise and frictional force per wavelength are increased in case of non-Newtonian fluid when compared with Newtonian fluid. Several graphs of physical interest are displayed and discussed.     

Investigation of secondary flow on an infinite yawed cylinder in a compressible stream

In this paper a study of the secondary flow on an infinite yawed cylinder in a compressible stream is made at stagnation for unit Prandtl number and for a given Mach number. The secondary flow profiles are calculated for different edge inclination angles. The chordwise and spanwise velocity profiles given by Crabtree¹ are used here in the calculation. It is found that the secondary flow profiles are the same for complementary edge inclination angles and they are maximum for the edge inclination angle of 45°. A comparison with the incompressible flow profiles² is made. It is found that the magnitude of the secondary flow profiles in a compressible stream is less than that in an incompressible stream for the same edge inclination angle.     

Radiation effects on a certain MHD free-convection flow

Free-convection heat and mass transfer due to the simultaneous action of buoyancy, radiation and transverse magnetic field is investigated near an isothermal sheet. The sheet is linearly stretched in the presence of a uniform free stream of constant velocity, temperature and concentration. A parametric study is performed to illustrate the influence of the radiation parameter, magnetic parameter, Prandtl number, Grashof number and Schmidt number on the profiles of the velocity components, temperature and concentration. Numerical results show that the radiation have significant influences on the velocity and temperature profiles, Nusselt number and local shear stress. The results indicate that the velocity, fluid's temperature and local shear stress decrease as the radiation parameter increases. The Nusslet number increases as the radiation parameter increases.     

Analytical solution of magnetohydrodynamic stagnation-point flow of a power-law fluid towards a stretching surface

A new kind of analytic technique, namely the homotopy analysis method (HAM), is employed to give an explicit analytical solution of the steady two-dimensional stagnation-point flow of an electrically conducting power-law fluid over a stretching surface when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. A uniform transverse magnetic field is applied normal to the surface. An explicit analytical solution is given by recursive formulae for the first-order power-law (Newtonian) fluid when the ratio of free stream velocity and stretching velocity is not equal to unity. For second and real order power-law fluids, an analytical approach is proposed for magnetic field parameter in a quite large range. All of our analytical results agree well with numerical results. The results obtained by HAM suggest that the solution of the problem under consideration converges.     

Viscous flow over a shrinking sheet with an arbitrary surface velocity

In this paper, an analytical solution in a closed form for the boundary layer flow over a shrinking sheet is presented when arbitrary velocity distributions are applied on the shrinking sheet. The solutions with seven typical velocity profiles are derived based on a general closed form expression. Such flow is usually not self-similar and the solution can only be implemented when the mass transfer at the wall is prescribed and determined by the moving velocity of the wall. The characteristics of the flows with the typical velocity distributions are discussed and compared with previous similarity solutions. The flow is observed to have quite different behavior from that of the self-similar flow reported in the literature and the results demonstrate distinctive momentum and energy transport characteristics. Some plots of the stream functions are also illustrated to show the difference in flow field between the shrinking sheet and the stretching sheet. An integral approach to solve boundary layer flow over a shrinking or stretching sheet with uncoupled arbitrary surface velocity and wall mass transfer velocity is outlined and the effectiveness of this approach is discussed.     

Velocity and Concentration Boundary Layers on Spinning Fibers

In this paper a mathematical model for the viscose wet spinning process is presented: We consider a single fibre, which is produced by pressing a basic solution of viscose into a bath containing sulphuric acid. H₂SO₄ diffuses into the viscose solution and reacts with the natrium hydroxide so that a solidifying fibre is formed which is pulled through the bath by drives. Due to the movement of the fibre and of diffusive transport of sulphuric acid into the fibre velocity and concentration boundary layers develop. Starting from the laminar boundary layer equations we investigate the flow and concentration fields in the bath induced by the fibre utilizing the Local Non‐Similarity method. Mass transfer in the fibre is modelled by transport equations for sulphuric acid and natrium hydroxide taking into account the neutralization reaction. The model of the fibre is coupled to the bath phase model by appropriate boundary conditions for the mass flow density and the chemical potential of sulphuric acid. The non‐constant diameter of the fibre is taken into account by a perturbation approach.     

Optimal Boundary Control of Steady-State Flow of a Viscous Inhomogeneous Incompressible Fluid

We study the problem of optimal boundary control of two-dimensional steady-state flow of a viscous inhomogeneous incompressible fluid. The role of control is played by the values of the velocity on a part of the boundary of the domain considered. On the remaining part of the boundary, the vector of flow velocity and the fluid density are given. We seek the fluid density as a scalar function (determined by the initial data) of the stream function, study the solvability of the problem, and obtain necessary optimality conditions.     

On the finite element approximation of a cascade flow problem

Summary The finite element analysis of a cascade flow problem with a given velocity circulation round profiles is presented. The nonlinear problem for the stream function with nonstandard boundary conditions is discretized by conforming linear triangular elements. We deal with the properties of the discrete problem and study the convergence of the method both for polygonal and nonpolygonal domains, including the effect of numerical integration.     

Fluctuating Powder-Driven Pulsed Water Jet

A study is made of the internal ballistics of a powder-driven pulsed water jet which generates a fluctuating, high velocity stream of liquid. The velocity fluctuations are caused by the use of a light piston which, together with the gases produced by the powder, forms an oscillating system. Calculations of the water jet parameters in the nonstationary and quasistationary approximations are compared. It is shown that the period of the stream velocity fluctuations depends on the initial pressure of the gases produced by the powder, the masses of the piston and water, and the geometry of the apparatus. The period of the fluctuations estimated in a linear approximation for instantaneous powder burnup is in good agreement with the quasistationary calculations.