Viscous and Inviscid Instabilities of Flow Along a Streamwise Corner

Here we consider the stability of flow along a streamwise corner formed by the intersection of two large flat plates held perpendicular to each other. Self-similar solutions for the steady laminar mean flow in the corner region have been obtained by solving the boundary layer equations for zero and nonzero streamwise pressure gradients. The stability of the mean flow is investigated using linear stability analysis. An eigensolver has been developed to solve the resulting linear eigenvalue problem either in a global mode to obtain an approximation to all the dominant eigenmodes or in a local mode to refine a particular eigenmode. The stability results indicate that the entire spectrum of two-dimensional and oblique viscous modes of a two-dimensional Blasius boundary layer is active in the case of a corner layer as well, but away from the cornerline. In a corner region of finite spanwise extent, the continuous spectrum of oblique modes degenerates to a discrete spectrum of modes of increasing spanwise wave number. The effect of the corner on the two-dimensional viscous instability is small and decreases the growth rate. The growth rate of outgoing oblique disturbances is observed to decrease, while the growth rate of incoming oblique disturbances is enhanced by the corner. This asymmetry between the outgoing and incoming viscous modes increases with increasing obliqueness of the disturbance. The instability of a zero pressure gradient corner layer is dominated by the viscous modes; however, an inviscid corner mode is also observed. The critical Reynolds number of the inviscid mode rapidly decreases with even a small adverse streamwise pressure gradient and the inviscid mode becomes the dominant one. Received 17 March 1998 and accepted 28 April 1999     

Stability of Plane Flow of a Liquid Dielectric in a Transverse Alternating Electric Field

The effect of an alternating arbitrary-frequency electric field on the stability of convective flow of a dielectric liquid occupying a vertical layer is investigated within the framework of the electrohydrodynamic approximation when charge formation is associated only with the nonuniform liquid polarization. The stability thresholds are determined in the linear approximation using Floquet theory. The competition between the dielectrophoretic and thermogravitational instability mechanisms is explored. It is shown that in the case of a harmonically modulated field either quasiperiodic perturbations or perturbations synchronous with the external action may be the most dangerous. One further critical perturbation mode corresponding to the subharmonic response to variation of the external field develops for triangular modulation. In the limiting case of low-frequency modulation the asymptotic behavior of the critical parameters is investigated using the Wentzel-Kramers-Brillouin method.     

Numerical-Asymptotic Expansion Matching for Computing a Viscous Flow Around a Sharp Expansion Corner

A computational technique which is based on a numerical-asymptotic expansion matching for computing the local singular behavior of a viscous flow around a sharp right-angle expansion corner is presented. Moffatt's (1964) asymptotic solution is extended and a matching with a time-marching finite-difference scheme of the Navier--Stokes equations is formulated. Local mesh refinement around the corner is required to meet the validity of the asymptotic solution. Flows in an expanding channel with expansion ratio D/d=3 at various Reynolds numbers 1≤Re≤700 are simulated. The results are compared with those from a standard finite-difference scheme that uses second-order forward/backward differences near the corner. It is found that the results of the standard scheme converge toward those of the present technique as the level of local refinement near the corner is increased. The time-dependent parameters of the first two terms of the asymptotic solution at the steady-state solution are also described for various cases of Re and D/d. It is demonstrated that the present method enhances the accuracy of the simulations and requires less refinements near the corners to achieve converged numerical results. Received 14 August 2000 and accepted 25 October 2001     

On Time-Periodic Flow of a Viscous Liquid past a Moving Cylinder

We show existence, uniqueness and spatial asymptotic behavior of a two-dimensional time-periodic flow around a cylinder that moves orthogonal to its axis, with a time-periodic velocity, v. The result is proved if the size of the data is sufficiently small, and the average of v over a period is not zero.     

Solidification and Flow of a Binary Alloy Over a Moving Substrate

We study the solidification and flow of a binary alloy over a horizontally moving substrate. A situation in which the solid, liquid and mushy regions are separated by the stationary two-dimensional interfaces is considered. The self-similar solutions of the governing boundary layer equations are obtained, and their parametric dependence is analysed asymptotically. The effect of the boundary layer flow on the physical characteristics is determined. It is found that the horizontal pulling and the resulting flow in the liquid enhance the formation of the mushy region.     

Parametric Study of Alternating Flow Patterns in Non-Reacting Multiple-Swirl Flows

Multiple nozzle combustors, under certain conditions, may result in flowfields that differ between nozzles in an alternating pattern. Previous work has provided some clues on the parameters which govern the appearance of this behavior, but there is a lack of systematic studies. A series of non-reacting simulations of adjacent swirling flows is used to investigate the effect of nozzle exit flare angle and swirl number on the presence of the alternating flow pattern. Two-nozzle simulations are shown to accurately predict if an asymmetric flow characteristic appears and are therefore used in the parametric investigation. Alternating flow patterns are predicted at nozzle exit flare angles of 105 degrees (for a swirl number of 0.79) and 120 degrees (for a swirl number of 0.69 and 0.79). Under conditions close to the stability boundary between symmetric and asymmetric flows, the nozzle exit flare and increased swirl number push the shear layers against the dome wall so that the flows between each nozzle are largely opposite in direction. An increase in nozzle exit flare above 120^° results in separated flows exiting from the inlet and a return to a symmetric flow state. This is consistent with a proposed physical mechanism based on hydrodynamic stability in turbulent opposed jets.     

Free Fluid Flow Through a Visco-Deformable Porous Medium with a Moving Boundary

One-dimensional Darcy-law flow through a porous matrix representing a high-viscosity liquid is investigated. The flow develops in a region which depends on time due to sedimentation. The problem considered simulates the geological process of sedimentation in a basin. In accordance with geological data, the permeability and viscosity coefficients of the matrix are assumed to depend nonlinearly on the porosity. The asymptotic properties of the flow are described for large times. The agreement between the results of asymptotic and numerical solutions is satisfactory at intermediate times and good at large times under the realistic sedimentary basin conditions. The simplicity of the asymptotic solution obtained makes it possible to vary the problem parameters and determine the porosity, pressure, and velocities for particular geological conditions by means of simple calculations.     

Heat and Mass Transfer in MHD Micropolar Flow Over a Vertical Moving Porous Plate in a Porous Medium

An analysis is presented for the problem of free convection with mass transfer flow for a micropolar fluid via a porous medium bounded by a semi-infinite vertical porous plate in the presence of a transverse magnetic field. The plate moves with constant velocity in the longitudinal direction, and the free stream velocity follows an exponentially small perturbation law. A uniform magnetic field acts perpendicularly to the porous surface in which absorbs the micropolar fluid with a suction velocity varying with time. Numerical results of velocity distribution of micropolar fluids are compared with the corresponding flow problems for a Newtonian fluid. Also, the results of the skin-friction coefficient, the couple stress coefficient, the rate of the heat and mass transfers at the wall are prepared with various values of fluid properties and flow conditions.     

关于超音速流中运动激波若干问题的研究

研究了在无粘完全气体流中的运动激波 ,讨论了激波运动速度D和来流速度U对激波后气流参数的影响 ,包括对激波后的总焓比值和总压比值以及对流转角的影响。计算结果表明它们不同于通常静止激波下所得到的结果。该内容涉及到超音速射流与障碍物或空腔体相互作用时出现的失稳状态下激波的振动和空腔体底部的反常加热问题。     

Collective Bow Shock Ahead of a Transverse System of Spheres in a Supersonic Flow Behind a Moving Shock Wave

The results of investigating the dynamics and physical conditions of formation of a collective bow shock ahead of a system of spheres with the line of centers normal to the supersonic flow behind a traveling shock wave are presented. Two types of shock-wave patterns that necessarily precede the formation of the collective shock wave and correspond to regular and Mach interaction of the bow shocks were detected experimentally. On the basis of a local gasdynamic-discontinuity interference theory, quantitative criteria of the existence of these regimes and of the formation of a common shock wave are determined. These criteria are confirmed in a series of experiments for the transitional regimes.     

不可压缩流动的移动粒子半隐式法数值模拟

介绍了一种新的移动粒子半隐式方法。该方法采用Lagrange描述,用一系列离散粒子代替流体,通过半隐式求解和时间推进法来进行计算,弥补了传统网格法对复杂形状、大变形、高速撞击等情况下网格划分和重构过于繁琐的缺点,在模拟不可压缩流动问题中得到了较好的效果。     

New Conserved Vorticity Integrals for Moving Surfaces in Multi-Dimensional Fluid Flow

For inviscid fluid flow in any n-dimensional Riemannian manifold, new conserved vorticity integrals generalizing helicity, enstrophy, and entropy circulation are derived for lower-dimensional surfaces that move along fluid streamlines. Conditions are determined for which the integrals yield constants of motion for the fluid. In the case when an inviscid fluid is isentropic, these new constants of motion generalize Kelvin’s circulation theorem from closed loops to closed surfaces of any dimension.     

Remark on Single Exponential Bound of the Vorticity Gradient for the Two-Dimensional Euler Flow Around a Corner

In this paper, we consider the two–dimensional Euler flow under a simple symmetry condition, with hyperbolic structure in a unit square \({D = \{(x_1,x_2):0 < x_1+x_2 < \sqrt{2},0 < -x_1+x_2 < \sqrt{2}\}}\). It is shown that the Lipschitz estimate of the vorticity on the boundary is at most a single exponential growth near the stagnation point.     

测量低密度气流速度和运动激波马赫数的火花放电法

本文在讨论了各种测量气流速度的方法,特别是Miller的放电法基础上,提出了一种测量低密度流场气流速度和运动激波马赫数的改进方法。本方法采用双曝光技术,有助于提高测量精度;在结构上和电路上的改进,克服了低密度流场中漏电问题。该方法适用于气流速度1200m/s以上,密度约0.05kg/cm~3的高速瞬态流场中的气流速度和运动激波马赫数的测量。     

Computational Modelling of Non-Newtonian Effects on Flow in Channels with Moving Wall Indentations

Non-Newtonian effects in a channel with moving wall indentations are assessed numerically by a finite volume method for solving the unsteady incompressible Navier-Stokes equations and using a power-law model exhibiting shear thinning viscosity and Casson's model as the constitutive equations for the non-Newtonian fluid. The computations show that for a non-Newtonian fluid, there are differences in the velocity profiles and in the structure and size of the reversed flow regions as compared with the corresponding Newtonian fluid. The comparison of non-Newtonian and Newtonian wall shear stress reveals a slight decrease in the magnitude on the average for the non-Newtonian case, eventually resulting in the strength of the “wave train” being slightly weaker than those corresponding to a Newtonian fluid.     

Moving boundary in a non-Newtonian fluid

Moving boundary value problem in non-Newtonian fluid is considered. Exact analytical solution for the flow of second-grade fluid for a rigid moving plate oscillating in its own plane, is obtained. The Doppler effect has been observed due to the motion of the plate. The shearing stress on the plate is also calculated. It is concluded that the solutions for stationary porous boundaries can be obtained from the solutions of moving rigid boundaries.