Origination of Microconvection in a Flat Layer with a Free Boundary

Stability of a flat layer with a free boundary in the model of microconvection is studied in the linear approximation of equilibrium. The most important physical case is considered, where the Boussinesq parameter and the Rayleigh number depend linearly on the Marangoni number. It is shown that longwave disturbances always decay. Neutral curves for a wide range of dimensionless parameters are constructed numerically; new (as compared to the Oberbeck–Boussinesq model) growing disturbances are found, which are caused by fluid compressibility. Based on numerical results, the areas of applicability of the microconvection, Oberbeck–Boussinesq, and viscous heatconducting fluid models are established.     

Stability of steady nonisothermal flow in a vertical layer with permeable boundaries in the microconvection model

The problem of the stability of steady convective viscous incompressible fluid flow in a vertical layer with boundaries at different temperatures is considered in the presence of transverse blowing through the layer. The complete spectral problem is solved for a silicon melt. The neutral curve is constructed and the critical Grashof number is found. The numerical calculations show that the presence of transverse blowing significantly affects the flow stability. As compared with the Oberbeck-Boussinesq model, in the microconvection model the instability develops at lower wavenumbers.     

Stability of Thermocapillary Flow in a Flat Layer with Allowance for the Soret Effect

The stability of thermocapillary two-component liquid flow is studied taking into account thermal diffusion. An explicit expression is obtained to construct neutral Marangoni numbers under the assumption of monotonicity of perturbations. The thermocapillary and hydrodynamic instability mechanisms are considered. It is shown that plane perturbations are the greatest hazard to the stability of return flow.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 86–92, September–October, 2005.     

Effect of Rotation on the Stability of Advective Flow in a Horizontal Fluid Layer at a Small Prandtl Number

The stability of advective flow in a rotating infinite horizontal fluid layer with rigid bound-aries is investigated for a small Prandtl number Pr = 0.1 and various Taylor numbers for perturbations of the hydrodynamic type. Within the framework of the linear theory of stability, neutral curves describing the dependence of the critical Grashof number on the wave number are obtained. The behavior of finite-amplitude perturbations beyond the stability threshold is studied numerically.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 29–38.Original Russian Text Copyright © 2005 by Schwarz.     

压力梯度对边界层两相流动稳定性的影响

分析了有压力梯度的边界层两相流动稳定性,推导出类似于Saffman理论的修正的稳定性方程,数值计算采用高精度的谱方法。结果说明,压力梯度对边界层两相流动稳定性有显著的影响,顺压梯度增强流动稳定性,而逆压梯度则促进流动失稳。在不同的压力梯度和浓度下,Stokes数对流动稳定性的影响是一致的,存在一个临界Stokes数,小Stokes数促进流动失稳,而大Stokes数则提高临界雷诺数,抑制流动失稳的最佳Stokes数为10的量级。     

Effect of Volume Energy Supply on the Stability of a Subsonic Vortex Flow

Calculations of the stability of an axisymmetric vortex flow of viscous heat-conducting gas with volume energy supply are presented. The unperturbed axisymmetric vortex flow was found numerically using a quasi-cylindrical approximation of the Navier-Stokes equations under the assumption of constant peripheral-velocity circulation in the ambient co-current flow. The volume energy supply in the viscous vortex core was modeled by an additional source term in the energy equation. The stability characteristics of the viscous vortex flow in a longitudinal vortex with respect to both axisymmetric and non-axisymmetric three-dimensional waves traveling along the vortex axis and corresponding to both positive and negative values of the azimuthal wave number were found using the time-dependent formulation of the linear stability theory for compressible three-dimensional plane-parallel flows.     

Steady Streamwise Structures in the Boundary Layer on a Swept Wing with Elevated Turbulence of the Incoming Flow

Results for a turbulized flow past the windward side of a swept wing model are presented. Origination of steady disturbances in the form of streamwise structures is found. The greatest effect on the formation of these disturbances is exerted by the curvature of the external flow streamlines. The secondary flow in the boundary layer leads to an increase in the characteristic scale of disturbances in the transverse direction, as compared to the flow around the model at a zero yaw angle.     

On the effect of the nonparallelism of the boundary layer flow over a flat plate on its stability characteristics

The effect of the nonparallelism of the boundary layer flow over a flat plate on its stability characteristics has been investigated by several authors, and it was claimed that the results of the theoretical calculations are already in good agreement with the experimental observations. However, this is not true. In this paper, this problem is reinvestigated, using two different methods. It is found that within the framework of linear theory, the theoretical results are in fact not in good agreement with the experimental observations. To settle this problem, nonlinear effect must be taken into consideration. Projects Supported by the Science Fund of the Chinese Academy of Sciences     

Models of the Interaction between a Laminar Boundary Layer and a Transonic Flow

Possible regimes of viscous-inviscid interaction at transonic external flow velocities are investigated. It is shown that different flow regimes can exist depending on the relation between such parameters as the disturbance amplitude and the Mach and Reynolds numbers. Corresponding mathematical models are formulated and the solutions of some problems describing linear regimes of disturbance development are obtained. The models developed make it possible to describe all the possible interaction regimes.     

Effect of Longitudinal Forced Motion on the Stability of Convection in a Plane Vertical Layer with Internal Heat Sources

The effect of longitudinal forced fluid motion on the mechanisms of instability of a convection flow developing in a plane vertical layer in the presence of internal heat sources is considered. It is found that forced motion which intensifies the central stream of the convection flow can lead to moderate stabilization of the hydrodynamic and thermal crisis mechanisms. In the presence of counterstream forced motion the flow stability increases sharply.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 14–17.Original Russian Text Copyright © 2005 by Lobov.     

Flow of an Inclined Surface-Charged Layer in a Longitudinal Electric Field

The motion of an inclined layer under the influence of an electric force acting in the opposite direction to the gravity force is investigated theoretically and experimentally. The motion of the layer is driven by the tension tangential to the free boundary associated with the interaction between the surface charge and the longitudinal electric field. The condition of ascent of the fluid along an inclined dielectric plane is found. The domains of stable layer motion are calculated.     

Stability of Double-Diffusive Natural Convection in a Vertical Porous Layer

Transport in Porous Media - The stability of double-diffusive buoyant flow in a vertical layer of Darcy porous medium whose boundaries are held at different constant temperatures and solute...     

Receptivity of the Swept Wing Boundary Layer to a Steady Flow Inhomogeneity

The boundary layer on a plate with an inclined blunt leading edge is investigated for a free-stream flow with a small span-periodic velocity inhomogeneity. This flow simulates the penetration of the outer turbulence into the swept wing boundary layer. It is shown that the boundary layer perturbations generated by the inhomogeneity generally have a streamwise velocity component significantly greater than the initial inhomogeneity amplitude. The dependence of the perturbations on the distance from the leading edge and the spanwise inhomogeneity period is found. It is shown that the swept wing boundary layer is less sensitive to the perturbation type in question than the straight wing boundary layer.     

Nonlinear Stability Analysis of Thin Viscoelastic Film Flow Traveling Down along a Vertical Cylinder

This paper investigates the weakly nonlinear stability theoryof a thin viscoelastic liquid film flowing down along the outsidesurface of a vertical cylinder. The long-wave perturbation method isemployed to solve for generalized nonlinear kinematic equations withfree film interface. The normal mode approach is first used to computethe linear stability solution for the film flow. The method of multiplescales is then used to obtain the weak nonlinear dynamics of the filmflow for stability analysis. The modeling results indicate that both thesubcritical instability and supercritical stability conditions arepossible to occur in a viscoelastic film flow system. The degree ofinstability in the film flow is further intensified by the lateralcurvature of cylinder. This is somewhat different from that of theplanar flow. The modeling results also indicate that by increasing theviscoelastic effect and decreasing the radius of the cylinder the filmflow can become less stable as traveling down along the verticalcylinder.     

Stability of a Steady Viscous Incompressible Flow Past an Obstacle

We derive a sufficient condition for stability of a steady solution of the Navier–Stokes equation in a 3D exterior domain Ω. The condition is formulated as a requirement on integrability on the time interval (0, +∞) of a semigroup generated by the linearized problem for perturbations, applied to a finite family of certain functions. The norm of the semigroup is measured in a bounded sub-domain of Ω. We do not use any condition on “smallness” of the basic steady solution.      

Mixed Convection Boundary-Layer Flow Near the Stagnation Point on a Vertical Surface in a Porous Medium: Brinkman Model with Slip

The steady boundary-layer flow near the stagnation point on an impermeable vertical surface with slip that is embedded in a fluid-saturated porous medium is investigated. Using appropriate similarity variables, the governing system of partial differential equations is transformed into a system of ordinary differential equations. This system is then solved numerically. The features of the flow and the heat transfer characteristics for different values of the governing parameters, namely, the Darcy–Brinkman, Γ, mixed convection, λ, and slip, γ, parameters, are analysed and discussed in detail for the cases of assisting and opposing flows. It is found that dual solutions exist for assisting flows, as well as those usually reported in the literature for opposing flows. A stability analysis of the steady flow solutions encountered for different values of the mixed convection parameter λ is performed using a linear temporal stability analysis. This analysis reveals that for γ  =  0 (slip absent) and Γ  =  1 the lower solution branch is unstable while the upper solution branch is stable.     

Stability of the Hypersonic Shock Layer on a Flat Plate

The stability of hypersonic viscous gas flow in a shock layer in the neighborhood of a flat plate is considered. The stability of the velocity, temperature, density, and pressure profiles calculated on the basis of the complete viscous shock layer equations is investigated within the framework of the linear stability theory with allowance for the shock wave relations. The calculated perturbation growth rates and phase velocities are compared with the experimental data obtained by means of electron-beam fluorescence.     

Stability of Solutal Convection in a Rotating Mushy Layer Solidifying from a Vertical Surface

We consider the effects of rotation in a mushy layer being cast from a vertical surface where the effects of Coriolis acceleration, gravity and centrifugal effects are included. It is demonstrated that the Coriolis acceleration and gravity play a passive role in convection and are excluded from the stability criteria. The stability criteria is presented as the critical centrifugal Rayleigh numbers referenced for locations far away (start of solidification) and close to (nearing end of solidification) the axis or rotation.     

Closed-Loop Stability Monitoring of Axial Flow Compression Systems

Monitoring systems are proposed for the detection of incipient instability in axial flow compression systems. The work employs generic features associated with the response to noise inputs of systems bordering on instability. Based on these generic features, a closed-loop monitoring system is proposed. Numerical simulation is used to illustrate the operation of the proposed closed-loop monitoring system.