The effect of an acoustic field on a secondary convective flow in a layer

The effect of a traveling sonic wave on a convective flow in a horizontal layer with a fixed linear temperature distribution on the boundaries is investigated. Convective rolls with axes parallel to the basic flow (lengthwise rolls) are considered. On the basis of a weakly nonlinear analysis, it is shown that the lengthwise rolls appear smoothly and the regular flows are stable near the stability threshold. A direct numerical simulation is performed. Secondary near-critical flow regimes and regimes corresponding to finite supercriticalities are investigated.     

Numerical simulation of receptivity of a hypersonic boundary layer to acoustic disturbances

Direct numerical simulations of the evolution of disturbances in a viscous shock layer on a flat plate are performed for a free-stream Mach number M _∞ = 21 and Reynolds number Re _L = 1.44 · 10⁵. Unsteady Navier-Stokes equations are solved by a high-order shock-capturing scheme. Processes of receptivity and instability development in a shock layer excited by external acoustic waves are considered. Direct numerical simulations are demonstrated to agree well with results obtained by the locally parallel linear stability theory (with allowance for the shock-wave effect) and with experimental measurements in a hypersonic wind tunnel. Mechanisms of conversion of external disturbances to instability waves in a hypersonic shock layer are discussed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 84–91, May–June, 2007.     

A computational solution of hydromagnetic‐free convective flow past a vertical plate in a rotating heat‐generating fluid with Hall and ion‐slip currents

Taking Hall and ion‐slip current into account, the unsteady magnetohydrodynamic heat‐generating free convective flow of a partially ionized gas past an infinite vertical plate in a rotating frame of reference is investigated theoretically. A computer program using finite elements is employed to solve the coupled non‐linear differential equations for velocity and temperature fields. The effects of Hall and ion‐slip currents as well as the other parameters entering into the problem are discussed extensively and shown graphically. Copyright © 2006 John Wiley & Sons, Ltd.     

Three-dimensional flow of Oldroyd-B fluid over surface with convective boundary conditions

The present study addresses the three-dimensional flow of an Oldroyd-B fluid over a stretching surface with convective boundary conditions. The problem formulation is presented using the conservation laws of mass, momentum, and energy. The solutions to the dimensionless problems are computed. The convergence of series solutions by the homotopy analysis method (HAM) is discussed graphically and numerically. The graphs are plotted for various parameters of the temperature profile. The series solutions are verified by providing a comparison in a limiting case. The numerical values of the local Nusselt number are analyzed.     

Experimental study and direct numerical simulation of the evolution of disturbances in a viscous shock layer on a flat plate

The evolution of disturbances in a hypersonic viscous shock layer on a flat plate excited by slow-mode acoustic waves is considered numerically and experimentally. The parameters measured in the experiments performed with a free-stream Mach number M _∞ = 21 and Reynolds number Re _L = 1.44 · 10⁵ are the transverse profiles of the mean density and Mach number, the spectra of density fluctuations, and growth rates of natural disturbances. Direct numerical simulation of propagation of disturbances is performed by solving the Navier-Stokes equations with a high-order shock-capturing scheme. The numerical and experimental data characterizing the mean flow field, intensity of density fluctuations, and their growth rates are found to be in good agreement. Possible mechanisms of disturbance generation and evolution in the shock layer at hypersonic velocities are discussed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 3–15, September–October, 2006.     

Theoretical analysis of acoustic instability of a hypersonic shock layer on a porous wall

The possibility of controlling the laminar-turbulent transition in hypersonic shock layers by means of porous coatings is considered. The linear stability of the shock layer to acoustic disturbances is analyzed. A dispersion relation is derived in an analytical form and analyzed for different characteristic values of porosity of the wall, which allows one to study the spectrum of acoustic disturbances in the shock layer. Analytical expressions for the growth rate of instability of acoustic disturbances are presented as functions of the reflection factor. Their structure indicates that the porous coating effectively decreases acoustic instability of the shock layer.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 44–54, January–February, 2005.     

Effect of overtaking disturbances on strong cylindrical shock in a self-gravitating gas

The effect of overtaking disturbances on the propagation of strong cylindrical shock in a self-gravitating gas has been studied by an approximate technique developed by Yadav (1992). Assuming an initial density distribution law ase _o=er^–w , wheree is the density at the axis of symmetry andw is a constant, the analytical expressions for shock velocity and shock strengths modified by overtaking waves have been obtained. The results accomplished here have been compared with those for freely propagating shock.The conclusions arrived here agreed with experimental results.Finally, the modified expressions for the pressure, the density and the particle velocity immediately behind the shock have also been derived.     

Boundary layer flow of a Jeffrey fluid with convective boundary conditions

The boundary layer stretched flow of a Jeffrey fluid subject to the convective boundary conditions was investigated. The governing dimensionless problems were computed by using the homotopy analysis approach. Convergence of the derived solutions was checked and the influence of embedded parameters was analyzed by plotting graphs. It was noticed that the velocity increases with an increase in the Deborah number. Furthermore, it was found that the temperature is also an increasing function of the Biot number. We further found that for fixed values of other parameters, the local Nusselt number increases by increasing the suction parameter and Deborah number. Numerical values of the skin friction coefficient and local Nusselt numbers were computed and examined. Copyright © 2011 John Wiley & Sons, Ltd.     

Distinctive features of the transonic flow past a cone-cylinder body at small angles of the bend in the body generator at the leading corner edge

The distinctive features of the transonic flow past cone-cylinder bodies with small angles of the bend in the body generator at the leading corner edge are considered. The mechanism of transonic flow restructuring downstream of the edge and the associated variation of the gasdynamic parameters are studied, the reasons for the formation of aerodynamic hysteresis are established, and the effect of the length of the cylindrical part of the body is determined.     

Absolute, convective, and global instability of a magnetic liquid jet

An infinite or semi-infinite jet of non-conductive magnetic liquid in a uniform longitudinal magnetic field can be absolutely or convectively unstable for different values of the flow parameters. Though the higher field inhibits the absolute instability, this inhibition is maximum at some field intensity. A critical value of the surface tension exists, above which the instability is absolute for any intensity of the field. If the jet has a large but finite length and proper boundary conditions are held at its beginning and end, it is always globally unstable. The unstable global mode is based on a pair of waves that propagate in opposite directions and reflect from one into the other at the flow boundaries.     

MHD effects on free convective flow over moving semi-infinite vertical cylinder with temperature oscillation

Numerical solutions of magnetodynamics(MHD) effects on the free convective flow of an incompressible viscous fluid past a moving semi-infinite vertical cylinder with temperature oscillation are presented.The dimensionless,unsteady,non-linear,and coupled governing partial differential equations are solved by using an implicit finite difference method of the Crank-Nicolson type.The velocity,temperature,and concentration profiles are studied for various parameters.The local skin-friction,the average skin-fr...     

Axisymmetric Powell-Eyring fluid flow with convective boundary condition: optimal analysis

The effects of axisymmetric flow of a Powell-Eyring fluid over an impermeable radially stretching surface are presented. Characteristics of the heat transfer process are analyzed with a more realistic condition named the convective boundary condition. Governing equations for the flow problem are derived by the boundary layer approximations. The modeled highly coupled partial differential system is converted into a system of ordinary differential equations with acceptable similarity transformations. The convergent series solutions for the resulting system are constructed and analyzed. Optimal values are obtained and presented in a numerical form using an optimal homotopy analysis method (OHAM). The rheological characteristics of different parameters of the velocity and temperature profiles are presented graphically. Tabular variations of the skin friction coefficient and the Nusselt number are also calculated. It is observed that the temperature distribution shows opposite behavior for Prandtl and Biot numbers. Furthermore, the rate of heating/cooling is higher for both the Prandtl and Biot numbers.     

Numerical investigation of the first transition in the three-dimensional problem of convective flow in a porous medium

The branching off of steady-state regimes from mechanical equilibrium is studied for the problem of filtration convection in a parallelepiped. The conditions for the geometric parameters under which stable continuous families of steady-state regimes develop are found. The stability of equilibria of the family with respect to three-dimensional perturbations is analyzed in a numerical experiment using a finite-difference method.     

Effects of under‐relaxation factors on turbulent flow simulations

Under‐relaxation factors are significant parameters affecting the convergence of a numerical scheme. Some earlier work has been done to optimize these parameters, but this was restricted to special flow domains, and the range of changes for under‐relaxation factors and convective algorithms are limited. In this paper, the effects of changing under‐relaxation factors for different variables, different convective schemes and grid sizes on the convergence of the numerical solution of three 2D turbulent flow situations are studied. These three flows are duct flow, trench flow and inclined free falling jet flow. Copyright © 2003 John Wiley & Sons, Ltd.     

Combined forced and free convective flow of water at 4°C past a semi-infinite vertical plate

Effects of buoyancy forces on forced and free convective flow of water at 4°C past a semi-infinite vertical plate at constant temperature are studied. Flow is assumed to be vertically upwards. Similarity solutions are derived and the resulting equations are solved numerically on a computer. Velocity and temperature profiles are shown graphically and numerical values of the skin friction and the rate of heat transfer are entered in tables. It is observed that the skin friction and the Nusselt number increase with increasing Gr/Re², where Gr is the Grashof number and Re is the Reynolds number     

Instability of small-amplitude convective flows in a rotating layer with free boundaries

The stability of steady convective flows in a horizontal layer with free boundaries, heated from below and rotating about a vertical axis, is studied in the Boussinesq approximation (Rayleigh-Bénard convection). The flows considered are convective rolls or square cells that are sums of two perpendicular rolls with equal wave numbers k. It is assumed that the Rayleigh number is almost critical in order for convective flows with a wave number k: R = R _c (k) + ε² to arise, the amplitude of the supercritical states being of the order of ε. It is shown that the flows are always unstable relative to perturbations that are the sum of one long-and two short-wave modes corresponding to linear rolls turned through small angles in opposite directions.     

Method of calculating surface disturbances over a point source and a dipole

Formulas for calculating the deviations of the free surface of a heavy fluid in steady flow past a point source and a point dipole are derived. Examples of numerical calculations made in accordance with these formulas are presented.     

Scenarios of the onset of unsteady regimes in the problem of plane convective flow through a porous medium

The problem of plane convective flow through a porous medium in a rectangular vessel with a linear temperature profile steadily maintained on the boundary is considered. The onset of unsteady regimes is investigated numerically. It is shown that their onset scenarios depend on the vessel dimensions and the seepage Rayleigh number and may be as follows: the generation of stable and unstable periodic regimes as a result of a one-sided bifurcation, the generation of a stable periodic regime as a result of an Andronov-Hopf cosymmetric bifurcation, the formation of a chaotic attractor, the branching-out of a stable quasi-periodic regime from a point of a single-parameter family of steady-state regimes, and the generation of unstable periodic regimes as a result of disintegration of homoclinic trajectories. The specifics of most of the bifurcations mentioned above are attributable to the cosymmetry of the problem considered.     

Shear flow disturbances due to interaction with convective rolls

The two-dimensional stationary problem of convection in a two-component stratified medium (for example, humid air) over a nonuniformly heated horizontal surface is solved in the linear approximation. In the case in which the surface temperature is harmonically dependent on the horizontal coordinate, convective rolls are formed above the surface. Depending on the background temperature stratification, situations characterized by temperature response sign reversal can occur (for example, a decrease in the temperature of the medium as a response to heating from beneath, or “negative” heat capacity of the medium). The disturbances arising in the background horizontal flow with vertical shear directed along the convective rolls are also calculated.