Interaction of an unsteady two‐phase jet with a layer of a disperse medium

Discharge of a twophase jet from a cylindrical channel into a bounded layer of a disperse medium is numerically simulated using the equations of the mechanics of heterogeneous media with allowance for the differences in velocity, temperature, and phase stresses. The effect of separation of the gas phase from the disperse phase in the layer is revealed and verified experimentally. A comparison with a similar process of gas discharge at equal initial pressures shows that in the interaction with the disperse layer, the twophase flow has a longer momentum and direction.     

Appearance of a “cold” layer upon explosive compacting of powders

Explosive compacting of powders is numerically simulated in the two-dimensional formulation. Different flow regimes depending on the detonation velocity are considered. Based on the calculations, the nature of the appearance of a “cold” layer upon explosive compacting of powders is revealed. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, 630090 Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 192–197. January–February, 2000.     

Laser–induced thermocapillary deformation of a thin liquid layer

An equation that describes the profile of laser–induced thermocapillary deformation of the thin layer of an absorbing liquid is obtained. Numerical estimates of the deformation profile are in agreement with experimental data. It is shown that with increase in the radiation power, the deformation depth of the liquid layer increases and leads to its rupture.     

Relaminarization of a turbulent boundary layer with a mach number M∞=4

Results of experimental studies are presented on relaminarization of a supersonic turbulent boundary layer behind an expansion fan for a freestream Mach number M=4 within a range of Reynolds numbers Re₁=8·10⁶ – 26·10⁶ m^–1. Experimental data on distributions of the mean velocity and massflow fluctuations and the skin friction force are obtained. Partial relaminarization of the boundary layer is reached in the experiments. The calculations of relaminarization criteria show that they can be used to predict the onset of the relaminarization process at high supersonic flow velocities.     

Time-resolved stereo PIV measurements of shock–boundary layer interaction on a supercritical airfoil

Time-resolved stereo particle-image velocimetry (TR-SPIV) and unsteady pressure measurements are used to analyze the unsteady flow over a supercritical DRA-2303 airfoil in transonic flow. The dynamic shock wave–boundary layer interaction is one of the most essential features of this unsteady flow causing a distinct oscillation of the flow field. Results from wind-tunnel experiments with a variation of the freestream Mach number at Reynolds numbers ranging from 2.55 to 2.79 × 10⁶ are analyzed regarding the origin and nature of the unsteady shock–boundary layer interaction. Therefore, the TR-SPIV results are analyzed for three buffet flows. One flow exhibits a sinusoidal streamwise oscillation of the shock wave only due to an acoustic feedback loop formed by the shock wave and the trailing-edge noise. The other two buffet flows have been intentionally influenced by an artificial acoustic source installed downstream of the test section to investigate the behavior of the interaction to upstream-propagating disturbances generated by a defined source of noise. The results show that such upstream-propagating disturbances could be identified to be responsible for the upstream displacement of the shock wave and that the feedback loop is formed by a pulsating separation of the boundary layer dependent on the shock position and the sound pressure level at the shock position. Thereby, the pulsation of the separation could be determined to be a reaction to the shock motion and not vice versa.     

Onset of Darcy–Brinkman convection in a binary viscoelastic fluid saturated porous layer

The onset of Darcy–Brinkman double-diffusive convection in a binary viscoelastic fluid-saturated porous layer is studied using both linear and weakly nonlinear stability analyses. The Oldroyd-B model is employed to describe the rheological behavior of the fluid. An extended form of Darcy–Oldroyd law incorporating the Brinkman’s correction and time derivative is used to describe the fluid flow and the Oberbeck–Boussinesq approximation is invoked. The onset criterion for stationary and oscillatory convection is derived analytically. The effects of rheological parameters, Darcy number, normalized porosity, Lewis number, solute Rayleigh number, and Darcy–Prandtl number on the stability of the system is investigated. The results indicated that there is a competition among the processes of thermal, solute diffusions and viscoelasticity that causes the convection to set in through the oscillatory modes rather than the stationary. The Darcy–Prandtl number has a dual effect on the threshold of oscillatory convection. The nonlinear theory based on the method of truncated representation of Fourier series is used to find the transient heat and mass transfer. Some existing results are reproduced as the particular cases of present study.     

Asymptotic analysis of the structure of long‐wave Görtler vortices in a hypersonic boundary layer

An asymptotic (at high Reynolds and Görtler numbers) model of nonlinear longwave Görtler vortices localized inside the boundary layer near a concave surface located in a hypersonic viscous gas flow in the regime of weak viscidinviscid interaction is constructed. The maximum wavelength is evaluated. Numerical solutions are obtained for an inviscid local limit in the linear approximation. It is shown that an increase in the freestream Mach number exerts a stabilizing effect on the vortices, and a change in the Prandtl number has no significant effect on them. For the case where the vortices form a threelayered disturbed flow structure, it is shown analytically for the first time that surface heating exerts a stabilizing action on the vortices.     

A new analytical solution to axisymmetric Biot＇s consolidation of a finite soil layer

A new analytical method is presented to study the axisymmetric Biot＇s consolidation of a finite soil layer. Starting from the governing equations of axisymmetric Blot＇s consolidation, and based on the property of Laplace transform, the relation of basic variables for a point of a finite soil layer is established between the ground surface （z= 0） and the depth z in the Laplace and Hankel transform domains. Combined with the boundary conditions of the finite soil layer, the analytical solution of any point in the transform domain can be obtained. The actual solution in the physical domain can be obtained by inverse Laplace and Hankel transforms. A numerical analysis for the axisymmetric consolidation of a finite soil layer is carried out.     

Modelling of particle layer detachment—Role of transient kinetic effects

Particle layers tend to build up on walls in many filtration and separation processes, calling for periodic removal in order to keep the apparatus running. Important factors are the adhesion of the layer on the substrate and the cohesion of the particles in the layer. Models describing such layer detachment generally assume constant and homogeneous conditions for the forces acting on the layer. But in reality detachment is extremely non-stationary concerning place and time, primarily due to changing conditi...     

Generation of the tollmien–schlichting wave in a supersonic boundary layer by two sinusoidal acoustic waves

The problem is solved using parabolized equations of stability for threedimensional perturbations of a compressible boundary layer on a flat plate. Nonlinearity is taken into account by quadratic terms that are most significant in estimates of the viscous critical layer of the stability theory. These terms are determined by the total field of two acoustic perturbations, and the equations become linear and inhomogeneous. The calculations are performed for one acoustic wave being stationary in the reference system fitted to the plate for Mach numbers M=2 and 5. Solutions are presented, which are identified very accurately with Tollmien–Schlichting waves at a rather large distance from the plate edge.     

Linear and nonlinear stability of double diffusive convection in a couple stress fluid–saturated porous layer

The linear and nonlinear stability of double diffusive convection in a layer of couple stress fluid–saturated porous medium is theoretically investigated in this work. Applying the linear stability theory, the criterion for the onset of steady and oscillatory convection is obtained. Emphasizing the presence of couple stresses, it is shown that their effect is to delay the onset of convection and oscillatory convection always occurs at a lower value of the Rayleigh number at which steady convection sets in. The nonlinear stability analysis is carried out by constructing a system of nonlinear autonomous ordinary differential equations using a truncated representation of Fourier series method and also employing modified perturbation theory with the help of self-adjoint operator technique. The results obtained from these two methods are found to complement each other. Besides, heat and mass transport are calculated in terms of Nusselt numbers. In addition, the transient behavior of Nusselt numbers is analyzed by solving the nonlinear system of ordinary differential equations numerically using the Runge–Kutta–Gill method. Streamlines, isotherms, and isohalines are also displayed.     

The onset of Görtler vortices in laminar boundary layer flow over a slightly concave wall

The onset of convective instability in the laminar boundary layer over the slightly curved wall is analyzed theoretically and compared with the existing experimental data. A new set of stability equations are derived by the propagation theory considering the relative instability under the linear stability theory. In this analysis the disturbances are assumed to have the form of longitudinal vortices and also to grow themselves in streamwise direction. The critical position to mark the onset of Görtler instability is obtained as a function of the Görtler number, where disturbances at the critical state are mainly confined to the hydrodynamic boundary layer. Comparing the theoretical predictions with available experimental and other theoretical results, the present predictions follow experimental trends fairly well with slightly higher critical Görtler numbers than those from the local stability theory. The propagation theory commanding the local eigenvalue analysis is successful to obtain stability conditions reasonably in Görtler vortex problems, relaxing the limitations by the conventional analyses.     

On appearance of “cold” layer in explosive consolidation of powders

Abstract. Numerical modeling of explosive consolidation of powders under two-dimensional conditions has been performed. Various regimes of flow depending on detonation velocity have been considered. The appearance of “cold” layer during explosive consolidation of powders has been studied by calculations. Received 12 July 1999 / Accepted 27 April 2000     

“Non-free” interaction of plane shock waves and the boundary layer in the neighborhood of the leading edge of a plate with slip

The interaction between a normally impinging shock wave and the boundary layer on a plate with slip is studied in the neighborhood of the leading edge using various experimental methods, including special laser technology, to visualize the supersonic conical gas flows. It is found that in the “non-free” interaction, when the leading edge impedes the propagation of the boundary layer separation line upstream, the structure of the disturbed flow is largely identical to that in the developed “free” interaction, but with higher parameter values and gradients in the leading part of the separation zone. The fundamental property of developed separation flows, namely, coincidence of the values of the pressure “plateau” in the separation zone and the pressure behind the oblique shock above the separation zone of the turbulent boundary layer, is conserved. Moscow. e-mail: ostap@inmech.msu.su. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 57–69, May–June, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 97-01-00099).     

Linear stability of a fluid channel with a porous layer in the center简

We perform a Poiseuille flow in a channel linear stability analysis of a inserted with one porous layer in the centre, and focus mainly on the effect of porous filling ratio. The spectral collocation technique is adopted to solve the coupled linear stability problem. We investigate the effect of permeability, σ, with fixed porous filling ratio ψ = 1/3 and then the effect of change in porous filling ratio. As shown in the paper, with increasing σ, almost each eigenvalue on the upper left branch has two subbranches at ψ = 1/3. The channel flow with one porous layer inserted at its middle （ψ = 1/3） is more stable than the structure of two porous layers at upper and bottom walls with the same parameters. By decreasing the filling ratio ψ, the modes on the upper left branch are almost in pairs and move in opposite directions, especially one of the two unstable modes moves back to a stable mode, while the other becomes more instable. It is concluded that there are at most two unstable modes with decreasing filling ratio ψ. By analyzing the relation between ψ and the maximum imaginary part of the streamwise phase speed, Cimax, we find that increasing Re has a destabilizing effect and the effect is more obvious for small Re, where ψ a remarkable drop in Cimax can be observed. The most unstable mode is more sensitive at small filling ratio ψ, and decreasing ψ can not always increase the linear stability. There is a maximum value of Cimax which appears at a small porous filling ratio when Re is larger than 2 000. And the value of filling ratio 0 corresponding to the maximum value of Cimax in the most unstable state is increased with in- creasing Re. There is a critical value of porous filling ratio （= 0.24） for Re = 500; the structure will become stable as ψ grows to surpass the threshold of 0.24; When porous filling ratio ψ increases from 0.4 to 0.6, there is hardly any changes in the values of Cimax. We have also observed that the critical Reynolds number is especially sensitive for small ψ where the fastest drop is observed, and there may be a wide range in which the porous filling ratio has less effect on the stability （ψ ranges from 0.2 to 0.6 at σ = 0.002）. At larger permeability, σ, the critical Reynolds number tends to converge no matter what the value of porous filling ratio is.     

“Anomalous” nonlinear wave phenomena in a supersonic boundary layer

Nonlinear evolution of high-amplitude periodic disturbances in a boundary layer on a flat plate for Mach numberM=2 is studied. An anomalous downstream evolution of the disturbances is found, quasi-two-dimensional disturbances being most unstable. The obtained phase velocities of the waves are 30–40% greater than the phase velocities of the Tollmien-Schlichting waves. The nonlinear evolution of vortex waves is accompanied by an increase in steady disturbances from the source of controlled vibrations. High-frequency disturbances decay, and a periodic wave train degenerates downstream into a quasiharmonic wave train. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 91–98, September–October, 1999.     

Numerical study of oscillating boundary layer flow over a flat plate using k–kL–ω turbulence model

Oscillating boundary layer flow over an infinite flat plate at rest was simulated using the k–k_L–ω turbulence model for a Reynolds number range of 32 ⩽ Re_δ ⩽ 10,000 ranging from fully laminar flow to fully turbulent flow. The k–k_L–ω model was validated by comparing the predictions with LES results and experimental results for intermittently turbulent and fully turbulent flow regimes. The good agreement obtained between the k–k_L–ω model prediction with the experimental and LES results indicate that the k–k_L–ω model is able to accurately simulate transient intermittently turbulent flow and as well as accurately predict the onset of turbulence for such oscillatory flows.     

A new method for solving Biot＇s consolidation of a finite soil layer in the cylindrical coordinate system

A new method is developed to solve Biot＇s consolidation of a finite soil layer in the cylindrical coordinate system. Based on the governing equations of Biot＇s consolidation and the technique of Laplace transform, Fourier expansions and Hankel transform with respect to time t, coordinate θ and coordinate r, respectively, a relationship of displacements, stresses, excess pore water pressure and flux is established between the ground surface （z = 0） and an arbitrary depth z in the Laplace and Hankel transform domain. By referring to proper boundary conditions of the finite soil layer, the solutions for displacements, stresses, excess pore water pressure and flux of any point in the transform domain can be obtained. The actual solutions in the physical domain can be acquired by inverting the Laplace and the Hankel transforms.