Oleg Likhachev

On streamwise vortices in a turbulent wall jet that flows over a convex surface

Flow visualization and correlation measurements revealed the existence of large streamwise vortices in a turbulent wall jet that is attached to a circular cylinder. These coherent structures were not to be found near the nozzle, nor were they artificially triggered, thus the vortices could be a product of centrifugal instability. The existence and scale of this large-scale coherent motion were corroborated by stability analysis applied to the measured mean flow.

Stability of a Compressible Laminar Wall-Jet With Heat Transfer

The flow of a plane, laminar, subsonic perfect gas wall jet with heat transfer through the wall was investigated theoretically. For the case under consideration the entire surface was maintained at a constant temperature which differed from the temperature of the ambient gas. The velocity and temperature distribution across the flow were calculated for a variety of temperature differences between the ambient gas and the surface. The boundary layer equations representing these flows were solved by using the Illingworth-Stewartson transformation, thus extending the classical Glauerts solution to a thermally non-uniform flow. The effects of heat transfer on the linear stability characteristics of the wall jet were assessed by making the local parallel flow approximation. Two kinds of unstable eigenmodes coexisting at moderate Reynolds numbers are significantly affected by the heat transfer. The influence of cooling or heating on the stability of the flow was expected in view ofthe experience accumulated in incompressible boundary layers, i.e. heating destabilizes and cooling stabilizes the flows. Cooling of the wall affects the small scale disturbances more profoundly, contrary to the results obtained for the large scale disturbances.

A vortex model for Richtmyer–Meshkov instability accounting for finite Atwood number

The vortex model developed by Jacobs and Sheeley [“Experimental study of incompressible Richtmyer–Meshkov instability,” Phys. Fluids 8, 405 (1996)] is essentially a solution to the governing equations for the case of a uniform density fluid. Thus, this model strictly speaking only applies to the case of vanishing small Atwood number. A modification to this model for small to finite Atwood number is proposed in which the vortex row utilized is perturbed such that the vortex spacing is smaller across the spikes and larger across the bubbles, a fact readily observed in experimental images. It is shown that this modification more effectively captures the behavior of experimental amplitude measurements, especially when compared with separate bubble and spike data. In addition, it is shown that this modification will cause the amplitude to deviate from the logarithmic result given by the heuristic models at late time.

An experimental study of small Atwood number Rayleigh-Taylor instability using the magnetic levitation of paramagnetic fluids

Experiments that take advantage of the properties of paramagnetic liquids are used to study Rayleigh-Taylor (RT) instability. A gravitationally unstable, miscible combination of a paramagnetic salt solution and a nonmagnetic solution is initially stabilized by a magnetic field gradient that is produced by the contoured pole-caps of a large electromagnet. Rayleigh-Taylor instability originates from infinitesimal random background noise with the rapid removal of current from the electromagnet, which results in the heavy liquid falling into the light liquid due to gravity and, thus, mixing with it. The mixing zone is visualized by backlit photography and is recorded with a digital video camera. Several miscible, small Atwood number (A ⩽ 0.1) combinations of paramagnetic and nonmagnetic solutions are used. It is found that the RT flow is insensitive to the viscosities of the fluids composing the two-fluid system, and that the growth parameter α also does not show dependence on the Atwood number when the exper...

Equilibrium state of trailing vortices: two-dimensional model of a far-field vortex wake

Abstract The equilibrium statistical mechanics of a system composed of a large number of two-dimensional point vortices is employed to describe the vortex system shed from aircraft wings. According to this theory, these higher energy states of the vortex system can only be achieved by segregating the point vortices of like kind into two clusters that descend with a constant velocity. The solution is given in terms of the integral constraints for each cluster: total circulation, center of inertia, and kinetic energy. The negative non-dimensional inverse temperature of the system and the length scale related to angular momentum of a single trailing vortex are obtained versus initial interaction energy of the vortex system. Comparison of the theoretical results with available experimental data shows good agreement between the calculated tangential velocity distribution in the trailing vortex and the data. The flow characteristics for three different wing loads are also compared to emphasize the effect of initial circulation distribution along a lifting wing on the vorticity distribution in the equilibrium trailing vortices.

On the Stability of a Laminar Wall Jet with Heat Transfer

The hydrodynamic stability of a low speed, plane, non-isothermal laminar wall jet at a constant temperature boundary condition was investigated theoretically and experimentally. The mean velocity and temperature profiles used in the stability analysis were obtained by implementing the Illingworth–Stewartson transformation that allows one to extend the classical Glauert solution to a thermally non-uniform flow. The stability calculations showed that the two unstable eigenmodes coexisting at moderate Reynolds numbers are significantly affected by the heat transfer. Heating is destabilizing the flow while cooling is stabilizing it. However, the large-scale instabilities associated with the inflection point of the velocity profile still amplify in spite of the high level of the stabilizing temperature difference. The calculated stability characteristics of the wall jet with heat transfer were compared with experimental data. The comparison showed excellent agreement for small amplitudes of the imposed perturbations. The agreement is less good for the phase velocities of the sub-harmonic wave and this is attributed to experimental difficulties and to nonlinear effects.

RESONANT-TRIAD INTERACTION IN A WALL JET

The subharmonic nonlinear route to transition in a wall jet with respect to the Craik resonant–triad instability is considered theoretically. The general technique based on linear stability theory, allowing one to reveal the resonant triads in a parametric space, was developed and successfully implemented for both the boundary layer and the wall jet. The analysis showed that only resonant interaction between inner instability modes occurring in the vicinity of the wall is prospective for an experimental observation. The detailed calculations were performed for the particular case of the resonant triad consisting of components which all become neutral at the same downstream location. At a sufficiently large initial amplitude of the two-dimensional (2D) Tollmien–Schlichting wave imposed on the basic flow, the rapid emergence of its 3D subharmonics occurs within a few wavelengths of the fundamental. It follows from the present results that a wall jet is very sensitive to the three-dimensional wavy perturbations propagating in a narrow band of wave angles around θ=58°.

Integral constraints in the study of Richtmyer-Meshkov turbulent mixing

An experimental study of the temporal evolution of the shock-induced Richtmyer-Meshkov instability in the turbulent regime with three-dimensional random interfacial perturbations is carried out. The primary interest is the growth rate of the turbulent mixing layer that develops after an impulsive acceleration of the perturbed interface between two gases (air/SF6) by a weak Ma = 1.2 incident shock wave. Planar Mie scattering is used to visualize the flow, and image sequences are captured using a high-speed video camera. The analysis of the total mixing width has been extended to study the growth behaviors of the bubbles and spikes, separately. A novel definition of the bubble and spike widths is introduced using the mass and linear momentum conservation laws. For the planar incident shock wave the newly defined bubble and spike widths increase in time as h b.s ∝ t θ, with a growth exponent θ = 1/2 that does not depend on either the initial conditions or the physical properties of the gases composing the interface.

An Experimental Study of the Turbulent Development of Richtmyer-Meshkov Instability from a Three-Dimensional Random Initial Perturbation

The Richtmyer-Meshkov instability (RMI) develops when a perturbed interface between two fluids of different densities is subjected to an impulsive acceleration. The acceleration causes the initial perturbations to grow and eventually become turbulent. The instability is of great fundamental interest in fluid mechanics and physics.

The Effects of Flow Instabilities on the Active Control of Separation

Steady-flow assumption provides a convenient criterion for flow separation linking the pressure gradient to the local characteristics of the boundary layer. However the boundary layer on the verge of separation is seldom (if at all) steady, it contains large eddies that are generated by instabilities. It was recently shown [1-3] that periodic addition of momentum may prevent separation with the same degree of control authority that is achieved by steady blowing, with one important difference: the momentum input required may be orders of magnitude smaller. This is particularly true when the input perturbations are amplified due to the instability of the mean flow [4]. It was also observed that the instability of a shear layer governs the minimum input required for a separated flow to reattach back to the surface. This determines the optimum frequency and amplitude of the harmonic perturbation necessary to force reattachment [4]. However the reattached flow encloses a bubble that may easily burst when the pressure gradient is further increased. An increase in the excitation frequency reduces the size of the bubble even though the amplitude of the excitation remains unchanged. This is so because the initial rate of amplification of the perturbations is higher and it increases the entraining capacity of the shear layer bounding the bubble. These concepts rely on the large span-wise coherence (i.e. the two-dimensionality) of the dominant turbulent structures that are triggered and enhanced by the periodic excitation. A separated mixing layer or one that bounds a bubble are not likely to be dominated by stream-wise vortices, however a boundary layer on a concave surface (such that exists on most of Liebeck’s airfoils [5]) or a wall jet on a convex surface may indeed be. Two cases are discussed in the paper, one that contains large streamwise vortices and one that does not.