Yuli Lifshitz

Study of Discrete Modes Branching in High-Speed Boundary Layers

The branching of discrete modes in high-speed boundary layers is investigated using parabolized stability equations. The fast and slow discrete modes associated with the fast and slow acoustic modes, respectively, are consideredin high-speedboundarylayersoveradiabaticandcooledwalls.Whereastheconventional linearstability theory approach leads to singular behavior in the vicinity of the fast-mode synchronization with the entropy and vorticity modes, the parabolized stability equation results do not reveal singular behavior of the solution and are consistent with the available direct numerical simulations of perturbations in high-speed boundary layers. Also, the parabolized stability equation results do not reveal a singular behavior in the vicinity of the point of synchronism of the slow and fast discrete modes.

Continuing nonlinear growth of Tollmien-Schlichting waves

This brief paper is concerned with the effect of mean flow distortions on spatially growing Tollmien-Schlichting waves in the Blasius boundary layer. It is shown that the coherent Reynolds stresses arising from the waves affect the mean flow by tending to reverse the sign of the cross-stream derivative of vorticity in the critical layer. If the wave amplitude is high enough to initiate the reversal, it further contributes to the wave amplification. That, in turn, increases the region of the vorticity derivative with opposite sign.

On Resonant Spreading of Harmonically Excited Turbulent Mixing Layer

*† The problem of three-dimensional coherent perturbations in two-dimensional turbulent mixing layer is considered. The theoretical model is derived by splitting the unsteady RANS problem, with the Prandtl algebraic eddy viscosity closure, into the mean and the coherent flow problems, which are connected by iterations. A thin layer approximation is used for the mean flow calculations, and a variant of velocity-vorticity formulation is developed for the coherent flow problem. This method is supplemented by amplitude transformation to separate the “fast” and the “slow” scales of the coherent flow. As a result, the equations for harmonic perturbations are solved on the same grid as the mean flow equations, reducing the computing time significantly. Parametric study was performed for the flow, where the mean-coherent interaction can be neglected (very small excitation amplitude), and for the flow with moderate level of excitation, which is usually utilized for active flow control. Results demonstrate weak dependence on a ratio of the wavenumbers in longitudinal and spanwise direction in the first case. In the case of moderate excitation, this dependence becomes strong. In particular, the calculations show an extraordinary increase of the coherent stress and the mixing layer spreading rate when these wavenumbers are close.

Periodic-Forcing Parameters for Control of Incipient Leading-Edge Separation

Separation control by two-dimensional periodic excitation is studied theoretically for nonsymmetrical flows over a parabola using a mathematical model of incompressible laminar flow with periodic perturbations. This model is based on the representation of the flow as the sum of the mean and the periodic components. The governing equations for both components are derived from the Navier–Stokes equations using time averaging. The momentum equations for the mean component comprise additional source terms that result from averaging the quadratic periodic terms. These source terms allow the control of separation. A numerical procedure has been developed to solve these equations along with equations of periodic flow, and to study the influence of inflow conditions, namely, frequency, amplitude, and the station where the excitation is inserted on the mean flow. Using this procedure, one can check if the given inflow conditions suppress the leading-edge separation of the flow over a parabola.

Low-Dimensional Models of Flow Over a Body of Revolution at High Incidence

The asymmetric part of flow over a body of revolution at high angle of attack is considered as coherent structures of the flow and a method of Proper Orthogonal Decomposition (POD) is applied to construct its low-dimensional model in the form of superposition of orthogonal functions. Results of the analysis show that the flow can be represented in the form of linear combination of odd and even functions, and the first two terms of the expansion capture 98.5% of its kinetic energy. Their coefficients are determined by the value of side force and the increment of normal force. The transient behavior of the flow is studied using Fourier transformation.