The problem of coherent perturbations in a turbulent shear layer is considered for the purpose of developing a mathematical model based on a triple decomposition that extracts the coherent components of random fluctuations. The governing equations for the mean and the coherent parts of flow are derived, assuming the eddy-viscosity equivalence for the random part of flow, and solved by iterations to provide a coupled solution of the problem as a whole. Calculations agree well with experimental data in the upstream part of the layer where the mean-coherent flow interaction is the most important. In this region, the interaction changes the mean flow velocity distribution in such a manner that the neutral stability curve is shifted upstream relative to its position in the undisturbed layer and the perturbation intensity decreases further downstream. Experiments show that the coherent waves suppress the turbulent Reynolds stress production downstream of this region, but the model fails to predict the layer spreading correctly probably due to an inadequate turbulence closure of the mean flow. For the case of a turbulent mixing layer, we suggest a new closure relation that takes into account this coherent-random interaction.

This paper aims at developing a parabolized stability equation transition analysis code coupled to the industrial inhouse accurate Reynolds-averaged Navier-Stokes code developed at Israel Aerospace Industries for stability analysis of three-dimensional boundary layers over swept wings. In the first step, the parabolized stability equation derivation in a body-fitted coordinate system is exposed, as well as its classical initialization, using the solution procedure of the global Chebyshev eigenvalue problem for the linear stability equations. This initialization procedure demands large user interactions, and it prevents the parabolized stability equation method to be of practical use in an industrial environment. Therefore, one exposes in the second step a new way to automatically generate the inflow solution of the linear stability equations needed by the parabolized stability equations. This new robust approach paves the way for innovative automatic industrial use of the parabolized stability equation technology without the need to involve the user. This approach supplies the inflow conditions required for the parabolized stability equation marching procedure without the need to solve the standalone linear stability global eigenvalue problem. The solution of the linear stability equations at initialization is now obtained by iteratively converging the local linear stability solver starting from the new inflow empirical approximation obtained in two special coordinate systems for crossflow and Tollmien-Schlichting, respectively. These formulas represent some invariant functions of the stability characteristics of the exact Navier-Stokes laminar boundary-layer profiles instead of self-similar boundary-layer profiles like the Falkner-Skan-Cooke. Standard academic validation test cases and industrial results of the parabolized stability equation/Reynolds-average Navier-Stokes codes on a generic unmanned aerial vehicle swept wing are exposed. Nomenclature c jk = entries of Jacobi transformation matrix, J c jk = entries of inverse Jacobi matrix, J −1 h = first Lamé coefficient K 1 = local curvature of the airfoil M, M ∞ = Mach number N = amplification factor (N-factor) Q ∞ = velocity vector at infinity R = Reynolds number U, V, W = velocity components along x, y, and z axes, respectively u k = velocity components in the Cartesian coordinate system w k = velocity components in the local curvilinear coordinate system x i = general curvilinear coordinates (where i is equal to 1, 2, or 3) x n , y n , z n = orthogonal normal to the leading-edge coordinate systemx s , y s , z s = orthogonal streamline-oriented coordinate system x,ỹ,z = orthogonal "tilde" coordinate system y i = Cartesian coordinate system (where i is equal to 1, 2, or 3) α = complex wave number in the longitudinal x direction α i = spatial amplification rate in the x direction α r = real wave number in the longitudinal x direction β = real wave number in the spanwise z direction β H = Hartree parameter Δ 0 = displacement thickness of the boundary layer in t...

No abstract

No abstract

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.