Linear amplification factor transport equation for stationary crossflow instabilities in supersonic boundary layers

Based on the database from linear stability theory (LST) analysis, a local amplification factor transport equation for stationary crossflow (CF) waves in low-speed boundary layers was developed in 2019. In this paper, the authors try to extend this transport equation to compressible boundary layers based on local flow variables. The similarity equations for compressible boundary layers are introduced to build the function relations between non-local variables and local flow parameters. Then, compressibility corrections are taken into account to modify the source term of the transport equation. Through verifications of different sweep angles, Reynolds numbers, angles of attack, Mach numbers, and different cross-section geometric shapes, the rationality and correctness of the new transport equation established in this paper are illustrated.

Investigating the Flowfield Physics Within Compressible Turbulent Boundary Layers

Predicting the velocity, the temperature and the heat transfer rates within compressible boundary layers remains a challenging problem. Under compressibility and high Reynolds conditions, the density variations become very significant, resulting in high heat transfer rates. The net result is an altering of the dynamics within the boundary layer that is significantly different from its laminar counterpart. Physical properties, such as the specific heat capacities, the viscosity and the thermal conductivity, which are often considered constant, now vary with respect to temperature, creating a strong coupling between the velocity and the temperature fields. Despite the progress made in this field of research, a common issue frequently expressed in the literature is the difficulty in acquiring high quality time-resolved velocity and temperature data in compressible flows, especially near the wall. The major objective of this study is to demonstrate the capabilities of the Integral-Differential Scheme (IDS) by solving the flow field challenges within compressible boundary layers. It was demonstrated that IDS have the capability of accurately solving the full Navier-Stokes equations under realistic conditions. In the case of the compressible boundary layer, the IDS capture the flow field physics. However, it was demonstrated that the IDS is highly sensitive to grid resolution as well as the prescribed boundary conditions.

Neutral stability curves of compressible Görtler flow generated by low-frequency free-stream vortical disturbances

Pre-transitional compressible boundary layers perturbed by low-frequency free-stream vortical disturbances and flowing over plates with streamwise-concave curvature are studied via matched asymptotic expansions and numerically. The Mach number, the Görtler number and the frequency of the free-stream disturbance are varied to obtain the neutral stability curves, i.e. curves in the space of the parameters that distinguish spatially growing from spatially decaying perturbations. The receptivity approach is used to calculate the evolution of Klebanoff modes, highly oblique Tollmien–Schlichting waves influenced by the concave curvature of the wall, and Görtler vortices. The Klebanoff modes always evolve from the leading edge, the Görtler vortices dominate when the influence of the curvature becomes significant and the Tollmien–Schlichting waves may precede the Görtler vortices for moderate Görtler numbers. For relatively high frequencies the triple-deck formalism allows us to confirm the numerical result of the negligible influence of the curvature on the Tollmien–Schlichting waves when the Görtler number is an order-one quantity. Experimental data for compressible Görtler flows are mapped onto our neutral-curve graphs and earlier theoretical results are compared with our predictions.

Classical Boundary-Layer Theory

Chapter 1 discusses the flows that can be described in the framework of Prandtl’s 1904 classical boundary-layer theory, including the Blasius boundary layer on a flat plate and the Falkner–Skan solutions for the boundary layer on a wedge surface. It presents Schlichting’s solution for the laminar jet and Tollmien’s solution for the viscous wake. These are followed by analysis of Chapman’s shear layer performed with the help of Prandtl’s transposition theorem. It also considers the boundary layer on the surface of a fast rotating cylinder with the purpose of linking the circulation around the cylinder with the speed of its rotation. It concludes discussion of the classical boundary-layer theory with analysis of compressible boundary layers, including the interactive boundary layers in hypersonic flows.

On computing the location of laminar–turbulent transition in compressible boundary layers

Evolution equations of small disturbances aimed to compute the location of a laminar–turbulent transition in boundary layers by the e