Parabolized stability equations (PSE) have opened new avenues to the analysis of the streamwise growth of linear and nonlinear disturbances in slowly varying shear flows such as boundary layers, jets, and far wakes. Growth mechanisms include both algebraic transient growth and exponential growth through primary and higher instabilities. In contrast to the eigensolutions of traditional linear stability equations, PSE solutions incorporate inhomogeneous initial and boundary conditions as do numerical solutions of the Navier-Stokes equations, but they can be obtained at modest computational expense. PSE codes have developed into a convenient tool to analyze basic mechanisms in boundary-layer flows. The most important area of application, however, is the use of the PSE approach for transition analysis in aerodynamic design. Together with the adjoint linear problem, PSE methods promise improved design capabilities for laminar flow control systems.

Parabolized stability equations

High-Order Finite-Difference Schemes for Numerical Simulation of Hypersonic Boundary-Layer Transition

Aircraft laminar flow control (LFC) from the 1930s through the 1990s is reviewed and the current status of the technology is assessed. Examples are provided to demonstrate the benefits of LFC for subsonic and supersonic aircraft. Early studies related to the laminar boundary-layer flow physics, manufacturing tolerances for laminar flow, and insect-contamination avoidance are discussed. LFC concept studies in wind-tunnel and flight experiments are the major focus of the paper. LFC design tools are briefly outlined for completeness.

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Aircraft Laminar Flow Control

The prediction of the laminar-turbulent transition of boundary layers is critically important to the development of hypersonic vehicles because the transition has a first-order impact on aerodynamic heating, drag, and vehicle operation. The success of transition prediction relies on a fundamental understanding of the relevant physical mechanisms. In the 20 years since the review by Kleiser & Zang (1991) on the direct numerical simulation (DNS) of the boundary-layer transition, significant progress has been made on DNS in the hypersonic flow regime and in the spatial DNS approach. Many high-order shock-capturing and shock-fitting finite-difference methods have been developed and extensively applied to numerical simulations of the hypersonic boundary-layer transition. DNS has become a powerful research tool and has led to discoveries of new transition mechanisms. This article reviews the recent progress of DNS on hypersonic boundary-layer receptivity, instability, and transition. The current status and future directions are also presented.

http://cfdhost.seas.ucla.edu/papers/2012/Zhong-X-2012-annurev-fluid-120710-101208.pdf

Direct Numerical Simulation on the Receptivity, Instability, and Transition of Hypersonic Boundary Layers

Reducing skin friction is important in nature and in many technological applications. This reduction may be achieved by reducing stresses in turbulent boundary layers, for instance tailoring biomimetic rough skins. Here we take a second approach consisting of keeping the boundary layer laminar as long as possible by forcing small optimal perturbations. Because of the highly non-normal nature of the underlying linearized operator, these perturbations are highly amplified and able to modify the mean velocity profiles at leading order. We report results of wind-tunnel experiments in which we implement this concept by using suitably designed roughness elements placed on the skin to enforce nearly optimal perturbations. We show that by using this passive control technique it is possible to sensibly delay transition to turbulence.

/pdf/delaying-transition-to-turbulence-by-a-passive-mechanism-57r2y2mls5.pdf

Delaying transition to turbulence by a passive mechanism.

The problem of turbulence onset in shear flows has attracted the attention of investigators for more than a century. Despite its complexity, interest in the laminar-turbulent transition has increased during the past few decades owing to i ts importance in both fundamental and applied aspects of fluid mechanics . The physical mechanisms of the transition phenomenon depend essen­ tially on the specific type of flow and the character of environmental disturbances. For boundary-layer flows two main classes of transition are known (Morkovin 1 968, 1 984; Morkovin & Reshotko 1 990). The first of them is connected with boundary-layer instabilities (described initially by linear stability theories), amplification, and interaction of different instability modes resulting in the laminar flow breakdown. This class is usually observed when environmental disturbances are rather small. The second class of transition, usually called bypass, is connected with "direct" nonlinear laminar-flow breakdown under the influence of external dis­ turbances . This is observed when high enough levels of environmental perturbations (free-stream disturbances, surfacc roughness, etc) are pre­ sent. This article focuses on the first class of transition because of its fun­ damental and practical importance in problems involving moving vehicles

Yury S. Kachanov

Papers

Physical mechanisms of laminar-boundary-layer transition