The current understanding of boundary-layer receptivity to external acoustic and vortical disturbances is reviewed. Recent advances in theoretical modeling, numerical simulations, and experiments are discussed. It is shown that aspects of the theory have been validated and that the mechanisms by which freestream disturbances provide the initial conditions for unstable waves are better understood. Challenges remain, however, particularly with respect to freestream turbulence

Boundary-layer receptivity to freestream disturbances

Laminar boundary layer separation: Instability and associated phenomena

The history of Laminar Flow Control (LFC) from the 1930s through the 1990s is reviewed and the current status of the technology is assessed. Early studies related to the natural laminar boundary-layer flow physics, manufacturing tolerances for laminar flow, and insect-contamination avoidance are discussed. Although most of this publication is about slot-, porous-, and perforated-suction LFC concept studies in wind tunnel and flight experiments, some mention is made of thermal LFC. Theoretical and computational tools to describe the LFC aerodynamics are included for completeness.

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Overview of Laminar Flow Control

Earlier theoretical work on the boundary‐layer receptivity problem utilized the triple‐deck framework, and typically produced only the leading‐order asymptotic result. The applicability of these predictions was limited to the generation of Tollmien–Schlichting‐type (viscosity‐conditioned) instabilities and rather high values of an appropriate Reynolds number. Generalizing the concepts behind the asymptotic theory of Goldstein and Ruban, the classical Orr–Sommerfeld theory is utilized to predict the receptivity due to small‐amplitude surface nonuniformities. This approach accounts for the finite Reynolds‐number effects, and can also be extended easily to problems involving other types of instabilities. It is illustrated here for the case of the Tollmien–Schlichting wave generation in a Blasius boundary layer, due to the interaction of a free‐stream acoustic wave with a region of short‐scale variation in one of the surface boundary conditions. The type of surface disturbances examined include regions of short‐scale variations in wall suction, wall admittance, and wall geometry (roughness). Results from the finite Reynolds‐number approach are compared in detail with previous asymptotic predictions, as well as the available experimental data.

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A finite Reynolds number approach for the prediction of boundary layer receptivity in localized regions

The boundary‐layer receptivity resulting from acoustic forcing over a flat plate with a localized surface irregularity is analyzed using perturbation methods. The length‐scale reduction, essential to acoustic receptivity, is captured within the framework of the classical stability theory. At first order, two disturbances are calculated: an unsteady disturbance resulting from the acoustic forcing and a steady disturbance resulting from the surface irregularity. These disturbance fields interact at second order to produce a traveling‐wave field bearing the frequency of the acoustic wave and wave numbers associated with Fourier components of the surface irregularity. Components of the traveling‐wave field scale linearly with both the acoustic forcing and the height of the surface irregularity. Receptivity occurs when the frequency and wave number of a traveling‐wave component perfectly match the local eigenmode. Results are in general agreement with asymptotic analyses for irregularities in the neighborhood of branch I. Downstream of branch I, the current results show significant deviations from the asymptotic theory. Comparisons to experiments show good agreement for receptivity amplitudes when the height of the surface irregularity is small.

Localized receptivity of boundary layers

A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite-difference and spectral methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T-S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T-S waves.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112089003113

A numerical study of the interaction between unsteady free-stream disturbances and localized variations in surface geometry

The similarity equations for rotationally symmetric flow above an infinite counter–rotating disk are investigated both numerically and analytically. Numerical solutions are found when α, the ratio of the disk's angular speed to that of the rigidly rotating fluid far from it, is greater than −0.68795. It is deduced that there exists a critical value αcr, of α above which finite solutions are possible. The value of α and the limiting structure as α → αcr are found using the method of matched asymptotic expansions. The flow structure is found to consist of a thin viscous wall region above which lies a thick inviscid layer and yet another viscous transition layer. Furthermore, this structure is not unique: there can be any number of thick inviscid layers, each separated from the next by a viscous transition layer, before the outer boundary conditions on the solution are satisfied. However, comparison with the numerical solutions indicates that a single inviscid layer is preferred.

On rotationally symmetric flow above an infinite rotating disk

Receptivity of a laminar boundary layer to the interaction of time-harmonic free-stream disturbances with a 3D roughness element is studied. The 3D nonlinear triple-deck equations are solved numerically to provide the basic steady-state motion. At high Reynolds numbers, the governing equations for the unsteady motion are the unsteady linearized 3D triple-deck equations. These equations can only be solved numerically. In the absence of any roughness element, the free-stream disturbances, to the first order, produce the classical Stokes flow, in the thin Stokes layer near the wall (on the order of our lower deck). However, with the introduction of a small 3D roughness element, the interaction between the hump and the Stokes flow introduces a spectrum of all spatial disturbances inside the boundary layer.

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R. J. Bodonyi

Papers

A numerical study of the interaction between unsteady free-stream disturbances and localized variations in surface geometry

On rotationally symmetric flow above an infinite rotating disk

Receptivity of a laminar boundary layer to the interaction of a three-dimensional roughness element with time-harmonic free-stream disturbances

A numerical method for treating strongly interactive three-dimensional viscous-inviscid flows

On the structure of a three-dimensional compressible vortex