Zones of influence in a two-dimensional, unsteady, hypersonic boundary layer

1990 ◽  
Vol 431 (1881) ◽  
pp. 37-59
Keyword(s):  
Boundary Layer ◽  
High Frequency ◽  
Viscous Sublayer ◽  
Base Flow ◽  
Nonlinear Flow ◽  
Hypersonic Boundary Layer ◽  
Two Dimensional ◽  
Leading Order ◽  
Asymptotic Structure

An asymptotic structure is developed for a linear, high-frequency, unsteady disturbance superimposed upon a steady, possibly separated, nonlinear flow. The unsteady viscous sublayer is found to split into a two-region structure. The leading-order flowfield is driven primarily by the upper region, which coincides with the region of non-parallel flow in the original steady viscous sublayer. It is found that introducing a viscous-inviscid interaction into the unsteady problem drastically alters the domain of dependence of the unsteady flow throughout the entire viscous sublayer. The determination of the correct domain of dependence is found to involve a subtle interplay between the convective terms, the pressure-displacement interaction and the non-parallel base flow. Preliminary extensions to fully nonlinear unsteady interactive boundary layers are noted.

On Numerical Prediction of the Stability of Hypersonic Boundary-Layer Flow Over a Row of Microcavities

2003 ◽  
Author(s):  
Vassilios Theofilis ◽  
Michel O. Deville ◽  
Peter W. Duck ◽  
Alexander Fedorov
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Flow Instability ◽  
Viscous Sublayer ◽  
Hypersonic Boundary Layer ◽  
Two Dimensional ◽  
Flow Stabilization ◽  
Two Dimensional Flow ◽  
Dimensional Boundary ◽  
Layer Flow

This paper is concerned with the structure of steady two–dimensional flow inside the viscous sublayer in hypersonic boundary–layer flow over a flat surface in which microscopic cavities (‘microcavities’) are embedded. Such a so–called Ultra Absorptive Coating (UAC) has been predicted theoretically [1] and demonstrated experimentally [2] to stabilize passively hypersonic boundary–layer flow. In an effort to further quantify the physical mechanism leading to flow stabilization, this paper focuses on the nature of the basic flows developing in the configuration in question. Direct numerical simulations are performed, addressing firstly steady flow inside a singe microcavity, driven by a constant shear, and secondly a model of a UAC surface in which the two–dimensional boundary layer over a flat plate and a minimum nontrivial of two microcavities embedded in the wall are solved in a coupled manner. The influence of flow– and geometric parameters on the obtained solutions is illustrated. Based on the results obtained, the limitations of currently used theoretical methodologies for the description of flow instability are identified and suggestions for the improved prediction of the instability characteristics of UAC surfaces are discussed.

Heat transfer in a periodic boundary layer near a two-dimensional stagnation point

1972 ◽  
Vol 56 (4) ◽  
pp. 619-627 ◽  
Author(s):  
Hiroshi Ishigaki
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Temperature Field ◽  
Velocity Field ◽  
Stagnation Point ◽  
High Frequency ◽  
High Frequency Oscillation ◽  
Main Stream ◽  
Two Dimensional ◽  
Mean Temperature

Following the previous velocity-field study (Ishigaki 1970), this paper studies how the temperature field in the laminar boundary layer near a two-dimensional stagnation point responds to the main-stream oscillation. The time-mean temperature field is of particular interest and is studied in detail. The velocity field is treated as known and is taken from the previous paper. In § 3 the solutions over the whole frequency range are obtained under the assumption of small amplitude oscillation and the results are compared with the existing approximate solutions for low and high frequency in terms of heat transfer. Time-mean heat transfer decreases at low frequency, but slightly increases at high frequency. Two factors that cause time-mean modification of the temperature field are examined quantitatively. In § 4 the finite amplitude case is treated under the assumption of high-frequency oscillation and a few examples of the time-mean temperature profile are shown.

scholarly journals Entrainment of short-wavelength free-stream vortical disturbances in compressible and incompressible boundary layers

2016 ◽  
Vol 797 ◽  
pp. 683-728 ◽  
Author(s):  
Xuesong Wu ◽  
Ming Dong
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Free Stream ◽  
Base Flow ◽  
Bypass Transition ◽  
Leading Order ◽  
Compressible Boundary Layers ◽  
Characteristic Wavelength ◽  
Incompressible Boundary ◽  
Edge Layer

The fundamental difference between continuous modes of the Orr–Sommerfeld/Squire equations and the entrainment of free-stream vortical disturbances (FSVD) into the boundary layer has been investigated in a recent paper (Dong & Wu, J. Fluid Mech., vol. 732, 2013, pp. 616–659). It was shown there that the non-parallel-flow effect plays a leading-order role in the entrainment, and neglecting it at the outset, as is done in the continuous-mode formulation, leads to non-physical features of ‘Fourier entanglement’ and abnormal anisotropy. The analysis, which was for incompressible boundary layers and for FSVD with a characteristic wavelength of the order of the local boundary-layer thickness, is extended in this paper to compressible boundary layers and FSVD with even shorter wavelengths, which are comparable with the width of the so-called edge layer. Non-parallelism remains a leading-order effect in the present scaling, which turns out to be more general in that the equations and solutions in the previous paper are recovered in the appropriate limit. Appropriate asymptotic solutions in the main and edge layers are obtained to characterize the entrainment. It is found that when the Prandtl number $\mathit{Pr}<1$, free-stream vortical disturbances of relatively low frequency generate very strong temperature fluctuations within the edge layer, leading to formation of thermal streaks. A composite solution, uniformly valid across the entire boundary layer, is constructed, and it can be used in receptivity studies and as inlet conditions for direct numerical simulations of bypass transition. For compressible boundary layers, continuous spectra of the disturbance equations linearized about a parallel base flow exhibit entanglement between vortical and entropy modes, namely, a vortical mode necessarily induces an entropy disturbance in the free stream and vice versa, and this amounts to a further non-physical behaviour. High Reynolds number asymptotic analysis yields the relations between the amplitudes of entangled modes.

The appearance of boundary-layer instabilities as a velocity minimum develops

1995 ◽  
Vol 451 (1942) ◽  
pp. 331-339 ◽  
Keyword(s):  
Boundary Layer ◽  
High Frequency ◽  
Two Dimensional ◽  
Unsteady Boundary Layer ◽  
Reversed Flow ◽  
Local Flow ◽  
Wall Velocity ◽  
Instability Modes ◽  
Classical Boundary ◽  
Special Concern

A theoretical investigation is described concerning instability modes of relatively high frequency and wavenumber in classical boundary layers with local flow reversal present. Of special concern is the two-dimensional unsteady boundary layer. It is shown that reversed flow sets in first at the wall rather than in the middle of the flow. The modes examined therefore are intermediate between ones previously studied for marginal separation, with a near-wall velocity minimum, and those for an off-wall velocity minimum. The order of appearance of instability modes, as time increases, is found to be marginal modes first, then intermediate modes, then off-wall modes. Comparisons with recent computations are described.

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