On boundary-layer transition in transonic flow
type: Item
instance of: scholarly article
title: On boundary-layer transition in transonic flow
zbMATH Open document ID: 0787.76037
DOI: 10.1007/BF00128969
published in: Journal of Engineering Mathematics
publication date: 1994-05-16T00:00:00Z
review text: The authors study the boundary-layer transition in transonic external flow. The mechanisms are identified with three major factors: (a) substantial external-flow deceleration; (b) rapid boundary-layer thickening; (c) three-dimensional nonlinear interactions. After introduction of suitable scales depending on the Reynold's number, the governing equations are written in the form: \(U_ X+V_ Y+W_ Z=0\), \(U_ T+UU_ X+VU_ Y+WU_ Z=-P_ X+U_{YY}\), \(W_ T+UW_ X+VW_ Y+WW_ Z=0+W_{YY}\) with \(U=V=W=0\) at \(Y=0\) and \(U\sim Y+A\), \(W\to 0\), as \(Y\to \infty\) coupled with the unsteady linearized transonic small perturbation equation: \(\overline m \overline P_{XX}-\overline P_{ZZ}+2\overline P_{XT}=\overline {P}_{\bar y\bar y}\) subject to \(\overline P\to 0\) as \(\bar y\to \infty\) and \(\overline P\to P\), \(\overline P_{\overline y}\to A_{XX}\) as \(\bar y\to 0\). Here, in scaled terms, \(A\) is the unknown displacement caused by the disturbance in the boundary layer, while \(P,\overline P\) are the unknown wall pressure and external pressure, respectively, and \(P\), \(A\) depend on \(X,Z,T\) with \(U,V,W\) dependent on \(X,Y,Z,T\). The matching with the oncoming stream and between the upper and main decks, in turn, is ensured. A further transonic regime is considered, in which the flow structure is for local Mach numbers closer to unity than in the previous one, and which is able also to incorporate directly the presence of an external shock impinging on the boundary layer. The interactive flow structure, the small disturbance, and the effect of separation and shock oscillation are studied. After the above three-dimensional theory, certain of the extra two-dimensional effects arising in transonic transition are described. Strong nonlinear three-dimensional growth and nonlinear triad interactions effects are investigated.
Mathematics Subject Classification ID: 76H05
Mathematics Subject Classification ID: 76D10
zbMATH DE Number: 469169
zbMATH Keywords: external-flow deceleration
zbMATH Keywords: nonlinear interactions
zbMATH Keywords: small perturbation equation
zbMATH Keywords: external shock
zbMATH Keywords: separation
zbMATH Keywords: shock oscillation
author: Rowena G. A. Bowles
author: Frank T. Smith
reviewed by: Silvio Nocilla
MaRDI profile type: Publication
cites work: BOUNDARY LAYER TRANSITION- FREESTREAM TURBULENCE AND PRESSURE GRADIENT EFFECTS
cites work: Q3790826
cites work: Finite‐time break‐up can occur in any unsteady interacting boundary layer
cites work: A reversed-flow singularity in interacting boundary layers
cites work: Two-dimensional disturbance travel, growth and spreading in boundary layers
cites work: On the first-mode instability in subsonic, supersonic or hypersonic boundary layers
cites work: On the development of large-sized short-scaled disturbances in boundary layers
cites work: Nonlinear instability and break-up of separated flow
cites work: Q5202745
cites work: The resonant-triad nonlinear interaction in boundary-layer transition
cites work: Three-dimensional instabilities in steady and unsteady non-parallel boundary layers, including effects of Tollmien-Schlichting disturbances and cross flow
cites work: The nonlinear interaction of Tollmien–Schlichting waves and Taylor-Görtler vortices in curved channel flows
cites work: Nonlinear interaction of near‐planar TS waves and longitudinal vortices in boundary‐layer transition
cites work: On strongly nonlinear vortex/wave interactions in boundary-layer transition
cites work: On hypersonic boundary-layer interactions and transition
cites work: An alternative approach to linear and nonlinear stability calculations at finite Reynolds numbers
cites work: Complete breakdown of an unsteady interactive boundary layer (over a surface distortion or in a liquid layer)
cites work: Remarks on disputed numerical results in compressible boundary-layer stability theory
cites work: Shock Wave Boundary-Layer Interactions in Laminar Transonic Flow
cites work: Shock-wave laminar boundary-layer interaction in supercritical transonic flow
cites work: Vortex-induced boundary-layer separation. Part 1. The unsteady limit problem Re [rightward arrow] [infty infinity]
cites work: On sublayer eruption and vortex formation
cites work: Transition theory and experimental comparisons on (I) amplification into streets and (II) a strongly nonlinear break-up criterion
full work available at URL: https://doi.org/10.1007/bf00128969
OpenAlex ID: W2009685099
description: scientific article; zbMATH DE number 469169