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  • Print publication year: 2011
  • Online publication date: June 2012

10 - Analytical Treatment of Shock Wave???Boundary-Layer Interactions



Motivation for Analytical Work in the Computer Age

Notwithstanding the success of powerful CFD codes in predicting complex aerodynamic flowfields, analytical methods continue to be a valuable tool in the study of viscous-inviscid interaction problems for the following reasons:

Such methods appreciably enhance physical insight by illuminating the underlying basic mechanisms and fine-scale features of the problem, including the attendant similitude properties [1]. An example in the case of shock wave–boundary-layer interaction (SBLI) is the fundamental explanation of the phenomena of upstream influence and free interaction provided by the pioneering triple-deck–theory studies of Lighthill [2], Stewartson and Williams [3], and Neiland [4].

Analysis provides an enhanced conceptual framework to guide both the design of related experimental studies and the correlation and interpretation of the resulting data. This was exemplified in a recent study of wall-roughness effects on shock-wave–turbulent boundary-layer interaction wherein a two-layered analytical theory revealed key features and appropriate scaling properties of the problem that were then used to design and evaluate a companion experimental program [5].

Analytical solutions can enhance substantially the efficiency and cost-reduction of large-scale numerical codes [6] by both providing accurate representation of otherwise difficult far-field boundary conditions and serving as an imbedded local element within a global computation to capture key smaller-scale physics. An example of the latter is the application of a small-perturbation theory of transonic normal shock–turbulent boundary-layer interaction in a global inviscid-boundary layer [7]; the resulting hybrid code provided more than 100-fold savings in design-related parametric-study costs.

A final noteworthy benefit is the occasional revelation of the deeper basic explanation for well-known empiricisms, such as the local pressure-distribution inflection-point criteria for incipient separation that are widely used by experimentalists.

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