Asymptotic solution to the problem of hypersonic flow over bodies in the neighborhood of the separation point of a thin shock layer

Messiter's thin shock layer approximation for hypersonic wings is applied to several non-conical shapes. Two calculation methods are considered. One gives the exact solution for a particular three-dimensional geometry which possesses a conical planform and also a conical distribution of thickness superimposed upon a surface cambered in the chordwise direction. Agreement with experiment is good for all cases, including that where the wing is yawed. The other method is a more general approach whereby the solution is expressed as a correction to an already known conical flow. Such a technique is applicable to conical planforms with either attached or detached shocks but only to the non-conical planform for the region in the vicinity of the leading edge when the shock is attached.

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Hypersonic Flow with Attached Shock Waves over Delta Wings

Aeronautical Quarterly ◽

10.1017/s0001925900005539 ◽

1970 ◽

Vol 21 (4) ◽

pp. 379-399 ◽

Cited By ~ 10

Author(s):

B. A. Woods

Keyword(s):

Shock Waves ◽

Hypersonic Flow ◽

Shock Layer ◽

Numerical Solutions ◽

Delta Wing ◽

Simple Wave ◽

Delta Wings ◽

Conical Flows ◽

Thin Shock Layer ◽

Flow Variables

SummaryHypersonic conical flows over delta wings are treated in the thin-shock-layer approximation due to Messiter. The equations are hyperbolic throughout, even in regions where the full equations are elliptic, and have not hitherto been solved for flows with attached shock waves. The concept of the simple wave has been used to construct a class of solutions for such flows; they contain discontinuities in flow variables and shock slope but, for the case of flow over a delta wing with lateral symmetry, agreement with results of numerical solutions of the full equations is good. The method is applied to plane delta wings at yaw, and to wings with anhedral and dihedral. For the flow at the tip of a rectangular wing, it is shown that two distinct solutions may be constructed.

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Hypersonic Flow Over Conical Wing-Body Combinations

Aeronautical Quarterly ◽

10.1017/s0001925900008507 ◽

1978 ◽

Vol 29 (4) ◽

pp. 285-304 ◽

Cited By ~ 1

Author(s):

R. Hillier

Keyword(s):

Hypersonic Flow ◽

Shock Layer ◽

The Body ◽

Practical Computation ◽

Comparison With Experiment ◽

Thin Shock Layer ◽

Slope Discontinuity ◽

The Common ◽

Good For ◽

Conical Wing

SummaryThis paper shows how thin shock layer theory may be applied to wing-body combinations and also to yawed wings of caret and diamond section. The common feature of these cases is the interaction of the crossflow with the body slope discontinuity and the manner in which the resulting disturbances propagate through the shock layer. Practical computation of surface pressures is straightforward and comparison with experiment appears to be fairly good for the limited results available.

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Hypersonic flow with attached shock waves over plane delta wings

Journal of Fluid Mechanics ◽

10.1017/s0022112077000196 ◽

1977 ◽

Vol 79 (2) ◽

pp. 361-377 ◽

Cited By ~ 4

Author(s):

B. A. Woods ◽

C. B. G. Mcintosh

Keyword(s):

General Solution ◽

Shock Waves ◽

Hypersonic Flow ◽

Shock Layer ◽

Delta Wing ◽

Numerical Calculations ◽

Delta Wings ◽

Thin Shock Layer ◽

New Form

A new form is given for the general solution to the thin-shock-layer equations for the flow over a nearly plane delta wing. Using this, the solution described conjecturally by Hayes & Probstein for symmetrical flow with attached shock waves over a plane delta wing is realized numerically. The flow construction devised for this purpose is applied also to yawed flows. The solutions obtained are found to agree moderately well with the results of numerical calculations from the full equations, but contain a number of anomalous features characteristic of the thin-shock-layer approximation.

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MHD Control of the Hypersonic Flow in the Shock Layer Around a Body

38th Fluid Dynamics Conference and Exhibit ◽

10.2514/6.2008-4287 ◽

2008 ◽

Author(s):

Andrea Cristofolini ◽

Carlo Borghi ◽

Gabriele Neretti ◽

Andrea Passaro ◽

Leonardo Biagioni

Keyword(s):

Hypersonic Flow ◽

Shock Layer

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A Note on the Thin-Shock-Layer Approximation

Aeronautical Quarterly ◽

10.1017/s0001925900007988 ◽

1977 ◽

Vol 28 (2) ◽

pp. 85-89 ◽

Cited By ~ 3

Author(s):

R Hillier ◽

B A Woods

Keyword(s):

Shock Layer ◽

Thin Shock Layer

SummaryThis Note proposes a restriction on possible solution procedures for thin-shock-layer theory. This restriction has been widely violated in solutions presented hitherto, although with negligible error apparently. Those cases are indicated where failure to apply the restriction leads to definite errors.

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