Hypersonic Flow with Attached Shock Waves over Delta Wings

1970 ◽  
Vol 21 (4) ◽  
pp. 379-399 ◽  
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.

Hypersonic flow with attached shock waves over plane delta wings

1977 ◽  
Vol 79 (2) ◽  
pp. 361-377 ◽  
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.

Flow Regimes over Delta Wings at Supersonic and Hypersonic Speeds

1976 ◽  
Vol 27 (1) ◽  
pp. 1-14 ◽  
Author(s):  
L C Squire
Keyword(s):  
Shock Layer ◽  
Delta Wing ◽  
Leading Edge ◽  
Flow Regimes ◽  
Lower Surface ◽  
Delta Wings ◽  
Thin Shock Layer ◽  
Wide Range ◽  
Wing Sweep ◽  
Edge Separation

SummaryThis paper concerns the boundaries between flow regimes for sharp-edged delta wings in supersonic flow and the relation of some predictions of thin-shock-layer theory to these boundaries. In particular, it is shown that the theory predicts that the attachment lines on the lower surface of a thin delta wing at supersonic speeds suddenly jump from just inboard of the leading edges to the centre line in certain flight conditions. In general there is close agreement between the conditions for this jump and the flight conditions corresponding to the change-over from attached flow to the leading-edge separation on the upper surface. Since the movement of the attachment lines on the lower surface must change the position of the sonic line and the nature of the expansion around the edge, it is suggested that the two phenomena are directly related. Thus thin-shock-layer theory can be used to establish the boundaries of the various flow regimes for a wide range of Mach number, incidence and wing sweep. The theory can also be used to predict the effects of wing thickness on leading-edge separation, but here the experimental data is very sparse and somewhat contradictory, so the value of the prediction in the case of thickness requires further investigation.

Three-dimensional wings in hypersonic flow

1972 ◽  
Vol 54 (2) ◽  
pp. 305-337 ◽  
Author(s):  
R. Hillier
Keyword(s):  
Exact Solution ◽  
Hypersonic Flow ◽  
Shock Layer ◽  
Three Dimensional ◽  
Leading Edge ◽  
The Other ◽  
Calculation Methods ◽  
Conical Flow ◽  
Thin Shock Layer ◽  
Good For

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.

Supersonic and hypersonic flow with attached shock waves over delta wings

1971 ◽  
Vol 325 (1561) ◽  
pp. 251-268 ◽  
Keyword(s):  
Shock Waves ◽  
Flow Field ◽  
Hypersonic Flow ◽  
Delta Wing ◽  
Cross Flow ◽  
Flow Region ◽  
Lower Surface ◽  
Uniform Flow ◽  
Nonuniform Flow ◽  
Sonic Line

A unified theory is developed for supersonic and hypersonic flow with attached shock waves over the lower surface of a delta wing at an angle of attack. The flow field on the lower surface of a delta wing consists of uniform flow regions near the leading edges, where the cross flow is supersonic and a nonuniform flow region near the central part, where the cross flow is subsonic. In the nonuniform flow region, the theory is based on the assumption that the flow differs slightly from the corresponding two-dimensional flow over a flat plate. Thus a linearized perturbation on a nonlinear flow field is first calculated and then strained and corrected so that the flow is matched continuously to the uniform flow which is obtained exactly. When compared with available exact numerical solutions the theory gives, in all cases, almost identical results, except near the crossflow sonic line where existing numerical methods fail to produce a discontinuous slope in the pressure curve, whereas the present theory predicts such a discontinuity and shows that the slope has a square root singularity at the crossflow sonic line similar to that in the supersonic linear theory.

Hypersonic Flow Over Conical Wing-Body Combinations

1978 ◽  
Vol 29 (4) ◽  
pp. 285-304 ◽  
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.

Errata: Unsteady Hypersonic Flow over Delta Wings with Detached Shock Waves

AIAA Journal ◽  
1976 ◽  
Vol 14 (11) ◽  
pp. 1663b-1663b
Author(s):  
W. H. Hui ◽  
H. T. Hemdan
Keyword(s):  
Shock Waves ◽  
Hypersonic Flow ◽  
Delta Wings

The calculation of inviscid hypersonic flow past the lower surface of a delta wing

1970 ◽  
Vol 44 (1) ◽  
pp. 113-127 ◽  
Author(s):  
E. A. Akinrelere
Keyword(s):  
Hypersonic Flow ◽  
Numerical Solutions ◽  
Delta Wing ◽  
Leading Edge ◽  
Lower Surface ◽  
Sonic Point ◽  
Pressure Distributions ◽  
Method Of Integral Relations ◽  
Integral Relations ◽  
The One

Kennett (1963) calculated the hypersonic flow fields past the lower (compression) surface of a delta wing, using the one-strip approximation of the method of integral relations. He obtained solutions only for wings with detached shocks. In this paper, his solutions are extended to wings with attached shocks. Here, the sonic point is inboard of the leading edge which makes the problem mixed. The solutions compare very well with the numerical solutions of the full equations by Babaev (1963a) both in the shock shapes and pressure distributions for various Mach numbers.

Delta Wings of Shapes Amenable to Exact Shock-wave Theory

1963 ◽  
Vol 67 (625) ◽  
pp. 39-40 ◽  
Author(s):  
T. Nonweiler
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Shock Waves ◽  
Hypersonic Flow ◽  
Cross Section ◽  
Wave Theory ◽  
Wave System ◽  
Delta Wings ◽  
Shock Wave Theory

SummaryA class of delta wings is considered, whose under-surface has an inverted-V, or inverted-W, cross section of such a form that, at the “design” Mach number and incidence, the shock waves formed are plane. The geometry of the shock-wave system and surface is described briefly, and comments made about the utility of the concept in relation to hypersonic flow studies.

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