Thin Shock Layer Theory Research Articles

Optimum lifting body shapes in hypersonic flow at high angles of attack

A variational procedure for the determination of lifting body configurations having a maximum lift-to-drag ratio K max in hypersonic flight at high angles of attack α, is proposed. It is based on an analytical solution to the problem for three-dimensional hypersonic flow over small aspect ratio wings using thin shock-layer theory. This reduces the variational problem of finding K max, and the corresponding optimized wing shape, to the minimization of a linear functional subject to various constraints. The contributions of nonequilibrium thermochemical effects and laminar or turbulent viscous drag effects are also included in the problem formulation. The solution shows that optimized wings have an unbent forward part and a concave lower surface. Due to bifurcation in the optimization process, the planform may have either a sharp apex or a straight nose cut. Corresponding values of K max(α) significantly exceed the limiting value K N=cot α for a flat wing. Real thermochemical effects and air viscosity are shown to cause a decrease in K max and sometimes to influence the optimized wing geometry; however, the relative increment of K max to K N is still retained.

Direct frequency domain calculation of open rotor noise

Fig. 1 Typical curved waverider (——) and a caret wing (-) and the supporting shock waves: 7 = 1.4; A/o>= 10; a = 25 deg.; fto = 0.1; 62=-2 References ^essiter, A. F., Lift of Slender Delta Wings According to Newtonian Theory, AIAA Journal, Vol. 1, No. 4, 1963, pp. 794-802. Hemdan, H. T., and Hui, W. H., Unsteady and Steady Aerodynamic Forces of Slender Delta Wings According to Newtonian Theory, Canadian Aeronautics and Space Journal, Vol. 23, No. 4, 1976, pp. 238-251. Malmuth, N. D., Three-Dimensional Perturbations on Hypersonic Wedge Flow, AIAA Journal, Vol. 2, No. 8, 1964, pp. 1383-1389. Hui, W. H., Supersonic and Hypersonic Flow with Attached Shock Waves over Delta Wings, Proceedings of the Royal Society of London, Series A, Vol. 325, 1971, pp. 251-267. Hemdan, H. T., Waverider Configurations According to Thin Shock-layer Theory, Acta Astronautica, Vol. 21, No. 8, 1990, pp. 571-582.

Waverider configurations according to thin shock-layer theory

This paper shows that the thin shock-layer theory can be completed in an analytical manner when the shock wave is attached to the leading edges of a non-planar triangular conical wing. Discontinuities appear only in the derivatives and not in the functions. Thus, the second derivative of each body and the shock is discontinuous at one point, and the first derivative of the transverse velocity components and pressure are discontinuous at one point. Bodies for which the slope is discontinuous at one point are also possible. A differentiable shock wave is assumed known and the body is calculated. Thus, bodies with smooth differentiable cross-sections in the inboard which are attached to planar segments in the outboard are obtained while bodies having infinite slope at the central axis are also possible. It is found that a parabolic arc shock in the inboard cannot permit an attached shock solution but other higher order polynomials can. Surface pressure coefficient, coefficients of normal and axial force, and the lift and drag forces of waveriders constructed from these bodies are calculated in closed-form for a wide range of the flow parameters.

Hypersonic Flow Over Conical Wing-Body Combinations

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.

Unsteady hypersonic flow over delta wings with detached shock waves

The problem of pitching oscillating slender delta wings with detached shock waves in hypersonic flow is studied using Messiter's thin shock-layer theory. The amplitude of oscillation is assumed small and a perturbation method is employed. Closed-form simple formulas are obtained for the unsteady pressure field and for the aerodynamic derivatives of the delta wings which are valid for general frequencies. It is found that within the thin shock-layer approximation, the slender delta wings with detached shock waves pitching in hypersonic stream are always stable dynamically. An accurate perturbation solution to Meissiter's functional-differential equation, which is required in calculating the steady and unsteady flowfields, is also obtained.