Unsteady Hypersonic Flow Research Articles

Oscillating two-dimensional hypersonic airfoils at small angles of attack

Pitching oscillations of two-dimensional pointed-nose thin airfoils with small surface curvature are considered in this paper. The analysis relies on recently developed theories for steady and unsteady hypersonic flows past such airfoils. For small surface curvature T and small reduced frequency k, a double series in i and k is assumed here and shown to lead to very simple systems of linear equations having first- or second-degree polynomial solutions. Thus, simple closed-form formulas for the unsteady surface pressure and the stability derivatives of any curved nonsymmetric airfoil (with different upper and lower surface shapes), pitching at a small angle of attack, are obtained. Results for symmetric wedges at zero incidence are compared with other available analytical and experimental calculations and the agreement is found to be generally good.

Instability of a hypersonic flow over a wedge in the Newtonian approximation

At the present time, there are a number of works in the literature that treat unsteady hypersonic flows in the Newtonian approximation [1–4]. Since the angle of incidence of the shock wave αs coincides in the zero-order approximation with the angle of inclination of the bodys [1], the latter is usually used in the boundary conditions on the shock. However, in the zero-order approximation αb can be used with the same justification. Both approaches are equally justified and give similar results for a steady flow. For unsteady flows the results can differ radically. It will be shown below that for an investigation of a flow over a fixed wedge with constant conditions in the free stream a steady-state pattern is obtained in the first case and a solution growing in time, in the second case.

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

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

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.

Higher-Order Solutions for Unsteady Hypersonic and Supersonic Flow

SummaryThe problem of unsteady hypersonic and supersonic flow with attached shock wave past wedge-like bodies is studied, using as a basis the assumption that the unsteady flow is a small perturbation from a steady uniform wedge flow. It is formulated in the most general case and applicable for any motion or deformation of the body. A method of solution to the perturbation equations is given by expanding the flow quantities in power series in M−2, M being the Mach number of the steady wedge flow. It is shown how solutions of successive orders in the series may be calculated. In particular, the second-order solution is given and shown to give improvements uniformly over the first-order solution.

Calculation of three-dimensional unsteady hypersonic gas flow past slender blunt bodies

Calculation of three-dimensional unsteady hypersonic gas flow past slender blunt bodies

Method of curved bodies in problems of unsteady hypersonic flow past slender bodies

The method of curved bodies involves replacing the unsteady flow past a body by steady flow past a different body obtained from the original body by suitable curvature of its form. The idea of the method was proposed by Vetchinkin in 1918 and was first carried out in [1]. Here the authors started from the assumption that the pressure on the body surface is determined only by its local angle of attack.

Boundary-layer induced pressures on a flat plate in unsteady hypersonic flight

Abstract : A procedure was developed for the calculation of unsteady hypersonic viscous interaction pressures. The procedure is based on the idea of the tangent wedge approximation and is valid for weak interactions. Examples were worked out, using this procedure to illustrate the weak pressure interactions in unsteady hypersonic flow. The results presented are based on the available solutions for boundary layer flows, without interactions, over a flat plate which undergoes unsteady motion in its own plane. Thus the case of small deviations from steady flows and the initial stage case (or a doubly infinite plate case) were considered for both insulated and isothermal plates. Induced pressures, to first approximation, are presented and the viscous interaction parameters are brought out. (Author)

Effect of wave reflections on the unsteady hypersonic flow over a wedge.

Effect of wave reflections on the unsteady hypersonic flow over a wedge.

Newtonian flow over a stationary body in unsteady flow.

The equations governing either two-dimensional or axisymmetric, unsteady hypersonic flow over a stationary body are developed on the hypothesis of a thin shock layer. These approximate equations are integrated to obtain a formal generalization of the NewtonBusemann formula for the pressure on the body. It is found that, just as in steady flow, tangential velocity, mass flux, and entropy are conserved by fluid particles within the shock layer; however, retarded-time effects render specific applications more complicated.

A Note on the Explosion Solution of Sedov with Application to the Newtonian Theory of Unsteady Hypersonic Flow

A Note on the Explosion Solution of Sedov with Application to the Newtonian Theory of Unsteady Hypersonic Flow