Steady Transonic Flow Research Articles

Unsteady Transonic Flow Analysis for Low Aspect Ratio, Pointed Wings

Oswatitsch and Keune's parabolic method for steady transonic flow is applied and extended to thin slender wings oscillating in the sonic flowfield. The parabolic constant for the wing was determined from the equivalent body of revolution. Laplace transform methods were used to derive the asymptotic equations for pressure coefficient, and the Adams-Sears iterative procedure was employed to solve the equations. A computer program was developed to find the pressure distributions, generalized force coefficients, and stability derivatives for delta, convex, and concave wing planforms. Input for the program includes planform shape, acceleration constant, pitch axis location, and frequency of oscillation. Sample calculations were performed for the delta, convex, and concave wings including a possible space shuttle configuration. The results were compared with those obtained by the slender body theory and by Landahl's theory. The present method obtained more negative dam ping-in-pitch than that predicted by Landahl's theory. In particular, the present method provides the stability derivatives in the low-frequency range where Landahl's theory breaks down.

Longitudinal Response of an Aircraft due to a Trailing Vortex Pair

ofoils and Wings, Transonic Aerodynamics, AGARD Conference Proceedings 35, 1968, pp. 11-1 to 11-23. Mager, A., On the Model of the Free, Shock-Separated, Turbulent Boundary Layer, Journal of the Aeronautical Sciences, Vol. 23, Feb. 1956, pp. 181-184. Smith, D. K., Wind Tunnel of the Pressure Distribution on a Two-Dimensional Airfoil with Pylon Mounted Stores at Mach Numbers from 0.70 to 0.90, AEDC-TR-73-71, March 1973, Arnold Engineering Development Center, Arnold Air Force Station, Tenn. Krupp, J. A., The Numerical Calculation of Plane Steady Transonic Flows Past Thin Lifting Airfoils, PhD. thesis, June 1971, University of Washington, Seattle, Wash. Studwell, V. E., Investigation of Transonic Aerodynamic Phenomena for Wing Mounted External Stores, PhD. thesis, June 1973, University of Tennessee Space Institute, Tullahoma, Tenn. Fig. 2 Variation of incremental lift coefficient per unit vortex strength with position of left vortex.

Nonlinear wave propagation on an arbitrary steady transonic flow

Here, we have studied the propagation of an arbitrary disturbance bounded in space on an arbitrary two- or three-dimensional transonic flow. First we have presented a general theory valid for an arbitrary system ofnfirst-order quasi- linear partial differential equations and then used the theory for the special case of gasdynamic equations. If a disturbance is created in the neighbourhood of a sonic point, only a part of the disturbance stays in the transonic region and it is bounded by a wave front perpendicular to the streamlines. This part of the disturbance is governed by a very simple partial differential equation and the problem essentially reduces to the discussion of one-dimensional waves. The disturbance decays in the neighbourhood of the points where the flow acceler- ates from a subsonic state to a supersonic state and it attains a steady state where the flow is decelerating.

Calculation of plane steady transonic flows

Transonic small disturbance theory is used to solve for the flow past thin airfoils including cases with imbedded shock waves. The small disturbance equations and similarity rules are presented, and a boundary value problem is formulated for the case of a subsonic freestream Mach number. The governing transonic potential equation is a mixed (elliptic-hyperbolic) differential equation which is solved numerically using a newly developed mixed finite difference system. Separate difference formulas are used in the elliptic and hyperbolic regions to account properly for the local domain of dependence of the differential equation. An analytical solution derived for the far field is used as a boundary condition for the numerical solution. The difference equations are solved with a line relaxation algorithm. Shock waves, if any, and supersonic zones appear naturally during the iterative process. Results are presented for nonlifting circular arc airfoils and a shock free Nieuwland airfoil. Agreement with experiment for the circular arc airfoils, and exact theory for the Nieuwland airfoil is excellent.

Study of self-similar and steady flows near singularities

One-dimensional steady state flow or a self-similar flow is represented by an integral curve of the system of ordinary differential equations and, in many important cases, the integral curve passes through a singular point. Kulikovskii & Slobodkina (1967) have shown that the stability of a steady flow near the singularity can be studied with the help of a simple first-order partial differential equation. In § 2 of this paper we have used their method to study steady transonic flows in radiation-gas-dynamics in the neighbourhood of the sonic point. We find that all possible one-dimensional steady flows in radiation-gas-dynamics are locally stable in the neighbourhood of the sonic point. A continuous disturbance on a steady flow, while decaying and propagating, may develop a surface of discontinuity within it. We have determined the conditions for the appearance of such a discontinuity and also the exact position where it appears. In §3 we have shown that their method can be easily generalized to study the stability of self-similar flows. As an example we have considered the stability of the self-similar flow behind a strong imploding shock. In this case we find that the flow is stable with respect to radially symmetric disturbances.

On the breakdown of plane transonic flow

The perturbation, problem for steady plane transonic flow is discussed (I) by means of particular exact solutions of the variational equations, and (II) by a general existence theorem valid for a modified Tricomi gas law. It is shown that even for a correctly set boundary-value problem and with arbitrarily smooth perturbations, the flow will, in general, be physically impossible because of infinite accelerations arising in the supersonic region. The breakdown of transonic flow adjacent to a semi-infinite body is proved for specified perturbations of the boundary.