An Integral Equation For The Linearized Supersonic Flow Over A Wing
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| Total Pages | : 102 |
| Release | : 1988 |
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In the first formulation. the integral equation for linearized steady supersonic flows appears in a form where it is necessary to approach the planform from above or below by a limiting process. In the present report, the problem is transformed analytically in such a manner that this limiting process no longer appears and that the resulting expressions are numerically tractable. It is believed that such a formulation gives more freedom to take the particularities of a given problem into account. The formulation is applied to compute the conical field which arises at the top of an airfoil. A possible numerical approach to the solution of the integral equation in the general case is described, but only in a rough outline.
| Author | : Karl G. Guderley |
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| Total Pages | : 79 |
| Release | : 1987 |
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This report derives an integral equation for the linearized supersonic unsteady potential flow over a wing. Every integral equation formulation for a problem that appears originally in the form of a partial differential equation presupposes the availability of a fundamental solution. Such a fundamental solution is available for the problem at hand in the literature. It is rederived here to show its particular properties. The integral equation originally obtained requires hat one carry out a limiting process in which one approaches the planform from above or below. This formulation is brought into a form in which this limiting process no longer appears and one works solely with information available at the planform. Examples which can be treated analytically bring some properties which have a bearing on a numerical approach into sharper focus. Keywords: Time dependent, Linearized potential flow, Integral equation, Fundamental solutions, Unsteady aerodynamics.
| Author | : Joseph Henry Clarke |
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| Total Pages | : 60 |
| Release | : 1963 |
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The problem of supersonic flow over an inclined flatplate delta wing with supersonic edges is solved to second order in incidence. This solution for surface pressure is uniform and fully analytic. The approach utilizes a reverse-flow integral method previously developed for secondorder problems. This method is augmented by a number of techniques appropriate to its framework. The simplification over standard techniques acgieved by using these reverse-flow methods is quite substantial and makes the problem tractible. Reverse-flow procedures give a volume-surface integral relation that connects the second-order forward flow over the body of interest with the linearized reverse-flow over a related body. A singular integral equation is generated from the integral relation by introducing the edge sweep of the reverse-flow wing as a free parameter. An inversion is available which gives the second-order solution on the surface of the wing. The solution is then made uniformly valid using techniques previously developed. (Author).
| Author | : Joseph Henry Clarke |
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| Total Pages | : 42 |
| Release | : 1963 |
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A general reverse-flow relation is obtained within the framework of second-order (in surface deflection) supersonic flow theory. From this it is shown that the second-order increment in the drag of an arbitrary quasicylindrical body can be expressed as surface and volume integrals of the first-order solutions corresponding to forward and reverse flow past the body. Analogous results are obtained for second-order transverse forces and moments on an arbitrary quasiplanar wing, except the first-order reverse flow must correspond to certain zero-thickness wings. Other similar results are possible. Thus, second order aerodynamic forces on bodies may be obtained from first-order solutions by quadrature. It is also shown that the reverse-flow integral relation can yield the pressure distribution on the surface by inversion of an integral equation constructed therefrom. It is thought that these results should be particularly useful for the Mach number range between that of linearized theory and that of full hypersonic small-disturbance theory. (Author).
| Author | : Marc H. Williams |
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| Total Pages | : 41 |
| Release | : 1989 |
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An integral equation for the time dependent linearized subsonic flow over a wing has been derived in a previous report by K.G. Guderley and Maxwell Blair (AD-A 176 684). The present alternative derivation due to Marc H. Williams is presented. The difference lies in the sequence of events. The original derivation was carried out in a coordinate system moving with the wing. Williams' derivation makes the crucial step in a coordinate fixed in the undisturbed air and then carries out a transformation to wing coordinates. In addition, this derivation clarifies the relation between the integral equation for steady and unsteady flow, and derives a formulation based on the Lorentz transform. Keywords: Subsonic flow; Time dependence; Unsteady aerodynamics; Integral equations. (edc).
| Author | : Wallace Dean Hayes |
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| Total Pages | : 348 |
| Release | : 1947 |
| Genre | : Aerodynamics, Supersonic |
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| Author | : Sidney M. Harmon |
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| Total Pages | : 42 |
| Release | : 1951 |
| Genre | : Aerofoils |
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The method of relating the solution of a flow field to the solution of a simpler or known boundary-value problem is extended, subject to edge corrections for finite plan forms, to the most general type of prescribed boundary conditions on a wing in the linearized potential field at subsonic and supersonic speeds. The general procedure for determining edge corrections is given specific "correspondence formulas" are developed for rectangular wings at subsonic and supersonic speeds for cases that do not require the solution of an integral equation.
| Author | : Sydney Goldstein |
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| Total Pages | : 56 |
| Release | : 1950 |
| Genre | : Aerodynamics, Supersonic |
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| Total Pages | : 956 |
| Release | : 1988 |
| Genre | : Aeronautics |
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| Publisher | : CUP Archive |
| Total Pages | : 268 |
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