Reverse-flow Integral Methods for Second-order Supersonic Flow Theory PDF Download
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Author: Joseph Henry Clarke Publisher: ISBN: Category : Languages : en Pages : 42
Book Description
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: Joseph Henry Clarke Publisher: ISBN: Category : Languages : en Pages : 42
Book Description
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: Joseph Henry Clarke Publisher: ISBN: Category : Languages : en Pages : 60
Book Description
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: Milton Van Dyke Publisher: ISBN: Category : Aerodynamics Languages : en Pages : 36
Book Description
Slender-body theory for subsonic and supersonic flow past bodies of revolution is extended to a second approximation. Methods are developed for handling the difficulties that arise at round ends. Comparison is made with experiment and with other theories for several simple shapes.
Author: Robert M. Bennett Publisher: ISBN: Category : Aerodynamics, Supersonic Languages : en Pages : 68
Book Description
The method of integral relations is applied in a one-strip approximation to the perturbation equations governing small motions of an inclined, sharp-edged, flat surface about the mean supersonic steady flow. Algebraic expressions for low reduced-frequency aerodynamics are obtained and a set of ordinary differential equations are obtained for general oscillatory motion. Results are presented for low reduced-frequency aerodynamics and for the variation of the unsteady forces with frequency. The method gives accurate results for the aerodynamic forces at low reduced frequency which are in good agreement with available experimental data. However, for cases in which the aerodynamic forces vary rapidly with frequency, the results are qualitatively correct, but of limited accuracy. Calculations indicate that for a range of inclination angles near shock detachment such that the flow in the shock layer is low supersonic, the aerodynamic forces vary rapidly both with inclination angle and with reduced frequency.
Author: Milton D. Van Dyke Publisher: ISBN: Category : Languages : en Pages : 29
Book Description
Methods are studied for imporving the existing perturbation theories of axial and inclined supersonic flow past bodies of revolution. For axial flow, a second-order solution is developed using an interation procedure based upon the linearized solution. The resulting second-order problem is reduced to an equivalent first-order problem by discovery of a particular solution. The second-order supersonic flow can then be computed with slight modification of the Karman-Moore procedure. For inclined flow, no particular solution of the second-order equation has been discovered. The second-order solution is derived for a cone, and agrees well with the exact solution. The slender-body series expansion of the second-order solution is found to cause large inaccuracies in both the axial and inclined flows. The conclusion that first-order theory predicts the inclined flow no better than slender-body theory is shown to be erroneous. Non-linearity in lift is shown to result primarily from viscous separation of the crossflow along the after portions of the body. (Author).
Author: Joseph Henry Clarke
Author: Joseph Henry Clarke
Author: Joseph Henry Clarke
Author: Milton Van Dyke
Author: 
Author: Robert M. Bennett
Author: Milton D. Van Dyke
Author: David A. Caughey
Author: Brown University. Division of Engineering
Author: Sydney Goldstein
Author: Milton Van Van Dyke