Transonic Flow past Lifting Airfoils
01 Dec 1973-AIAA Journal (American Institute of Aeronautics and Astronautics (AIAA))-Vol. 11, Iss: 12, pp 1766-1768
About: This article is published in AIAA Journal.The article was published on 1973-12-01. It has received 6 citations till now. The article focuses on the topics: Subsonic and transonic wind tunnel & Transonic.
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TL;DR: In this article, a new subgrid-scale turbulence model involving all the transport equations of the subgrid scale stresses and including a dissipation rate equation is proposed for large-eddy simulation (LES) of unsteady flows which present nonequilibrium turbulence spectra.
Abstract: A new subgrid-scale turbulence model involving all the transport equations of the subgrid-scale stresses and including a dissipation rate equation is proposed for large-eddy simulation (LES) of unsteady flows which present nonequilibrium turbulence spectra. Such a situation in flow physics occurs when unsteadiness is created by forced boundary conditions, but also in more complex situations, when natural unsteadiness develops due to the existence of organized eddies. This latter phenomenon explains the instability found in a porous-walled chamber with mass injection. Due to the high value of Reynolds number, the presence of wall boundaries, and the use of relatively coarse grids, the spectral cutoff may be located before the inertial zone of the energy spectrum. The use of transport equations for all the subgrid-scale stress components allows us to take into account more precisely the turbulent processes of production, transfer, pressure redistribution effects, and dissipation, and the concept of turbulent viscosity is no longer necessary. Moreover, some backscatter effects can possibly arise. As a result of modeling in the spectral space, a formally continuous derivation of the model is obtained when the cutoff location is varied, which guaranties compatibility with the two extreme limits that are the full statistical Reynolds stress transport model of Launder and Shima and direct numerical simulation. In the present approach, due to the presence of the subgrid-scale pressure-strain correlation term in the stress equations, the new subgrid model is able to account for history and nonlocal effects of the turbulence interactions, and also to describe more accurately the anisotropy of the turbulence field. The present model is first calibrated on the well-known fully turbulent channel flow. For this test case, the LES simulation reveals that the computed velocities and Reynolds stresses agree very well with the DNS data. The application to the channel flow with wall mass injection which undergoes a transition process from laminar to turbulent regime and the development of natural unsteadiness is then considered for illustrating the potentials of the method. LES results are compared with experimental data including the velocity components, the turbulent stresses, and the transition location. A satisfactory agreement is obtained for both the mean quantities and the turbulent field. In addition, structural information of the flow is provided.
167 citations
10 Jan 2000
9 citations
TL;DR: In this article, an approach to lifting wing theory at Mach one is presented that utilizes an integral method similar to the Karman-Pohlhausen method in boundary layer theory, which can easily be used to determine the lift on wings of finite aspect ratio and also to solve transient lifting problems.
Abstract: An approach to lifting wing theory at Mach one is presented that utilizes an integral method similar to the Karman-Pohlhausen method in boundary layer theory. As in any integral method the results obtained are approximate in nature. Nonetheless, comparison with experimental data shows good agreement in cases for which experimental data are available. The method can easily be used to determine the lift on wings of finite aspect ratio and also to solve transient lifting problems. The method is demonstrated by solving for the pressure distribution on a lifting airfoil of arbitrary symmetric cross-section, the lift on a wing of rectangular planform, and the transient lift on an airfoil due to a sudden change in angle of attack. These cases were chosen to illustrate the versatility of the method and are not meant to be exhaustive of all possibilities. The computational time required to obtain numerical results is very small in all cases considered.
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References
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01 May 1957
TL;DR: In this article, a method for the approximate solution of the nonlinear equations transonic flow theory is presented for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows.
Abstract: A method is presented for the approximate solution of the nonlinear equations transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.
79 citations
31 Dec 1967
TL;DR: In this article, a new development of the analytical hodograph theory of Chaplygin, Cherry and Lighthill is based on integral transform methods, and transonic potential flows around a family of non-lifting and lifting quasi-elliptical two-dimensional aerofoils are obtained, and various practical examples shown.
Abstract: A new development of the analytical hodograph theory of Chaplygin, Cherry and Lighthill is based on integral transform methods. Transonic potential flows around a family of both non-lifting and lifting quasi-elliptical two-dimensional aerofoils are obtained, and various practical examples shown. The closure of a-symmetrical aerofoils in the physical plane is ensured by a special construction. In view of the longTStanding debate on this question, a discussion of the physical aspects of these flows has been added as an Appendix. Other Appendices discuss local aspects of the hodograph transformation, and numerical problems.
53 citations
01 Jan 1971
TL;DR: Generalized relaxation methods application to transonic flow problems, combining with numerical integration theory for ordinary differential equations as mentioned in this paper have been applied to the problem of transonic fluid flow problems in the literature.
Abstract: Generalized relaxation methods application to transonic flow problems, combining with numerical integration theory for ordinary differential equations
24 citations