A direct boundary integral method for the three-dimensional lifting flow. (English) Zbl 0866.76050
Summary: A regularized integral formulation in velocity vector terms for three-dimensional incompressible non-lifting and lifting flows is developed. In the case of lifting flow, the circulatory flow around the body is generalized by a discrete distribution of inner vortices, and a vectorial equality in velocity terms is used as an equivalent of the equal-pressure Kutta condition. The numerical comparison with the panel method, in the case of non-lifting flow, shows the superiority of the present method. Also, a two-dimensional lifting flow is simulated (using a high spanwise wing), and comparison with the analytic solution shows a very good concordance even at high incidence.
MSC:
| 76M15 | Boundary element methods applied to problems in fluid mechanics |
| 76B10 | Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing |
Keywords:
regularized integral formulation; velocity vector; discrete distribution of inner vortices; Kutta condition; high spanwise wingReferences:
| [1] | Hess, J. L.; Smith, A. M.O., Calculation of nonlifting potential flow about arbitrary three-dimensional bodies, J. Ship Res., 8, 2, 22-44 (1964) |
| [2] | Hess, J. L., The problem of three-dimensional lifting flow and its solution by means of surface singularity distribution, Comput. Methods Appl. Mech. Engrg., 4, 183-319 (1974) · Zbl 0285.76002 |
| [3] | Dragoş, L.; Dinu, A., Application of the boundary integral equation method to subsonic flow past bodies and wings, Acta Mechanica, 86, 1, 83-93 (1991) · Zbl 0732.76065 |
| [4] | Dragoş, L., Boundary element method (BEM) in the theory of thin airfoils, Rev. Roumaine Math. Pures Appl., 34, 6, 523-531 (1989) · Zbl 0676.76056 |
| [5] | Pascal, M., Circuitazione superficiale II, Atti dei Lincei, 30, 117 (1921) · JFM 48.0950.02 |
| [6] | Bassanini, P.; Casciola, C. M.; Lancia, M. R.; Piva, R., A boundary integral formulation for the kinetic field in aerodynamics. Part II: application to unsteady 2D flows, Eur. J. Mech. B/Fluids, 11, 1, 69-92 (1991) · Zbl 0754.76058 |
| [7] | Grodtkjaer, E., A direct integral equation method for the potential flow about arbitrary bodies, The Danish Center for Applied Mathematics and Mechanics, The Technical University of Denmark, Report No. 21 (December 1971) |
| [8] | Kozlov, S. V.; Lifanov, I. K.; Mikhailov, A. A., A new approach to mathematical modelling of flow of ideal fluid around bodies, Sov. J. Numer. Anal. Math. Modelling, 6, 3, 209-222 (1991) · Zbl 0820.76012 |
| [9] | Argyris, J. H.; Scharpf, D. W., Two and three-dimensional potential flow by the method of singularities, Aero. J. Roy. Aero. Soc., 73, 959-961 (1969) |
| [10] | Gray, L. J.; Lutz, E., On the treatment of corners in the boundary element method, J. Comput. Appl. Math., 32, 369-386 (1990) · Zbl 0733.65069 |
| [11] | Guiggiani, M.; Gigante, A., A general algorithm for multidimensional Cauchy principal value integrals in the boundary element method, Trans. ASME, J. Appl. Mech., 57, 906-915 (1990) · Zbl 0735.73084 |
| [12] | Katz, J.; Plotkin, A., Low speed aerodynamics, (From Wing Theory to Panel Methods (1991), McGraw-Hill: McGraw-Hill New York) · Zbl 0976.76003 |
| [13] | Giesing, J. P., Potential flow about two-dimensional airfoils, Douglas Aircraft Company Report No. LB 31946 (May 1968) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
