Impact of an ideal fluid jet on a curved wall: The inverse problem. (English) Zbl 0935.76007
Summary: This paper analyzes an ideal fluid jet impinging a wall. The usual two-dimensional model of jet flow uses an ideal, incompressible, weightless fluid, and maps this flow in a way that reduces it to a problem of complex analysis that cannot be solved analytically. An efficient procedure is presented here for solving the inverse problem numerically in the case of an arbitrary wall shape, i.e. the design of a wall corresponding to a prescribed velocity (or pressure) distribution. In similar studies, as in airfoil design, important constraints have to be applied to the prescribed distribution in order to ensure the existence of a solution. Not only is this not the case here, but also a constraint must be added to impose the uniqueness of the solution.
MSC:
| 76B10 | Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing |
| 76M40 | Complex variables methods applied to problems in fluid mechanics |
| 35R30 | Inverse problems for PDEs |
Software:
kirchReferences:
| [1] | Birkhoff, G.; Zarantonello, E. H., Jets, Wakes and Cavities (1957), Academic Press · Zbl 0077.18703 |
| [2] | Dias, F.; Elcrat, A. R.; Trefethen, L. N., Ideal jet flow in two dimensions, J. Fluid Mech., 185, 275-288 (1987) · Zbl 0633.76013 |
| [3] | Dias, F.; Vanden-Broeck, J.-M., Flows emerging from a nozzle and falling under gravity, J. Fluid Mech., 213, 465-477 (1990) · Zbl 0698.76049 |
| [4] | Elcrat, A. R.; Trefethen, L. N., Classical free-streamline flow over a polygonal obstacle, J. Comput. Appl. Math., 14, 251-265 (1986) · Zbl 0577.76018 |
| [5] | Gurevich, M. I., Theory of Jets in an Ideal Fluid (1966), Pergamon Press |
| [6] | Hureau, J.; Brunon, E.; Legallais, Ph., Ideal free streamline flow over a curve obstacle, J. Comput. Appl. Math., 72, 193-214 (1996) · Zbl 0857.76015 |
| [7] | Hureau, J.; Legallais, Ph., Résolution du problème inverse pour un profil, AAAF J., 32, 3.3-3.10 (1996) |
| [8] | Hureau, J.; Mudry, M.; Nieto, J.-L., Une méthode générale de numérisation d’écoulements avec sillage de Helmholtz, C.R. Acad. Sci. Paris, 305, 331-334 (1987), série II · Zbl 0625.76015 |
| [9] | Hureau, J.; Weber, R., Impinging free jets of ideal fluid, J. Fluid Mech., 372, 357-374 (1998) · Zbl 0922.76066 |
| [10] | Jacob, C., Introduction Mathématiqueàla Mécanique des Fluides (1959), Gauthier-Villars · Zbl 0092.42502 |
| [11] | Lévi-Civita, T., Scie e leggi di resistenzia, Rendiconti del circolo Mathematico di Palermo, 23 (1907) · JFM 38.0753.04 |
| [12] | Lighthill, M. J., A new method of two-dimensional aerodynamic design, Reports and Memorandum, \(n^o 2112 (1945)\) |
| [13] | Milne-Thomson, L. M., Theoretical Hydrodynamics (1968), Macmillan & Co Ltd. · Zbl 0164.55802 |
| [14] | Peng, W.; Parker, D. F., An ideal fluid jet impinging on an uneven wall, J. Fluid Mech., 333, 231-255 (1997) · Zbl 0894.76008 |
| [15] | Toison, F.; Hureau, J., Calcul de la surface libre d’un canal dont le radier a une forme quelconque, (Sixièmes journées de l’hydrodynamique, Nantes (1997)), 107-118 |
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