Abstract
The plane problem of the plate planing at a constant velocity on the surface of a heavy, ideal, incompressible, finite-depth fluid is considered. The approximate, depth-independent expression for the force acting on the plate is derived from the linear distribution of the fluid velocity along the plate and the height of the flow stagnation point, without regard for jet formation near the leading edge. In this approximate formulation the plate drag depends on its velocity and the trailing edge immersion and does not depend on the planing angle. Experiments and numerical calculations in the exact formulation are performed in the near-critical flow regimes. It is shown that the wave patterns in the experiments and numerical calculations coincide, the formula for the drag being in agreement with the numerical experiments. An approximate criterion of the formation of waves going away from the plate in the forward direction is proposed.
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References
L. I. Sedov, Two-Dimensional Problems in Hydromechanics and Aeromechanics (Interscience Publ. Co., New York, 1965).
L. N. Sretenskii, Theory of Wave Motions of Fluids [in Russian] (Nauka, Moscow, 1977).
D. V. Maklakov, “New Analytical Formulas and Theorems for theWave Drag,” Uch. Zap. Kazan Un-ta, Ser. Fiz.-Mat. Nauki 157 (3), 72 (2015).
Handbook of an Aircraft Designer, Vol. II: Hydromechanics of Hydroplanes [in Russian] (TsAGI, 1938).
L. M. Kotlyar, “Heavy Fluid Outflow from beneath a Shield,” in: Proceedings of a Seminar on Boundary Value Problems [in Russian] (Kazan, 1970), issue 7, p. 160.
S. Chen and G. Doolen, “Lattice Boltzmann Method for Fluid Flows,” Annu. Rev. Fluid Mech. 30, 329 (1998).
S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (OxfordUniv. Press,Oxford, 2001).
Xflow—a New Program Complex for Simulating Physical Processes Related with Hydrogasdynamics and Heat and Mass Transfer, http://www.cadmaster.ru/magazin/articles/cm-60-13.html
M. A. Lavrent’ev and B. V. Shabat, Methods of Theory of Functions of a Complex Variable [in Russian] (Nauka, Moscow, 1973).
Yu. L. Yakimov, “Approximate Formula for Extension at the Conformal Mapping of a Domain Having a Narrow Region,” Sib. Mat. Zh. 3 (6), 956 (1962).
M. A. Lavrent’ev and B.V. Shabat, Problems of Fluid Dynamics and Their Mathematical Models [in Russian] (Nauka, Moscow, 1977).
A. Yu. Yakimov, “Equations for NonlinearWaves on ShallowWater,” Fluid Dynamics 47 (6), 789 (2012).
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Original Russian Text © E.V. Filatov, A.Yu. Yakimov, 2018, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2018, No. 5, pp. 29–37.
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Filatov, E.V., Yakimov, A.Y. Drag of a Plate Planing on the Shallow Water with Formation of Waves. Fluid Dyn 53, 608–615 (2018). https://doi.org/10.1134/S0015462818050075
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DOI: https://doi.org/10.1134/S0015462818050075