On the boundary, which represents the cavity surface, the gas velocity equals to the water velocity . The velocity vector is tangential to the surface. The gas temperature equals to the water temperature. (12) where is mid-cavity section area, is atmospheric pressure, is hydrostatic pressure, is gas volume flow rate, is water velocity, is cavitation number at the cavity bottom. On the outlet boundary, the static pressure is determined from the gas loss law. To validate this method several typical cases were computed and the results were compared with known experimental data. 2.1. Asymmetrical cavity deformation induced by gas jets interaction with liquid surface An attempt to estimate cavity shape when the round subsonic jet accumulates on its edge was performed in the work [9]. The pressure distribution was taken as the results of the experiment where the jet interacted with the flat barrier. The results were compared with the results of the experiment. Figure 22 shows the scheme of the experimental assembly. The ventilated cavity is formed behind cavitatot moving underwater, the inflow jet is directed toward the water flow. Fig. 22: Experimental assembly scheme Two nozzles are installed inside the cavity, they are perpendicular to the cavity axis. Figure 15 shows the cavity photo, which was made in the experiment. Fig. 23: Cavity photo Data necessary for the computation. The cavitator velocity is m/sec, its radius is mm. Cavitation number of the non-disturbed cavity is . Cavity is deformed by the subsonic jets flowed from two symmetrically disposed nozzles. Nozzle diameter is mm. The distance from the cavitator to the center of the nozzle outlet section along the cavity axis is mm. The hydrostatic pressure is Pa. Inflowing gas has stagnation temperature К. Inflow gas mass flowrate is kg/sec. Relative impulse of the inflowing gas is . Series of calculations under different specific jet impulses were carried out. Further the results for two relative impulse values of each jet and is presented. These values correspond to the mass flow of the gas kg/sec and kg/sec. Computational grid contains 457000 cells. Time step is sec. Figure 24a shows the computational domain boundary before deformations and Figure 24b shows computed boundary deformed under gas jets. Fig. 24a: Half of the cavity before deformation Fig. 24b: Half of the cavity deformed under the influence of the inclined gas jet Figure 25 shows the cavity number distribution along the surface of the cavity bow part. The cavity pressure at the bow is somewhat higher then the pressure of the cavity main part. It is due to the inflowing jet interaction with water surface that has considerable relative impulse. The cavity number distribution has peak at the region of the interaction jet with water. Fig. 25: The cavity number distribution along the surface of the cavity Figure 26 shows the gas flow velocity distribution in the longitudinal section of the cavity. Fig. 26: The gas flow velocity distribution in the longitudinal section of the cavity Figures 27-28 show disturbed and non-disturbed cavity profiles in the longitudinal section passing the centre of the nozzle, which were received in [9] and numericaly. Fig. 27: disturbed and non-disturbed cavity profiles (calculation and experiment). The jet impulse is , the angle of the nozzle installation is 900 Fig.
28: disturbed and non-disturbed cavity profiles (calculation and experiment). The jet impulse is , the angle of the nozzle installation is 900 Figure 29 shows the plots of the flat cross sections, that are obtained in this work and in [9] for and the angle of the nozzle installation 90 degrees. There are some differences, but they are in the range of accuracy that was accepted deriving (8). Fig. 29: Cavity cross sections, The compare of the result of the numerical computation and the experimental data shows their good correspondence. So we can make a conclusion about good choice of method and its realization according to these types of tasks. CONCLUSIONS Two numerical methods allowing for modeling of supercavitational flows were considered. The first method is based on numerical solving of the multiphase Reynold equations. This method is robust in a wide range of stationary and non-stationary cases. The method was verified by solving a series of typical unit problems. It was shown that it is possible to get physically valid results only in the framework of inhomogeneous flow model. The predicted cavity length is shorter than that observed in experiments. The issue of gas losses from the cavity remains to be clarified. The main shortcomings of the method are extensive computational recourses and long computational time. This method requires further careful validation that could be done by considering typical unit problems. In some cases, for example, interaction gas jets with the cavity walls, the aforementioned shortcomings can be avoided using the method developed in this work. Namely, only the gas flow in cavity is computed numerically, while the cavity shape is calculated using analytical expressions, which were validated by numerous experiments. The gas losses are predicted using experimental correlations. The method was applied to several problems. The numerical results agree well with available experimental data. This encourages us to use this method for more realistic configurations. REFERENCES 1. J.W. Lindau, R.F. Kunz, S. Venkateswaran, D.A. Boger Application of preconditioned, multiple-species, Navier-Stokes models to cavitating flows // Proceedings of 4th International Symposium on Cavitation. California Institute of Technology Pasadena, California, USA, 20-23 June, 2001 2. Jules W. Lindau, Robert F. Kunz, Jason M. Mulherin, James J. Dreyer, David R. Stinebring Fully Coupled, 6-Dof To URANS, Modeling Of Cavitating Flows Around A Supercavitating Vehicle // 5th International Symposium on Cavitation (CAV2003), Osaka, Japan, November 1-4, 2003 3. A. Hosangadi, V. Ahuja, and S. Arunajatesan A Generalized Compressible Cavitation Model // Proceedings of 4th International Symposium on Cavitation. California Institute of Technology Pasadena, California, USA, 20-23 June, 2001 4. G.V. Logvinovich Hydrodunemic of the flow with free surfaces. -- Kiev: Naukova dumke, 1969 (in Russia) 5. Ansys CFX 10.0 User's Manual 6. A.L. Stasenko Physics mechanics of multiphase flows: Tutorial. ¬ M.: MIPT, 2004 (in Russia) 7. A.N. Varyukhin Deformations of the cavity boundaries by gas jets.-- J. Applied mechanics and technical physics, Novosibirsk, 2008 (in Russia) 8. Y.F. Zhuravlev Methods of disturbances in space jet-stream flows. -- TsAGI works, 1532, Moscow 1973 (in Russia) 9. Y.F. Zhuravlev, B.I. Romanovsky Cavity boundary deformations by gas jets flowing inside it.--
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