The Principle of Independence of the Cavity Sections Expansion (Logvinovich's Principle) as the Basis for Investigation on Cavitation Flows

Abstract : For the investigation of complex non-steady cavitation flows in three dimensions it is extremely important to find a simple model which on one hand would correspond to the basic laws of a fluid stream (the laws of conservation of energy and momentum) and on the other hand would be simple enough for the numerical calculation. This model was presented by G. V. Logvinovich, and was called 'The Principle of Independence of the Cavity Sections Expansion'. In the present lecture the deduction of the principle of independence from the equation of conservation of energy is adduced. It is shown that for the stationary cavities the results obtained on the basis of the principle of independence agree with the results obtained on the basis of the slender body theory and the numerical methods as well as with the experimental data. It is shown that for the special case - the cavitation number equals zero - the cavity shape determined on the basis of the principle of independence agrees with the well-known Levinson-Gurevich asymptotic. The application of the principle of independence for the calculation of some types of the non-stationary cavities and cavities with variable external pressure (the vertical cavities in the gravitational field) is considered.