Cavitation Noise Modelling at 

 Ship Hydrodynamic Laboratories 



Gavriel A. Matveyev 



and 

 Alexei S. Gorshkoff 

 Krylov Ship Research Institute 

 Leningrad, USSR 



ABSTRACT 



Theoretical and experimental correlation of visual 

 and accoustical effects of cavitation are considered. 

 The Froude similarity is treated critically because 

 of the pressure effects on the coefficient of cavity 

 energy transformation into cavitation noise as well 

 as because of the increase of noise absorption or 

 cavitation resistance of water. Though in large 

 cavitation tunnels which have no free surface the 

 nonstationary boundary conditions can be reproduced 

 less perfectly, their capability of simulation 

 at full-scale pressure is regarded as the leading 

 factor. It is suggested that extrapolation formulae 

 should take into account the effect of the rate of 

 pressure increase (or pressure gradient) in the 

 cavity collapse area. This corresponds to an 

 increase in the square of acoustic pressure on the 

 model, compared to the prototype, inversely pro- 

 portional to the linear scale of modelling. 



1. COMPARISON OF VISUAL AND ACOUSTIC EFFECTS OF 

 CAVITATION 



The occurrence of strong visual and noise effects 

 of cavitation are usually considered to be coinci- 

 dent. When this coincidence is actually the case, 

 it provides certain conveniences. The measurement 

 of noisiness makes it possible to detect cavitation 

 on structural elements not easily accessible for 

 inspection. Visual observation of cavitation on 

 models is used for the prediction of noisiness of 

 various prototypes. However, the experiments 

 involving visual and acoustical recording of 

 cavitation indicate that there may be a considerable 

 discrepancy between these two manifestations of 

 cavitation. It is interesting to discover the 

 nature and the cause of the discrepancy by means 

 of a mathematical model of an elementary cavitation 

 process which is described by the well-known 

 differential equation of a single spherical cavity 

 growth 



3-2 



RR + J R^ 



fh - 1 



(1) 



Here R and R are the cavity radius and its initial 

 value, respectively; p and p^ are the variable 

 component and the initial value of ambient pressure; 

 P(3» P, Yi and V are vapor pressure, density, and 

 the surface tension and kinematic tension coefficient, 

 respectively. 



Computations were made by equation (1) for the 

 negative pressure pulse 



p{T) 



Pm-re 



1-T 



(2) 



which is characterized by the time scale, T, and 

 the amplitude, p^. Such a pulse represents the 

 region of negative pressure having the length, L, 

 on the profile with the maximum negative pressure 



coefficient, C 



pm' 

 pU^ 



in the flow with velocity, U: 



"pm 



L 

 V 



Linearization of Eq. (1) with respect to 6 = z-z 

 for the small-amplitude oscillation frequency gives 



^-^ 



/3<Po-Pd 



2Y 



2v 



R 



(3) 



According to (3), oscillatory properties of the 

 cavity disappear at pg = 1 ata when Rg < 10~^ m. 

 Bearing in mind that the natural period is limited 

 by the pulse duration, T, computations were made 

 for 



lo"* kg/m^; R = 10 ^+10"^ m; L = IQ-^+lO-lm; 



Po 



V = 10+20 m/s 



pm 



1.5. 



494 



