Pressure Fields and Cavitation 

 in Turbulent Shear Flows 



Roger E. A. Arndt 

 University of Minnesota 

 Minneapolis , Minnesota 



William K. George 



State University of New York at Buffalo 



Buffalo, New York 



ABSTRACT 



Cavitation in turbulent shear flows is the result 

 of a complex interaction between an unsteady 

 pressure field and a distribution of free stream 

 nuclei. Experimental evidence indicates that 

 cavitation is incited by negative peaks in pressure 

 that are as high as ten times the rms level. This 

 paper reviews the current state of knowledge of 

 turbulent pressure fields and presents new theory 

 on spectra in a Lagrangian frame of reference. 

 Cavitation data are analyzed in terms of the avail- 

 able theory on the unsteady pressure field. It is 

 postulated that one heretofore unconsidered factor 

 in cavitation scaling is the highly intermittent 

 pressure fluctuations which contribute to the high 

 frequency end of the pressure spectrum. Because of 

 limitations on the response time of cavitation 

 nuclei , these pressure fluctuations play no role 

 in the inception process in laboratory experiments. 

 However, in large scale prototype flows, cavitation 

 nuclei are relatively more responsive to a wider 

 range of the pressure spectrum and this can lead to 

 substantially higher values of the critical cavi- 

 tation index. Unfortunately, this issue is clouded 

 by the fact that higher cavitation indices can be 

 found in prototype flows because of gas content 

 effects. Some cavitation noise data are also 

 examined within the context of available theory. 

 The spectrum of cavitation noise in free shear 

 flows has some similarity to the noise data found 

 by Blake et al. (1977) with the exception that there 

 appears to be a greater uncertainty in the scaling 

 of the rate of cavitation events which leads to a 

 substantial spread in the available data. 



1 . INTRODUCTION 



The physical processes involved in cavitation 

 inception have been studied for many years . Much 

 of this research has been directed toward an under- 



standing of the dynamics of bubble growth and the 

 determination of the sources of cavitation nuclei 

 and their size and number in a given flow situation. 

 This research has led to a general understanding of 

 some of the environmental factors involved in 

 scaling experimental results from model to prototype. 

 More recently, considerable attention has been 

 paid to the details of the boundary layer flow over 

 streamlined bodies and the role of viscous effects 

 in the cavitation process. This research has shown 

 that viscous effects such as laminar separation 

 and transition to turbulence can have a major impact 

 on the inception process and that there can be 

 considerable variation between model and prototype 

 in the critical conditions for cavitation. 



In the absence of viscous effects, the scaling 

 problem reduces to an understanding of the size 

 distribution of nuclei and the temporal response 

 of these nuclei to pressure variations as viewed 

 in a Lagrangian frame of reference. This was first 

 treated in detail by Plesset (1949) . As already 

 mentioned, consideration of viscous effects shows 

 that the cavitation inception process can be 

 considerably altered by either laminar separation 

 or transition to turbulent flow. Obviously these 

 phenomena are interrelated and are strongly Reynolds 

 number dependent. The recognition of the importance 

 of these factors has had considerable impact on the 

 direction of cavitation research in recent years. 

 Several papers in this symposium deal directly with 

 this aspect of the cavitation scaling problem. 



It is reasonably well understood that intense 

 pressure fluctuations, either at the trailing edge 

 of a laminar separation bubble or in the transition 

 region, can have a major effect on the inception 

 process on streamlined bodies. However, these 

 phenomena will be excluded from this review. The 

 focus of this paper will be on the relationship 

 between the temporal pressure field and cavitation 

 inception in free turbulent shear flows and fully 

 developed boundary layer flows. Scant attention 

 has been given to this problem, even though the 



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