476 Conference of Global Chinese Scholars on Hydrodynamics STOCHASTIC STUDY OF CAVITATION BUBBLES NEAR BOUNDARY WALL Li S, Zuo Z G, Li S C* School of Engineering, Warwick University, Coventry, UK *The corresponding author, E-mail: s.li@warwick.ac.uk ABSTRACT: A proposed Markov stochastic model for the random behavior of cavitation bubble(s) near compliant walls is introduced. Also for verification of the model a versatile facility for observing the effects of wall compliance on the stochastic behavior of single/multi-bubbles has been designed and built purposely at the Fluid Dynamics Research Centre, the University of Warwick (UK). This paper briefly intro- duces the previous work and the testing facility as well as current on going work. KEY WORDS: cavitation, bubble behavior, bubble boundary interaction, Markov model 1. Introduction The effects of wall compliance on boundary layer instability, transition and drag reduction have been extensive investigated. The potential of its cavitation-mitigation is also studied experimentally [1] and numerically [2] in the case of a Static Single Bubble (SSB). In real flow environments, we need to know if these two types of effects can play an effective-joint role in cavitation mitigation*. A stochastic model has been proposed to simulate the behavior of cavitation bubble [3]. Recently a versatile facility was designed to observe wall compliance influences on the statistical charac- teristics of laser induced single bubble and real cavitation bubbles under various flow/boundary conditions [4].In order to capture the fast moving and tiny bubbles, extremely high speed camera systems have been adopted for the observation of bubble behavior. 2. Stochastic Model 2.1 SSB study The SSB studies show that artificially induced single bubble in a static-open fluid will collapse less violently with bubble migration (towards the boundary wall) reduced or even repelled, subject to three parameters: the initial relative distance (γ), wall inertia (m*) and stiffness (k*) ,  = max / R S , * m = 3 max / R m  , * k = max ) /( R p p k c   . Here, S is the initial distance of bubble centre to the wall; Rmax is the maximum radius of bubble, m is the wall inertia, k is the stiffness, p∞ is a reference pressure and pc is the saturated vapour pressure. 2.2. Random nature of real bubbles ‘The behaviour of cavitation bubbles in real flow situation is a multibubble performance pos- sessing strong stochasticity’. The stochasticity ‘originates from the randomness of nuclei in the liquid and from the cavitation mechanism by which the nuclei are cavitated; and is further enhanced and characterised by three kind interactions throughout the entire life time of bubbles. One is the bubble- boundary interaction. The second is the interaction between bubbles. The third is between the bubbles and the unsteady/fluctuating flow field’ [5]. There- fore, the bubble behaviour through out its life, i.e. its inception, growth, collapse and rebound, is an en- tirely stochastic process. The quantities characterising the random move- ment (or behaviour) of the bubbles, ) (   , are sug- gested as )) ( ), ( ), ( ( ) (      J Y R  . Here, Ω is a 3-dimensional discrete-state space composed of a set of 3 random variables. They are characteristic bubble size R(ω) (e.g. the volume- equivalent radius Rvol), its distance to the wall Y(ω) (or its relative value Y/Rmax), and micro-jet magnitude J(ω) (at least, three values of -1, 0 and 1, that represent repelling, no and attracting micro-jets, can be assigned to J(ω)). Based on the SSB studies,these * The fact that cavitation is closely associated with the pressure-fluctuation level or laminar turbulence transition gives us a clue that these compliance-effects, on both the bubble collapsing and the transition postponement, could be thus jointly made contributions to the cavitation mitigation