Cavitation Model

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Cav­i­ta­tion is a com­plex mul­ti­phase hy­dro­dy­nam­ics phe­nom­e­non that has re­ceived much at­ten­tion over the past sev­er­al decades. In a cav­i­ta­tion flow, a gas phase can be gen­er­at­ed in the liq­uid phase if the lo­cal pres­sure drops be­low the va­por pres­sure. In such flow con­di­tion, the flu­id den­si­ties are rapid­ly changed from the liq­uid (~ 880 kg/­m3 in the case of diesel fu­el) to va­por phase (~ 1.2 kg/­m3). Such a low-pres­sure con­di­tion can be gen­er­at­ed in a liq­uid flow, for ex­am­ple, due to abrupt turn­ing of the flow di­rec­tion.

To cap­ture the mul­ti­phase na­ture of the flow, a cal­cu­la­tion mod­el must take in­to ac­count the ma­jor physics in­volved in the cav­i­tat­ing flow. One of most im­por­tant and crit­i­cal phe­nom­e­na is the chang­ing of the speed of sound in the cav­i­tat­ing flow. Fig­ure 1 shows the vari­a­tion of the speed of sound for the mix­ture of ni­tro­gen gas and liq­uid(wa­ter) as a func­tion of their vol­ume frac­tion, as­sum­ing that in the pure gas and liq­uid phas­es, the val­ues are 340 m/­s and 1450 m/­s, re­spec­tive­ly. In the mix­ture, the speed of sound can drop to a val­ue sig­nif­i­cant­ly less than ei­ther, for ex­am­ple, 10 m/­s. There­fore, su­per­son­ic flow can hap­pen and should be tak­en in­to con­sid­er­a­tion in the mod­el, es­pe­cial­ly, for the high-pres­sure, high-speed in­ter­nal flow as shown in Fig. 2.

A num­ber of ap­proach­es were made to mod­el the com­plex cav­i­tat­ing flows, which can be clas­si­fied in two ma­jor cat­e­gories. The first ap­proach starts with con­struct­ing an equa­tion of state (EOS) cor­re­spond­ing to the liq­uid, the gas, and the mix­ture phase, re­spec­tive­ly. Since the EOSs in the gas and liq­uid phase are well de­fined, the well posed­ is al­ways guar­an­teed when a valid EOS in the mix­ture phase is pro­vid­ed. The sec­ond ap­proach is the non-equi­lib­ri­um mul­ti­phase flow mod­el, which does not need to use the EOS for the mix­ture phase. Rather, the in­ter­face vari­ables in the mix­ture must cal­cu­late through the re­lax­ation process, which ac­com­pa­nies an aux­il­iary equa­tion to clo­sure the sys­tems. Al­so, the cou­pling process be­tween the gov­ern­ing equa­tions would be re­quired.

So far, in LS-DY­NA, a sim­ple but ro­bust barotrop­ic mod­el is im­ple­ment­ed by de­scrib­ing an EOS in the gas, liq­uid, and mix­ture (ho­mo­ge­neous equi­lib­ri­um mod­el, HEM).