L. Hadj-Taïeb, E. Hadj-Taïeb, and C. Thirriot
Transient flow, vapour cavitation, finite differences, Lax–Wendroff scheme
A mathematical model which describes the transient flow with vapour cavitation is presented. Homogeneous bubbly cavitating two-phase flow will occur as a consequence of pressure reduction. By analogy with the gas release phenomenon, when the liquid pressure in the pipe drops below the saturation vapour pressure, vapour will be released from the liquid according to Henry’s law. The distribution of the formed vapour bubbles is assumed to be uniform and the vapour within the bubbles acts isothermally. The two constitutive equations of continuity and momentum, written in conservation form, yield to a quasi-homogeneous flow model which have the same form inside as well as outside the cavitation region, but with different density expressions as pressure functions. A two-step finite differences numerical scheme is applied for the computation of the transient cavitating flow. Computation results are favourably compared with some numerical examples obtained from relevant literature. Consistent agreement has been obtained between numerical predictions and experimental measurements in prototype pipelines.
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