A genuine mathematical model for one dimensional, unsteady, two phase (liquid-gas) flows is presented that intends to solve the complex problem of two phase behavior of fluids. The mechanism of the model describes the fluid flow characteristics of the mixture, supposing that the conditions for homogeneous vaporization are fulfilled and the condensate fraction of the composite fluid keeps constant. In particular, the equation of momentum conservation for the gas phase is derived from the Voinov equation. For its domain of validity (bubbly flows), the model is of hyperbolic type and can be written in the conservative form. The numerical results obtained for the water hammer phenomena show that the present work is able to supply accurate results, at least of the same degree of confidence as the results provided by an ordinary, commercial CFD code, still with a considerable reduction in computational time.

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