G050046 数学的に適切な2流体モデル方程式について

抄録

It is well-known that a conventional two-fluid model equation system, one-pressure two-fluid model equation system, is mathematically ill-posed as an initial-value problem. In order to improve this problem, it has recently been reported that the introduction of an interfacial pressure term is effective. In the present study, eigenvalue analysis of a three-pressure two-fluid model equation system, where a surface-averaged pressure of a liquid on interface is incorporated so as to treat violent collapse of cavitation bubble, is performed, and then the results are compared with the conventional those. As a result, it is shown that the conventional model equation system has two complex eigenvalues in the range of the nearly equal gas and liquid steady uniform flow velocities, whereas all eigenvalues of three-pressure two-fluid model equation system are real in the wide region of the gas and liquid velocities and void fraction. Consequently, the three-pressure two-fluid model equation system is mathematically well-posed.