REASONS FOR THE OCCURRENCE OF SPURIOUS SOLUTIONS IN 2-PHASE FLOW CODES

This paper discusses the mathematical models used as a basis for the c alculation of critical conditions in two-phase flow. In practice, solu tions are obtained with the aid of discretized versions of such models . It has now been established that the portrait of solutions in the ph ase space of any analytic model does not stand in a one-to-one relatio n to the map of solutions of any discretized version of such a model. As a result, computer outputs may develop spurious solutions. Branches of such spurious solutions often depart from the correct analytic sol ution in a haphazard manner, and bear no relation to the correct solut ion. Such degenerate solutions do not differ from their correct counte rparts by merely containing acceptable numerical or truncation errors, but fail to fit the correct solutions even approximately. In the case of the most common analytic models used in two-phase flows through ch annels of varying cross-sectional areas, spurious solutions develop wh en the correct solution passes through or close to the saddle point in phase space. The paper examines two modes of obtaining critical-flow solutions. In some cases, a steady-state version (partial derivative p artial derivative t = 0) of the more general model is used. In other c ases, the full equation (partial derivative/partial derivative t not e qual 0) is used, and the solution contains a transient but converges t o the steady-state mode. This paper shows that the implied critical cr oss-section locations are identical in either mode of operation. The r eason for the occurrence of spurious solutions is found in a term whic h assumes the indeterminate singular form 0/0 in the steady-state vers ion of the model. By a suitable transformation, it is shown that this term is also present in the factor of partial derivative sigma/partial derivative t in the time-dependent version. It has been shown earlier that solutions passing through the singular point can be obtained wit h the aid of the theory of dynamical systems. In order to exclude the possibility of the appearance of spurious solutions, the numerical cod e, in either version, must be so arranged as to start the integration with the singular point.