Sensitivity Analysis of Two-Phase Flow Problems

Publisher Website
Google Scholar
Abstract
The mathematical derivation and application of two deterministic sensitivity analysis methods, the direct approach of sensitivity (DAS) and the adjoint sensitivity method (ASM), are presented for two-phase flow problems. The physical problems investigated are formulated by the transient onedimensional two-phase flow diffusion model, which consists of a system of four coupled quasi-linear first-order partial differential equations. The DAS method provides the sensitivity coefficients of all primary dependent variables at each time and space location with respect to a single input parameter. On the other hand, the ASM provides the sensitivity coefficients of a single response function at a specified time and space location with respect to all input parameters. The systems of governing equations of both sensitivity methods developed possess the same characteristic directions as those of the original physical model. Therefore, the same numerical methods for the solution of these equations have been selected as for the solution of the physical problem, i.e., Turner scheme and modified Turner (NAIAD) scheme. Special techniques to incorporate the boundary conditions of the ASM governing equations for each numerical scheme have been developed. The sensitivity coefficients computed by both methods have been verified against results from standard parametric studies. Two sample problems are thoroughly investigated. The first problem considers the transient fluid behavior in a uniformly heated channel subjected to an inlet flow decay. The second problem considers the transient fluid response within the same channel when a pressure step change at the channel inlet is imposed. Both methods predict satisfactorily the sensitivity coefficient behavior in space and time in comparison with parametric studies, even when a moving boiling boundary exists within the flow field. Certain coefficients in the thermodynamic correlations of the liquid density and the liquid saturation enthalpy, as well as the boundary conditions of the problems, were found to be the most “sensitive” input parameters in both problems investigated. Some input parameters of minor significance in the steady-state conditions were found to be very “influential” during the transient and vice versa. The behavior of most of the sensitivity coefficients, in space and time, cannot be estimated without a systematic sensitivity analysis method.