Adjoint sensitivity analysis of the two-phase two-fluid model based on an approximate Riemann solver

Riemann solver;adjoint method;two-phase flow

Hu, Guojun

关键词: Riemann solver;    adjoint method;    two-phase flow;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/101475/HU-DISSERTATION-2018.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

A new shock-capturing upwind numerical solver (i.e. forward solver) and an adjoint sensitivity analysis framework for the two-phase two-fluid model are developed and verified. Both the numerical solver and the adjoint sensitivity analysis framework are based on an analytical analysis of the two-phase two-fluid model.The challenge (due to the arbitrary equation of state) in the analytical analysis of the two-phase system is overcome by introducing several new auxiliary variables. With the help of new auxiliary variables and thermodynamic transformations, the Jacobian matrix of the system can be simplified to a well-structured form, which is convenient for an analytical analysis. Approximate eigenvalues and eigenvectors are obtained using the difference in the thermodynamic properties of liquid and gas phases. The approximate eigenvalues and eigenvectors are essential for constructing the upwind numerical solver, because they provide correct upwind information of the system. Both the numerical solver and the adjoint sensitivity analysis framework are verified with several numerical tests.For the forward tests, the results show that the solver is stable, accurate, and robust. Results from the new solver are in a very good agreement with either analytical solution or measurement data. The grid convergence study shows that the solver using a Roe-type numerical flux is first-order accurate in space and the solver using a WENO-type numerical flux is at least second-order accurate in space. For the adjoint tests, the results show that the adjoint sensitivity analysis framework works well for both steady-state problems and time-dependent problems. The adjoint sensitivities (with respect to initial conditions, boundary conditions, or physical model parameters) are verified by either analytical sensitivities or forward sensitivities.A critical and unique feature of the new solver is that the formulation does not depend on the form of equation of state, which ensures that the solver is applicable to practical two-phase flow problems, such as a boiling pipe. The successful application of the solver to a boiling pipe is very encouraging, as it opens up the possibility of applying many other advanced methods to two-phase flow problems.