Unstructured Finite Volume approach for 3-D unsteady Thermo-Structural Analysis using Bi-Conjugate Gradient Stabilized method

摘要

The structural members subjected to severe thermal environments are generally encountered in high speed flows. The optimization of these structural members needs a coupled Fluid -Thermo-Structural analysis. As a first step towards a coupled Fluid -Thermo-Structural analysis, an unsteady 3-D Thermo-Structural analysis is attempted in the present work. As finite volume method is the most popular method for fluid flow analysis. The same methodology is adopted for thermo-structural analysis in the present work. An implicit time stepping is adapted to achieve uniform time stepping while solving heat conduction and structural dynamics equation. The implementation of implicit scheme results in a system algebraic equations and are solved using Bi-Conjugate Gradient Stabilized (Bi-CGStab) method. The space discretization is carried out using arbitrarily oriented tetrahedral elements and a new least square based methodology is used for the evaluation of derivatives avoiding the reconstruction of variables at the nodes. As a first step, an unstructured finite volume code for the solution of 3-D unsteady heat conduction equation is developed. The code has been validated for various Neumann and Dirichlet boundary conditions. The results are compared with the analytical solution available for semi-infinite body heat conduction and are found to be in good agreement. Then the code is further extended for the unsteady structural dynamics equations and an integrated linear elastic Thermo- Structural analysis was carried out for the case of internally heated hollow sphere. The unstructured finite volume method in conjunction with Bi-CGStab solver results in an efficient unsteady Thermo-Structural solver and can be easily extended for an integrated Fluid-Thermo-Structural analysis.