Development of A Navier Stokes Solver for Compressible Viscous Flows and Coupling It With Optimızation Codes

Abstract

In the thesis, Navier Stokes solvers have been developed for incompressible and compressible flows. Then the codes have been matched with the optimization algorithms and optimisation studies have been performed. For an incompressible 2d flow, only 3 equations (u, v, P) are required whereas for a compressible 2d flow 5 equations (u, v, P, T, ρ) are required. Compressible flow solution takes longer to complete in general. Normally available commercial flow solvers work either as incompressible or compressible flow solvers. Faster convergence is achieved by using a lower order algorithm, or using a coarse mesh or solving the problem as incompressible. Besides, in computational aerodynamics fast solutions for 3d geometries are achieved first for incompressible flow, then improvement in the solution is obtained with a compressible solver, so generally two solutions are performed. (two step approach) The main idea here is to solve the problem as if it was an incompressible problem first, then use the results obtained as initial conditions for the compressible solution to speed up the convergence. Benefits of the code: • The development of a code that has a structure capable of handling the two solutions together is preferable. • The development of an in-house Navier stokes solver code provides flexibility in the applications of different problems that makes it possible to utilise various physical models (such as, non-standart viscosity, turbulence, non-ideal gas equation representations) and different discretisation methods. • An in-house code (flow solver) is much easier to use along with optimization codes compared to commercial solvers. For commercial flow solvers matching the flow solver with the optimization code requires scripting, i.e., reading specific lines on the output files of the program which can cause problems and slow down the overall solution due to writing/deleting thousands of files, processing them, opening the external flow solver many times. The flow solver developed for the compressible flows has been preconditioned with incompressible flow solver. The coherence between compressible and incompressible flow solvers have been improved by using pseudo-transient under-relaxation. It has been observed that preconditioning increases the solution stability and it can also offer savings in solution time. The developed flow solvers have been applied to lid driven cavity and impinging jet flow problems. Results that have been obtained for incompressible and compressible flow regimes have been compared with the results in the literature, and a good coherence has been observed. Finally, optimisation studies have been performed. Within the context of the optimisation of solver parameters, reduction in computational time has been realised by varying under-relaxation parameters, iteration numbers for the momentum and pressure correction equations. Within the scope of the optimisation studies for impinging jet flow, stagnation point Nusselt number that is important for heat transfer has been studied to be maximised, and for this, boundary conditions as well as geometric parameters have been taken as variable. As an optimisation case study towards lid driven cavity flow problem, optimisation implementation for lid driven cavity flow has been developed and for a specific temperature target, location of the required heat sink and boundary conditions have been optimised.