AbstractsEngineering

On the numerical solution of compressible fluid flow and radiative heat transfer problems

by Georgios Lygidakis




Institution: Technical University of Crete (TUC); Πολυτεχνείο Κρήτης
Department:
Year: 2015
Keywords: Ροή συμπιεστού ρευστού; Εξισώσεις RANS; Μοντελοποίηση τύρβης; Μετάδοση θερμότητας μέσω ακτινοβολίας; Τρισδιάστατα υβριδικά μη-δομημένα πλέγματα; Κεντροκομβική μέθοδος πεπερασμένων όγκων; Παράλληλη επεξεργασία; Μέθοδος πολυπλέγματος; Προσαρμογή πλέγματος; Compressible fluid flow; RANS equations; Turbulence modelling; Radiative heat transfer; Three-dimensional unstructured hybrid grids; Node-centered finite-volume scheme; Parallel processing; Agglomeration multigrid method; H-refinement
Record ID: 1155214
Full text PDF: http://hdl.handle.net/10442/hedi/35571


Abstract

In this study the development of a methodology for the numerical solution of steady-state compressible fluid flow and radiative heat transfer problems is reported. For the discretization of the computational domains, three-dimensional unstructured hybrid grids with tetrahedral, prismatic and pyramidical elements are employed along with a node-centered finite-volume scheme. Flow modelling is achieved via the Reynolds-Averaged Navier-Stokes (RANS) equations, along with appropriate two-equation turbulence models, namely, k-ε (in three versions), k-ω and SST. For the computation of the inviscid fluxes an upwind method, applying Roe's approximate Riemann solver, is implemented, together with a higher-order accurate spatial scheme, while for the viscous ones the required gradients are evaluated with an element-based (edge-dual volume) or a nodal-averaging approach. The time advancement of the aforementioned equations is achieved with either an explicit scheme, applying a second-order temporal accurate four-stage Runge-Kutta (RK(4)) method, or an implicit one, implementing the Jacobi or the Gauss-Seidel algorithm. For the modelling of radiative heat transfer in general enclosures through absorbing, emitting, and either isotropically or anisotropically scattering gray media, the time-dependent or steady (non time-dependent) Radiative Transfer Equation (RTE) is employed. Similarly to fluid flow, a second-order accurate spatial scheme along with appropriate slope limiters is applied to increase accuracy of the solution, especially at the boundary regions, while time integration is obtained with simple iterative approximations or the same to flow model explicit scheme. In order to increase the efficiency of the proposed methodology additional acceleration techniques are used, namely, an edge-based data structure, a parallelization strategy based on the domain decomposition approach and MPI library functions, and an agglomeration multigrid method employed in isotropic or directional formulation for the flow solver and in spatial, angular or nested spatial/angular one for radiative heat transfer algorithm. Finally, the h-refinement technique is incorporated to increase accuracy at pre-selected regions of the examined grid, by enriching them with more nodes during the solution procedure; as a result, the generation of dense meshes from the very beginning is avoided. Based on the aforementioned methods, an academic CFD code, named Galatea, was developed; it has been validated against three- and quasi-three-dimensional benchmark test cases presented in the open literature, while its results have been compared with wind tunnel experimental data as well as results obtained by reference numerical solutions, confirming its capability to effectively perform such simulations in terms of accuracy, geometric flexibility and computational efficiency. Σκοπός της παρούσας Διδακτορικής Διατριβής ήταν η ανάπτυξη μεθοδολογίας για την αριθμητική επίλυση προβλημάτων μόνιμης ροής συμπιεστού ρευστού και μετάδοσης θερμότητας μέσω ακτινοβολίας. Η…