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Multi-scale models and computational methods for aerothermodynamics

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VKI PHDT 2014-05, Alessandro Munafò, Multi-scale models and computational methods for aerothermodynamics, ISBN 978-2-87516-074-4, 251 pgs

Multi-scale models and computational methods for aerothermodynamics

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  • Multi-scale models and computational methods for aerothermodynamics


Multi-scale models and computational methods for aerothermodynamics
By Alessandro Munafò

PhD Thesis from the von Karman Institute/Ecole Centrale de Paris, January 2014, ISBN 978-2-87516-074-4, 251 pgs


This thesis aimed at developing multi-scale models and computational methods for aerothermodynamics applications.

The research on multi-scale models has focused on internal energy excitation and dissociation of molecular gases in atmospheric entry flows. The scope was two-fold: to gain insight into the dynamics of internal energy excitation and dissociation in the hydrodynamic regime and to develop reduced models for Computational Fluid Dynamics applications. The reduced models have been constructed by coarsening the resolution of a detailed rovibrational collisional model developed based on ab-initio data for the system provided by the Computational Quantum Chemistry Group at NASA Ames Research Center. Different mechanism reduction techniques have been pro- posed. Their application led to the formulation of conventional macroscopic multi-temperature models and vibrational collisional models, and innovative energy bin models. The accuracy of the reduced models has been assessed by means of a systematic comparison with the predictions of the detailed rovibrational collisional model. Applications considered are inviscid flows behind normal shock waves, within converging-diverging nozzles and around axisym- metric bodies, and viscous flows along the stagnation-line of blunt bodies. The detailed rovibrational collisional model and the reduced models have been coupled to two flow solvers developed from scratch in FORTRAN 90 programming language (shocking_f90 and solver_fvmcc_f90). The results obtained have shown that the innovative energy bin models are able to reproduce the flow dynamics predicted by the detailed rovibrational collisional model with a noticeable benefit in terms of computing time. The energy bin models are also more accurate than the conventional multi-temperature and vibrational collisional models.

The research on computational methods has focused on rarefied flows. The scope was to formulate a deterministic numerical method for solving the Boltzmann equation in the case of multi-component gases with internal energy by accounting for both elastic and inelastic collisions. The numerical method, based on the weighted convolution structure of the Fourier transformed Boltzmann equation, is an extension of an existing spectral-Lagrangian method, valid for a mono-component gas without internal energy. During the development of the method, particular attention has been devoted to ensure the conservation of mass, momentum and energy while evaluating the collision operators. Conservation is enforced through the solution of constrained optimization problems, formulated in a consistent manner with the collisional invariants.

The extended spectral-Lagrangian method has been implemented in a parallel computational tool (best; Boltzmann Equation Spectral Solver) written in C programming language.

Applications considered are the time-evolution of an isochoric gaseous system initially set in a non-equilibrium state and the steady flow across a normal shock wave. The accuracy of the proposed numerical method has been assessed by comparing the moments extracted from the velocity distribution function with Direct Simulation Monte Carlo (DSMC) method predictions. In all the cases, an excellent agreement has been found. The computational results obtained for both space homogeneous and space inhomogeneous problems have also shown that the enforcement of conservation is mandatory for obtaining accurate numerical solutions.

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