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A kinetic Fokker-Planck algorithm for simulating multiscale gas flows

Hepp, Christian (2023) A kinetic Fokker-Planck algorithm for simulating multiscale gas flows. Dissertation, Justus-Liebig-Universität Giessen. doi: 10.22029/jlupub-14954.

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Official URL: https://jlupub.ub.uni-giessen.de//handle/jlupub/15572

Abstract

Numerical, aerodynamic analysis of spacecraft requires the modeling of rarefied hypersonic flows. Such flow regimes are usually dominated by broad shock waves and strong expansion flows. In such areas of the flow the gas is far from its equilibrium state and therefore conventional modeling approaches such as the Euler or Navier-Stokes equations cannot be used. Instead, non-equilibrium modeling approaches must be applied. While most non-equilibrium flow solvers are computationally expensive, a recently introduced kinetic Fokker-Planck (FP) method shows the potential of describing non-equilibrium flows with satisfactory accuracy and, at the same time, significantly reducing computational costs. However, the application of kinetic FP solvers was so far still limited to simple, single species gases. The aim of this study is to extend the capabilities of the kinetic FP approach for describing complex gas flows. Particular attention is paid to the modeling of non-equilibrium aerodynamics, as it is relevant for describing spacecraft related gas flows. Methods for describing polyatomic species as well as gas mixtures within the kinetic FP framework are constructed. All models are intensively validated by comparison to already established numerical methods, as well as in comparison to experimental studies. Excited energy states are modeled by a stochastic jump process described by a master equation. This approach allows the description of both continuous and discrete energy levels. Gas mixtures are modeled based on the hard-sphere and variable hard-sphere collision potentials. For both cases, FP models are constructed for an arbitrary number of species. The efficiency of the described models is investigated and different strategies are proposed to use kinetic FP methods efficiently. The expansion of synthetic air from an axially symmetric orifice is numerically reproduced using the developed models and results are compared with experimental measurements. Although the numerical simulations capture several magnitudes of Knudsen numbers, from the continuum flow in the reservoir up to the free-molecular far field, good agreement between simulation and experiment is seen.

Item URL in elib:https://elib.dlr.de/196186/
Document Type:Thesis (Dissertation)
Title:A kinetic Fokker-Planck algorithm for simulating multiscale gas flows
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Hepp, ChristianUNSPECIFIEDhttps://orcid.org/0000-0001-8465-9926UNSPECIFIED
Date:10 March 2023
Journal or Publication Title:TU Gießen
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
DOI:10.22029/jlupub-14954
Number of Pages:200
Status:Published
Keywords:Fokker-Planck; kinetic theory; numerical simulation; rarefied flows
Institution:Justus-Liebig-Universität Giessen
Department:FB 07 - Mathematik und Informatik, Physik, Geographie
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:other
DLR - Research area:Raumfahrt
DLR - Program:R - no assignment
DLR - Research theme (Project):R - no assignment
Location: Göttingen
Institutes and Institutions:Institute for Aerodynamics and Flow Technology > Spacecraft, GO
Deposited By: Grabe, Dr. Martin
Deposited On:25 Aug 2023 13:51
Last Modified:25 Aug 2023 13:51

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