A numerical study of hypersonic flows using the full Navier-Stokes equations with different air models
Kim, Moon-Sang
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Permalink
https://hdl.handle.net/2142/19155
Description
Title
A numerical study of hypersonic flows using the full Navier-Stokes equations with different air models
Author(s)
Kim, Moon-Sang
Issue Date
1991
Doctoral Committee Chair(s)
Lee, Ki D.
Department of Study
Aerospace Engineering
Discipline
Aeronautical and Astronautical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Aerospace
Language
eng
Abstract
A two-dimensional, axisymmetric, full Navier-Stokes solver has been developed with equilibrium and nonequilibrium air models. The effects of a real gas are investigated numerically in the hypersonic flow regime.
The code employs several different upwind schemes to examine their effect on the accuracy and stability of the numerical solutions. A finite volume method is used with curvilinear coordinates, and the first-order, upwind schemes are extended to second-order accuracy in space. The steady-state solutions are obtained using an approximately factorized implicit scheme, including fully implicit boundary conditions, to accelerate the convergence.
The numerical accuracy is improved by introducing the closed-control-volume concept in the metric quantity calculations. This idea is verified by a blunt-nosed flow case with a scrambled grid.
In general, the fastest convergence in an implicit scheme is obtained when the same residual and correction operators are applied. A new simplified Jacobian matrix is derived for Roe's flux difference splitting scheme because of the complexity involved in deriving the full Jacobian matrix, and which yields a faster convergence compared to the use of a different correction operator such as Steger-Warming's.
The difficulties that arise in generating a grid for a complex geometry can be avoided by using a multi-block grid topology. The effects of grid topology are discussed, and several grid dependence studies are performed. For the better resolution in the numerical solutions, a solution-adapted grid is also studied.
The effects of a real gas are investigated by introducing two different air models: equilibrium and nonequilibrium. The equilibrium air model consists of eleven species, and uses the Helmholtz free energy minimization technique to obtain the species compositions. On the other hand, the nonequilibrium air model uses five species, six reactions, and one temperature model. The species compositions are computed by solving the species continuity equations implicitly, including the species production terms. The binary diffusion terms are excluded from this research. Because different time scales exist between the flow and the chemical reactions, the governing equations become stiff, and present convergence difficulties. An efficient loosely coupling procedure is developed to overcome this problem. The numerical results obtained by simulating a hypersonic flow around a blunt-nosed, flat-based projectile show that the air models not only influence the range of values of flow quantities but can also change the entire flow structure.
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