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Development and numerical investigation of magneto-fluid-dynamics formulations
Khan, Ovais U.
Khan, Ovais U.
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Dissertation
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2009-12
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Electronic dissertations
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Abstract
Magnetofluiddynamics (MFD) is the branch of fluid dynamics that involves mutual
interaction of electrically conducting non-magnetic fluids and magnetic fields. MFD offers
promising advances in flow control and propulsion of future hypersonic vehicles. With
the advent of computational fluid dynamics (CFD), the numerical study of inherently
complicated fluid dynamics problems, such as flows at high velocities, high-temperature
re-entry bodies, and mixed subsonic-supersonic flows, has become an interesting area of
research. Further advancement in high-speed cluster machines and development of efficient
algorithms has made it possible to explore MFD problems numerically.
In this work, development and validation of numerical algorithms for the simulation
of MFD problems of supersonic and hypersonic flows have been conducted. Validity of low
magnetic Reynolds number approximation has been checked with respect to the results
obtained from full MFD equations. In addition to the two commonly used formulations for
MFD, a third formulation based on the decomposition of a magnetic field for solving full
MFD equations was explored. The governing equations were transformed to a generalized
computational domain and discretized using a finite difference technique. A time-explicit
multistage Runge-Kutta scheme augmented with total variation diminishing (TVD)
limiters for time integration was implemented. The developed codes were validated with
the existing closed form solution of the magnetic Rayleigh problem for both two- and threedimensional
cases. The results obtained from decomposed full MFD equations compare
well with the results obtained by solving low magnetic Reynolds number approximation
and classical full MFD equations for a wide range of magnetic Reynolds numbers. It is
shown that the decomposed full MFD technique requires substantially less computation
time compare to classical full MFD equations for the solution of flow fields with strong
imposed magnetic fields.
Finally, high-speed flows over a backward-facing step that is subject to an applied
magnetic field were numerically simulated. The global domain of computation was
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decomposed into upstream and downstream domains from the step location. The low
magnetic Reynolds number approximation under a multiblock grid approach was used
for modeling the backstep flow. Pressure distribution for the Navier-Stokes analysis was
found to be in good agreement with the experimental data. Different types of magnetic
field distributions were investigated. Both uniform and variable electrical conductivity
distributions were considered. It was observed that an increase in the separation zone
and displacement of oblique shock wave towards the exit section occurs subsequent to
application of the magnetic field. A comparison of results obtained with uniform and
variable electrical conductivities showed a reduction in magnetic interaction for variable
electrical conductivity.
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Thesis (Ph.D.)--Wichita State University, College of Engineering, Dept. of Aerospace Engineering
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Wichita State University