Doctor of Philosophy / Department of Mechanical and Nuclear Engineering / Mingchang (James) Chen / To describe the behavior of a gas composed of spherical particles that rotate,
the kinetic theory approach is presented. First-order approximations to the
Boltzmann-Curtiss transport equation yield conservation equations that govern
the translational velocity and rotation of the particles. The
resulting equations match the form of the equations of morphing continuum
theory (MCT), a theory derived from the principles of rational continuum
thermomechanics. A direct comparison of corresponding terms provides
expressions related to the new coefficients within MCT, showing a clear
departure from classical expressions derived from a kinetic treatment of
classical fluids. The identical expressions for the coefficients in the Cauchy
stress and viscous diffusion terms in the kinetic linear momentum equation
suggests that the coupling coefficient introduced by MCT outweighs the
contribution of the classical kinematic viscosity. The kinetic theory equations
reduce to the form of the Navier-Stokes equations when the local rotation is
equated to the
angular velocity, but the predominance of the coupling coefficient results in a
viscous term that differs slightly from the classical expression derived using
the Boltzmann distribution function. For simple cases of irrotational and
incompressible flows, the kinetic equations mimic the form of the classical
momentum equations derived from classical kinetic theory. This result is
consistent with the fact that the difference between the two kinetic approaches
is the local rotation of spherical particles.
Preliminary numerical simulations of the MCT governing equations are discussed,
with an emphasis on the importance of the new coupling coefficient. Turbulent
incompressible profiles are achieved by setting dimensionless parameters to
particular values. The key parameter involves the ratio of the coupling
coefficient to the kinematic viscosity. The relationship between the coupling
coefficient and kinematic viscosity is shown to be the
driving force for the development of transitional and turbulent boundary layer
profiles.
Compressible turbulence results are generated using the same dimensionless
parameter values that generated turbulence in the incompressible case. For
supersonic
flow over a cylinder, MCT displays an inverse energy cascade from small to
large scales. In addition to visualizing turbulent processes, the results from
MCT display the importance of coupling the linear and angular momenta
equations, which is strengthened when the coupling coefficient increases. The
expressions
from kinetic theory coupled with the numerical results in MCT indicate that the
physical phenomena driving a fluid composed of spherical particles depends
heavily on the physical properties of the coupling coefficient.
| Identifer | oai:union.ndltd.org:KSU/oai:krex.k-state.edu:2097/38897 |
| Date | January 1900 |
| Creators | Wonnell, Louis |
| Source Sets | K-State Research Exchange |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
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