Primitive numerical simulation of circular Couette flow

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Hasiuk, Jan
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James D. Iversen
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Aerospace Engineering

The Department of Aerospace Engineering seeks to instruct the design, analysis, testing, and operation of vehicles which operate in air, water, or space, including studies of aerodynamics, structure mechanics, propulsion, and the like.

The Department of Aerospace Engineering was organized as the Department of Aeronautical Engineering in 1942. Its name was changed to the Department of Aerospace Engineering in 1961. In 1990, the department absorbed the Department of Engineering Science and Mechanics and became the Department of Aerospace Engineering and Engineering Mechanics. In 2003 the name was changed back to the Department of Aerospace Engineering.

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  • Department of Aerospace Engineering and Engineering Mechanics (1990-2003)

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The azimuthal-invariant, 3-d cylindrical, incompressible Navier-Stokes equations are solved to steady state for a finite-length, physically realistic model. The numerical method relies on an alternating-direction implicit (ADI) scheme that is formally second-order accurate in space and first-order accurate in time. The equations are linearized and uncoupled by evaluating variable coefficients at the previous time iteration. Wall grid clustering is provided by a Roberts transformation in radial and axial directions. A vorticity-velocity formulation is found to be preferable to a vorticity-streamfunction approach. Subject to no-slip, Dirichlet boundary conditions, except for the inner cylinder rotation velocity (impulsive start-up) and zero-flow initial conditions, nonturbulent solutions are obtained for sub- and supercritical Reynolds numbers of 100 to 400 for a finite geometry where R[subscript] outer/R[subscript] inner = 1.5, H/R[subscript] inner = 0.73 and H/[delta]R = 1.5. An axially-stretched model solution is shown to asymptotically approach the 1-d analytic Couette solution at the cylinder midheight. Flowfield change from laminar to Taylor-vortex flow is discussed as a function of Reynolds number. Three-dimensional velocities, vorticity and streamfunction are presented via 2-d graphs and 3-d surface and contour plots. A Prandtl-Van Driest turbulence model based on an effective isotropic eddy viscosity hypothesis was applied resulting in accurate 1-d turbulent flow solutions assuming long cylinders. A small aspect ratio correction factor was empirically determined. Comparisons to experiment are very good. Extending the nonturbulent analysis, 3-d turbulent flow equations are developed for Prandtl-Van Driest and energy-dissipation turbulence models. The energy-dissipation model includes corrections for streamline curvature, system rotation and low-Re effects. Solutions of the 3-d equations involve current work in progress.

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Fri Jan 01 00:00:00 UTC 1988