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Aerospace Engineering

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#### Navier-Stokes solutions of 2-D transonic flow over unconventional airfoils

A finite-volume code has been written to solve the complete, Reynolds-averaged Navier-Stokes equations around unconventional airfoils. The numerical algorithm is based on a flux-difference splitting form of a total variation diminishing (TVD) scheme. Various modifications to the scheme have been incorporated to provide a spatially second-order-accurate scheme in physical space. The scheme is conservative at steady state but employs nonconservative differencing during the integration to steady state to allow incorporation of implicit boundary conditions in the farfield. A zero-equation eddy viscosity model has been employed to represent the effects of turbulence. The code is validated by comparisons with flat plate and NACA 0012 data. Excellent results were obtained for both attached flow and shock induced separation cases. Numerical results are also presented for transonic flow over an unconventional airfoil and show good agreement.

#### Primitive numerical simulation of circular Couette flow

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.

#### Optimal tensioning of nonlinear antenna structures

A new technique is described for optimizing the shape of a hoop/column antenna by adjusting the tensioning loads. The antenna structure is modelled using finite element procedures which include the geometric nonlinearities. The finite element equations constitute nonlinear equality constraints in the optimization problem. The new optimization technique solves this optimization problem without the introduction of either Lagrange multipliers or penalty functions. The results for two sample problems are presented in this dissertation.

#### Diffusion-deposition of particles from a continuous line source into a disturbed atmospheric boundary layer

The transport, diffusion, and dry deposition of small particle material emitted from an idealized continuous line source into the atmosphere over a forward-facing step, a backward-facing step, and a rectangular block are stimulated. The description of the atmospheric flow pattern near the obstruction is obtained by numerically solving the Navier-Stokes equations with the k-(epsilon) two-equation turbulence model. Gosman's upwind finite difference scheme which is modified to be a time marching approach is selected as the numerical method. For the estimation of the pollutant concentration and deposition the gradient-transfer model is applied. The Crank-Nicolson scheme which is modified to be the Gauss-Seidel with Successive-Over-Relaxation method is used. Comparisons and analyses are performed based on these numerical predictions of the flow fields and particulate diffusion and deposition. The result is a better understanding of the properties of the disturbed atmospheric flow and of the distribution of suspended and deposited particles near the obstruction.

#### Leaky Lamb waves in an anisotropic plate. I: An exact solution and experiments

The propagation of leaky Lamb waves in a plate consisting of a general balanced symmetric composite material is considered. The problem has been examined both analytically as well as experimentally. An exact solution for the dispersion equation was obtained. Numerical results for complex‐valued wavenumber were obtained for an isotropic material (aluminum) and a (0/90_{3})_{s} graphite/epoxy laminate. Excellent agreement for the isotropic case and a satisfactory agreement for the anisotropic case between the theory and experiment were observed.

#### Application of graph theory to the nonlinear analysis of large space structures

A new graph representation of nonlinear large space structures is introduced. During the loading process the structural graph changes its levels as the nonlinear regions in the large space structure change configuration. This variable structured graph is used to order the nodes and members of the discretized nonlinear structural model. A new algorithm is used to change the established order of the nonlinear model and updates the condensed nonlinear stiffness matrix equation for the structure. In addition to accounting for structural nonlinearities this algorithm can take into consideration plastic hinge formation and fracture of members in large space structures.

#### Effect of radial inflow on vortex intensification and its application to wind vortex generators

A new wind vortex turbine, called "tornado-type wind generator system," was studied both theoretically and experimentally for the purpose of better understanding the basic nature of a vortex flow and further improvement of its power efficiencies. Analytical solutions were obtained from the Navier-Stokes equations for the velocity distributions along the radial distance. The result demonstrates the important nature of a vortex structure that, in order to intensify a vortex inside the tower, radial inflow must be provided from the side walls. Based upon this concept, the essential contribution of our experimental work was to furnish the radial inflow by utilizing the dynamic head of incoming wind;One circular model of 0.36 m(14") diameter with 0.58 m(23") height and two spiral models of 0.36 m inner diameter with 0.36 m height and 0.48 m(19") inner diameter with 0.58 m height were tested in a newly constructed wind tunnel of 1.22 x 1.22 m(4' x 4') at wind speeds from 2.54 m/s (5.68 mph) to 6.1 m/s(13.65 mph). It was found that for intensifying a vortex in such a tower it is more important to require the radial inflow in the boundary layer region rather than across the entire height of the tower. The maximum power efficiency, C(,p), obtained for the circular model with the radial inflow supply was about 3.8, which is about one order higher than that of conventional wind mills. This C(,p) was increased more than 100% in some cases as compared to that without the radial inflow supply. The maximum C(,p) for the large spiral model with the radial inflow supply was the highest, a value of 9, which is 22.5 times that of conventional windmills. This C(,p) was increased only about 15-30% as compared to that without the radial inflow supply because the spiral model produces the radial inflow by itself due to the decreasing radius of the spiral curvature. Static pressure measurements in the vortex core of the large spiral model showed that the maximum static pressure drop at the vortex center was more than 10 times the dynamic head of the wind with the radial inflow supply. The radial inflow lowered the pressure in the vortex core, a consequence of vortex intensification;In conclusion, extracting wind energy by creating and maintaining an extremely low pressure region of an intensified vortex at the turbine exit through viscous pumping is an improvement for wind machines in the aspect of C(,p) and consequently is a cost effective procedure.

#### Energy balance calculations for a multipole target plasma fusion reactor

Thermonuclear fusion reactors have not yet achieved breakeven; high plasma temperatures are required to obtain high reaction rates. Accompanying the high plasma temperatures are high bremsstrahlung radiation losses, plasma instabilities, first wall problems and large amounts of energy for plasma containment. To reduce the detrimental effects and maintain high reaction rates, a two component target plasma system was proposed with one of the fuel species acting as a target plasma magnetically confined at a relatively low temperature. The second fuel species is then injected at high energy into the target plasma to interact with the confined plasma as it slows down, depositing energy and undergoing fusion reactions. The reactor confinement scheme chosen to contain the target plasma was the multipoled Octahedrally Symmetric MAgnetiC well (OSMAC) which has been studied previously at Iowa State University;The energy balance calculations performed for the two component reactor configuration included a newly modeled asymptotic slowing down number density and plasma temperature effects through Doppler broadening of the fusion cross section. The new slowing down number density was compared with models from Fokker-Planck and Boltzmann collision term approaches. This new model allows the relatively easy introduction of finite geometry effects. A numerical comparison of relaxation rate formulae was accomplished. Both D-('3)He and D-T fuel cycles were considered;As a result of this work it becomes evident that D-('3)He and D-T fueled two component reactors operating according to the assumptions made and equations used herein is incapable of achieving breakeven conditions. It is implied that the operating conditions used herein require the reassessment and redevelopment of the physics model of fast ions slowing down in a cold plasma. A new slowing down number density model presented herein has been found comparable with existing models. Included in this dissertation is a computer program for finding Doppler broadened cross sections.

#### A two-dimensional unsteady Euler equation solver for flows in arbitrarily shaped regions using a modular concept

#### Application of an upwind algorithm to the parabolized Navier-Stokes equations

A new computer code for the solution of the three-dimensional parabolized Navier-Stokes (PNS) equations has been developed. The code employs a state-of-the-art upwind algorithm to capture strong shock waves. The algorithm developed in this work is implicit, uses finite-volumes, and is second-order accurate in the crossflow directions. The new code is validated through application to several laminar supersonic and hypersonic flows. In two dimensions, calculations were performed for supersonic laminar flow past a flat plate, hypersonic laminar flow past a 15(DEGREES) compression corner, and hypersonic laminar flow into a converging inlet. Results obtained using the present algorithm are in excellent agreement with experimental data as well as with previous numerical calculations. The method was validated for three-dimensional flow by computing hypersonic flows past two simple body shapes: a circular cone of 10(DEGREES) half-angle and a generic all-body hypersonic vehicle. Cone flow solutions were computed at angles of attack of 12(DEGREES), 20(DEGREES), and 24(DEGREES) and results are in agreement with experimental data. Results are also presented for the flow past the all-body vehicle at angles of incidence of 0(DEGREES) and 10(DEGREES).

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