Airfoil endwall contouring has been widely studied during the past two decades for the reduction of secondary losses in turbine passages. Although many endwall contouring methods have been suggested by researchers, an analytical tool based on the passage design parameters is still not available for designers. Hence, the best endwall contour shape is usually decided through an optimization study. Moreover, a general guideline for the endwall shape variation can be extrapolated from the existing literature. It has not been validated whether the optimum endwall shape for one passage can be fitted to other similar passage geometry to achieve, least of all a non-optimum but a definite, reduction in losses. Most published studies were conducted at low exit Mach numbers and only recently some studies on the effect of endwall contouring on aerodynamics performance of a turbine passage at high exit Mach numbers have been published. There is, however, no study available in the open literature for a very high turning blade with a transonic design exit Mach number and the effect of endwall contouring on the heat transfer performance of a turbine passage. During the present study, a robust, aerodynamic performance based numerical optimization methodology for turbine endwall contouring has been developed. The methodology is also adaptable to a range of geometry optimization problems in turbomachinery. It is also possible to use the same methodology for multi-objective aero-thermal optimization. The methodology was applied to a high turning transonic turbine blade passage to achieve a geometry based on minimum total pressure loss criterion. The geometry was then compared with two other endwall geometries. The first geometry is based on minimum secondary kinetic energy value instead of minimum total pressure loss criterion. The second geometry is based on a curve combination based geometry generation method found in the literature. A normalized contoured surface topology was extracted from a previous study that has similar blade design parameters. This surface was then fitted to the turbine passage under study in order to investigate the effect of such trend based surface fitting. Aerodynamic response of these geometries has been compared in detail with the baseline case without any endwall contouring. A new non-contoured baseline design and two contoured endwall designs were provided by Siemens Energy, Inc. The pitch length for these designs is about 25% higher than the turbine passage used for the endwall optimization study. The aerodynamic performance of these endwalls was studied through numerical simulations. Heat transfer performance of these endwall geometries was experimentally investigated in the transonic turbine cascade facility at Virginia Tech. One of the contoured geometries was based on optimum aerodynamic loss reduction criterion while the other was based on optimum heat transfer performance criterion. All the three geometries were experimentally tested at design and off-design Mach number conditions. The study revealed that endwall contouring results in significant performance benefit from the heat transfer performance point of view. / Ph. D.

The possibility of misalignments at interfaces would be increased due to individual parts' assembly and external factors during its operation. In actual engine representative conditions, the upstream misalignments have effects on turbines performance through the nozzle guide vane passages. The current experimental aerodynamic investigation over the nozzle guide vane passage was concentrated on the backward-facing step of upstream misalignments. The tests were performed using two types of vane endwall platforms in a 2D linear cascade: flat endwall and axisymmetric converging endwall. The test conditions were a Mach number of 0.85, Re_ex 1.5*10^6 based on exit condition and axial chord, and a high freestream turbulence intensity (16%), at the Virginia tech transonic cascade wind tunnel. The experimental results from the surface flow visualization and the five-hole probe measurements at the vane-passage exit were compared with the two cases with and without the backward-facing step for both types of endwall platforms. As a main source of secondary flow, a horseshoe vortex at stagnation region of the leading edge of the vane directly influences other secondary flows. The intensity of the vortex is associated with boundary layer thickness of inlet flow. In this regard, the upstream backward-facing step as a misalignment induces the separation and attachment of the inlet flow sequentially, and these cause the boundary layer of the inlet flow to reform and become thinner locally. The upstream-step positively affects loss reduction in aerodynamics due to the thinner inlet boundary layer, which attenuates a horseshoe vortex ahead of the vane cascade despite the development of the additional vortices. And converging endwall results in an increase of the effect of the upstream misalignment in aerodynamics, since the inlet boundary layer becomes thinner near the vane's leading edge due to local flow acceleration caused by steep contraction of the converging endwall. These results show good correlation with many previous studies presented herein. / Master of Science

Two instruments mounted in a piggyback arrangement were developed for time-resolved measurements of dynamic flow quality in a transonic cryogenic wind tunnel. The first one is a dual hot-wire aspirating probe for measurement of stagnation pressure and temperature. The second is a miniature high-frequency response angle probe consisting of surface mounted pressure sensors. The aspirating probe was tested in the 0.3-m Transonic Cryogenic Tunnel (TCT) at NASA-Langley Research Center. Stagnation pressure and temperature measurements were taken in the free-stream of the settling chamber and test section. Data were also obtained in the unsteady wake shed from an airfoil oscillating at 5 Hz. The investigation revealed the presence of large stagnation pressure and temperature fluctuations in the settling chamber occurring at the blade passing frequency of the tunnel driving fan. The fluctuations in the test section are of a much more random nature and have amplitudes much lower than those in the test section. The overall results are consistent with previous tunnel disturbance measurements in the 0.3-m TCT. In the unsteady wake shed from the oscillating airfoil, stagnation temperature fluctuations as high as 42 K rms were observed. The high-frequency angle probe is a four sensor, pyramid type probe capable of simultaneously measuring time resolved stagnation and static pressures and two orthogonal flow angles. Using measurements from both probes, all flow parameters of interest can be deduced. Aerodynamic behavior of a full size model of the probe was established in an open air jet of known conditions. / M.S.

Transonic utter is an aeroelastic instability characterized by part-chord shocks over an airfoil and single mode oscillations leading to a drop in the utter boundary. We present a numerical study that examines the influence of shocks, shock-boundary layer interactions, and three-dimensional flow features on the transonic utter boundary. Using energy concepts we show that shocks and shock-boundary layer interactions have a profound influence on the stability of an aeroelastic system. Viscosity stabilizes the aeroelastic system through thickness effects up-to the bottom of the transonic dip. Beyond, shock induced separation not only stalls the aeroelastic system, but also makes it oscillate about a new equilibrium position. In this region, where viscous effects are dominant, the inviscid utter boundary shows multiple utter points. Modal contributions to the response of the aeroelastic systems |viscous and inviscid | indicate that viscosity restricts higher mode participation. Restriction of higher modes by viscosity is responsible for the elimination of multiple utter points that are present in the inviscid case. Multiple forcing frequencies are observed in those regions of the utter boundary where viscous effects are dominant. Further, the shock dynamics exhibit shock-reversal where-in the shock motion predicted by the viscous simulation is 180_ out of phase relative to that of the inviscid case. At Mach numbers beyond the shock-stall region the shock moves close to the trailing edge of the airfoil, and inviscid and viscous simulations predict almost a similar utter boundary. Three-dimensional transonic flow structures on a finite-span wing aeroelastic model de-stabilizes it relative to an equivalent two-dimensional model.

A numerical scheme has been developed to solve the quasilinear form of the transonic stream function equation. The method is applied to compute steady two-dimensional axisymmetric solar wind-type problems. A single, perfect, non-dissipative, homentropic and polytropic gas-dynamics is assumed. The four equations governing mass and momentum conservation are reduced to a single nonlinear second order partial differential equation for the stream function. Bernoulli's equation is used to obtain a nonlinear algebraic relation for the density in terms of stream function derivatives. The vorticity includes the effects of azimuthal rotation and Bernoulli's function and is determined from quantities specified on boundaries. The approach is efficient. The number of equations and independent variables has been reduced and a rapid relaxation technique developed for the transonic full potential equation is used. Second order accurate central differences are used in elliptic regions. In hyperbolic regions a dissipation term motivated by the rotated differencing scheme of Jameson is added for stability. A successive-line-overrelaxation technique also introduced by Jameson is used to solve the equations. The nonlinear equationfor the density is a double valued function of the stream function derivatives. The velocities are extrapolated from upwind points to determine the proper branch and Newton's method is used to iteratively compute the density. This allows accurate solutions with few grid points. The applications first illustrate solutins to solar wind models. The equations predict that the effects of vorticity must be confined near the surface and far away the streamlines must resemble the spherically symmetric solution. Irrotational and rotational flows show this behavior. The streamlines bend toward the rotation axis for rapidly rotating models because the coriolis force is much larger than the centrifugal force. Models of galactic winds are computed by considering the flow exterior to a surface which surrounds a uniform density oblate spheroid. Irrotational results with uniform outward mass flux show streamlines bent toward the equator and nearly spherical sonic surfaces. Rotating models for which Bernoulli's function is not constant show the sonic surface is deformed consistent with the one-dimensional theory.

Thesis. 1976. Sc.D.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / Microfiche copy available in Archives and Barker. / Vita. / Includes bibliographical references. / Sc.D.

No description available.

In this thesis, we investigate flow past an array of micro-electro-mechanical-type (MEMS-type) heating elements placed on a flat surface, where MEMS devices have hump-shaped surfaces, using the triple deck theory. In this work we start by investigating the problem with a single heating element. MEMS devices can be used to control the fluid dynamics over the surface. Hence, we present a review of the boundary layer and the triple deck theories, followed by a literature review of the problem of flow past an array of MEMS devices. Next, we formulate our problem with the aid of the method of matched expansions for supersonic and subsonic flows. Thirdly, we solve analytically the linear version of the problem for supersonic flows. Thereafter, the non-linear problem is solved numerically where a detailed description of a hybrid method to solve the formulated non-linear problem for supersonic flow is exhibited. Fourthly, for subsonic flows we continue investigating flow past a heating element placed on a flat surface. Linear analysis of this problem is conducted. A novel numerical method to solve the non-linear problem for subsonic flows is described. The results are then discussed. In a similar context, we formulate a problem which can be considered as an the extension of previous subsonic flow problem to the three dimensional case. Analytical results are obtained using the Fourier transform where the linear approximation of the problem is considered and numerical results are then obtained using the Fast Fourier Transform. Finally, we consider a case of transonic flow past a heating element placed on a flat surface, where MEMS device has a hump-shaped surface. This transonic flow problem is non-linear in the upper deck and the lower deck equations where they should be solved simultaneously. Hence, a numerical method is required where we will use a finite difference method in stream-wise direction and Chebyshev collocation method in the wall normal direction. The results are then analysed. In conclusion, the use of localised heating elements in boundary layers for flow types considered in the thesis can contribute to the possibility of favourably controlling the fluid flow perturbations.

First, we investigate the steady Euler flows through a general 3-D axially symmetric infinitely long nozzles without irrotationality. Global existence and uniqueness of subsonic solution are established, when the variation of Bernoulli's function in the upstream is sufficiently small and mass flux has an upper critical value. / Second, we concerns the following transonic shock phenomena in a class of de Laval nozzles with porous medium posed by Courant-Friedrichs: Given a appropriately large receiver pressure pr, if the upstream flow is still supersonic behind the throat of the nozzle, then at a certain place in the diverging part of the nozzle a shock front intervenes and the gas is compressed and slowed down to subsonic speed. The position and the strength of the shock front are automatically adjusted so that the end pressure at the exit becomes pr. We investigate this problem for the full Euler equations, the stability of the transonic shock is proved when the upstream supersonic flow is a small steady perturbation of the uniform supersonic flow and the corresponding pressure at the exit has a small perturbation. / Duan, Ben. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 125-137). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERONAUTICS. / Vita. / Includes bibliographical references. / by Woodrow Whitlow, Jr. / Ph.D.