Previously, the concept of the tolerant wind tunnel, developed in the Department of Mechanical Engineering, U. B. C., was tested only for stationary models. In the present study, the concept is investigated for unsteady airfoil motion. The new wind tunnel test section, using the opposite effects of solid and open boundaries, is a new approach to reduce wall blockage effects. Consisting of vertical airfoil slats uniformly spaced on both side walls in the test section, it is designed to produce a nearly free-air test environment for the test model, which leads to negligible or small corrections to the experimental results. The performance of this wind tunnel for unsteady model testing is examined experimentally with a two-dimensional NACA 0015 airfoil in a simple plunging sinusoidal motion. The airfoil is mounted vertically in the center plane of the test section between solid ceiling and floor. An oscillating table is designed to give the airfoil an accurate plunging sinusoidal motion. A full range of open area ratio is tested by varying the number of slats mounted inside the side walls. Pressure distribution along the airfoil surface and displacement of the airfoil are measured as functions of time by a data acquisition system designed for this research. Lift and moment are obtained by integration of the pressure distribution at every time increment. Using a numerical model based on the singularity distribution method, the free air case results for a NACA 0015 airfoil in the same unsteady motion are obtained. Comparison with the linear theory results by Sears¹ are discussed. Comparing with the numerical and the linear theory results, the experimental investigation shows that the new test section produces low-correction data. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

No description available.

The phenomena of stall and surge in axial-centrifugal compressors is investigated through high-response measurements of both the pressure field and the flowfield throughout the surge cycle. A unique high-response forward-facing and aft-facing probe provides flow information. Several axial-centrifugal compressors are examined, both in compressor rigs and engines. Extensive discussion is presented on the differences in axial and centrifugal rotors and their effect on the system response characteristics. The loading parameters of both are examined and data is presented that shows the increased tolerance of the centrifugal stage to instability. The dynamics of the compressor blade response are shown to be related to the transport time of a fluid particle moving through a blade passage. The data presented provides new insight into the dynamic interactions that occur prior to and during stall and surge. In addition, the inception of rotating stall and the inception of surge are shown to be the same phenomena . An analytical dynamic model (DYNTECC) is applied to one of the compression systems and the results are compared to data. The results show that the model can capture the global effects of rotating stall and surge. The data presented, along with the analytical results, provide useful information for the design of active and passive stall control systems. / Ph. D.

No description available.

No description available.

We consider the flow of nonlinear Maxwell fluids in the unsteady quasistatic case, where the effect of inertia is neglected. We study the well-posedness of the resulting PDE initial-boundary value problem. This well-posedness depends on the unique solvability of an elliptic boundary value problem. We first present results for the 3D case, locally and globally in time, with sufficiently small initial data, and for a simple shear flow problem, locally in time with arbitrary initial data; after that we extend our results to some 3D flow problems, locally in time, with large initial data. Additionally, we present results for models of White-Metzner type in 3D flow, locally and globally in time, with sufficiently small initial data. We solve our problem using an iteration between elliptic and hyperbolic linear subproblems. The limit of the iteration provides the solution of our original problem. / Ph. D.

Ph. D.

A two-dimensional, inviscid, incompressible procedure is presented for predicting the unsteady lift on turbomachinery blades caused by the upstream potential disturbance of downstream flow obstructions. The method is applied to a particular geometry which consists of a rotor, a downstream stator, and downstream struts which support the engine casing. Using the Douglas-Neumann singularity superposition computer program to model the downstream flow obstructions, classical equations of thin airfoil theory are then employed, to compute the unsteady lift on the upstream rotor blades. Very good agreement between the Douglas-Neumann program and experimental measurements was obtained for the downstream stator-strut flow field. The calculations for the unsteady lift due to the struts were in good agreement with the experiments in showing that the unsteady lift due to the struts decays exponentially with increased axial separation of the rotor and the struts. However, the calculations for the unsteady lift due to the stator were two orders of magnitude smaller than that measured in experiments. This is attributed to the strong viscous interaction between the rotor and stator blade rows. / M.S.

Separating and reattaching flows are important in a large number of engineering configurations. The flow through a sudden expansion (backward-facing step) represents a conceptually simple case of this class of flows and hence has been the subject of numerous studies. The present study focuses on the effect of the expansion ratio (defined as the ratio of downstream channel height to upstream channel height) on the unsteady flow features in the reattachment region and further downstream. It is known that this flow demonstrates two different instabilities; the Kelvin-Helmholtz shear layer instability, which scales with the shear layer thickness, and the instability associated with the separation bubble, which scales with the step height and has similarities to K´arman vortex shedding behind a cylinder.In addition to these, there is also a possibility of the presence of the ‘preferred’ mode of the jet issuing from the inlet channel of the sudden expansion, especially at high expansion ratios, where the flow resembles a wall jet. The aim of this study is to investigate experimentally the changes in the instability of the separation bubble, as the expansion ratio is changed, and its possible interactions with the other instabilities in the flow.One might expect some changes in the flow with expansion ratio, as at low expansion ratios, the configuration represents a simple backward-facing step geometry, while at high expansion ratios, the geometry approaches that of a wall jet. A variable expansion ratio backward-facing step facility has been developed in an open circuit wind tunnel.This facility permits continuous variation of the expansion ratio from 1 to around 6. Attention is focused on the turbulent regime of the flow, where the flow structure has been found in previous studies to be relatively insensitive to the Reynolds number. The inlet conditions have been kept constant with a thin turbulent boundary layer at the step, the boundary layer thickness at separation being approximately 14 % of the inlet channel height. The Reynolds number based on the inlet channel height, H, is kept constant at Re=48,000 and the expansion ratio is varied by changing the channel height downstream of the step. Detailed hot wire measurements have been made to characterize the spatial variation of the dominant frequencies in the flow at different expansion ratios. The expansion ratio has been varied from a low value of 1.14 to a high value of 3.25, and detailed measurements are obtained for five expansion ratios of 1.14, 1.3, 1.5, 2.0 and 3.0. Further, to elucidate the dominant vortical structures in the flow, Particle Image Velocimetry measurements have been undertaken simultaneously with hot wire measurements for the case of expansion ratio 1.5, which have permitted the conditional averaging of vorticity fields.These investigations have brought forth some interesting features of the flow over a backward-facing step. Results for the time-mean properties of the flow indicate that the shear layer separating from the step deviates from a free mixing layer behaviour away from the step, possibly due to its interaction with the wall and the recirculation region underneath it. At any given streamwise location, the shear layer momentum thickness, θ, is seen to increase with the expansion ratio. Further, upto reattachment, the momentum thickness of the shear layer is seen to scale with the step height, h, independent of its initial thickness at separation, θo, as long as the boundary layer at separation is sufficiently thin as compared to the step height. Investigations for the unsteady flow features show that the frequency of the dominant peak in the velocity spectrum, supposed to represent the passage frequency (Strouhal number, S, based on the step height, h, and the inlet velocity, U) of the vortical structures, varies in the cross stream (y) direction, in addition to its expected variation in the streamwise (x) direction. The variation of the Strouhal number in the cross stream direction is seen to scale with the local momentum thickness of the shear layer, except for locations very close to the step. To characterize the development of the dominant frequency in the streamwise direction, the maximum value of the Strouhal number at a streamwise location is taken to be the representative value for that streamwise location. The Strouhal number is seen to decrease in the streamwise direction, from a very high value near the step, to a value of approximately 0.08 in the reattachment region, and remains constant further downstream. This value, supposed to represent the large scale structures shed from the reattachment region, is seen to remain very close to 0.08 for all Expansion ratios investigated. Conditional averaging of the vorticity fields in the reattachment region is done for an expansion ratio of 1.5, to get a detailed picture of the unsteady flow field. The hot wire signal at the outer edge of the shear layer in the reattachment region, which represents the non-dimensional structure passage frequency of S=0.08, is used as the conditioning signal. Results seem to indicate that the recirculation region, or the ‘bubble’ divides into two cells, and sheds the downstream cell quasi-periodically. The passage of these structures through the reattachment region seems to be concomitant With a local vertical motion of the shear layer. Further, the streamwise development of the local Strouhal number, Sθ, based on the local momentum thickness of the shear layer, and the local free stream velocity, Umax, indicates a possibility of a coupling between the shear layer and the structures shed from the reattachment region.

Two-dimensional flow in a viscous incompressible fluid, generated by a circular cylinder executing large-amplitude rectilinear oscillations in a plane perpendicular to its axis and parallel to one of the sides of a surrounding rectangular box filled with incompressible fluid is studied numerically. The circular cylinder moves back and forth through its own wake, resulting in an extremely complex flow field. For ease of implementing boundary conditions, a numerically generated body-fitted coordinate system is used. At each time step, the physical domain is doubly-connected, and a cut is introduced in order to map it into a rectangular computational domain. A body-fitted grid is generated by solving a pair of Laplace equations with a simple grid spacing control method which preserves the essential one-to-one property of the mapping. A finite difference/pseudo-spectral technique is used in this work to solve the Navier-Stokes equations in velocity-vorticity formulation. The time integration of the vorticity transport equation is handled by a fully explicit three-level Adams-Bashforth method. The two Poisson equations for the velocity components are 11-banded and block-diagonal in form, and are solved by a preconditioned biconjugate gradient routine. An integral constraint on the vorticity field is used to determine the boundary vorticity that simultaneously satisfies the no-slip and no-penetration conditions. The surface vorticity is uniquely determined by a general solution procedure developed in this study which is valid for flows over multiple solid bodies. With this approach, the physical process of vorticity generation on the solid boundary is properly simulated and the principle of vorticity conservation is satisfied. Results for various test cases and the complex vortex shedding phenomena generated by an oscillating circular cylinder are presented and discussed.