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<p>The aerodynamic excitation of the diametral acoustic modes of an axisymmetric cavity-duct system is investigated experimentally. The change experienced by the acoustic diametral modes with the increase of the mean flow Mach number is investigated numerically. The first objective of this research is to examine the ability of the axisymmetric free shear layer forming along the cavity mouth to excite the asymmetric diametral modes which do not have preferred azimuthal orientations. The dependency of the system aeroacoustic response on both the cavity length and its depth is investigated to determine the limitations imposed by the relative dimensions of the cavity on the excitation process. The azimuthal behaviour of the self-excited diametral modes is also characterized.</p> <p> An experimental set-up is designed to ensure the coincidence of the frequencies of the shear layer oscillation with the acoustic resonance frequencies. The selection of the test section dimensions is based on finite element simulation of the acoustic diametral modes for several geometries. To simulate the diametral modes at different flow Mach numbers, a finite difference code is developed based on a two-step computational aeroacoustic approach. This approach allows the simulation of the acoustic field, taking into account the convection effect of the mean flow.</p> <p>The experimental results show that the diametral modes are very liable to be self-excited when the mean flow Mach number is higher than 0.1. The level of acoustic pressure during the diametral mode resonance increases rapidly with the increase of the ratio of the cavity depth, d, to the pipe diameter, D. However, the maximum acoustic pressure during each resonance decreases with the increase of the ratio of the cavity length, L, to the pipe diameter, D. The selfexcitation of the diametral modes is sustainable with d/D as small as 1/12. Further reduction in this ratio may result in complete suppression of the resonance. For deep cavities, d/D>3/12, the first and second diametral modes are more liable to excitation than the higher order modes. This is attributed to the fact that the low order modes have relatively higher radial acoustic particle velocity amplitude at the cavity mouth compared to the higher order ones. For d/D=l/12, the higher order modes have relatively higher radial acoustic particle velocity amplitude and consequently their tendency to be self-excited increases. For long cavities, L/D>2/3, the duct longitudinal acoustic modes start to be excited and become more dominant as the cavity length is further increased. The excitation mechanism of these longitudinal modes has not been investigated in this work since sufficient details already exist in the literature.</p> <p>The azimuthal behaviour of the diametral modes is characterized for all the tested cases. For short cavities, the diametral modes are classified as spinning modes; while for long cavities, L/D> 1/2, the orientation of the mode changes randomly over time. Small imperfections in the axisymmetric geometry result in what is described as partially spinning modes. An analytical model is developed to describe quantitatively the spinning behaviour of the diametral modes. The free shear layer and the diametral modes are found to be fully coupled in the azimuthal direction. The random behaviour of the diametral modes in the case of long cavities is attributed to the increase of randomness in the turbulent shear layer </p> <p>The numerical simulations show that the diametral modes experience considerable changes with the increase of the mean flow Mach number. At the cavity mouth, both the amplitude and phase distributions of the acoustic particle velocity are altered with the increase of the Mach number. This demonstrates the importance of considering the effect of the mean flow on the acoustic power production process. Moreover, the resonance frequency of the diametral modes decreases with the increase of the Mach number.</p> / Thesis / Doctor of Philosophy (PhD)

The first two steps in the development of an integrated multidisciplinary design optimization procedure capable of analyzing the nonlinear fluid flow about geometrically complex aeroelastic configurations have been accomplished in the present work. For the first step, a three-dimensional unstructured grid approach to aerodynamic shape sensitivity analysis and design optimization has been developed. The advantage of unstructured grids, when compared with a structured-grid approach, is their inherent ability to discretize irregularly shaped domains with greater efficiency and less effort. Hence, this approach is ideally suited fro geometrically complex configurations of practical interest. In this work the time-dependent, nonlinear Euler equations are solved using an upwind, cell-centered, finite-volume scheme. The discrete, linearized systems which result from this scheme are solved iteratively by a preconditioned conjugate-gradient-like algorithm known as GMRES for the two-dimensional cases and a Gauss-Seidel algorithm for the three-dimensional; at steady-state, similar procedures are used to solve the accompanying linear aerodynamic sensitivity equations in incremental iterative form. As shown, this particular form of the sensitivity equation makes large-scale gradient-based aerodynamic optimization possible by taking advantage of memory efficient methods to construct exact Jacobian matrix-vector products. Various surface parameterization techniques have been employed in the current study to control the shape of the design surface. Once this surface has been deformed, the interior volume of the unstructured grid is adapted by considering the mesh as a system of interconnected tension springs. Grid sensitivities are obtained by differentiating the surface parameterization and the grid adaptation algorithms with ADIFOR, an advanced automatic-differentiation software tool. To demonstrate the ability of this procedure to analyze and design complex configurations of practical interest, the sensitivity analysis and shape optimization has been performed for several two- and three-dimensional cases. In two-dimensions, an initially symmetric NACA-0012 airfoil and a high-lift multi-element airfoil were examined. For the three-dimensional configurations, an initially rectangular wing with uniform NACA-0012 cross-sections was optimized; in additions, a complete Boeing 747-200 aircraft was studied. Furthermore, the current study also examines the effect of inconsistency in the order of spatial accuracy between the nonlinear fluid and linear shape sensitivity equations. The second step was to develop a computationally efficient, high-fidelity, integrated static aeroelastic analysis procedure. To accomplish this, a structural analysis code was coupled with the aforementioned unstructured grid aerodynamic analysis solver. The use of an unstructured grid scheme for the aerodynamic analysis enhances the interactions compatibility with the wing structure. The structural analysis utilizes finite elements to model the wing so that accurate structural deflections may be obtained. In the current work, parameters have been introduced to control the interaction of the computational fluid dynamics and structural analyses; these control parameters permit extremely efficient static aeroelastic computations. To demonstrate and evaluate this procedure, static aeroelastic analysis results for a flexible wing in low subsonic, high subsonic (subcritical), transonic (supercritical), and supersonic flow conditions are presented. / Ph. D.

A mathematical model for the determination of the aerodynamic forces acting on an aircraft is presented. The mathematical model is based on the generalization of the idea of aerodynamically steady motions. One important use of these results is the determination of steady (time-invariant) aerodynamic forces and moments. Such aerodynamic forces can be determined using computer simulation by determining numerically the associated steady flows around the aircraft when it is moving along such generalized steady trajectories. The method required the extension of standard (inertial) CFD formulations to general non-inertial reference frames. Generalized Navier-Stokes and Euler equations have been derived. The formulation is valid for all ranges of Mach numbers including transonic flow. The method was implemented numerically for the planar case using the generalized Euler equations. The developed computer codes can be used to obtain numerical flow solutions for airfoils moving in general steady motions (i.e. circular motions). From these numerical solutions it is possible to determine the variation of the lift, drag and pitching moment with respect to the pitch rate at different Mach numbers and angles of attack. One of the advantages of the mathematical model developed here is that the aerodynamic forces become well-defined functions of the motion variables (including angular rates). In particular, the stability derivatives are associated with partial derivatives of these functions. These stability derivatives can be computed using finite differences or the sensitivity equation method. / Ph. D.

Continuous adjoint methods and optimal control theory are applied to a pressure-matching inverse design problem of quasi 1-D nozzle flows. Pontryagin’s Minimum Principle is used to derive the adjoint system and the reduced gradient of the cost functional. The properties of adjoint variables at the sonic throat and the shock location are studied, revealing a logarithmic singularity at the sonic throat and continuity at the shock location. A numerical method, based on the Steger-Warming flux-vector-splitting scheme, is proposed to solve the adjoint equations. This scheme can finely resolve the singularity at the sonic throat. A non-uniform grid, with points clustered near the throat region, can resolve it even better. The analytical solutions to the adjoint equations are also constructed via Green’s function approach for the purpose of comparing the numerical results. The pressure-matching inverse design is then conducted for a nozzle parameterized by a single geometric parameter. In the second part, the adjoint methods are applied to the problem of minimizing drag coefficient, at fixed lift coefficient, for 2-D transonic airfoil flows. Reduced gradients of several functionals are derived through application of a Lagrange Multiplier Theorem. The adjoint system is carefully studied including the adjoint characteristic boundary conditions at the far-field boundary. A super-reduced design formulation is also explored by treating the angle of attack as an additional state; super-reduced gradients can be constructed either by solving adjoint equations with non-local boundary conditions or by a direct Lagrange multiplier method. In this way, the constrained optimization reduces to an unconstrained design problem. Numerical methods based on Jameson’s finite volume scheme are employed to solve the adjoint equations. The same grid system generated from an efficient hyperbolic grid generator are adopted in both the Euler flow solver and the adjoint solver. Several computational tests on transonic airfoil design are presented to show the reliability and efficiency of adjoint methods in calculating the reduced (super-reduced) gradients. / Ph. D.

A technique to obtain the sensitivity of the static aeroelastic response of a three dimensional wing model is designed and implemented. The formulation is quite general and accepts any aerodynamic and structural analysis capability. A program to combine the discipline level, or local, sensitivities into global sensitivity derivatives is developed. A variety of representations of the wing pressure field are developed and tested to determine the most accurate and efficient scheme for representing the field outside of the aerodynamic code. Chebyshev polynomials are used to globally fit the pressure field. This approach had some difficulties in representing local variations in the field, so a variety of local interpolation polynomial pressure representations are also implemented. These panel based representations use a constant pressure value~ a bilinearly interpolated value, or a biquadratic ally interpolated value. The interpolation polynomial approaches do an excellent job of reducing the numerical problems of the global approach for comparable computational effort. Regardless of the pressure representation used, sensitivity and response results with excellent accuracy have been produced for large integrated quantities such as wing tip deflection and trim angle of attack. The sensitivities of such things as individual generalized displacements have been found with fair accuracy. In general, accuracy is found to be proportional to the relative size of the derivatives to the quantity itself. / Ph. D.

An experimental investigation was conducted to compare the supersonic mixing performance between a novel aerodynamic ramp injector and a physical ramp injector. The aerodynamic ramp injector consisted of nine, flush-wall jets arranged to produce multiplicative fuel-vortex interactions for mixing enhancement in a supersonic main flow. The physical ramp injector was a previously optimized and tested swept-ramp design. Test conditions included a Mach 2.0 freest ream of air with a Reynolds number of 3.63 x 10⁷ per meter and helium injection with jet-to-freestream momentum flux ratios of 1.0 and 2.0. Planar-laser Rayleigh scattering and conventional probing techniques including species composition sampling were employed to interrogate the flow field at several downstream locations. Results show that with increasing jet momentum, the aero-ramp exhibited a significant increase in penetration while the physical ramp showed no discernible change. The near-field mixing of the aero-ramp was superior to that of the physical ramp. At the higher jet momentum, the far-field mixing of the aero-ramp was comparable to the physical ramp. In all cases, the total pressure losses suffered with the aero-ramp were less than those incurred with the physical ramp. For both injectors, the total pressure losses decreased with increasing jet momentum. Finally, an analytical relationship predicting the Rayleigh scattering intensity as a function of helium concentration, pressure, and temperature was derived and experimentally validated. It is concluded that these results merit further studies and parametric optimization of the aero-ramp or similar configurations. It is also concluded that further studies may be conducted to establish the absolute quantitative nature of the Rayleigh scattering technique. / Ph. D.

An approximate scheme for the rapid calculation of first estimates to the laminar heat transfer distribution over isothermal axisymmetric blunt bodies is developed. The method devised is free of any integral relations and reduces the required computing effort to a simple slide rule task. The simplicity of the method is due to the introduction of a new heat transfer parameter which is shown, from a semiempirical study, to undergo only moderate variation in regions where the heat transfer experiences order of magnitude changes. Based on these results, a series expansion for the parameter of interest is obtained through the fourth order term. Even though the perfect gas laws are employed in the series expansion, the resulting effect on the heat transfer ratio is felt to·be small. To substantiate the method, the heat transfer computed by the present scheme was compared with experimental, first-order exact, and Lees' approximate scheme for six body shapes of general interest. In all cases, fair to moderately good results were obtained. It is felt that any loss in accuracy is readily compensated for by the fact that the present method requires no numerical integration and therefore is extremely easy to apply. / Master of Science

A computational study of the air flow in a helical rocket pump inducer has been performed using a 3-D elliptic flow procedure including viscous effects. The inlet flow is considered turbulent and fully developed. The geometric, definition of the inducer blade shape and the calculation grid are first presented, followed by a discussion of the flow calculation results displayed in various new graphical representations. The general characteristics expected from previous experimental and analytical work appear in the simulation and were quantitatively studied. The tip leakage flow observed has velocities of the order of the blade tip speed and is partially convected across the entire passage. The important boundary layer development on the blade pressure side and suction side creates radial outward flows, whereas a radial inward motion develops in the core region, with velocities of same order, and from shroud to hub. Secondary and tip leakage flows combine to give a region of high flow losses and blockage near the shroud wall, and the secondary flow pattern is nearly fully developed by the inducer exit. Original details were also resolved in the flow calculation. A circumferential vortex develops near the shroud, immediately upstream of the suction side of the swept-back leading edge. A simplified air-LH2 analogy permitted the prediction of cavitation inception in the liquid hydrogen pump, and the results obtained correspond qualitatively well with water flow visualizations. The accordance of the model with available air test data at the inlet and exit of the inducer is generally very good, with the total pressure losses in excellent agreement. / Master of Science