Thesis (M.Eng.)(Mechanical)--University of Pretoria, 2006. / Includes summary. Includes bibliographical references. Available on the Internet via the World Wide Web.

The work presented in this thesis was performed with the aim of developing improved prediction methods for aerodynamic and aeroelastic analysis to be used in aircraft design. The first part of the thesis concerns the development of a viscous-inviscid interaction model for steady aerodynamic predictions. Since an inviscid, potential flow, model already is available, the main focus is on the development of a viscous model consisting of a three-dimensional integral boundary layer model. The performance of the viscous-inviscid interaction model is evaluated and it is found that the accuracy of the predictions as well as the computational cost appear to be acceptable for the intended application. The presented work also includes an experimental study aimed at analyzing steady and unsteady aerodynamic characteristics of a laminar flow wing model. An enhanced understanding of these characteristics is presumed to be useful for the development of improved aerodynamic prediction models. A combination of nearly linear as well as clearly nonlinear aerodynamic variations are observed in the steady as well as in the unsteady experimental results and it is discussed how these may relate to boundary layer properties as well as to aeroelastic stability characteristics. Aeroelastic considerations are receiving additional attention in the thesis, as a method for prediction of how flutter characteristics are affected by modeling uncertainties is part of the presented material. The analysis method provides an efficient alternative for obtaining increased information about, as well as enhanced understanding of, aeroelastic stability characteristics. / <p>QC 20170816</p>

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This dissertation presents measurements of unsteady surface pressure on airfoils encountering flow disturbances. Analysis of measurements made on an airfoil immersed in turbulence and comparisons with inviscid theory are presented with the goal of determining the effect of angle of attack on an airfoils inviscid response. Unsteady measurements made on the surface of a linear cascade immersed in periodic flow are presented and analyzed to determine the relationship between the blades inviscid response and tip leakage vortex strength. Measurements of fluctuating surface pressure were made on a NACA 0015 airfoil immersed in grid generated turbulence. The airfoil model has a 2' chord and spans the 6' Virginia Tech Stability Wind Tunnel test section. Two grids were used to investigate the effects of turbulence length scale on the surface pressure response. A large grid which produced turbulence with an integral scale 13% of the chord and a smaller grid which produced turbulence with an integral scale 1.3% of the chord. Measurements were performed at angles of attack from 0 to 20. An array of microphones mounted subsurface was used to measure the unsteady surface pressure. The goal of this measurement was to characterize the effects of angle of attack on the inviscid response. Lift spectra calculated from pressure measurements at each angle of attack revealed two distinct interaction regions; for reduced frequencies < 10 a reduction in unsteady lift of up to 7 decibels (dB) occurs while an increase occurs for reduced frequencies > 10 as the angle of attack is increased. The reduction in unsteady lift at low reduced frequencies with increasing angle of attack is a result that has never before been shown either experimentally or theoretically. The source of the reduction in lift spectral level appears to be closely related to the distortion of inflow turbulence based on analysis of surface pressure spanwise correlation length scales. Furthermore, while the distortion of the inflow appears to be critical in this experiment, this effect does not seem to be significant in larger integral scale (relative to the chord) flows based on the previous experimental work of McKeough (1976) suggesting the airfoils size relative to the inflow integral scale is critical in defining how the airfoil will respond under variation of angle of attack. A prediction scheme is developed that correctly accounts for the effects of distortion when the inflow integral scale is small relative to the airfoil chord. This scheme utilizes Rapid Distortion Theory to account for the distortion of the inflow with the distortion field modeled using a circular cylinder. Measurement of the unsteady surface pressure response of a linear cascade in periodic disturbance is presented. Unsteady pressure was measured on the suction and pressure side of two cascade blades with an array of 24 microphones (12 per blade side) mounted subsurface. The periodic disturbance was generated using a pair of vortex generators attached to a moving end wall. Measurements were made for 8 tip gaps (t/c = 0.00825, 0.0165, 0.022, 0.033, 0.045, 0.057, 0.079, 0.129) and phased averaged with respect to the vortex generator pair position. This measurement was motivated by the results presented by Ma (2003). The work of Ma (2003) suggested that tip leakage vortex shedding in the presence of a periodic disturbance is heavily influenced by the inviscid response of the cascade blade. This conclusion was arrived at by Ma's (2003) observation that as the tip gap is increased the amount of fluctuation in the tip leakage vortex circulation increases dramatically, in fact, many times the circulation in the inflow vortices. Unsteady pressure measurements reveal that the blade response involves a complex interaction of both inviscid response and viscous phenomena. However, a close relationship between unsteady tip loading and tip leakage vortex circulation is revealed suggesting the inviscid response is significant in determining the tip leakage vortex circulation. Additionally, predictions using inviscid theory agree well with measured levels of unsteady tip loading. As such, inviscid theory may be useful for predicting the tip leakage circulation and perhaps, pressure fluctuations in the tip leakage vortex. / Ph. D.

In this thesis, gas-kinetic methods for inviscid and viscous flow simulations are developed. Initially, the finite volume gas-kinetic methods are investigated for 1-D flows as a preliminary study and are discussed in detail from theoretical and numerical points of view. The preliminary results show that the gas-kinetic methods do not produce any unphysical flow phenomena. Especially the Gas-Kinetic BGK method, which takes into account the particle collisions, predicts compressible flows accurately. The Gas-Kinetic BGK method is then extended for the solution of 2-D and 3-D inviscid and viscous flows on unstructured/hybrid grids. The computations are performed in parallel. Various inviscid and viscous test cases are considered and it is shown that the Gas-Kinetic BGK method predicts both inviscid and viscous flow fields accurately. The implementation of hybrid grids for viscous flows reduces the overall number of grid cells while enabling the resolution of boundary layers. The parallel computations significantly improve the computation time of the Gas-Kinetic BGK method which, in turn, enable the method for the computation of practical aerodynamic flow problems.

This diploma thesis deals with computing of edit influences on assigned stiff body from the flow of inviscid liquid. There are derived equations for computation of the influences during translational or torsional wobble and follow-up calculation of the units of their tensors.

Flaps used in modern aircraft are known to produce high-intensity noise. Their blunt side edges of the wing's flap produce vorticial wakes which are the main contributors to the noise generated. A concept called continuous mold-line (CML) link flap has been studied rigorously for its impact on the acoustic behavior of the wing. These studies found that eliminating the blunt side tips with a continuous mold-line reduces the noise generated by the wing, drastically. However, very few studies have discussed the effects of mold-line shape on its aerodynamic characteristics. Therefore, the objective of this research is to investigate the effect of shape and geometry on the aerodynamics of CML wings. First, the shape of the continuous mold-line is parametrized using a hyperbolic tangent curve. Then, using ANSYS FLUENT a computational model is developed to calculate the lift and drag generated by different CML configurations. Both, inviscid and viscous studies are performed using FLUENT's pressure-based solver. The effect of span and slope at the mid-point of the transition zone are discussed. The study found that the slope at the mid-point of the transition zone does not affect the overall lift generated by the wing. Also, increasing the span of the transition zone initially increases the drag and begins to decrease at higher span lengths. Overall, it was found that the aerodynamic characteristics (such as lift, drag, and efficiency) of the CML wing are better than the conventional blunt tip hinged flap. / Master of Science / Flaps used in modern aircraft are known to produce high-intensity noise. One of the main contributors to the high-intensity noise is the blunt side edges of the wing's flap. To eliminate the noise produced by the flaps, researchers have come up with a concept called continuous mold-line (CML) link flap. In this concept, we join the flap side edge with the main wing and thus remove the side edges. Studies undertaken till now have mainly focused on the acoustic aspects of the CML wing. Hence, this study focuses on the effect the mold-line shape has on the wing's aerodynamic behavior. The study first discusses a parametric curve that will be used to define the shape of the CML region of the wing. Then, the study calculates the aerodynamic characteristics, such as lift and drag generated by the wing, using the commercial software ANSYS FLUENT. The results obtained by changing the slope at the mid-point and length of the CML region are discussed. Finally, the study presented also compares the aerodynamic characteristics (such as lift, drag, and efficiency) of the CML wing are better than the conventional blunt tip hinged flap.

This dissertation is concerned with the mathematical modeling of the flow in a porous cylinder with a focus on applications to solid rocket motors. After discussing the historical development and major contributions to the understanding of wall injected flows, we present an inviscid rotational model for solid and hybrid rockets with arbitrary headwall injection. Then, we address the problem of pressure integration and find that for a given divergence free velocity field, unless the vorticity transport equation is identically satisfied, one cannot find an analytic expression for the pressure by direct integration of the Navier-Stokes equations. This is followed by the application of a variational procedure to seek novel solutions with varying levels of kinetic energies. These are found to cover a wide spectrum of admissible motions ranging from purely irrotational to highly rotational fields. Subsequently, a second law analysis as well as an extension of Kelvin's energy theorem to open boundaries are presented to verify and corroborate the variational model. Finally, the focus is shifted to address the problem of laminar viscous flow in a porous cylinder with regressing walls. This is tackled using two different analytical techniques, namely, perturbation and decomposition. Comparisons with numerical Runge--Kutta solutions are also provided for a variety of wall Reynolds numbers and wall regression speeds.

These thesis review some recent results on the construction of very high order multidimensional upwind schemes for the solution of steady and unsteady conservation laws on unstructured triangular grids. We also consider the extension to the approximation of solutions to conservation laws containing second order dissipative terms. To build this high order schemes we use a sub-triangulation of the triangular Pk elements where we apply the distribution used for a P1 element. This manuscript is divided in two parts. The first part is dedicated to the design of the high order schemes for scalar equations and focus more on the theoretical design of the schemes. The second part deals with the extension to system of equations, in particular we will compare the performances of 2nd, 3rd and 4th order schemes. The first part is subdivided in four chapters: The aim of the second chapter is to present the multidimensional upwind residual distributive schmes and to explain what was the status of their development at the beginning of this work. The third chapter is dedicated to the first contribution: the design of 3rd and 4th order quasi non-oscillatory schemes. The fourth chapter is composed of two parts: We start by understanding the non-uniformity of the accuracy of the 2nd order schemes for advection-diffusion problem. To solve this issue we use a Finite Element hybridisation. This deep study of the 2nd order scheme is used as a basis to design a 3rd order scheme for advection-diffusion. Finally, in the fifth chapter we extend the high order quasi non-oscillatory schemes to unsteady problems. In the second part, we extend the schemes of the first part to systems of equations as follows: The sixth chapter deals with the extension to steady systems of hyperbolic equations. In particular, we discuss how to solve some issues such as boundary conditions and the discretisation of curved geometries. Then, we look at the performance of 2nd and 3rd order schemes on viscous flow. Finally, we test the space-time schemes on several test cases. In particular, we will test the monotonicity of the space-time non-oscillatory schemes and we apply residual distributive schemes to acoustic problems.

Least-squares finite element method (LSFEM) is employed to simulate 2-D and axisymmetric flows governed by the compressible Euler equations. Least-squares formulation brings many advantages over classical Galerkin finite element methods. For non-self-adjoint systems, LSFEM result in symmetric positive-definite matrices which can be solved efficiently by iterative methods. Additionally, with a unified formulation it can work in all flight regimes from subsonic to supersonic. Another advantage is that, the method does not require artificial viscosity since it is naturally diffusive which also appears as a difficulty for sharply resolving high gradients in the flow field such as shock waves. This problem is dealt by employing adaptive mesh refinement (AMR) on triangular meshes. LSFEM with AMR technique is numerically tested with various flow problems and good agreement with the available data in literature is seen.