In Part I, a method is developed for determining the optimal control laws for a class of aerodynamical systems whose dynamics are linear in the thrust and nonlinear in the lift and thrust angle. Due to the presence of the linear thrust control, a singular subarc exists along which it is often possible to eliminate the Lagrange multipliers from the control equations. Conditions under which this elimination is possible are derived, and expressions for thrust and the rate of change of lift and thrust angle are obtained that depend only on state variables and a small number of time-invariant parameters. The optimal values of the unknown parameters are determined by a direct search in parameter space for that set which minimizes the system performance function. As a result, the proposed method is considerably simpler than standard numerical techniques that require a separate search in function space for each component of the control vector. Furthermore, since the control vector is generated by the direct solution of differential equations, the method appears suitable for use with in-flight guidance computers. Several numerical examples are presented consisting of one, two, and three dimensional control. In each case, it is shown that the search in multi-dimensional function space can be replaced by an equivalent search in the parameter space of initial conditions. In Part II, a three stage numerical algorithm is developed for a general class of optimal control problems. The technique is essentially a combination of the direct and indirect approaches. Like the indirect approach, the control law equations are used to eliminate the control vector from the system and adjoint equations. However, instead of trying to solve the two point boundary-value problem directly, the augmented performance function is first considered to be a function of the unknown initial conditions and is minimized by a gradient search in the initial condition space. It is shown that it is sufficient to search over the surface of any sphere for the intersection of the line μλ*₀ where λ*₀ is the classical solution of initial values. As a result, this first approach is not dependent on a good initial estimate of the optimal trajectory, and is therefore used in the first two stages of the proposed algorithm to provide the property of rapid initial convergence. The property of rapid final convergence is obtained by employing either a modified method of matching end points, or a method of determining the optimal step size for the gradient method of the first two stages. Either combination results in a three stage numerical algorithm that has good initial convergence, good final convergence, and which requires storage at terminal points only. Several examples are presented consisting of both bounded and unbounded control. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

This thesis is a study of the interference forces acting on one cylinder comprising a group of three and four cylinders when situated in a free stream flow. The spacing of the cylinders was such that the lines joining their axes formed an equilateral triangle, and a square respectively. The study is split into two parts, (a) potential flow over the groups of cylinders (b) real flow over the groups of cylinders. Bound with copies of the authors' published papers.~Bibliography: pages 132-137.

This thesis focuses on CFD analysis of the Aircar 5.0 flying car prototype. The theoretical part covers basic information about the connection between the aerodynamics of airplanes and cars as well as cars themselves. The computational part begins with the calibration of the mathematical model, continues with the CFD simulations, which have the role to determine basic aerodynamic characteristics of the Aircar in vehicle mode. There are several configurations tested to find out their influence on aerodynamic stability and their advantages and disadvantages are summed up in the conclusion chapter.

Master of Science

Ground vehicles are subjected to crosswind from various origins such as weather, topography of the ambient environment (land, forest, tunnels, high bushes...) or surrounding traffic. The trend of lowering the weight of vehicles imposes a stronger need for understanding the coupling between crosswind stability, the vehicle external shape and the dynamic properties. Means for reducing fuel consumption of ground vehicles can also conflict with the handling and dynamic characteristics of the vehicle. Streamlined design of vehicle shapes to lower the drag can be a good example of this dilemma. If care is not taken, the streamlined shape can lead to an increase in yaw moment under crosswind conditions which results in a poor handling. The development of numerical methods provides efficient tools to investigate these complex phenomena that are difficult to reproduce experimentally. Time accurate and scale resolving methods, like Detached-Eddy Simulations (DES), are particularly of interest, since they allow a better description of unsteady flows than standard Reynolds Average Navier-Stokes (RANS) models. Moreover, due to the constant increase in computational resources, this type of simulations complies more and more with industrial interests and design cycles. In this thesis, the possibilities offered by DES to simulate unsteady crosswind aerodynamics of simple vehicle models in an industrial framework are explored. A large part of the work is devoted to the grid design, which is especially crucial for truthful results from DES. Additional concerns in simulations of unsteady crosswind aerodynamics are highlighted, especially for the resolution of the wind-gust boundary layer profiles. Finally, the transient behaviour of the aerodynamic loads and the flow structures are analyzed for several types of vehicles. The results simulated with DES are promising and the overall agreement with the experimental data available is good, which illustrates a certain reliability in the simulations. In addition, the simulations show that the force coefficients exhibit highly transient behaviour under gusty conditions. / ECO2 Crosswind Stability and Unsteady Aerodynamics for Ground Vehicles

This work aims to identify the key flow parameters that influence flame acceleration in a semi-confined square channel. A transverse fluidic jet was used as an active flow blockage mechanism and to introduce turbulence into the propagating flame. Three experimental parameters were used to examine the relative influence of (1) mixture reactivity defined here as system equivalence ratio (SER), (2) jet mixture composition (JMC), and the momentum ratio (MR) on the acceleration of laminar premixed methane flame. High-speed PIV and schlieren photography were utilized to characterize the instantaneous flow-field conditions throughout the flame-jet interaction. Using these diagnostic techniques, flame front positions and local velocity vector fields have been spatially and temporally resolved. Changes in flame properties including flame structure, velocity, and vorticity were tracked as a function of time. Stoichiometric equivalence ratios were more effective in the production of vorticity and the promotion of flame acceleration. The stoichiometric condition accelerated the flame to the highest final flame velocity of the three parameters examined. Different compositions of the jet mixture demonstrated that the flame acceleration is primarily affected by the jet turbulence and not on the reactivity of the jet compositions. Out of the three parameters examined, the momentum ratio parameter had the least amount of influence on the flow field and flame acceleration. The increase of 33 % in the momentum ratio had negligible effect in the final flame front velocity and implies that the jet turbulence is the main driving mechanism for flame acceleration.

As industry transitions to a net-zero carbon future, turbulent premixed combustion will remain an integral process for power generating gas turbines and are also desired for aviation engines due to their ability to minimize pollutant emissions. However, accurately predicting the behavior of a turbulent reacting flow field remains a challenge. To better understand the dynamics of premixed reacting flows, this study experimentally investigates the evolution of turbulence in a high-speed bluff-body combustor. The combustor is operated across a range of equivalence ratios from 0.7-1 to quantify the role of heat release and flame scales on the evolution of turbulence as the flow evolves from reactants to products. High-speed particle image velocimetry and CH* chemiluminescence imaging systems are simultaneously employed to quantify turbulent flame and flow dynamics. The results demonstrate that the flame augments turbulence fluctuations as the flow evolves from reactants to products for all cases. However, turbulence fluctuations increase monotonically with the heat of combustion and corresponding turbulent flame speed. Nondimensional spatial profiles of turbulence are used to develop a correlation to predict the increase in turbulent fluctuations in an extended progress variable space. A Reynolds Averaged Navier Stokes (RANS) decomposition is also explored to better characterize the effects of heat release on turbulence evolution dynamics. The correlations and RANS decomposition can guide modeling capabilities to better predict confined turbulent reacting flows and accelerate design strategies for premixed turbines with carbon-free fuels.

The Rotating Detonation Combustor (RDC) has, in recent years, been a subject of great interest in the pressure-gain combustion research community. Researchers have been investigating the RDC as a potential improvement over current combustors in today's turbomachinery-based power generation systems. With the theoretical efficiency boost that detonations provide over deflagrating combustors, RDCs have the promise to be a next step in fuel/cost savings in the power generation industry. One mode of research to push an RDCs capabilities is the potential use of combustible carbon/hydrocarbon solid particles in addition to liquid or gaseous fuels. These particles are a source of high energy density and, once added, can reduce the amount of liquid/gaseous fuel needed while operating at the same fuel-to-air ratio. These organic particles are derived from grown sources making them cost-effective and sustainable, in contrast to mined or drilled fossil fuels. Carbon black, peanut flour, and powdered sugar were seeded into a 6-inch diameter RDC operating on a gaseous hydrogen-air mixture. This was done at the leanest hydrogen-air ratio possible where the combustor, operating on just gaseous fuel, would still experience stable detonation waves. Solid fuel was then seeded in place of the gaseous fuel at varying ratios to study its effects on the ability of the combustor to continue to experience detonations. In general, while stable detonations were achieved when solid fuel began replacing the gaseous fuel, the greater the concentration of solid particles compared to gaseous fuel, the greater the likelihood of irregular detonation modes. These modes were observed using a high-speed camera: taking back-end imaging observations to measure characteristics of present detonation waves, including wave number, speed, stability, and phase angle. CTAPs were also added along the length of the outer body of the RDC to take pressure measurements during operation.

Temperature measurements can be difficult to obtain across many different harsh environments such as engine combustion chambers, engine exhaust temperatures, and explosion fireballs. While there are alternate methods to measure fluid temperature such as laser measurements, acoustic measurements, and camera imaging techniques, these methods can often be expensive, difficult to implement, and not able to see within the environment. Thermocouples are popular sensors because they are cheap and easy to implement across a wide range of applications and can measure temperature in areas where other methods cannot reach or see. However, while these sensors are very popular and versatile, they do have some disadvantages, mainly, the response time. When the testing environment becomes harsh, the thermocouple size increases so that the sensor can survive. Unfortunately, when the thermocouple size increases, so does the time that it takes to sense the gas temperature. For this research, the environment will mimic an explosive environment with very fast temperature rise times that will require quick sensor response. This will not be achievable with a single thermocouple; so, multiple thermocouples will be used. This research focuses on evaluating past multi-thermocouple reconstruction techniques to determine which available method is the most accurate and feasible to implement. Of the methods researched, this work has found that a frequency domain method proposed by Forney and Fralick provides temperature estimates as accurate as 0.5% off the average steady state temperature with an average percent error of 5%.

Fluids-related issues in the Aerospace industry are often multiphase in scope. Numerical modeling, such as computational fluid dynamics, is used to describe these problems, as they are difficult or impossible to describe analytically. This research uses computational fluid dynamics to describe multiphase problems related to melting-solidification and particle impingement. Firstly, a numerical model was established that uses the Volume-of-Fluid method to resolve a melting/solidifying particle. This model was verified against experiments and simplified analytical models, and a mesh independence study was done to ensure the results were independent of the mesh sizing. Next, the model was applied to two separate but related problems. The Artemis program has renewed interest in lunar dust mitigation. It is proposed that lunar regolith partially melts and becomes "sticky" when coming into contact with a jet flame, like a landing rocket. The method above was applied to a lunar regolith particle to show how these "sticky" particles can adhere to surfaces. The direct resolution methodology was also applied to a melted sand particle impinging and infiltrating a yttria-stabilized zirconia thermal barrier coating, as seen in engine turbines. Sand can infiltrate the thermal barrier coating and decrease its effectiveness. The infiltration from a single particle was compared to the infiltration from a stream of melted sand. These three efforts showcase the usefulness of directly resolving small particles using the Volume-of-Fluid method.