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Student Number : 9804064R - MSc research report - School of Mechanical, Industrial and Aeronautical Engineering - Faculty of Engineering and the Built Environment / A qualitative and quantitative study of the hydraulic analogy; that is the analogy between flow with a free surface and two dimensional compressible gas flow, is described. The experimentation was done using a water table, and results are compared with Computational Fluid Dynamic (CFD) results for actual free surface flow models, and a fictitious gas model. Different test cases are considered (i) a wedge moving at steady supersonic/supercritical speeds of Froude or Mach number equal to 2.38, 3.12 and 4.31 (ii)unsteady motion of a wedge accelerating to supersonic speeds and then decelerating. Quantitative results for the experimental case are achieved by using a colour encoding slope detection technique. Qualitatively, with respect to wave angles, the fictitious gas case shows the best agreement to the experimental case, but at higher Froude/Mach numbers the free surface models also show good agreement. Quantitatively, with respect to wave location and depth profile, the free surface models show better agreement to the experimental case. For the unsteady case the resulting flow patterns are quite similar for the two cases considered, namely the experimental and free surface CFD cases.

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Two-dimensional supersonic flows out of rocket nozzles are one of three flow types: over-, perfectly-, or under-expanded. In under-expanded flows, an expansion fan is centered at the top and bottom tip of the rocket nozzle. When the waves from the expansion wave cross through the centerline and intersect the free boundary, the waves are reflected as compression waves. For higher exit-to-ambient pressure ratios, the compression waves coalesce and eventually form a barrel shock. The purpose of this study was to use the Method of Characteristics (MOC), a mathematical procedure for solving hyperbolic partial differential equations, to simulate the formation of the barrel shock. A MOC code was developed in the Python programming language to accomplish task. Results of the MOC code compared favorably with CFD results.

An instrument for the direct measurement of skin friction in complex supersonic and hypersonic flows was developed. The flows were complex because they were of very short duration, with high temperature and shocks and often injection, mixing, and combustion. A wall-mounted, miniature cantilevered beam device measured the small tangential shear force on the non-intrusive floating element. Semiconductor strain gages mounted at the beam’s base measure the small strains that are generated. By modifying the geometry of the sensing unit, this design can be adapted for a variety of test flows. The use of engineering plastics and short beam length provide high frequency response and make the beam stiff so that the floating head’s deflection due to the shear is negligible, allowing for a non-nulling design. Measurements were made in scramjet models at the NASA Ames 16-inch Shock Tunnel and the General Applied Science Laboratory HYPULSE facility. Test flow conditions were harsh with the facilities simulating Mach 14 enthalpy conditions (320 atm and 10000 R total temperatures) for 0.3-2 milliseconds. The use of engineering plastics reduces heat transfer, so that measurements can be made in these very hot impulsive flows without thermal contamination of the data. Skin friction data in agreement with other correlations and measurements were obtained at both facilities. Mach 2.4 cold flow tests were also performed in the Virginia Tech Supersonic Tunnel. These helped verify the concept and to establish pressure gradient sensitivity in the case of a shock wave impacting directly on the sensing head. Analysis of the measurement uncertainty in the cold supersonic flow tests showed that an uncertainty of approximately 10 percent is achievable. An uncertainty of 15-20% is estimated for the most severe hot cases. An assortment of variations were applied to the gage to extend gage life. The most significant was the replacement of the oil in the sensing gap with a silicon rubber, eliminating service requirements. Tests at all of the facilities confirmed that the rubber-filled gages provided approximately the same level of accuracy as was achieved with the original oil-filled gage design, except when shocks impacted the gage head. / Ph. D.

In the pursuit of developing hypersonic cruise vehicles, unstart is a major roadblock to achieving stable flight. Unstart occurs when a sudden instability in the combustor of a vehicle’s propulsion system creates an instantaneous pressure rise that initiates a shock. This shock travels upstream out of the inlet of the vehicle, until it is ejected from the inlet and creates a standing shockwave that chokes the flow entering the vehicle, thereby greatly reducing its propulsive capability. In severe cases, this can lead to the loss of the vehicle. This thesis presents the results of a computational study of the dynamics of unstart near Mach 5 and presents some possible precursor signals that may indicate its presence in flight. Using SU2, an open-source CFD code developed at Stanford University, the Unsteady Reynolds-Averaged Navier-Stokes equations are used to develop a model for flow in a scramjet inlet-isolator geometry, both in the fully started state and during unstart. The results of these calculations were compared against experimental data collected by J. Wagner, at the University of Texas, Austin. In the present computations, unstart was initiated through the use of an artificial body force, which mimicked a moveable flap used in the experiments. Once the results of the code were validated against these experiments, a selection of parametric studies were conducted to determine how the design of the inlet-isolator by Wagner affected the flow, and thus how generalizable the results can be. In addition, precursor signals indicative of unstart were identified for further study and examined in the different parametric studies. It was found that a thick boundary layer is conducive to a stronger precursor signal and a slower unstart. In addition, an aspect ratio closer to 1:1 promotes flow mixing and reduces the unstart speed and strength. Moreover, an aspect ratio in this range reduces the precursor signal strength but, if a thick boundary layer is present, will smear the signal out over a larger area, potentially making it easier to detect. <br>

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.

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In this thesis, effects of sonic lateral jets on aerodynamics of missiles and missilelike geometries are investigated numerically by commercial Computational Fluid Dynamics (CFD) software FLUENT. The study consists of two parts. In the first part, two generic missile-like geometries with lateral jets, of which experimental data are available in literature, are analyzed by the software for validation studies. As the result of this study, experimental data and CFD results are in good agreement with each other in spite of some discrepancies. Also a turbulence model study is conducted by one of test models. It is also found out that k-&epsilon / turbulence model is the most suitable model for this kind of problems in terms of accuracy and ease of convergence. In the second part of the thesis, parametric studies are conducted on a generic supersonic missile, NASA TCM, to see the effect of jet parameters on missile and component force and moments in pitch plane. Variable parameters are jet location, jet mass flow rate and angle of attack. As a result, it was found out that downstream influence zone of jet exit is more than the upstream influence zone. Normal force occurring by the interaction of the free stream and jet plume are amplified whenever the jet exit is located between lifting surfaces. Greater pitching moments are obtained when the jet exit moment arm with respect to moment reference center or jet mass flow rate is increased.

The main objective of this thesis is to develop a comprehensive model with the capability of modeling both a high Reynolds number and high magnetic Reynolds number turbulent flow for application to supersonic combustor. The development of this model can be divided into three categories: one, the development of a self-consistent MHD numerical model capable of modeling magnetic turbulence in high magnetic Reynolds number applications. Second, the development of a gas discharge model which models the interaction of externally applied fields in conductive medium. Third, the development of models necessary for studying supersonic combustion applications with plasma-assistance such the extension of chemical kinetics models to extremely high temperature and non-equilibrium phenomenon.