<div>A 7° half-angle cone with a highly-swept fin was tested in the Boeing/AFOSR Mach-6 Quiet Tunnel at 0.0° angle of attack. Previous measurements of the surface heat transfer using temperature sensitive paint revealed heating streaks on the cone surface related to streamwise vortices generated by the fin shock. High-frequency measurements of the cone-surface pressure fluctuations revealed that transition occurs in the streak region at sufficiently-high freestream unit Reynolds numbers under quiet flow. In this work, high-resolution measurements of the surface heat transfer are obtained using infrared thermography and a polyether-ether-ketone wind-tunnel model. In addition, a novel model design made it possible to measure pressure fluctuations throughout the streak region on the cone surface.</div><div><br></div><div>A slender cone with a sharp nosetip and a fin swept back 75° with a 3.18 mm leading-edge radius served as the primary geometry for this work. Two laminar heating streaks</div><div>were measured on the cone surface. These travel along a line of nearly-constant azimuth. A hot spot develops in the streak farthest from the fin, which then moves upstream with increasing freestream Reynolds number. Downstream of this hot spot, the streaks begin to spread in azimuth. The heat transfer along the outer streak shows a threefold increase near the hot spot before decreasing back to nearly two times the laminar streak heating. The amplitude of the pressure fluctuations increases simultaneously with the heat transfer, reaching a peak of nearly 9% of the Taylor-Maccoll pressure for a 7° straight cone. Power spectral densities calculated from these fluctuations demonstrate spectral broadening, which is indicative of boundary-layer transition. Using surface-pressure-fluctuation and heat-flux measurements, transition onset was estimated to occur at an axial length Reynolds number of 2.2×10⁶. Pressure sensors that were rotated through the streak region showed that multiple instabilities amplify between the heating streaks, upstream of the transition onset location. Downstream of transition onset, the highest-amplitude instabilities are localized to the hot spot in the outer streak. The effect of freestream noise on transition was also investigated with this geometry. Under conventional noise levels, transition onset was estimated to occur at an axial length Reynolds number of 0.93×10⁶, and only one instability was measured in the streak region with a frequency similar to the second-mode instability.</div><div><br></div><div>Four configurations were tested to investigate the effect of fin sweep and nosetip bluntness under quiet flow. Fins with 70° and 75° sweep were each tested with nominally sharp and 1-mm-radius nosetips. Increasing fin sweep was shown to move the heating streaks on the cone closer to the fin and to decrease the peak-to-peak spacing of the streaks. In addition, transition onset occurred at lower freestream unit Reynolds numbers for the 70° sweep case. Increasing nosetip radius had little effect on the heating streaks, other than to delay the transition location. A blunt nosetip was shown to delay transition more for the 75° sweep fin as compared to the 70° fin. Similar instabilities were measured for all four of the configurations in this work. The frequency of the instabilities appears to be correlated with the peak-to-peak distance of the heating streaks, which can be viewed as an indirect measurement of the vortex diameter.</div><div><br></div><div>Lastly, the first quantitative measurements of heat transfer on the fin were made using the infrared thermography apparatus. Peak heating on the fin, not including the leading edge, is lower than peak heating rates on the cone. One broad heating streak was measured close to the corner, and smaller low-heating streaks were measured farther outboard. The heating within the streak closest to the corner was shown to agree well with a fully-laminar computed basic state, indicating that the flow on the fin is laminar up to at least 6.31×10⁶ m⁻¹. Using miniaturized Kulite sensors, pressure fluctuations were measured at twelve locations on the fin surface. No obvious conclusions could be drawn from these Kulite measurements, and there is no clear indication that transition occurs on the fin within the maximum quiet</div><div>freestream conditions.</div>

<div>Wind-tunnel experiments with a sharp 7-degree half-angle cone and a 33% scale Boundary Layer Transition (BOLT) model were performed in the Boeing/AFOSR Mach 6 Quiet Tunnel to investigate the effects of forward- and backward-facing steps on boundary-layer instability and transition. Each model was modified to include intentional steps just downstream of the nosetip. Experiments were performed at different freestream Reynolds numbers and varying step sizes. Infrared thermography was used to calculate surface heat transfer, and high-frequency pressure sensors were used to measure pressure fluctuations. A replica measurement technique was used to accurately measure step heights on the BOLT flight vehicle and the wind tunnel model.</div><div><br></div><div>A 7-degree half-angle cone was tested at 0-degree and 6-degree angles of attack. Step heights ranged from 0.610 mm to 1.219 mm. At a 0-degree angle of attack, no significant increases in heat transfer were observed with any of the forward- or backward-facing steps. However, a 250 kHz instability was measured with the forward-facing steps. Growth of the instability was similar to a second-mode. At a 6-degree angle of attack, an increase in heat transfer was observed on the windward ray with the forward-facing steps. Sharp increases in heating rates and increased pressure fluctuations were indications of boundary-layer transition. Elevated heating rates and pressure fluctuations were not measured with the backward-facing steps.</div><div><br></div><div>The BOLT model was tested at 0-degree, 2-degree, and 4-degree angles of attack and 2-degree and 4-degree yaw angles. Step heights ranged from 0.076 mm to 1.016 mm. At a 0-degree angle of attack and 0-degree yaw angle, thin wedges of heating were observed with the backward-facing steps. Instabilities were measured near these wedges of heating and are thought to be caused by a secondary instability. The effects of the steps were magnified on the windward side of the BOLT model at angles of attack. Wedges of heating were wider and more intense. At higher angles of attack, the onset of heating was further upstream. Sensors near and directly underneath the wedges of heating measured pressure fluctuations that were indicative of a turbulent flow. Wedges of heating were also observed at a 4-degree yaw angle, but only with the 1.016 mm backward-facing step.</div>

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Flow temperature sensing remains important for many hypersonic aerodynamics and propulsion applications. Flight test applications, in particular, demand robust and accurate sensing, making thermocouple sensors attractive. Even for these extremely well-developed sensors, the prediction of stresses (hoop, radial, and axial) within thermocouple sheaths for custom-configured probes remains a topic of great concern for ensuring adequate lifetime of sensors. In contemporary practice, high-fidelity simulations must be run to prove if a new design will work at all, albeit at significant time and expense. Given the time and money it takes to run high-fidelity simulations, rapid optimization of sensor configurations is often impossible, or at a minimum, impractical. The developments presented in this Thesis address the need for hypersonic flow temperature sensor structural predictions which are compatible with rapid design iteration. The derivation and implementation of a new analytical, low-order model to predict stresses (hoop, radial, and axial) within the sheath of a thermocouple are provided. The analytical model is compared to high-fidelity ANSYS mechanical simulations as well as simplified experimental data. The predictions using the newly developed structural low-order model are in excellent agreement with the numerically simulated results and experimental results with an absolute maximum percent error of approximately 4% and 9.5%, respectively, thus validating the model. A MATLAB GUI composed of the combination of a thermal low-order model outlined in additional references [1] through [6] and the new structural low-order model for thermocouples was developed. This code is capable of solving a highly generalized version of the 1-D pin fin equation, allowing for the solution of the temperature distribution in a sensor taking into account conduction, convection, and radiation heat transfer which is not possible with other existing analytical solutions. This temperature distribution is then used in the analytical structural low-order model. This combination allows for the thermal and structural performance of a thermocouple to be found analytically and compared quickly with other designs. / M.S. / Thermocouples are a device for measuring temperature, consisting of two wires of different metals connected at two different points. This configuration produces a temperature-dependent voltage as a result of the thermoelectric effect. Preexisting curves are used to relate the voltage to temperature. Thermocouples are extensively used in high-temperature high-stress environments such as in rockets, jet engines, or any high-corrosive environment. Accurately predicting the stresses within the sheath of a metal-clad thermocouple in extreme conditions is required for many research areas including hypersonic aerodynamics and various propulsion applications. Even for these extremely well-developed and widely used sensors, the accurate prediction of stresses within the metal sheath remains a topic of great concern for ensuring the sensor’s survivability in these extreme conditions. Current engineering practice is to use high-fidelity numerical simulations (Finite Element Analysis) to predict the stresses within the sheath. Perhaps the biggest drawback to this approach is the time it takes to model, mesh, and set-up these simulations. Comparative studies between different designs using numerical simulations are almost impossible due to the time requirement. This Thesis will present an analytically derived quasi-3D solution to find the stresses within the sheath. These equations were implemented into a low-order model that can handle varying temperature, geometry, and material inputs. This model was validated against both high-fidelity numerical simulations (ANSYS Mechanical) and a simplified experiment. The predictions using this newly developed structural low-order model are in excellent agreement with the numerically simulated results and experimental results.

The Volume-of-Fluid method, an Eulerian multiphase flow model that adds a volume fraction transport equation to the CFD governing equations, is widely used for any fluid-fluid interface tracking problem. There are important aspects of multiphase flow that impact aircraft flight, especially flight in extreme environments. These extreme environments can range from wet, icy conditions to sandstorms, and volcanic debris. The problems posed by these harsh environments are only exacerbated by aircraft that tend to travel at higher Mach-numbers. The specific aims of the proposed research include application of the Volume-of-fluid method to the following aspects of aircraft flight: shock-droplet interactions, and molten CMAS infiltrating a thermal barrier coating. Passive scalars are used in novel ways to elucidate droplet breakup physics. From this, a mechanism for how instabilities form on the air-droplet interface is discovered. It is also found that non-cavitating droplet breakup becomes much less dependent on Mach number at higher Mach numbers. A cavitation model designed for underwater explosions is adapted to the shock-droplet problem, and results show that cavitation phenomena is greatly dependent on Mach number, but the adapted model overpredicts cavitation effects. 2D and 3D CFD models are developed for the CMAS infiltration problem, and those are compared to analytical models from literature, and a new proposed analytical model called the feathery pipe network model. Results show that feathery pipe network model is both computationally inexpensive, and allows parameterization of useful properties.

The spatial stability of hypersonic conical boundary layers is investigated utilizing different numerical techniques. First, the development and verification of a Linearized Compressible Navier-Stokes solver (LinCS) is presented, followed by an investigation of different effects that affect the stability of the flow in free-flight/ground tests, such as: high-enthalpy effects, wall-temperature ratio, and three-dimensionality (i.e. angle-of-attack). A temporally/spatially high-order of accuracy parallelized Linearized Compressible Navier-Stokes solver in disturbance formulation was developed, verified and employed in stability investigations. Herein, the solver was applied and verified against LST, PSE and DNS, for different hypersonic boundary-layer flows over several geometries (e.g. flat plate - M=5.35 & 10; straight cone - M=5.32, 6 & 7.95; flared cone - M=6; straight cone at AoA = 6 deg - M=6). The stability of a high-enthalpy flow was investigated utilizing LST, LinCS and DNS of the experiments performed for a 5 deg sharp cone in the T5 tunnel at Caltech. The results from axisymmetric and 3D wave-packet investigations in the linear, weakly, and strongly nonlinear regimes using DNS are presented. High-order spectral analysis was employed in order to elucidate the presence of nonlinear couplings, and the fundamental breakdown of second mode waves was investigated using parametric studies. The three-dimensionality of the flow over the Purdue 7 deg sharp cone at M=6 and AoA =6 deg was also investigated. The development of the crossflow instability was investigated utilizing suction/blowing at the wall in the LinCS/DNS framework. Results show good agreement with previous computational investigations, and that the proper basic flow computation/formation of the vortices is very sensitive to grid resolution.

A key remaining challenge in the design of hypersonic vehicles is the incomplete understanding of the process of boundary-layer transition. Turbulent heating rates are substantially higher than those for a laminar boundary layer, and large uncertainties in transition prediction therefore demand conservative, inefficient designs for thermal protection systems. It is only through close collaboration between theory, experiment, and computation that the state of the art can be advanced, but experiments relevant to flight require ground-test facilities with very low disturbance levels. To enable this work, a unique Mach 6 low-disturbance wind tunnel, previously of NASA Langley Research Center, is established within a new pressure-vacuum blow-down infrastructure at Texas A&M. A 40-second run time at constant conditions enables detailed measurements for comparison with computation. The freestream environment is extensively characterized, with a large region of low-disturbance flow found to be reliably present for unit Reynolds numbers Re < 11×10^6 m-1. Experiments are performed on a 5º half-angle flared cone model at Re = 10×10^6 m-1 and zero angle of attack. For the study of the second-mode instability, well-resolved boundary-layer profiles of mean and fluctuating mass flux are acquired at several axial locations using hot-wire probes with a bandwidth of 330 kHz. The second mode instability is observed to undergo significant growth between 250 and 310 kHz. Mode shapes of the disturbance agree well with those predicted from linear parabolized stability equation (LPSE) computations. A 17% (40 kHz) disagreement is observed in the frequency for most-amplified growth between experiment and LPSE. Possible sources of the disagreement are discussed, and the effect of small misalignments of the model is quantified experimentally. A focused schlieren deflectometer with high bandwidth (1 MHz) and high signal-to-noise ratio is employed to complement the hot-wire work. The second-mode fundamental at 250 kHz is observed, as well as additional harmonic content not discernible in the hot-wire measurements at two and three times the fundamental. A bispectral analysis shows that after sufficient amplification of the second mode, several nonlinear mechanisms become significant, including ones involving the third harmonic, which have not hitherto been reported in the literature.

During atmospheric entry, a spacecraft's aeroshell uses a thermal protection system (TPS) to withstand severe thermal loads. Heating to the vehicle surface arises as convective, catalytic and radiative heat flux due to the high temperature of the shockwave compressed gases surrounding the aeroshell. The problem for the TPS designer is that the heat load estimates are based on phenomenological models which have questionable validity and, thus, large uncertainty. As an example, recent analyses of heat loads for a proposed aerocapture vehicle designed for Titan differ by up to an order of magnitude. This uncertainty stems from the complexity of the blunt body flow field and the associated physical effects: thermochemical nonequilibrium; ablation and vehicle surface catalycity; and radiating flow. The motivation for this thesis is to develop computational tools that give accurate estimates of vehicle heat transfer as an input for design calculations. With that goal in mind, this thesis work has focussed on one aspect of this problem and that is the modelling of thermochemical nonequilibrium. The longer term goal is to produce tools which can be used to compute the high-temperature, radiating flow fields about aeroshell configurations; the modelling work presented here on thermochemical nonequilibrium effects is a foundation for tackling the radiating flow problem. The modelling work was implemented in an existing flow solver which solves the compressible Navier-Stokes equations with a finite volume method. As part of this work, the flow solver was verified by two methods: the Method of Manufactured Solutions to verify the spatial accuracy for purely supersonic flow; and the Method of Exact Solutions --- the flow problem being an oblique detonation wave --- to verify the spatial accuracy for flows with embedded shocks. Validation of the flow solver, without any of the complexity of thermochemical nonequilibrium, was performed by comparing numerical simulation results to experiments which measured shock detachment on spheres fired into noble gases. A model for chemical nonequilibrium based on the Law of Mass Action and using finite-rate kinetics was coupled with the flow solver. The implementation was verified on two test problems. The first treated a closed-vessel reactor of a hydrogen-iodine mixture, and the second computed the chemically relaxing flow behind a normal shock in air. For validation, the implementation was tested by computing ignition delay times in hydrogen-air mixtures and comparing to experimental results. It was found that the selection of a chemical kinetics scheme can complicate validation, that is, a poor choice of reaction scheme leads to poor computational results yet the implementation is correct. As further validation, a series of experiments on the shock detachment distance on spheres fired into air was compared against numerical simulations based on the present work. Two models for species diffusion were also implemented: Fick's first law approximation and the Stefan-Maxwell equations. These models were verified by comparison to an exact solution for binary diffusion of two semi-infinite slabs. The more general problem of thermochemical nonequilibrium was also pursued. A multi-temperature model, one translational/rotational temperature and multiple vibrational temperatures, was developed as appropriate for hypersonic flows. The model uses the Landau-Teller expression to compute the rate of vibrational-translational energy exchange and the Schwartz-Slawsky-Herzfeld expression for vibrational-vibrational energy exchange. The time constants for the rate expressions are estimated by a number of methods such as the use of SSH theory and the Millikan-White correlation. The coupling of vibrational nonequilibrium effects with the fluid dynamics was tested by computing the flow of nitrogen over an infinite cylinder. The simplified problem of a vibrationally relaxing flow behind a shock, without reactions, was compared to other calculations in the literature. This case tested the multi-temperature formulation, with oxygen and nitrogen each being ascribed their own vibrational temperatures. The coupling of chemistry and vibrational nonequilibrium uses the model by Knab, Fruehauf and Messerschmid. The complete model for thermochemical nonequilibrium was verified by calculating the relaxation of oxygen behind a strong shock. The models developed provide a basis for computing radiating flow fields, however the radiating flow problem cannot be attempted based on this work alone. Instead, a more immediate application of the modelling work was the simulation of expansion tube operation. It is desirable to simulate an impulse facility to give the experimenters access to aspects of experiment that are not directly attainable by experiment; especially a complete characterisation of the test flow properties. The modelling work and code development, as part of this thesis, addresses this need of experimenters. Two large-scale simulations are presented as a demonstration of the modelling work: (a) a simulation of an expansion tube in expansion mode; and (b) a simulation of an expansion tube in nonreflected shock tube mode.