Recent investigations of a strut-braced wing (SBW) aircraft show that, at high positive load factors, a large tensile force in the strut leads to a considerable compressive axial force in the inner wing, resulting in a reduced bending stiffness and even buckling of the wing. Studying the influence of this compressive force on the structural response of SBW is thus of paramount importance in the early stage of SBW design. The purpose of the this research is to investigate the effect of compressive force on aeroelastic stability of the SBW using efficient structural finite element and aerodynamic lifting surface methods. A procedure is developed to generate wing stiffness distribution for detailed and simplified wing models and to include the compressive force effect in the SBW aeroelastic analysis. A sensitivity study is performed to generate response surface equations for the wing flutter speed as functions of several design variables. These aeroelastic procedures and response surface equations provide a valuable tool and trend data to study the unconventional nature of SBW. In order to estimate the effect of the compressive force, the inner part of the wing structure is modeled as a beam-column. A structural finite element method is developed based on an analytical stiffness matrix formulation of a non-uniform beam element with arbitrary polynomial variations in the cross section. By using this formulation, the number of elements to model the wing structure can be reduced without degrading the accuracy. The unsteady aerodynamic prediction is based on a discrete element lifting surface method. The present formulation improves the accuracy of existing lifting surface methods by implementing a more rigorous treatment on the aerodynamic kernel integration. The singularity of the kernel function is isolated by implementing an exact expansion series to solve an incomplete cylindrical function problem. A hybrid doublet lattice/doublet point scheme is devised to reduce the computational time. SBW aircraft selected for the present study is the fuselage-mounted engine configuration. The results indicate that the detrimental effect of the compressive force to the wing buckling and flutter speed is significant if the wing-strut junction is placed near the wing tip. / Ph. D.

Bats have many impressive flight characteristics such as the ability to rapidly change direction, carry substantial loads, and maintain good flight efficiency. For several years, researchers have been working towards an understanding of the specific aerodynamic phenomena which relate the unique wing structure of bats to their flight abilities. Computational fluid dynamics, a powerful tool used extensively across aerospace research, has led to substantial progress in the understanding of insect flight. However, due to technical challenges, numerical simulation has seen limited use in bat flight research. For this research, we develop, validate, and apply computational modeling techniques to three modes of bat flight: straight flight, sweeping turn, and U-turn maneuver. 3D kinematic data collection was achieved using a 28 camera multi-perspective optical motion capture system. The calibration of the cameras was conducted using a multi-camera self-calibration method. Point correspondences between cameras and frames was achieved using a human-supervised software package developed for this project. After the collection of kinematic data, we carried out aerodynamic flow simulations using the incompressible Navier-Stokes solver, GenIDLEST. The immersed boundary method (IBM) was used to impose moving boundary conditions representing the wing kinematics. Validation of the computational model was preformed through a grid independence study as well as careful evaluation of other relevant simulation parameters. Verification of the model was performed by comparing simulated aerodynamic loads to the expected loads based on the observed flight trajectories. Additionally, we established that we had a sufficient resolution of the wing kinematics, by calculating the sensitivity of the simulation results to the number of kinematic markers used during motion capture. For this study, three particular flights are analyzed—a straight and level flight, a sweeping turn, and a sharp 180 degree turn. During straight flight, typical flight velocities observed in the flight tunnel were 2-3 m/s resulting in a Reynolds number of about 12,000. Lift generation occurred almost exclusively during the downstroke, and peaks mid-downstroke. At the beginning of each downstroke, the effective angle of attack of the wings transitions from negative to positive and a leading edge vortex (LEV) quickly forms. LEVs are known to augment lift generation in flapping flight and allow lift to remain high at large angles of attack. During the end of each downstroke, the LEVs break up and lift drops substantially. As the wingbeat cycle transitions from downstroke to upstroke, the wings rotate such that the wing chordline is vertical as the wing moves upward. This wing rotation is critical for mitigating negative lift during the upstroke. Many of the basic flight mechanisms used for straight flight—i.e. LEV formation, wing rotation during upstrokes—were also observed during the sweeping turn. In addition, asymmetries in the wing kinematics and consequently the aerodynamics were observed. Early in the turn, the bank angle was low and elevated levels of thrust were generated by the outer wing during both the upstroke and downstroke causing a yaw moment. As the bat moved towards the middle of the turn, the bank angle increased to 20-25 degrees. Although the bank angle remained nominally constant during the middle and later portion of the turn, there was variation within each wingbeat cycle. Specifically, the bank angle dropped during each upstroke and subsequently was recovered during each downstroke as a consequence of elevated lift on the outer wing. Banking served to redirect the net force vector laterally causing a radial, centripetal force. Considering the mass of the bat, the nominal flight velocity, and the radius of curvature, the magnitude of the radial force fully explained the expected centripetal acceleration during the middle and later portion of the turn. Over the entire turn, yaw was found to be important in initiating the turn while banking was more important during the middle part of the turn. Over the course of 5 wingbeat cycles, the change in bearing angle (direction of flight) was about 45 degrees. Analysis of the U-turn flight showed many of the same characteristics as were observed during the sweeping turn, as well as a few key differences. The bat's ability to rotate its body rapidly appears to be more limited than its ability to change its trajectory. For this reason, the yaw rotation began about one to two cycles before the rapid bearing angle change and was stretched out over several wingbeat cycles. At the apex of the U-turn, the bat combined a high roll angle with a low flight velocity magnitude to very rapidly redirect its bearing direction and negotiate a low radius of curvature flight trajectory. Increases in roll angle occurred almost exclusively during the downstrokes, while both the upstroke and downstroke were active in generating yaw. Elevated thrust on the left outer wing during the end of the upstroke was observed throughout the flight, and elevated drag on the right inside wing did not appear to have an impact on the turn. We hope that this project motivates and facilitates further computational analysis into bat flight aerodynamics. Additionally, the data and findings will be useful for applications such as the design of bioinspired MAVs or flexible membrane energy harvesting technology. / Doctor of Philosophy / Bats have many impressive flight characteristics such as the ability to rapidly change direction, carry substantial loads, and maintain good flight efficiency. A better understanding of the physics of how bats fly can help scientists and engineers build more maneuverable, quieter, and more efficient bioinspired micro air vehicles. This engineering approach leverages the incredible capabilities observed in nature, but requires detailed knowledge of the animal as a prerequisite. Computational fluid dynamics, a powerful tool used extensively across aerospace research, has led to substantial progress in the understanding of animal flight broadly. However, due to technical challenges, numerical simulation has seen limited use in bat flight research. For this research, we develop, validate, and apply computer modeling techniques to the investigation of bat flight aerodynamics. Three particular modes of flight were analyzed—a straight and level flight, a sweeping turn, and a sharp 180 degree turn. During straight flight, typical flight velocities observed in the flight tunnel were 2-3 m/s. Lift generation, the force keeping the bat aloft, occurred almost exclusively during the downstroke, and peaks mid-downstroke. As the wing flap transitions from downstroke to upstroke, the wings rotate such that the wing is vertical as it moves upward. This wing rotation is critical for maximizing lift force during flight. During the sweeping turn, asymmetries in the wing kinematics and consequently the aerodynamics were observed. Early in the turn, the bank angle was low and elevated levels of thrust were generated by the outer wing during both the upstroke and downstroke causing rotation of the bat. As the bat moved towards the middle of the turn, the bank angle increased to 20-25 degrees. Banking served to redirect the net force vector laterally causing a turning force. Over the course of 5 wingbeat cycles, the change in direction of flight was about 45 degrees. Analysis of the U-turn flight showed many of the same characteristics as were observed during the sweeping turn, as well as a few key differences. At the apex of the U-turn, the bat combined a high roll angle with a low flight velocity magnitude to very rapidly redirect its bearing direction and negotiate a low radius of curvature flight trajectory. We hope that this project motivates and facilitates further computer simulations studying bat flight aerodynamics. Additionally, the data and findings will be useful for applications such as the design of bioinspired MAVs or flexible membrane energy harvesting technology.

Axisymmetric and swirling jets are generic flows that characterize many natural and man-made flows. These include cylindrical shear layer/mixing layer flows, aircraft jets and wakes, shedding of leading edge and wing tip vortices, tornadoes, astrophysical plasma flows and flows in mechanical devices such as supersonic combustion chambers and cyclone separators. These and other applications have resulted in a high level of interest in the stability of axisymmetric and swirling jets. To date, the majority of studies on stability of axisymmetric and swirling jets have been completed under the assumption of steady flow in both axial and azimuthal (swirl) directions. Yet, flows such as the ones mentioned above can have an inherent unsteadiness. Moreover, such unsteadiness can be used to control stability and thus flow characteristics in axisymmetric and swirling jets. In this work effects of periodic variations on the temporal stability of axisymmetric and swirling jets is examined. The unsteadiness is introduced in the former as a periodic variation of the axial velocity component of the flow, and in the latter as a periodic variation of the azimuthal (swirl) velocity component of the flow. The temporal linear hydrodynamic stability of both steady inviscid axisymmetric and swirling jets is reviewed. An analytical dispersion relation is obtained in both cases and solved numerically. In the case of the steady axisymmetric jet, growth rate and celerity of unstable axisymmetric and helicalmodes are determined as functions of axial wavenumber. Results show that the inviscid axisymmetric jet is unstable to all values of axisymmetric and helical modes. In the case of the steady swirling jet, growth rate and celerity of axisymmetric modes are determined as functions of the axial wavenumber and swirl number. Results show that the inviscid swirling jet is unstable to all values of axial and azimuthal wavenumber, however, it is shown that increasing the swirl decreases the growth rate and increases the celerity of axisymmetric disturbances. The effects of periodic variations on the stability of a mixing layer is also reviewed. Results show that when the instability time scale is much smaller than the mean time scale a transformation of the time variable may be taken that, when the quasi-steady approach works, will reduce the unsteady field to that of the corresponding steady field in the new time scale. The price paid for this transformation, however, is a modulation of the amplitude and phase of the unsteady modes. Extending the results from the unsteady mixing layer, the stability of a periodically unsteady inviscid axisymmetric jet is considered. An analytical dispersion relation is obtained and results show that for the unsteady inviscid axisymmetric jet, the quasi-steady approach works. Following this, the stability of a periodically unsteady swirling jet is considered and an analytical dispersion relation is obtained. It is shown that for the unsteady inviscid swirling jet, the quasi-steady approach does not work. Resulting modulations of unsteady modes are shown via a numerical solution to the unsteady dispersion relation. In both cases, using established results for unsteady mixing layers, these results are substantiated analytically by showing that the unsteady axisymmetric jet can be reduced the the exact equational form of the steady axisymmetric jet in a new time scale, whereas the unsteady swirling jet cannot. / Master of Science

Unsteady aerodynamic modeling is indispensable in the design process of rotary air vehicles, flapping flight and agile unmanned aerial vehicles. Undesirable vibrations can cause high-frequency variations in motion variables whose effects cannot be well predicted using quasi-steady aerodynamics. Furthermore, one may exploit the lift enhancement that can be generated through an unsteady motion for optimum design of flapping vehicles. Additionally, undesirable phenomena like the flutter of fixed wings and ensuing limit cycle oscillations can be exploited for harvesting energy. In this dissertation, we focus on modeling the unsteady nonlinear aerodynamic response and present various applications where unsteady aerodynamics are very relevant. The dissertation starts with experiments for measuring unsteady loads on an NACA-0012 airfoil undergoing a plunging motion under various operating conditions. We supplement these measurements with flow visualization to obtain better insight into phenomena causing enhanced lift. For the model, we present the frequency response function for the airfoil at various angles of attack. Experiments were performed at reduced frequencies between 0.1 and 0.95 and angles of attack up to 65 degrees. Then, we formulate an optimization problem to unify the transfer function coefficients for each regime independently to obtain one model that represents the global dynamics. An optimization-based finite-dimensional (fourth-order) approximation for the frequency responses is developed. Converting these models to state-space form and writing the entries of the matrices as polynomials in the mean angle of attack, a unified unsteady model was developed. In the second set of experiments, we measured the unsteady plunging forces on the same airfoil at zero forward velocity. The aim is to investigate variations of the added forces associated with the oscillation frequency of the wing section for various angles of attack. Data of the measured forces are presented and compared with predicted forces from potential flow approximations. The results show a significant departure from those estimates, especially at high frequencies indicating that viscous effects play a major role in determining these forces. In the second part of this dissertation, we consider different applications where unsteady loads and nonlinear effects play an important role. We perform a multi-objective aerodynamic optimization problem of the wing kinematics and planform shape of a Pterosaur replica ornithopter. The objective functions included minimization of the required cycle-averaged aerodynamic power and maximization of the propulsive efficiency. The results show that there is an optimum kinematic parameter as well as planform shape to fulfill the two objectives. Furthermore, the effects of preset angle of attack, wind speed and load resistance on the levels of harvested power from a composite beam bonded with the piezoelectric patch are determined experimentally. The results point to a complex relation between the aerodynamic loading and its impact on the static deflection and amplitudes of the limit cycle oscillations as well as the level of power harvested. This is followed by testing of a centimeter scale micro wind turbine that has been proposed to power small devices and to work as a micro energy harvester. The experimental measurements are compared to predicted values from a numerical model. The methods developed in this dissertation provide a systematic approach to identifying unsteady aerodynamic models from numerical or experimental data that may work within different regimes. The resulting reduced-order models are expressed in a state-space form, and they are, therefore, both simple and efficient. These models are low-dimensional linear systems of ordinary differential equations so that they are compatible with modern flight dynamic models. The specific form of the obtained added force model, which defines the added forces as a function of plunging velocity and drag forces, guarantees that the resulting model is accurate over a range of high frequencies. Moreover, presented applications give a sense of the broad range of application of unsteady aerodynamics. / Ph. D.

The development of aerodynamic boundary layers on wind turbine blades is an important consideration in their performance. It can be quite challenging to replicate full scale conditions in laboratory experiments, and advanced diagnostics become valuable in providing data not available from traditional means. A new variant of Doppler global velocimetry (DGV) known as cross-correlation DGV is developed to measure boundary layer profiles on a wind turbine blade airfoil in the large scale Virginia Tech Stability Wind Tunnel. The instrument provides mean velocity vectors with reduced sensitivity to external conditions, a velocity measurement range from 0ms^-1 to over 3000ms^-1, and an absolute uncertainty. Monte Carlo simulations with synthetic signals reveal that the processing routine approaches the Cramér-Rao lower bound in optimized conditions. A custom probe-beam technique is implanted to eliminate laser flare for measuring boundary layer profiles on a DU96-W-180 wind turbine airfoil model. Agreement is seen with laser Doppler velocimetry data within the uncertainty estimated for the DGV profile. Lessons learned from the near-wall flow diagnostics development were applied to a novel benchmark model problem incorporating the relevant physical mechanisms of the high amplitude periodic turbulent flow experienced by turbine blades in the field. The model problem is developed for experimentally motivated computational model development. A circular cylinder generates a periodic turbulent wake, in which a NACA 63215b airfoil with a chord Reynolds number Re_c = 170, 000 is embedded for a reduced frequency k = (pi)fc/V = 1.53. Measurements are performed with particle image velocimetry on the airfoil suction side and in highly magnified planes within the boundary layer. Outside of the viscous region, the Reynolds stress profile is consistent with the prediction of Rapid Distortion Theory (RDT), confirming that the redistribution of normal stresses is an inviscid effect. The fluctuating component of the phase- averaged turbulent boundary layer profiles is described using the exact solution to laminar Stokes flow. A phase lag similar to that in laminar flow is observed with an additional constant phase layer in the buffer region. The phase lag is relevant for modeling the intermittent transition and separation expected at full scale. / Ph. D.

Biological systems offer novel and efficient solutions to many engineering applications, including marine propulsion. It is of interest to determine how fish interact with the water around them, and how best to utilize the potential their methods offer. A stingray-like fin was chosen for analysis due to the maneuverability and versatility of stingrays. The stingray fin was modeled in 2D as a sinusoidal wave with an amplitude increasing from zero at the leading edge to a maximum at the trailing edge. Using this model, a parametric study was performed to examine the effects of the fin on surrounding water in computational fluid dynamics (CFD) simulations. The results were analyzed both qualitatively, in terms of the pressure contours on the fin and vorticity in the trailing wake, and quantitatively, in terms of the resultant forces and the mechanical power requirements to actuate the desired fin motion. The average thrust was shown to depend primarily on the relationship between the swimming speed and the frequency and wavelength (which both are directly proportional to the wavespeed of the fin), although amplitude can be used to augment thrust production as well. However, acceleration was shown to significantly correlate with a large variation in lift and moment, as well as with greater power losses. Using results from the parametric study, the potential for power regeneration was also examined. Relationships between frequency, velocity, drag, and power input were determined using nonlinear regression that explained more than 99.8% of the data. The actuator for a fin was modeled as a single DC motor-shaft system, allowing the combination of the energetic effects of the motor with the fin-fluid system. When combined, even a non-ideal fin model was able to regenerate more power at a given flow speed than was required to swim at the same speed. Even in a more realistic setting, this high proportion of regenerative power suggests that regeneration and energy harvesting could be both feasible and useful in a mission setting. / Master of Science / Animals interact with the world much differently than engineered systems, and can offer new and efficient ways to solve engineering problems, including underwater vehicles. To learn how to move an underwater vehicle in an environmentally conscious way, it is useful to study how a fish’s movements affect the manner in which it moves through the water. Through careful study, the principles involved can be implemented for an efficient, low-disturbance underwater vehicle. The particular fish chosen for in-depth study was the stingray, due to its maneuverability and ability to travel close to the seafloor without disturbing the sediment and creatures around it. In this work, computational analysis was performed on a model of a single stingray fin to determine how the motion of the fin affects the water around it, and how the water affects the fin in turn. The results were analyzed both in terms of the wake behind the fin and in terms of how much power was required to make the fin move in a particular way. The speed of the fin motion was found to have the strongest effect in controlling swimming speed, although the lateral motion of the fin also helped with accelerating faster. Additionally, the potential for a robotic stingray fin to harness power from the water around it was examined. Based on results from simulations of the fin, a mathematical model was formulated to relate energy harvesting with the flow speed past the fin. This model was used to determine how worthwhile it was to use energy harvesting. Analysis of the model showed that harvesting energy from the water was quite efficient, and would likely be a worthwhile investment for an exploration mission.

The influence of tip clearance and angle of attack upon the mid-span unsteady pressure response of a vibrating flat plate was investigated experimentally. Unsteady pressure measurements were taken for a variety of incidence angles, vibration frequencies and tip clearances over a Mach number range of 0.2 to 0.6. It was found that changes in tip clearance had an effect on measured pressure fluctuations at higher angles of attack and larger Mach numbers. It was also observed that the amplitude of the unsteady pressure increased as the incidence angle was increased. The plate was mechanically induced to oscillate in translation, simulating the flISt bending mode. Averaged Fast Fourier Transforms were used to determine pressure oscillation amplitudes and phase lags with respect to the plate motion. / Master of Science

This study focuses on measuring and normalizing the roughness noise of multiple roughness types across numerous layouts and flow speeds. Using the Virginia Tech Anechoic Wall Jet Facility, far field noise was recording for the flow of a turbulent wall jet boundary layer over cubes, hemispheres, and gravel, with element heights in the range of 14.3 - 55.2% of the boundary layer thickness. The sound radiated from the various layouts showed that the elements acted as independent sources when separated by three element diameters center-to-center or more. When the elements were placed shoulder to shoulder, interaction between the elements and shielding of the higher velocity flow lowered the noise per element produced. The far field roughness noise was then normalized using the theory of Glegg et al. (2007), which assumes a dipole efficiency factor. Comparisons were made between the theoretical drag spectrum model proposed by Glegg et al. (1987) and a modified version of this model made using the empirical data gathered. Overall, the theory of Glegg et al. (2007) succeeds greatly in collapsing the data into its non-dimensional drag spectra, but the original model spectrum did not fit well. The modified spectrum showed much greater fit with the data at all layouts and speeds. The collapse of the data using the theory of Glegg et al. (2007) confirms that roughness noise is dipole in nature. / Master of Science

The impressive kinematic capabilities and structural adaptations presented by bio-locomotion continue to inspire some of the advancements in today's small-scaled flying and swimming vehicles. These vehicles operate in a low Reynolds number flow regime where viscous effects dominate flow interactions, which makes it challenging to generate lift and thrust. Overcoming these challenges means utilizing non-conventional lifting and flow control mechanisms generated by unsteady flapping body motion. Understanding and characterizing the aerodynamic phenomena associated with the unsteady motion is vital to predict the unsteady fluid loads generated, to implement control methodologies, and to assess the dynamic stability and control authority of airborne and underwater vehicles. This dissertation presents experimental results for forced oscillations on multi-element airfoils and hydrofoils for Reynolds numbers between Re=104 and Re=106. The document divides the work into four main sections: The first topic presents wind tunnel measurements of lift forces generated by an oscillating trailing edge flap on a NACA-0012 airfoil to illustrate the effects that frequency and pitching amplitude have on lift enhancement. The results suggest that this dynamic trailing edge flap enhances the mean lift by up to 20% in the stalled flow regime. Using frequency response approach, it is determined that the maximum enhancement in circulatory lift amplitude occurs at stalled angles of attack for lower pitching amplitudes. The second topic presents wind tunnel measurements for lift and drag generated by a sinusoidal and non-sinusoidal oscillations of a NACA-0012 airfoil. The results show that 'trapezoidal' pitching enhances the mean lift and the RMS lift by up to 50% and 35% in the pre-stall flow regime, respectively, whereas the 'reverse sawtooth' and sinusoidal pitching generate the most substantial increase of the lift-to-drag ratio in stall and post-stall flow regimes, respectively. The third topic involves a study on the role of fish-tail flexibility on thrust and propulsive efficiency. Flexible tails enhance thrust production in comparison to a rigid ones of the same size and under the same operating conditions. Further analysis indicates that varying the tail's aspect ratio has a more significant effect on propulsive efficiency and the thrust-to-power ratio at zero freestream flow. On the other hand, changing the material's property has the strongest impact on propulsive efficiency at non-zero freestream flow. The results also show that the maximum thrust peaks correspond to the maximum passive tail amplitudes only for the most flexible case. The final topic aims to assess the unsteady hydrodynamic forces and moments generated by a three-link swimming prototype performing different swimming gaits, swimming speeds, and oscillatory frequencies. We conclude that the active actuation of the tail's first mode bending produces the most significant thrust force in the presence of freestream flow. In contrast, the second mode bending kinematics provides the most significant thrust force in a zero-freestream flow. / Doctor of Philosophy / It is by no surprise that animal locomotion continues to inspire the design of flying and swimming vehicles. Although nature produces complex kinematics and highly unsteady flow characteristics, simplified approximations to model bio-inspired locomotion in fluid flows are experimentally achievable using low degrees of freedom motion, such as pitching airfoils and trailing edge flaps. The contributions of this dissertation are divided into four primary foci: (a) wind tunnel force measurements on a flapped NACA-0012 airfoil undergoing forced pitching, (b) wind tunnel measurements of aerodynamic forces generated by sinusoidal and non-sinusoidal pitching of a NACA-0012 airfoil, (c) towing tank measurements of thrust forces and torques generated by a one-link swimming prototype with varying tail flexibilities, and (d) towing tank measurements of hydrodynamic forces and moments generated by active tail actuation of a multi-link swimming prototype. From our wind tunnel measurements, we determine that lift enhancement by a trailing edge flap is achieved under certain flow regimes and oscillating conditions. Additionally, we assess the aerodynamic forces for a sinusoidal and non-sinusoidal pitching of an airfoil and show that 'trapezoidal' pitching produces the largest lift coefficient amplitude whereas the sinusoidal and 'reverse sawtooth' pitching achieve the best lift to drag ratios. From our towing tank experiments, we note that the role of tail flexibility enhances thrust generation on a swimming device. Finally, we conclude that different kinematics on an articulating body strongly affect the hydrodynamic forces and moments. The results of the towing tank measurements are accessible from an online public database to encourage research and contribution in underwater vehicle design through physics-based low-order models that can accommodate hydrodynamic principles and geometric control concepts.

A stator cascade was developed to simulate the flow conditions within a close-stage-spacing transonic axial compressor. Experiments were conducted in a linear transonic blowdown cascade wind tunnel with an inlet Mach number of 0.65. The bow shock from the downstream rotor was simulated by a single moving normal shock generated with a shock tube. First, steady pressure data were gathered to ensure that the stator cascade operated properly without the presence of the shock. Next, the effects of the passing shock on the stator flow field were investigated using shadowgraph photography and Digital Particle Image Velocimetry (DPIV). Measurements were taken for three different shock strengths. In every case studied, a vortex formed near the stator trailing edge as the shock impacted the blade. The size of this vortex was shown to be directly related to the shock strength, and the vortex remained present in the trailing edge flow field throughout the cycle duration. Analysis of the DPIV data showed that the vortex acts as a flow blockage, with the extent of this blockage ranging from 2.9% of the passage for the weakest shock, to 14.3% of the passage for the strongest shock. The vortex was also shown to cause flow deviation up to 75° for the case with the strongest shock. Further analysis estimated that the total pressure losses due to shock-induced vorticity ranged from 46% to 113% of the steady wake losses. Finally, the total pressure loss purely due to the upstream-propagating normal shock was estimated to be roughly 0.22%. / Master of Science