Shock Train/Boundary-Layer Interaction in Rectangular Scramjet Isolators

Numerous studies of the dual-mode scramjet isolator, a critical component in preventing inlet unstart and/or vehicle loss by containing a collection of flow disturbances called a shock train, have been performed since the dual-mode propulsion cycle was introduced in the 1960s. Low momentum corner flow and other three-dimensional effects inherent to rectangular isolators have, however, been largely ignored in experimental studies of the boundary layer separation driven isolator shock train dynamics. Furthermore, the use of two dimensional diagnostic techniques in past works, be it single-perspective line-of-sight schlieren/shadowgraphy or single axis wall pressure measurements, have been unable to resolve the three-dimensional flow features inside the rectangular isolator. These flow characteristics need to be thoroughly understood if robust dual-mode scramjet designs are to be fielded. The work presented in this thesis is focused on experimentally analyzing shock train/boundary layer interactions from multiple perspectives in aspect ratio 1.0, 3.0, and 6.0 rectangular isolators with inflow Mach numbers ranging from 2.4 to 2.7. Secondary steady-state Computational Fluid Dynamics studies are performed to compare to the experimental results and to provide additional perspectives of the flow field. Specific issues that remain unresolved after decades of isolator shock train studies that are addressed in this work include the three-dimensional formation of the isolator shock train front, the spatial and temporal low momentum corner flow separation scales, the transient behavior of shock train/boundary layer interaction at specific coordinates along the isolator's lateral axis, and effects of the rectangular geometry on semi-empirical relations for shock train length prediction. A novel multiplane shadowgraph technique is developed to resolve the structure of the shock train along both the minor and major duct axis simultaneously. It is shown that the shock train front is of a hybrid oblique/normal nature. Initial low momentum corner flow separation spawns the formation of oblique shock planes which interact and proceed toward the center flow region, becoming more normal in the process. The hybrid structure becomes more two-dimensional as aspect ratio is increased but corner flow separation precedes center flow separation on the order of 1 duct height for all aspect ratios considered. Additional instantaneous oil flow surface visualization shows the symmetry of the three-dimensional shock train front around the lower wall centerline. Quantitative synthetic schlieren visualization shows the density gradient magnitude approximately double between the corner oblique and center flow normal structures. Fast response pressure measurements acquired near the corner region of the duct show preliminary separation in the outer regions preceding centerline separation on the order of 2 seconds. Non-intrusive Focusing Schlieren Deflectometry Velocimeter measurements reveal that both shock train oscillation frequency and velocity component decrease as measurements are taken away from centerline and towards the side-wall region, along with confirming the more two dimensional shock train front approximation for higher aspect ratios. An updated modification to Waltrup \& Billig's original semi-empirical shock train length relation for circular ducts based on centerline pressure measurements is introduced to account for rectangular isolator aspect ratio, upstream corner separation length scale, and major- and minor-axis boundary layer momentum thickness asymmetry. The latter is derived both experimentally and computationally and it is shown that the major-axis (side-wall) boundary layer has lower momentum thickness compared to the minor-axis (nozzle bounded) boundary layer, making it more separable. Furthermore, it is shown that the updated correlation drastically improves shock train length prediction capabilities in higher aspect ratio isolators. This thesis suggests that performance analysis of rectangular confined supersonic flow fields can no longer be based on observations and measurements obtained along a single axis alone. Knowledge gained by the work performed in this study will allow for the development of more robust shock train leading edge detection techniques and isolator designs which can greatly mitigate the risk of inlet unstart and/or vehicle loss in flight.

THE TERMINATION PHASE: THERAPISTS’ PERSPECTIVE ON THE THERAPEUTIC RELATIONSHIP AND OUTCOME

The termination phase of treatment is recognized as a significant aspect of the therapy process and yet remains vastly understudied in psychotherapy literature. In the present study, therapists’ perspectives were used to examine how three elements of the therapy relationship (working alliance, real relationship and transference) during the termination phase relate to perceived client sensitivity to loss, termination phase evaluation and overall treatment outcome. Self-report data was gathered from 233 therapists, recruited from two Divisions of the American Psychological Association. Therapists completed measures for their work with a client with whom they could identify a termination phase of treatment. Results revealed that the working alliance and real relationship during the termination phase related positively to termination phase evaluation and overall treatment outcome, whereas negative transference during the termination phase related negatively to overall treatment outcome. Therapists’ perceptions of client sensitivity to loss related positively to both negative and positive transference during the termination phase. Post-hoc analyses revealed only the working alliance during the termination phase uniquely predicted overall treatment outcome in a model with the three therapy relationship elements examined together. On the other hand, all three therapy relationship variables during the termination phase uniquely predicted termination phase evaluation, when examined together. Limitations and implications of these findings are discussed, and recommendations for future study are suggested.