Dissertation Defense Announcements

To stay competitive within the gas turbine community, turbine aero designers strive to maximize the total work output of each turbine stage through a combination of airfoil design improvements and increased total pressure ratio. Although increasing the mass flow rate could achieve a higher power target, the resultant increase in turbine annulus would result in structural limitations due to longer blades which cause increased strain on the blade root as well as amplified flutter and rotor dynamic excitation. An alternative path to achieving higher power output is to maximize the loading of each turbine stage through increased pressure ratio, but this may lead to airfoil limit loading and high aerodynamic losses.

This research systematically develops a detailed methodology to simulate the prediction of airfoil limit loading as well as provides a thorough investigation into the factors that influence the limit loading condition. A computational baseline was established using data previously collected at the Pratt & Whitney Canada High-Speed Wind Tunnel at Carleton University near design conditions using the Reynolds-Averaged Naiver-Stokes shear stress transport k-ω turbulence model (SST) with γ transition. An adaptive mesh refinement algorithm was developed based on the normalized local cell gradients of total pressure, total temperature, density, turbulent kinetic energy, turbulent eddy viscosity and the specific dissipation rate of turbulence. An overall reduction in computational cost was determined as 50% per simulation. The SST turbulence model with Gamma transition was found to have superior predictive veracity compared to other eddy viscosity turbulence models for the limit loading condition.

Variation of turbine inflow conditions were analyzed for four different transonic turbine airfoils based on the potential flow conditions exhausted by an upstream combustor. Influence of inflow conditions was found to be minimal on the exit flow profile with the exception of the mass-flow averaged total pressure loss coefficients. Results show incidence variation to change the total pressure loss coefficient differently for each airfoil, whereas turbulence intensity and turbulent length scale predicted a drastic rise in loss with increased turbulence level for all airfoils considered. The geometric characteristics of each airfoil were also investigated for influence on the stages to limit loading. Similar to previous experimental work, the limit loading pressure ratio and the mass-flow averaged outlet flow angle were strongly correlated with the airfoil outlet metal angle. It was also determined that the airfoil stagger and trailing edge blockage ratio play a role in the determination of the sublimit loading range, although no definitive parameter could be isolated due to lack of specific geometric constraints.

Lastly, the effect of transient vortex shedding on the nature of the trailing edge shock system and subsequent influence on the stages towards limit loading were investigated. A detailed review of the boundary layer states at the trailing edge were performed showing that all of the modeling approaches predicted laminar boundary layer profiles along the pressure surface trailing edge and turbulent profiles along the suction surface. Each modeling strategy (unsteady Reynolds-Averaged Navier Stokes, Delayed Detached Eddy Simulation and turbulence model free) predicted separation along the suction surface during limit loading due to acoustic wave propagation caused by the shock-base pressure interaction, although with varying degrees of size and magnitude. Temporal evolution of the mass flow averaged total pressure loss coefficient downstream of the airfoil allowed for the dominant vortex shedding frequency to be determined and subsequent Strouhal number to be calculated. It was found that each transient modeling strategy predicted the vortex frequency differently. A formal documentation and review were made outlining the required simulation time step to achieve accurate temporal resolution as well as approximate vortex shedding period. Qualitative images of numerical Schlieren (normalized density gradient) contours were presented and reviewed showing large differences in the prediction of vortex shape, size, and subsequent shock influence. Although conclusions were made on modeling ability, without extensive experimental documentation no concrete justification can be made at this time, outlining the importance of an experimental investigation.

Service-learning combines academic coursework with volunteer community service experiences. Its components include the coursework, community service, course credit, and reflection on the experience. Critical service-learning emphasizes social justice (Mitchell, 2008). The broader literature explores both service-learning and critical service-learning, which result in more connections to local communities. Yet, both maintain a central focus on the students engaged in community service, overlooking the rich history of volunteer service within the communities being served. African American communities have been woven together with rich histories of service to the community. Without this historical knowledge, the future of service-learning is destined to continue to utilize an unsustainable model that relies on outside volunteers who come into underserved communities for short periods of time and return to their own lives, leaving the communities to wait on the next wave of volunteers to enter. If the outcomes of service-learning are to impact marginalized communities significantly, then service-learning programs must consider the rich histories of volunteering within these communities. The implications of this study suggest that traditional service learning programs should expand their understanding of the valuable history of volunteering within the Black community.

Since the 1954 Brown v. Board of Education ruling against school segregation, Black women teachers (BWTs) have had perpetually high rates of attrition, despite their legacy of providing high quality, emancipatory education. Thus, the purpose of this study was to contextualize the attrition of critical BWTs to better understand the factors that would support their sustainability in urban schools. Specifically, I investigated (a) the relationship between Black women’s intersectional identities and their experiences as critical educators in urban schools, (b) the compounding factors that led to their ultimate departure, and (c) the complexities of their decision to leave the profession.

Using Black feminist thought and cognitive dissonance theory as my framework, I employed sista circle methodology to study fifteen post-service critical Black women teachers. Each participant engaged in an individual interview, one of three sista circles, and a written reflection. Data analysis revealed three major themes that offer rich context and a complex narrative of why critical BWTs love and leave the classroom: instinct vs. opposition, commitments vs. personal needs, and dissonance-reduction strategies. As they are examined, these themes suggest several actions that can be taken by key stakeholders to support their professional sustainability.

In the past few decades, pairwise distance based statistical methods have been developed to identify spatial and/or temporal clusters of disease, study the association between the dissimilarity of ecological communities and distance in geographical locations. With emergence of high-throughput technologies, pairwise distance base methods are widely used in the analysis of genetics and genomics data, especially when the data structure fails the fundamental assumptions of classical multivariate analysis, including independency and normality. However, much of existing knowledge has been around non-parametric or semi-parametric estimations usually employing permutation techniques to assess statistical significance, which are known to be computationally expensive and sensitive to the choice of permutation.

Majority of this thesis focuses on linear regression of pairwise distance matrices. We consider the pairwise correlation structure between the distances and investigate the large sample properties of the ordinary least square estimator of the model coefficients. Extensive simulations are conducted to evaluate the performance of our method with finite sample size.

Another major component of the thesis is the human microbiome data analysis. We analyze the integrative Human Microbiome Project (iHMP) data set of composition of microbial communities in the digestive tracts of humans by using multiple statistical methods, including our proposed method. The results are presented and interpreted. Existing challenges and future works are also discussed.