Accurate models for the mixing of fuel and oxidizer at small, unresolved flow length scales are critical to the predictive skill of large eddy simulation (LES) of turbulent combustion. Subfilter scalar variance and subfilter scalar dissipation rate are important parameters in combustion modeling approaches based on a conserved scalar, but are prone to numerical and modeling errors due to the nature of practical LES computations. This work examines the errors incurred in these models using a novel method that couples LES scalar modeling with direct numerical simulation (DNS) of homogeneous isotropic turbulence and offers modeling and numerical techniques to address these errors. In the coupled DNS-LES method, DNS velocity fields are evolved simultaneously with LES scalar fields. The filtered DNS velocities are supplied to the LES scalar equations, instead of solving the LES momentum equations. This removes the effect of errors in the filtered scalar evolution from the scalar modeling analysis. Results obtained using the coupled DNS-LES approach, which permits detailed study of physics-related and numerical errors in scalar modeling, show that widely used algebraic dynamic models for subfilter scalar variance lack accuracy due to faulty equilibrium modeling assumptions and sensitivity to numerical error. Transport equation models for variance show superior performance, provided that the scalar dissipation rate model coefficient is set appropriately. For this purpose, a new dynamic approach for nonequilibrium modeling of subfilter scalar dissipation rate is developed and validated through a priori tests in an inhomogeneous jet flow and using the coupled DNS-LES method for assessment of numerical error effects. Explicit filtering is assessed as means to control numerical error in LES scalar modeling and the scalar equations are reformulated to account for the explicit filtering technique. Numerical convergence of the mean subfilter scalar variance prediction with increasing grid resolution is demonstrated. / text

published_or_final_version / abstract / toc / Mechanical Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / abstract / toc / Electrical and Electronic Engineering / Master / Master of Philosophy

published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy

published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy

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The dissertation describes a study of the instructional validity of the Arizona Instrument to Measure Standards (AIMS), a standards-based assessment. The study addresses the third- and fifth-grade mathematics portion of the 2005 AIMS test, focusing on two performance objectives per grade level. The study centers on the following questions: Can variation in students' mathematics achievement on AIMS be explained by instructional validity measures, namely: (1) alignment between test items and instructional characteristics and (2) by the degree of teacher emphasis on the two skills of interest to the study? Does the relationship between these measures and AIMS performance differ across grade levels? What possible explanations exist to account for grade level differences? Is there a relationship between the instructional validity measures and performance on the objectives of interest to this study?The dissertation discusses the evolution of thinking about instructional validity as standardized testing has changed. The study methods, including developing alignment measures from interview transcripts and classroom assessment examples collected from 16 third-grade teachers and 20 fifth-grade teachers in one school district are also described. Findings include that, although the method of using qualitative data to gauge instructional validity yields rich information about instructional practice, there was little instructional variation between classrooms in the district studied. This may have occurred because the district requires teachers to provide instruction exactly as specified in the district-adopted mathematics text. Some between-grade level differences do exist in the curricular alignment with AIMS. Teachers attempted to overcome this in their instruction despite district mandates to the contrary. Results support the instructional sensitivity of AIMS at third grade, but not at fifth grade. Differences in instructional sensitivity across grade levels might be linked to curricular differences; some third-grade teachers reported supplementing the curriculum to address the state standards while fifth-grade teachers largely reported that this was not necessary. Interestingly, the degree of alignment at third- and fifth-grade did not vary, although fifth-grade teachers placed more emphasis the study objectives. This speaks to third-grade teacher commitment to address the standards, and the challenges in emphasizing them when district-adopted curricula are not well-aligned with state standards.