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Within the design process, computational fluid dynamics is typically used to compute specific quantities that assess the performance of the apparatus under investigation. These quantities are usually integral output functions such as force and moment coefficients. However, to accurately model the configuration, the geometric features and the resulting physical phenomena must be adequately resolved. Due to limited computational resources a compromise must be made between the fidelity of the solution obtained and the available resources. This creates a degree of uncertainty about the error in the computed output functions. To this end, the current study attempts to address this problem for two-dimensional inviscid, incompressible flows on unstructured grids. The objective is to develop an error estimation and grid adaptive strategy for improving the accuracy of output functions from computational fluid dynamic codes. The present study employs a discrete adjoint formulation to arrive at the error estimates in which the global error in the output function is related to the local residual errors in the flow solution via adjoint variables as weighting functions. This procedure requires prolongation of the flow solution and adjoint solution from coarse to finer grids and, thus, different prolongation operators are studied to evaluate their influence on the accuracy of the error correction terms. Using this error correction procedure, two different adaptive strategies may be employed to enhance the accuracy of the chosen output to a prescribed tolerance. While both strategies strive to improve the accuracy of the computed output, the means by which the adaptation parameters are formed differ. The first strategy improves the computable error estimates by forming adaptation parameters based on the level of error in the computable error estimates. A grid adaptive scheme is then implemented that takes into account the error in both the primal and dual solutions. The second strategy uses the computable error estimates as indicators in an iterative grid adaptive scheme to generate grids that produce accurate estimates of the chosen output. Several test cases are provided to demonstrate the effectiveness and robustness of the error correction procedure and the grid adaptive methods.

This study seeks to reduce the degree of uncertainty that often arises in computational fluid dynamics simulations about the computed accuracy of functional outputs. An error estimation methodology based on discrete adjoint sensitivity analysis is developed to provide a quantitative measure of the error in computed outputs. The developed procedure relates the local residual errors to the global error in output function via adjoint variables as weight functions. The three major steps in the error estimation methodology are: (1) development of adjoint sensitivity analysis capabilities; (2) development of an efficient error estimation procedure; (3) implementation of an output-based grid adaptive scheme. Each of these steps are investigated. For the first step, parallel discrete adjoint capabilities are developed for the variable Mach version of the U2NCLE flow solver. To compare and validate the implementation of adjoint solver, this study also develops direct sensitivity capabilities. A modification is proposed to the commonly used unstructured flux-limiters, specifically, those of Barth-Jespersen and Venkatakrishnan, to make them piecewise continuous and suitable for sensitivity analysis. A distributed-memory message-passing model is employed for the parallelization of sensitivity analysis solver and the consistency of linearization is demonstrated in sequential and parallel environments. In the second step, to compute the error estimates, the flow and adjoint solutions are prolongated from a coarse-mesh to a fine-mesh using the meshless Moving Least Squares (MLS) approximation. These error estimates are used as a correction to obtain highlyurate functional outputs and as adaptive indicators in an iterative grid adaptive scheme to enhance the accuracy of the chosen output to a prescribed tolerance. For the third step, an output-based adaptive strategy that takes into account the error in both the primal (flow) and dual (adjoint) solutions is implemented. A second adaptive strategy based on physics-based feature detection is implemented to compare and demonstrate the robustness and effectiveness of the output-based adaptive approach. As part of the study, a general-element unstructured mesh adaptor employing h-refinement is developed using Python and C++. Error estimation and grid adaptation results are presented for inviscid, laminar and turbulent flows.

Switchgrass (Panicum virgatum) has been widely investigated because of its notable properties as an alternative pasture grass and as an important biofuel source. The goal of this study was to determine soil suitability for Switchgrass in Mississippi. A linear weighted additive model was developed to predict site suitability. Multicriteria analysis and Sensitivity analysis were utilized to optimize the model. The model was fit using seven years of field data associated with soils characteristics collected from NRCS-USDA. The best model was selected by correlating estimated biomass yield with each model’s soils-based output for Switchgrass suitability. Pearson’s r (correlation coefficient) was the criteria used to establish the ‘best’ soil suitability model. Coefficients associated with the ‘best’ model were implemented within a Geographic Information System (GIS) to create a map of relative soil suitability for Switchgrass in Mississippi. A Geodatabase associated with soil parameters was constructed and is available for future GIS use.

Coal plays a significant role in electricity production worldwide and will into the foreseeable future. Technologies that improve efficiency and lower emissions are becoming more popular. High pressure reactors and oxyfuel combustion can offer these benefits. Designing new reactors effectively requires accurate single particle modeling. This work models a high-pressure, high-temperature, high-heating rate, entrained-flow, char oxidation data set to generate kinetic parameters. Different modeling methods were explored and a sensitivity analysis on char burnout was performed by varying parameters such as total pressure, O2 partial pressure, O2 and CO2 mole fractions, gas temperature, diameter, and pre-exponential factor. Pressure effects on char burnout modeling were found to be dependent on the set of kinetic parameters chosen. Using kinetic parameters from Hurt-Calo (2001) as opposed to values obtained from Niksa-Hurt (2003) yielded a trend seen in real data sets, that reaction order changes with temperature. Varying O2 mole fraction and partial pressure showed the most significant changes in char burnout. Varying diameter, total pressure, the pre-exponential factor, CO2 environment, and gas temperature all changed the char burnout extent as well. The effect of changing those parameters decreases in the order they are listed. Increasing any of these parameters resulted in an increase in char burnout except for particle diameter and CO2 mole fraction which led to a decrease. Char formation pressure affects reactivity, and a peak in reactivity is shown in this work at the 6 atm condition.

Nonsmoothness appears in various applications in chemical engineering, including multi-stream heat exchangers, nonsmooth flash calculation, process integration. In terms of numerical approaches, convex/concave relaxations of static and dynamic systems may also exhibit nonsmoothness. These relaxations are used in deterministic methods for global optimization. This thesis presents several new theoretical results for nonsmooth sensitivity analysis, with an emphasis on convex relaxations. Firstly, the "compass difference" and established ODE results by Pang and Stewart are used to describe a correct subgradient for a nonsmooth dynamic system with two parameters. This sensitivity information can be computed using standard ODE solvers. Next, this thesis also uses the compass difference to obtain a subgradient for the Tsoukalas-Mitsos convex relaxations of composite functions of two variables. Lastly, this thesis develops a new general subgradient result for Tsoukalas-Mitsos convex relaxations of composite functions. This result does not limit on the dimensions of input variables. It gives the whole subdifferential of Tsoukalas-Mitsos convex relaxations. Compare to Tsoukalas-Mitsos’ previous subdifferential results, it does not require additionally solving a dual optimization problem as well. The new subgradient results are extended to obtain directional derivatives for Tsoukalas-Mitsos convex relaxations. The new subgradient results and directional derivative results are computationally approachable: subgradients in this article can be calculated both by the vector forward AD mode and reverse AD mode. A proof-of-concept implementation in Matlab is discussed. / Thesis / Master of Applied Science (MASc)

Yes / Cooling towers are a relatively inexpensive and consistent method of ejecting heat from several industries such as thermal power plants, refineries, and food processing. In this research, an earlier model from literature was to be validated across three different case studies. Unlike previous models, this model considers the height of the fill as the discretised domain, which produces results that give it in a distribution form along the height of the tower. As there are limitations with the software used (gPROMS) where differential equations with respect to independent variables in the numerator and denominator cannot be solved, a derivative of the saturation vapour pressure with respect to the temperature of the air was presented. Results shown were in agreement with the literature and a parametric sensitivity analysis of the cooling tower design and operating parameters were undertaken. In this work the height of fill, mass flowrates of water and air were studied with respect to sensitivity analysis. Results had shown large variations in the outlet temperatures of the water and air if the mass flows of water and air were significantly reduced. However, upon high values of either variable had shown only small gains in the rejection of heat from the water stream. With respect to the height of the fill, at larger heights of the fill, the outlet water temperature had reduced significantly. From a cost perspective, it was found that a change in the water flowrate had incurred the largest cost penalty with a 1% increase in flowrate had increased the average operating cost by 1.2%. In comparison, a change in air flowrate where a 1% increase in flowrate had yielded an average of 0.4% increase in operating cost.

Yes / The coupling of thermal (Multi Stage Flash, MSF) and membrane processes (Reverse Osmosis, RO) in desalination systems has been widely presented in the literature to achieve an improvement of performance compared to an individual process. However, very little study has been made to the combined Multi Effect Distillation (MED) and Reverse Osmosis (RO) processes. Therefore, this research investigates several design options of MED with thermal vapor compression (MED_TVC) coupled with RO system. To achieve this aim, detailed mathematical models for the two processes are developed, which are independently validated against the literature. Then, the integrated model is used to investigate the performance of several configurations of the MED_TVC and RO processes in the hybrid system. The performance indicators include the fresh water productivity, energy consumption, fresh water purity, and recovery ratio. Basically, the sensitivity analysis for each configuration is conducted with respect to seawater conditions and steam supply variation. Most importantly, placing the RO membrane process upstream in the hybrid system generates the overall best configuration in terms of the quantity and quality of fresh water produced. This is attributed to acquiring the best recovery ratio and lower energy consumption over a wide range of seawater salinity.