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Automated Design of Optimized Arrays for Single Phase Jet Impingement Heat Transfer
Keywords: Jet Impingement, Optimization, Single Phase
Research over the past several decades has shown that an array of impinging jets is capable of efficiently removing large amounts of thermal energy with applications such as cooling microelectronics, turbine blades, combustion chambers, and processed metals. Though there is a significant body of research, there is little ability to effectively design an optimized jet impingement array with predictable behavior. One method of optimization uses predefined empirical correlations to maximize parameters of interest, such as the method proposed by Fabbri and Dhir (2005). It is a process that focuses on the minimization of pumping power and fluid flow rate for a given surface to inlet temperature difference. This is accomplished by using two experimentally derived correlations: one correlation for the friction factor and another for the Nusselt number for an array of orifices normally impinging on a flat surface. Each of these correlations is only valid for the domain from which they were derived, limiting the usefulness of this approach. Martin (1977) and Lee & Vafai (1999) take similar approaches. Performance is not always measured in terms of lowest pressure drop or highest Nusselt number. Jiji & Dagan (1988) propose using the temperature non-uniformity as a performance measure. They found that, for a given heater area and constant flow rate, increasing the number of jets slightly decreased the surface temperature non-uniformity overall thermal resistance. The challenge of empirically derived equations is that they are only accurate for the range of independent variables from which they were examined. Such independent variables include the Reynolds number, Redn ; Prandtl number Pr; jet-to-jet spacing, S; minimum distance between orifice plate and impingement surface, H; jet diameter, dn; number of jets, N; and impingement angle, θ. If any of these variables are outside the given range, the accuracy of the correlation is questionable. This is the key to the model proposed by Lindeman et al. (2013a) – a model capable of predicting heat transfer to an arbitrary array of impinging jets spanning a very large range for each of these variables. The Lindeman et al. (2013a) model provides a way to vary all independent variables in an impinging array, with arbitrary heater geometry. The results of the model have shown to have a mean absolute error of 2.9% when compared to experiment, and 15.8% when compared with correlations in literature (2013b). This model frees one from the inherent constraints of empirically derived correlations and allows for numerical optimization techniques that are not possible using correlations. One such technique uses the optimization algorithms within the Dakota software (Adams, 2011). The optimization process focused on the placement of jets, rather than a systems level approach, because system variables are fairly well modeled through pump curves, and heat exchanger effectiveness, among other techniques– they can easily be integrated into current systems-level optimizations. Currently unavailable is a method for optimizing jet locations in an arbitrary array. To do this, the model from Lindeman et al. (2013a) was used to obtain a surface-average heat transfer coefficient for a particular arrangement and compare this with other arrangements. All of the modeling was done assuming free jets, and no confinement (i.e., the drain is on all four sides of the heater). Given this setup, the objective function of this study became the surface-averaged heat transfer coefficient and the design variables the locations of the jets. Jet impingement angle varied between 30 degrees and 90 degrees, with respect to the surface. Results will be presented showing that Dakota is capable of using the model proposed by Lindeman et al. (2013a) to generate a non-intuitive jet arrangement that performs better than an intuitive solution. Additional results show how the tool can generate unique, optimized solutions for very non-uniform heat sources.
Brett A. Lindeman,
University of Wisconsin - Madison
Madison, WI

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