Sensitivity and Uncertainty Analysis in Computational Thermal Models

摘要

Computational tools have been extensively applied to predict component temperatures before an actual vehicle is built for testing [1, 2, 3, 4, and 5]. This approach provides an estimate of component temperatures during a specific driving condition. The predicted component temperature is compared against acceptable temperature limits. If violations of the temperature limits are predicted, corrective actions will be applied. These corrective actions may include adding heat shields to the heat source or to the receiving components. Therefore, design changes are implemented based on the simulation results. Sensitivity analysis is the formal technique of determining most influential parameters in a system that affects its performance. Uncertainty analysis is the process of evaluating the deviation of the design from its intended design target. In the case of thermal protection, uncertainty analysis is applied in order to determine the variation of the calculated component temperature around its nominal value. It has been a common understanding that no engineering analysis is complete without conducting uncertainty analysis. Though sensitivity and uncertainty analysis topics have been widely discussed in engineering applications, a very limited number of authors have addressed the need for uncertainty analysis in computational thermal models for automotive applications. The only relevant work [6] focused on the formulation of sensitivity analysis for conjugate heat transfer problems. The purpose of this paper however is to present the uncertainty associated with CFD simulation results when applied to vehicle thermal models. From the user's side, we need to address the effect of uncertainties associated with input data, how they affect the final results and determine most influential input parameters. Therefore, sensitivity and uncertainty analysis should be consistently conducted before results from whenever CFD analysis is implemented for design changes or modifications. Depending on the complexity of the problem being analyzed, two methods are used for this purpose; local sensitivity analysis using Taylor series and a global sensitivity analysis using the Fourier Amplitude Sensitivity Test (FAST). Model uncertainties are expressed as the relative standard deviation of calculated results over the uncertain domain of input parameters. Parametric sensitivities are expressed as the sensitivity coefficient, when Taylor series is applied. Using the FAST method, parametric sensitivity is expressed as the partial variance for each parameter, which measures the contribution of each parameter to the overall uncertainty of predicted component temperatures. In addition to uncertainties associated with CFD calculations, it is critical for the design and release engineers to assess the impact of the calculated temperatures on the component or system durability. This step requires knowledge of component temperatures at various driving conditions, time durations at any given temperature, vehicle duty cycle and the effect of temperature on the performance of components and systems being addressed. In this paper, issues related to the thermal protection process uncertainty are also addressed.