One of the key inputs 1-D transient simulation takes is a detailed front end cooling flow map. These maps that are generated using a full vehicle Three-dimensional Computational Fluid Dynamics (3D CFD) model require expensive computational resources and time. This paper describes how an adaptive sampling of the design space allowed the reduction of computational efforts while keeping desired accuracy of the analysis. The idea of the method was to find a pattern of Design of Experiments (DOE) sampling points for 3D CFD simulations that would allow a creation of an approximation model accurate enough to predict output parameter values in the entire design space of interest.
Three procedures were implemented to get the optimal sampling pattern. One of them, called Procedure #1 below employed the observations listed below, identification of the areas that would require less sampling points by analyzing approximation errors, manual reduction of the points in such areas, building an approximation model with the points left in the sampling set, and further accuracy evaluation in removed points where output parameter values are known. Input parameters identified in this study were AGS opening, fan speed and vehicle speed. The output parameters monitored were the flow through the heat exchangers radiator, condenser and transmission oil cooler. Accuracy assessments of approximations made of different point sets provided hints on the sensitivity to each of the inputs and areas where the sampling density could be reduced. Areas of the cooling flow map that required more or less sampling points density were assessed with the help of following observations. Cooling flow to heat exchangers varied linearly for AGS opening greater than 50%. Cooling flow to heat exchangers varied linearly for higher vehicle speeds in the range of 39 mph to 80 mph. For vehicle speeds greater than 65 mph, the fan speed changes played a minor role. The approximation model had bigger error for a low vehicle speed and high fan speed combinations. The approximation model worked effectively when the idle and peak vehicle speed cases where included in the sample data set.
Another procedure, called Procedure #2 below used was an Optimal Latin Hypercube DOE method to sample the design space that was simulated by an accurate approximation model built with all available 3D CFD simulation results (also called Dataset A - 123 runs). The smaller DOE started with 25 sampling points was used to make another approximation model and the accuracy of the approximation was assessed against the most accurate model.
The above steps were repeated in the third method, called Procedure #3 below where Isight simulations were started with a relatively small number of sampling points, extra sampling points were added in the areas where the model performed the worst and in key areas identified by the cooling flow parameter sensitivity studies mentioned above. Such additions were made with Isight Adaptive DOE procedure that allowed an efficient way to fill the least populated areas of the design space with sampling points.
Both the manual DOE and adaptive DOE procedures yielded patterns that had minimal number of sampling points while providing predefined accuracy levels of the front-end cooling airflow evaluations in the entire design space.