A response surface model of a diesel spray, parameterized by the internal geometries of a nozzle, is established in order to design the nozzle geometries optimally for spray mixing. The explanatory variables are the number of holes, the hole diameter, the inclined angle, the hole length, the hole inlet radius, K-factor and the sac diameter. The model is defined as a full second-order polynomial model including all the first-order interactions of the variables, and a total of 40 sets of numerical simulations based on D-optimal design are carried out to calculate the partial regression coefficients. Partial regression coefficients that deteriorate the estimate accuracy are eliminated by a validation process, so that the estimate accuracy is improved to be ±3% and ±15% for the spray penetration and the spread, respectively. Then, the model is applied to an optimization of the internal geometries for the spray penetration and the spray spread through a multi-objective genetic algorism. Through the optimization, it is found that both the penetration and the spread can be improved at the same time by reducing the pressure loss attributed to the flow separation at the hole inlet and by discharging the fuel before the turbulence produced at the hole inlet is damped. Thus, the optimization of the nozzle internal geometry could have the equivalent effects of increasing the fuel pressure in improving the penetration and the spread.
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