Multi-objective optimization of rectangular cooling channel design using Design of Experiments (DOE)

Abstract

In scramjet engines, the optimal design of a regenerative cooling channel is critical for cooling, reducing pressure loss on the walls of the combustion chamber and improving heat sink utilization of fuel. In this study, thermal performance factor (η) and proportion of chemical heat sink in total heat sink (ψ) are introduced as objective functions, additionally, multi-objective optimizations are performed on a rectangular cooling channel using the DOE (design of experiments) method. Two suitable regression models for objective functions η and ψ are quantitatively generated by employing the RSM (response surface methodology), and the R-squared of the regression models are 98.34 % and 97.44 %, respectively. The precision and dependability of the models, as well as the degree of significance of the variables including the mass flow rate (ṁ), aspect ratio (AR), and wall thickness (tw) are assessed via the ANOVA (analysis of variance). The results show that the linear variables x1 (ṁ) and interaction variable x1x2 (ṁ, AR) are the most essential variables in forecasting η and ψ, respectively. The complex effects of linear and interactive variables on the objective functions are discussed. When the cracking rate is less than 40 %, the effect of x1 (ṁ) on η initially decreases and then increases. By contrast, x3 (tw) causes an increase in η initially, followed by a decrease. The variables affecting ψ are x1 (ṁ), x2 (AR), and x3 (tw), in the descending order in terms of effect degree. In addition, to optimize η and ψ simultaneously (weight distribution is equal to one-half for both sides), an optimal point with ṁ = 378.89 g/s, AR = 1, and tw = 1.5 mm is introduced, which yields η = 0.898 and ψ = 0.505. The maximum error between the value fitted using the regression model and the value calculated from simulations is 3.03 %.