Modelling of Suddenly Expanded Flow Process in Supersonic Mach Regime using Design of Experiments and Response Surface Methodology

The present work is an attempt to model, analyze, and control the flow at the base of an abruptly expanded circular duct by using design of experiments (DOE) and response surface methodology (RSM). Tiny-jets in the form of orifice were positioned at an interval of 900, 6.5 mm from the primary axis of the main jet of the nozzle. Experiments were conducted to measure two responses namely, base pressure without the use of micro jets or active control (WoC) and base pressure with the use of micro jets or active control (WC). Mach number (M), nozzle pressure ratio (NPR), area ratio (AR) and length to diameter ratio (L/D) were considered as input variables (parameters), which control the outputs (i.e. base pressure). Non-linear regression models based on central composite design (CCD) and Box-Behnken design (BBD) have been developed in order to facilitate the input-output relationships. Moreover, the significance of main, square and interaction terms of the developed models have been tested by performing analysis of variance (ANOVA). The ANOVA and significance test results and their respective correlation coefficient values indicate that both the CCD and BBD regression models are statistically adequate for both the base pressure responses of without control and with control respectively. The performances of the nonlinear models have been validated for accuracy prediction by use of 15 test cases. The performance of BBD model is found to be better in forecasting base pressure for both cases of without control and with control when compared to the CCD model.

Keywords:

base pressure , Mach number , area ratio , length to diameter ratio , Central composite design , Box-Behnken design , Analysis of Variance