Application of Response Surface Methodology to optimization of a standard Ranque–Hilsch vortex tube refrigerator

In the present study, an attempt is made to evaluate the effect of certain geometrical parameters on cooling performance of Ranque–Hilsch vortex tube (RHVT). Number of intakes in nozzle “n”, cold orifice diameter “dc” and inlet pressure “Pi” are selected as influencing parameters at different levels n = 1, 2, 3; dc = 7, 9, 11 mm and Pi = 2, 2.5, 3 bar. The experiments are conducted based on three factors, two levels and central composite face centered design (CCF) with full factorial. The results are analyzed according to the principle of Response Surface Methodology (RSM). The equation to the response surface is developed using the design of experiments features of the commercial software package MINITAB-16. The goodness of fit of the regression model is examined using the Analysis of Variance (ANOVA) and the F-ratio test. The values of R2 and R2(adj.) are close to 100% which shows a very high correlation between the observed and predicted values. Results show sensitivity value of ΔTc,max respect to n is negative (∂Re/∂A < 0). It means that increasing in n cause decreasing in ΔTc,max and for low orifice diameter it has significant effect. The cold orifice diameter has more effect on ΔTc,max. Its sensitivity value is 65.8% and 51.1% more than n and Pi, respectively. It is shown that for d c ∗  < 0.5, ( d c ∗  = dc/D), increasing d c ∗ causes the cold air temperature difference to increase and for d c ∗  > 0.5, increasing d∗c tends the cold air temperature difference to decrease. The results show that the optimum value of d c ∗ for the maximum cold air temperature difference and efficiency is d c ∗  = 0.5. The RHVT was optimized using RSM based on CCD. The optimum values of n, dc, and Pi were 2, 9.48 mm, and 3.2 bar respectively, where 46.44 °C (ΔTc,max) could be obtained from the proposed model.