Alekhin, A. Numerical investigation of a double-circuit Ranque–Hilsch vortex tube [Текст] / A. Alekhin, V. Bianco, A. Khait, A. Noskov// International Journal of Thermal Sciences. – 2014. –Vol. 89. – p. 272-282

Numerical Method For Calculation Of Combustion In Burner Devices



For a two-loop vortex tube, the results of the kth turbulence model can serve as a good starting point for eddy-resolving turbulence models such as SAS-SST or LES. In a study [Alekhin, A. Numerical investigation of a double-circuit Ranque–Hilsch vortex tube [Текст] / A. Alekhin, V. Bianco, A. Khait, A. Noskov// International Journal of Thermal Sciences. – 2014. –Vol. 89. – p. 272-282.], conducted on a full 3d model, the best results were obtained on the LES model, the anisotropic RSM-LRR and SAS-SST models showed slightly worse results, and the worst results were obtained on the standard k-e and k-e RNG turbulence models.
The authors of [[Alekhin, A. Numerical investigation of a double-circuit Ranque–Hilsch vortex tube [Текст] / A. Alekhin, V. Bianco, A. Khait, A. Noskov// International Journal of Thermal Sciences. – 2014. –Vol. 89. – p. 272-282.]] note that high radial velocities were obtained for LES, which lead to intense mass transfer in the radial direction, and, as a result, to a more accurate prediction of the energy separation effect of the flow. At the same time, the RSM-LRR and SAS-SST models represent a good compromise between accuracy and calculation speed.
A higher accuracy of calculation on the RSM model is also confirmed by studies [Xingwei Liu, Investigation of the energy separation effect and flow mechanism inside a vortex tube [Текст] / Liu Xingwei, Liu Zhongliang //Applied Thermal Engineering. – 2014. – Vol. 67. – Iss. 1–2. – p.494-506.], however, it should be noted that the use of the RSM model for calculating a single-flow VT in [Skye, H.M. Comparison of CFD Analysis to Empirical Data in A Commercial Vortex Tube [Текст]/ H.M. Skye, G.F. Nellis, S.A. Klein // International Journal of Refrigeration. – 2006. – Vol. 29. – p.71-80.] led to a VT reversal that was not observed in the experiment.
The eddy viscosity turbulence models are based on Boussinesq's assumption [Boussinesq, J. Theorie de l` Ecoulemen Tourbillant [Текст] / J. Boussinesq // Mem. Presentes par Divers Savants Acad. Sci. Inst. Fr. – 1877. – Vol 23, – p. 46-50.]. This hypothesis suggests a linear relationship between the turbulent stress tensor and the average strain rate tensor: