Numerical CFD analysis and experimental investigation of the geometric performance parameter influences on the counter-flow Ranque-Hilsch vortex tube (C-RHVT) by using optimized turbulence model

  • Adib BazgirEmail author
  • Mohammadreza Khosravi-Nikou
  • Ali Heydari


This research article demonstrates how using different turbulence models may affect the temperature detachment (the temperature diminution of cold air (∆Tc = Ti − Tc)) inside straight counter-flow Ranque-Hilsch Vortex Tube (RHVT). The code is utilized to find the optimized turbulence model for energy separation by comparison with the experimental data of the setup. To obtain the results with a minimum error, various turbulence models have been investigated in steady state and transient time-dependence modes. Results show that RNG k-ε turbulence model has the best correspondence with the obtained experimental data from the setup; therefore, by using a RNG k-ε turbulence model with respect to Finite Volume Method (FVM), all the computations have been carried out. Moreover, some geometric parameters are focused on the length of hot tube and number of nozzle intakes within divergent and convergent hot-tube. Numerical results present that there is an optimum angle for obtaining the highest refrigeration performance, and 2ο divergence is the optimal candidate under our numerical analysis conditions. Length of hot tube which exceeds a critical length has slight effect on the refrigeration capacity. The critical length is L = 166 mm in our study. Temperature reduction sensitivity can be reduced by increasing number of nozzles and maximum temperature reduction can be obtained.



Artificial neural network


Computational fluid dynamic


Finite volume method


Reynolds average navier stokes


Renormalized group


Ranque-Hilsch vortex tube




Ranque-Hilsch effect


Large eddy simulation


Vortex tube

∆Tc = ( Tin − TC)

Temperature difference between inlet and cold outlet

ΔT = ( TH − TC)

Temperature difference between hot and cold outlets


Specific heat at constant absolute pressure (−1.K−1)


Coefficients (i = 1, 2) used in ε equation


Constants in Eq. 14


Constants in Eq. 13


Diameter of vortex tube (mm)

\( \overset{\cdot }{m} \)

Mass flow rate (kg.s−1)


Diameter of inlet nozzle (mm)


Total energy (kJ)


Generation of turbulence kinetic energy


Turbulence kinetic energy (m2.s−2)


Thermal conductivity (W.m−1.K−1)


Length (mm)


Number of inlet nozzle


Absolute pressure (pa)


Cooling rate


Turbulent Prandtl number


Specific constant of an ideal gas (J/kgmol-K)


Twice the strain rate tensor (s−1)


Temperature (K)


Absolute fluid velocity component in i-direction (m/s)


Contribution of the fluctuating dilatation


Mach number


Mechanical energy

Greek symbols


Inverse effective Prandtl numbers in Eq. 11


Inverse effective Prandtl numbers in Eq. 12


Kronecker delta


Shear stress (N.m−2)


Deviatoric stress tensor (N.m−2)


Turbulence dissipation rate (m−2.s−3)


Cold mass fraction


Dynamic viscosity (kg.m−1.s−1)


Kinematic viscosity (m2.s−1)

\( \widehat{\upsilon} \)

Ratio of effective viscosity to the dynamic viscosity


Specific heat ratio


Density (kg.m−3)


Pressure Loss Ratio

η0, β, η

Coefficients in RNG k- ε model


Isentropic efficiency



Cold gas




Hot gas


Inlet gas



i, j, k

Cartesian indicates











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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Adib Bazgir
    • 1
    Email author
  • Mohammadreza Khosravi-Nikou
    • 1
  • Ali Heydari
    • 1
  1. 1.Ahvaz Faculty of PetroleumPetroleum University of Technology (PUT)AhvazIran

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