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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

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Abstract

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.

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Abbreviations

ANN:

Artificial neural network

CFD:

Computational fluid dynamic

FVM:

Finite volume method

RANS:

Reynolds average navier stokes

RNG:

Renormalized group

RHVT:

Ranque-Hilsch vortex tube

RH:

Ranque-Hilsch

RHE:

Ranque-Hilsch effect

LES:

Large eddy simulation

VT:

Vortex tube

∆T c = ( T in − T C):

Temperature difference between inlet and cold outlet

ΔT = ( T H − T C):

Temperature difference between hot and cold outlets

C p :

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

C εi :

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

C μ :

Constants in Eq. 14

C υ :

Constants in Eq. 13

D:

Diameter of vortex tube (mm)

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

Mass flow rate (kg.s−1)

d n :

Diameter of inlet nozzle (mm)

E:

Total energy (kJ)

G k :

Generation of turbulence kinetic energy

k:

Turbulence kinetic energy (m2.s−2)

Ke :

Thermal conductivity (W.m−1.K−1)

L:

Length (mm)

N:

Number of inlet nozzle

P:

Absolute pressure (pa)

Q c :

Cooling rate

Prt :

Turbulent Prandtl number

R:

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

S :

Twice the strain rate tensor (s−1)

T:

Temperature (K)

ui :

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

YM :

Contribution of the fluctuating dilatation

Ma:

Mach number

W:

Mechanical energy

α k :

Inverse effective Prandtl numbers in Eq. 11

α ε :

Inverse effective Prandtl numbers in Eq. 12

δ ij :

Kronecker delta

τ:

Shear stress (N.m−2)

(τ ij)eff :

Deviatoric stress tensor (N.m−2)

ε :

Turbulence dissipation rate (m−2.s−3)

α :

Cold mass fraction

μ:

Dynamic viscosity (kg.m−1.s−1)

υ :

Kinematic viscosity (m2.s−1)

\( \widehat{\upsilon} \) :

Ratio of effective viscosity to the dynamic viscosity

γ:

Specific heat ratio

ρ:

Density (kg.m−3)

λ :

Pressure Loss Ratio

η 0, β, η :

Coefficients in RNG k- ε model

η is :

Isentropic efficiency

c:

Cold gas

eff:

Effective

h:

Hot gas

in:

Inlet gas

is:

isentropic

i, j, k:

Cartesian indicates

n:

nozzle

t:

turbulent

st:

static

a:

Atmospheric

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Authors and Affiliations

  1. Ahvaz Faculty of Petroleum, Petroleum University of Technology (PUT), P.O. Box 6198144471, Ahvaz, Iran

    Adib Bazgir, Mohammadreza Khosravi-Nikou & Ali Heydari

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  1. Adib Bazgir
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Bazgir, A., Khosravi-Nikou, M. & Heydari, A. 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. Heat Mass Transfer 55, 2559–2591 (2019). https://doi.org/10.1007/s00231-019-02578-1

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