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Investigation of a vortex tube using three different RANS-based turbulence models

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Abstract

The main objective of this study is to capture the function of temperature separation inside a vortex tube (VT), firstly, via testing it at different inlet pressures (4, 5, 6, and 7 bar) and then examining the best performance of the VT through computational fluid dynamics (CFD) along with three various Reynolds-averaged Navier–Stokes-based turbulence models, i.e., standard \(k - \varepsilon\), standard \(k - \omega\), and shear-stress transport \(k - \omega\). Moreover, a comparison between CFD outputs and experimental data, at the inlet pressure of 7 bar, demonstrates that the standard \(k - \varepsilon\) model outperforms other turbulence models utilized in this study. The internal flow behavior is also examined for further illustration of its features via CFD. It is reported that a convergent–divergent virtual duct is formed through the streamline at the region wherein injected flow (from the inlet nozzles into the vortex chamber) swirls toward the cold orifice, resulting in an expansion. Consequently, the Mach number goes above one and temperature drops. Thus, the sudden expansions alongside free and forced vortices as well as the secondary circulation flow have a significant impact on energy separation in the VT.

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Abbreviations

\(A\) :

Area (m2)

\(C_{p}\) :

Constant pressure-specific heat capacity of air at room temperature (J kg−1 K−1)

\(c\) :

Speed of sound (m s−1)

\(E_{\text{ij}}\) :

Mean strain rate tensor

\(h\) :

Enthalpy for unit mass (J kg−1)

\(h_{0}\) :

Total enthalpy for unit mass (J kg−1)

\(K\) :

Thermal conductivity (W m−1 K−1)

\(k\) :

Turbulence kinetic energy (m2 s−3)

\(M\) :

Mach number

\(\dot{m}\) :

Mass flow rate (kg s−1)

\(p\) :

Pressure (pa)

\(P_{0}\) :

Total pressure (Pa)

\({ \Pr }\) :

Prandtl number

\(R\) :

Specific constant of an ideal gas (J kg−1 K−1)

\(T\) :

Static temperature (K)

\(T_{0}\) :

Total temperature (K)

\(U_{\text{R}}\) :

Uncertainty

\(u\) :

Mass-averaged velocity (m s−1)

\(u^{{\prime }}\) :

Fluctuating velocity components (m s−1)

\(c_{{1\upvarepsilon}} , \, c_{{2\upvarepsilon}} , \, c_{\upmu} , \, \sigma_{k} , \, \sigma_{\upvarepsilon}\) :

Constants of \(k - \varepsilon\) model

\(\alpha , \, \alpha^{*} , \, \beta , \, \beta^{*} , \, \sigma , \, \sigma^{*} , \, \beta_{0}\) :

Constants of standard \(k - \omega\) model

\(\alpha_{1} , \, \alpha_{2} , \, \beta_{1} , \, \beta_{2} , \, \beta^{*} , \, \sigma_{{{k}1}} , \, \sigma_{{{k}1}} , \, \sigma_{{\upomega1}} , \, \sigma_{{\upomega2}}\) :

Constants of SST \(k - \omega\) model

\(\alpha_{k}\) :

Inverse effective Prandtl number for \(\varepsilon\) equation

\(\alpha_{\upvarepsilon}\) :

Inverse effective Prandtl number for \(k\) equation

\(\xi\) :

Cold gas mass fraction

\(\tau\) :

Stress tensor

\(\rho\) :

Density (kg m−3)

\(\mu\) :

Dynamic viscosity (kg m−1 s−1)

\(\nu\) :

Kinematic viscosity (m2 s−1)

\(\nu_{\text{t}}\) :

Kinematic turbulence viscosity (m2 s−1)

\(\varepsilon\) :

Turbulence dissipation rate (m2 s−3)

\(\omega\) :

Angular velocity (s−1)

\(\varOmega\) :

Absolute value of vorticity

c:

Cold stream

h:

Hot stream

in:

Inlet

eff:

Effective

0:

Total

t:

Turbulence

i, j, k:

Cartesian indices

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Acknowledgements

Authors are sincerely grateful to Dr. Mohsen Davazdah Emami, the associate professor in Mechanical Engineering, and Alireza Amiriyoon, the Thermodynamic and Heat Transfer laboratory expert, at the Department of Mechanical Engineering, Isfahan University of Technology, Iran.

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Authors and Affiliations

  1. Isfahan University of Technology, Isfahan, Islamic Republic of Iran

    Jaber Sadeghiseraji, Jafar Moradicheghamahi & Amir Sedaghatkish

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  1. Jaber Sadeghiseraji
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Correspondence to Amir Sedaghatkish.

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Appendices

Appendix 1

See Table 6.

Table 6 Experimental data
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Appendix 2

See Fig. 19.

Fig. 19
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Compressor and tank

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Sadeghiseraji, J., Moradicheghamahi, J. & Sedaghatkish, A. Investigation of a vortex tube using three different RANS-based turbulence models. J Therm Anal Calorim 143, 4039–4056 (2021). https://doi.org/10.1007/s10973-020-09368-6

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