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# Numerical study of the Ranque-Hilsch vortex tube

Fian Assemien

► To cite this version:

Fian Assemien. Numerical study of the Ranque-Hilsch vortex tube. Complex Systems Academy. Complex Days, Mar 2019, Nice, France., Complex Days, 2, Complex Days. hal-03865487

HAL Id: hal-03865487

https://hal.science/hal-03865487

Submitted on 29 Mar 2023

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Distributed under a Creative Commons Attribution 4.0 International License
NUMERICAL STUDY OF THE RANQUE-HILSCH VORTEX TUBE

Fian ASSEMIEN
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Presentation and applications

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RHVT

Georges Joseph Ranque (1931)

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Rudolph Hilsch (1946)

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## METHODS

### Experimental study

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#### Measurements

* Temperature

* Pressure

* Velocities

* Flow rates

### Numerical study

$$ \frac{\partial \rho}{\partial t} + \text{div}(\rho \mathbf{v}) = 0 $$

$$ \frac{\partial(\rho\mathbf{v})}{\partial t} + \text{div}(\rho\mathbf{v} \otimes \mathbf{v}) = -\nabla p + \text{div}(\bar{\tau}) $$

$$ \frac{\partial(\rho h_t - p)}{\partial t} + \text{div}(\rho \mathbf{v} h_t) = \text{div}(\mathbf{v} \cdot \bar{\tau} - \mathbf{q}) $$

* Navier-Stokes equations

* Turbulence model

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