A vortex tube is a device that separates compressed air into two streams: one with a higher temperature (hot stream) and the other with a lower temperature (cold stream). This thesis performs a numerical investigation of the flow structure in a vortex tube using the shear stress transport k-ω turbulence model with viscous heating. The internal flow structure of the vortex tube consists of a forced vortex, transitional and free vortex regions, as shown by the static temperature radial distribution. This distribution provides an understanding of the energy separation mechanism of the vortex tube by correlating it with the density gradient along the radial direction.
The simulation results were validated using experimental data obtained from the literature for the same vortex tube parameters.
Introduction
- Overview
- Statement of the Problem
- Research Objectives
- Relevant Literature
- Theory and Work Principles
- Vortex Tube Parametric Studies
- Review of Experimental Studies
- Review of Numerical Simulation
Then investigate the effect of the inlet pressure on the energy separation performance of the RHVT. Interestingly, they found that the conical vortex tube design has significant potential to improve the energy separation of the vortex tube. The temperature difference in the axial region demonstrates the energy separation of the vortex generator.
The literature [28] suggests that the internal taper angle is positively correlated with the energy separation in the vortex tube due to the expansion of the secondary circulation flow.
![Figure 2: Airflow Structure in the Counterflow Vortex Tube [5]](https://thumb-ap.123doks.com/thumbv2/azpdfco/10575069.0/27.892.227.684.395.558/figure-2-airflow-structure-counterflow-vortex-tube-5.webp)
Methods
Research Design
Numerical Setup
- Geometry Design of Vortex Tube
- Mesh Generation
- Setup and Solution
For the CFD analysis of a vortex tube, it is crucial to choose the appropriate geometry because the flow behavior of the vortex tube is complex. Therefore, it is not smart to replicate the physical flow behavior in a vortex tube using a 2D model with an axisymmetric approximation. Implementing symmetric boundary conditions and simulating only a quarter of the body can help save computational resources without compromising accuracy.
Mesh generation is often the most time-consuming step in CFD simulations, accounting for 50% of the simulation time. To ensure the accuracy of the results, simulations are performed for different number of cells to eliminate the errors caused by the mesh coarseness. Flow behavior in a vortex tube is generally recognized to be complex, and its simulation requires the use of some simplifying assumptions.
In addition, a no-slip condition is imposed on the tube walls, which means that the gas velocity at the tube surface is zero. 21 complex flow behavior in a vortex tube and are critical in accurately modeling the phenomenon. All flow variables such as velocity and pressure remain constant along a circle of constant radius in a vortex tube.
ANSYS workbench is used to solve the ideal gas and storage equations simultaneously to perform a numerical investigation of the Ranque-Hilsch vortex tube. The swirling fluid flow inside the vortex tube is classified as a subcritical flow, requiring the use of a pressure-based solver to solve the Navier-Stokes equations (7) and (8) and the Energy Equation (10) in the ANSYS workbench software that uses the finite volume method.
Thesis Case Study
- Case One: Validation
- Case Two: The Effect of the Tube Internal Tapering Angle
- Case Three: Effect of Tube Length-to-Diameter Ratio
- Case Four: Effect of Inlet Pressure
- Case Five: Effect of Cold Mass Fraction
The internal taper angle is the angle formed between the conical surface inside the vortex tube and the axial direction of the vortex tube. The effect of the vortex tube internal taper angle on the energy separation of the RHVT was investigated by various researchers, including Hamdan et al. 46]; they found that changing the internal taper angle has a significant effect on vortex tube performance.
To numerically investigate the effect of the tube internal taper angle on the energy separation of the RHVT using the same cold mass fraction. 75] have shown a correlation between increasing the Lt/Dt ratio and energy separation in the vortex tube. In this study, we investigate the effect of the Lt/Dt ratio on energy separation by varying the ratio while keeping the cold mass fraction and other parameters constant at 0.56, as listed in Table 4.
For the boundary condition, we used the same conditions as in Case One with a cold mass fraction of 0.56, since previous studies have shown that the vortex tube works efficiently when the cold mass fraction exceeds 0.55 and Lt/Dt is greater than 8.33 . The results of this study will contribute to a better understanding of the vortex tube performance and help optimize its design for different applications. Previous studies have investigated the influence of the cold mass fraction on vortex tube performance.
77] found that the energy separation in the vortex tube is significantly affected by the cold mass fraction. In this study, we investigate the impact of the cold mass fraction on energy separation by changing the hot outlet side pressure for the optimal vortex tube in case three while maintaining the same boundary conditions (Table 6).
Results and Discussions
Validation
Optimization of The Vortex Tube Energy Separation
- Effect of Tube Internal Tapering Angle
- Effect of Tube Length-to-Diameter Ratio
- Effect of the Inlet Pressure
- Effect of the Cold Mass Fraction
The results indicate that the vortex tube's maximum radial velocity appears converging at an angle of 1o. In contrast, Figure 17 (b) shows the radial distribution of static pressure for a diverging vortex tube at the exact axial location. As shown in Figure 19, the results indicate that the taper angle of the vortex tube significantly affects the static temperature.
Although the relationship between Lt/Dt ratio and radial velocity in the convergent vortex tube may not be straightforward, an increase in Lt/Dt. The optimal temperature separation for the convergent vortex tube occurs at a Lt/Dt ratio of 3. The cold mass fraction indicates the proportion of the gas's total mass flow rate leaving the vortex tube's cold outlet relative to the inlet mass flow rate.
This mainly affects the temperature difference between the cold and hot outlets of the vortex tube. Moreover, the cold mass fraction plays an important role in the vortex tube's energy separation performance. The cold mass fraction's impact on the vortex tube is particularly important, given the hot exhaust pressure's influence on it.
Based on the findings presented in Figure 41, the tangential velocity inside the vortex tube is also affected by the cold mass fraction. The results show that increasing the cold mass fraction can increase the static pressure in the vortex tube. Based on Figure 46, it can be seen that the changes affect the static temperature inside the vortex tube in the cold mass fraction.
This section investigated the effect of changes in the cold mass fraction on the performance of the optimal vortex tube obtained from Case 3.
Flow Structure of the Optimal Vortex Tube
- Velocity Distribution
- Pressure Distribution
- Thermal Distribution
- Density
As the figure shows, the total velocity decreases as the flow moves axially along the vortex tube due to the conversion of kinetic energy into thermal energy. The figures show that the vortex flow is losing strength as it moves in the axial direction due to viscous forces, which help to realize the transfer of kinetic energy to thermal energy. Moreover, the velocity contour represents the tangential velocity in the vortex tube in the plane of symmetry, as depicted in Figure 52 (b).
It is observed that the flow inside the vortex tube reaches zero at distinct radial points, as described at the axial locations of z/L and 0.80. For example, the axial velocity in the annular region can reach zero if the length of the vortex tube is extremely long. The radial velocity profile in Figure 54 shows a distinct pattern due to the turbulence within the vortex tube.
Eventually, this kinetic energy difference between the molecules is converted into thermal energy, leading to a temperature gradient in the vortex tube. Due to the tube diameter gradient across the vortex tube and the collapse of the vortex, the static pressure is affected by the axial position of the flow, as the pressure decreases as the flow approaches the hot end. In addition, the total pressure in the axial position changes negatively; as the flow moves toward the hot outlet, the total pressure decreases due to the gradient in diameter along the vortex tube and the decay in the vortex.
The figure showed that the maximum pressure differences between the center and annulus of the vortex tube occurred at the axial location of z/L =0.15. Consequently, the gas density inside the vortex tube can vary axially and radially, affected by the rotational motion of the fluid.
Conclusion
Conclusion
The optimal length-to-diameter ratio on the energy separation was found to be 3. In addition, a reduced tube length increases gas velocity and turbulence, resulting in an improved cooling effect of the vortex tube. The internal flow structure of a vortex tube consists of three regions: a forced vortex, a transition region and a free vortex.
Managerial Implications
Research Implications
Patel, “A review on vortex tube cooling and applications,” International Journal of Advance Research in Science and Engineering, vol. Kurosaka, "Acoustic Flow in Rotating Flow and the Ranque-Hilsch Vortex-Tube Effect," Journal of Fluids Engineering, vol. Kırmacı, “Exergy analysis and performance of a Ranque–Hilsch counterflow vortex tube having different nozzle numbers at different oxygen and air inlet pressures,” International Journal of Refrigeration , vol.
Unger, "Numerical studies of the compressible flow and energy separation in the Ranque-Hilsch vortex tube," International Journal of Heat and Mass Transfer, vol. Klein, "Parametric and internal investigation of the vortex tube using a CFD model," International Journal of Refrigeration , vol. Polyaev, "Flow and thermodynamic properties of energy separation in a double-circuit vortex tube - an experimental study".
Promvonge, “Experimental investigation on energy separation in a counterflow Ranque-Hilsch vortex tube: Effect of cooling a hot tube,” International Communications in Heat and Mass Transfer, vol. Farhadi, “Experimental Analysis of a Ranque-Hilsch Vortex Tube for Optimizing Nozzle Numbers and Diameters,” Applied Thermal Engineering, vol. Oweimer, “Experimental study of vortex tube energy separation under different tube design,” Experimental Thermal and Fluid Science, vol.
Parekh, “Experimental investigation of Ranque-Hilsch vortex tube and techno-economic evaluation of its industrial utility,” Applied Thermal Engineering, vol. Gutsol, “Simulation of gas species and temperature separation in the counterflow Ranque-Hilsch vortex tube using the large eddy simulation technique,” International Journal of Heat and Mass Transfer, vol.
![Figure 10: Effect of the Number of Elements on the Cold and Hot Outlet Temperature Parameters Dimensions [mm]](https://thumb-ap.123doks.com/thumbv2/azpdfco/10575069.0/40.892.218.679.122.322/figure-effect-number-elements-outlet-temperature-parameters-dimensions.webp)
