Numerical study of energy separation in a vortex tube with different RANS models

https://doi.org/10.1016/j.ijthermalsci.2011.07.011Get rights and content

Abstract

The aim of the present paper is to investigate numerically the energy separation mechanism and flow phenomena within a vortex tube. A 3D computational domain has been generated considering the quarter of the geometry and assuming periodicity in the Azimuthal direction which was found to exhibit correctly the general behaviour expected from a vortex tube. Air is selected as the working fluid. The flow predictions reported here are based upon four turbulence models, namely, the kɛ, kω and SST kω two-equations models and the second moment closure model (RSM). The models results are compared to experimental data obtained from the literature. Four cases have been considered by changing the inlet pressure from 200 up to 380 kPa. It has been observed that all the above mentioned models are capable of predicting fairly well the general flow features but only the advanced RSM model is capable of matching correctly the measured cold and hot outlet temperatures. All the other models over predict the mean temperature difference by values up to twice the measured data.

Highlights

► Energy separation and flow phenomena within a vortex tube were studied numerically. ► A 3D computational domain was generated considering the quarter of the geometry. ► The flow predictions are based upon kɛ, kω and SST kω models and the RSM model. ► All the models predict fairly well the general flow features. ► Only the RSM model matches correctly the measured cold and hot outlet temperatures.

Introduction

Vortex tube is a simple energy separating mechanical device that produces hot and cold streams simultaneously from a compressed gas source. It is compact and simple to fabricate with no moving parts. This device can be used for cooling and heating. Nowadays, vortex tubes provide attractive applications, such as gas dehydration, removal of water vapour and droplets from natural gas streams, gas dewpointing, and process and spot cooling for industrial processes with cold air guns.

Since its invention by Ranque in 1933 and its improvement by Hilsch [1], many efforts have been made to explain the thermal separation phenomenon based on theoretical, numerical and experimental analysis. However, its coefficient of performance remained low and the mechanism of energy separation still ambiguous. Since then, other proposals have followed along the years in order to achieve performance enhancements by; increasing the number of inlet nozzles, changing the tube diameter, varying the cold and hot outlet diameters, and/or changing the working fluid [2], [3], [4], [5], [6], [7], [8], [9].

Other studies were focussed in understanding the global behaviour of the flow in vortex tube by means of thermodynamic laws to determine the optimal performances of this device [10], [11], [12].

Nowadays, new development in CFD tools and measurement techniques can help understand better some of the flow phenomena and allow for the visualisation of the fluid flow paths within the vortex tube which would then on its turn, allow investigating how this energy separation phenomenon is occurring. Consequently, in the last decade, research was focussed in producing detailed data on the flow in different vortex tube configurations by both; experimental measurements and numerical predictions. For instance, the experimental work was mainly concentrated on the influence of the geometry and the parameters of the vortex tube on its performance [13], [14], [15], [16], [17], [18], [19].

In parallel, several numerical studies have been dedicated to this subject. For example, Fröhlingsdorf and Unger [20] simulated numerically the compressible flow and energy separation phenomena using the CFD code CFX. They extended an axisymmetric model by integrating relevant terms for the shear-stress-induced mechanical work. Behera et al. [21] conducted numerically a detailed parameters analysis of a vortex tube. The velocity components and the flow patterns have been evaluated using the CFD code Star-CD. Optimal design parameters of the vortex tube, such as number of nozzles, nozzle profiles, cold end diameter, length to diameter ratio and cold and hot gas fractions, have been also determined. Their paper also showed comparison between the CFD predictions and experimental measurements. Aljuwayhel et al. [22] investigated numerically the energy separation mechanism and flow phenomena within a counter-flow vortex tube. A two-dimensional axisymmetric computational domain was used for their study. Then, the computational predictions were compared to experimental data obtained from a laboratory vortex tube operating with room temperature compressed air. The work also included a parametric study to investigate the effects of varying the diameter and length of the vortex tube. Skye et al. [23] presented a comparison between the performance predicted by numerical predictions and experimental measurements using a commercially available vortex tube. In their study, they considered a two-dimensional steady axisymmetric computational domain. They presented results obtained with both; the standard and renormalisation group k–epsilon turbulence models. Eiamsa-ard and Promvonge [24] presented a numerical analysis of flow field and temperature separation in a uni-flow vortex tube type. In particular, they studied the effects of the turbulence modelling (kɛ model and ASM), effects of numerical schemes (hybrid, upwind and second-order upwind) and grid density on the calculation of energy separation in the vortex tube. They argued that the use of the ASM improves slightly the accuracy of the predictions in comparison with those obtained with the kɛ model. Farouk and Farouk [25] used the large eddy simulation approach to predict the flow and temperature fields in a vortex tube. Behera et al. [26] generated a three-dimensional computational grid of a vortex tube and conducted a numerical study using the CFD code Star-CD to analyse the flow parameters and energy separation mechanism inside the tube. Computations have been realised for different fluid properties and flow parameters to understand the energy transfer mechanisms. Rattanongphisat et al. [27] presented a three-dimensional numerical predictions using the standard kɛ model to simulate the physical behaviour of the flow such as temperature and pressure inside the vortex tube. The outlet temperatures predicted by the simulation have agreed with experimental data obtained from the laboratory tests. Akhesmeh et al. [28] also used the standard kɛ turbulence model but with a two-dimensional axisymmetric domain to study the flow fields and the associated temperature separation within a vortex tube. Simulations have been carried out for various cold outlet mass-flow rates and showed a reasonable agreement with experimental data.

It is clear from the present literature survey that the vortex tube device has received a considerable interest among the research society during the last years and a substantial amount of work both; numerical and experimental, has been published on the subject. However, there seems to be a large gap in the theory that explains this energy separation phenomenon in a satisfactory manner. The experimental work is most of the time limited to integral values which is understandable due to the small dimensions of the device and the relatively high operating pressures. On the other hand, recent developments in the CFD field, makes it now possible to examine in more details the mechanism of thermal separation in vortex tubes. Nevertheless, in the above mentioned previous work, there seems to be only few attempts made to take into account the 3D nature of the flow. Furthermore, most of the numerical work was conducted using the basic two-equation kɛ model. There is no doubt that this model remains to date, the most used in the industry, from one hand, due to its robustness and stability and from the other, due to it’s relatively lower computational cost. In spite of that, this classical model is known to lack some of the basic flow physics such as the sensitivity to flow anisotropy and rotation which are both the principal ingredients in the mechanism driving the vortex tube device. As results, more advanced RANS models but still computationally cost effective in comparison with other approaches such as LES or DNS have to be considered for the flow simulation of this device.

Thus, this paper shows numerical predictions obtained with three two-equation type turbulence models, namely, the kɛ model, kω model, and SST kω model and a more advanced Reynolds-Stress Model (RSM). All runs are carried out using a 3D computational domain for various inlet pressures and compared with the available experimental data.

Section snippets

Description of the problem

A schematic representation of the vortex tube configuration highlighting the device dimensions and the system axis is shown in Fig. 1. This configuration has been the subject of an experimental study conducted by Dincer et al. [17]. In Fig. 1, the total length (135 mm) is presented as the sum of the tube length (133 mm) and the vortex chamber width (2 mm), which are dimensions used by Dincer et al. [17]. Air is introduced to the tube tangentially through four identical nozzles of an inlet section A

Computational domain and mesh

Bearing in mind that the flow in the vortex tube is actually 3-dimensional, a multi-blocks structured grid (Fig. 2) has been generated. The advantage of the domain symmetry was actually used to limit the computational domain to only the quarter of the device and using periodic conditions which should account for any secondary motion that might exist. In addition the present grid is generated using equidistant hexahedral cells to minimise all the errors associated with cells extrusion,

Results and discussions

The results in this section are presented as follows; first, the turbulence models predictions are compared with experimental data, then the flow within the vortex tube is analysed by considering the velocity and temperature fields from all these models. In addition, a detailed comparison is made between models predictions in terms of profiles at different locations of the domain. Finally, contours of temperature and turbulent energy in the mid-plane of the tube are analysed.

Conclusions

A numerical study has been carried out to investigate the energy separation mechanism and flow phenomena within a vortex tube using four different turbulence models, namely, standard kɛ, kω, SST kω models and RSM model. The predicted mean temperature difference between the hot and cold exits has been compared with the available experimental data [17]. Results show that all the models are able to reproduce the general dynamics and separation of energy within the vortex tube. However, the

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