# Three dimensional numerical (3D CFD) study of effect of pressure-outlet and pressure-far-field boundary conditions on heat transfer predictions inside vortex tube

Three dimensional numerical (3D CFD) study of effect of pressure-outlet and pressure-far-field boundary conditions on heat transfer predictions inside vortex tube

Department of Mathematics, Payame Noor University (PNU), Tehran 19395-3697, Iran

Corresponding Author Email:
Page:
21-25
|
DOI:
https://doi.org/10.18280/psees.020104
10 April 2018
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Accepted:
12 April 2018
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Published:
31 March 2018
| Citation

OPEN ACCESS

Abstract:

A vortex tube can be used as a heating device for preheating the pipes inside a solar heater. A vortex tube usually has some parts such as: A vortex-chamber, one or more inlet nozzles, a cold end orifice, a control valve at hot end and a working tube. The vortex-chamber is a main part of vortex tube which the pressured gas is injected into this part tangentially. An appropriate design of vortex-chamber’s geometry leads to better efficiency and good performance of vortex tube. In this study, the computational fluid dynamics (CFD) model is created on basis of an experimental model and is a three-dimensional (3D) steady compressible model that utilizes the k-ε turbulent model to solve the nonlinear flow field equations. In this study a comparison between usage of two different boundary conditions (Pressure-Outlet and Pressure-Far-Field) has been presented. The results show that there is no essential difference between these two boundary conditions for heat transfer predicting inside a vortex tube separator. So, the scientists which work on numerical aspects of vortex tubes and have no access to the experimental data can use the Pressure Far Field boundary condition.

Keywords:

vortex tube, heat transfer, energy separation, boundary condition

1. Introduction

In fact the first version of this device (vortex tube) was explored or invented based on an accidental investigation (by Ranque [1]). Several years later a German scientist [2] directed his efforts on improving this amazing device and vortex tube was introduced academically for the first time in 1947. As seen in Fig. 1, a vortex tube includes different parts such as: one or more inlet nozzles, a vortex-chamber, a cold end orifice, a throttle valve that is located at the end of main tube and a working tube. When pressured fluid is entered into the vortex-chamber tangentially via the nozzles, a strong rotational flow field is created. When the fluid tangentially swirls to the center of the vortex tube it is expanded and cooled.

## 1.jpg

Figure 1. A schematic drawing of Ranque-Hilsch vortex tube

2. Basic Concepts

The performance measurements on the VT systems (usually) are pointed and presented based on the temperature differences (there is no difference what kind of the VT is used, RHVT, PVT). There are three definitions; first, the cold temperature difference or $\Delta T_{\text { cold }}$ (difference between cold and inlet sides), the total temperature difference or $\Delta T$ (difference between cold and hot sides) and the hot temperature difference or $\Delta T_{\text { hot }}$ (difference between hot and inlet sides), these definitions are as bellow:

$\Delta T_{h}=T_{h}-T_{i n l e t}$    (1)

$\Delta T_{C}=T_{i n l e t}-T_{C}$    (2)

3. Physical Model Description

The 3D CFD model is created on basis of that was used by Skye et al. [33] in their experimental (Fig. 2) work. It is noteworthy that, an ExairTM 708 slpm vortex tube was used by Skye et al. [33] to perform all tests and to take all of the experimental data. The dimensional geometry of this vortex tube has been summarized in the Tab. 1. The 3D CFD mesh grid is shown in Fig. 3. In this model a regular organized mesh grid has been used. All radial line of this model of meshing has been connected to the centerline and the circuit lines have been designed organized from wall to centerline. So, the volume units that have been created in this model are regular cubic volumes. This meshing system helps the computations to be operated faster than the irregular and unorganized meshing, and the procedure of computations have been done more precisely.

## 2.jpg

Figure 2. Schematic of vortex tube that used by Skye et al.

Table 1. Geometric measurements of the vortex tube that was used by Skye et al. [33]

 Measurement Value Working tube length 106 mm Nozzle height 0.97 mm Nozzle width 1.41 mm Nozzle total inlet area (An) 8.2 mm2 Cold exit diameter 6.2 mm Cold exit area 30.3 mm2 Hot exit diameter 11 mm Hot exit area 95 mm2

For this reason the CFD model has been assumed a rotational periodic condition. Hence, only a sector of the flow domain with angle of 60° needs to consider for computations as shown in Fig. 3.

(a)

## 3b.png

(b)

Figure 3. a and b) 3D CFD model of vortex chamber with six straight nozzles

4. Results and Discussion

In this section, the purpose is to demonstrate this claim which there is no difference between the pressure-far-field boundary condition and pressure-outlet boundary condition. As seen in Figure 4 and 5 cold exit temperature and hot exit temperature at both boundary conditions have good agreement with each other (in this section, reports are based on contours data).

## 4.png

Figure 4. Cold Exit Temperature: comparison of two boundary condition(pressure-far-field and pressure-outlet) and experimental data

## 5.png

Figure 5. Hot Exit Temperature: comparison of two boundary condition(pressure-far-field and pressure-outlet) and experimental data

In Fig. 4 the cold temperature of gas which exits from cold exhaust has been compared in three states as function of cold mass fraction, including: experimental data, setting pressure-far-field boundary condition and setting pressure-outlet boundary condition. As seen in Fig. 5 the hot exit temperature has been illustrated as function of cold mass fraction in three mentioned states.

Some parameters such as axial velocity, tangential velocity, total pressure and total temperature at three sections (Z/L=0.1, 0.4 and 0.7) of the working tube have been studied as a function of dimensionless radial distance (r/R), meanwhile the total temperature on the wall of vortex tube has been investigated as a function of dimensionless length (Z/L) of working tube. Fig. 6 and 7 shows axial velocity and tangential velocity of fluid inside the working tube in three mentioned section respectively which have been obtained at different dimensionless radial distances. This Figure illustrates a comparison form of CFD results with employing two different boundary conditions.

## 6.png

Figure 6. Axial Velocity: indication of axial velocity at three section (Z/L=0.1, 0.4, 0.7)

## 7.png

Figure 7. Tangential Velocity: indication of tangential velocity at three section (Z/L=0.1, 0.4, 0.7)

## 8.png

Figure 8. Variation of total pressure at three section (Z/L=0.1, 0.4 and 0.7)

## 9.png

Figure 9. Changing in total temperature pressure at three section (Z/L=0.1, 0.4 and 0.7)

The variation of total pressure and total temperature for different value of dimensionless radial distances at three sections (Z/L=0.1, 0.4 and 0.7) of working tube has been shown in Figure 8 and 9 respectively.

The total temperature results on working tube have been shown in Fig. 10. This Figure indicates the variation of total temperature on wall at pressure-far-field boundary condition and pressure-outlet boundary condition in comparison form.

## 10.png

Figure 10. Comparison between the results of pressure-far-field boundary condition and pressure-outlet boundary condition on the wall of working tube

## 11-2.png

Figure 11. Total temperture of a vortex tube with pressure far field boundary condition

where, in Fig. 10, Z/L represents the dimensionless length of the vortex tube. With these validations, this theory has been demonstrated that there is no difference between pressure-far-field boundary condition and pressure-outlet boundary condition. Hereinafter the CFD researchers that haven’t the pressures at exhausts of vortex tube can do their predictions. By employing this method, having the pressures at exits is not important but knowing the information about vortex tube geometry and conditions of inlet gas is necessary. Figure 11 shows the total temperature contour for a vortex tube using Pressure-Far-Field boundary condition.

5. Conclusions

An optimization model of vortex-chamber has been modeled in this paper. We developed a 3D computational fluid dynamic model to simulate a vortex-chamber of vortex tube. Some changes have been implemented on boundary conditions and the effect of these changes has been studied to achieve the better performance of vortex tube. Primitive results have been validated with Skye et al.’s experimental data and show a good agreement with these results. This research shows that the pressure-outlet boundary condition can be replaced by pressure-far-field boundary condition and pressure-far-field boundary condition is as same as pressure-outlet boundary condition.

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