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Experimental study of the thermal separation in a vortex tube
Experimental Thermal and Fluid Science 46 (2013) 175–182
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Experimental study of the thermal separation in a vortex tube Yunpeng Xue ⇑, Maziar Arjomandi, Richard Kelso School of Mechanical Engineering, The University of Adelaide, South Australia 5005, Australia
a r t i c l e
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Article history: Received 17 June 2012 Received in revised form 9 October 2012 Accepted 16 December 2012 Available online 27 December 2012 Keywords: Ranque effect Ranque-Hilsch vortex tube Forced and free vortex Thermal separation Vortex flow
a b s t r a c t A vortex tube, a simple mechanical device capable of generating separated cold and hot fluid streams from a single injection, has been used in many applications, such as heating, cooling, and mixture separation. To explain its working principle, both experimental and numerical investigations have been undertaken and several explanations for the temperature separation in have been proposed. However, due to the complexity of the physical process in the vortex tube, these explanations do not agree with each other well and there has not been a consensus. This paper presents an experimental study of the flow properties in a vortex tube focusing on the thermal separation and energy transfer inside the tube. A better understanding of the flow structure inside the tube was achieved, based on the observed three-dimensional velocity, turbulence intensity, temperature and pressure distributions. The gradual transformation of a forced vortex near the inlet to a free vortex at the hot end is reported in this work. The calculated exergy distribution inside the vortex tube indicates that kinetic energy transformation outwards from the central flow contributes to the temperature separation. Experimental results found in this research show a direct relationship between the formation of hot and cold streams and the vortex transformation along the tube. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction From a single injection of compressed air, a Ranque-Hilsch vortex tube generates instant cold and hot streams at the opposite ends of the tube. Fig. 1 shows the structure of a counter-flow vortex tube, which consists of a straight tube with a port for tangential injection and exits at each end. With the tangential injection of compressed gas, the cold stream is exhausted from the central exit near the inlet, and the hot stream is exhausted from the peripheral exit at the other end of the tube. Xue et al. [1] summarised different explanations for the thermal separation in a vortex tube. The critical analysis of these explanations reveals that there has not been a well-accepted explanation for the temperature separation in a vortex tube so far. To identify the mechanism of thermal separation in a vortex tube, understanding of the physical process inside the tube is essential. Xue et al. [2] conducted a qualitative analysis of the flow behaviour in a vortex tube using flow visualization techniques, in which a flow recirculation, named the multi-circulation, was identified, whereby part of the central flow moved outwards and returned to the hot end. Hence, they suggested that flow streams separate with different temperatures because of the sudden expansion near the inlet to generate the cold flow, and partial stagnation of the multi-circulation near the hot end to generate the hot flow. ⇑ Corresponding author. E-mail address: [email protected] (Y. Xue). 0894-1777/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2012.12.009
The flow properties inside the vortex tube have been studied by many researchers, in order to validate the internal flow behaviour. It was reported by Takahama [3] that the flow inside a vortex tube behaves as a forced vortex based on measurements of the swirl velocity. To explain the existence of the secondary flow in a vortex tube, Ahlborn and Groves [4] measured both azimuthal velocity and axial velocity. Their results suggested that the flow consisted of a Rankine vortex, with a forced vortex in the centre and free vortex in the periphery. Detailed measurements of the flow in a counter-flow vortex tube, including the 3-D velocity distribution, temperature and pressure gradients, were conducted by Gao et al. [5]. However, due to difficulties in obtaining experimental measurements inside the vortex tube, there has not been a consistent understanding of the flow behaviour, so further clarification of the flow properties is required. Energy transfer between different layers of flow inside the vortex tube is believed to be the main reason for the thermal separation as discussed previously [1]. Therefore, an energy analysis needs to be included in a thorough investigation of the vortex tube. Saidi and Allaf Yazdi [6] derived a equation based on the thermodynamic principles to calculate the rate of entropy generation in a vortex tube and provided a new method to optimize the tube’s dimensions and operating conditions. Moreover, in their numerical study, Frohlingsdorf and Unger [7] reported that it is possible to analyse the energy separation by calculating the work done on fluid due to viscous shear. Dincer et al. [8,9] performed an analysis of the exergy performance of a vortex tube, in which the effects of
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Fig. 1. Structure of a counter-flow vortex tube.
different nozzles and working fluids were investigated. Energy transfer between different layers of flow has also been simulated by Aljuwayhel et al. [10] and Behera et al. [11], in which energy transfer due to viscous shear and heat transfer were given as the main reasons for the thermal separation. However, inconsistent distributions of shear work and heat transfer along the tube indicate the need for further verification of the energy analysis. In order to identify the dominant factors in the generation of separate cold and hot streams in a vortex tube, this paper presents an energy analysis of the internal flow based on the measurements of the flow properties and velocity distributions. In a specially designed large-scale vortex tube, three-dimensional velocity distributions, static temperature and static pressure inside the tube were measured and used to perform the energy analysis. It is found that the kinetic energy transferred from the central stream to the peripheral stream is not the dominant reason for the temperature drop in the vortex tube but contributes to the temperature rise near the hot end. Instead, the sudden expansion near the inlet and partial stagnation of the multi-circulation in the rear part of the vortex tube are the main factors in generating cold and hot streams respectively.
2. Experimental apparatus Due to the strong swirling motion of the flow, the high turbulence intensity inside the vortex tube and the small dimensions of the tube, it is difficult to conduct high fidelity experimental investigations. The experimental study becomes more complicated
when the measurements are taken by intrusive probes causing vortex shedding and stronger turbulence. In order to obtain accurate quantitative observations of the flow in a vortex tube, a large-scale tube with a length of 2000 mm and diameter of 60 mm was employed in this work as shown in Fig. 1. To allow the measurements of flow properties at different locations of the tube, 35 inline holes were drilled along the acrylic tube with a distance of 50 mm from each other. The tube length in this experiment was fixed at 21 times of the tube diameter, i.e. L/D = 21 from the inlet. A round inlet nozzle with a diameter of 6 mm, a cold exit with a diameter of 14 mm and a hot exit of 1 mm gap, formed by inserting a 58 mm plug into the 60 mm tube, were chosen based on an optimization of the temperature difference [12]. Compressed air was injected through the inlet nozzle at 2.6 bar and 297.15 K. During the experiments the vortex tube was positioned horizontally on a table and measurement devices were inserted into the tube through the holes along the tube. A Turbulent Flow Instrumentation brand Cobra probe was used to obtain 3-D velocity, static pressure and turbulence intensity profiles at different locations along the tube. The small dimension of the probe head ensured a minimum disturbance introduced to the internal flow. The probe was mounted on a manual traverse vertically with a positioning accuracy of 0.01 mm in the radial direction. By adjusting the angular position of the tube, the cobra probe was inserted through the centre of the tube, so the flow profiles were measured in the radial direction of the tube. A useful feature of the cobra probe software was its provision of a measure of acceptable data. Fig. 2 shows the results of a typical measure-
Fig. 2. Typical measurement result of the total velocity using the cobra probe.
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Fig. 3. Principle and structure of the rotatable Pitot tube.
measured pressures. Therefore, using the rotatable probe, the flow angle, total and static pressure within the vortex tube could be found. Comparisons with the cobra probe showed excellent agreement. The total temperature distribution along the vortex tube was measured using a T-type thermocouple inserted into the tube through the holes. Due to the tube dimensions and construction of the vortex tube, the temperature difference in this experiment was not as significant as it is in a commercial vortex tube. Due to the low Mach number of the flow and the relatively small temperature change in the tube, a recovery factor of 1 was assumed, based on which the static temperature was calculated. For an experimental result F ¼ Fðx1 ; x2 xi Þ; the uncertainty of a measurement can be expressed as:
uF i ¼ ment of the total velocity using the cobra probe at 1 kHz sampling frequency and 5.12 s sampling time. Here, a total of 5120 measurement samples were obtained with velocity variation between 25.8 m/s and 43.1 m/s and an average velocity of 34.8 m/s. The high turbulence intensity of the flow is clear from the fluctuation of the instantaneous velocity relative to the average velocity. The turbulence intensity was calculated using the following equation:
I uv w ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ðu02 þ v 02 þ w02 Þ 3 V
Here, Iuv w is the turbulence intensity, u0 v 0 and w0 are time-varying velocity fluctuating components and V is the time-averaged mean velocity. In this sample, the turbulence intensity was 13.2%, which indicated a relatively low intensity turbulent flow inside the vortex tube. Due to limitations in its measurement range, the cobra probe can provide accurate measurements of 3-D velocity when the flow velocity is between 2 m/s and 50 m/s. For the velocity higher than 50 m/s, the acceptable data collection by the cobra probe was less than 80%. Therefore, a Rotatable Pitot Tube (RPT) was employed to measure the pressure and velocity beyond this range. Fig. 3 presents the working principle and structure of the rotatable Pitot tube, which consists of a 1 mm tube sealed at one end, with a 0.2 mm measurement hole in its side and a pressure sensor connected at the other end. Thus when the tube is rotating at a constant angular velocity, the surface pressure of the tube at variable angles is collected, from which pressure and velocity profiles can be found. Fig. 4 shows measurements obtained by a rotatable Pitot tube positioned in a uniform flow and in a vortex tube separately. In each case, the peak pressures were obtained when the measurement hole was aligned with the oncoming flow, indicating the total pressure. From the pressure distribution in a uniform flow and knowing the static pressure, the angular phase where the surface pressure equals the static pressure was found. Hence, the flow direction and total velocity can be calculated based on these
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xi @F ux F @xi i
Here uF i is the experimental uncertainty induced by factor i, xi represents factor i, F is the mathematical expression of the experimental result, and uxi is the uncertainty of factor q i. The total ffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 2 ffi experimental uncertainties can be calculated as RF ¼ ðuF i Þ. The uncertainties in the experimental results in this work are summarised below in Table 1. 3. Flow properties and energy analysis To understand the flow behaviour inside the vortex tube, the 3-D velocity distributions along the tube were measured. Fig. 5 shows a typical measurement of the swirl velocity at L/D = 20, in which the turbulence intensity and percentage of acceptable data are presented. The data show the existence of a high degree of swirl in the centre of the vortex tube, accompanied by high turbulence intensity. Thus, due to the high turbulence intensity, it is very difficult to measure the actual velocity components and receive acceptable data in the central part. The data also show the presence of a boundary layer at the wall of the vortex tube and this, too, is accompanied by an increase in the turbulence intensity and a lower percentage of acceptable data. The swirl velocity profile at L/D = 20 is consistent with the formation of an irrotational vortex in this region. This type of motion near the hot end presents a different description of the flow structure in a vortex tube as presented in [7,11,13]. In the following section, the measured data of 3-D velocity distributions at several positions will be analysed, which represent a typical configuration of the flow behaviour inside the tube. Fig. 6 shows the swirl velocity distributions along the vortex tube at L/D = 1, 5, 10, 15 and 20. It can be seen from the figure that the swirling flow indicates the presence of a forced vortex near the cold exit, i.e. L/D = 1, with a maximum velocity of 54.1 m/s at 3 mm from the wall and a minimum velocity close to 0 at the centre of the tube. As the flow moves to the hot end, the peripheral swirl velocity decreases and the location of the maximum velocity gradually moves to the centreline of the tube. Similarly, the swirl
Fig. 4. Pressure distributions measured by the rotatable Pitot tube in a uniform flow and flow inside the vortex tube respectively.
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Table 1 Summarised experimental uncertainties. Measurement result
Experimental uncertainty (%)
Velocity measured from Cobra probe Pressure measured from Cobra probe Pressure measured from RPT Temperature Local density Kinetic energy density Exergy density
0.5 0.3 0.3 1 1.05 1.3 2
velocity of the central flow decreases gradually as well when it moves to the cold end. Hence, it can be summarised that the swirl flow inside the vortex tube changes from a forced vortex to an irrotational vortex model. This is contrary to most research work in this area, in which the swirl velocity distribution along a vortex tube has been described as a forced vortex throughout the whole tube [1]. To the best of authors’ knowledge the gradual transformation of the forced vortex structure to a free vortex formation along the tube has not been reported previously and is reported in this work for the first time [3–5,11,14–16]. Similar observation of the velocity distribution inside the vortex tube is showed in a numerical study [17], but no comments on the transformation was reported. It can be understood that the forced vortex formation near the cold end is the result of tangential injection of the air. When the flow moves to the hot end, due to friction near the wall of the tube, the swirl velocity component at the periphery decreases. When the flow reaches the hot end, the swirl velocity in the centre increases, forcing the flow to form a free vortex. As the central flow moves to the cold end, the swirl velocity in the central region is decelerated due to the lower velocity in the peripheral layer. Part of the kinetic energy is transferred outwards by the friction between the free vortex in the centre and the peripheral flow, which improves the performance of the tube. the kinetic energy of the flow will be further discussed, based on the distribution of the kinetic energy density as shown in Fig. 16. Fig. 7 reports the axial velocity distributions in the vortex tube. The positive velocity in the central region indicates the flow moves to the cold nozzle and the negative velocity means the fluid flows to the hot end. The maximum axial velocity at L/D = 20 appears in the centre of the tube, which shows the flow turned back along the centre by the plug. As the central flow moves to the cold end, the outwards radial flow induced by the increasing centrifugal acceleration, causes the excursion of maximum axial velocity from the centre as shown by the asymmetric profiles in the figure (L/D = 15). This also indicates the formation of the above-men-
tioned multi-circulations near the hot end. The maximum axial velocity at L/D = 5 is also located away from the centre, which can be explained by the turn back of the flow in the front part of the tube as described in [1,2]. It can be concluded from the figure that the cold stream exhausted from the cold nozzle has larger volume flow rate than the central flow near the hot end, which is moving towards the cold end. This supports the statement that the cold stream mainly comes from the turn-back flow near the injection [2]. It should be noted that the quality of the data collection near the inlet is relatively poor due to the high injection velocity and sudden expansion near the inlet, so a more accurate measurement of the velocity near the inlet is recommended. Fig. 8 shows the radial velocity distribution along the tube, which has not been investigated in previous studies due to its small magnitude. Positive velocity in the figure indicates that the flow is moving outwards. Hence, the negative radial velocity at L/D = 1 shows that flow is moving to the centre and indicates the existence of the turn-back flow in front part of the tube. At L/ D = 5, 10 and 20, the swirling flow departs from the centre and moves upwards, which is indicated by the positive velocity in the central region of the tube. These offsets of the radial velocity at L/D = 10, 15 and 20, can be explained by the asymmetry of the flow in the vortex tube with single injection as stated in [2]. At L = 15D, corresponding to the position of the multi-circulation, the outwards flow from the centre indicates the formation of the multicirculation. However, due to the unsymmetrical flow generated by a single injection and small magnitude of the radial velocity, accurate measurements of the radial velocity in a vortex tube with symmetrical injections is recommended, since this will provide a more reliable description of the internal flow structure without the complicating influence of asymmetry. Based on the 3-D velocity distribution discussed above, the flow structure inside a counter-flow vortex tube can be summarised as shown in Fig. 9. When the compressed air is injected tangentially into a vortex tube, it starts rotating and moving to the hot end. The inner part of the flow undergoes an expansion, turns back in the front part of the tube and escapes from the cold nozzle. In this process, the temperature of the fluid drops due to the sudden expansion in the centre of the forced vortex and forms a cold core in the front part of the tube. The peripheral flow moves to the hot end and then is turned back by the plug. Due to the sudden increase of the angular velocity at the hot end, the central flow moves outwards, which is indicated by the radial velocity at L/D = 15. Then part of the central flow mixes with the peripheral flow and flows back to the hot end again. In this way, the multi-circulation is formed as shown in Fig. 9. The effects of stagnation and mixing within multi-circulations contribute to the temperature
Fig. 5. Swirl velocity and turbulence intensity at L/D = 20.
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Fig. 6. Swirl velocity profiles at different positions along the vortex tube.
Fig. 7. Axial velocity profiles at different positions along the vortex tube.
Fig. 8. Radial velocity profiles at different positions along the vortex tube.
using a rotatable Pitot tube at L/D = 1. The accuracy of the collected data is demonstrated by the agreement of the measurement results obtained using both the cobra probe and the rotatable Pitot tube at L/D = 1. It can be concluded from the total velocity distribution that the swirl velocity is the largest velocity component. The total velocity distribution was further used to analyse the energy gradient in the vortex tube. In order to analyse the kinetic energy gradient along the tube, both the total velocity and turbulence intensity are used. The overall turbulence intensity of the flow inside the vortex tube is summarised and presented in Fig. 11. It can be observed that stronger turbulence exists in the central region of the flow, which is also shown in Fig. 5. In the peripheral region, as the flow moves to the hot end, the turbulence intensity of the flow continues to increase. Near the wall, the turbulence intensity of the flow at L/ D = 10 is stronger than that at L/D = 15, which may be explained by the mixture of the central flow and peripheral flow in the multi-circulation region. The static pressure profiles inside the vortex tube, determined using the Cobra probe, are shown in Fig. 12. Also illustrated are the static pressure measurements made by the rotatable Pitot tube at L/D = 1. It can be observed that the two measurements agree well with each other. It can be observed from Fig. 12 that the static pressure decreases from the cold end to the hot end in the peripheral region, whereas, in the central part, it decreases from the hot end to L/D = 15 and then increases to the cold end. The pressure gradients along the tube so provide direct evidence that the swirl velocity distribution is being transformed from a forced vortex to an irrotational vortex model [12]. In the central region of the tube, it is found the static pressure is lower than the ambient pressure, which explains the suction at the cold nozzle when the cold flow ratio is small [12]. The minimum static pressure around L/D = 15 presents positive support for the hypothesized flow structure. As the flow moves towards the cold end, part of the central flow moves outwards to the peripheral flow and generates the region with minimum pressure, which is located between the multi-circulation and the bifurcation point (named as theoretical axial stagnation point in [12] and shown in Fig. 9). The increase of the static pressure from L/D = 15 is due to the turn back of the peripheral flow from the bifurcation point. It is consistent with the observed flow down the tube along the periphery and a return to the cold end along the centreline. Stagnation temperature profiles were also measured using the T-type thermocouple. The static temperature can be calculated from the stagnation temperature and Mach number at the same location, using the following equation:
Ts ¼ rise in a vortex tube. In a previous study, the maximum temperature along the wall was found to exist away from the hot exit [18], and this was explained by the presence of the multi-circulation [1]. As shown in Fig. 10, the total velocity inside the vortex tube was measured using a cobra probe and these results were validated
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Tt 1 þ 12 ðc 1ÞM 2
Here Ts is the static temperature, Tt is total temperature, c is ratio of specific heat and M is the Mach number of the flow. In this experiment, the ratio of specific heats is 1.4 for the air flow inside the vortex tube and the Mach number is calculated as M ¼ V t =C, here Vt is the total velocity presented above and C is the local speed
Fig. 9. Hypothesized flow structure inside a counter-flow vortex tube.
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Fig. 13. Static temperature profiles at different positions within the vortex tube. Fig. 10. Total velocity profiles at different positions along the vortex tube.
Fig. 14. Local density of the flow in the vortex tube. Fig. 11. The turbulence intensity profiles of the flow inside the vortex tube.
induced by the effect of friction in the boundary layer. As the flow moves towards the hot end, a thicker boundary layer is indicated by the higher temperature near the wall as shown in Fig. 13. At the hot end, i.e., L/D = 20, the temperatures of the central flow and peripheral flow are found to be almost the same, which implies that the central fluid comes from the peripheral flow after being turned back by the hot end plug. Using the measured static pressure and temperature distributions, local density was calculated as:
q¼
Fig. 12. Static pressure distributions at different positions along the vortex tube.
pffiffiffiffiffiffiffiffiffiffi of sound, which can be calculated using C ¼ cRT s . Since the measurement of static temperature is not available, the measured total temperature was used to estimate the static temperature. Errors in the estimation of the speed of sound induced by using the total temperature instead of the static temperature were calculated and found less than 0.25%. The static temperature was calculated using this local speed of sound and used to estimate the speed of sound again. The calculations were iterated until the induced errors were found to be less than 0.01%, at which point the static temperature was converged. Fig. 13 presents the calculated static temperature gradients along the vortex tube. It is seen from the figure that similar temperature gradients were observed inside the tube as shown in other studies, although the performance of the vortex tube was not optimal due to the dimensions of the tube and input parameters. It can be seen that the lowest temperature occurs in the peripheral layer near the injection, which indicates the mixture of the hot stream and cold stream in the central region. At L/D = 1, the higher temperature near the wall of the tube is
Ps RT s
Here PS and TS are the static pressure and temperature respectively, and R is the universal gas constant. Fig. 14 presents the local density of the flow in the vortex. It can be seen from the figure that the density of the flow decreases from the cold end to the hot end and the maximum density occurs in the periphery near the injection. For the central flow, its density decreases from the hot end plug and reaches the minimum value around the position of L/ D = 15, where minimum static pressure occurs. Then, the density keeps increasing to the cold exit. Hence, the minimum density of the flow occurs in the region between the bifurcation point and the multi-circulation due to the outwards movement of the central flow. This tendency of the local density inside the vortex tube shows positive supports for the hypothesized flow structure discussed above. As discussed in [1], several explanations have been proposed as the reason for the temperature separation in a vortex tube and the core of the subject among these hypotheses is the clarification of the energy transfer between different layers of flow. If the energy transfer between layers is significant, kinetic energy transfer outwards due to the viscosity and turbulence of the flow should be considered as a reasonable explanation for the separation. On the contrary, sudden expansion and stagnation could also be considered as the dominant factor in the temperature separation. The
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clarification of the mechanism can be therefore achieved by the examination of the energy gradient within the tube. The total energy inside a vortex tube consists of three parts, i.e. kinetic energy, potential energy and enthalpy. To calculate the energy gradient, flow properties inside the vortex tube are required and presented above, including the velocity, density, turbulence intensity, static pressure and static temperature. The kinetic energy within a control volume can be calculated as:
Ek ¼ Ek;Mean þ Ek;Turbulence Here, Ek;Mean is the average kinetic energy of the flow and Ek;Turbulence is the kinetic energy of the turbulence component of the flow. The average kinetic energy and turbulent fluctuation of the velocity are calculated as following:
Ek;Mean ¼
1 mV 2 2
Ek;Turbulence ¼
1 1 1 mV 02 ¼ mðu02 þ v 02 þ w02 Þ ¼ m 3ðVIuv w Þ2 2 2 2
Here, m is mass of the control volume, V is the time-averaged overall velocity, V0 is time-varying velocity fluctuating component, u0 , v0 and w0 present the time-varying velocity fluctuating component in swirl, axial and radial direction respectively, and Iuvw is the overall turbulence intensity. Gravitational potential energy of the control volume is given as:
Eg ¼ mgz Here, g is gravitational acceleration and z is the net height. The enthalpy of the control volume can be expressed as:
Ein ¼ mC p ðDTÞ Here, Cp is the specific heat at constant pressure and DT is the temperature difference between a local substance and reference condition. In a study of rotating air flow, the gravitational potential energy is generally ignored due to its small magnitude. Hence, the total energy of the control volume inside the vortex tube can be given as:
Et ¼ Ein þ Ek In analysing compressible flow, the entropy of the control volume is very useful and should be included. The entropy change for a process can be written as follows:
Si So ¼ C p ln
Ti Pi Rln To Po
Here, R is the gas constant, T and P represent the temperature and pressure, the subscripts ‘‘i’’ and ‘‘o’’ represent the instantaneous and reference conditions of a process separately. Thus, the exergy of the flow can be derived from the above-mentioned equations and expressed as:
1 1 Eex ¼ mC p ðT i T o Þ þ mV 2 þ m 3ðVIuv w Þ2 2 2 Ti Pi mT o C p ln Rln To Po In order to perform a detailed analysis of the exergy distribution inside the vortex tube, the density of the local fluid was used instead of the control volume, which indicates the exergy density inside the tube. Therefore, the equation is written in the following form:
1 1 eex ¼ qi C p ðT i T o Þ þ qi V 2i þ qi 3ðVIuv w Þ2i 2 2 Ti Pi qi T o C p ln Rln To Po Here, qi is the local density, which is calculated using the following equation:
Fig. 15. Kinetic energy density profiles of the flow within the vortex tube.
qi ¼
Pi RT i
Here, Pi and Ti are the local static pressure and static temperature respectively. Thus, based on the measured static pressure and calculated static temperature inside the vortex tube, local density of the flow can be calculated. In the calculation of the exergy density, Cp is the specific heat at constant pressure and is 1006 J/ kg K in the temperature range considered, Ti and To are instant and reference temperature, V is the time-averaged overall velocity, R is 286.9 J/kg K, Pi and Po are instant and reference pressure, standard atmosphere was used as the reference condition, and To = 293.15 K, Po = 101325 Pa. Fig. 15 summarizes the kinetic energy density of the flow inside the tube. It can be concluded from the figure that the kinetic energy of the peripheral flow decreases from the cold end to the hot end, while the kinetic energy of the central flow decreases form the hot end to the cold end. The decrease in the kinetic energy is induced by the viscosity of the fluid. At L/D = 1, the maximum kinetic energy occurs in the peripheral part near the tube, which presents the boundary effect as shown in Fig. 10. Due to the wall friction, the total velocity in the peripheral region decreases as the flow moves to the hot end, which leads to the decrease in the kinetic energy. The kinetic energy density of the central flow decreases from L/D = 20 to the cold end, and the kinetic energy is transferred outwards during the transformation of a free vortex at the hot end to a forced vortex at the cold end. Fig. 16 presents the calculated exergy density inside the vortex tube at different locations. It is shown that the exergy in the peripheral region decreases from the inlet, which is caused by the flow into the inner part of the vortex tube from the peripheral flow. The flow into the inner tube is also demonstrated by the decrease of local density in the periphery from inlet and increase of local density in the central region of the tube from L/D = 15 (Fig. 14). Heat transfer from the wall of the tube to ambient air contributes to the gradually decreasing exergy density from L/D = 10 to the hot end. At the hot end, due to the inwards flow near the plug the exergy density increases by a significant magnitude. As the central flow returns to the cold end, energy is transferred outwards during the process of transformation from an irrotational vortex near the hot end to a forced vortex near the cold end, which leads to the decrease of exergy density in the central region. The increase of the exergy density in the central region of the tube from L/D = 15 is caused by the turn back of the peripheral flow as shown in Fig. 9. In the peripheral region of the flow, the slightly changed exergy density near the hot end indicates that partial stagnation and mixture of the flow contribute much to the temperature rise via the structure of multi-circulation. Overall, in the cold core, none of the energy transferred outwards indicates the governing factor for temperature drop in a vortex tube is the effect of sudden expansion. Heat transferred
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Fig. 16. Exergy density profiles at different positions within the vortex tube.
from the tube to the ambient air causes the reduction of exergy density in the peripheral part of the flow from the cold end to the hot end. Energy transferred from the central free vortex flow outwards to the periphery has a positive influence on the temperature rise at the hot end. The slightly decreased exergy density of the peripheral flow near the hot end shows there is no energy transferred into the peripheral flow, and hence indicates that the partial stagnation and mixture of the multi-circulation are the dominant factors in the temperature rise. However, due to the limited temperature difference in this experiment, it is not possible to perform an accurate calculation of the temperature rise because of the energy transferred outwards. 4. Conclusion Although several explanations for the temperature separation in a vortex tube have been proposed, due to the complexity of the internal flow, there has not been a well accepted explanation and the physical process inside the vortex tube remains unclear. This ongoing research focuses on the flow properties inside a counter-flow vortex tube aiming to locate the dominant reason for the temperature separation in a vortex tube. This experimental study presents detailed measurements of the flow properties inside a counter-flow vortex tube. The threedimensional velocity distributions inside the vortex tube lead to a new understanding of the flow behaviour in the vortex tube. It is noted that in the central region of the tube, the irrotational vortex at the hot end was transformed to a forced vortex near the injection, and kinetic energy is only transferred outwards from the hot end to the cold end. The locations of the maximum axial velocity indicate the change of the flow structure and support the hypothesis of a multi-circulation as stated in [1,2]. A stronger turbulent flow in the central region is indicated by the turbulence intensity distribution, which is further used to calculate the exergy density in the vortex tube. Static and total pressure gradients in the vortex tube provide positive support for the proposed flow structure. The static temperature gradient is also presented, from which the region of expansion can be located. Using the detailed flow properties, the exergy density inside the vortex tube is calculated and provides positive support for the proposed hypothesis in [1]. Sudden expansion near the cold end is considered as the main reason for the temperature drop, since there is no energy transferred outwards from the central region. The slightly changed exergy density near
the hot end indicates that the temperature rise is mainly due to the partial stagnation of the structure of multi-circulation. Kinetic energy is transferred outwards from the irrotational vortex in the central region and contributes to the temperature rise in the periphery near the hot end. References [1] Y. Xue, M. Arjomandi, R. Kelso, A critical review of temperature separation in a vortex tube, Experimental Thermal and Fluid Science 34 (2010) 1367–1374. [2] Y. Xue, M. Arjomandi, R. Kelso, Visualization of the flow structure in a vortex tube, Experimental Thermal and Fluid Science 35 (2011) 1514–1521. [3] H. Takahama, Studies on vortex tubes, Bulletin of JSME 8 (1965) 433–440. [4] B. Ahlborn, S. Groves, Secondary flow in a vortex tube, Fluid Dynamics Research 21 (1997) 73–86. [5] C.M. Gao, K.J. Bosschaart, J.C.H. Zeegers, A.T.A.M. De Waele, Experimental study on a simple Ranque-Hilsch vortex tube, Cryogenics 45 (2005) 173–183. [6] M.H. Saidi, M.R. Allaf Yazdi, Exergy model of a vortex tube system with experimental results, Energy 24 (1999) 625–632. [7] W. Fröhlingsdorf, H. Unger, Numerical investigations of the compressible flow and the energy separation in the Ranque-Hilsch vortex tube, International Journal of Heat and Mass Transfer 42 (1999) 415–422. [8] K. Dincer, Y. Yilmaz, A. Berber, S. Baskaya, Experimental investigation of performance of hot cascade type Ranque-Hilsch vortex tube and exergy analysis, International Journal of Refrigeration 34 (2011) 1117–1124. [9] K. Dincer, A. Avci, S. Baskaya, A. Berber, Experimental investigation and exergy analysis of the performance of a counter flow Ranque-Hilsch vortex tube with regard to nozzle cross-section areas, International Journal of Refrigeration 33 (2010) 954–962. [10] N.F. Aljuwayhel, G.F. Nellis, S.A. Klein, Parametric and internal study of the vortex tube using a CFD model, International Journal of Refrigeration 28 (2005) 442–450. [11] U. Behera, P.J. Paul, K. Dinesh, S. Jacob, Numerical investigations on flow behaviour and energy separation in Ranque-Hilsch vortex tube, International Journal of Heat and Mass Transfer 51 (2008) 6077–6089. [12] Y. Xue, M. Arjomandi, R. Kelso, Experimental study of the flow structure in a counter flow Ranque-Hilsch vortex tube, International Journal of Heat and Mass Transfer 55 (2012) 5853–5860. [13] S. Eiamsa-ard, P. Promvonge, Numerical investigation of the thermal separation in a Ranque-Hilsch vortex tube, International Journal of Heat and Mass Transfer 50 (2007) 821–832. [14] T. Dutta, K.P. Sinhamahapatra, S.S. Bandyopdhyay, Comparison of different turbulence models in predicting the temperature separation in a RanqueHilsch vortex tube, International Journal of Refrigeration 33 (2010) 783–792. [15] O.V. Kazantseva, S.A. Piralishvili, A.A. Fuzeeva, Numerical simulation of swirling flows in vortex tubes, High Temperature 43 (2005) 608–613. [16] T. Farouk, B. Farouk, Large eddy simulations of the flow field and temperature separation in the Ranque-Hilsch vortex tube, International Journal of Heat and Mass Transfer 50 (2007) 4724–4735. [17] A. Secchiaroli, R. Ricci, S. Montelpare, V. D’Alessandro, Numerical simulation of turbulent flow in a Ranque-Hilsch vortex tube, International Journal of Heat and Mass Transfer 52 (2009) 5496–5511. [18] O. Aydin, M. Baki, An experimental study on the design parameters of a counterflow vortex tube, Energy 31 (2006) 2427–2436.
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Experimental study of the thermal separation in a vortex tube Yunpeng Xue ⇑, Maziar Arjomandi, Richard Kelso School of Mechanical Engineering, The University of Adelaide, South Australia 5005, Australia
a r t i c l e
i n f o
Article history: Received 17 June 2012 Received in revised form 9 October 2012 Accepted 16 December 2012 Available online 27 December 2012 Keywords: Ranque effect Ranque-Hilsch vortex tube Forced and free vortex Thermal separation Vortex flow
a b s t r a c t A vortex tube, a simple mechanical device capable of generating separated cold and hot fluid streams from a single injection, has been used in many applications, such as heating, cooling, and mixture separation. To explain its working principle, both experimental and numerical investigations have been undertaken and several explanations for the temperature separation in have been proposed. However, due to the complexity of the physical process in the vortex tube, these explanations do not agree with each other well and there has not been a consensus. This paper presents an experimental study of the flow properties in a vortex tube focusing on the thermal separation and energy transfer inside the tube. A better understanding of the flow structure inside the tube was achieved, based on the observed three-dimensional velocity, turbulence intensity, temperature and pressure distributions. The gradual transformation of a forced vortex near the inlet to a free vortex at the hot end is reported in this work. The calculated exergy distribution inside the vortex tube indicates that kinetic energy transformation outwards from the central flow contributes to the temperature separation. Experimental results found in this research show a direct relationship between the formation of hot and cold streams and the vortex transformation along the tube. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction From a single injection of compressed air, a Ranque-Hilsch vortex tube generates instant cold and hot streams at the opposite ends of the tube. Fig. 1 shows the structure of a counter-flow vortex tube, which consists of a straight tube with a port for tangential injection and exits at each end. With the tangential injection of compressed gas, the cold stream is exhausted from the central exit near the inlet, and the hot stream is exhausted from the peripheral exit at the other end of the tube. Xue et al. [1] summarised different explanations for the thermal separation in a vortex tube. The critical analysis of these explanations reveals that there has not been a well-accepted explanation for the temperature separation in a vortex tube so far. To identify the mechanism of thermal separation in a vortex tube, understanding of the physical process inside the tube is essential. Xue et al. [2] conducted a qualitative analysis of the flow behaviour in a vortex tube using flow visualization techniques, in which a flow recirculation, named the multi-circulation, was identified, whereby part of the central flow moved outwards and returned to the hot end. Hence, they suggested that flow streams separate with different temperatures because of the sudden expansion near the inlet to generate the cold flow, and partial stagnation of the multi-circulation near the hot end to generate the hot flow. ⇑ Corresponding author. E-mail address: [email protected] (Y. Xue). 0894-1777/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2012.12.009
The flow properties inside the vortex tube have been studied by many researchers, in order to validate the internal flow behaviour. It was reported by Takahama [3] that the flow inside a vortex tube behaves as a forced vortex based on measurements of the swirl velocity. To explain the existence of the secondary flow in a vortex tube, Ahlborn and Groves [4] measured both azimuthal velocity and axial velocity. Their results suggested that the flow consisted of a Rankine vortex, with a forced vortex in the centre and free vortex in the periphery. Detailed measurements of the flow in a counter-flow vortex tube, including the 3-D velocity distribution, temperature and pressure gradients, were conducted by Gao et al. [5]. However, due to difficulties in obtaining experimental measurements inside the vortex tube, there has not been a consistent understanding of the flow behaviour, so further clarification of the flow properties is required. Energy transfer between different layers of flow inside the vortex tube is believed to be the main reason for the thermal separation as discussed previously [1]. Therefore, an energy analysis needs to be included in a thorough investigation of the vortex tube. Saidi and Allaf Yazdi [6] derived a equation based on the thermodynamic principles to calculate the rate of entropy generation in a vortex tube and provided a new method to optimize the tube’s dimensions and operating conditions. Moreover, in their numerical study, Frohlingsdorf and Unger [7] reported that it is possible to analyse the energy separation by calculating the work done on fluid due to viscous shear. Dincer et al. [8,9] performed an analysis of the exergy performance of a vortex tube, in which the effects of
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Fig. 1. Structure of a counter-flow vortex tube.
different nozzles and working fluids were investigated. Energy transfer between different layers of flow has also been simulated by Aljuwayhel et al. [10] and Behera et al. [11], in which energy transfer due to viscous shear and heat transfer were given as the main reasons for the thermal separation. However, inconsistent distributions of shear work and heat transfer along the tube indicate the need for further verification of the energy analysis. In order to identify the dominant factors in the generation of separate cold and hot streams in a vortex tube, this paper presents an energy analysis of the internal flow based on the measurements of the flow properties and velocity distributions. In a specially designed large-scale vortex tube, three-dimensional velocity distributions, static temperature and static pressure inside the tube were measured and used to perform the energy analysis. It is found that the kinetic energy transferred from the central stream to the peripheral stream is not the dominant reason for the temperature drop in the vortex tube but contributes to the temperature rise near the hot end. Instead, the sudden expansion near the inlet and partial stagnation of the multi-circulation in the rear part of the vortex tube are the main factors in generating cold and hot streams respectively.
2. Experimental apparatus Due to the strong swirling motion of the flow, the high turbulence intensity inside the vortex tube and the small dimensions of the tube, it is difficult to conduct high fidelity experimental investigations. The experimental study becomes more complicated
when the measurements are taken by intrusive probes causing vortex shedding and stronger turbulence. In order to obtain accurate quantitative observations of the flow in a vortex tube, a large-scale tube with a length of 2000 mm and diameter of 60 mm was employed in this work as shown in Fig. 1. To allow the measurements of flow properties at different locations of the tube, 35 inline holes were drilled along the acrylic tube with a distance of 50 mm from each other. The tube length in this experiment was fixed at 21 times of the tube diameter, i.e. L/D = 21 from the inlet. A round inlet nozzle with a diameter of 6 mm, a cold exit with a diameter of 14 mm and a hot exit of 1 mm gap, formed by inserting a 58 mm plug into the 60 mm tube, were chosen based on an optimization of the temperature difference [12]. Compressed air was injected through the inlet nozzle at 2.6 bar and 297.15 K. During the experiments the vortex tube was positioned horizontally on a table and measurement devices were inserted into the tube through the holes along the tube. A Turbulent Flow Instrumentation brand Cobra probe was used to obtain 3-D velocity, static pressure and turbulence intensity profiles at different locations along the tube. The small dimension of the probe head ensured a minimum disturbance introduced to the internal flow. The probe was mounted on a manual traverse vertically with a positioning accuracy of 0.01 mm in the radial direction. By adjusting the angular position of the tube, the cobra probe was inserted through the centre of the tube, so the flow profiles were measured in the radial direction of the tube. A useful feature of the cobra probe software was its provision of a measure of acceptable data. Fig. 2 shows the results of a typical measure-
Fig. 2. Typical measurement result of the total velocity using the cobra probe.
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Fig. 3. Principle and structure of the rotatable Pitot tube.
measured pressures. Therefore, using the rotatable probe, the flow angle, total and static pressure within the vortex tube could be found. Comparisons with the cobra probe showed excellent agreement. The total temperature distribution along the vortex tube was measured using a T-type thermocouple inserted into the tube through the holes. Due to the tube dimensions and construction of the vortex tube, the temperature difference in this experiment was not as significant as it is in a commercial vortex tube. Due to the low Mach number of the flow and the relatively small temperature change in the tube, a recovery factor of 1 was assumed, based on which the static temperature was calculated. For an experimental result F ¼ Fðx1 ; x2 xi Þ; the uncertainty of a measurement can be expressed as:
uF i ¼ ment of the total velocity using the cobra probe at 1 kHz sampling frequency and 5.12 s sampling time. Here, a total of 5120 measurement samples were obtained with velocity variation between 25.8 m/s and 43.1 m/s and an average velocity of 34.8 m/s. The high turbulence intensity of the flow is clear from the fluctuation of the instantaneous velocity relative to the average velocity. The turbulence intensity was calculated using the following equation:
I uv w ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ðu02 þ v 02 þ w02 Þ 3 V
Here, Iuv w is the turbulence intensity, u0 v 0 and w0 are time-varying velocity fluctuating components and V is the time-averaged mean velocity. In this sample, the turbulence intensity was 13.2%, which indicated a relatively low intensity turbulent flow inside the vortex tube. Due to limitations in its measurement range, the cobra probe can provide accurate measurements of 3-D velocity when the flow velocity is between 2 m/s and 50 m/s. For the velocity higher than 50 m/s, the acceptable data collection by the cobra probe was less than 80%. Therefore, a Rotatable Pitot Tube (RPT) was employed to measure the pressure and velocity beyond this range. Fig. 3 presents the working principle and structure of the rotatable Pitot tube, which consists of a 1 mm tube sealed at one end, with a 0.2 mm measurement hole in its side and a pressure sensor connected at the other end. Thus when the tube is rotating at a constant angular velocity, the surface pressure of the tube at variable angles is collected, from which pressure and velocity profiles can be found. Fig. 4 shows measurements obtained by a rotatable Pitot tube positioned in a uniform flow and in a vortex tube separately. In each case, the peak pressures were obtained when the measurement hole was aligned with the oncoming flow, indicating the total pressure. From the pressure distribution in a uniform flow and knowing the static pressure, the angular phase where the surface pressure equals the static pressure was found. Hence, the flow direction and total velocity can be calculated based on these
177
xi @F ux F @xi i
Here uF i is the experimental uncertainty induced by factor i, xi represents factor i, F is the mathematical expression of the experimental result, and uxi is the uncertainty of factor q i. The total ffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 2 ffi experimental uncertainties can be calculated as RF ¼ ðuF i Þ. The uncertainties in the experimental results in this work are summarised below in Table 1. 3. Flow properties and energy analysis To understand the flow behaviour inside the vortex tube, the 3-D velocity distributions along the tube were measured. Fig. 5 shows a typical measurement of the swirl velocity at L/D = 20, in which the turbulence intensity and percentage of acceptable data are presented. The data show the existence of a high degree of swirl in the centre of the vortex tube, accompanied by high turbulence intensity. Thus, due to the high turbulence intensity, it is very difficult to measure the actual velocity components and receive acceptable data in the central part. The data also show the presence of a boundary layer at the wall of the vortex tube and this, too, is accompanied by an increase in the turbulence intensity and a lower percentage of acceptable data. The swirl velocity profile at L/D = 20 is consistent with the formation of an irrotational vortex in this region. This type of motion near the hot end presents a different description of the flow structure in a vortex tube as presented in [7,11,13]. In the following section, the measured data of 3-D velocity distributions at several positions will be analysed, which represent a typical configuration of the flow behaviour inside the tube. Fig. 6 shows the swirl velocity distributions along the vortex tube at L/D = 1, 5, 10, 15 and 20. It can be seen from the figure that the swirling flow indicates the presence of a forced vortex near the cold exit, i.e. L/D = 1, with a maximum velocity of 54.1 m/s at 3 mm from the wall and a minimum velocity close to 0 at the centre of the tube. As the flow moves to the hot end, the peripheral swirl velocity decreases and the location of the maximum velocity gradually moves to the centreline of the tube. Similarly, the swirl
Fig. 4. Pressure distributions measured by the rotatable Pitot tube in a uniform flow and flow inside the vortex tube respectively.
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Table 1 Summarised experimental uncertainties. Measurement result
Experimental uncertainty (%)
Velocity measured from Cobra probe Pressure measured from Cobra probe Pressure measured from RPT Temperature Local density Kinetic energy density Exergy density
0.5 0.3 0.3 1 1.05 1.3 2
velocity of the central flow decreases gradually as well when it moves to the cold end. Hence, it can be summarised that the swirl flow inside the vortex tube changes from a forced vortex to an irrotational vortex model. This is contrary to most research work in this area, in which the swirl velocity distribution along a vortex tube has been described as a forced vortex throughout the whole tube [1]. To the best of authors’ knowledge the gradual transformation of the forced vortex structure to a free vortex formation along the tube has not been reported previously and is reported in this work for the first time [3–5,11,14–16]. Similar observation of the velocity distribution inside the vortex tube is showed in a numerical study [17], but no comments on the transformation was reported. It can be understood that the forced vortex formation near the cold end is the result of tangential injection of the air. When the flow moves to the hot end, due to friction near the wall of the tube, the swirl velocity component at the periphery decreases. When the flow reaches the hot end, the swirl velocity in the centre increases, forcing the flow to form a free vortex. As the central flow moves to the cold end, the swirl velocity in the central region is decelerated due to the lower velocity in the peripheral layer. Part of the kinetic energy is transferred outwards by the friction between the free vortex in the centre and the peripheral flow, which improves the performance of the tube. the kinetic energy of the flow will be further discussed, based on the distribution of the kinetic energy density as shown in Fig. 16. Fig. 7 reports the axial velocity distributions in the vortex tube. The positive velocity in the central region indicates the flow moves to the cold nozzle and the negative velocity means the fluid flows to the hot end. The maximum axial velocity at L/D = 20 appears in the centre of the tube, which shows the flow turned back along the centre by the plug. As the central flow moves to the cold end, the outwards radial flow induced by the increasing centrifugal acceleration, causes the excursion of maximum axial velocity from the centre as shown by the asymmetric profiles in the figure (L/D = 15). This also indicates the formation of the above-men-
tioned multi-circulations near the hot end. The maximum axial velocity at L/D = 5 is also located away from the centre, which can be explained by the turn back of the flow in the front part of the tube as described in [1,2]. It can be concluded from the figure that the cold stream exhausted from the cold nozzle has larger volume flow rate than the central flow near the hot end, which is moving towards the cold end. This supports the statement that the cold stream mainly comes from the turn-back flow near the injection [2]. It should be noted that the quality of the data collection near the inlet is relatively poor due to the high injection velocity and sudden expansion near the inlet, so a more accurate measurement of the velocity near the inlet is recommended. Fig. 8 shows the radial velocity distribution along the tube, which has not been investigated in previous studies due to its small magnitude. Positive velocity in the figure indicates that the flow is moving outwards. Hence, the negative radial velocity at L/D = 1 shows that flow is moving to the centre and indicates the existence of the turn-back flow in front part of the tube. At L/ D = 5, 10 and 20, the swirling flow departs from the centre and moves upwards, which is indicated by the positive velocity in the central region of the tube. These offsets of the radial velocity at L/D = 10, 15 and 20, can be explained by the asymmetry of the flow in the vortex tube with single injection as stated in [2]. At L = 15D, corresponding to the position of the multi-circulation, the outwards flow from the centre indicates the formation of the multicirculation. However, due to the unsymmetrical flow generated by a single injection and small magnitude of the radial velocity, accurate measurements of the radial velocity in a vortex tube with symmetrical injections is recommended, since this will provide a more reliable description of the internal flow structure without the complicating influence of asymmetry. Based on the 3-D velocity distribution discussed above, the flow structure inside a counter-flow vortex tube can be summarised as shown in Fig. 9. When the compressed air is injected tangentially into a vortex tube, it starts rotating and moving to the hot end. The inner part of the flow undergoes an expansion, turns back in the front part of the tube and escapes from the cold nozzle. In this process, the temperature of the fluid drops due to the sudden expansion in the centre of the forced vortex and forms a cold core in the front part of the tube. The peripheral flow moves to the hot end and then is turned back by the plug. Due to the sudden increase of the angular velocity at the hot end, the central flow moves outwards, which is indicated by the radial velocity at L/D = 15. Then part of the central flow mixes with the peripheral flow and flows back to the hot end again. In this way, the multi-circulation is formed as shown in Fig. 9. The effects of stagnation and mixing within multi-circulations contribute to the temperature
Fig. 5. Swirl velocity and turbulence intensity at L/D = 20.
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Fig. 6. Swirl velocity profiles at different positions along the vortex tube.
Fig. 7. Axial velocity profiles at different positions along the vortex tube.
Fig. 8. Radial velocity profiles at different positions along the vortex tube.
using a rotatable Pitot tube at L/D = 1. The accuracy of the collected data is demonstrated by the agreement of the measurement results obtained using both the cobra probe and the rotatable Pitot tube at L/D = 1. It can be concluded from the total velocity distribution that the swirl velocity is the largest velocity component. The total velocity distribution was further used to analyse the energy gradient in the vortex tube. In order to analyse the kinetic energy gradient along the tube, both the total velocity and turbulence intensity are used. The overall turbulence intensity of the flow inside the vortex tube is summarised and presented in Fig. 11. It can be observed that stronger turbulence exists in the central region of the flow, which is also shown in Fig. 5. In the peripheral region, as the flow moves to the hot end, the turbulence intensity of the flow continues to increase. Near the wall, the turbulence intensity of the flow at L/ D = 10 is stronger than that at L/D = 15, which may be explained by the mixture of the central flow and peripheral flow in the multi-circulation region. The static pressure profiles inside the vortex tube, determined using the Cobra probe, are shown in Fig. 12. Also illustrated are the static pressure measurements made by the rotatable Pitot tube at L/D = 1. It can be observed that the two measurements agree well with each other. It can be observed from Fig. 12 that the static pressure decreases from the cold end to the hot end in the peripheral region, whereas, in the central part, it decreases from the hot end to L/D = 15 and then increases to the cold end. The pressure gradients along the tube so provide direct evidence that the swirl velocity distribution is being transformed from a forced vortex to an irrotational vortex model [12]. In the central region of the tube, it is found the static pressure is lower than the ambient pressure, which explains the suction at the cold nozzle when the cold flow ratio is small [12]. The minimum static pressure around L/D = 15 presents positive support for the hypothesized flow structure. As the flow moves towards the cold end, part of the central flow moves outwards to the peripheral flow and generates the region with minimum pressure, which is located between the multi-circulation and the bifurcation point (named as theoretical axial stagnation point in [12] and shown in Fig. 9). The increase of the static pressure from L/D = 15 is due to the turn back of the peripheral flow from the bifurcation point. It is consistent with the observed flow down the tube along the periphery and a return to the cold end along the centreline. Stagnation temperature profiles were also measured using the T-type thermocouple. The static temperature can be calculated from the stagnation temperature and Mach number at the same location, using the following equation:
Ts ¼ rise in a vortex tube. In a previous study, the maximum temperature along the wall was found to exist away from the hot exit [18], and this was explained by the presence of the multi-circulation [1]. As shown in Fig. 10, the total velocity inside the vortex tube was measured using a cobra probe and these results were validated
179
Tt 1 þ 12 ðc 1ÞM 2
Here Ts is the static temperature, Tt is total temperature, c is ratio of specific heat and M is the Mach number of the flow. In this experiment, the ratio of specific heats is 1.4 for the air flow inside the vortex tube and the Mach number is calculated as M ¼ V t =C, here Vt is the total velocity presented above and C is the local speed
Fig. 9. Hypothesized flow structure inside a counter-flow vortex tube.
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Fig. 13. Static temperature profiles at different positions within the vortex tube. Fig. 10. Total velocity profiles at different positions along the vortex tube.
Fig. 14. Local density of the flow in the vortex tube. Fig. 11. The turbulence intensity profiles of the flow inside the vortex tube.
induced by the effect of friction in the boundary layer. As the flow moves towards the hot end, a thicker boundary layer is indicated by the higher temperature near the wall as shown in Fig. 13. At the hot end, i.e., L/D = 20, the temperatures of the central flow and peripheral flow are found to be almost the same, which implies that the central fluid comes from the peripheral flow after being turned back by the hot end plug. Using the measured static pressure and temperature distributions, local density was calculated as:
q¼
Fig. 12. Static pressure distributions at different positions along the vortex tube.
pffiffiffiffiffiffiffiffiffiffi of sound, which can be calculated using C ¼ cRT s . Since the measurement of static temperature is not available, the measured total temperature was used to estimate the static temperature. Errors in the estimation of the speed of sound induced by using the total temperature instead of the static temperature were calculated and found less than 0.25%. The static temperature was calculated using this local speed of sound and used to estimate the speed of sound again. The calculations were iterated until the induced errors were found to be less than 0.01%, at which point the static temperature was converged. Fig. 13 presents the calculated static temperature gradients along the vortex tube. It is seen from the figure that similar temperature gradients were observed inside the tube as shown in other studies, although the performance of the vortex tube was not optimal due to the dimensions of the tube and input parameters. It can be seen that the lowest temperature occurs in the peripheral layer near the injection, which indicates the mixture of the hot stream and cold stream in the central region. At L/D = 1, the higher temperature near the wall of the tube is
Ps RT s
Here PS and TS are the static pressure and temperature respectively, and R is the universal gas constant. Fig. 14 presents the local density of the flow in the vortex. It can be seen from the figure that the density of the flow decreases from the cold end to the hot end and the maximum density occurs in the periphery near the injection. For the central flow, its density decreases from the hot end plug and reaches the minimum value around the position of L/ D = 15, where minimum static pressure occurs. Then, the density keeps increasing to the cold exit. Hence, the minimum density of the flow occurs in the region between the bifurcation point and the multi-circulation due to the outwards movement of the central flow. This tendency of the local density inside the vortex tube shows positive supports for the hypothesized flow structure discussed above. As discussed in [1], several explanations have been proposed as the reason for the temperature separation in a vortex tube and the core of the subject among these hypotheses is the clarification of the energy transfer between different layers of flow. If the energy transfer between layers is significant, kinetic energy transfer outwards due to the viscosity and turbulence of the flow should be considered as a reasonable explanation for the separation. On the contrary, sudden expansion and stagnation could also be considered as the dominant factor in the temperature separation. The
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clarification of the mechanism can be therefore achieved by the examination of the energy gradient within the tube. The total energy inside a vortex tube consists of three parts, i.e. kinetic energy, potential energy and enthalpy. To calculate the energy gradient, flow properties inside the vortex tube are required and presented above, including the velocity, density, turbulence intensity, static pressure and static temperature. The kinetic energy within a control volume can be calculated as:
Ek ¼ Ek;Mean þ Ek;Turbulence Here, Ek;Mean is the average kinetic energy of the flow and Ek;Turbulence is the kinetic energy of the turbulence component of the flow. The average kinetic energy and turbulent fluctuation of the velocity are calculated as following:
Ek;Mean ¼
1 mV 2 2
Ek;Turbulence ¼
1 1 1 mV 02 ¼ mðu02 þ v 02 þ w02 Þ ¼ m 3ðVIuv w Þ2 2 2 2
Here, m is mass of the control volume, V is the time-averaged overall velocity, V0 is time-varying velocity fluctuating component, u0 , v0 and w0 present the time-varying velocity fluctuating component in swirl, axial and radial direction respectively, and Iuvw is the overall turbulence intensity. Gravitational potential energy of the control volume is given as:
Eg ¼ mgz Here, g is gravitational acceleration and z is the net height. The enthalpy of the control volume can be expressed as:
Ein ¼ mC p ðDTÞ Here, Cp is the specific heat at constant pressure and DT is the temperature difference between a local substance and reference condition. In a study of rotating air flow, the gravitational potential energy is generally ignored due to its small magnitude. Hence, the total energy of the control volume inside the vortex tube can be given as:
Et ¼ Ein þ Ek In analysing compressible flow, the entropy of the control volume is very useful and should be included. The entropy change for a process can be written as follows:
Si So ¼ C p ln
Ti Pi Rln To Po
Here, R is the gas constant, T and P represent the temperature and pressure, the subscripts ‘‘i’’ and ‘‘o’’ represent the instantaneous and reference conditions of a process separately. Thus, the exergy of the flow can be derived from the above-mentioned equations and expressed as:
1 1 Eex ¼ mC p ðT i T o Þ þ mV 2 þ m 3ðVIuv w Þ2 2 2 Ti Pi mT o C p ln Rln To Po In order to perform a detailed analysis of the exergy distribution inside the vortex tube, the density of the local fluid was used instead of the control volume, which indicates the exergy density inside the tube. Therefore, the equation is written in the following form:
1 1 eex ¼ qi C p ðT i T o Þ þ qi V 2i þ qi 3ðVIuv w Þ2i 2 2 Ti Pi qi T o C p ln Rln To Po Here, qi is the local density, which is calculated using the following equation:
Fig. 15. Kinetic energy density profiles of the flow within the vortex tube.
qi ¼
Pi RT i
Here, Pi and Ti are the local static pressure and static temperature respectively. Thus, based on the measured static pressure and calculated static temperature inside the vortex tube, local density of the flow can be calculated. In the calculation of the exergy density, Cp is the specific heat at constant pressure and is 1006 J/ kg K in the temperature range considered, Ti and To are instant and reference temperature, V is the time-averaged overall velocity, R is 286.9 J/kg K, Pi and Po are instant and reference pressure, standard atmosphere was used as the reference condition, and To = 293.15 K, Po = 101325 Pa. Fig. 15 summarizes the kinetic energy density of the flow inside the tube. It can be concluded from the figure that the kinetic energy of the peripheral flow decreases from the cold end to the hot end, while the kinetic energy of the central flow decreases form the hot end to the cold end. The decrease in the kinetic energy is induced by the viscosity of the fluid. At L/D = 1, the maximum kinetic energy occurs in the peripheral part near the tube, which presents the boundary effect as shown in Fig. 10. Due to the wall friction, the total velocity in the peripheral region decreases as the flow moves to the hot end, which leads to the decrease in the kinetic energy. The kinetic energy density of the central flow decreases from L/D = 20 to the cold end, and the kinetic energy is transferred outwards during the transformation of a free vortex at the hot end to a forced vortex at the cold end. Fig. 16 presents the calculated exergy density inside the vortex tube at different locations. It is shown that the exergy in the peripheral region decreases from the inlet, which is caused by the flow into the inner part of the vortex tube from the peripheral flow. The flow into the inner tube is also demonstrated by the decrease of local density in the periphery from inlet and increase of local density in the central region of the tube from L/D = 15 (Fig. 14). Heat transfer from the wall of the tube to ambient air contributes to the gradually decreasing exergy density from L/D = 10 to the hot end. At the hot end, due to the inwards flow near the plug the exergy density increases by a significant magnitude. As the central flow returns to the cold end, energy is transferred outwards during the process of transformation from an irrotational vortex near the hot end to a forced vortex near the cold end, which leads to the decrease of exergy density in the central region. The increase of the exergy density in the central region of the tube from L/D = 15 is caused by the turn back of the peripheral flow as shown in Fig. 9. In the peripheral region of the flow, the slightly changed exergy density near the hot end indicates that partial stagnation and mixture of the flow contribute much to the temperature rise via the structure of multi-circulation. Overall, in the cold core, none of the energy transferred outwards indicates the governing factor for temperature drop in a vortex tube is the effect of sudden expansion. Heat transferred
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Fig. 16. Exergy density profiles at different positions within the vortex tube.
from the tube to the ambient air causes the reduction of exergy density in the peripheral part of the flow from the cold end to the hot end. Energy transferred from the central free vortex flow outwards to the periphery has a positive influence on the temperature rise at the hot end. The slightly decreased exergy density of the peripheral flow near the hot end shows there is no energy transferred into the peripheral flow, and hence indicates that the partial stagnation and mixture of the multi-circulation are the dominant factors in the temperature rise. However, due to the limited temperature difference in this experiment, it is not possible to perform an accurate calculation of the temperature rise because of the energy transferred outwards. 4. Conclusion Although several explanations for the temperature separation in a vortex tube have been proposed, due to the complexity of the internal flow, there has not been a well accepted explanation and the physical process inside the vortex tube remains unclear. This ongoing research focuses on the flow properties inside a counter-flow vortex tube aiming to locate the dominant reason for the temperature separation in a vortex tube. This experimental study presents detailed measurements of the flow properties inside a counter-flow vortex tube. The threedimensional velocity distributions inside the vortex tube lead to a new understanding of the flow behaviour in the vortex tube. It is noted that in the central region of the tube, the irrotational vortex at the hot end was transformed to a forced vortex near the injection, and kinetic energy is only transferred outwards from the hot end to the cold end. The locations of the maximum axial velocity indicate the change of the flow structure and support the hypothesis of a multi-circulation as stated in [1,2]. A stronger turbulent flow in the central region is indicated by the turbulence intensity distribution, which is further used to calculate the exergy density in the vortex tube. Static and total pressure gradients in the vortex tube provide positive support for the proposed flow structure. The static temperature gradient is also presented, from which the region of expansion can be located. Using the detailed flow properties, the exergy density inside the vortex tube is calculated and provides positive support for the proposed hypothesis in [1]. Sudden expansion near the cold end is considered as the main reason for the temperature drop, since there is no energy transferred outwards from the central region. The slightly changed exergy density near
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