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An experimental study of nozzle number on Ranque Hilsch counter-flow vortex tube
Accepted Manuscript An Experimental Study of Nozzle Number on Ranque Hilsch Counter-Flow Vortex Tube Hany Ahmed, M. Salem Ahmed, M. Attalla, A. Abo El –Wafa PII: DOI: Reference:
S0894-1777(16)30350-8 http://dx.doi.org/10.1016/j.expthermflusci.2016.11.034 ETF 8956
To appear in:
Experimental Thermal and Fluid Science
Received Date: Revised Date: Accepted Date:
14 June 2016 7 August 2016 27 November 2016
Please cite this article as: H. Ahmed, M. Salem Ahmed, M. Attalla, A. Abo El –Wafa, An Experimental Study of Nozzle Number on Ranque Hilsch Counter-Flow Vortex Tube, Experimental Thermal and Fluid Science (2016), doi: http://dx.doi.org/10.1016/j.expthermflusci.2016.11.034
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An Experimental Study of Nozzle Number on Ranque Hilsch Counter-Flow Vortex Tube Hany Ahmed1,2, M. Salem Ahmed3, M. Attalla4*, A. Abo El –Wafa5 1 Mechanical Department, Faculty of Eng., Asuit University, Asuit, Egypt 2 Mechanical Department, College of Eng., Taif University, Taif, 888, Saudi Arabia 3 Mechanical Department, Faculty of Industrial Education, Sohag University, Sohag, Egypt 4 Department of Mechanical Engineering, Faculty of Engineering, South Valley University, Qena 83521, Egypt 5 Qarun Petroleum Company, Egypt * Corresponding Author, e-mail: [email protected]
Abstract The present study investigates the effects of the orifice nozzle number and the inlet pressure experimentally on the cooling performance of the counter flow type vortex tube. The energy generation has been conducted using a generator of type stream–tek generator model GNMD-KIT with the number of nozzles (2, 3, and 6), and aspect ratio 1.6 and, an inner diameter of 7.5 mm. In the experiments, for each of the orifices, inlet pressures have been adjusted from 200 kPa to 600 kPa. The energy separation to be investigated here focuses on the cold temperature difference and coefficient of performance for cooling. The experimental results concluded in this paper proved that the higher effect of nozzle number is for nozzle number three and hence that nozzle number could affect the energy separation efficiently. A comparison of the present experiments with other published works has been conducted. An analytical study of the characteristics equation has been carried out to evaluate the best correlation of the ratio of cold temperature difference to the inlet temperature as a function of pressure, cold mass fraction and nozzle numbers. The goodness of fit of the regression model is inspected using the analysis of variance and t-test. The values of R2 are adjusted close to 97 % which show a very good agreement between the experimental and predicted values. Key words: Ranque Hilsch, Vortex tube, Nozzle number, counter flow, energy separation Nomenclature AR
Aspect ratio, [-]
B
Width of nozzle, [m]
CF
Cold mass fraction, [-]
COP
Coefficient of performance [-]
Cp
Specific heat [kJ/kg. K]
D
Inner diameter of vortex tube, [m]
d
Diameter of cold tube, [m]
L
Length of the tube, [m]
m
Mass flow rate, [kg/s]
N
Number of nozzle, [-]
P
Pressure, [Pa]
T
Temperature, [K]
R
Universal gas constant, [8.314472 J/K. Mol]
W
Height of nozzle, [m]
Subscript atm
Atmosphere
c
Cold
h
Hot
i
Inlet
Acronyms CVT
Counter vortex tube
RHVT
Ranque-Hilsh vortex tube
VT
Vortex tube
Introduction: The vortex tube is a simple device operating as a refrigeration machine without any moving part e.g. rotating shaft or piston cylinder [1]. It consists of a nozzle, a vortex hall, a separating cold plate, a hot valve, and a hot and cold end tube as shown in Fig.1 [2]. The vortex tube was first discovered by Ranque [3, 4], who was granted a French patent for the device in 1932 and a United States patent in 1934. In 1945, Rudolf Hilsch [5] conducted an experiment on vortex tube that focused on the thermal performance with different geometrical parameters. The vortex tube or RHVT can be classified into two types: counter-flow RHVT
and uni-flow RHVT [6]. In the counter-flow vortex tube type, the cold flow move is in the opposite direction with respect to the hot stream, while in the uni-flow type, the hot and cold stream flow is in the same direction. In general, the counter flow RHVT has been recommended more than the uni-flow RHVT for its efficient energy separation. The RHVT is widely used for cooling and heating applications. The major application is conducted for cooling purposes, e.g. cooling the electric device, cooling machinery during operation. In spite of its small capacity, the vortex tube is very useful for certain applications because it is simple, compact, light, and it requires no refrigerant [7]. In the recent years, it has been known that vortex tube is a low cost and an effective solution for many spot cooling problems. The separation mechanism inside the vortex tube remains until today not completely undisclosed [8 - 9]. Up to date, more than hundred investigations on the energy separation in the RHVT for both numerical and experimental study. Numerous investigators have conducted on the energy separation in the RHVT by using turbulence modeling. Frohlingsdorf and Unger [10] used the computational code based on CFX along with k-ε model to investigate the energy separation inside the vortex tube. Behera et al. [11] used the CFD code (Star-CD) to investigate the temperature separation in vortex tube. In their study, the effect of the secondary circulation and length of the hot tube on energy separation have been also calculated. Shamsoddini and Nezhad [12] studied the effect of the nozzle number on the flow and power of cooling process of a vortex tube using a three-dimensional numerical fluid flow dynamic model. Eiamsa-ard and Promvonge [13] studied the energy separation numerically in a uni-flow vortex tube using kappa-epsilon model. They concluded that the maximum temperature gradients appear in the outer regions close to the tube wall and the separation effect in the core region near the inlet nozzle. Farouk and Farouk [14] used large eddy simulation method to predict the flow and temperature field in the vortex tube. Farouk et al. [15] computed the temperature and flow field of the species mass fraction in counter-flow vortex tube with nitrogen and helium as a working fluid. The artificial neural networks and employing the experimental data were used to predict the effect of length to diameter ratio and nozzle number on performance of counter-flow RHVT by Dincer et al. [16]. At the same time with the numerical works, many experimental investigations have been performed to study the performance of the vortex tube. Here are some of the experimental works on temperature separation in the vortex tube explained as follows:
Bovand et al. [17] have investigated the effect of curvature numerically on the performance of vortex tubes. They studied curvature angles of 0 and 110°. The results showed that the efficiency of straight vortex tube is higher than the curved vortex tube with angle of 110°. They indicated that CFD model could be successfully used for the determination of heating and cooling performances of curvature effects on Ranque-Hilsch vortex tube. Bovand et al. [18] studied the effect of certain geometrical parameters on cooling performance of RanqueHilsch vortex tube. They used an experimental setup having two levels and a central composite face design. They analyzed the results according to the principle of Response Surface Methodology (RSM). They found that the optimum value of the number of nozzles was 2, cold orifice diameter 9.48 mm and inlet pressure 3.2 bar. Bovand et al. [19] conducted a CFD analytically to determine the effect of vortex tube curvature on their performance. They found that the curvature of vortex tube caused a decrease in the swirl velocity and the diffusion process in vortex tube. Results showed that the straight and 150° curved vortex tube had a higher performance as a refrigerator than other curvature angles. Saidi and Valipour [20] have investigated the influence of the RHVT diameter and hot tube length, number of nozzle on the cold temperature difference in a counter-flow vortex tube. They observed that the maximum cold air temperature difference was found at tube length to vortex diameter ratio ranged from 20 to 55.5, and cold orifice diameter ratio, β = 0.5. Pinar et al. [21] have investigated the effect and optimization of process parameters in a counter flow vortex tube on temperature difference through the Taguchi method. It has been observed that the optimum setting of process parameters maximizing the temperature difference is an inlet pressure of 650 kPa, a nozzle number of 2, and a cold mass fraction of 0.7. Dincer et al. [22] have studied the effects of control valve geometry, plug location and the number of nozzles on energy separation under different inlet pressures. Valipour and Niazi [23] have investigated the effects of axial curvature and turning angle of main tube on the efficiency of vortex tube under different inlet pressure. Wu et al. [2] have presented the effect of the conventional nozzle, the proposed nozzle and the nozzle of Archimedes on the energy separation of vortex tube. Their results concluded that the enhanced nozzle provided a better cooling performance with temperature of cold gas of about 2.2 ˚C and 5 ˚C lower than those presented by the nozzle with a normal rectangle and with Archimedes coil, respectively. The effect of generator vortex angle of rotating flow on the performance of the RHVT has been studied by Xue and Arjomandi [24]. They showed that the maximum cooling efficiency obtained was between the vortex generator angles of 4.8 and 6.7˚. Kirmaci [25] has
investigated the effects of the nozzle numbers and inlet pressures on the energy separation of vortex tube using air and oxygen as working fluids. He observed that the temperature rise between hot and cold fluid reduces with increasing nozzle number. Besides, the cold temperature reductions for using both two working fluids (air and oxygen) increase with the increase of the inlet pressure. The experimental work of Hamdan et al. [8, 26] reported the effect of nozzle parameters on the energy separation of the vortex tube. Their results indicated that the maximum energy separation is achieved with tangential nozzle orientation while the symmetry/asymmetry of nozzles has a minimal effect on the performance of the energy separation. Singh et al. [27] reported the effect of different parameters such as the nozzle number, hot end area and mass fractions on the performance of RHVT. They showed that the effect of the nozzle geometry was more important than the cold orifice design in getting high temperature separations. Gao et al. [28] used a special pitot tube and thermocouple techniques to measure the pressure, velocity and temperature distribution inside the vortex tube which the pitot tube has only a diameter of 1 mm with one hole. They observed that rounding off the entrance can be improved and extend to the secondary circulation gas flow and enhance the system performance. Aydin and Baki [7] have studied the temperature separation experimentally in a counter-flow vortex tube with various geometrical and thermo-physic parameters. In their work, the geometry of tube was optimized to the maximum of the temperature difference between the inlet and cold temperatures by changing the various dimensions of the tube such as the diameter of the inlet nozzle and the angle of the control valve. Nouri-Borujerdi et al. [29] studied the effect of certain geometrical parameters experimentally on cooling performance of Ranque-Hilsch vortex tube. Their findings showed that when the N increased, the vortex tube with a larger L/D was better than vortex tube with lower L/D. The above-cited review of literature clearly indicates that the energy separation and the efficiency of a vortex tube are significantly affected by the various geometrical parameters. Despite a lot of studies have been carried out in RHVT, the effect of nozzle number on energy separation is still open to doubt. There is a disagreement over the effect of nozzle number on the performance of vortex tube. Some of the studies suggested that decreasing nozzle number improves temperature separation [20]; others proposed that the performance increases with increasing nozzle number [11, 30]. This study is conducted to investigate the ways to provide some new insights into the energy separation of the vortex tube under different operating parameters. It is rarely in all vortex tube studies to examine the effect of a
number of nozzles on the total temperature difference and the coefficient of performance in cooling. Therefore, in the present study, we have examined the effect of the number of nozzles on the performance of vortex tube with special vortex geometry of aspect ratio (AR), of 1.6 and hot vortex tube to diameter ratio (L/D), of 15 on the total cold temperature difference and the coefficient of performance in cooling. Also, this study has been carried out experimentally at inlet pressure varied from 2 to 6 bar and cold mass frication varied from 0.4 to 0.9. The additional aim of this study is to develop an empirical equation for cold temperature difference as a function of number of nozzles (N), inlet pressure (Pi) and cold mass frication (CF). Hence, the effect of using different nozzle numbers on the performance of vortex tube is investigated to obtain the optimum nozzle number. 2. Experimental Work 2.1 Experimental set-up The counter- flow vortex tube (CVT) and the arrangement of the experimental system are shown in Fig.2. The experimental set-up shows the locations of vital instruments used for measuring pressures, temperatures and flow rates. The compressed air is supplied from the compressor through a calibrated orifice meter. An air filter and a pressure regulator are installed upstream of the orifice flow meter to filter the air and maintain the downstream pressure at 8 bar. The compressed air reaches the vortex tube after passing through a dehumidifier device and filter. Filter separator follows the pressure vessel to separate the water droplet incoming from the pressure vessel. Then the cold air stream leaves the tube through the central of the vortex generator (cold exit), while the hot air stream at the periphery exhausts out of the other exit (hot exit). The mass flow rate of the inlet air and cold air discharge are measured by ultrasonic flow (Model: STRANS FUG1010-Simens Co., Germany). The cold mass fraction (CF) is attended by the cone-shaped valve placed on the hot outlet of the main tube. The cold air temperature is measured at the exit of the cold air tube while the hot air temperature was measured. All the data for temperature are measured by using RTD (RTD – Model: TX251). The inlet pressure and pressure through the cold stream is measured using pressure transducer (Danfoss – Model: AkS-33). All measured data are collected by Data acquisition incorporated with the counter vortex tube system. Table 1 summarizes the specifications of all devices.
A hot tube L =112.5 mm with inner diameter of vortex tube, D equal to 7.5 mm, (L/D = 15) and constant area of nozzles entrance of aspect ratio, AR = 1.6 have been used in this study and can be defined by the following equation:
AR W B
(1)
where B and W are nozzle width and height respectively. Fig.3 shows a photo of the CVT system. A stream –tek generators kit model GNMD-KIT of three nozzles, N = 2, 3, and 6 have been conducted. Fig. 4 shows a stream –tek generator of model GNMD-KIT of numbers, N = 2, 3, and 6 . The experimental tests had been performed several times to have reached a steady state when reading of temperature and pressure does not change any more. In order to determine the reliability of the experimental results, an uncertainty analysis has been conducted on all measured quantities [31, 32]. Performing the error analysis, the maximum uncertainties in determining these parameters are given in Table 2. The maximum uncertainties of dimensionless parameters were ± 3.56 % for temperature, ± 5.78% for mass flow rates and 2.78% for inlet pressure. Table 1 Measurement Devises Specifications Devise Air Compressor
Air Filter
Air Pressure Regulator
Pressure Transmitter
Temperature Measured
Specifications/Accuracy Model: KS-150, Capacity: 1.5 m3/min Motor Power: 7.5/10 kW/Hp Maximum Working Pressure: 8 bar Model: SDPC:DC600-06 Operating Pressure: 1 – 8.5 bar Maximum Flow Rate: 11500 L/min Ambient Temperature: -10 C – 60 C Filter Precision: 20 μm Model: AR 3000-03 Ambient Temperature: -5 C – 60 C Pressure Regulation Range: 0.5 – 8.5 bar Accuracy: ± 0.1 % Model: Danfos: AKS-33 Pressure Range 1- 20 bar Operating Temperature: 0 C – 80 C Accuracy: Up To 0.1 % Model: RTD-Tx-251 Temperature Range: -100 C – 1350 C Operating Temperature: -20 C – 70 C
Air Flow Rate
Operating Humidity: 5 to 95 % RH Accuracy: Better Than 0.1 % Model: STRANS FUG1010 Operating Temperature: -18 C – 60 C Flow Temperature: -28 C – 93 C
Table 2 Measured parameters and their accompanied errors parameters Pressure, [Pa] Temperature, [K] Mass flow rate, [kg/s] Length of tube, [mm] Diameter of tube, [mm] Diameter of vortex tube, [mm] COP
Maximum errors % 0.105 0.86 2.07 0.113 0.175 0.154 0.134
2.2 Work procedure High pressure air from the compressor is directed tangentially into the vortex tube. The high pressure gas expands in the vortex tube and separates into the cold and hot streams. The cold gas leaves the central orifice near the entrance nozzle while the hot gas discharges the periphery at the far end of the tube. The control valve is being used to control the flow rate of the hot stream. Before starting the experimental tests, the throttling valve is set in fully open. Then the air tank works and by use of the valve that is applied on the vortex tube inlet position. This would help to regulate cold mass fraction. During this procedure, the mass flow rates of air at cold and hot exit are determined by using the ultrasonic flow meter. During the experiments, measurements are performed including pressure, temperature and flow rates at the inlet of vortex tube and the exit of hot tube. 2.3 Data reduction The cold temperature difference, (Ti – Tc) represents an important parameter for the performance of the CVT in the energy separation. where Ti = inlet air temperature, K Tc = cold air temperature (exit from cold tube side), K Cold mass fraction, CF, represents the parameter which governs the temperature separation and is expressed by:
c m CF m
(2)
Where m c is mass flow rate of cold air. Kg/s where m is mass flow rate of total air. Kg/s
m c m h m
(3)
and m h is mass flow rate of hot air. Kg/s Vortex tube can be used in cooling and heating processes; in the case of Vortex tube for cooling process it is called refrigerator vortex tube. The performance of cooling vortex tube is measured using the followings equations: for the refrigerator is defined as follow [8]:
COP
Cooling Load Isothermal Compression Energy
(4)
COP
m cC p Ti Tc RTi ln Pi Patm m
(5)
C p 1 Tc Ti COP CF R ln Pi Patm
(6)
Where : Cp = specific heat , kJ/kg K Pi = inlet pressure , bar Patm = 1 bar, atmospheric pressure Ti = inlet air temperature, K Tc = cold air temperature, K 3. Correlated Equation The analytical study of the characteristic equations (based on partial differentiation and equating to zero, or other conventional optimization gradient methods) for fruitful results is very difficult due to the interlaced effects of performance parameters on its characteristics. To overcome this difficulty and to meet the goal of locating an objective characteristics performance, some statistical random search techniques have been programmed to determine the best correlation equations (subjected to standard statistical tests as shown in Table 3
below). The results are least-square fitted into several trial correlation equations to reach the most acceptable representative equation with accepted standard statistical t-tests by using SPSS program version 13 [16]. Fig. 5 shows the deviation between the experiments values and the calculated values. The final equation is:
Ti Tc Ti 0.0337 0.0218 lnCF 0.0098
Pi 3.7 103 N 3
(7)
The above correlation is valid for aspect ratio (AR) of 1.6 and vortex tube to diameter ratio (L/D) of 15. Table 3 Statistical tests for the correlated equation. No. Data
Multiple R
R2
Std. error
t-test for the equation coefficients in respective order *
90
0.87
0.75
0.00465
11.84, -12.27, 7.322, - 7.15
*
Values of t-test show significant 97% confidence in all calculated coefficients of the equation.
4. Results and Discussion The effects of nozzle numbers, N = 2, 3, and 6, on the performance of vortex tube are thoroughly investigated. They have included the cold temperature difference, coefficient of performance for cooling and comparison of the present data with other published data also conducted. The experiments have been performed under different operating and design conditions which included inlet air pressure varying from 2 to 6 bar, aspect ratio, AR = 1.6 lengths of hot tube to diameter ratio, L/D = 15. 4.1 Comparison with other published data The results of ninety point test are presented in comparison with other published data by Rafiee et al [33] , Hilsch [5] and Stephan et al [34] in a form of Tc Ti Tmax against cold fraction CF, and inlet pressure of 6 bar as in the Fig.6 This comparison shows that the variation of similar relation in this work is nearly in similar trend to other researches. It has been observed that the value of Tc Ti Tmax decreases gradually with the increase in cold mass fraction in the range of 0.25-0.5 especially for Hilsch [5]. With more increase in cold mass fraction, the value of temperature difference ratio rapidly decreases. The geometrical parameters of the vortex tube in their experimental studies are illustrated in Table 4.
Table 4 Geometrical characteristics of vortex tubes Parameters
Authors Present
Hilsch [5]
Work Length of tube, L [mm]
Rafiee et
Stephan
al. [33]
et al. [34]
112.5
300
250
352
7.5
9.2
18
17.6
5
2.6
9
6.5
2,3,6
1
2,3,4,6
1
6
6
6
6
Aspect ratio, AR [-]
1.6
--
--
--
Shape of main tube
Straight
Straight
Curved
Straight
Diameter of vortex tube, D Diameter of cold tube, d [mm] Number of nozzle, N [-] Inlet Pressure, Pi [bar]
4.2 The effect on cold temperature difference Fig.7 (a, b, c) shows the effect of inlet pressure on cold temperature (∆Tc = Ti –Tc) at conditions of vortex tube to diameter ratio is, L/D, 15 and aspect ratio, AR, is 1.6, and nozzle number are 2, 3, and 6. In general, the cold temperature difference decreases with the increase of cold mass fraction. From Fig 7 (a, b, and c), it is clear that the inlet pressure has more effect on cold temperature difference. In case of N = 2, the temperature differences for inlet pressure of 2 bar, 3 bar, 4 bar, 5 bar, and 6 bar are 18.5 °C, 19.6 °C, 21.7 °C, 22.9 °C and 22.9 °C respectively as shown in Fig. 7a. In other words, the temperature differences increases with increasing of inlet pressure. But the rate of change decreases with increasing cold mass fraction increases. This situation can be explained by the chocking of the flow [1]. When the inlet pressure is increased, flow velocity outside of the inlet nozzle increases. After the chocking takes place, velocity and mass flow rate outside of the inlet nozzle don’t increase anymore, even though inlet pressure increases [13, 35]. This result is compatible with those results from Eiams and Promvonge [1, 13] and Eiams et at. [6, 18]. Also the maximum value of cold temperature difference takes place at nozzle number is 3 for all inlet pressure as shown in Fig. 7b. Furthermore, it is noted that from Fig. 7c, the value of temperature at 6 bar sharply decreases more than other pressures beginning from cold mass fraction at 0.65. This may be due to the tangential high velocity, so the higher momentum transfer for hot fluid, resulting in a worse energy temperature separation and thus, cold air temperature difference sharply decreases [ 26]. This phenomenon could be due to strong swirling flow which is caused by accelerated flow and increased flow rate when cold mass
fraction is more than 0.65 [35, 26]. This strong swirling flow causes high friction dissipation with the lowest turbulent between the flow layers and it causes an increase in flow temperature. At this time, hot and cold flows are mixed and cold temperature difference will be reduced sharply [26, 36]. In present study we have assumed that vortex tube is used as a refrigerator for a local or spot cooling at ambient temperature is 28 °C. Fig. 8 (a, and b) illustrates the effect of nozzle numbers on the cold temperature difference (∆Tc = Ti –Tc) at conditions of inlet air pressure varying from 2 to 6 bar with increments 1 bar, L/D = 15, aspect ratio, AR = 1.6, and cold mass fraction is ranging from 0.4 to 0.9. We see that as the number of nozzles increases, energy of cooling increases, while cold outlet temperature decreases moderately. In the vortex tube with three nozzles, the cold temperature increases by 8.8% and 16% relative vortex tube with two and six nozzles respectively. Chang et al. [36 - 37] tested experimentally the effect of nozzle number on energy separation for (N = 3, 4, and 6) and showed that the cold temperature differences corresponding to N = 6 is maximum, and at number of nozzle reduced to 3 the value ∆Tc is minimum at cold mass fraction less than 0.3 (CF < 0.3). But, as the value of cold mass frication is increases to 0.4 (CF ≥ 0.4) the relation reverses. This result is compatible with presented experimental results, where the cold mass frication started from 0.4. On the contrary, increasing nozzle number (N > 3 ) cause the decrease in the cold temperature difference. Also, this result may be due to that behind N = 3, the flow at nozzle level becoming more turbulent causing the hot and cold flows mix together in turn of enhancing the cold temperature difference [36, 38]. But in the case of nozzle, N = 6, increase in the number of nozzles may cause an increase in the outlet temperature of cold air side temperature. These results are related to the energy of the working fluid. There is probably a critical energy for vortex tube using three nozzles. The higher kinetic energy means higher velocity at the same time [8]. In case of three nozzle vortex tube, the generator flow increases the efficiency because of reducing energy loss [8, 26]. The comparison of experimental results with predictions by correlation equation No. (7) for inlet pressure of 6 bar is shown in Fig. 8a. It illustrates that the cold temperature difference is in a good agreement with experimental data, especially at nozzle number at N = 3 and 6 is 1 % and 2.7 % respectively. The maximum difference between the results predication by equation (7) and experimental data is 6.6 % at nozzle number of 2.
4.3 The effect on coefficient of performance for cooling Figure 9 (a, b, c) shows the effect of nozzle numbers on the coefficient of performance for cooling at conditions of inlet air pressure varying from 2 bar to 6 bar with an increment of 1 bar, L/D = 15 and aspect ratio is 1.6. In general, the values of coefficient of performance for cooling for the three number of nozzles, N =2, 3 and 6 increase with the decrease of cold mass fraction. Also, it can be seen that the COP increases as inlet pressure increases. The COP of the cold outlet does not increase with the same rate after the inlet pressure has a value greater than 4 bar (Pi > 4 bar) which indicates that the pressure have less impact on the COP and other parameters such as characteristics of nozzles start dominating the performance. The increase of energy separation with the increase of inlet pressure is expected since the main driving force for the energy separation is the vortex angular momentum [26, 37]. The relation between coefficient of performance of cooling versus cold mass fraction and cold outlet temperature is presented in equations (5) and (6). The mass fraction where maximum coefficient of performance for cooling reached for cold outlet is different from the mass fraction where coldest temperature is attained and this is expected since coefficient of performance depends on mass fraction and cold outlet temperature [34, 36]. Correspondingly, the interaction between temperature difference and mass flow rate is used to calculate the coefficient of performance which causes the optimum for temperature difference to be different from the one for the coefficient of performance. It is revealed that the higher values of coefficient of performance are for N = 3. Hence, the highest value of coefficient of performance for mass cold fraction is 0.4, L/D = 15 and inlet pressure 6 bar is equal to 0.21 as shown in Fig.9 (b). This is due to the fact that at the exit of nozzles, some free vortices are formed and such forced vortices decrease with the increase of the nozzle [38, 39]. The vortices play a major role in confining and mixing cold and hot flow inside the vortex tube and the reduction in the number of vortices causes less mixing of central cold flow with peripheral hot flow [12]. The effect of vortex tube nozzle number on coefficient of performance for cooling is shown in Fig. 10 (a, b). Apparently, the maximum value of coefficient of performance is found at the vortex nozzle number 3. This result may be due to the high pressure losses and the generated vortex is not sufficiently strong to support resilient energy separation at low number of inlet nozzles (N = 2) [35]. At high number of nozzles (N = 6) the nozzle outlet velocity gets smaller since more nozzles are available to vent the compressed air [36 - 37].
An increase in the nozzle number results in accelerated flow and an increase in flow rate and consequently it causes to create the strong swirling flow. But there are two noteworthy phenomenon, first, for the vortex tube with lower number of nozzle (N = 3) this strong swirling flow causes high friction dissipation with the lowest turbulent between the flow layers and it causes an increase in cold temperature [35, 36]. Second, for the vortex tube with a larger nozzle number (N = 6), the strong swirling flow (due to an increase in nozzle) also causes an increase in friction dissipation but with increased turbulence (large area in the vortex tube) [36], hot and cold flows are mixed and cold temperature difference will be reduced. Therefore, for present vortex geometry (L/D = 15, and AR = 1.6) it was found that the optimum number of nozzles is 3 nozzles vortex tube.
5. Conclusions A series of experiments has been performed to study the effect of variation of nozzle numbers on the performance of vortex tube which included: cold temperature difference, coefficient of performance for cooling and cooling capacity. An analytical study of the characteristics equation has been carried out to evaluate the best correlation of the ratio of cold temperature difference to the inlet temperature as a function of pressure, cold mass fraction and nozzle numbers. The following findings have been concluded from the experimental results: 1. The values of cold temperature difference are for N =3 and the height value equal to 25 C. 2. The values of coefficient of performance for N =3 and its height value is equal to 0.21. 3. The comparison between the present data with the other published data of the relation between the dimensionless cold temperature difference and cold mass fraction has been conducted and hence it showed a nearly similar trend to other researches.
References [1]
S. Eiams-ard, P. Promvonge. Review of Ranque-Hilsch effects in vortex tube, Renewable &
Sustainable Energy Review, Vol. 12, pp.1822- 842, 2008. [2]
Y. T. Wu Y. Ding, Y. B. Ji, C. F. Ma, and M. C. Ge. Modification and experimental research on
vortex tube, Int. J. of Refrigeration, Vol.20, pp.1042- 1049, 2007. [3]
G. J. Ranque. Experimental on expansion in a vortex with simultaneous exhaust of hot air and
cold air, J. Phy. Radium (Paris), Vol.4, pp. 112-114, Jun, 1933.
[4]
G. J. Ranque. Method and apparatus for obtaining from a fluid under pressure two outputs of
fluid at different temperature, US patent, 1:952, 281, 1934. [5]
R. Hilsch. The use of expansion of gases in a centrifugal field as a cooling process, Rev. Sci.
Instrum, 18-2:108- 13, 1947. [6]
S. Eiams-ard, K. Wongcharee, and P. Promvonge. Experimental investigation on energy
separation in a counter-flow Ranque-Hilsch vortex tube: Effect of cooling a hot tube, Int. J. Communications in Heat and Mass Transfer, Vol.37, pp.156-162, 2010. [7]
O. Aydın, and M. Baki. An experimental study on the design parameters of a counter-flow
vortex tube, Energy J., Vol.31, pp. 2763-2772, 2006. [8]
M. O. Hamdan, B. Alsayyed, and E. Elnajjar. Nozzle parameters affecting vortex tube energy
separation performance, 'Heat Mass Transfer J., Vol. 49, pp.533-541, 2013. [9]
M. Avci. The effect of nozzle aspect ratio and nozzle number on the performance of the Ranque-
Hilsch Vortex tube, Applied Thermal Engineering, Vol. 50, pp. 302-308, 2013. [10] W. Frohlingsdorf, and H. Unger. Numerical investigation of the compressible flow and energy separation in Ranque-Hilsch vortex tube, Int. J. of Heat and Mass Transfer, Vol. 42, pp.415-422, 1999. [11] U. Behera, PJ. Paul, K. Dinesh, S. Jacob. Numerical investigation on flow and temperature separation in Ranque-Hilsch vortex tube, Int. J. of Heat and Mass Transfer, Vol. 51, pp. 25-26, 60776089, 2008. [12] R. Shamsoddini, A. H. Nezhad. Numerical analysis of the effects of nozzle number on the flow and power of cooling of a vortex tube, Int. J. of Refrigeration, Vol. 33, pp.774-782, 2010. [13] S. Eiamsa-ard, P. Promvong, Numerical simulation of flow field and temperature separation in a vortex tube,' Int. communication in Heat and Mass Transfer, Vol. 35, no. 8, pp. 937-947, 2008. [14] T. Farouk, B. Farouk. Large eddy simulation of the flow field and temperature separation in the Ranque-Hilsch vortex tube, Int. J. of Heat and Mass Transfer, Vol. 50, pp. 4724-4735, 2007. [15] T. Farouk, B. Farouk, A. Gutsol. Simulation of gas species and temperature separation in the counter-flow Ranque-Hilsch vortex tube using large eddy simulation technique, Int. J. of Heat and Mass Transfer, Vol. 52, pp. 3320-3333, 2009. [16] K. Dincer, S. Tasdemir, S. Baskaya, B. Z. Uysal. Modeling of the effects of length to diameter ratio and nozzle number on the Performance of the counter-flow Ranque-Hilsch vortex tubes using artificial neural network, Applied Thermal Engineering, Vol. 28, pp. 2380-2390, 2008. [17] M. Bovand, M. S. Valipour, K. Dincer, A. Tamayol. “Numerical analysis of the curvature effects on Ranque–Hilsch vortex tube refrigerators”. Applied Thermal Engineering Vol. 65, pp. 176-183, 2014. [18] C. M. Bovand, M. S. Valipour, K. Dincer, S. Eiamsa-ard. “Application of Response
Surface Methodology to optimization of a standard Ranque–Hilsch vortex tube refrigerator.” Applied Thermal Engineering, Vol. 67, pp. 545-553, 2014. [19] M. Bovand, M. S. Valipour, S. Eiamsa-ard, A. Tamayol. “Numerical analysis for curved vortex tube optimization.” Int. Communication in Heat and Mass Transfer, Vol. 50, pp. 98107, 2014. [20] M. H. Saidi, M. S. Vaalipour. Experimental modeling of vortex tube refrigeration, Applied Thermal Engineering, Vol. 23, pp. 1971-1980, 2003. [21] A. M. Pinar, O. Uluer, V. V. Kırmacı. Statistical assessment of counter-flow vortex tube performance for different nozzle number, cold mass fraction, and inlet pressure via Taguchi method, Exp. Heat Transf., Vol. 22, pp. 271-282, 2009. [22] K. Dincer, S. Baskaya, B. Z. Uysal, I. Ucgul. Experimental investigation of the performance of a Ranque-Hilsch vortex tube with regard to a plug located at the hot tube, Int. J. of Refrigeration, Vol. 32, pp. 87-94, 2009. [23] M. S. Valipour, N. Niazi. Experimental modeling of curved Ranque-Hilsch vortex tube refrigeration, Int. J. of Refrigeration, Vol. 34, pp. 1109-1116, 2011. [24] Y. Xue, M. Arjomandi. The effect of vortex angle on the efficiency of the Ranque-Hilsch vortex tube, Experimental Thermal Fluid Sci., Vol. 33, pp. 54-57, 2008. [25] V. Kirmaci. Exergy analysis and performance of a counter flow Ranque-Hilsch vortex tube having various nozzle numbers at different inlet pressure of oxygen and air, Int. J. of Refrigeration, Vol.32, pp.1626-1633, 2009. [26] M. O. Hamdan, A. Alawar, E. Elnajjar, and W. Siddique. Experimental analysis on vortex tube energy separation performance, Heat Mass Transfer J., Vol. 47, pp. 1637-1642, 2011. [27] P. K. Singh. An experimental performance evaluation of vortex tube, IE (I) J-MC, Vol.84, pp.149-153, 2004. [28] C. M. Gao, K. J. Bosschaart, J. C. H. Zeegers, and A. T. A. M. Waele. Experimental study on a simple Ranque- Hilsch vortex tube, Gryogenics, Vol. 45, pp. 173-183, 2005. [29] A. Nouri-Borujerdi, M. Bovand, S. Rashidi, K Dincer. “Geometric parameters and response surface methodology on cooling performance of vortex tubes”. Int. Journal of Sustainable Energy, pp.1-15, 2016. [30] P. Promvonge and S. Eiamsa-ard. Investigation on the Vortex Thermal Separation in a Vortex Tube Refrigerator, Science Asia Journal, Vol. 31, pp. 215–223, 2005. [31] M. Attalla, M. Salem, A. Abo EL-Wafa. An experimental investigation of the optimum geometry for energy separation of the Ranque-Hilsch vortex tube, Int. Journal of Mechanic & Mechatronrics Engineering, Vol. 14, pp. 31-37, 2014.
[32] M. Attalla, M. Salem. Experimental investigation of heat transfer for a jet impinging obliquely on a flat surface, Exp. Heat Transf. J. Vol. 28, pp. 378-391, 2015. [33] S. E. Rafiee, S. Ayenehpour, and M. M. Sadeghiazad. A study on the optimization of the angle of curvature for a Ranque–Hilsch vortex tube, using both experimental and full Reynolds stress turbulence numerical modeling, Heat Mass Transfer, DOI 10.1007/s00231-015-1562-y, 2015. [34] K. Stephan, S. Lin, M. Durst, F. Seher, D, Huang. An investigation of energy separation in a vortex tube, Int. J. Heat Mass Transf, Vol. 26, pp. 341–348, 1993. [35] R. Liew, J. C. H. Zeegers, J. G. M. Kuerten, and W. R. Michalek. Maxwell’s Demon in the Ranque-Hilsch Vortex Tube, Physical Review Letters, Vol. 109, 05450-1:4, 2012. [36] K. Chang, Q. Li, G. Zhou, Q. Li. Experimental investigation of vortex tube refrigerator with a divergent hot tube, International Journal of Refrigeration, Vol. 34, pp. 322-327, 2011. [37] S. Mohammadi and F. Farhdi. Experimental analysis of a Ranque–Hilsch vortex tube for optimizing nozzle numbers and diameter, Applied Thermal Engineering, Vol. 61, pp. 500-506, 2013. [38] S. U. Nimbalkar, M. R. Muller. An experimental investigation of the optimum geometry for the cold end orifice of a vortex tube, Applied Thermal Engineering, Vol. 29, pp. 509-514, 2009. [39] O. Aydin, B. Markal, and M. Avci. A new geometry for a counter-flow Ranque-Hilsch vortex tube, Applied Thermal Engineering, Vol. 30, pp. 2505-2511, 2010.
Fig. 1 A schematic diagram of the Counter Ranque-Hilck vortex tube, [2]
5 6
4 3 2
5 6
7
5
1
6
Fig. 2 Schematic diagram of the CVT system 1. Air Compressor 2. Filter Separator 3. Pressure Regulator Valve with Gauge 4. Pressure Vessel 5. Pressure Transmitter 6. Digital Flow Meter and Temperature 7. Counter Vortex Tube (CVT)
Fig. 3 Photo of the experimental set-up
Fig. 4 Generators with 2, 3, and 6 nozzles
Fig. 5 The deviation between the experiments values and the calculated values
1.2 Pi = 6 bar
(Ti-Tc)/∆Tmax [-]
1 0.8 0.6 Present Work
0.4
Hilsch [5] Rafiee et al. [33]
0.2
Stephan et al. [34]
0 0
0.2
0.4
0.6
0.8
1
CF [-]
Fig. 6 A comparison of the dimensionless cold temperature difference against CF with other published data
24 Pi = 6 bar
N=2
P = 5 bar P = 4 bar
Ti-Tc [◦C]
21
P = 3 bar P = 2 bar
18
15
12 0.35
0.45
0.55
0.65 CF [-] (a)
0.75
0.85
0.95
27 Pi = 6 bar P = 5 bar P = 4 bar P = 3 bar P = 2 bar
N=3
Ti-Tc [◦C]
24
21
18
15 0.35
0.45
0.55
0.65
0.75
0.85
0.95
CF [-] (b)
24 Pi = 6 bar
N=6
P = 5 bar P = 4 bar
Ti-Tc [◦C]
21
P = 3 bar P = 2 bar
18
15
12 0.35
0.45
0.55
0.65
0.75
0.85
0.95
CF [-] (c) Fig. 7(a, b, c) Variation of total temperature difference with nozzle numbers at conditions of L/D = 15 and AR = 1.6
27 CF = 0.4
Ti-Tc [◦C]
24
Equation 7 at 6 bar
21 18
Pi = 6 bar P = 5 bar P = 4 bar P = 3 bar P = 2 bar
15 12 1
2
3
4
5
6
7
N [-] (a)
21 CF = 0.9
◦
Ti-Tc [ C]
18
15
12 Pi = 6 bar
P = 5 bar
P = 4 bar
P = 3 bar
P = 2 bar
9 1
2
3
4
5
6
7
N [-] (b) Fig. 8 (a, b) Effect of number of nozzle on cold temperature difference at CF = 0.4, and CF = 0.9
0.25 Pi = 6 bar
N=2
P = 5 bar
0.2
P = 4 bar
COP [-]
P = 3 bar
0.15
P = 2 bar
0.1 0.05 0 0.35
0.45
0.55
0.65
0.75
0.85
0.95
CF [-] (a)
0.25 Pi = 6 bar
N=3
P = 5 bar
0.2
P = 4 bar
COP [-]
P = 3 bar
0.15
P = 2 bar
0.1 0.05 0 0.35
0.45
0.55
0.65 CF [-] (b)
0.75
0.85
0.95
0.25 Pi = 6 bar
N=6
P = 5 bar
0.2
P = 4 bar
COP [-]
P = 3 bar
0.15
P = 2 bar
0.1 0.05 0 0.35
0.45
0.55
0.65
0.75
0.85
0.95
CF [-] (c) Fig. 9 (a, b, c) Variation of COPREF with number of nozzles, L/D = 15 and AR = 1.6
0.25 CF = 0.4
COP [-]
0.2 0.15 0.1 0.05
Pi = 6 bar
P = 5 bar
P = 4 bar
P = 3 bar
P = 2 bar
0 1
2
3
4 N [-] (a)
5
6
7
0.04 CF = 0.9
COP [-]
0.03
0.02
0.01 Pi = 6 bar
P = 5 bar
P = 4 bar
P = 3 bar
P = 2 bar
0 1
2
3
4
5
6
N [-] (b) Fig. 10 (a, b) Effect of number of nozzle on COP at CF = 0.4, and CF = 0.9
7
Highlights:
- The effect of nozzle number of RHVT have been investigated. - The correlation equation has been carried out as function of nozzle number. - The comparison between present data with other published data has been conducted. - It is observed that the best number of nozzle is three nozzle.
S0894-1777(16)30350-8 http://dx.doi.org/10.1016/j.expthermflusci.2016.11.034 ETF 8956
To appear in:
Experimental Thermal and Fluid Science
Received Date: Revised Date: Accepted Date:
14 June 2016 7 August 2016 27 November 2016
Please cite this article as: H. Ahmed, M. Salem Ahmed, M. Attalla, A. Abo El –Wafa, An Experimental Study of Nozzle Number on Ranque Hilsch Counter-Flow Vortex Tube, Experimental Thermal and Fluid Science (2016), doi: http://dx.doi.org/10.1016/j.expthermflusci.2016.11.034
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An Experimental Study of Nozzle Number on Ranque Hilsch Counter-Flow Vortex Tube Hany Ahmed1,2, M. Salem Ahmed3, M. Attalla4*, A. Abo El –Wafa5 1 Mechanical Department, Faculty of Eng., Asuit University, Asuit, Egypt 2 Mechanical Department, College of Eng., Taif University, Taif, 888, Saudi Arabia 3 Mechanical Department, Faculty of Industrial Education, Sohag University, Sohag, Egypt 4 Department of Mechanical Engineering, Faculty of Engineering, South Valley University, Qena 83521, Egypt 5 Qarun Petroleum Company, Egypt * Corresponding Author, e-mail: [email protected]
Abstract The present study investigates the effects of the orifice nozzle number and the inlet pressure experimentally on the cooling performance of the counter flow type vortex tube. The energy generation has been conducted using a generator of type stream–tek generator model GNMD-KIT with the number of nozzles (2, 3, and 6), and aspect ratio 1.6 and, an inner diameter of 7.5 mm. In the experiments, for each of the orifices, inlet pressures have been adjusted from 200 kPa to 600 kPa. The energy separation to be investigated here focuses on the cold temperature difference and coefficient of performance for cooling. The experimental results concluded in this paper proved that the higher effect of nozzle number is for nozzle number three and hence that nozzle number could affect the energy separation efficiently. A comparison of the present experiments with other published works has been conducted. An analytical study of the characteristics equation has been carried out to evaluate the best correlation of the ratio of cold temperature difference to the inlet temperature as a function of pressure, cold mass fraction and nozzle numbers. The goodness of fit of the regression model is inspected using the analysis of variance and t-test. The values of R2 are adjusted close to 97 % which show a very good agreement between the experimental and predicted values. Key words: Ranque Hilsch, Vortex tube, Nozzle number, counter flow, energy separation Nomenclature AR
Aspect ratio, [-]
B
Width of nozzle, [m]
CF
Cold mass fraction, [-]
COP
Coefficient of performance [-]
Cp
Specific heat [kJ/kg. K]
D
Inner diameter of vortex tube, [m]
d
Diameter of cold tube, [m]
L
Length of the tube, [m]
m
Mass flow rate, [kg/s]
N
Number of nozzle, [-]
P
Pressure, [Pa]
T
Temperature, [K]
R
Universal gas constant, [8.314472 J/K. Mol]
W
Height of nozzle, [m]
Subscript atm
Atmosphere
c
Cold
h
Hot
i
Inlet
Acronyms CVT
Counter vortex tube
RHVT
Ranque-Hilsh vortex tube
VT
Vortex tube
Introduction: The vortex tube is a simple device operating as a refrigeration machine without any moving part e.g. rotating shaft or piston cylinder [1]. It consists of a nozzle, a vortex hall, a separating cold plate, a hot valve, and a hot and cold end tube as shown in Fig.1 [2]. The vortex tube was first discovered by Ranque [3, 4], who was granted a French patent for the device in 1932 and a United States patent in 1934. In 1945, Rudolf Hilsch [5] conducted an experiment on vortex tube that focused on the thermal performance with different geometrical parameters. The vortex tube or RHVT can be classified into two types: counter-flow RHVT
and uni-flow RHVT [6]. In the counter-flow vortex tube type, the cold flow move is in the opposite direction with respect to the hot stream, while in the uni-flow type, the hot and cold stream flow is in the same direction. In general, the counter flow RHVT has been recommended more than the uni-flow RHVT for its efficient energy separation. The RHVT is widely used for cooling and heating applications. The major application is conducted for cooling purposes, e.g. cooling the electric device, cooling machinery during operation. In spite of its small capacity, the vortex tube is very useful for certain applications because it is simple, compact, light, and it requires no refrigerant [7]. In the recent years, it has been known that vortex tube is a low cost and an effective solution for many spot cooling problems. The separation mechanism inside the vortex tube remains until today not completely undisclosed [8 - 9]. Up to date, more than hundred investigations on the energy separation in the RHVT for both numerical and experimental study. Numerous investigators have conducted on the energy separation in the RHVT by using turbulence modeling. Frohlingsdorf and Unger [10] used the computational code based on CFX along with k-ε model to investigate the energy separation inside the vortex tube. Behera et al. [11] used the CFD code (Star-CD) to investigate the temperature separation in vortex tube. In their study, the effect of the secondary circulation and length of the hot tube on energy separation have been also calculated. Shamsoddini and Nezhad [12] studied the effect of the nozzle number on the flow and power of cooling process of a vortex tube using a three-dimensional numerical fluid flow dynamic model. Eiamsa-ard and Promvonge [13] studied the energy separation numerically in a uni-flow vortex tube using kappa-epsilon model. They concluded that the maximum temperature gradients appear in the outer regions close to the tube wall and the separation effect in the core region near the inlet nozzle. Farouk and Farouk [14] used large eddy simulation method to predict the flow and temperature field in the vortex tube. Farouk et al. [15] computed the temperature and flow field of the species mass fraction in counter-flow vortex tube with nitrogen and helium as a working fluid. The artificial neural networks and employing the experimental data were used to predict the effect of length to diameter ratio and nozzle number on performance of counter-flow RHVT by Dincer et al. [16]. At the same time with the numerical works, many experimental investigations have been performed to study the performance of the vortex tube. Here are some of the experimental works on temperature separation in the vortex tube explained as follows:
Bovand et al. [17] have investigated the effect of curvature numerically on the performance of vortex tubes. They studied curvature angles of 0 and 110°. The results showed that the efficiency of straight vortex tube is higher than the curved vortex tube with angle of 110°. They indicated that CFD model could be successfully used for the determination of heating and cooling performances of curvature effects on Ranque-Hilsch vortex tube. Bovand et al. [18] studied the effect of certain geometrical parameters on cooling performance of RanqueHilsch vortex tube. They used an experimental setup having two levels and a central composite face design. They analyzed the results according to the principle of Response Surface Methodology (RSM). They found that the optimum value of the number of nozzles was 2, cold orifice diameter 9.48 mm and inlet pressure 3.2 bar. Bovand et al. [19] conducted a CFD analytically to determine the effect of vortex tube curvature on their performance. They found that the curvature of vortex tube caused a decrease in the swirl velocity and the diffusion process in vortex tube. Results showed that the straight and 150° curved vortex tube had a higher performance as a refrigerator than other curvature angles. Saidi and Valipour [20] have investigated the influence of the RHVT diameter and hot tube length, number of nozzle on the cold temperature difference in a counter-flow vortex tube. They observed that the maximum cold air temperature difference was found at tube length to vortex diameter ratio ranged from 20 to 55.5, and cold orifice diameter ratio, β = 0.5. Pinar et al. [21] have investigated the effect and optimization of process parameters in a counter flow vortex tube on temperature difference through the Taguchi method. It has been observed that the optimum setting of process parameters maximizing the temperature difference is an inlet pressure of 650 kPa, a nozzle number of 2, and a cold mass fraction of 0.7. Dincer et al. [22] have studied the effects of control valve geometry, plug location and the number of nozzles on energy separation under different inlet pressures. Valipour and Niazi [23] have investigated the effects of axial curvature and turning angle of main tube on the efficiency of vortex tube under different inlet pressure. Wu et al. [2] have presented the effect of the conventional nozzle, the proposed nozzle and the nozzle of Archimedes on the energy separation of vortex tube. Their results concluded that the enhanced nozzle provided a better cooling performance with temperature of cold gas of about 2.2 ˚C and 5 ˚C lower than those presented by the nozzle with a normal rectangle and with Archimedes coil, respectively. The effect of generator vortex angle of rotating flow on the performance of the RHVT has been studied by Xue and Arjomandi [24]. They showed that the maximum cooling efficiency obtained was between the vortex generator angles of 4.8 and 6.7˚. Kirmaci [25] has
investigated the effects of the nozzle numbers and inlet pressures on the energy separation of vortex tube using air and oxygen as working fluids. He observed that the temperature rise between hot and cold fluid reduces with increasing nozzle number. Besides, the cold temperature reductions for using both two working fluids (air and oxygen) increase with the increase of the inlet pressure. The experimental work of Hamdan et al. [8, 26] reported the effect of nozzle parameters on the energy separation of the vortex tube. Their results indicated that the maximum energy separation is achieved with tangential nozzle orientation while the symmetry/asymmetry of nozzles has a minimal effect on the performance of the energy separation. Singh et al. [27] reported the effect of different parameters such as the nozzle number, hot end area and mass fractions on the performance of RHVT. They showed that the effect of the nozzle geometry was more important than the cold orifice design in getting high temperature separations. Gao et al. [28] used a special pitot tube and thermocouple techniques to measure the pressure, velocity and temperature distribution inside the vortex tube which the pitot tube has only a diameter of 1 mm with one hole. They observed that rounding off the entrance can be improved and extend to the secondary circulation gas flow and enhance the system performance. Aydin and Baki [7] have studied the temperature separation experimentally in a counter-flow vortex tube with various geometrical and thermo-physic parameters. In their work, the geometry of tube was optimized to the maximum of the temperature difference between the inlet and cold temperatures by changing the various dimensions of the tube such as the diameter of the inlet nozzle and the angle of the control valve. Nouri-Borujerdi et al. [29] studied the effect of certain geometrical parameters experimentally on cooling performance of Ranque-Hilsch vortex tube. Their findings showed that when the N increased, the vortex tube with a larger L/D was better than vortex tube with lower L/D. The above-cited review of literature clearly indicates that the energy separation and the efficiency of a vortex tube are significantly affected by the various geometrical parameters. Despite a lot of studies have been carried out in RHVT, the effect of nozzle number on energy separation is still open to doubt. There is a disagreement over the effect of nozzle number on the performance of vortex tube. Some of the studies suggested that decreasing nozzle number improves temperature separation [20]; others proposed that the performance increases with increasing nozzle number [11, 30]. This study is conducted to investigate the ways to provide some new insights into the energy separation of the vortex tube under different operating parameters. It is rarely in all vortex tube studies to examine the effect of a
number of nozzles on the total temperature difference and the coefficient of performance in cooling. Therefore, in the present study, we have examined the effect of the number of nozzles on the performance of vortex tube with special vortex geometry of aspect ratio (AR), of 1.6 and hot vortex tube to diameter ratio (L/D), of 15 on the total cold temperature difference and the coefficient of performance in cooling. Also, this study has been carried out experimentally at inlet pressure varied from 2 to 6 bar and cold mass frication varied from 0.4 to 0.9. The additional aim of this study is to develop an empirical equation for cold temperature difference as a function of number of nozzles (N), inlet pressure (Pi) and cold mass frication (CF). Hence, the effect of using different nozzle numbers on the performance of vortex tube is investigated to obtain the optimum nozzle number. 2. Experimental Work 2.1 Experimental set-up The counter- flow vortex tube (CVT) and the arrangement of the experimental system are shown in Fig.2. The experimental set-up shows the locations of vital instruments used for measuring pressures, temperatures and flow rates. The compressed air is supplied from the compressor through a calibrated orifice meter. An air filter and a pressure regulator are installed upstream of the orifice flow meter to filter the air and maintain the downstream pressure at 8 bar. The compressed air reaches the vortex tube after passing through a dehumidifier device and filter. Filter separator follows the pressure vessel to separate the water droplet incoming from the pressure vessel. Then the cold air stream leaves the tube through the central of the vortex generator (cold exit), while the hot air stream at the periphery exhausts out of the other exit (hot exit). The mass flow rate of the inlet air and cold air discharge are measured by ultrasonic flow (Model: STRANS FUG1010-Simens Co., Germany). The cold mass fraction (CF) is attended by the cone-shaped valve placed on the hot outlet of the main tube. The cold air temperature is measured at the exit of the cold air tube while the hot air temperature was measured. All the data for temperature are measured by using RTD (RTD – Model: TX251). The inlet pressure and pressure through the cold stream is measured using pressure transducer (Danfoss – Model: AkS-33). All measured data are collected by Data acquisition incorporated with the counter vortex tube system. Table 1 summarizes the specifications of all devices.
A hot tube L =112.5 mm with inner diameter of vortex tube, D equal to 7.5 mm, (L/D = 15) and constant area of nozzles entrance of aspect ratio, AR = 1.6 have been used in this study and can be defined by the following equation:
AR W B
(1)
where B and W are nozzle width and height respectively. Fig.3 shows a photo of the CVT system. A stream –tek generators kit model GNMD-KIT of three nozzles, N = 2, 3, and 6 have been conducted. Fig. 4 shows a stream –tek generator of model GNMD-KIT of numbers, N = 2, 3, and 6 . The experimental tests had been performed several times to have reached a steady state when reading of temperature and pressure does not change any more. In order to determine the reliability of the experimental results, an uncertainty analysis has been conducted on all measured quantities [31, 32]. Performing the error analysis, the maximum uncertainties in determining these parameters are given in Table 2. The maximum uncertainties of dimensionless parameters were ± 3.56 % for temperature, ± 5.78% for mass flow rates and 2.78% for inlet pressure. Table 1 Measurement Devises Specifications Devise Air Compressor
Air Filter
Air Pressure Regulator
Pressure Transmitter
Temperature Measured
Specifications/Accuracy Model: KS-150, Capacity: 1.5 m3/min Motor Power: 7.5/10 kW/Hp Maximum Working Pressure: 8 bar Model: SDPC:DC600-06 Operating Pressure: 1 – 8.5 bar Maximum Flow Rate: 11500 L/min Ambient Temperature: -10 C – 60 C Filter Precision: 20 μm Model: AR 3000-03 Ambient Temperature: -5 C – 60 C Pressure Regulation Range: 0.5 – 8.5 bar Accuracy: ± 0.1 % Model: Danfos: AKS-33 Pressure Range 1- 20 bar Operating Temperature: 0 C – 80 C Accuracy: Up To 0.1 % Model: RTD-Tx-251 Temperature Range: -100 C – 1350 C Operating Temperature: -20 C – 70 C
Air Flow Rate
Operating Humidity: 5 to 95 % RH Accuracy: Better Than 0.1 % Model: STRANS FUG1010 Operating Temperature: -18 C – 60 C Flow Temperature: -28 C – 93 C
Table 2 Measured parameters and their accompanied errors parameters Pressure, [Pa] Temperature, [K] Mass flow rate, [kg/s] Length of tube, [mm] Diameter of tube, [mm] Diameter of vortex tube, [mm] COP
Maximum errors % 0.105 0.86 2.07 0.113 0.175 0.154 0.134
2.2 Work procedure High pressure air from the compressor is directed tangentially into the vortex tube. The high pressure gas expands in the vortex tube and separates into the cold and hot streams. The cold gas leaves the central orifice near the entrance nozzle while the hot gas discharges the periphery at the far end of the tube. The control valve is being used to control the flow rate of the hot stream. Before starting the experimental tests, the throttling valve is set in fully open. Then the air tank works and by use of the valve that is applied on the vortex tube inlet position. This would help to regulate cold mass fraction. During this procedure, the mass flow rates of air at cold and hot exit are determined by using the ultrasonic flow meter. During the experiments, measurements are performed including pressure, temperature and flow rates at the inlet of vortex tube and the exit of hot tube. 2.3 Data reduction The cold temperature difference, (Ti – Tc) represents an important parameter for the performance of the CVT in the energy separation. where Ti = inlet air temperature, K Tc = cold air temperature (exit from cold tube side), K Cold mass fraction, CF, represents the parameter which governs the temperature separation and is expressed by:
c m CF m
(2)
Where m c is mass flow rate of cold air. Kg/s where m is mass flow rate of total air. Kg/s
m c m h m
(3)
and m h is mass flow rate of hot air. Kg/s Vortex tube can be used in cooling and heating processes; in the case of Vortex tube for cooling process it is called refrigerator vortex tube. The performance of cooling vortex tube is measured using the followings equations: for the refrigerator is defined as follow [8]:
COP
Cooling Load Isothermal Compression Energy
(4)
COP
m cC p Ti Tc RTi ln Pi Patm m
(5)
C p 1 Tc Ti COP CF R ln Pi Patm
(6)
Where : Cp = specific heat , kJ/kg K Pi = inlet pressure , bar Patm = 1 bar, atmospheric pressure Ti = inlet air temperature, K Tc = cold air temperature, K 3. Correlated Equation The analytical study of the characteristic equations (based on partial differentiation and equating to zero, or other conventional optimization gradient methods) for fruitful results is very difficult due to the interlaced effects of performance parameters on its characteristics. To overcome this difficulty and to meet the goal of locating an objective characteristics performance, some statistical random search techniques have been programmed to determine the best correlation equations (subjected to standard statistical tests as shown in Table 3
below). The results are least-square fitted into several trial correlation equations to reach the most acceptable representative equation with accepted standard statistical t-tests by using SPSS program version 13 [16]. Fig. 5 shows the deviation between the experiments values and the calculated values. The final equation is:
Ti Tc Ti 0.0337 0.0218 lnCF 0.0098
Pi 3.7 103 N 3
(7)
The above correlation is valid for aspect ratio (AR) of 1.6 and vortex tube to diameter ratio (L/D) of 15. Table 3 Statistical tests for the correlated equation. No. Data
Multiple R
R2
Std. error
t-test for the equation coefficients in respective order *
90
0.87
0.75
0.00465
11.84, -12.27, 7.322, - 7.15
*
Values of t-test show significant 97% confidence in all calculated coefficients of the equation.
4. Results and Discussion The effects of nozzle numbers, N = 2, 3, and 6, on the performance of vortex tube are thoroughly investigated. They have included the cold temperature difference, coefficient of performance for cooling and comparison of the present data with other published data also conducted. The experiments have been performed under different operating and design conditions which included inlet air pressure varying from 2 to 6 bar, aspect ratio, AR = 1.6 lengths of hot tube to diameter ratio, L/D = 15. 4.1 Comparison with other published data The results of ninety point test are presented in comparison with other published data by Rafiee et al [33] , Hilsch [5] and Stephan et al [34] in a form of Tc Ti Tmax against cold fraction CF, and inlet pressure of 6 bar as in the Fig.6 This comparison shows that the variation of similar relation in this work is nearly in similar trend to other researches. It has been observed that the value of Tc Ti Tmax decreases gradually with the increase in cold mass fraction in the range of 0.25-0.5 especially for Hilsch [5]. With more increase in cold mass fraction, the value of temperature difference ratio rapidly decreases. The geometrical parameters of the vortex tube in their experimental studies are illustrated in Table 4.
Table 4 Geometrical characteristics of vortex tubes Parameters
Authors Present
Hilsch [5]
Work Length of tube, L [mm]
Rafiee et
Stephan
al. [33]
et al. [34]
112.5
300
250
352
7.5
9.2
18
17.6
5
2.6
9
6.5
2,3,6
1
2,3,4,6
1
6
6
6
6
Aspect ratio, AR [-]
1.6
--
--
--
Shape of main tube
Straight
Straight
Curved
Straight
Diameter of vortex tube, D Diameter of cold tube, d [mm] Number of nozzle, N [-] Inlet Pressure, Pi [bar]
4.2 The effect on cold temperature difference Fig.7 (a, b, c) shows the effect of inlet pressure on cold temperature (∆Tc = Ti –Tc) at conditions of vortex tube to diameter ratio is, L/D, 15 and aspect ratio, AR, is 1.6, and nozzle number are 2, 3, and 6. In general, the cold temperature difference decreases with the increase of cold mass fraction. From Fig 7 (a, b, and c), it is clear that the inlet pressure has more effect on cold temperature difference. In case of N = 2, the temperature differences for inlet pressure of 2 bar, 3 bar, 4 bar, 5 bar, and 6 bar are 18.5 °C, 19.6 °C, 21.7 °C, 22.9 °C and 22.9 °C respectively as shown in Fig. 7a. In other words, the temperature differences increases with increasing of inlet pressure. But the rate of change decreases with increasing cold mass fraction increases. This situation can be explained by the chocking of the flow [1]. When the inlet pressure is increased, flow velocity outside of the inlet nozzle increases. After the chocking takes place, velocity and mass flow rate outside of the inlet nozzle don’t increase anymore, even though inlet pressure increases [13, 35]. This result is compatible with those results from Eiams and Promvonge [1, 13] and Eiams et at. [6, 18]. Also the maximum value of cold temperature difference takes place at nozzle number is 3 for all inlet pressure as shown in Fig. 7b. Furthermore, it is noted that from Fig. 7c, the value of temperature at 6 bar sharply decreases more than other pressures beginning from cold mass fraction at 0.65. This may be due to the tangential high velocity, so the higher momentum transfer for hot fluid, resulting in a worse energy temperature separation and thus, cold air temperature difference sharply decreases [ 26]. This phenomenon could be due to strong swirling flow which is caused by accelerated flow and increased flow rate when cold mass
fraction is more than 0.65 [35, 26]. This strong swirling flow causes high friction dissipation with the lowest turbulent between the flow layers and it causes an increase in flow temperature. At this time, hot and cold flows are mixed and cold temperature difference will be reduced sharply [26, 36]. In present study we have assumed that vortex tube is used as a refrigerator for a local or spot cooling at ambient temperature is 28 °C. Fig. 8 (a, and b) illustrates the effect of nozzle numbers on the cold temperature difference (∆Tc = Ti –Tc) at conditions of inlet air pressure varying from 2 to 6 bar with increments 1 bar, L/D = 15, aspect ratio, AR = 1.6, and cold mass fraction is ranging from 0.4 to 0.9. We see that as the number of nozzles increases, energy of cooling increases, while cold outlet temperature decreases moderately. In the vortex tube with three nozzles, the cold temperature increases by 8.8% and 16% relative vortex tube with two and six nozzles respectively. Chang et al. [36 - 37] tested experimentally the effect of nozzle number on energy separation for (N = 3, 4, and 6) and showed that the cold temperature differences corresponding to N = 6 is maximum, and at number of nozzle reduced to 3 the value ∆Tc is minimum at cold mass fraction less than 0.3 (CF < 0.3). But, as the value of cold mass frication is increases to 0.4 (CF ≥ 0.4) the relation reverses. This result is compatible with presented experimental results, where the cold mass frication started from 0.4. On the contrary, increasing nozzle number (N > 3 ) cause the decrease in the cold temperature difference. Also, this result may be due to that behind N = 3, the flow at nozzle level becoming more turbulent causing the hot and cold flows mix together in turn of enhancing the cold temperature difference [36, 38]. But in the case of nozzle, N = 6, increase in the number of nozzles may cause an increase in the outlet temperature of cold air side temperature. These results are related to the energy of the working fluid. There is probably a critical energy for vortex tube using three nozzles. The higher kinetic energy means higher velocity at the same time [8]. In case of three nozzle vortex tube, the generator flow increases the efficiency because of reducing energy loss [8, 26]. The comparison of experimental results with predictions by correlation equation No. (7) for inlet pressure of 6 bar is shown in Fig. 8a. It illustrates that the cold temperature difference is in a good agreement with experimental data, especially at nozzle number at N = 3 and 6 is 1 % and 2.7 % respectively. The maximum difference between the results predication by equation (7) and experimental data is 6.6 % at nozzle number of 2.
4.3 The effect on coefficient of performance for cooling Figure 9 (a, b, c) shows the effect of nozzle numbers on the coefficient of performance for cooling at conditions of inlet air pressure varying from 2 bar to 6 bar with an increment of 1 bar, L/D = 15 and aspect ratio is 1.6. In general, the values of coefficient of performance for cooling for the three number of nozzles, N =2, 3 and 6 increase with the decrease of cold mass fraction. Also, it can be seen that the COP increases as inlet pressure increases. The COP of the cold outlet does not increase with the same rate after the inlet pressure has a value greater than 4 bar (Pi > 4 bar) which indicates that the pressure have less impact on the COP and other parameters such as characteristics of nozzles start dominating the performance. The increase of energy separation with the increase of inlet pressure is expected since the main driving force for the energy separation is the vortex angular momentum [26, 37]. The relation between coefficient of performance of cooling versus cold mass fraction and cold outlet temperature is presented in equations (5) and (6). The mass fraction where maximum coefficient of performance for cooling reached for cold outlet is different from the mass fraction where coldest temperature is attained and this is expected since coefficient of performance depends on mass fraction and cold outlet temperature [34, 36]. Correspondingly, the interaction between temperature difference and mass flow rate is used to calculate the coefficient of performance which causes the optimum for temperature difference to be different from the one for the coefficient of performance. It is revealed that the higher values of coefficient of performance are for N = 3. Hence, the highest value of coefficient of performance for mass cold fraction is 0.4, L/D = 15 and inlet pressure 6 bar is equal to 0.21 as shown in Fig.9 (b). This is due to the fact that at the exit of nozzles, some free vortices are formed and such forced vortices decrease with the increase of the nozzle [38, 39]. The vortices play a major role in confining and mixing cold and hot flow inside the vortex tube and the reduction in the number of vortices causes less mixing of central cold flow with peripheral hot flow [12]. The effect of vortex tube nozzle number on coefficient of performance for cooling is shown in Fig. 10 (a, b). Apparently, the maximum value of coefficient of performance is found at the vortex nozzle number 3. This result may be due to the high pressure losses and the generated vortex is not sufficiently strong to support resilient energy separation at low number of inlet nozzles (N = 2) [35]. At high number of nozzles (N = 6) the nozzle outlet velocity gets smaller since more nozzles are available to vent the compressed air [36 - 37].
An increase in the nozzle number results in accelerated flow and an increase in flow rate and consequently it causes to create the strong swirling flow. But there are two noteworthy phenomenon, first, for the vortex tube with lower number of nozzle (N = 3) this strong swirling flow causes high friction dissipation with the lowest turbulent between the flow layers and it causes an increase in cold temperature [35, 36]. Second, for the vortex tube with a larger nozzle number (N = 6), the strong swirling flow (due to an increase in nozzle) also causes an increase in friction dissipation but with increased turbulence (large area in the vortex tube) [36], hot and cold flows are mixed and cold temperature difference will be reduced. Therefore, for present vortex geometry (L/D = 15, and AR = 1.6) it was found that the optimum number of nozzles is 3 nozzles vortex tube.
5. Conclusions A series of experiments has been performed to study the effect of variation of nozzle numbers on the performance of vortex tube which included: cold temperature difference, coefficient of performance for cooling and cooling capacity. An analytical study of the characteristics equation has been carried out to evaluate the best correlation of the ratio of cold temperature difference to the inlet temperature as a function of pressure, cold mass fraction and nozzle numbers. The following findings have been concluded from the experimental results: 1. The values of cold temperature difference are for N =3 and the height value equal to 25 C. 2. The values of coefficient of performance for N =3 and its height value is equal to 0.21. 3. The comparison between the present data with the other published data of the relation between the dimensionless cold temperature difference and cold mass fraction has been conducted and hence it showed a nearly similar trend to other researches.
References [1]
S. Eiams-ard, P. Promvonge. Review of Ranque-Hilsch effects in vortex tube, Renewable &
Sustainable Energy Review, Vol. 12, pp.1822- 842, 2008. [2]
Y. T. Wu Y. Ding, Y. B. Ji, C. F. Ma, and M. C. Ge. Modification and experimental research on
vortex tube, Int. J. of Refrigeration, Vol.20, pp.1042- 1049, 2007. [3]
G. J. Ranque. Experimental on expansion in a vortex with simultaneous exhaust of hot air and
cold air, J. Phy. Radium (Paris), Vol.4, pp. 112-114, Jun, 1933.
[4]
G. J. Ranque. Method and apparatus for obtaining from a fluid under pressure two outputs of
fluid at different temperature, US patent, 1:952, 281, 1934. [5]
R. Hilsch. The use of expansion of gases in a centrifugal field as a cooling process, Rev. Sci.
Instrum, 18-2:108- 13, 1947. [6]
S. Eiams-ard, K. Wongcharee, and P. Promvonge. Experimental investigation on energy
separation in a counter-flow Ranque-Hilsch vortex tube: Effect of cooling a hot tube, Int. J. Communications in Heat and Mass Transfer, Vol.37, pp.156-162, 2010. [7]
O. Aydın, and M. Baki. An experimental study on the design parameters of a counter-flow
vortex tube, Energy J., Vol.31, pp. 2763-2772, 2006. [8]
M. O. Hamdan, B. Alsayyed, and E. Elnajjar. Nozzle parameters affecting vortex tube energy
separation performance, 'Heat Mass Transfer J., Vol. 49, pp.533-541, 2013. [9]
M. Avci. The effect of nozzle aspect ratio and nozzle number on the performance of the Ranque-
Hilsch Vortex tube, Applied Thermal Engineering, Vol. 50, pp. 302-308, 2013. [10] W. Frohlingsdorf, and H. Unger. Numerical investigation of the compressible flow and energy separation in Ranque-Hilsch vortex tube, Int. J. of Heat and Mass Transfer, Vol. 42, pp.415-422, 1999. [11] U. Behera, PJ. Paul, K. Dinesh, S. Jacob. Numerical investigation on flow and temperature separation in Ranque-Hilsch vortex tube, Int. J. of Heat and Mass Transfer, Vol. 51, pp. 25-26, 60776089, 2008. [12] R. Shamsoddini, A. H. Nezhad. Numerical analysis of the effects of nozzle number on the flow and power of cooling of a vortex tube, Int. J. of Refrigeration, Vol. 33, pp.774-782, 2010. [13] S. Eiamsa-ard, P. Promvong, Numerical simulation of flow field and temperature separation in a vortex tube,' Int. communication in Heat and Mass Transfer, Vol. 35, no. 8, pp. 937-947, 2008. [14] T. Farouk, B. Farouk. Large eddy simulation of the flow field and temperature separation in the Ranque-Hilsch vortex tube, Int. J. of Heat and Mass Transfer, Vol. 50, pp. 4724-4735, 2007. [15] T. Farouk, B. Farouk, A. Gutsol. Simulation of gas species and temperature separation in the counter-flow Ranque-Hilsch vortex tube using large eddy simulation technique, Int. J. of Heat and Mass Transfer, Vol. 52, pp. 3320-3333, 2009. [16] K. Dincer, S. Tasdemir, S. Baskaya, B. Z. Uysal. Modeling of the effects of length to diameter ratio and nozzle number on the Performance of the counter-flow Ranque-Hilsch vortex tubes using artificial neural network, Applied Thermal Engineering, Vol. 28, pp. 2380-2390, 2008. [17] M. Bovand, M. S. Valipour, K. Dincer, A. Tamayol. “Numerical analysis of the curvature effects on Ranque–Hilsch vortex tube refrigerators”. Applied Thermal Engineering Vol. 65, pp. 176-183, 2014. [18] C. M. Bovand, M. S. Valipour, K. Dincer, S. Eiamsa-ard. “Application of Response
Surface Methodology to optimization of a standard Ranque–Hilsch vortex tube refrigerator.” Applied Thermal Engineering, Vol. 67, pp. 545-553, 2014. [19] M. Bovand, M. S. Valipour, S. Eiamsa-ard, A. Tamayol. “Numerical analysis for curved vortex tube optimization.” Int. Communication in Heat and Mass Transfer, Vol. 50, pp. 98107, 2014. [20] M. H. Saidi, M. S. Vaalipour. Experimental modeling of vortex tube refrigeration, Applied Thermal Engineering, Vol. 23, pp. 1971-1980, 2003. [21] A. M. Pinar, O. Uluer, V. V. Kırmacı. Statistical assessment of counter-flow vortex tube performance for different nozzle number, cold mass fraction, and inlet pressure via Taguchi method, Exp. Heat Transf., Vol. 22, pp. 271-282, 2009. [22] K. Dincer, S. Baskaya, B. Z. Uysal, I. Ucgul. Experimental investigation of the performance of a Ranque-Hilsch vortex tube with regard to a plug located at the hot tube, Int. J. of Refrigeration, Vol. 32, pp. 87-94, 2009. [23] M. S. Valipour, N. Niazi. Experimental modeling of curved Ranque-Hilsch vortex tube refrigeration, Int. J. of Refrigeration, Vol. 34, pp. 1109-1116, 2011. [24] Y. Xue, M. Arjomandi. The effect of vortex angle on the efficiency of the Ranque-Hilsch vortex tube, Experimental Thermal Fluid Sci., Vol. 33, pp. 54-57, 2008. [25] V. Kirmaci. Exergy analysis and performance of a counter flow Ranque-Hilsch vortex tube having various nozzle numbers at different inlet pressure of oxygen and air, Int. J. of Refrigeration, Vol.32, pp.1626-1633, 2009. [26] M. O. Hamdan, A. Alawar, E. Elnajjar, and W. Siddique. Experimental analysis on vortex tube energy separation performance, Heat Mass Transfer J., Vol. 47, pp. 1637-1642, 2011. [27] P. K. Singh. An experimental performance evaluation of vortex tube, IE (I) J-MC, Vol.84, pp.149-153, 2004. [28] C. M. Gao, K. J. Bosschaart, J. C. H. Zeegers, and A. T. A. M. Waele. Experimental study on a simple Ranque- Hilsch vortex tube, Gryogenics, Vol. 45, pp. 173-183, 2005. [29] A. Nouri-Borujerdi, M. Bovand, S. Rashidi, K Dincer. “Geometric parameters and response surface methodology on cooling performance of vortex tubes”. Int. Journal of Sustainable Energy, pp.1-15, 2016. [30] P. Promvonge and S. Eiamsa-ard. Investigation on the Vortex Thermal Separation in a Vortex Tube Refrigerator, Science Asia Journal, Vol. 31, pp. 215–223, 2005. [31] M. Attalla, M. Salem, A. Abo EL-Wafa. An experimental investigation of the optimum geometry for energy separation of the Ranque-Hilsch vortex tube, Int. Journal of Mechanic & Mechatronrics Engineering, Vol. 14, pp. 31-37, 2014.
[32] M. Attalla, M. Salem. Experimental investigation of heat transfer for a jet impinging obliquely on a flat surface, Exp. Heat Transf. J. Vol. 28, pp. 378-391, 2015. [33] S. E. Rafiee, S. Ayenehpour, and M. M. Sadeghiazad. A study on the optimization of the angle of curvature for a Ranque–Hilsch vortex tube, using both experimental and full Reynolds stress turbulence numerical modeling, Heat Mass Transfer, DOI 10.1007/s00231-015-1562-y, 2015. [34] K. Stephan, S. Lin, M. Durst, F. Seher, D, Huang. An investigation of energy separation in a vortex tube, Int. J. Heat Mass Transf, Vol. 26, pp. 341–348, 1993. [35] R. Liew, J. C. H. Zeegers, J. G. M. Kuerten, and W. R. Michalek. Maxwell’s Demon in the Ranque-Hilsch Vortex Tube, Physical Review Letters, Vol. 109, 05450-1:4, 2012. [36] K. Chang, Q. Li, G. Zhou, Q. Li. Experimental investigation of vortex tube refrigerator with a divergent hot tube, International Journal of Refrigeration, Vol. 34, pp. 322-327, 2011. [37] S. Mohammadi and F. Farhdi. Experimental analysis of a Ranque–Hilsch vortex tube for optimizing nozzle numbers and diameter, Applied Thermal Engineering, Vol. 61, pp. 500-506, 2013. [38] S. U. Nimbalkar, M. R. Muller. An experimental investigation of the optimum geometry for the cold end orifice of a vortex tube, Applied Thermal Engineering, Vol. 29, pp. 509-514, 2009. [39] O. Aydin, B. Markal, and M. Avci. A new geometry for a counter-flow Ranque-Hilsch vortex tube, Applied Thermal Engineering, Vol. 30, pp. 2505-2511, 2010.
Fig. 1 A schematic diagram of the Counter Ranque-Hilck vortex tube, [2]
5 6
4 3 2
5 6
7
5
1
6
Fig. 2 Schematic diagram of the CVT system 1. Air Compressor 2. Filter Separator 3. Pressure Regulator Valve with Gauge 4. Pressure Vessel 5. Pressure Transmitter 6. Digital Flow Meter and Temperature 7. Counter Vortex Tube (CVT)
Fig. 3 Photo of the experimental set-up
Fig. 4 Generators with 2, 3, and 6 nozzles
Fig. 5 The deviation between the experiments values and the calculated values
1.2 Pi = 6 bar
(Ti-Tc)/∆Tmax [-]
1 0.8 0.6 Present Work
0.4
Hilsch [5] Rafiee et al. [33]
0.2
Stephan et al. [34]
0 0
0.2
0.4
0.6
0.8
1
CF [-]
Fig. 6 A comparison of the dimensionless cold temperature difference against CF with other published data
24 Pi = 6 bar
N=2
P = 5 bar P = 4 bar
Ti-Tc [◦C]
21
P = 3 bar P = 2 bar
18
15
12 0.35
0.45
0.55
0.65 CF [-] (a)
0.75
0.85
0.95
27 Pi = 6 bar P = 5 bar P = 4 bar P = 3 bar P = 2 bar
N=3
Ti-Tc [◦C]
24
21
18
15 0.35
0.45
0.55
0.65
0.75
0.85
0.95
CF [-] (b)
24 Pi = 6 bar
N=6
P = 5 bar P = 4 bar
Ti-Tc [◦C]
21
P = 3 bar P = 2 bar
18
15
12 0.35
0.45
0.55
0.65
0.75
0.85
0.95
CF [-] (c) Fig. 7(a, b, c) Variation of total temperature difference with nozzle numbers at conditions of L/D = 15 and AR = 1.6
27 CF = 0.4
Ti-Tc [◦C]
24
Equation 7 at 6 bar
21 18
Pi = 6 bar P = 5 bar P = 4 bar P = 3 bar P = 2 bar
15 12 1
2
3
4
5
6
7
N [-] (a)
21 CF = 0.9
◦
Ti-Tc [ C]
18
15
12 Pi = 6 bar
P = 5 bar
P = 4 bar
P = 3 bar
P = 2 bar
9 1
2
3
4
5
6
7
N [-] (b) Fig. 8 (a, b) Effect of number of nozzle on cold temperature difference at CF = 0.4, and CF = 0.9
0.25 Pi = 6 bar
N=2
P = 5 bar
0.2
P = 4 bar
COP [-]
P = 3 bar
0.15
P = 2 bar
0.1 0.05 0 0.35
0.45
0.55
0.65
0.75
0.85
0.95
CF [-] (a)
0.25 Pi = 6 bar
N=3
P = 5 bar
0.2
P = 4 bar
COP [-]
P = 3 bar
0.15
P = 2 bar
0.1 0.05 0 0.35
0.45
0.55
0.65 CF [-] (b)
0.75
0.85
0.95
0.25 Pi = 6 bar
N=6
P = 5 bar
0.2
P = 4 bar
COP [-]
P = 3 bar
0.15
P = 2 bar
0.1 0.05 0 0.35
0.45
0.55
0.65
0.75
0.85
0.95
CF [-] (c) Fig. 9 (a, b, c) Variation of COPREF with number of nozzles, L/D = 15 and AR = 1.6
0.25 CF = 0.4
COP [-]
0.2 0.15 0.1 0.05
Pi = 6 bar
P = 5 bar
P = 4 bar
P = 3 bar
P = 2 bar
0 1
2
3
4 N [-] (a)
5
6
7
0.04 CF = 0.9
COP [-]
0.03
0.02
0.01 Pi = 6 bar
P = 5 bar
P = 4 bar
P = 3 bar
P = 2 bar
0 1
2
3
4
5
6
N [-] (b) Fig. 10 (a, b) Effect of number of nozzle on COP at CF = 0.4, and CF = 0.9
7
Highlights:
- The effect of nozzle number of RHVT have been investigated. - The correlation equation has been carried out as function of nozzle number. - The comparison between present data with other published data has been conducted. - It is observed that the best number of nozzle is three nozzle.