Investigation on the Vortex Thermal Separation in a Vortex Tube Refrigerator

Transcription

1 doi: 1.236/sieneasia SieneAsia 31 (2): Investigation on the Vortex Thermal Separation in a Vortex Tube Refrigerator Pongjet Promvonge* and Smith Eiamsa-ard Department of Mehanial Engineering, Faulty of Engineering, King Mongkut s Institute of Tehnology Ladkrabang, Bangkok 2, Thailand. * orresponding author, kppongje@kmitl.a.th Reeived 2 Sep 24 Aepted 18 Apr 2 ABSTRAT: This paper desribes the experimental study of the temperature separation phenomenon in a ounter-flow type vortex tube. Effets of (1) the number of inlet tangential nozzles, (2) the old orifie diameter, and (3) tube insulations on the temperature redution and isentropi effiieny of the tube were experimentally investigated. The temperature drops of the old air obtained from these tests were in good agreement with available data for omparison at a similar sale of operating onditions. The experimental results showed that the insulated vortex tube with 4 inlet nozzles and old orifie diameter of.d yielded the highest temperature redution (temperature separation) and isentropi effiieny at about 3 o and 33% respetively. KEYWORDS: vortex tube, ounter-flow type vortex tube, energy separation, thermal/temperature separations, temperature redution. INTRODUTION The Ranque-Hilsh vortex tube is a mehanial devie operating as a refrigerating mahine without any moving parts, by separating a ompressed gas stream into a low total temperature region and a high one. Suh a separation of the flow into regions of low and high total temperature is referred to as the temperature (or energy) separation effet. Generally, the vortex tube an be lassified into two types. One is the ounterflow type (often referred to as the standard type) and the other is the parallel or uni-flow type. The ounterflow vortex tube onsists of an entrane blok of nozzle onnetions with a old orifie, a vortex tube (or hot tube) and a one-shaped valve. A soure of ompressed gas (e.g. air) at high pressure enters the vortex tube tangentially through one or more inlet nozzles at a high veloity. The expanding air inside the tube then reates a rapidly spinning vortex. The air flows through the tube rather than pass through the old orifie loated next to the nozzles beause the orifie is of a muh smaller diameter than the tube. Therefore, the one valve is applied at the hot tube end in order to ontrol the outlet hot air flow or to let the old air pass through the old orifie as needed. The length of the tube is typially between 3 and tube diameters, and no optimum value has been determined between these limits. As the air expands down the tube, the pressure drops sharply to a value slightly above the atmospheri pressure, and the air veloity an approah the speed of sound. entrifugal ation will keep this onstrained vortex lose to the inside surfae of the tube. The uniflow vortex tube omprises of an entrane blok of inlet nozzles, a vortex tube and a one-shaped valve with a entral orifie. Unlike the more popular ounterflow version, the old air exit is loated onentrially with the annular exit for the hot air. The operation of the uni-flow vortex tube is similar to the operation of the ounter-flow one. Nowadays the property of vortex tube has a great variety of appliation in many industries. It has been widely used in the ooling industrial fields espeially grilling, turning and welding on aount of the various advantages of vortex tube suh as ooling without moving part, non-eletriity onsuming, tiny, lightweight and inexpensive working hemial substane inside the vortex tube, unompliated ooling point, leanliness, onveniene and non-f s free from pollution. The vortex tube was first disovered by G. J. Ranque (1933), a metallurgist and physiist who was granted a Frenh patent for the devie in 1932, and a United States patent in The initial reation of the sientifi and engineering ommunities to his invention was disbelief and apathy. Sine the vortex tube was thermodynamially highly ineffiient, it was abandoned for several years. Interest in the devie was revived by Hilsh (1947), a German engineer, who reported an aount of his own omprehensive experimental and theoretial studies aimed at improving the effiieny of the vortex tube. After Hilsh 1, an experimental study

2 216 SieneAsia 31 (2) was made by Sheper 2 who measured the veloity, pressure, and total and stati temperature gradients in the Ranque-Hilsh vortex tube, using probes and visualization tehniques. Martynovskii and Alekseev 3 studied experimentally the effet of various design parameters of vortex tubes. The veloity, temperature and pressure profiles agreed with the hypothesis of Fulton 4 and supported the suggestion of the onversion of a free vortex into a fored vortex inside the tube. Blatt and Trush investigated experimentally the performane of the uni-flow vortex tube and improved its performane by adding a radial diffuser to the end of the shortened tube instead of a one valve. Bruun 6 presented the experimental data of pressure, veloity and temperature profiles in the ounter-flow vortex tube with a ratio of.23 for the old to total mass flow rate and onluded that radial and axial onvetive terms in the equations of motion and energy were equally important. Williams 7 studied the ounter-flow type vortex tube with methane and Algerian natural gas with a high methane ontent, in order to estimate the effets of gas supply temperature and pressure. A ritial inlet Reynolds number was identified at whih the separation was a maximum. Takahama et al. 8 investigated experimentally the energy separation performane of a steam-operated standard vortex tube and reported that the performane worsened with wetness of steam at the nozzle outlet beause of the effet of evaporation. Takahama and Yokosawa 9 examined the possibility of shortening the hamber length of a standard vortex tube by using divergent tubes for the vortex hamber. Stephan et al. 1 measured temperatures in the standard vortex tube with air as a working medium in order to support a similarity relation of the old gas exit temperature with the old gas mass ratio, established using dimensional analysis. Ahlborn et al. 11 arried out measurements in standard vortex tubes to support their models for alulating limits of temperature separation. Flohlingsdorf and Unger 12 predited numerially the ompressed flow and energy separation phenomena in the vortex tube through the FX ode. Promvonge 13 introdued a mathematial model for the simulation of a strongly swirling ompressible flow in the vortex tube by using an algebrai Reynolds stress model (ASM) and the k-ε turbulene model to investigate flow harateristis and energy separation in a uni-flow vortex tube. It was found that a temperature separation in the tube exists and preditions of the flow and temperature fields agree well with measurements. The ASM yielded more aurate predition than the k-ε model. Guillaume and Jolly 14 ompared the two vortex tubes plaed in a harged onfiguration and those plaed in series by onneting the old disharge of one stage into the inlet of the following stage. From their results, it was found that for similar inlet temperatures, a two-stage vortex tube ould produe a higher temperature redution than one of the vortex tubes operating independently. Promvonge and Eiamsa-ard experimentally studied the energy and temperature separations in the vortex tube with a snail entrane. In their experimental results, the use of snail entrane ould help to inrease the old air temperature drop and improve the vortex tube effiieny in omparison with those of original tangential inlet nozzles. The analysis in the previous researh has been found that the vortex thermal separation phenomenon omes mainly from the diffusion proess of mean kineti energy. Low temperatures (or large temperature separation), both total and stati, are found near the tube axis, beoming lower towards the orifie or the old exit of the ounter-flow vortex tube. One might want to know how the diffusion proess of mean kineti energy affets the design of the vortex tube. In general, the vortex tube is designed to obtain either (i) the maximum temperature separation or (ii) the maximum effiieny. At a given supply pressure, however, many vortex tubes with different design parameters an yield the same temperature separation. The separation phenomenon in the tube is understood learly. If any design parameter of a partiular vortex tube affets the flow field, it would ertainly affet the performane of the tube. The proess of thermal gas separation in the vortex tube has aused a great deal of interest beause of its extreme simpliity and seemingly paradoxial behavior. It seems possible with an input gas pressure of only a few atmospheres, to obtain an axial ool gas urrent whose stagnation temperature is from to 7 o below the initial stagnation temperature of the input gas. At the same time the peripherally rotating gas urrent leaves the tube with a stagnation temperature signifiantly greater than that of the input ompressed gas. This paper introdues an experimental researh on temperature redution (old tube) and temperature rise (hot tube) harateristis in the ounter-flow vortex tube. The main goals of this study were (1) to investigate the effets of vortex tube geometry suh as the number of inlet nozzles, old orifie diameter, and tube with or without insulation, on temperature separation and isentropi effiieny and (2) to study the wall temperature distribution along the whole length of the hot air tube. MATERIALS AND METHODS Experimental Apparatus In the design of a vortex tube, there are several tube parameters to be onsidered, suh as (1) insulated and

3 SieneAsia 31 (2) 217 non-insulated tubes, (2) old orifie diameter, and (3) the number of the inlet tangential nozzles. There are no ritial dimensions of these parameters that would result in a unique value of maximum temperature separation. Knowledge of the temperature separation phenomenon suggests a relative design proedure for the vortex tube with the physial realities of its operation. For fixed inlet onditions (supply pressure), a very small diameter of the vortex tube would offer onsiderably higher bak pressures and, therefore, the tangential veloities between the periphery and the ore would not differ substantially due to the lower speifi volume of air (still high density) while the axial veloities in the ore region are high. This would lead to low diffusion of kineti energy whih also means low temperature separation. On the other hand, a very large tube diameter would result in lower overall tangential veloities both in the ore and in the periphery region, whih would produe low diffusion of mean kineti energy and also low temperature separation. A very small old orifie diameter would give a higher bak pressure in the vortex tube, resulting, as disussed above, in low temperature separation. On the other hand, a very large old orifie diameter would tend to draw air diretly from the inlet and yield weaker tangential veloities near the inlet region, resulting in low temperature separation. Similarly, a very small inlet nozzle would give rise to onsiderable pressure drop in the nozzle itself, leading to low tangential veloities and hene low temperature separation. A very large inlet nozzle would fail to establish proper vortex flow resulting again in low diffusion of kineti energy and therefore low temperature separation. The inlet nozzle loation should be as lose as possible to the orifie to yield high tangential veloities near the orifie. A nozzle loation away from the orifie would lead to low tangential veloities near the orifie and hene low temperature separation. In this experimental test run, the vortex tube with the inner tube diameter of 16 mm and length of 88 mm was made of Plexiglas whih an be divided into two setions; one is the hot air tube of 72 mm (4D) in length and the other is the old air tube of 16 mm (1D) in length. The old orifie plate was mounted between the hot and old tubes made of Plexiglas of 2 mm in thikness. The vortex tube was insulated with 2 mm thik Aero-flex pipe insulation. The hange of the old orifie diameters was varied from.4d to.9d. The inlet nozzle hamber mounted between the hot and old tubes was made of Plexiglas of 2 mm in thikness and inlet nozzles with a diameter of 2 mm (D/ 9) were plaed equally around the hamber periphery, depending on the number of the nozzles used. The ounter-flow vortex tube and the arrangement of the experimental system are depited in Figures 1 and 2. The experimentation started when a ompressed air from a ompressor flows through the ontrol valve and the pressure gauge and then air-filter before entering the vortex tube. Inside the vortex tube, the air is separated into two urrents and esapes into the atmosphere through hot and old tubes. The old air would flow out from the old orifie plates installed near the inlet nozzles, whereas the hot air esapes from the end of hot tube equipped with the one-shaped valve. The mass rates of the flow of the old air and hot air disharges are measured by standard pipe orifie flow meters and their ratio, alled a old mass fration is hanged by regulating the one-shaped valve opening. In the experiments, the old disharge thermoouple is installed downstream of the old disharge orifie. old air temperature is measured at the middle of the old air tube while the hot disharge thermoouples are loated immediately upstream of the one-shaped valve and the hot air temperature is measured at a 1/8 tube radius from the inner wall of the hot air tube. All temperature data were measured with irononstantan thermoouples type K and reorded with a signal-proessing unit on a personal omputer. old tube Hot tube one valve old air D Nozzle L Lh old orifie plate Tube with insulation Fig 1. Basi operation of the Ranque-Hilsh standard vortex tube or ounter-flow vortex tube.

4 218 SieneAsia 31 (2) Ti Pi T Th VORTEX TUBE Th 11 HOT AIR To 14 OLD AIR Fig 2. Experimental apparatus, 1) air ompressor, 2) ontrol valve, 3) air filter, 4) pressure gage, -6) a set of orifie flow meters, 7-9) thermoouple probe, 1) old orifie plate, 11) one-shape valve, 12 and 14) orifie flow meter, 13 and ) thermoouple probe, 16) data logger, and 17) P omputer. Data Redution Equations The most important parameter indiating the vortex tube performane is the old mass fration whih an be expressed as; m µ = m (1) i old air temperature drop is expressed as: ( T) = Ti T (2) temperature differene is expressed as: ( T) h = Th Ti (3) To alulate the ooling effiieny of the vortex tube, the priniple of adiabati expansion of ideal gas will be used. As the air flows into the vortex tube, the expansion in isentropi proess ours. This an be written as follows: ( T) = ηis( T) isen (4) Temperature differene in isentropi proess is: ( T) is P a = Ti 1 Pi γ 1 γ Isentropi effiieny is expressed as: Ti T ηis = γ 1 P γ a Ti 1 P i () (6) onfirmator matory Test Before the results of experimental work are reported, the data are ompared with previous measured data of Hilsh 1 and Guillaume and Jolly 14.

5 SieneAsia 31 (2) 219 Table 1. omparison of the present tube with the previous investigator. Vor ortex tube harateristi The details of geometries and working onditions of the present vortex tube and the previous work are shown in Table 1. Figure 3 displays the temperature redution in the old tube against the old mass fration for the present tube, Hilsh s tube and Guillaume and Jolly s tube. It is worth noting that the temperature redution distributions for all tubes show a similar trend despite different tube sizes and inlet onditions. All tubes yield a maximum temperature redution at the old mass fration between.3 and.4, having a maximum temperature derease value at about 16. A lose examination reveals that when using a single tangential inlet nozzle, the temperature drop profile of the present tube is very lose to that of Hilsh s tube 1 but is slightly different with Guillaume and Jolly s tube Present Hilsh Guillaume and work (1947) Jolly (21) Pressure at the inlet,(bar) Hot tube length, L h 4D 32D - old tube length, L 1D 1D - Vortex tube diameter, (mm) 16 (D) 9.2 (D) 6.4 (D) Nozzle diameter, D/9 D/9 D/3 Number of inlet nozzles, 1, and 4 old orifie diameter,.d - - Vortex hamber - - 2D Present work Hilsh (1947) Guillaume and Jully (21) This omparison has been made to help inrease the onfidene in the present measurements only. RESULTS AND DISUSSION Temperatur emperature e Redution In the present experiment, measurements of the vortex tube with and without insulation at inlet T i -T, o 2 1 Insulated Non-insulated old mass fration, µ 3 2 (a) old tube Insulated Non-insulated Temperature redution, T i -T ( o ) T h -T i, o old mass fration, µ Fig 3. omparison of temperature redution in the old tube for the present work and previous work old mass fration, µ (b) Hot tube Fig 4. Effet of the insulated and non-insulated tubes on temperature variation in (a) old tube and (b) hot tube, T i =29.

6 22 SieneAsia 31 (2) temperature and pressure of 29 and 3. bar respetively were made for the old orifie diameter of.d using the single inlet nozzle. The outside surfae temperature of the non-insulated hot tube exposing to the surrounding was about - 6, but this redued to some 32 when using the insulated tube. The temperature differenes between the inlet and the tube temperatures against various old mass frations are shown in Figures 4a and 4b for the old and hot tubes, respetively. In the figure, the insulated tube provided a higher temperature redution than the non-insulated one. At a old mass fration of.34, the highest temperature redutions at the old tube of the insulated and non-insulated tubes were 19 and 18, respetively. In addition, in the hot tube the maximum temperature inreases of the insulated and non-insulated tubes were found to be 24 and 2, respetively, at a old mass fration of.87. The average temperature differenes between the insulated and non-insulated tubes were in a range of 2 to 3 for the old tube, and of 2 to for the hot tube. This is beause the insulated tube gave a less energy loss to the surroundings than the noninsulated one, ausing the higher temperature differene within the tube. For the old mass fration ranging from.1 to.4, the temperature redution in the old tube inreased, but then dereased for the old mass fration over.4. In the hot tube, for the old mass fration ranging from.1 to.8, the temperature proportionally inreased, but then dereased rapidly for the old mass fration above.8. 2 The experimental result of temperature drops for different old orifie diameters ranging from.4d to.9d using one inlet nozzle is depited in Figure. The highest temperature redution was ahieved for all old orifie diameters when the old mass fration was in a range of.3 to.4. Thus, the maximum temperature drop ourred if the one valve was adjusted to let the old mass flow rate leave the old tube at 3 to 4% of the inlet air. The derease in temperature in the old tube was found to be 18, 19,, 14, 12, and 1 for using old orifie diameter of.4d,.d,.6d,.7d,.8d and.9d at the old mass fration of.364,.37,.381,.378,.373, and.372, respetively. Furthermore, the old orifie diameter of.d yielded the highest potential of temperature redution in the old tube than the others. Using the old orifie diameter ranging from.6d to.9d (bigger than that of.d) would allow some hot air in viinity of the tube wall to exit the tube with the old air. Both the hot air and old air as flowing out were mixed together whih further affeted the old air to have higher temperature. On the other hand, for a small old orifie diameter of.4d, it has a higher bak pressure and makes the temperature redution at the old tube lower. The effet of the number of inlet nozzles on temperature redution in the insulated vortex tube was experimentally investigated as shown in Figure 6. The inrease in the number of inlet nozzles led to onsiderable temperature separation. In the figure, the use of 4 inlet nozzles resulted in a higher temperature 3 2 d/d=.4 d/d=. d/d=.6 d/d=.7 d/d=.8 d/d= inlet nozzle 2 inlet nozzles 4 inlet nozzles T i -T, o 1 T i -T, o old mass fration, µ Fig. Effet of the old orifie diameters on temperature redution in the insulated vortex tube, T i = old mass fration, µ Fig 6. Effet of the number of inlet nozzles on temperature redution in the insulated vortex tube, T i =29.

7 SieneAsia 31 (2) 221 redution in the old tube than that of 1 and 2 inlet nozzles for the old orifie diameter of.d. The highest temperature drops also were 19, 29 and 3 for using 1, 2 and 4 nozzles, respetively. Mostly the maximum thermal separation ourred at a old mass fration between.3 and.4. hanging the number of inlet nozzles from 1 to 2 and 4 helped to speed up the flow and to inrease the mass flow rate and strong swirl flow into the vortex tube. In addition, this gave rise to higher frition dissipation between the boundary of the flows and a higher momentum transfer from the ore region to the wall region. This redued temperature in the tube ore while inreased temperature in the tube wall area. Wall all Temperatur emperature e Distribution Wall temperatures of the hot tube were measured at axial stations equally spaed along the axial distane downstream of the old orifie plate as an be seen in Figure 7. Figure 8 displays the wall temperature distributions in terms of temperature differene between the wall and the inlet at different old mass frations. In a range from x/d=1 to x/d=11, the wall temperature distribution tended to inrease, reahing a maximum at x/d=11. After x/d=11, the wall temperature distribution tended to derease beause the hot air near the tube wall region and the old air in the ore region were mixed together due to deaying of swirl flow lose to the exit of hot tube. The temperature of the tube wall inreased proportionally with the old mass fration, exept when the old mass fration approahed unity. It an be observed that at x/d=11, the temperature at the tube wall with 4 inlet nozzles was 78 above the inlet temperature for the old mass frations of.829. Isentropi Effiieny There was a substantial inrease in the isentropi effiieny and the behavior of the effiieny with old old air x/d=. thermoouple stations Fig 7. Arrangement of thermoouples along the hot tube wall. T w -T i, o old mass fration=.49 old mass fration=.1 old mass fration=.248 old mass fration=.328 old mass fration=.4 old mass fration=.8 old mass fration=.6 old mass fration=.636 old mass fration=.829 old mass fration=.921 Isentropi effiieny, % inlet nozzle 2 inlet nozzles 4 inlet nozzles x/d Fig 8. The axial wall temperature distribution along the hot tube of the insulated vortex tube with 4 inlet nozzles and old orifie of.d, T i = old mass fration, µ Fig 9. Relationship between isentropi effiieny and the old mass fration for the insulated vortex tube.

8 222 SieneAsia 31 (2) mass fration at a different number of inlet nozzles is depited in Figure 9. The use of 4 inlet nozzles generated a stronger swirling flow and momentum transfer than that of 1 and 2 inlet nozzles, resulting in higher thermal separation and effiieny. The isentropi effiieny for the 2 and 4 nozzles ould be improved and inreased around 2% and 6% better than that for the single nozzle, respetively. Moreover, the maximum isentropi effiieny of an insulated vortex tube with 4 nozzles and old orifie diameter of.d was found to be 33%. Empirial orrelation In the experimental optimization, the temperature redution data using 1, 2 and 4 inlet nozzles were seleted for omparison with Hilsh s work and Guillaume and Jolly s work as an be seen in Figure 1. In the figure, the maximum old air temperature drop or thermal separation took plae at the old mass fration ranging from.3 to.4. With the help of experimental data, the following empirial orrelations of the insulated vortex tube with different inlet nozzles an be expressed: Following present work (1 inlet nozzle), and a ubi fitting yields, T = 2. 46µ µ µ T,max (7) Following present work (2 inlet nozzles), and a ubi fitting yields, T = µ µ µ T,max (8) (T i -T )/ (T i -T ) max inlet nozzle 2 inlet nozzles 4 inlet nozzles Hilsh (1947) Guillaume and Jolly (21) old mass fration, µ Fig 1. omparison between non-dimensional temperature redution with old mass fration of previous work and the present work. Following present work (4 inlet nozzles), and a ubi fitting yields, T = 379. µ 83. µ µ T,max (9) The above orrelations an be used to help design a vortex tube system to obtain the highest temperature separation in the vortex tube with insulation. Following Hilsh (1947), and a ubi fitting yields, (1) Following Guillaume and Jolly (21), and a ubi fitting yields, T = 73. µ 127. µ µ + 6. T,max (11) Empirial equations (7), (8) and (9) are derived from the present experimental results showing the range of highest temperature separation in the vortex tube at the old mass fration required. When ompared to empirial orrelations (1) and (11) obtained from previous works, they show similar orrelations. ONLUSIONS An experimental study on the temperature separation in the vortex tube has been arried out and this researh finding an be summarized as follows: 1. The inrease of the number of inlet nozzles led to higher temperature separation in the vortex tube. 2. Using the tube with insulation to redue energy loss to surroundings gave a higher temperature separation in the tube than that without insulation around 2-3 for the old tube and 2- for the hot tube. 3. A small old orifie (d/d=.4) yielded higher bakpressure while a large old orifie (d/d=.7,.8, and.9) allowed high tangential veloities into the old tube, resulting in lower thermal/energy separation in the tube. NOMENLATURE Pa atmospheri pressure [bar] Pi inlet pressure [bar] T temperature differene [ o ] T temperature redution [ T i T, o ] T,max maximum temperature redution[ T i T,max, o ] T h temperature inreasing [ T h T i, o ] Ti inlet air temperature [K] T old air temperature at the old tube [K] T T,max = µ 98µ 44µ 39

9 SieneAsia 31 (2) 223 Th hot air temperature at the hot tube [K] Tw hot wall temperature at the hot tube [K] d diameter of old orifie [mm] D diameter of the vortex tube [mm] L length of the tube [mm] µ old mass fration [ m /m i ] m i inlet mass airflow rate [kg/s] m old mass airflow rate [kg/s] δ diameter of inlet nozzle [mm] speifi heat ratio η γ is isentropi effiieny [%] REFERENES 1. Hilsh R (1947) The Use of Expansion of Gases in a entrifugal Field as a ooling Proess. Review of Sientifi Instruments 18 (2), Sheper GW (191) The Vortex Tube; Internal Flow Data and a Heat Transfer Theory. Journal of the ASRE, Refrigerating Engineering 9, Martynovskii VS and Alekseev VP (196) Investigation of the Vortex Thermal Separation Effet for gases and Vapors. Soviet Physis-Tehnial Physis 1, Fulton D (19) Ranque s Tube. Journal of the ASRE, Refrigerating Engineering 8, Blatt TA and Trush RB (1962) An Experimental Investigation of an Improved Vortex ooling Devie. Amerian Soiety of Mehanial Engineers Winter Annual Meeting, November 2-3, U.S.A. 6. Bruun HH (1969) Experimental Investigation of the Energy Separation in Vortex Tubes. Journal of Mehanial Engineering Siene 11 (6), Williams A (1971) ooling of Methane with Vortex Tubes. Journal of Mehanial Engineering Siene 13 (6), Takahama H, Kawamura M, Kato B and Yokosawa H (1979) Performane harateristis of Energy Separation in a Steam Operated Vortex Tube. International Journal of Engineering Siene 17, Takahama H and Yokosawa H (1981) Energy Separation in Vortex Tubes with a Divergent hamber. Transation of the ASME, Journal of Heat Transfer 13, Stephan K, Lin S, Durst M, Huang F and Seher D (1983) An Investigation of Energy Separation in a Vortex Tube. International Journal of Heat and Mass Transfer 26, Ahlborn B, Keller JU, Staudt R, Treitz G and Rebhan E (1994) Limits of Temperature Separation in a Vortex Tube. Journal Physis D: Applied Physis 27, Frohlingsdorf W and Unger H (1999) Numerial investigations of the ompressible flow and the energy separation in the Ranque-Hilsh vortex tube. International Journal of Heat and Mass Transfer 42, Promvonge P (1999) Numerial Simulation of Turbulent ompressible Vortex-Tubes Flow. Pro. of the 3 rd ASME/JSME Joint Fluid Engineering onferene, Sanfraniso, USA. 14. Guillaume DW and Jolly III JL (21) Demonstrating the ahievement of the lower temperatures with two-stage vortex tubes. Review of Sientifi Instruments 72 (8), Promvonge P and Eiamsa-ard S (24) Experimental Investigation of Temperature Separation in a Vortex Tube Refrigerator with Snail Entrane. ASEAN Journal on Siene & Tehnology for Development 21 (4),