EXPERIMENTAL STUDY AND CFD ANALYSIS ON VORTEX TUBE

Transcription

1 HEFAT28 6 th International Conferene on Heat Transfer, Fluid Mehanis and Thermodynamis 3 June to 2 July 28 Pretoria, South Afria Paer number: KM1 EXPERIMENTAL STUDY AND CFD ANALYSIS ON VORTEX TUBE Kalal M.* Matas R and Linhart J. *Author for orresondene Deartment of Power System Engineering, University of West Bohemia, Plzen, 36 14, Czeh Reubli, kalal@kke.zu.z ABSTRACT In this exerimental study of the vortex tube erformane has been arried out to investigate the arameters affeting vortex tube oeration. Four ases have been studied, in whih the influenes of the tube length L, the number of entrane nozzles Nz, old air orifie diameters d and inlet ressure under various ondition. The effets of these arameters on the hot and old outlet temerature as funtion of old air mass ratio (ε ) are disussed and resented. And also the oeffiient of erformane (COP) of the vortex tube as a refrigerator and as a heat um has been alulated. Three Dimension numerial modelling of vortex tube has been evolved through CFD analysis by using the k ε turbulene model. Axial, radial and tangential omonents of the veloity together with the temerature and ressure fields within the vortex tube are simulated. Preditions from the resent CFD simulations were omared with data obtained from our exeriments under the same geometrial and oerating onditions. INTRODUCTION The vortex tube has been used in industrial aliations of ooling and heating roesses beause of a simle, omat, light and quiet in oeration devie. Comressed air is ejeted tangentially through a generator into the vortex sin hamber. At u to soni seed this air stream revolves toward the hot end where some esaes through the ontrol valve. The remaining air, still sinning, is fored bak through the entre of this outer vortex. The inner stream gives off kineti energy in the form of heat to the outer stream and exits the vortex tube as old air., as shown shematially in figure 1. The vortex tube was first disovered by Ranque [1] but was revived and imroved in effiieny by Hilsh [2]. A reent review of the existing literature is given in Coerill [3]. In site of the resent uses and the various studies, no adequate hysial exlanation is available for the atual transort mehanism. Ahlborn, et al, [4] identified the temerature slitting henomenon of a Ranque Hilsh vortex tube in whih a stream of gas divides itself into a hot and a old flow as a natural heat um mehanism, whih is enabled by a seondary irulation. Ahlborn, et al. [5] onsidered the vortex tube as a refrigeration devie whih ould be analyzed as a lassial thermodynami yle, relete with signifiant temerature slitting, refrigerant, and oolant loos, exansion and omression branhes, and natural heat exhangers. Figure 1 Shemati diagram of the vortex tube. The effet of various arameters, suh as nozzle area, old orifie area, hot end area and L/D ratio of the tube length to the tube diameter, on the erformane of the vortex tube was investigated by Singh [6]. There were exerimentally tested variations of the old air temerature T with reset to the hange of the hot end area for different L/D. They showed the old air temerature T at all the tested ratios L/D dereased if the hot end was oened. Also the effets of length and diameter on the rinial vortex tube are onsidered by Saidi et al [7]. They showed variation of effiieny versus different L/D of vortex tube. An exerimental investigation of the energy searation roess in the vortex tube was onduted by Stehan [8]. There were measured temerature rofiles at different ositions along the vortex tube axis with onlusion the vortex tube length has an imortant influene on the transort mehanism inside. Ting-Quan [9] they are resented exerimental results of the energy searation in the vortex tube under different oerating onditions showing the temerature

2 hanges of the old and hot streams as a funtion of the inlet ressure. In this study there was found that the hot stream temerature inreased with the inlet ressure rising, and that the old stream temerature dereased with the inlet ressure. Takahama et al [1] they are resulted in several formulas for determining the erformane and effiieny of the vortex tubes under a variety of oerating onditions, whih indued the otimum ratios of the vortex tube dimensions orresonding to the highest effiieny. NOMENCLATURE COP [-] Coeffiient of erformane [J/kgK] Seifi heat at onstant ressure D vt [mm] Inner diameter of vortex tube d [mm] Cold end diameter H [kj/kg] Total enthaly k [W/mK] Thermal ondutivity L [mm] Length of vortex tube ṁ [kg/s]] Mass flow rate of the old air ṁ i [kg/s] Mass flow rate of the hot air N z [-] Number of entrane nozzle [Pa] Pressure Q [kw] Cooling ower T [K] Temerature u [m/s] Veloity vetor W P [kw] Work ower these investigators tried to emloy higher-order turbulene models but they ould not get onverged solutions due to numerial instability in solving the strongly swirling flows. The CFD and exerimental studies onduted towards the otimization of the Ranque Hilsh vortex tubes are resented by Uendra et al [15]. They showed the swirl, axial and radial veloity omonents of the flow, the flow attern was obtained through CFD. The otimum old end diameter, the ratios of the vortex tube length to diameter and otimum arameters for obtaining the maximum hot gas temerature and minimum old gas temerature are obtained through CFD analysis and validated through exeriments. EXPERIMENTAL SETUP A omressed air with a maximum ressure 8 [kpa] and a maximum volume flow rate of a bout 12 [m3/h], will be used in this study. In this exerimental test run, the vortex tube with the inner tube diameter D vt of 21 [mm] and virus tubes length L of 2 u to 145 [mm] was made of glass. The arrangement of exerimental aaratus and measuring devies whih is used for the determination of the erformane of the ounter flow vortex tube is shown in figure2. Seial haraters T [ C] Temerature differene ρ [kg/m 3 ] Density γ [-] Seifi heat ratio τ [N/m 2 ] Stress tensor omonent ε [-] Cold air mass ratio Subsrits h i Cold air Hot air Inlet Figure 2 Shemati diagram of the exerimental setu So far there are very lenty of available researhes to validate the reliability of CFD analyses for investigating the flow and temerature within the vortex tube. Ahlborn et al [11] show the deendene of vortex tube erformane on the normalized ressure dro by using a numerial model. Frohlingsdorf and Unger [12] resent a detailed analysis of various arameters of the vortex tube through CFD tehniques to simulate the henomenon of flow attern, thermal searation, ressure gradient et. And also it utility as a tool for otimal design of vortex tube towards the otimization of number of nozzles, nozzle rofiles, old end diameter, length to diameter ratio, old and hot gas frations and omarison of the exerimental results with orresonding CFD analysis. Aljwayhel et al. [13] also studied the energy searation mehanism and flow henomena in a ounter flow vortex tube using the CFD ode Fluent with the standard k-ε model and the RNG k-ε model. They reorted that the RNG k-ε model rovides better reditions. This is ontrary to results of Skye et al. [14] laimed that for vortex tubes erformane, the standard k-ε model erforms better than the RNG k-ε model desite using the same ommerial CFD ode Fluent. Some of The exerimentation was started when the air was omressed by the air omressor (1). The high ressure air asses through the ressure tank (2) to suress imats and through the valve (3), where its mass rate is regulated. Inlet ressure is read by the ressure gage (4), and then goes through the dust filter (5) and ooler (6) with ylone searator (7). The mass flow rate of the inlet air is measured using an orifie (8). Then the omressed air is introdued tangentially into the vortex tube (1), where it exands and searates into the hot and old air streams. The old air in the entral region leaves the vortex tube near the entrane, while the hot air goes out to the surrounding at the far end of the vortex tube. The ontrol valve (11) ontrols the flow rate of the hot air. Just after the ie, the mass flow rate of the hot air is measured using the venture tube (13). Thermooules numbered 9, 12 and 14 measure the inlet and outlet temeratures. All data about temeratures and ressures are olleted with data aquisition system (15) with the outut signals being led to the PC (16). The rogram was written in Lab VIEW 7.2 to ontrol the data logging arameters and to dislay the obtained results.

3 Proessing of Results In this setion, various exeriments on the different omonents of the vortex tube, setu under various onditions, and four ases have been done to investigate their influene. The influenes of the vortex tube length L, the number of entrane nozzles N z, old air orifie diameters d, have been defined as shown in Table 1. Case L d N z P i D vt [mm] [mm] [-] [bar] [mm] 1 2, 4, 6, 8, 1, , 1, 12, , , 4, 5, 6, 7 21 Table 1 Investigated Case for Various Oeration Conditions. In the investigation, the inlet mass flow ṁ is an imortant arameter together with ε and the inlet ressure P in, whih is ontrolled by the needle valve laed at hot exhausts. During the exerimental test, the vortex tube diameter D vt is always equal to 21 mm. As for the vortex hamber, the inner diameter of the inner ring is always equal to 4 mm. The ε is varied systemially. The ε is defined as follows: ε = m m i where ṁ reresents the mass flow rate of the old stream released, while ṁ reresents the inlet or total mass flow rate of the i ressurized inlet working fluid. Therefore, it hanges in the range ε 1. Influene of Tube Length In order to, investigate the effet of inreasing the length of the vortex tube. Six different tube lengths made of glass (2, 4, 6, 8, 1 and 145 mm) have been designed and investigated as a funtion of the ε. The geometry of the system is the one of Case 1 in Table 1. Figure 3(a) and (b) showed hot and old outlet temeratures and maximum temerature different between hot and old outlet as a funtion length tune ratio L/D vt resetively, under the same oeration ondition. The results for six different tube lengths ratio: 1, 2, 3, 4, 5 and 75, the influene of the tube length is lear from this figure. When the L/D vt inreases from 1 u to 4 the hot outlet temerature inreases. The old outlet temerature dro with the L/D vt inreases from 1 u to 5. From the analysis result it has been observed that vortex tube an be oerated in suh a way that it an be used to rodue maximum hot air temerature and/or to rodue minimum old air temerature. Figure 3b shows the maximum T h inreases with inreasing the L/D vt from 1 to 5; with longer than that the maximum T h dereases. Singh [6] onluded that the tube length should be longer than 45D vt, and also Saidi [7] was suggested the otimum value of L/D vt is within the following ranges 2 L/D vt 55. In order to, obtain a better i erformane. In our measurements, the result of the study of the influene of the tube length suggests that a tube length of 1 mm is good erformane, orresonding to L/D vt is about 5. That means there is a ritial vortex tube length over whih the majority of the energy transfer takes lae. Temerature [C] 12 1 Maximum temerature differene (Th-T) Th T Length ratio [L/D] (a) Tube length ratio (L/Dvt) (b) Figure 3 (a) Hot and old temerature at deferent length tube ratio (b) Temerature deferene at deferent length tube ratio Influene of the Diameter of Cold Orifie To determine the effet of the old air orifie diameter d on the hot and old air temerature, the orifies with different diameters of 8, 1, 12 and 14 mm, were designed, fabriated and obtained exerimentally for L/D vt = 3 at variations the ε. The geometry of the system is the one of Case 3 in Table 1. The figure 4 shows the outlet air temerature differene as a funtion of the dimensionless old air orifie diameter (d /D vt ). It is shown that for (d /D vt ) <.57, inreasing (d /D vt ) auses the outlet air temerature differene to inrease and for (d /D vt ) >.57, inreasing (d /D vt ) tends the outlet air temerature differene to derease. From the analysis and exeriments it has been observed that vortex tube an be oerated in suh a way that it an be used to rodue maximum hot gas temerature and/or to rodue minimum old gas temerature.

4 Temerature differene Th-T, [C] Inlet ressre 5 bar at CAMR= Dimensionless old air orifie diameter [-] Figure 4 The outlet air temerature differene as funtion of the dimensionless old air orifie diameters (L/D vt ). Influene of Entrane Nozzles To study the effet of number of entrane nozzles, two shaes of nozzle were designed and fabriated, having 2 and 4 entrane, with onstant outlet ross-setional area. Variations of the hot and old air temerature as funtion of the ε are shown in Figure 5. With the entrane nozzle number inreasing, the flow in the main tube beomes more turbulent due to greater interation of inlet flows. Therefore the old and hot streams are mixed in the main tube, leading to energy searation, hot and old temerature redution. The result is that with the two entrane nozzles shows better erformane than four entrane nozzles. Temerature [C] Inlet ressure 6 bar 2 entranes nozzle 4 entranes nozzle 2 entranes nozzle 4 entranes nozzle Cold air mass ratio [-] Figure 5 The hot and old air temerature at different ε and entranes nozzle. Case 3: Influene of Inlet Pressure The influene of the inlet ressure at 2, 4, 5, 6 and 7 bar on the temerature of the hot and old outlet air is learly distintive as shown in Figure 6. The geometry of the system is the one of Case 4 in Table 1. Result shows that the temerature of the hot outlet inreases with inlet ressure inreasing, and that the old outlet temerature dereases with inlet ressure. The erformane of the vortex tube an be imroved by inreasing the inlet ressure to the ritial value. It should be noted that when the inlet ressure inreases, with the same system and same old fration, the inlet flow inreases too. Temerature [C] Cold mass fration =.8 T.hot T.old Cold mass fration = Inlet ressures [bar] Figure 6 The hot and old temerature for different inlet ressures, Case 4. Thermal Effiienies for Vortex tube The vortex tube an be used not only as a ooler, but also as a heater. So the definition of the effiieny should onsider both effets. For different aliations, different effiienies are used. The oeffiient of erformane (COP) of a ooler is normally defined as the ooling ower Q gained by the system divided by the work ower W inut. So the COP of the ooler, denoted by COP r is exressed as: Q COPr = (1) W Here the ooling ower an be alulated aording to the ooling aaity of the old exhaust gas (e.g. the heat neessary to heat u the old exhaust gas from the old exhaust temerature to the alied temerature. Here T in is hosen.). Q = m ( Tin T ) (2) In a onventional refrigeration system, there is a omressor, so the work ower is the inut ower of the omressor. But in the VT system, usually a omressed gas soure is used, so it is not easy to define the work ower. By analogy the work used to omress the gas from the exhaust ressure u to the inut ressure with a reversible isothermal omression roess, W = m in R mt in ln( in a ) (3) as used in [16], an be exressed as ε ( Ti T ) COPr = γ 1 Ti rm ln( i a ) (4) γ For the heat um, the oeffiient of erformane is resented as the heating ower divided by the work ower used. For the vortex tube system, the heating ower an be exressed as the heating aaity of the hot exhaust gas. Q h = mh ( Th Tin ) (5) The work ower used by the system is taken the same as used above for the ooler. So the oeffiient of erformane of the vortex tube as a heater, denoted as COP hr is:-

5 ε ( 1 ε )( Th T i ) γ 1 i r m ln( i a ) γ COP hr = (6) T Figures 7 and 8 showed the Coeffiient of erformane of the otimize vortex tube length. There was a substantial inrease in the COP. COP as ooler [%] L=145 L=1 L=8 L=6 L=4 L= Cold mass fration [-] Figure 7 Coeffiient of erformane of the otimized vortex tube as a refrigerator for differene length. COP as heater [%] L=145 L=1 L=8 L=6 L=4 L= Cold mass fration [-] Figure 8 Coeffiient of erformane of the otimize vortex tube as a heat um for differene length The behavior of the COP r with old air mass fration for six different vortex tube length (2, 4, 6, 8, 1, 145 mm) at same oerating ondition to diameter ratio (L/D vt ) is deited in Figure 7. It an be seen that COP r inreases by inreasing the length tube u to 1 mm and it dereases at longer length (145mm). Also it shows that the maximum COP r effet ours as old air mass frations between.56 and.75. The COP values of the vortex tube for length tube equal 2 to u 145 mm as a heat mahine is shown in figure 8. It is observed that the COP h of the vortex tube as a heat mahine inreases with inreasing the length of the vortex tube u to 1 mm and then dereases with longer length. The COP of vortex tube is very low as omared to COP of Carnot yle. However this is a unique devie whih rodues both heating and ooling effets simultaneously without using any other form of energy than omressed air at moderate ressure. This devie an be used effetively in roess environments where heating and ooling oututs of vortex tubes an be onurrently used. NUMERICAL MODEL The numerial modelling of a vortex tube has been arried with the CFD system of Fluent. The henomenon under onsideration of the vortex tube is ratially an unvisous, steady, omressible and turbulent flow. The equations of mass, momentum and energy onservation er unit mass solved by fluent volume an be exressed as follows: The Mass Conservation Equation ρ +. ( ρ u ) = (7) t The Momentum Conservation Equations ( ρ u) +. ( ρ u ) = + τ (8) t Where ρ is the density of the fluid, u is the fluid veloity omonents, is the stati ressure, τ is the visous stress tensor, (gravity is negleted). The Energy Conservation Equation for a fluid region an be written in terms of total enthaly ( ρh) t +. uh = + t k ( ρ ) H ( τ u ) Where H defined as total enthaly, k and are the thermal ondutivity and heat aaity of the fluid, resetively. CFD Model of Vortex Tube The model was imlemented and meshed using the ommerially available geometry re-roessor GAMBIT. The simulations were done with the finite volume ode FLUENT. Geometry of the vortex tube simulated by a 3D CFD model is deited in figure 9. It is shown simle vortex tube with four tangential inlet nozzles. The length is 2mm and inside diameter 21mm. The geometry omes from the simultaneously measured vortex tube and the hot outlet valve wasn t simulated omletely and the ontrol valve was relaed by the ressure outlet with variable value. The only arameter varied during the simulations in this study was the hot air outlet ressure. This results in the variation of mass flow rates in the old and the hot exit streams. Boundary Conditions Comutational mesh of the eriodial segment has about 1.2 million mixed ells. The ressure and temerature data obtained from the exeriments are sulied as inut for the analysis. The boundary onditions given to simulate the vortex tube henomenon at different regions are as follows: The inlet region of the vortex tube (at inlet of nozzle) with inlet mass flow rate.35 kg/s was hosen to math our exerimental inlet mass flow rate and the total temerature at the inlet was set to (9)

6 3 K. Pressure boundary ondition to the hot end region of vortex tube with ressure varying so as to vary the mass flow at the hot end to obtain the otimum value. And the tube walls were onsidered to be adiabati with no sli boundary ondition for the veloity omonents. Inlet air entrifugal fore that is reated by the vortex. However, both stati and total ressure dereases as the flow rogresses toward the hot outlet near the outer radius in the axial diretion. Towards the entre, the flow is in the oosite diretion and therefore the ressure inreases in the axial diretion, albeit a very small amount. Cold outlet Hot outlet Figure 9. Three dimensional CFD model of vortex tube with four entrane nozzles PROCESSING OF RESULTS This setion desribes a detailed analysis of the CFD model results obtained from FLUENT. The numerial model was seen to agree reasonably with exerimental data. However, the rimary urose of the numerial modelling was to develo an understanding of the hysial roesses that rodue the vortex tube s remarkable temerature searation aabilities. It is lear from Figures 1 that CFD is able to redit a substantial temerature searation for the vortex tube. The total temerature inreases in both the radial diretion and axial diretions. Figure 11 Total ressure as a funtion of radius at several axial ositions. Figure 12 Stati ressure as a funtion of radius at several axial ositions. Figure 1 Total temerature as a funtion of radius at several axial ositions. Figures 11 and 12 illustrate the total ressure and stati ressure rofiles. It an be seen that both the stati and the total ressures are inreasing in the radial diretion as a result of the Figure 13 shows the radial rofiles of the axial veloity at different axial loations (x = 5 mm, x = 1 mm, x = 15 mm and x = 2 mm). The maximum axial veloity is near the tube wall and the diretion of the flow near the wall is towards the hot end exit and the diretion of the flow along the axis is towards the old end exit. It was observed that the maximum value of the axial veloity dereased with inreasing axial distane exet at inlet nozzles and at the hot outlet. At axial loations of 5, 1, 15, and 2 mm the maximum axial veloity was found to be 9, 86, 8 and 78 m/s, resetively.

7 The axial veloity rofiles show that the flow reversal takes lae at about 6 mm from the entre of the tube. The axial veloity in the old ore is direted towards the old end exit. The axial veloity in the old ore was found to inrease with a derease in the axial distane. Figure 15 Radial veloities as a funtion of radius at several axial ositions. Figure 13 Axial veloities as a funtion of radius at several axial ositions. Tangential veloity as a funtion of radius at several axial ositions is shown in figure 14. The tangential veloity is negative to all radial diretion. The tangential veloity inrease in the axial diretion and in the radial diretion and then begins to dereases at a radius of 5 mm, whih is aroximately the entre line of the re-irulating region. Figure 15 shows the radial veloity as a funtion of radius at several axial ositions. As it is shown, the magnitude of the radial veloity everywhere is less than 2 m/s exet for inlet nozzle and hot outlet; it was found 25 and 7 mm, resetively for short distane at a radius of 6 mm. (a) (b) Figure 16. Veloity vetor lot from CFD of ross lane at, (a) inlet and old outlet (b) hot outlet. Figure 14 tangential veloities as a funtion of radius at several axial ositions. The visualization of the veloity vetor rofile inside the vortex tube heled to understand the details of fluid flow. The following two figures 16(a) and (b) illustrate the distribution of veloity vetor rofile at ross lane of inlet, old air outlet and

8 hot air outlet, resetively. It an be found that the veloities higher at near the wall than that one in the enter. The maximum veloity is about 12m/s at near wall. COMPARISON OF CFD MODEL AND EXPERIMANTAL DATA The inlet mass flow rate in the CFD model was seified as a onstant.334 kg/s, whih is onsistent with the measured total temerature at the inlet to the vortex tube for length 2 mm. The results of the exerimental model were omared with 3D model. Figures 17 showed the exeriments and CFD analysis of the hot and old outlet temerature of air as a funtion of the arameter ε. It an be seen that for 2mm the maximum hot outlet temerature of 49.7 o C (at ε =.56) is obtained from CFD analysis and about 55.5 o C is obtained from exeriments at the same of ε. And a minimum old outlet temerature of o C (at ε =.139) is obtained from CFD analysis and about o C (at ε =.73) is obtained from exeriments. Temerature [] CFD, T Ex.T [ C] CFD, Th Ex.Th [ C],2,4,6,8 Cold air mass ratio [-] Figure 17 The exeriment and CFD analysis of the hot and old air outlet temerature as a funtion of CAMR. CONCLUSION The exeriments were erformed in tubes with inner diameter of 21 mm, made of glass. The following onstrutional arameters were tested and tried to be otimized. Five different vortex tubes of lengths 2, 4, 6, 8, 1 and 145 mm, with 2 and 4 entrane nozzles and four different diameters of the old outlet, namely 8, 1, 12 and 14 mm were tested. Exerimental results of the hot and old air outlet temeratures of the vortex tube, with the dimensionless old air mass ratio ε and the inlet air ressure as arameters are resented. It is lear from our exeriments that the higher inlet ressure auses the greater temerature differene of the two outlet air streams. And also the analysis shows temerature differene between hot and old air outlet an be maximized by inreasing the length to diameter ratio of vortex tube. The exerimental studies have shown that for 1 mm length vortex tube, the old outlet diameter of 12 mm is ideal for the maximum temerature differene between hot and old air temerature. The investigations have shown that L/D vt = 5 is otimum for ahieving best thermal erformane for 21 mm diameter vortex tube with 2 entrane nozzles. The urose of this study was to reate a CFD model of the vortex tube for use as a design tool in otimizing vortex tube erformane. The CFD model is 3D steady one numerial modeling of vortex tube has been evolved by using the k ε turbulene model. Axial, radial and tangential omonents of the veloity together with the temerature and the ressure fields within the vortex tube are simulated. Preditions from the resent CFD simulations were omared with data obtained from our exeriments under the same geometrial and oerating onditions. REFERENCES [1] Ranque GJ. [1933], Exerienes sure la detente giratoire ave rodutions simultaneesd un ehaement d air hand et d un ehaement d air froid, J Phys Radium, Vol.4, [2] Hilsh R.[1947], The use of the exansion of gases in a entrifugal field as a ooling roess, Rev Si Instrum, Vol. 8, [3] Coerill T.[1998], Thermodynamis and Fluid Mehanis of a Ranque Hilsh Vortex Tube, Ph. D. Thesis, University of Cambridge. [4] Ahlborn B, Keller JU, Rebhan E. [1988], The Heat Pum in a Vortex Tube, Journal Non-Equilib Thermodyn, Vol. 23 No.2, [5] Ahlborn BK, Gordon JM. [2], The Vortex Tube as a Classial Thermodynami Refrigeration Cyle, Journal Alied Phys, Vol. 88, No.6, [6] P.K. Singh, R.G.Tathgir, D. Gangaharyulu, and G.S. Grewal. [24], An exerimental erformane evaluation of vortex tube, Journal of Institution of Engineers, Vol. 84, [7] Saidi M H and Valiour M S. [23], Exerimental modelling of vortex tube refrigerator. Alied thermal engineering. 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