Parametric Review of Ranque-Hilsch Vortex Tubepaper.uscip.us/ajhmt/ajhmt.2017.1012.pdfHence, the tube is widely known as RHVT (Ranque-Hilsch Vortex Tube). The device is simple in construction

Columbia International Publishing American Journal of Heat and Mass Transfer (2017) Vol. 4 No. 3 pp. 115-145 doi:10.7726/ajhmt.2017.1012

Review

______________________________________________________________________________________________________________________________ *Corresponding e-mail: [email protected] 1 Indira College of engineering and Management, Pune, Maharashtra, India-410506 2 Government College of Engineering, Karad, Maharashtra, India-415124

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Parametric Review of Ranque-Hilsch Vortex Tube

Kiran D. Devade1* and Ashok Pise2

Received: 25 April 2017; Returned for revision: 17 June 2017; Received in revised form: 19 June 2017; Accepted: 30 June 2017; Published online: 26 August 2017 © Columbia International Publishing 2017. Published at www.uscip.us

Abstract Vortex tube is the device that separates pressurized fluid into hot and cold fluid streams simultaneously. The scientific community has done extensive experimental and theoretical studies since invention of vortex tube to augment the performance of the tube by varying geometrical and operational parameters; the paper deals with parametric review of all such work. The review takes into account effect of almost 14 parameters on performance of vortex tube. It includes developments in tube geometry like L/D ratio, number of nozzles; hot end valve angle and cold orifice diameter etc. are discussed along with different fluids and operational parameters like CMF and stagnation point etc. The focus of most of the theoretical and experimental studies was to investigate mechanism of thermal separation and geometry optimization. The main objective of this review is to discuss efforts made in order to enhance the refrigeration effect so that, missing links could help for future research. Keywords: Vortex Tube; Energy Separation; Cold Mass Fraction; Stagnation Point; L/D Ratio

Nomenclature Capital Letters A Area, mm2 Cp Specific heat, KJ-kg-1k-1 D Diameter of the tube, mm I irreversibility L length of tube, mm ṁ mass flow rate, kg-sec-1 N Number Q Heat added, dissipated, refrigeration effect, KJ-kg-1 R Gas constant, KJ-kg-1k-1 S entropy generation, KJ-kg-1k-1

Kiran Devade and Ashok Pise/ American Journal of Heat and Mass Transfer (2017) Vol. 4 No. 3 pp. 115-145

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Small Letters d diameter, mm k specific heat ratio t temperature, K Greek Letters ∆ Difference, K γ index of expansion η efficiency Γ (k-1)/k Subscripts a ambient c cold g generation h hot i inlet is isentropic m mean max maximum n nozzle o orifice rf factor s stagnation sa ambient stagnation t tube tc total temperature cold end Abbreviations CMF cold mass fraction L/D length to diameter ratio RPM revolutions per minute PCM Phase Change Materials

1 Introduction Vortex tube produces hot and cold streams of fluid from tangentially supplied compressed fluid. It is one of the non-conventional refrigeration devices. Ranque G.J. (Ranque, 1933) invented the vortex tube. The tube being inefficient it was unnoticed until Hilsch (Hilsch, 1947) started working on enhancing efficiency of the tube. After invention, Ranque’s explanation to the vortex effect was criticised. (Westley, 1954; Brun, 1933) The investigations took momentum following Hilsch work. Hence, the tube is widely known as RHVT (Ranque-Hilsch Vortex Tube). The device is simple in construction and consists of inlet nozzle/s, vortex chamber, vortex generator, tube with valves on hot end, cold tube containing orifice. Figure 1 shows the general construction of the tube and flow pattern inside the vortex tube. The important terms frequently related to vortex tube are as follows.


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1.1 Cold mass fraction It is the ratio of cold mass of fluid to the total mass of fluid supplied at inlet. It is commonly termed as cold fraction, cold mass fraction, or as coefficient of energy separation. 𝐶𝑀𝐹 = �̇�𝑐 �̇�𝑎⁄ (1) 1.2 Total temperature difference It is the difference between the temperature at hot outlet and temperature at cold outlet. Eq.2 Cold end temperature drop is the difference between inlet temperature and cold end temperature. Eq. 3 Hot end temperature rise is the difference between hot end temperature and inlet temperature. Eq.4 ∆𝑡 = 𝑡ℎ − 𝑡𝑐 (2) ∆𝑡𝑐 = 𝑡𝑖 − 𝑡𝑐 (3) ∆𝑡ℎ = 𝑡ℎ − 𝑡𝑖 (4) 1.3 Stagnation Point This is the point at which core stream reverses its direction, and starts moving from hot end to cold end. Beyond this point, there is no energy separation phenomenon. This is the point at which axial flow velocity component is zero.

Fig. 1. Geometry of the vortex tube

1.4 Core and Peripheral stream The separated flow in vortex tube has two elements, the hot flow that occurs at periphery is termed as peripheral stream and the cold flow near tube axis is core stream. 1.5 Isentropic Temperature Difference

∆𝑇𝑠 = 𝑇𝑎 − 𝑇𝑠 = 𝑇𝑎 (1 − (𝑃𝑖

𝑃𝑎)

𝛾−1 𝛾⁄

) (5)

1.6 Isentropic efficiency 𝜂𝑖𝑠 = Δ𝑇𝑐 Δ𝑇𝑠⁄ (6)


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1.7 COP, coefficient of performance COP of vortex tube is the ratio of refrigeration effect to the compressor work required to provide compressed fluid. These are common terms used in performance analysis of vortex tube.

2 Principle of Operation

The working principle of vortex tube is complex in nature. Many theories exist that discuss the mechanism of separation. The mechanism of the working of the vortex tube is as follows. Compressed fluid enters tangentially inside the tube through the nozzle as shown in Fig.2.

Fig. 2. Flow patterns in vortex tube

At entry, the fluid expands and attains high velocity. The particular geometry of the nozzle and the vortex chamber creates swirling flow. Fluid travels in a spiral like motion along the periphery of the tube at around million RPM. The valve located at the end of the tube restricts this swirling flow. The pressure of the fluid near the exit valve increases slightly because of partial closure of the valve. With the valve closure, the flow becomes stagnant and kinetic energy of the flow converts into heat energy. The flow of fluid reverses from slightly high-pressure region created at the hot end of the low-pressure region at entry. The reversed stream flows through the core of the tube. Peripheral high velocity flow surrounds or encompasses the reversed flow stream. The peripheral stream makes the central layer to rotate, thus central layer gains rotation at the expense of heat. This causes heat transfer to take place between reversed core stream and peripheral stream. Therefore, fluid stream passing through the core cools below the inlet temperature of the fluid in the vortex tube, while the fluid stream in forward direction is heated. The cold stream leaves out through the diaphragm on the cold side, while the hot stream escapes through the valve opening on the hot end. The amount of cold mass of fluid and the cold end temperature changes are dependent on opening or closing of the hot end valve. The cold and hot stream emerging out simultaneously has derived attention of many researchers. This separation of streams is also known as thermal separation, energy separation, or vortex effect. The energy separation phenomenon is a mystery to scientific community. Until date, 27 theories explain the energy separation mechanism. Out of these 11 theories, find wide support. Table.1 summarizes major theories evolved so far along with the geometrical and operational parameters used for explanation of energy separation mechanism. Variation of geometrical and operational parameters has significant effect on energy separation.


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The core of this review is to identify effect of all vortex tube related parameters on energy separation. Table 1 Summary of the theories proposed

Year Author Theory Proposed

1931 Ranque [1] Compression and expansion

1947 Hilsch [2] Friction

1948 Kessner [114] Free and forced vortex

1950 Fulton [85] Friction and Turbulence

1951 Scheper[115] Heat transfer

1982 Kurosaka[116] Acoustic Streaming

1983 Stephan and lin[83] Goertler Vortices

1983 Amitani[117] Compressibility

1997 Ahelborn[118] Secondary circulation

2002 Mischner[97] Entropy Generation 2010 Xue[119] Multiple circulation

* Researchers have proposed other 16 theories. Scientific community does not support these.

3 Parametric Review of Vortex Tubes

Energy separation being a complex phenomenon, many researchers has focussed on escalating the performance of vortex tube. Variety of experimental and numerical work is available in the literature. Parametric review majorly focuses on understanding the missing links to propose probable areas of research in coming future. Geometrical, operational and important functional parameters affect the performance of vortex tube. The paper deals with effect of these parameters on performance and their interdependence. 3.1 Effect of Diameter of Tube (D)

Diameter of tube is one of the geometry parameters that have significant effect on performance. Hilsch (Hilsch, 1947) explained the effect of diameter of tube on performance. Hilsch reported that the efficiency of the tube increases, with increase in tube diameter and hence emphasizes use of large diameter tubes. Hilsch reported that the heat loss from centre to periphery become less significant for large diameter tube. In contrast to this, Aljuwayhel et al. (Aljuwayhel, Nellis, & Klein, 2005) reported reduction in energy separation with increase in diameter for the reason that, as diameter of the tube increases, the gradient of angular velocity decreases. Khazei et al. observed (Khazaei, Teymourtash, & Jafarian, 2012) that small diameter tube has worst effect on performance because of low tangential velocities in the tube. Keyes (Keyes, 1960) found that tube diameter, influences vortex strength, as with a reduction in tube diameter the periphery Mach number increases. A very large tube diameter results in lower tangential velocities, both in the core and periphery region, which would produce a low diffusion of mean kinetic energy and low


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temperature separation. As these results are contrast to each other, selection of tube diameter for study was the question. Soni and Thomson (Soni & Thomson, 1975) used EVOP (Evolutionary Operations); this is simplex modification for designing best dimensions. Soni and Thomson claimed that the tube manufactured by these relations has produced maximum temperature drop and efficiency. Suppose for a tube of diameter, D = 26 mm Length of tube, 𝐿 > 45𝐷 Area of Nozzle, 𝐴𝑛 = 0.11 ± 0.01(𝐴𝑡) (7) Area of orifice, 𝐴𝑜 = 0.08 ± 0.01(𝐴𝑡) (8) On the other hand, Takahama (Takahama & Kawashima, Vortex tube optimization studies, 1960; Takahama, 1965) has proposed some correlations based on his experimental results. The geometry relations suggested by Takahama are as follows, (𝑑𝑛 𝐷⁄ ) ≤ 0.2 (9) (𝑁𝑑𝑛

2 𝐷2⁄ ) = 0.16 𝑡𝑜 0.20 (10) 𝑑𝑐 < (𝐷 − 2𝑑𝑛) (11) (𝑑𝑐

2 𝑁𝑑𝑛2⁄ ) ≤ 2.3 (12)

These relations are based on the experimental data and forms conditions for optimum performance of vortex tube. There is a significant variation in calculated dimensions using Soni and Takahama relations. Table 2 shows the estimated dimensions using the relations. The L/D ratio used by Takahama was 55 similar to the one proposed by Soni. In spite of this, the variation in other geometry parameters is around 70 to 90%. This variation in dimensions may contribute to different results. Table 2 Dimensions of different tubes

Researcher length Nozzle dia.(mm) Orifice dia. (mm)

N

Soni 1300 1.5-2 1.6-1.8 2 Takahama 1430 5.2 15.6 4 Hilsch 33 D 2.3 4.3 1 D=19.2 for Hilsch, D=26 for Soni and Takahama

The study shows that there has been very less findings of effect of tube diameter. There is need to depict the effect of change in tube diameter on energy separation since the exact effect is still unknown as the results shown are contradictory. Some relations for optimum design were proposed but these relations result into a significant geometry variation. 3.2 Effect of Length of Tube (L) Length of the tube along which the flow and energy separation occurs happens to be important geometrical parameter. A numerical investigation of Aljuwayhel (Aljuwayhel, Nellis, & Klein, 2005) has shown that there exists an effective length of vortex tube for obtaining the conditions, at which the tube delivers best performance. Increasing or decreasing the tube length beyond this effective length has detrimental effect on performance. Stagnation point in the flow field puts limitation on length of vortex tube. The length of the tube should be sufficient to encompass the stagnation point. Excess tube length does not indicate any energy separation zone ahead to stagnation point. (Oliver,


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Numerical prediction of primary and secondary flows in a Ranque-Hilsch vortex tube, 2008) Takahama and Yokosawa (Takahama & Yokosawa, Energy Separation in Votex Tubes with Divergent Section, 1981) used a diverging tube to reduce the effective length of tube and obtain optimum performance. Celik (Celik, Yilmaz, Kaya, & Karagoz, 2016) et al. have noticed that short length tube are more efficient compared to long tubes. Oliver (Oliver, Boyle, & Reynolds, Computer Aided Study of the Ranque–Hilsch Vortex Tube Using Advanced Three-Dimensional Computational Fluid Dynamics Software, 2006) used reduced length tube based on the position of stagnation point to encompass it within tube length. As stagnation point puts limitation on tube length, there is, need to establish relationship between the flow parameters and stagnation point to fix the length of tube for defined operating parameters. There is still a question on effective length of the tube for best performance, hence in majority of works the fraction usually called as length to diameter ratio (L/D ratio) has been utilised to take into account the effect of these two parameters. Length and diameter have individual effect on performance of the tube. L/D ratio addresses the combined effect of these two parameters. 3.3 Effect of L/D ratio Individual studies on diameter and length of tube affects L/D ratio. In addition, it is not possible to keep L/D constant and predict changes; hence, effect of change in L/D ratio becomes a useful parameter. These experimental studies (Gulyaev, 1966; Dyskin, 1989; Saidi & Allaf Yazdi, 1999; Aydin & Baki, 2006; Saidi & Valipour, 2003; Polisel, Rocha, & Simões-Moreira, 2007) have observed effect of change in L/D ratio. Researchers have tested vortex tube from one to 800 L/D ratio. Majority of the studies (66%) have worked with L/D ratio in the range of 1 to 20. Figure 3 shows the range of L/D ratios used during experimental and numerical analysis of vortex tube. Gulyaev (Gulyaev, 1966) suggested that L/D > 13 for increasing energy separation. Dyskin (Dyskin, 1989) incorporated detwister on cold end side, and proved that length of tube decreases for optimum performance using detwister. Saidi and Valipour (Saidi & Valipour, 2003) optimized L/D ratio for best efficiency, and suggested that for achieving higher efficiency, L/D ratio should be in the range of20 ≤ 𝐿 𝐷 ≤ 55.5⁄ . Aydin (Aydin & Baki, 2006) based on the experimental results suggested that L/D20, but the trend of the results obtained is exactly opposite of few researchers (Hilsch, 1947; Promvonge & Eiamsa-ard, 2005; Devade & Pise, 2016). Cockerill (Cockerill, 1995) experimentally analysed that L/D ratio equal to 60 and 64 produces effective temperature separation. Piralishvili (Piralishvili & Polyaev, Flow and Thermodynamic Characteristics of Energy Separation in a Double-Circuit Vortex Tube An Experimental Investigation, 1996) reported that the kinetic energy losses are minimised, with lower L/D ratios (i.e.1-12). Saidi et al. in (Saidi & Allaf Yazdi, 1999) another analysis has shown that exergy destruction decreases and temperature difference increases, with increase of L/D. Singh et al. reported that, change in L/D ratio does not affect energy separation (Singh, Tathgir, Gangacharyulu, & Grewal, 2004). Markal et al. noticed (Markal, Aydin, & Avci, 2010) that smaller L/D ratio deteriorate performance because of mixing of the cold and hot streams. Effect of L/D ratio was analysed numerically by (Behera U. , Paul, Dinesh, & Jacob, 2008; Dincer, Tasdemir, Baskaya, & Uysal, 2008; Ameri & Behnia, 2009; Bramo & Pourmahmoud, 2010; Pourmahmoud & Bramo, 2011; Kandil & Abdelghany, 2015; Pourmahmoud, Feyzi, Orang, &


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Paykani, 2015; Rafiee & Sadeghiazad, 2014; Linhart, Kalal, & Matas, 2005). Behera (Behera U. , Paul, Dinesh, & Jacob, 2008) has shown that increase in length, increases efficiency by 25% because of displacement of stagnation point. Dincer et al. (Dincer, Tasdemir, Baskaya, & Uysal, 2008) related the performance of tube with stagnation point. The finding of the study was stagnation point depends upon the length and the other geometry of the tube. Marques et al. based on constructal design theory (Marques, Isoldi, Santos, & Rocha, 2012) proposed that optimised performance can be obtained at L/D=5. Bramo and Pourmahmoud (Bramo & Pourmahmoud, 2010) noticed interesting observation that for smaller L/D ratio equal to 8 and 9 stagnation point shifts towards hot end and then shifts towards cold end for L/D ratio>10 to30. Thus, L/D ratio has relation with the stagnation point as seen for length of tube. Kandil and Abdelghany (Kandil & Abdelghany, 2015) reported that the tube performance varies with L/D at different cold mass fractions.

Fig. 3. Frequency of different L/D ratio used for analysis

The results obtained by researchers for different L/D ratio suggests that for every operating condition the optimum tube length varies with cold mass fraction and other geometry parameters. Arriving at a generalised conclusion is not possible since the results of optimum L/D do not match. The results obtained apply to their tested conditions only. This prompts to have a generalised optimum L/D ratio, which could ensure repeatability of results. Stagnation point if bears relationship with L/D ratio, the relation needs to be established. Such a relation may become a tool to design vortex tube for efficient operation. For this, the flow patterns should be analysed at different L/D ratios to capture the stagnation point and exact relationship with L/D ratio. 3.4 Effect of Nozzle Number and Nozzle Geometry (Nn) Nozzle is the entry point through which the fluid enters tangentially in the vortex tube; range of nozzle number used is 1 to 8 (except 7) out of this 2,4 and 6 is common as seen in Fig.4. Similarly, common nozzle geometry is circular and square slot along with the other geometries as seen in

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Fig.5. Extensive experimental and numerical work is evident for number of nozzles and nozzle geometry. Experimental work has been performed by these (Saidi & Valipour, 2003; Promvonge & Eiamsa-ard, 2005; Dincer, Tasdemir, Baskaya, & Uysal, 2008; Takahama, 1965; Takahama & Soga, 1966; Kirmaci, 2009; Dincer, Avci, Baskaya, & Berber, 2010; Eiamsa-ard, Wongcharee, & Promvonge, 2010; Chang, Li, Zhou, & Qiang, 2011; Mohmmadi & Farhadi, 2013) with regard to nozzle number (Avci, 2013; Bovand, Rashidi, & Esfahani, 2016) and nozzle geometry. Researchers have obtained varying results for effect of nozzle numbers on energy separation. Some of these (Saidi & Valipour, 2003; Kirmaci, 2009; Dincer, Avci, Baskaya, & Berber, 2010; Avci, 2013) have observed the decay in performance with increase in nozzle number, the reason of decay is increase in turbulence of the flow. While few (Promvonge & Eiamsa-ard, 2005; Eiamsa-ard, 2010; Bovand, Rashidi, & Esfahani, 2016) have mentioned that increase in nozzle number enhances the energy separation. The increase in energy separation and drop in cold end temperature occurs because of the intense swirl produced with increasing the number of nozzles. Chang (Chang, Li, Zhou, & Qiang, 2011) has observed that the effect of nozzle number on energy separation is dependent on CMF. Three or more number of nozzles performs better for CMF<0.3 and at higher CMF lower nozzle number performs better. Takahama (Takahama, 1965), based on experimental studies proposed that, (Area Ratio) 𝐴𝑛 𝐴𝑡 ≥ 0.087⁄ . Takahama observed that for smaller values of area ratio, the forced vortex formed at core becomes weak.

Fig. 4. Frequency of number of nozzles used for analysis

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Fig. 5. Frequency of nozzle geometries used for analysis

Numerical predictions by these (Dincer, Tasdemir, Baskaya, & Uysal, 2008; Ameri & Behnia, 2009; Pinar, Uluer, & Kırmaci, 2009; Uluer, Kirmaci, & Atas, 2009; Kocabas, Korkmaz, Sorgucu, & Donmez, 2010; Shamsoddini & Nezhad, 2010; Polat & Kirmaci, 2011; Pourmahmoud, Hassanzadeh, & Moutaby, 2012; Rafiee & Rahimi, 2013; Rafiee & Masoud, 2014) have also commented (Rafiee & Sadeghiazad, 2014) on number of nozzles and size of nozzles. The findings were similar to that of experimental results, a mix prediction exists, wherein some researchers (Dincer, Tasdemir, Baskaya, & Uysal, 2008; Uluer, Kirmaci, & Atas, 2009; Kocabas, Korkmaz, Sorgucu, & Donmez, 2010; Polat & Kirmaci, 2011; Pourmahmoud, Hassanzadeh, & Moutaby, 2012) have observed drop in performance of energy separation with increase in nozzle number. Some of these (Ameri & Behnia, 2009; Rafiee & Rahimi, 2013) have noticed increase in cooling capacity/energy separation/ performance for converging shape nozzles. Shamsoddini and Nezhad (Shamsoddini & Nezhad, 2010) have noticed that with increase in nozzle numbers, cold end temperature decreases but power of cooling escalates. Shamsoddini proposed a correlation for power of cooling and nozzle numbers. 𝑄𝑐 = 73.14 + 4553ln (𝑁 − 3.9624) (13) Power of cooling 𝑄𝑐 is total temperature difference between ambient and cold end, 𝑄𝑐 =̇ �̇�𝑐𝑐𝑝(𝑇𝑠𝑎 − 𝑇𝑡𝑐) (14)

The extrapolation of the correlation suggested that, for nozzle number 40 and 1000 the cooling capacity reaches 98% and 100% respectively. It is very impractical to accommodate large number of nozzles along a small tube periphery. The results of Rafiee (Rafiee & Sadeghiazad, 2016) have confirmed increase in energy separation, with increase in nozzle number, but this change is dependent on CMF. This is similar to the findings of Chang (Chang, Li, Zhou, & Qiang, 2011). Figure 5 shows various nozzle geometries used. It shows that very few researchers have worked with spiral and helical nozzles. Pourmahmoud (Pourmahmoud, Hassanzadeh, & Moutaby, 2012) has also commented that the stagnation point moves to the farthest end of hot tube, when helical nozzles are used. Spiral and Helical nozzles improve the performance of vortex tube. The probable reason is

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spiral and helical nozzles guide the flow for smooth tangential entry, there is initial pressure drop in these nozzles, and these nozzles assist in increasing swirl intensity of the flow. The increase in performance with helical and spiral nozzles is around 3 to 4.5% as compared to straight nozzles. The discussion above presents mixed result, the similar results are available for nozzle geometries. Among all geometries tested, convergent spiral entry (Bovand, Rashidi, & Esfahani, 2016; Darokar, Borse, & Devade, 2012; Wu, Ding, Ji, Ma, & Ge, 2007), Archimedean spiral and helical nozzles (Behera U. , Paul, Dinesh, & Jacob, 2008; Ameri & Behnia, 2009; Pourmahmoud, Hassanzadeh & Moutaby, 2013; Alekhin, Bianco, Khai, & Noskov, 2015; Behera U. , et al., 2005; Piralishvili & Fuzeeva, 2005; Pourmahmoud, Jahangiramini, & Izadi, 2013; Rafiee & Sadeghiazad, 2014)are more efficient. The results are CMF dependent, certain operating conditions, show rise in separation, and fall for others. Analysis of displacement of stagnation point in case of spiral and helical nozzles is required along with effect on tangential velocities and swirl intensities. More studies are required in view of comparison between straight and other geometries. The opinion of majority of researchers is nozzle number should not be more than 2 to 3, and contradictions are still there, this needs support of flow field visualisations and findings. Angular entry other than tangential entry needs focus, as it may change the tangential velocity component. Correlation developed applies to specific operating condition and it is impractical. There is a need of generalised correlation to take into account the effect of influencing parameters. CMF puts a limit on the number of nozzles; the explanation for effect of CMF on nozzle number is required. 3.5 Effect of Cold Orifice Diameter (do) Cold orifice diameter through which cold stream leaves has been the topic of interest since the invention. Cold orifice diameter refers to cold diaphragm diameter or cold end diameter. The literature shows efforts taken in optimizing the cold end diameter. These experimental (Hilsch, 1947; Deemter, 1952; Takahama, 1965; Gulyaev, 1966; Borisenko, Safonov, & Yakovlev, 1968; Saidi & Valipour, 2003; Promvonge & Eiamsa-ard, 2005; Aydin & Baki, 2006; Polisel, Rocha, & Simões-Moreira, 2007; Wu, Ding, Ji, Ma, & Ge, 2007) studies have discussed the effect of cold end diameter (Chang, Li, Zhou, & Qiang, 2011; Valipour & Niazi, 2011; Mohmmadi & Farhadi, 2013; Bovand, Rashidi, & Esfahani, 2016) on energy separation. Some studies (Nimbalkar & Muller, 2009) have reported that secondary circulation occurs because of cold orifice dimensions. Hilsch (Hilsch, 1947) in his initial studies has agreed that there exists a favourable diaphragm diameter and smaller diameter diaphragm can produce good separation. Deemter (Deemter, 1952) agreed with Hilsch and noticed that smaller diameter results are in agreement with experiment and large diameter results deviate. According to secondary circulation theory, energy separation is more for larger orifice diameters (𝑑𝑜 𝐷⁄ > 0.5). Gulyaev (Gulyaev, 1966) proposed that when 𝑑𝑜 𝐷⁄ = 0.565 the tube has shown maximum refrigeration capacity hence, 𝑑𝑜 𝐷⁄ should be in range of 0.5 to 0.57. Borisenko et al. (Borisenko, Safonov, & Yakovlev, 1968) results have demonstrated that maximum temperature drop occurs at 𝑑𝑜 𝐷⁄ = 0.45, while tube operates with maximum efficiency at𝑑𝑜 𝐷⁄ = 0.58. It was also noted that with increase in orifice diameter efficiency increases along with CMF. Saidi and Valipour (Saidi & Valipour, 2003) experimentally observed that for 𝑑𝑜 𝐷⁄ < 0.5, cold end temperature difference increases, while at𝑑𝑜 𝐷⁄ > 0.5, cold end temperature difference decreases, this is obvious because of reversal of flow as per secondary circulation theory. Devade and Pise (Devade & Pise, 2014), as shown in Fig.6 obtain the similar results.


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Fig. 6. effect of diameter ratio on energy separation, Devade and Pise [65]

Similar trend is observed by (Promvonge & Eiamsa-ard, 2005) reported that at lower values of diameter ratio, high backpressure exists, and at higher values of diameter ratio, higher tangential velocities exist. Optimum performance is thus occurs at𝑑𝑜 𝐷⁄ = 0.5. Nimbalkar and Muller (Nimbalkar & Muller, 2009) demonstrated the reasons for using,𝑑𝑜 𝐷⁄ > 0.5 by showing existence of secondary circulation at smaller diameters. Figure 7 shows the schematic of occurrence of secondary circulations inside the flow field. Devade and Pise (Devade & Pise, Optimization of thermal performance of Ranque Hilsch Vortex Tube: MADM techniques, 2016) have shown that for tested L/D ratios, diameter ratio should be greater than 0.5 to obtain optimized performance. Marques et al. based on constructal design theory (Marques, Isoldi, Santos, & Rocha, 2012) proposed that optimised performance occurs at𝑑𝑜 𝐷⁄ = 0.4; this is in contrast to the experimental evidence. Numerical studies carried out so far have (Deemter, 1952; Sibulkin, 1962; Soni & Thomson, 1975; Aljuwayhel, Nellis, & Klein, 2005; Behera U. , Paul, Dinesh, & Jacob, 2008; Ameri & Behnia, 2009; Khazaei, Teymourtash, & Jafarian, 2012; Rafiee & Masoud, 2014; Liu & Liu, 2014; Kandil & Abdelghany, 2015) successfully observed secondary flows and have commented on orifice diameter. Sibulkin (Sibulkin, 1962) during his studies with vortex tube and orifice diameter concluded that changing𝑑𝑜 𝐷⁄ < 0.5 has very less significant result on vortex flow. Correlations proposed by Soni and Thomson (Soni & Thomson, 1975) have already been mentioned with earlier section of tube diameter. Ameri and Behnia (Ameri & Behnia, 2009) proposed the optimum 𝑑𝑜 𝐷⁄ =0.58 for obtaining highest efficiency. Kandil (Kandil & Abdelghany, 2015) investigated that secondary circulations occur for certain range of do/D, i.e. 0.368 to 0.4561. Figure 8 shows the diameter ratio used in various experimental and numerical studies. It indicates that most of the theoretical studies have used𝑑𝑜 𝐷⁄ ≥ 0.5, almost 59% studies have used diameter ratio greater than equal to 0.5. The discussions above clearly indicate that cold orifice diameter is responsible for

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secondary circulations inside vortex tube. Intensity of secondary circulation is more at 𝑑𝑜 𝐷⁄ < 0.5 , but this ratio can produce maximum cold temperature drop at low CMF. Hence, it is clear that vortex tube can provide either high CMF or lower ∆Tc. At 𝑑𝑜 𝐷⁄ > 0.5, cold temperature drop reduces because of rise in CMF. Thus cold orifice diameter becomes significant parameter in the design of vortex tubes. The focus on optimizing the low temperature with higher CMF is the requirement. Investigation is required to obtain optimum combination of CMF and ∆Tc. If it happens simultaneously, there could be substantial enhancement in the efficiency of vortex tube.

3.6 Effect of Tube Angle (ϕ)

Tube angle is one of the performance influencing parameters of vortex tube. Researchers have worked with straight, diverging, converging, curved and combination of these geometries. Figure 9 shows the various tube geometries used by researchers during research. The literature indicates that there were numerous studies performed on straight tube; very few studies have been reported with converging (Rafiee & Sadeghiazad, Experimental Study and 3D CFD Analysis on the Optimization of Throttle Angle for a Convergent Vortex Tube, 2016; Herrada, Perez-Sabroid, & Barrero, 1999) and diverging (Gulyaev, 1966; Borisenko, Safonov, & Yakovlev, 1968; Takahama & Yokosawa, 1981; Piralishvili & Polyaev, 1996; Poshernev & Khodorkov, 2004; Chang, Li, Zhou, & Qiang, 2011; Devade & Pise, 2016) tubes, tubes with curved geometry (Valipour & Niazi, 2011; Bovand M. , Valipour, Dincer, & Tamayol, 2014; Bovand M. , Valipour, Eiamsa-ard, & Tamayol, 2014) and combination of straight and divergent/convergent sections (Devade & Pise, 2012; Devade & Pise, 2014; Guen, et al., 2013), even bent (Takahama & Tanimoto, 1974)vortex chambers. Almost 83% researchers have used straight tubes and 17% have used the other angular geometry.

Fig. 7. Secondary circulations in vortex tube

Gulyaev (Gulyaev, 1966) used divergent vortex tube in order to shorten the length of the tube. Gulyaev reported that tubes with 40 divergence angle should have L/D 13 for obtaining better temperature drop. Diverging section tubes have shown rise in performance by 20-25% as compared to straight tube, this is because of vortex deceleration as observed in divergent tubes. Borisenko (Borisenko, Safonov, & Yakovlev, 1968) also proposed that the reason behind performance enhancement in diverging tube is that diverging tube adopts volume changes of gas and mixing of cold and hot stream is minimised in diverging tubes. Takahama (Takahama & Yokosawa, Energy Separation in Votex Tubes with Divergent Section, 1981) reported that in divergent section tubes, the forced vortex region is wider as compared to straight tube; the wider


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section contributes in energy separation. Chang et al. (Chang, Li, Zhou, & Qiang, 2011) reported that in divergent tubes the swirling velocity decreases, at reduced swirl velocity the friction losses and internal viscous losses are minimised, thus efficiency increases. 40 divergences produces maximum cooling efficiency, this is in support of Gulyaev (Gulyaev, 1966). Similar findings are observed by (Devade & Pise, 2016) for divergence angle. Researchers have used diverging geometries (Borisenko, Safonov, & Yakovlev, 1968) on cold and hot end side along with tube. Converging tubes on the other hand provide high cooling efficiency along with higher values of CMF in contrast to diverging tubes. In diverging tubes, CMF in the range of 0.2-0.3 gives best performance of energy separation. The same range increases to 0.3-0.45 in case of convergent tubes. (Rafiee & Sadeghiazad, Experimental Study and 3D CFD Analysis on the Optimization of Throttle Angle for a Convergent Vortex Tube, 2016; Devade & Pise, 2014). In case of a curved tube as noted by (Valipour & Niazi, 2011) the performance declines. The findings suggest that straight tubes are more efficient as compared to curved tubes. Numerical studies by these researchers (Herrada, Perez-Sabroid, & Barrero, 1999; Pouraria & Zangooee, 2012; Bovand M. , Valipour, Dincer, & Tamayol, 2014; Bovand M. , Valipour, Eiamsa-ard, & Tamayol, 2014; Alekhin, Bianco, Khai, & Noskov, 2015; Devade & Pise, 2016; Rafiee & Sadeghiazad, 2016) have also contributed in understanding of effect of divergence, convergence angle. Pouraria and Zangooee (Pouraria & Zangooee, 2012) confirmed that performance of tube improves with divergence angle. Cold mass fraction limits the optimum divergence angle for maximum efficiency. Curved tubes were analysed by Bovand et al (Bovand M. , Valipour, Dincer, & Tamayol, 2014; Bovand M. , Valipour, Eiamsa-ard, & Tamayol, 2014), and the study suggests that straight tubes give superior performance compared to curved tube. Converging tube analysis by Rafiee (Rafiee & Sadeghiazad, 2016) reported that the pressure drop in convergent tube is 5% more than that of straight tube, and the flow separation is dominant, hence cooling and heating efficiencies are higher. Devade and Pise (Devade & Pise, 2014) reported similar findings, that converging tubes optimise the CMF and ∆Tc.

Fig. 8. Diameter ratio of do/D utilised

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Fig. 9. Types of tube geometry used for analysis

The discussion presents that the unfocussed area of vortex tube is the divergence angle of the tube. Divergence angle happens to be one of the parameters that help to improve efficiency in the range of (5-25%). CMF puts limitation on use of divergence and convergence angle, thus there is need to define the optimum performance limits for converging and diverging tubes. As noticed CMF restricts the use of L/D, number of nozzles, divergence angle, cold orifice diameter, it is therefore required to find the optimum performing combination of these parameters. The numerical analysis with diverging tube and straight tube shows the dependence of tube performance on geometrical parameters. The reasons of enhancement in performance with the use of divergent angle need attention. In addition, the effect of divergence angle on tube length reduction needs experimental and numerical evidence. 3.7 Effect of Hot End Valves/Plug/Cones (ϴ)

Plugs used on hot end side restrict the peripheral flow. These plugs/valves/cone angle and geometry have considerable effect on energy separation. The positions of these valves/plugs determine the cold mass fraction and in turn the energy separation. Experimental and numerical studies have demonstrated the effect of valves on flow field and overall performance. Figure 10 shows the various valve angles researchers used during analysis.

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Fig. 10. Hot end valves of different angles used by researchers

Many researchers during their experimental studies (Marshall, 1977; Dyskin, 1989; Aydin & Baki, 2006; Dincer, Baskaya, Uysal, & Ucgul, 2009; Markal, Aydin, & Avci, 2010; Dincer, Yilmaz, Berber, & Baskaya, 2011; Devade & Pise, 2012; Im & Yu, 2012; Avci, 2013; Devade & Pise, 2014) have used different valves (Devade & Pise, 2016; Bovand, Rashidi, & Esfahani, 2016) and shapes. Dyskin (Dyskin, 1989) used detwister on hot end and observed that the heating effect increase by 3 to50. Detwister improves swirling intensity and hence both heating as well as cooling performance of tube enhances. Dincer et al. used conical valves (Dincer, Baskaya, Uysal, & Ucgul, 2009) and reported that maximum temperature difference occurs at 30 and 600 valve angle. Markal et al. examined (Markal, Aydin, & Avci, 2010) the valve angles effect and reported that at higher valve angles, flow becomes more unstable because of sudden change in direction of hot streams. Dincer et al. (Dincer, Yilmaz, Berber, & Baskaya, 2011) investigated the cascading effect on hot end, and the results state that cascading improves efficiency of the system. Devade and Pise (Devade & Pise, 2012) utilised the effect of valve angles to enhance efficiency of the tube, and observed that 600 angles valve was best for heating and 450 angles valve improves overall performance (cooling as well as heating).

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Fig. 11. Hot end configurations

Rafiee et al. (Rafiee & Sadeghiazad, 2016) demonstrated the influence of valve angle on energy separation. The results of Rafiee et al. show that the valve on hot end was responsible in moving the stagnation point towards cold end, thus affecting the energy separation. The highest tangential velocity and pressure drop occurs for valve of 600 angles. In other configurations, to improve the performance of vortex tube, researchers’ used various arrangements. Figure 11 shows the other geometry configurations used by researchers. In these cascade is re-introduction of the hot flow as inlet to another vortex tube, some of the researches have tried insulation and cooling with water jacket, while detwister is used on hot end to guide the flow axially reducing losses. Among this insulated tube (Promvonge & Eiamsa-ard, 2005) has shown rise in performance by 5%, while cooling on hot tube (Eiamsa-ard, Wongcharee, & Promvonge, 2010) has shown 4.7 to 9% enhancement in cooling efficiency. Detwister improves heating by 3 to 50. The discussion above indicates that, 450 and 600 angles valve are more efficient and frequently used by researchers. The discussions above state the importance of valve angle on energy separation. The results vary depending upon valve angle and hot end configurations. The important is the position of stagnation point. Since the position of stagnation point changes with valve angle, the exact flow physics of stagnation point formation and its movement is the major issue to address. Cooling with use of PCM can also be another area to focus. 3.8 Effect of Cold Mass Fraction (CMF)

Cold mass fraction is the ratio of cold mass of fluid to the total mass of fluid supplied. The discussion so far has many times witnessed cold mass fraction exerts limitation to the performance enhancement with almost all of the geometry parameters. Thus, CMF happens to be the significant parameter governing the tube performance.

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The effects of CMF on energy separation and exergy destruction were studied by Saidi and Yazdi (Saidi & Allaf Yazdi, 1999) and it was found that the device performs better at CMF=0.7, as the exergy destruction is minimum. Promvonge and Eiamsa-ard (Promvonge & Eiamsa-ard, 2005) experimentally noticed that the highest cold end temperature drop is obtained at CMF=0.345 for tubes with and without insulation. However, it is an observation that at highest cold end temperature drop the tube performance significantly reduces, the reason behind drop in performance is the lower CMF obtained. A correlation proposed by Hilsch (Hilsch, 1947) for temperature drop in terms of CMF is as follows,

∆𝑡𝑐

∆𝑡𝑐,𝑚𝑎𝑥= 1.0916(𝐶𝑀𝐹)3 − 4.2581(𝐶𝑀𝐹)2 + 2.8563𝐶𝑀𝐹 + 0.4641 (15)

∆𝑡𝑐

∆𝑡𝑐,𝑚𝑎𝑥= 5.78(𝐶𝑀𝐹)3 − 9.8(𝐶𝑀𝐹)2 + 4.4𝐶𝑀𝐹 + 0.39 (16)

Devade and Pise (Devade & Pise, 2016) also proposed relation for Temperature drop as, ∆𝑡𝑐

∆𝑡𝑐,𝑚𝑎𝑥= 1.0916(𝐶𝑀𝐹)3 − 4.2581(𝐶𝑀𝐹)2 + 2.8563𝐶𝑀𝐹 + 0.464 (17)

The correlation proposed by Stephan and Lin (Stephen, Lin, Durst, Huang, & Seher, 1983) was, ∆𝑡𝑐

∆𝑡𝑐,𝑚𝑎𝑥= 0.815(𝐶𝑀𝐹)3 − 3.101(𝐶𝑀𝐹)2 + 1.54𝐶𝑀𝐹 + 0.792 (18)

Cockerill also have proposed such relationship between CMF and temperature ratio, ∆𝑡𝑐

∆𝑡𝑐,𝑚𝑎𝑥= 3.23(𝐶𝑀𝐹)3 − 7.97(𝐶𝑀𝐹)2 + 3.97𝐶𝑀𝐹 + 0.39 (19)

The correlation dictates the effect of CMF on temperature drop. Figure 12 shows the effect of CMF on temperature separation. It indicates that maximum temperature drop occurs at a particular CMF (Devade & Pise, 2016). i.e. maximum cold end temperature drop is observed between CMF=0.36 to 0.44. There is good agreement of the results of all the correlations. The conclusion from the discussion in this section and the earlier sections is that, cold mass fraction significantly affects the operation of vortex tube. It limits the energy separation. Cold mass fraction puts limit on the L/D ratio; do, Ø, Nn, valves on hot end side. It is also interesting to know that as inlet pressure increases, the cold mass fraction reduces significantly. Moreover, with increase in CMF, COP of the tube increases but cold end temperature drop reduces, and hot end temperature rise increases. (Devade & Pise, 2016) The optimum operating cold mass fractions of straight tube, diverging tube, converging tubes may be different. As per the study of the authors, it is possible to obtain optimum cold mass fraction and cold end temperature drop together, if converging tubes are used (Devade & Pise, Investigation of Refrigeration Effect Using Short Straight-Divergent Tubes, 2012).


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Fig. 12. Effect of CMF on temperature separation

In order to enhance the performance of the tube, the prime requirement is to obtain maximum CMF. CMF governs the mass flow rate of cold and hot streams at respective outlet. Cold mass fraction is the only deciding parameter that could provide us the optimized geometry for attaining the best result in absence of mechanism of separation. Since cold mass fraction is the limiting parameter, the approach of designing vortex tube should be CMF based. CMF itself would figure out the combination of geometry and related parameters that would achieve best performance. Studies on tube designed in this fashion are required in the coming future. The comparison of optimum CMF for straight tube, diverging tube, and converging tubes is the requirement in coming future. Dimension similarity is the base for such comparisons, i.e. L/D ratio, Nozzle number, diameter ratio and valve geometries stand as fixed. Cold mass fraction affects the position of stagnation point. Hence, close observation of flow field is required to predict influence of CMF on stagnation point.

3.9 Effect of Stagnation Point

The earlier discussions have made it clear that stagnation point occurs in the flow field. The stagnation point is not fixed and it keeps moving with change in operating parameters. Stagnation point in the flow field is the point on axis at which the axial velocity of the flow becomes zero. Baker (Baker, 1956)named stagnation point during his initial findings as turnaround point.

The position of stagnation point on axis decides the magnitude of energy separation. The literature has commented on stagnation points and its effects. Baker (Baker, 1956) during his experiments with starch as fluid observed the presence of stagnation point in the flow field, which he called as turn-around point. This point leaves a hot spot on the walls of the tube. Baker noticed that opening of hot end valve makes the point to move beyond tube limits. Stagnation point occurs irrespective of the inclination of the tube.

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Stephan and Lin (Stephen, Lin, Durst, Huang, & Seher, 1983) mentioned that the variation in wall temperature could help to locate the stagnation point on axis. Fulton (Fulton, 1950) has observed that beyond the stagnation point (region close to hot end), axial velocity varies with radius i.e. (low at axis and high at periphery). The wall in this region is hotter, and highest temperature on wall attributes to exact location of stagnation point on axis. Camire (Camire, 1992) has noted that when CMF is more, stagnation point is near hot end, conversely when hot mass flow rate is more stagnation point is close to cold end. The position of stagnation point governs cooling and heating effect. At optimum CMF, stagnation point is located within the tube, on axis. Rafiee et al. (Rafiee & Sadeghiazad, 2016), has demonstrated that increase in hot end valve angles, improves the optimum CMF because of displacement of stagnation point towards cold end. Bramo and Pourmahmoud (Bramo & Pourmahmoud, 2010) have also provided the relation between L/D ratio and stagnation point. The discussion above demonstrates the role of stagnation point on working of vortex tube. For efficient working of the tube, stagnation point should occur close to hot end valve. The vortex tube should be designed such that, stagnation point should occur near to hot end valve so that highest efficiency can be obtained. Fixed stagnation point close to hot end valve delivers maximum cooling effect and when it is near cold end side, tube delivers maximum heating effect. The vortex tube can effectively perform in both the modes, provided the stagnation point location is fixed. 3.10 Effect of Inlet Pressure (Pi) The effect of inlet pressure on performance of vortex tube is quiet obvious, and all the studies so far have agreed upon it. As the pressure at the inlet increases, the temperature separation tends to increase. With increase in inlet pressure CMF reduces (Devade & Pise, 2016). The exergy loss also increases with increase in supply pressure (Kirmaci, 2009). In addition, the common observation is that vortex tube delivers highest efficiency at moderate operating pressures. In such case when vortex tube operates even at low pressure (Ahlborn, Camire, & Keller, 1996), the energy separation exists. However, until date very few researchers have worked on low-pressure vortex tubes. The effect of CMF and occurrence of stagnation point in low-pressure tubes need support from scientific community. Pressure range commonly used is 0.3 to 13 bars; in this range, most of the researchers have used pressure from 2 to 11 bars. Pressure for natural gas as fluid at entry is upto 42 bars. 3.11 Effect of Working Fluids Literature shows experimental and numerical results with varieties of fluids in vortex tube to understand the effect of fluid properties on performance of the tube. The more commonly used fluid for the experimental and numerical investigations is air. In addition, various other fluids like water (Balmer, 1998), monoatomic (Linderstr0m-Lang, 1965; Gulyaev, 1966), diatomic (Baker, 1956; Aydin & Baki, 2006; Kirmaci, 2009; Agarwal, Naik, & Gawale, 2014), tri-atomic gases, two-phase fluids (Collins & Lovelace, 1979; Takahama, Kato, & Yokosawa, 1979), mixtures of gases, steam and organic and inorganic refrigerants (Han, et al., 2013) have been used. Numerical studies (Farouk, Farouk, & Gutsol, 2009; Pinar, Uluer, & Kırmaci, 2009; Polat & Kirmaci, 2011; Khazaei, Teymourtash, & Jafarian, 2012; Baghdad, Ouadha, & Addad, 2012; Thakare & Parekh, 2014) are also available with different fluids mentioned above in the literature. Figure 13 shows the frequency of use of various fluids, it can be seen that majority of research has been performed on air as working fluid. Energy separation and efficiency for triatomic gas (Agarwal, Naik, & Gawale, 2014) like CO2 is 15% more as compared to air and diatomic gas N2 because of higher molecular weight and low


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specific heat. In contrast to this, Khazei et al. (Khazaei, Teymourtash, & Jafarian, 2012) observed higher energy separation for gases, with lower molecular weight and high specific heat. The energy separation (Thakare & Parekh, 2014) increases with increase in thermal diffusivity and thermal conductivity. The typical temperature separation for few gases is as shown in Fig. 14. As compared to other gases, the temperature separation for helium is more. Among variety of fluids tested by the researchers, results for few fluids are presented for illustration.

Fig. 13. Fluids used for analysis

Fig. 14. Cold end temperature drop for different fluids at Pi = 300KPa [66, 90, and 93]

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In all the working fluids, the energy separation exists. The performance of each fluid depends largely on the fluid properties like specific heat ratio, thermal conductivity, kinematic viscosity, thermal diffusivity and inherent throttling properties like boiling point, latent heat of vaporisation etc. Studies with different fluids are required to study the effect on energy separation at low pressures. The steam or two-phase mixtures (Collins & Lovelace, 1979; Takahama, Kato, & Yokosawa, 1979) at dryness fraction <0.8 do not show any energy separation, this conclusion needs to be analysed for reasons of non-separation. 3.12 Exergy Studies Exergy is the available energy; many researchers handled analysis of exergy in vortex tube. Experimental (Saidi & Allaf Yazdi, 1999; Kirmaci, 2009; Dincer, Avci, Baskaya, & Berber, 2010; Dincer, Yilmaz, Berber, & Baskaya, 2011) and numerical (Baghdad, Ouadha, & Addad, 2012; Mischner & Bespalov, 2002) exergy analysis is performed to present cooling and heating performance in terms of exergy. Exergy efficiency of the tube is the capacity to utilise the available energy. Saidi developed (Saidi & Allaf Yazdi, 1999) a model for exergy analysis of vortex tube. The equation for rate of exergy generation is,

𝑆𝑔 = 𝑚𝑖 (𝑐𝑝𝑙𝑛(𝑇ℎ 𝑇𝑐⁄ )1−𝑐𝑚𝑓

1+(1−𝑐𝑚𝑓)(𝑇ℎ𝑇𝑐

−1)+ 𝑅𝑙𝑛

𝑃𝑖

𝑃𝑐) (20)

Saidi (Saidi & Allaf Yazdi, 1999) noticed that exergy destruction is minimum at CMF=0.7 and exergy efficiency increases, with nozzle diameter. Kirmaci (Kirmaci, 2009) mentioned that exergy efficiency of oxygen is more as compared to air and exergy loss increases with pressure at inlet. Dincer (Dincer, Yilmaz, Berber, & Baskaya, 2011) et al. observed that exergy efficiency is dependent on inlet pressure, CMF and velocity of cold end stream. Dincer also concluded that the exergy efficiency of cascade system is 80 to 90% more than single RHVT. Celik (Celik, Yilmaz, Kaya, & Karagoz, 2016) et al. introduced the irreversibility factor for vortex tube. The irreversibility factor is,

𝐼𝑟𝑓 =�̇�𝑖

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1

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𝐶𝑀𝐹

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Celik concluded that the range of irreversibility is from 0.69 to 2.2, the process in vortex tube is irreversible and the irreversibility increases with pressure at inlet. Mischner and Bespalov (Mischner & Bespalov, 2002) proposed entropy generation theory as justification to energy separation process inside vortex tube. The above discussion shows that the less attended exergy analysis is also significant parameter. Efforts are required in view of increasing exergy efficiency of vortex tube. The irreversibility’s for geometry variations in tube needs attention. 3.13 Turbulence Models Until date a variety of approaches applied for theoretical reasoning of energy separation are available in the literature. Until 1990’s maximum study to know physics used analytical approach to solve the equations by making some assumptions. After invent of numerical methods, the use of such methods has become common. Researchers started simulating the vortex tube phenomenon numerically. Experimental results ensure the validity of the numerical work. As the flow mechanism is complex including turbulent eddies, swirl effects, viscosity effects etc. researchers have tried various numerical models. Figure 15 shows the frequency of use of various turbulence models for numerical analysis of the vortex tubes,


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Fig. 15. Turbulence models used for vortex tube analysis

Depending upon the parameters involved in the flow physics various turbulence models were used (Gutsol, 1997; Bezprozvannykh & Mottl, 1999; Bezprozvannykh & Mottl, The Ranque-Hilsch Effect: CFD Modeling, 2002; Aljuwayhel, Nellis, & Klein, 2005; Behera U. et al., 2005; Linhart, Kalal, & Matas, 2005; Eiamsa-ard & Promvonge, 2006; Wang, et al., 2006; Oliver, Boyle, & Reynolds, 2006; Skye, Nellis, & Klein, 2006) to capture the physics. The use of turbulent models for analysis of vortex flow (Eiamsa-ard & Promvonge, 2007; Farouk & Farouk, 2007; Akheshmeh, Pourmahmoud, & Sedgi, 2008; Behera U. , Paul, Dinesh, & Jacob, 2008; Oliver, 2008; Pourmahmoud & Akhesmeh, 2008; Ameri & Behnia, 2009; Farouk, Farouk, & Gutsol, 2009; Secchiaroli, Ricci, Montelpare, & D’Alessandro, 2009; Bramo & Pourmahmoud, 2010) began in 1990. Numerical results for varieties of different models (Dutta, Sinhamahapatra, & Bandyopdhyay, 2010; Shamsoddini & Nezhad, 2010; Baghdad, Ouadha, & Addad, 2012; Khazaei, Teymourtash, & Jafarian, 2012; Pourmahmoud, Hassanzadeh, & Moutaby, 2012; Pourmahmoud, Jahangiramini, & Izadi, 2013; Rafiee & Rahimi, 2013; Rafiee & Masoud, 2014; Rafiee & Sadeghiazad, 2014) are available for their efficiency and closeness to realistic situation inside the vortex phenomenon. Few models were successfully captured flow phenomenon and occurrence of secondary flow, stagnation point, hot and cold separation etc. Yet the clear understanding of the phenomenon (Liu & Liu, 2014; Bovand M. , Valipour, Eiamsa-ard, & Tamayol, 2014; Bovand M. , Valipour, Dincer, & Tamayol, 2014; Alekhin, Bianco, Khai, & Noskov, 2015; Thakare & Parekh, 2014; Thakare, Monde, Patil, & Parekh, 2015) is still undefined. Nevertheless, these studies helped to understand the effect of all geometric and operating parameters on the performance of the vortex tube. Some of the interesting studies are these, where the stagnation point was successfully located and the displacement of stagnation point (Bramo & Pourmahmoud, 2010) captured. Along with this, the location of stagnation point was marked with reference to the highest wall temperature. Then the comparison of numerical turbulent models (Dutta, Sinhamahapatra, & Bandyopdhyay, 2010) demonstrates results to identify the best model getting close to experimental results. The numerical analysis of curved tubes (Bovand M. , Valipour, Dincer, & Tamayol, Numerical analysis of the curvature effects on RanqueeHilsch vortex tube refrigerators, 2014; Bovand M. , Valipour, Eiamsa-

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ard, & Tamayol, 2014) presents interesting findings of stagnation point and energy separation in curved geometry. The effect of hot end vales was analysed (Rafiee & Sadeghiazad, 2016) with reference to the stagnation point and the results indicate the effect of displacement of stagnation point on energy separation. Out of the different turbulence models, k-є, standard k-є, RNG k-є and some studies with LES provide better results. The results of k-є, standard k-є, RNG k-є and LES are in good agreement with the experimental results. Despite of detailed work carried out; with the numerical studies, so far physics of vortex tube operation is still a mystery. This mystery needs to be resolved. This indicates that there is need to develop a model that can clearly simulate the vortex tube phenomenon. 3.14 Other Related Theoretical Work Available literature on vortex tube also mentions used of various optimization techniques other than the numerical studies. These methods include, ANN (Artificial Neural Network) (Dincer, Tasdemir, Baskaya, & Uysal, 2008; Kocabas, Korkmaz, Sorgucu, & Donmez, 2010; Uluer, Kirmaci, & Atas, 2009; Korkamaz, Gumusel, & Markal, 2012), EVOP (Evolutionary Operations) (Soni & Thomson, 1975) Taguchi and ANOVA(Analysis of Variance) (Pinar, Uluer, & Kırmaci, 2009; Kumar, Padmanabhan, & Sarma, 2014), ODFS (Output Dependent Feature Scaling) ANFIS (Adaptive Network based Fuzzy Information System) (Polat & Kirmaci, 2011), RSM (Roughness Surface Methodology) (Bovand M. , Valipour, Dincer, & Eiamsa-ard, 2014) and MADM (Multiple Attribute Decision Making) (Devade & Pise, 2016). These are the few studies carried out to perform the theoretical optimization of the vortex tubes. There are few correlations available with regard to vortex tube. Other optimization methods like GA (Generic Algorithm), ABC (Ant Bee Colony), TLBO (Teaching Learning Based Algorithm), and PSO (Particle Swarm Optimization) also need a thought for their application to vortex problem. The literature shows that the objective function for tubes is clear and available. Use of this heuristic approach for optimization of vortex tube also needs attention of scientific community.

4 Conclusion The review of literature and the discussions made in each section illustrates that still there are many areas to focus in view of optimization of vortex tube. Studies for estimating the relationship between operating parameters and stagnation point are required. Stagnation point determines the length of tube and position of stagnation point inside the tube in turn is dependent on valve geometry and cold mass fraction. This inter-dependence of parameters needs mathematical formulation. Identifying the governing relationships between operating and geometrical parameters is the need of clean and green energy objectives. Cold mass fraction happens to be the most critical parameter of the vortex tube, and it governs/ dictates entire geometrical design of the tube. Cold mass fraction puts limitation on the effective length of tube and diameter of the tube, in turn the L/D ratio for optimum performance. Cold mass fraction also limits the number of nozzles. There exists an optimum value of cold mass fraction up to, which a particular nozzle number gives highest performance and then it declines. Increase in pressure reduces cold mass fraction and enhances the cooling by reducing cold end temperature. The conventional approach can get close to either higher CMF or low temperatures. Achieving both results simultaneously is the major task.


139

A maximum cold mass fraction is possible, when the converging type tubes are used, but there is need of more studies focussed on converging tubes and angle of convergence. The literature shows that diverging tubes assist in shortening the tube length. The relationship between divergence angle and tube length for best performance needs to be developed. Studies with different fluids have shown the temperature separation irrespective of thermo-physical and chemical property differences. The behaviour of temperature separation is dryness fraction dependent, this need experimental and numerical evidence. The numerical studies have come up with interesting results but still the exact physics cannot reveal. Varieties of turbulent models dictate the need of a complete model that can simulate realistic conditions to understand the physics. Hence there is need to develop a model, that can simulate the realistic flow conditions and can provide vivid demonstration of the flow field. Any small attempt in these directions would be a great contribution to knowledge. This may help to re-invent the Maxwell-Demon.

Acknowledgement

Authors are thankful for the efforts taken by the scientific community towards realizing the vortex tube phenomenon. This paper would never have been possible without their contributions.

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Documents

Parametric Review of Ranque-Hilsch Vortex Tubepaper.uscip.us/ajhmt/ajhmt.2017.1012.pdfHence, the tube is widely known as RHVT (Ranque-Hilsch Vortex Tube). The device is simple in construction