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Performance characteristics of energy separation in a steam-operated vortex tube
omo-7225/79/0601-0735182.00/0
PERFORMANCE CHARACTERISTICS OF ENERGY SEPARATION IN A STEAM-OPERATED VORTEX TUBE HEISHICHIROTAKAHAMAt and HITOSHI KAWAMURAS Departmentof MechanicalEngineering,Faculty of Engineering,Nagoya University, 1, Furo-cho,Chikusaku, Nagoya, 464, Japan SEIZO KATOS Departmentof Mechanical and Materials Engineering,School of Engineering,Mie University, 1515, Kamihama-cho,Tsu, 514, Japan
HAJIME YOKOSAWA’ Collegeof GeneralEducation,Nagoya University Abstract-Energy separationperformanceof a steam-operatedvortex tube is experimentallyinvestigated, and some reasonable criteria and expressions to estimate the energy separationperformanceare also introduced.The performancecharacteristicsdefined by the above expressions are the same as those of ideal gas in the high superheatedregion,and are well expressed independentlyof the degreeof superheat, total mass flow rate and dischargeresistance. When steam is in the wet region at the nozzle outlet, the performanceconsiderablydecreases because of the energy waste from moisture vaporization.And no energy is separated when the dryness fraction is less than approximately0.98. Some technical data includingthe optimumoperatingconditionsare also offered.
INTRODUCTION
stored in a compressed gaseous fluid is easily separated into higher and lower energy flows by using the Ranque-Hilsch vortex tube effect. The vortex tube as a mechanical device has the advantage of very simple structure with no moving element. There is current interest, therefore, in its practical applications, and it may be reasonable to employ vortex tubes for quick start-up of steam power generation units. A vortex tube, for example, may be installed between the boiler and the turbine on restarting the units stopped while the demand of electric power decreases at night and over the weekend. The hot flow extracted from the vortex tube is led into the turbine nozzles in order to produce more quickly the optimum blade temperature, while the cold one serves for heat recovery in the reheater or in the condenser. There are relatively many studies devoted to vortex tubes which have been operated with air as a working fluid. These results characterize the ideal case of vortex tubes, because air behaves more like ideal gas than steam or vapor. Starostin and Itkin[ll, and Metenin[2] have conducted experiments with high superheated steam, and Martynovskii and Alekseev[3] with humid air. In practice, however, these experimental results are not so extensive as to provide applicable data for steam operated vortex tube design and for optimum operating conditions. The present research is concerned with the performance characteristics of overall energy separation by using steam as a working fluid. The systematic experiment covers a wide range of steam conditions from the high superheated state (enough to produce the ideal grade performance as air) to the wetted state (without causing any energy separation like liquid). The purpose of the present experiment is to confirm the availability of the energy separation when using superheated steam, to establish criteria to express generally the energy separation performance, and to present technical data including the optimum operating conditions. Furthermore, the undesirable effect of wetness on the energy separation performance is qualitatively investigated, together with the estimation of the critical dryness fraction necessary to bring about the effective energy separation. THE ENERGY
tprofessor. SResearchAssociate. #Assoc. Professor. “ResearchAssociate. 735
736
H. TAKAHAMA THE
et al.
EXPERIMENTS
Vortex tube design
Only a few attempts have been made to provide optimal design conditions for vortex tubes even operated with air[A 51.Takahama[S, 61 recommends the following geometrical dimensions derived from his systematic experimental runs with air: d,lD S 0.2,
NdgD’ = 0.16-0.20, d, < D - 2d,,
d:INdS, s 2.3
(1)
where d,, is the diameter of nozzles, D the vortex chamber diameter, d, the diameter of the cold orifice and N the number of nozzles. Taking into consideration that very high superheated steam possesses nearly the same thermal properties as air, we employ the dimensions satisfying eqn (1). Considering the boiler capacity, the heat dissipation loss and the thermal stress of materials, the vortex tube in the present experiments is designed to have the following dimensions D = 18.67, d, = 3.8,
d, = lO.O(mm), N = 4.
(2)
The length of the vortex chamber, L, is nearly 55D. Experimental apparatus
Figure 1 shows the vortex tube designed above and its experimental layout. The vortex chamber is made of stainless steel (1.5 mm thick) and the nozzle block of brass. Steam generated in the boiler BO and superheated in the superheater SH is introduced to the steam chamber SC through the automatic temperature regulator AT. The pressure in the steam chamber is controlled by the relief valve RV. Then steam enters the vortex chamber VC through the four tangential nozzles. Energy separation occurs subsequently in this strong swirling flow field. A hot stream having a higher temperature, T,,, than the inlet steam temperature, Tnl, is exhausted from the hot end, and a cold stream having a lower one, T,, from the cold end. The both ends are located so far from the honeycombs that the vortex motion vanishes there. The mass flow rates, G,, and G,, are estimated accurately from the weight of condensed water. The different orifices are located downstream from the both ends only to investigate the effect of discharging resistance on the energy separation performance for practical applications. Additional piping lines are also laid to supply air and wet steam. Experimental conditions
The present experiments are carried out with the following three conditions as shown in Table 1. First the experiments are made under the constant total mass flow rate (Gt = 1.7 x
Fig. 1. Schematic diagram of the experimental layout: CP, air compressor; RV, relief valve; AC, air cooler; FN, flow nozzle: SV, stop valve: FO, flow orifice: AT, automatic temperature regulator; SH, superheater: BO, boiler: PU, feed water pump; SC, steam chamber; VF, flow rate regulating valve; OR, orifice: H, honeycomb: VC, vortex chamber; C, calorimeter: CD, condenser.
131
Performance characteristics of energy separation Table 1. Test conditions: 1. High superheated region (G, = 1.7~IO-* kg/s): 2. Low superheated region (G, = 1.7x IO-*kg/s); 3. Dry air; 4. Wet steam (X,, = 0.98); 5. Effect of total mass flow rate; 6. Effect of discharge resistance: Values in parentheses are standard deviation in respective experiments
Gt
On1
K
Tnl
Pnl
x10-2
kg/s
MPa abs
K
83.5 54.8 30.3 16.6
(4.0) (2.3) (3.0) (1.0)
1.69 1.71 1.73 1.69
(0.04) (0.03) (0.02) (0.09)
0.335 0.331 0.323 0.310
(0.015) (0.015) (0.016) (0.002)
494.3 465.3 439.8 424.4
(2.6) (1.9) (3.5) (1.1)
2
9.9 7.2 5.0
(0.7) (0.2) (0.2)
1.69 1.73 1.73
(0.09) (0.12) (0.08)
0.304 0.309 0.310
(0.002) (0.002) (0.002)
417.1 414.4 412.4
(0.8) (0.2) (0.5)
3
-
1.71
(0.12)
0.296
(0.002)
405.5
(0.3)
4
-
1.66
(0.04)
0.229
(0.098)
307.1
(1.0)
5
56.6 41.7
(1.2) (3.0)
2.46 0.80
(0.16) (0.03)
0.475 0.187
(0.002) (0.004)
479.6 432.5
(1.2) (2.5)
57.8 58.0 54.4
(2.0) (1.7) (2.7)
1.74 1.78 1.63
(0.09) (0.07) (0.08)
0.318 0.334 0.364
(0.014) (0.012) (0.030)
466.5 468.4 468.1
(0.8) (1.1) (1.1)
1
6
10m2kg/s) in order to investigate the effect of degree of superheat and of wetness on energy separation performance, second under the constant degree of superheat (&I= 55 K) to investigate the effect of total mass flow rate, and finally under the constant mass flow rate and degree of superheat to investigate the effect of discharge resistance. The vortex tube is thermally insulated with glass wool, felt and foamed styrene. The adiabatic efficiency defined as %d
=
((1- t)hh + ‘fh,)/h,,
where h is enthalpy and subscripts h, c and nl refer to hot end, cold end and nozzle inlet, respectively, is large (n7,d> 0.998) enough to disregard the error due to heat loss [7]. RESULTS
Longitudinal
AND DISCUSSIONS
temperature distributions near the vortex tube wall
The steam temperature near the vortex tube wall is measured by a fine thermocouple (1.6 mm sheath dia. and 0.3 mm wire dia.). The sensible junction is located 0.5 mm off from the wall surface in order to avoid the error due to heat conduction through the sheath and the wall. This distance was determined by the fact that the static wall temperature is measured at 0.0250 off from the wall made of an adiabatic material[51. The results thus obtained are shown in Fig. 2. The measured temperature may be less than the recovery temperature for the turbulent boundary layer, T, defined as T, = T,+ Pf’3u:1(2C,)
where T, is the static temperature, u, the velocity, P, the Prandtl number and C, the specific heat at constant pressure. In estimating the difference between the static temperature and the recovery one, we may regard the tangential velocity in the vortex tube, U, as u,. Since at the nozzle outlet the injected jet velocity U,,, = 250-370 m/s (Mach number 0.5-0.8) under the condition of G, = 1.7 X 10T2kg/s and &, = 55 K, the maximum temperature difference reaches approximately 30 K. As U decreases exponentially with the increase of the axial distance from the nozzles, L[6], the temperature is reduced to the static temperature at z > 15D. It is seen from the figure that an increase in temperature of the hot side and a decrease in temperature of the cold side definitely occur in the case of superheated steam. The thermal separation is completed mainly at Z(Z = z/D) < 15 during which the swirling velocity almost lJE.SVol. 17. No b-F
H. TAKAHAMA
738
et al.
0
wet
8ni t$
steam Xnl = 0.98
000AA~m 5s 55 5s
15
I o
1.5
5
0.8
0.5
0.5
0.5
0.5
0.65
0.5
Fig. 2. Longitudinal temperature distributions near the vortex tube wall.
diminishes, and the gained temperature remains constant at 2 > 15. The temperature gain increases with the increase in the ratio of cold mass flow rate to the total one, 5. Therefore, the thermal separation effect is considered sufficiently high for employing steam-operated vortex tubes for practical applications. Criteria of energy separation
eflect
As shown in the Mollier diagram (Fig. 3), steam stored in the steam chamber expands from nl to n2 at the nozzles and is discharged in the states denoted by h and c at the hot and cold ends, respectively. Due to the energy separation effect, specific enthalpy increases by Ah,, = hh - h.r and decreases by Ah, = h, - h,, in the vortex tube. These two separated energies should be simultaneously taken into account to estimate overall performance of the energy separation effect, since both gained and lost energy may be used for practical application. The following expressions are employed in this paper to estimate the performance; one of them is formulated based on the jet kinetic energy to produce a strongly swirling flow field, H,, defined as H,, = G,Ah, = G,U:,/2 = G,r,lJ2~2Ah.,
(5)
which should be regarded as the input power of vortex tubes[lO], and in which 1+4 = 0.978 is the coefficient of deceleration of the jet just after leaving nozzle[9], q5 the velocity coefficient of nozzle and Ah,, the reversible adiabatic heat drop in the nozzle. Expressing the flow rates of gained energy, Hh = (1 - [)G,Ah,,, and those of lost energy, H, = kG,Ah,, in values relative to
Fig. 3. Change in the state of steam in the vortex tube on Mollier diagram.
Performance
characteristics
739
of energy separation
the criterion H,, we get the following estimation for the energy separation performance &, = H,,/Hn = (I- ()Ah,,/Ah, (6)
[c = HJH. = lAh JAh..
The sum of H, and the reversible adiabatic heat drop from the state n2 to c, GtAh,,, has been considered as the reference value for the cooling effect. Expanding this concept to the hot side, we have another expression v/n= (I- Wd(Ah
+ Ah,,) (7)
nc = SAhJ@h, + Ah,,).
Moreover, it may be appropriate to introduce the concept of a heat cycle completed in the vortex tube system in which steam is compressed adiabatically from ph and pC to pnl. The following expression is also obtained in terms of the coefficient of performance et = ((1 - 5)Ah,,- 5‘Ahc)/{(l- I)AS + 5AU
(8)
where Ah,, and Ah,, are adiabatic compression work done between ph and pnl, and between pC and pnlr respectively. In case we use either the gained or lost energy alone, the coefficient of performance is given by lh =
(1- OAhhl{(l - [)A&,
+ 5Ah,s) (9)
ec = - [AhJ{(l - Z)Ah,s+ 5Ahr,}. Energy separation performance in high superheated region Efect of degree of superheat. The experimental results of the energy separation per-
formance which have been carried out in the high superheated region with ~9,~ > 15 K are shown in Fig. 4. The results for air are also indicated in the figure. It is seen that the performance characteristic can be expressed by a single line including that for air. The energy separation em, 0
80
0
55
&= K
1.7X10+
jq,,a
0.0 -
Fig. 4. Energy separation performance
in high superheated
region.
H. TAKAHAMA
740
et al.
performance of vortex tubes operated with steam, whose &, > 15 K, is nearly the same as those with the ideal gas, The maximum performance is obtained when the value of 5 falls between 0.6 and 0.7, and approximately 70% of the kinetic energy of the jet can be converted to separated energy for practical use. The coefficients of performance of vortex tubes, given by eqns (8) and (9), are plotted in Fig. 5. It becomes clear that this expression is also useful to estimate the total performance. Although the coefficient of performance of vortex tubes is the same order as that of the refrigerating cycle using cold air, vortex tubes have the advantage of supplying steam over a considerably wide temperature range by a simple operation of the regulating valve. Efect of total mass flow rate. Total mass flow rate of steam supplied to the nozzles may be one of the important factors affecting the energy separation performance. The absolute amount of separated energy increases with an increase of G, at the constant value of 5. As the kinetic energy of the jet at the nozzles also increases nearly proportionally to Grr the energy separation performance expressed by 4’is well expressed in the same curves shown in Fig. 4. Under the present experimental condition the tangential Reynolds number at the nozzle outlet, R,, = U,2D/~,Z[10], is (4-8) x 16. Tangential velocity profile in the vortex chamber which is a physically important factor to energy separation phenomenon hardly changes in the present region of R, referring to the detailed experimental results on velocity profiles for air[91. Hence it appears that the performance characteristic in terms of 5 is independent of G,. Efect of discharge resistance. Additional pipe lines including valves and elbows are connected to the vortex tube in applying it to an actual system. Consequently, it must be taken into account in advance that the additional discharge resistance lowers the energy separation performance. In order to investigate the effect, experiments have been made using orifices placed at 15D downstream from the hot and colds ends. The diameter ratios of the orifices to the pipe, & are 0.8, 0.6 and 0.4, and their total pressure losses are approximately 0.005 MPa, 0.02MPa and 0.12 MPa, respectively. The results are as follows: when p 20.8, the energy separation performance is nearly the same as one without orifice (/? = 1): when p ~0.8, however, the decrease of the amount of separated energy becomes appreciable, and it drops to nearly 55% of the energy amount without the orifice. Therefore, we should pay attention to the decrease in the amount of separated energy, and should try to make the additional pressure loss as low as possible in employing vortex tubes. It is of interest that the energy separation performance expressed by l behaves quantitatively in the same manner as one without the orifice shown in Fig. 4. In general the kinetic energy of the jet also decreases with a decrease of p at the constant mass flow rate, because the pressure level in the vortex chamber rises due to the discharge resistance. And the energy amount to be separated also decreases owing to the decrease of the kinetic energy of the jet. Both decreasing rates seem to be almost the same in the experiments. Energy separation performance in low superheated region
As the degree of superheat of steam fed to the vortex tube is reduced, the thermal separation decreases as shown in Fig. 2. Especially when &, 5 10 K, the temperature excess in t?t kg/s 1.7x10-2
2.5x104
l
%O
0.4 [
ec et
A 0
Fig. 5. Coefficient of performance,
A n
eqns (8) and (9).
Performance
characteristics
of
741
energy separation
the annular region becomes negative near the nozzle section in 0 < 2 < 5. Corresponding to the thermal separation, the energy separation performance, [, decreases with a decrease of 0,, as shown in Fig. 6, and reduces to only 40% when 0,r = 5 K compared with the performance obtained when &, > 15 K and/or air. This cause will be described later. Energy separation performance
in wet region
Experiments in the wet region have been conducted using wet steam whose dryness fraction at the nozzle inlet, xnl, has been kept constant at 0.98. The experimental results are shown by the cross signs on Figs. 2 and 6. The temperatures at the hot and cold ends are only equal to the saturation temperatures corresponding to their pressures, and consequently there is no possibility of energy separation in the wet region. Although the dryness fractions at the hot and cold ends, xh and x0 become higher than at the nozzle inlet, steam still remains in the wet region as shown in Fig. 7. It can be considered that all the energy to be separated is transformed into the latent heat of vaporization of the moisture contained in the wet steam, and that the steam changes only at constant enthalpy in the vortex tube. Such a result is obtained by using liquid as a working fluid. Eflect of wetness. In order to investigate the undesirable effect of wetness on the energy separation performance, the state of steam at the nozzle outlet shown in Fig. 8 was obtained by feeding the low superheated and wet steam. It is clearly seen that the state of steam is always in the superheated region at the nozzle outlet in the case of &, = 15 K, and that when 0,, 5 10 K, the state of steam enters the wet region. This wet steam at the nozzle outlet becomes superheated at both ends due to the separated energy which is superior to the latent heat of moisture vaporization. The energy separation performance, however, decreases by the heat wasted to moisture vaporization in comparison with the performance obtained for the high superheated steam. In the extreme case of supplying wet steam to the vortex tube, no energy separation occurs. It may be concluded that the same energy separation performance as obtained for the ideal gas can be expected as long as there is steam in the superheated region at the nozzle outlet. On the other hand, when the steam enters the wet region almost all moisture is spattered to the annular flow region by centrifugal force, and the moisture wastes the energy to be gained as the latent heat of its vaporization. A part of the steam dropped into the back
;j X wet steam
0
0.2
0.4
Fig. 6. Fig. 7. Fig. 6. Energy separation performance in low superheated and wet region. Fig. 7. Dryness fraction of steam flowing out of the both ends.
0.6
J
0.8
1.0
142
H. TAKAHAMA
wet steam
et al.
Xnl:0.99
2
x-x
A--
fI /-o.a&
Fig. 8. State of steam at nozzle outlet (low superheated
steam supplied).
flow region from the annular one condenses by the energy to be lost by the vortex tube effect, and the condensed moisture is released again to the annular flow region. Thus, the moisture checks the vortex tube energy separation effect, and makes temperature and specific enthalpy uniform. It is practically important to estimate the minimum value of dryness fraction of steam which yields the effective energy separation. Assuming that all the moisture at the nozzle outlet, G, is spattered to the annular flow region, and that all the energy to be gained in the annular region is consumed to evaporate the moisture into the dry saturated steam, we get (1- [)G,Ah,, = G,,L = G,(l -X,&5
(10)
where L is the latent heat of vaporization. The equation reduces to xnz= 1- I(1- tWt,,/L).
(11)
The result of eqn (11) calculated by using the experimental data Ahh is shown in Fig. 9. The solid line indicates the minimum value of dryness fraction, i.e. the effective energy separation can be expected in the region above the solid line. . Or kg/s
Bn1
0
1.1x10-* 2.5
55 55
A
1.1
80
0
K
Fig. 9. Critical dryness fraction to produce available energy separation CONCLUDING
REMARKS
The overall characteristics of a steam-operated vortex tube were investigated experimentally. Reasonable criteria and expressions to estimate the energy separation performance were introduced, and some technical data including the optimum operating conditions were also offered. Furthermore, the effects of difference in thermal properties of working fluids on the performance were examined with attention to the undesirable effect of steam wetness. From the experimental results, we may conclude as follows: (1) Geometrical dimensions for vortex tube operated with air, eqn (l), can be used for one operated with steam.
Performance characteristics of energy separation
743
(2) The energy separation performance of both gained and lost energy is well expressed in terms of 3 defined as eqn (6). Other estimations expressed by 17[eqn (7)] and E [eqn (9)) were also useful. (3) As far as steam is in the superheated region at the nozzle outlet, the energy separation performance expressed by 5 is the same as that for air and is presented by the same curve independently of the degree of superheat, total mass flow rate and discharge resistance. (4) When steam is in the wet region at the nozzle outlet, even though steam supplied is superheated, the performance considerably decreases. And any effective energy separation does not result when the dryness fraction at the nozzle outlet is less than approximately 0.98. (5) Additional pressure loss due to pipe lines set downstream of the hot and cold ends should be made as low as possible in employing vortex tubes, since the pressure loss decreases in the absolute amount of separation energy. NOMENCLATURE C, specific heat at constant pressure D inner diameter of vortex chamber d, diameter of nozzle outlet d, diameter of cold orifice C mass flow rate G, = Gh + G, total mass flow rate H enthalpy flow rate h specific enthalpy Ahh = h,, - h,, , specific enthalpy increase Ah, = h, - h.1 specific enthalpy decrease Ah, adiabatic compression work done between p,, and p., A$, adiabatic compression work done between pc and p., L length of vortex chamber or latent heat of vaporization N number of nozzles P, Prandtl number p pressure &, tangential Reynolds number T temperature T, recovery temperature 7, static temperature U tangential velocity u, velocity X dryness fraction of steam Z = z/D nondimensional axial distance I axial distance from nozzle Greek symbols /? diameter ratio of orifice to pipe
e coefficient of performance, eqns (8) and (9) 4 energy separation performance, eqn (6) n energy separation performance, eqn (7) vOl.dadiabatic efficiency, eqn (3) 0 degree of superheat Y kinematic viscosity I = GJG, cold flow fraction d velocity coefficient of nozzle $ = 0.978 coethcient of deceleration of jet just after leaving nozzle Subscripts n I values at nozzle inlet n2 values at nozzle outlet h values at hot end of vortex tube c values at cold end of vortex tube 2 values at Z s isentropic process
REFERENCES [I] P. I. STAROSTIN and M. S. ITKIN, Thermal Engng IS, 31 (1968). [2] V. I. METENIN, Soviet Physics-Technical Physics 5, 1025 (l%l). [3] V. S. MARTINOVSKH and V. P. ALEKSEEV, Soviet Physics-Technical Physics 1.2233 (1956). 141Y. SONI and W. J. THOMSON, J. Heat Transfer WC, 316 (1975). [5] H. TAKAHAMA and K. KAWASHIMA, Mem. Fat. Engng, Nagoya Univ. 12,227 (1960). [6] H. TAKAHAMA, Bulletin of Japan Sot. Mech. Engrs 8, 433 (1965).
744
H. TAKAHAMA et al.
171H. TAKAHAMA, T. IKEDA and H. KAWAMURA, Preprint of Japan Sot. Mech. Engrs 133-4,77 (1973). [8] H. TAKAHAMA, Trans. Japan SW. Mech. Engrs 32,503 (1964). f9] H. TAKAHAMA, i?ui?efin of Japan Sot. Mech. Engrs. 9, 121 (19b6). [lo] J. J. KEYS Jr., In Proc. l%O Heat Transfer and Fluid Mechanics Institute, pp. 31-46. Stanford University Press, California (1960). (Received 30 October 1978)
PERFORMANCE CHARACTERISTICS OF ENERGY SEPARATION IN A STEAM-OPERATED VORTEX TUBE HEISHICHIROTAKAHAMAt and HITOSHI KAWAMURAS Departmentof MechanicalEngineering,Faculty of Engineering,Nagoya University, 1, Furo-cho,Chikusaku, Nagoya, 464, Japan SEIZO KATOS Departmentof Mechanical and Materials Engineering,School of Engineering,Mie University, 1515, Kamihama-cho,Tsu, 514, Japan
HAJIME YOKOSAWA’ Collegeof GeneralEducation,Nagoya University Abstract-Energy separationperformanceof a steam-operatedvortex tube is experimentallyinvestigated, and some reasonable criteria and expressions to estimate the energy separationperformanceare also introduced.The performancecharacteristicsdefined by the above expressions are the same as those of ideal gas in the high superheatedregion,and are well expressed independentlyof the degreeof superheat, total mass flow rate and dischargeresistance. When steam is in the wet region at the nozzle outlet, the performanceconsiderablydecreases because of the energy waste from moisture vaporization.And no energy is separated when the dryness fraction is less than approximately0.98. Some technical data includingthe optimumoperatingconditionsare also offered.
INTRODUCTION
stored in a compressed gaseous fluid is easily separated into higher and lower energy flows by using the Ranque-Hilsch vortex tube effect. The vortex tube as a mechanical device has the advantage of very simple structure with no moving element. There is current interest, therefore, in its practical applications, and it may be reasonable to employ vortex tubes for quick start-up of steam power generation units. A vortex tube, for example, may be installed between the boiler and the turbine on restarting the units stopped while the demand of electric power decreases at night and over the weekend. The hot flow extracted from the vortex tube is led into the turbine nozzles in order to produce more quickly the optimum blade temperature, while the cold one serves for heat recovery in the reheater or in the condenser. There are relatively many studies devoted to vortex tubes which have been operated with air as a working fluid. These results characterize the ideal case of vortex tubes, because air behaves more like ideal gas than steam or vapor. Starostin and Itkin[ll, and Metenin[2] have conducted experiments with high superheated steam, and Martynovskii and Alekseev[3] with humid air. In practice, however, these experimental results are not so extensive as to provide applicable data for steam operated vortex tube design and for optimum operating conditions. The present research is concerned with the performance characteristics of overall energy separation by using steam as a working fluid. The systematic experiment covers a wide range of steam conditions from the high superheated state (enough to produce the ideal grade performance as air) to the wetted state (without causing any energy separation like liquid). The purpose of the present experiment is to confirm the availability of the energy separation when using superheated steam, to establish criteria to express generally the energy separation performance, and to present technical data including the optimum operating conditions. Furthermore, the undesirable effect of wetness on the energy separation performance is qualitatively investigated, together with the estimation of the critical dryness fraction necessary to bring about the effective energy separation. THE ENERGY
tprofessor. SResearchAssociate. #Assoc. Professor. “ResearchAssociate. 735
736
H. TAKAHAMA THE
et al.
EXPERIMENTS
Vortex tube design
Only a few attempts have been made to provide optimal design conditions for vortex tubes even operated with air[A 51.Takahama[S, 61 recommends the following geometrical dimensions derived from his systematic experimental runs with air: d,lD S 0.2,
NdgD’ = 0.16-0.20, d, < D - 2d,,
d:INdS, s 2.3
(1)
where d,, is the diameter of nozzles, D the vortex chamber diameter, d, the diameter of the cold orifice and N the number of nozzles. Taking into consideration that very high superheated steam possesses nearly the same thermal properties as air, we employ the dimensions satisfying eqn (1). Considering the boiler capacity, the heat dissipation loss and the thermal stress of materials, the vortex tube in the present experiments is designed to have the following dimensions D = 18.67, d, = 3.8,
d, = lO.O(mm), N = 4.
(2)
The length of the vortex chamber, L, is nearly 55D. Experimental apparatus
Figure 1 shows the vortex tube designed above and its experimental layout. The vortex chamber is made of stainless steel (1.5 mm thick) and the nozzle block of brass. Steam generated in the boiler BO and superheated in the superheater SH is introduced to the steam chamber SC through the automatic temperature regulator AT. The pressure in the steam chamber is controlled by the relief valve RV. Then steam enters the vortex chamber VC through the four tangential nozzles. Energy separation occurs subsequently in this strong swirling flow field. A hot stream having a higher temperature, T,,, than the inlet steam temperature, Tnl, is exhausted from the hot end, and a cold stream having a lower one, T,, from the cold end. The both ends are located so far from the honeycombs that the vortex motion vanishes there. The mass flow rates, G,, and G,, are estimated accurately from the weight of condensed water. The different orifices are located downstream from the both ends only to investigate the effect of discharging resistance on the energy separation performance for practical applications. Additional piping lines are also laid to supply air and wet steam. Experimental conditions
The present experiments are carried out with the following three conditions as shown in Table 1. First the experiments are made under the constant total mass flow rate (Gt = 1.7 x
Fig. 1. Schematic diagram of the experimental layout: CP, air compressor; RV, relief valve; AC, air cooler; FN, flow nozzle: SV, stop valve: FO, flow orifice: AT, automatic temperature regulator; SH, superheater: BO, boiler: PU, feed water pump; SC, steam chamber; VF, flow rate regulating valve; OR, orifice: H, honeycomb: VC, vortex chamber; C, calorimeter: CD, condenser.
131
Performance characteristics of energy separation Table 1. Test conditions: 1. High superheated region (G, = 1.7~IO-* kg/s): 2. Low superheated region (G, = 1.7x IO-*kg/s); 3. Dry air; 4. Wet steam (X,, = 0.98); 5. Effect of total mass flow rate; 6. Effect of discharge resistance: Values in parentheses are standard deviation in respective experiments
Gt
On1
K
Tnl
Pnl
x10-2
kg/s
MPa abs
K
83.5 54.8 30.3 16.6
(4.0) (2.3) (3.0) (1.0)
1.69 1.71 1.73 1.69
(0.04) (0.03) (0.02) (0.09)
0.335 0.331 0.323 0.310
(0.015) (0.015) (0.016) (0.002)
494.3 465.3 439.8 424.4
(2.6) (1.9) (3.5) (1.1)
2
9.9 7.2 5.0
(0.7) (0.2) (0.2)
1.69 1.73 1.73
(0.09) (0.12) (0.08)
0.304 0.309 0.310
(0.002) (0.002) (0.002)
417.1 414.4 412.4
(0.8) (0.2) (0.5)
3
-
1.71
(0.12)
0.296
(0.002)
405.5
(0.3)
4
-
1.66
(0.04)
0.229
(0.098)
307.1
(1.0)
5
56.6 41.7
(1.2) (3.0)
2.46 0.80
(0.16) (0.03)
0.475 0.187
(0.002) (0.004)
479.6 432.5
(1.2) (2.5)
57.8 58.0 54.4
(2.0) (1.7) (2.7)
1.74 1.78 1.63
(0.09) (0.07) (0.08)
0.318 0.334 0.364
(0.014) (0.012) (0.030)
466.5 468.4 468.1
(0.8) (1.1) (1.1)
1
6
10m2kg/s) in order to investigate the effect of degree of superheat and of wetness on energy separation performance, second under the constant degree of superheat (&I= 55 K) to investigate the effect of total mass flow rate, and finally under the constant mass flow rate and degree of superheat to investigate the effect of discharge resistance. The vortex tube is thermally insulated with glass wool, felt and foamed styrene. The adiabatic efficiency defined as %d
=
((1- t)hh + ‘fh,)/h,,
where h is enthalpy and subscripts h, c and nl refer to hot end, cold end and nozzle inlet, respectively, is large (n7,d> 0.998) enough to disregard the error due to heat loss [7]. RESULTS
Longitudinal
AND DISCUSSIONS
temperature distributions near the vortex tube wall
The steam temperature near the vortex tube wall is measured by a fine thermocouple (1.6 mm sheath dia. and 0.3 mm wire dia.). The sensible junction is located 0.5 mm off from the wall surface in order to avoid the error due to heat conduction through the sheath and the wall. This distance was determined by the fact that the static wall temperature is measured at 0.0250 off from the wall made of an adiabatic material[51. The results thus obtained are shown in Fig. 2. The measured temperature may be less than the recovery temperature for the turbulent boundary layer, T, defined as T, = T,+ Pf’3u:1(2C,)
where T, is the static temperature, u, the velocity, P, the Prandtl number and C, the specific heat at constant pressure. In estimating the difference between the static temperature and the recovery one, we may regard the tangential velocity in the vortex tube, U, as u,. Since at the nozzle outlet the injected jet velocity U,,, = 250-370 m/s (Mach number 0.5-0.8) under the condition of G, = 1.7 X 10T2kg/s and &, = 55 K, the maximum temperature difference reaches approximately 30 K. As U decreases exponentially with the increase of the axial distance from the nozzles, L[6], the temperature is reduced to the static temperature at z > 15D. It is seen from the figure that an increase in temperature of the hot side and a decrease in temperature of the cold side definitely occur in the case of superheated steam. The thermal separation is completed mainly at Z(Z = z/D) < 15 during which the swirling velocity almost lJE.SVol. 17. No b-F
H. TAKAHAMA
738
et al.
0
wet
8ni t$
steam Xnl = 0.98
000AA~m 5s 55 5s
15
I o
1.5
5
0.8
0.5
0.5
0.5
0.5
0.65
0.5
Fig. 2. Longitudinal temperature distributions near the vortex tube wall.
diminishes, and the gained temperature remains constant at 2 > 15. The temperature gain increases with the increase in the ratio of cold mass flow rate to the total one, 5. Therefore, the thermal separation effect is considered sufficiently high for employing steam-operated vortex tubes for practical applications. Criteria of energy separation
eflect
As shown in the Mollier diagram (Fig. 3), steam stored in the steam chamber expands from nl to n2 at the nozzles and is discharged in the states denoted by h and c at the hot and cold ends, respectively. Due to the energy separation effect, specific enthalpy increases by Ah,, = hh - h.r and decreases by Ah, = h, - h,, in the vortex tube. These two separated energies should be simultaneously taken into account to estimate overall performance of the energy separation effect, since both gained and lost energy may be used for practical application. The following expressions are employed in this paper to estimate the performance; one of them is formulated based on the jet kinetic energy to produce a strongly swirling flow field, H,, defined as H,, = G,Ah, = G,U:,/2 = G,r,lJ2~2Ah.,
(5)
which should be regarded as the input power of vortex tubes[lO], and in which 1+4 = 0.978 is the coefficient of deceleration of the jet just after leaving nozzle[9], q5 the velocity coefficient of nozzle and Ah,, the reversible adiabatic heat drop in the nozzle. Expressing the flow rates of gained energy, Hh = (1 - [)G,Ah,,, and those of lost energy, H, = kG,Ah,, in values relative to
Fig. 3. Change in the state of steam in the vortex tube on Mollier diagram.
Performance
characteristics
739
of energy separation
the criterion H,, we get the following estimation for the energy separation performance &, = H,,/Hn = (I- ()Ah,,/Ah, (6)
[c = HJH. = lAh JAh..
The sum of H, and the reversible adiabatic heat drop from the state n2 to c, GtAh,,, has been considered as the reference value for the cooling effect. Expanding this concept to the hot side, we have another expression v/n= (I- Wd(Ah
+ Ah,,) (7)
nc = SAhJ@h, + Ah,,).
Moreover, it may be appropriate to introduce the concept of a heat cycle completed in the vortex tube system in which steam is compressed adiabatically from ph and pC to pnl. The following expression is also obtained in terms of the coefficient of performance et = ((1 - 5)Ah,,- 5‘Ahc)/{(l- I)AS + 5AU
(8)
where Ah,, and Ah,, are adiabatic compression work done between ph and pnl, and between pC and pnlr respectively. In case we use either the gained or lost energy alone, the coefficient of performance is given by lh =
(1- OAhhl{(l - [)A&,
+ 5Ah,s) (9)
ec = - [AhJ{(l - Z)Ah,s+ 5Ahr,}. Energy separation performance in high superheated region Efect of degree of superheat. The experimental results of the energy separation per-
formance which have been carried out in the high superheated region with ~9,~ > 15 K are shown in Fig. 4. The results for air are also indicated in the figure. It is seen that the performance characteristic can be expressed by a single line including that for air. The energy separation em, 0
80
0
55
&= K
1.7X10+
jq,,a
0.0 -
Fig. 4. Energy separation performance
in high superheated
region.
H. TAKAHAMA
740
et al.
performance of vortex tubes operated with steam, whose &, > 15 K, is nearly the same as those with the ideal gas, The maximum performance is obtained when the value of 5 falls between 0.6 and 0.7, and approximately 70% of the kinetic energy of the jet can be converted to separated energy for practical use. The coefficients of performance of vortex tubes, given by eqns (8) and (9), are plotted in Fig. 5. It becomes clear that this expression is also useful to estimate the total performance. Although the coefficient of performance of vortex tubes is the same order as that of the refrigerating cycle using cold air, vortex tubes have the advantage of supplying steam over a considerably wide temperature range by a simple operation of the regulating valve. Efect of total mass flow rate. Total mass flow rate of steam supplied to the nozzles may be one of the important factors affecting the energy separation performance. The absolute amount of separated energy increases with an increase of G, at the constant value of 5. As the kinetic energy of the jet at the nozzles also increases nearly proportionally to Grr the energy separation performance expressed by 4’is well expressed in the same curves shown in Fig. 4. Under the present experimental condition the tangential Reynolds number at the nozzle outlet, R,, = U,2D/~,Z[10], is (4-8) x 16. Tangential velocity profile in the vortex chamber which is a physically important factor to energy separation phenomenon hardly changes in the present region of R, referring to the detailed experimental results on velocity profiles for air[91. Hence it appears that the performance characteristic in terms of 5 is independent of G,. Efect of discharge resistance. Additional pipe lines including valves and elbows are connected to the vortex tube in applying it to an actual system. Consequently, it must be taken into account in advance that the additional discharge resistance lowers the energy separation performance. In order to investigate the effect, experiments have been made using orifices placed at 15D downstream from the hot and colds ends. The diameter ratios of the orifices to the pipe, & are 0.8, 0.6 and 0.4, and their total pressure losses are approximately 0.005 MPa, 0.02MPa and 0.12 MPa, respectively. The results are as follows: when p 20.8, the energy separation performance is nearly the same as one without orifice (/? = 1): when p ~0.8, however, the decrease of the amount of separated energy becomes appreciable, and it drops to nearly 55% of the energy amount without the orifice. Therefore, we should pay attention to the decrease in the amount of separated energy, and should try to make the additional pressure loss as low as possible in employing vortex tubes. It is of interest that the energy separation performance expressed by l behaves quantitatively in the same manner as one without the orifice shown in Fig. 4. In general the kinetic energy of the jet also decreases with a decrease of p at the constant mass flow rate, because the pressure level in the vortex chamber rises due to the discharge resistance. And the energy amount to be separated also decreases owing to the decrease of the kinetic energy of the jet. Both decreasing rates seem to be almost the same in the experiments. Energy separation performance in low superheated region
As the degree of superheat of steam fed to the vortex tube is reduced, the thermal separation decreases as shown in Fig. 2. Especially when &, 5 10 K, the temperature excess in t?t kg/s 1.7x10-2
2.5x104
l
%O
0.4 [
ec et
A 0
Fig. 5. Coefficient of performance,
A n
eqns (8) and (9).
Performance
characteristics
of
741
energy separation
the annular region becomes negative near the nozzle section in 0 < 2 < 5. Corresponding to the thermal separation, the energy separation performance, [, decreases with a decrease of 0,, as shown in Fig. 6, and reduces to only 40% when 0,r = 5 K compared with the performance obtained when &, > 15 K and/or air. This cause will be described later. Energy separation performance
in wet region
Experiments in the wet region have been conducted using wet steam whose dryness fraction at the nozzle inlet, xnl, has been kept constant at 0.98. The experimental results are shown by the cross signs on Figs. 2 and 6. The temperatures at the hot and cold ends are only equal to the saturation temperatures corresponding to their pressures, and consequently there is no possibility of energy separation in the wet region. Although the dryness fractions at the hot and cold ends, xh and x0 become higher than at the nozzle inlet, steam still remains in the wet region as shown in Fig. 7. It can be considered that all the energy to be separated is transformed into the latent heat of vaporization of the moisture contained in the wet steam, and that the steam changes only at constant enthalpy in the vortex tube. Such a result is obtained by using liquid as a working fluid. Eflect of wetness. In order to investigate the undesirable effect of wetness on the energy separation performance, the state of steam at the nozzle outlet shown in Fig. 8 was obtained by feeding the low superheated and wet steam. It is clearly seen that the state of steam is always in the superheated region at the nozzle outlet in the case of &, = 15 K, and that when 0,, 5 10 K, the state of steam enters the wet region. This wet steam at the nozzle outlet becomes superheated at both ends due to the separated energy which is superior to the latent heat of moisture vaporization. The energy separation performance, however, decreases by the heat wasted to moisture vaporization in comparison with the performance obtained for the high superheated steam. In the extreme case of supplying wet steam to the vortex tube, no energy separation occurs. It may be concluded that the same energy separation performance as obtained for the ideal gas can be expected as long as there is steam in the superheated region at the nozzle outlet. On the other hand, when the steam enters the wet region almost all moisture is spattered to the annular flow region by centrifugal force, and the moisture wastes the energy to be gained as the latent heat of its vaporization. A part of the steam dropped into the back
;j X wet steam
0
0.2
0.4
Fig. 6. Fig. 7. Fig. 6. Energy separation performance in low superheated and wet region. Fig. 7. Dryness fraction of steam flowing out of the both ends.
0.6
J
0.8
1.0
142
H. TAKAHAMA
wet steam
et al.
Xnl:0.99
2
x-x
A--
fI /-o.a&
Fig. 8. State of steam at nozzle outlet (low superheated
steam supplied).
flow region from the annular one condenses by the energy to be lost by the vortex tube effect, and the condensed moisture is released again to the annular flow region. Thus, the moisture checks the vortex tube energy separation effect, and makes temperature and specific enthalpy uniform. It is practically important to estimate the minimum value of dryness fraction of steam which yields the effective energy separation. Assuming that all the moisture at the nozzle outlet, G, is spattered to the annular flow region, and that all the energy to be gained in the annular region is consumed to evaporate the moisture into the dry saturated steam, we get (1- [)G,Ah,, = G,,L = G,(l -X,&5
(10)
where L is the latent heat of vaporization. The equation reduces to xnz= 1- I(1- tWt,,/L).
(11)
The result of eqn (11) calculated by using the experimental data Ahh is shown in Fig. 9. The solid line indicates the minimum value of dryness fraction, i.e. the effective energy separation can be expected in the region above the solid line. . Or kg/s
Bn1
0
1.1x10-* 2.5
55 55
A
1.1
80
0
K
Fig. 9. Critical dryness fraction to produce available energy separation CONCLUDING
REMARKS
The overall characteristics of a steam-operated vortex tube were investigated experimentally. Reasonable criteria and expressions to estimate the energy separation performance were introduced, and some technical data including the optimum operating conditions were also offered. Furthermore, the effects of difference in thermal properties of working fluids on the performance were examined with attention to the undesirable effect of steam wetness. From the experimental results, we may conclude as follows: (1) Geometrical dimensions for vortex tube operated with air, eqn (l), can be used for one operated with steam.
Performance characteristics of energy separation
743
(2) The energy separation performance of both gained and lost energy is well expressed in terms of 3 defined as eqn (6). Other estimations expressed by 17[eqn (7)] and E [eqn (9)) were also useful. (3) As far as steam is in the superheated region at the nozzle outlet, the energy separation performance expressed by 5 is the same as that for air and is presented by the same curve independently of the degree of superheat, total mass flow rate and discharge resistance. (4) When steam is in the wet region at the nozzle outlet, even though steam supplied is superheated, the performance considerably decreases. And any effective energy separation does not result when the dryness fraction at the nozzle outlet is less than approximately 0.98. (5) Additional pressure loss due to pipe lines set downstream of the hot and cold ends should be made as low as possible in employing vortex tubes, since the pressure loss decreases in the absolute amount of separation energy. NOMENCLATURE C, specific heat at constant pressure D inner diameter of vortex chamber d, diameter of nozzle outlet d, diameter of cold orifice C mass flow rate G, = Gh + G, total mass flow rate H enthalpy flow rate h specific enthalpy Ahh = h,, - h,, , specific enthalpy increase Ah, = h, - h.1 specific enthalpy decrease Ah, adiabatic compression work done between p,, and p., A$, adiabatic compression work done between pc and p., L length of vortex chamber or latent heat of vaporization N number of nozzles P, Prandtl number p pressure &, tangential Reynolds number T temperature T, recovery temperature 7, static temperature U tangential velocity u, velocity X dryness fraction of steam Z = z/D nondimensional axial distance I axial distance from nozzle Greek symbols /? diameter ratio of orifice to pipe
e coefficient of performance, eqns (8) and (9) 4 energy separation performance, eqn (6) n energy separation performance, eqn (7) vOl.dadiabatic efficiency, eqn (3) 0 degree of superheat Y kinematic viscosity I = GJG, cold flow fraction d velocity coefficient of nozzle $ = 0.978 coethcient of deceleration of jet just after leaving nozzle Subscripts n I values at nozzle inlet n2 values at nozzle outlet h values at hot end of vortex tube c values at cold end of vortex tube 2 values at Z s isentropic process
REFERENCES [I] P. I. STAROSTIN and M. S. ITKIN, Thermal Engng IS, 31 (1968). [2] V. I. METENIN, Soviet Physics-Technical Physics 5, 1025 (l%l). [3] V. S. MARTINOVSKH and V. P. ALEKSEEV, Soviet Physics-Technical Physics 1.2233 (1956). 141Y. SONI and W. J. THOMSON, J. Heat Transfer WC, 316 (1975). [5] H. TAKAHAMA and K. KAWASHIMA, Mem. Fat. Engng, Nagoya Univ. 12,227 (1960). [6] H. TAKAHAMA, Bulletin of Japan Sot. Mech. Engrs 8, 433 (1965).
744
H. TAKAHAMA et al.
171H. TAKAHAMA, T. IKEDA and H. KAWAMURA, Preprint of Japan Sot. Mech. Engrs 133-4,77 (1973). [8] H. TAKAHAMA, Trans. Japan SW. Mech. Engrs 32,503 (1964). f9] H. TAKAHAMA, i?ui?efin of Japan Sot. Mech. Engrs. 9, 121 (19b6). [lo] J. J. KEYS Jr., In Proc. l%O Heat Transfer and Fluid Mechanics Institute, pp. 31-46. Stanford University Press, California (1960). (Received 30 October 1978)