Applied Thermal Engineering 27 (2007) 2145–2152 www.elsevier.com/locate/apthermeng

High-pressure water as the driving fluid in an ejector refrigeration system M.D. Butterworth, T.J. Sheer

*

School of Mechanical, Industrial and Aeronautical Engineering, University of the Witwatersrand, Johannesburg, Private Bag 3, WITS 2050, South Africa Received 25 September 2004; accepted 18 July 2005 Available online 23 March 2007

Abstract Results are presented from an experimental investigation into the use of high-pressure water as the driving fluid in an ejector refrigeration system, the purpose of which was to chill water. The investigation originated from the concept of boosting the refrigeration capacity available for local-area use in underground mines, by utilising directly the high static pressures available from pipelines carrying large quantities of water down deep mine shafts. Previous studies of liquid–gas ejectors (jet pumps) were limited to driving water pressures up to 1950 kPa. The present work considers driving pressures between 4000 and 15,000 kPa, for which no design or performance information could be found in the literature. An experimental facility was used to investigate vacuum boiling under batch (static) operating conditions. The dimensions of the ejector components (nozzle and mixing tube diameters and mixing tube length) could be varied in order to achieve the best performance. No previously-reported ejector system has achieved a reduction in the process liquid temperature in the evaporator (which is saturated at the evaporator pressure) to a level below the temperature of the driving fluid. In contrast, the present work demonstrated that such a cooling effect could occur under batch conditions with driving water pressures above 5000 kPa. Using the measured evaporator transient temperature response it was possible to estimate the performance of a continuously-operating water cooling system.  2005 Elsevier Ltd. All rights reserved. Keywords: Water-jet ejector; Ejector refrigeration; High-pressure ejector

1. Introduction This paper discusses the use of high-pressure waterpowered ejectors (jet pumps) for chilling water by direct vacuum evaporation and presents an experimentally based method for designing such ejectors. Water-driven liquid ejectors are based on the same concept as steam jet refrigeration systems, used widely in the chemical industry because of their simplicity of design and low capital cost. These advantages would also be applicable to water-driven ejector systems when high-pressure *

Corresponding author. Tel.: +27 11 717 7304; fax: +27 11 339 7997. E-mail address: [email protected] (T.J. Sheer). 1359-4311/$ - see front matter  2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2005.07.011

water is available at low cost, for example by utilising the static heads available from vertical pipelines in deep mine shafts (typically 15,000 kPa and greater). The particular application that led to this investigation was the need to take every opportunity to chill the water used for both cooling and mining purposes at various localities in deep mines. 1.1. Previous work on liquid-powered gas ejectors Raynerd [1] described the principle of operation of a water-jet ejector for extracting vapor or gas from a space, which is that the motive liquid (water) discharges as a jet from a nozzle, drawing the vapor or gas into a mixing tube and diffuser. The ejector thereby operates

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Nomenclature c me P Qd R

specific heat of water (J/kg K) mass of water in evaporator (kg) water pressure (kPa or MPa) driving water flow rate (m3/s) correlation coefficient (–)

as a vacuum pump. When the high kinetic energy waterjet penetrates the body of the slow-moving vapor, energy is transferred between the two and the resulting mixture is accelerated in the direction of the water jet. Entrainment takes place in the mixing direction, downstream of the nozzle, and the fluids mix within the mixing tube. In the case of water vapor extraction, most of the entrained vapor condenses within the cold water jet. Witte [2,3] used water at pressures of up to 1950 kPa to provide the motive energy in entraining air at 100 kPa and raising its pressure to 1000 kPa, a pressure ratio of 10:1. Using a multi-jet nozzle (19 orifices with diameters of 6 mm each) and liquid flow rates up to 44 l/s, he measured mass flow ratios (motive fluid/entrained fluid) up to 528:1 in a closed-discharge arrangement. Several researchers have reported ejector performance results in a lower motive pressure range between 270 and 580 kPa, although the ejectors were functioning as vacuum pumps in only two cases. Berman and Efimochkin [4] raised the pressure of extracted air from 5.9 to 88 kPa using motive water at a supply pressure of 580 kPa and flow rates up to 81 l/s; at these conditions the pressure ratio was 14.9:1 and the mass flow ratio 7300:1. The authors found that multi-orifice nozzles could achieve a volume flow ratio (entrained fluid/motive fluid) oneand-a-half times that possible with single-orifice nozzles. In earlier smaller-scale tests, Takashima [5] used motive water at 370 kPa and a flow rate of 2 l/s to raise air pressure from 13 kPa to 136 kPa with a single-orifice nozzle; the pressure ratio was 10.5:1 and the mass flow ratio 36,500:1. Using a multi-orifice nozzle with a motive liquid flow rate of 2.5 l/s, he reported that the volume flow ratio doubled from 0.18:1 to 0.36:1; the pressure ratio was then 9.5:1 (from 21 to 199 kPa) and the mass flow ratio 11,100:1. Performance curves produced by Mangnall [6] for commercially-available water-jet ejectors indicate that for a motive pressure of 220 kPa, mass flow ratios of 3000:1 and 33,000:1 would typically be achieved with suction pressures of 25 and 3.5 kPa, respectively. These values are also influenced by water temperature. At higher motive pressures the curves indicate a diminishing mass flow ratio improvement with rise in motive pressure. At a motive pressure of 580 kPa and making some assumptions, these curves give values of mass flow ratio that are not dissimilar to those obtained by Ber-

t Ti Td TPR

time to cool water (s) initial water temperature (C) driving water temperature (C) thermodynamic performance ratio (–)

man and Efimochkin [4]. Regarding published information on liquid-powered ejector design, e.g. [5], it is clear that the performance depends particularly on the following geometrical parameters: (i) ratio of the cross-sectional areas of the nozzle(s) to the throat; (ii) shape of nozzle; (iii) length of diffuser throat; (iv) divergence angle of the diffuser outlet; (v) distance between the nozzle outlet and the diffuser throat. These parameters are discussed further in Section 2 below. 1.2. Water vapor refrigeration Water vapor refrigeration (WVR) systems rely on the evaporative cooling of the refrigerant, in this case the process water itself. By subjecting liquid water to a pressure below the saturation pressure corresponding to the temperature to which the water will be cooled, the water boils. Only a small fraction of the waterÕs mass need be evaporated for an appreciable temperature reduction, due to the high enthalpy of vaporization of water. Thus 0.17 per cent of a given mass of water must be converted to vapor in order to cool it by 1 C. The very high specific volume of saturated water vapor at low pressures (e.g. 94 m3/kg at 12 C and 1.4 kPa) necessitates handling a large volume flow rate of water vapor for any given cooling requirement [7]. This property differentiates water vapor from conventional refrigerants and requires the application of radically different design criteria for WVR system components. Steam-jet ejectors, known in refrigeration applications for over a century, can be used to produce the low-pressure conditions required in the WVR evaporator [8] but are only economical if the cost of steam is low. Water-powered ejectors do not seem to have previously been considered for this application.

2. Establishment of optimum ejector geometry 2.1. Design parameters The most significant determinant of performance in an ejector refrigeration system is the ejector geometry and accordingly it was essential to be able to quantify the effect of various geometric parameters. These were initially established using some published information

M.D. Butterworth, T.J. Sheer / Applied Thermal Engineering 27 (2007) 2145–2152

on the design of liquid-driven ejectors [5,6,9,10] and then the relative importance of each was evaluated experimentally, to determine the best ejector geometry and other requirements for peak performance. A general method for optimising the design of liquid/ liquid jet pumps was suggested by Vyas and Kar [10] in which component dimensions (suction nozzle, driving nozzle, mixing tube and diffuser) were expressed as dimensionless ratios. They described the entrainment of the suction fluid by viscous friction and acceleration of the resulting mixture by momentum transfer with the driving fluid in the mixing tube (throat); complete mixing was assumed by the end of the throat, as is the case with other researchers [1,9]. The approach of Vyas and Kar was followed for the initial design in the present work. A direct comparison with MangnallÕs curves [6] for liquid/gas ejectors was not possible because of the large difference in mass flow ratios. Other useful comments on the design of liquid/gas ejectors were provided by Bonnington [9] who suggested methods of improving mixing and of selecting suitable nozzles to produce highvelocity jets of small water droplets. Droplet size is acknowledged as a very important factor in achieving high entrainment efficiency but droplet size effects have not been considered explicitly in the present or previous work. Nozzle suppliers can generally supply information on the effect of water pressure on droplet size [11]. Fig. 1 illustrates the experimental water vapor refrigeration unit that was constructed to investigate the effects of geometry and operating parameters on system performance. The test facility consisted of seven major components and was fabricated from stainless steel except for the

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transparent mixing tube. Component numbers below are as in Fig. 1. The figure also indicates the positions where temperature and pressure measurements were taken. 1. Evaporator (capacity 10.5 l). This was assumed to be essentially adiabatic during operation, because of the small temperature differences involved. 2. High-pressure nozzle. 3. Mixing tube. 4. Diffuser (3 or 4 semi-cone angle). 5. Vacuum pump. 6. Receiver/drain tank. 7. High-pressure positive-displacement pump (not shown); maximum capacity 3 l/s, 15,000 kPa. The test facility was used to investigate the effects of the following ranges of ejector geometries and operating conditions: (i) Driving water pressures of 4000–15,000 kPa. (ii) Driving nozzle diameters of 1.6 and 2.4 mm. The nozzles [11] had 15 cone angles with fine flow vanes in the inlets. (iii) Driving water flow rates of 0.2–0.7 l/s. (iv) Mixing tube diameters of 50 and 75 mm. (v) Mixing tube lengths of 0–1600 mm. (vi) Motive water temperatures of 16–24 C. The distance between the driving nozzle and the mixing tube inlet was adjusted (see Fig. 1) to give maximum suction performance in each case, before the effects of various combinations of the preceding parameters were

5

2

MIXING TUBE TEMPERATURE & PRESSURE

DRAIN TANK VAPOUR PRESSURE

3

4

DRIVING WATER TEMPERATURE

NOZZLE ADJUSTING SCREW

DRAIN TANK VAPOUR TEMPERATURE

EVAPORATOR VAPOUR TEMPERATURE EVAPORATOR WATER TEMPERATURE

EVAPORATOR VAPOUR PRESSURE

1

DRAIN TANK DISCHARGE WATER TEMPERATURE

6

Fig. 1. Ejector test facility.

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2.2. Test method and limitations of the test unit Observing the effect of changing the evaporator pressure (and hence system performance) under varying operating conditions would best be done with the system running continuously, rather than on a batch basis. Unfortunately, the limited size of the receiver vessel restricted the operating time, because all water (driving and evaporated) was discharged into the vessel and there was no provision for draining it while the system was operating. Continuous operation could in principle have been achieved by draining the receiver vessel through a barometric leg and discharging the water under vacuum to the atmosphere. Because the available laboratory could not accommodate the 8.2 m leg that would have been required at JohannesburgÕs altitude, it was only possible to operate the system in batch mode. Consequently, the refrigeration effect was calculated from initial water temperature and volume, and final evaporator temperature. The procedure for doing this is discussed in Section 4 hereunder. Good thermal performance of the system depended on maintaining large temperature differences, particularly between water in the evaporator and the high-pressure driving water; the initial evaporator water temperature was constant for all tests. Under batch operating conditions, these two temperatures eventually converged and, although the final temperature of water in the evaporator was a useful indicator of ejector performance, it could not be used to quantify or predict thermodynamic duty for the various configurations under continuous operation. It was therefore necessary to examine transient performance data from batch operation tests, to predict expected performance characteristics and trends for a continuously operating plant. This and other issues are examined in the next section. Instrumentation was provided to allow the following quantities to be recorded during tests, as indicated in Fig. 1: evaporator water temperature; evaporator vapor pressure and temperature; driving water temperature; mixing tube temperatures and pressures at inlet and outlet; receiver vapor pressure and temperature; receiver discharge water temperature. Temperatures were measured using small thermocouples situated in the fluid, away from the wall.

3. Test results

25

Evaporator temperature (°C)

determined. It was in general found that it was best to locate the nozzle directly at the entrance to the throat.

20 15

24°C 16°C

10 5 0 0

5

10

15

20

Driving pressure (MPa)

Fig. 2. Comparison of ejector performance with driving water temperatures of 16 and 24 C.

are illustrated in Fig. 2, by comparing the final evaporator water temperatures for two driving water temperatures over a range of motive pressures. For these tests the values of the main parameters were: throat diameter 50 mm; driving nozzle diameter 1.6 mm; mixing tube length 1600 mm; initial evaporator water temperature between 30 and 34 C; evaporator was adiabatic. The ratio of the receiver tank pressure to the evaporator pressure was found to increase from 1.6 to 3.2 during these tests, as the driving pressure increased and the evaporator pressure consequently reduced. The effect of a reduced driving water temperature on performance has been reported by Mangnall [6], who found that a higher vacuum was achieved when colder driving water was used and that the vacuum increased as driving water pressure was increased. Test data from the present work, represented in Fig. 3, show the observed relationship between the temperature and pressure of driving water and the final temperature of water in the evaporator. In this figure the Ôapproach temperatureÕ is defined as the difference between the final

4

Approach temperature (°C)

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2 0 -2 -4 -6 -8

-10

System performance, measured in terms of the final temperature of water in the evaporator, consistently improved as the temperature of motive water was reduced and as drive water pressure was increased. These effects

0

5

10

15

20

Driving pressure (MPa)

Fig. 3. Effect of driving water pressure on ejector performance in terms of ÔapproachÕ temperature.

M.D. Butterworth, T.J. Sheer / Applied Thermal Engineering 27 (2007) 2145–2152 30

Evaporator temperature (°C)

evaporator water temperature and the driving water temperature. The figure compares performance measured at various pressures and shows that with driving water pressures above 5000 kPa the final temperature of water in the evaporator was less than the temperature of the driving water. As the driving pressure was further increased, the evaporator temperature fell at a diminishing rate. One of the important geometrical parameters is the mixing tube length. The system performance improved as the mixing tube length was increased, as shown in Fig. 4 for a 50 mm diameter mixing tube and a 1.6 mm drive nozzle, although a diminishing rate of improvement is apparent at lengths greater than 200 mm. The effect of varying the mixing tube and drive nozzle diameters, thereby varying their area ratio, was compared for two area ratios, 976 and 2197, with a mixing tube length of 1000 mm and driving water pressures of 4–15 MPa. Actual mixing tube and nozzle diameters are listed in Table 1, together with the driving water temperature. Fig. 5 compares the results for configurations A and C of Table 1 and shows that for a given nozzle size the ejector with a 50 mm diameter mixing tube outperformed the larger one with a 75 mm tube. It can also be seen that the performance of both ejectors followed a similar trend as the driving water pressure was increased. To confirm the effect of mixing

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25

20 A C

15

10

5 0

5

10

15

20

Driving pressure (MPa)

Fig. 5. Ejector performance: configurations A and C.

tube diameter on performance, Fig. 6 compares results for configurations B and D, using two ejectors with identical area ratios but different mixing tube and nozzle diameters. An important observation from Fig. 6 is that the data points follow nearly identical trends over the range of motive water pressures, indicating that, provided the area ratio is kept constant, the performance remains the same for various mixing tube and nozzle diameter combinations. To summarise the main findings of the experimental programme, the trends outlined below were found to apply for the ejector configurations tested.

Evaporator temperature (°C)

30

1. Motive water temperature has a significant impact on thermodynamic performance, with low motive water temperatures allowing lower water temperatures in the evaporator to be achieved (Fig. 3).

25 20 15 10

30

5

0

500

1000

1500

2000

Mixing tube length (mm)

Fig. 4. Effect of mixing tube length on ejector performance: 50 mm diameter mixing tube and 1.6 mm diameter nozzle.

Table 1 Ejector configuration, area ratio and operating parameters Configuration

Nozzle diameter (mm)

Mixing tube diameter (mm)

Area ratio

Drive water temperature (C)

A B C D

1.6 1.6 1.6 2.4

50 50 75 75

976 976 2197 976

16 24 16 22

Evaporator temperature (°C)

0

25

20

15

D B

10

5 0

5

10

15

20

Driving pressure (MPa) Fig. 6. Ejector performance: configurations D and B.

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2. Performance improved as the motive water pressure was increased, but the rate of improvement diminished as the pressure approached 15 MPa. (The operational limit of the supply water pump prevented tests at pressures above 15 MPa.) This effect was observed for all the motive water temperatures considered, as shown by the ‘‘approach’’ temperature in Fig. 3. Munday and Bagster [12] proposed a theory for compressible-flow ejectors according to which, after choking of the secondary flow (the extracted vapor) is reached at some position along the mixing tube, an increase in the primary flow energy does not result in a further increase in capacity. A similar effect may explain the present results, but this is speculation. 3. Performance improved as mixing tube length was increased. For the 50 mm-diameter tube, the performance limit was reached at a tube length of approximately 1.5 m. 4. Tests to consider various area ratios were limited by the availability of components. However, for the range of components tested it was found that: • an area ratio of 434 or less resulted in significant reductions in performance, and • good performance was obtained with an area ratio between 434 and 2197. Of the configurations tested, the best performance was achieved with an area ratio of 976.

4. Predicting performance for continuous operation Results presented thus far have shown performance trends for an ejector operating under batch conditions. The performance of a continuously operating ejector could only be estimated by using the experimental data to calculate the initial cooling power achieved when evaporator temperatures were similar to those that could reasonably be expected in a continuously operating system. Estimates made use of transient temperature data for the initial stages, recorded for the evaporator water and at the mixing tube outlet, as shown in Fig. 7. 40

Experimental observations, summarised below, support the hypothesis that a continuously operating high-pressure ejector will tend to evaporate water at or somewhat below the temperature of the driving water, and that its performance can be calculated as a function of the time taken for the evaporator temperature to reach that of the driving water. Summary of experimental observations: 1. At high driving water pressures, evaporator water temperature rapidly reached the driving water temperature, and then decreased at a reduced rate. 2. Visual observations confirmed that the evaporator water boiled vigorously at the start of each test, and the rate of boiling progressively diminished as the test continued. 3. The temperature of the mixed stream increased rapidly (Fig. 7), indicating that the rate at which heat was transferred from the evaporator to the mixed stream was greatest at the start of each test. For the example illustrated in Fig. 7, the Ôthermodynamic performanceÕ (i.e. the rate of heat removal from the water in the evaporator) was calculated to be 12.6 kW, with a corresponding hydraulic power of 4.9 kW (see Eq. (1)); in this case 4.0 kg of water was cooled from 33 C to the driving water temperature of 22.5 C in a time of 14 s (corrected for instrument response), using 0.33 l/s of driving water at 15 MPa. The nozzle and mixing tube diameters were 1.6 mm and 50 mm, respectively. Further examples for selected evaporator water masses are listed in Table 2. The previously stated hypothesis is further supported by the results listed in Table 2, as the thermodynamic performance essentially remained constant for all masses, and the time taken for the evaporator temperature to reach the motive water temperature increased in proportion to the mass of water in the evaporator. Another aspect to be considered with regard to continuous operation is that the introduction of the feed water directly into the vapor space using a spray manifold would eliminate the effect of immersion depth [13]. Therefore, continuous operation would allow all of the water introduced into the evaporator to be cooled to

Temperature (°C)

35 30

Mixed

25

Table 2 Performance for selected masses of water in evaporator

20 15

Evaporator

10

Evaporator mass (kg)

Time to reach motive water temperature (s)

Cooling duty (kW)

4 5 6 8

14.0 16.5 22.0 27.0

12.6 12.7 11.8 11.9

5 0 0

20

40

60

80

100

120

140

160

Time (seconds)

Fig. 7. Evaporator and mixing tube transient temperature response.

M.D. Butterworth, T.J. Sheer / Applied Thermal Engineering 27 (2007) 2145–2152

Duty/Hydraulic power

3 2.5 2 1.5 1 5

10

15

20

Driving pressure P (MPa)

Fig. 8. Effect of driving water pressure on thermodynamic performance.

the temperature that was achievable during batch operation only at the surface of the water in the evaporator. The effect of motive water pressure on continuous operation was also considered (Fig. 8) and the results confirmed the trend observed during batch tests, where thermodynamic performance deteriorated as motive water pressure was reduced. Conversely, the results showed that the ratio between cooling duty and hydraulic power (i.e. the net benefit) increased with motive water pressure, but at a decreasing rate as the pressure approached 15 MPa. A correlation is proposed, using estimates derived from transient data (Fig. 8), to predict the performance ratio (expressed as the ratio of thermodynamic performance to input hydraulic power) for specific operating conditions over the observed range of driving water pressures. The ratio of thermodynamic performance to hydraulic power, termed here the thermodynamic performance ratio (TPR), is calculated from the transient test data as TPR ¼ me cðT i  T d Þ=ðtQd P Þ

ð1Þ

The estimated uncertainty in the TPR values due to measurement errors is 5%. A polynomial fitted to the resulting points in Fig. 8 has the following equation: TPR ¼ 0:016P 2 þ 0:46P  0:83

ðR2 ¼ 0:95Þ

ð2Þ

where P is the driving water pressure (MPa). This correlation should not be regarded as a firm basis for design because of the limitations on the testing conditions.

5. Conclusions The principal objective of the study was to evaluate the feasibility of using high-pressure water as the motive fluid in an ejector refrigeration system. Ejector performance was studied by varying the main component dimensions, specifically the nozzle diameter and the diameter and length of the mixing tube. The position of the nozzle relative to the ejector throat was not found

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to affect performance significantly. Within the limited range of components available, area ratio had a significant effect on performance, which to some extent could be predicted for ejectors operating with similar motive water temperatures (Fig. 6). No previously-reported ejector system has achieved Ôsub-coolingÕ of the process fluid, i.e. a reduction in fluid temperature within the evaporator to a level below that of the driving fluid. In contrast, the present work demonstrates that Ôsub-coolingÕ can occur at driving water pressures above 5 MPa. For the optimum configuration operating with a driving water pressure of 15 MPa, a Ôsub-coolingÕ effect of 8 C was observed. This is because the reduced pressure at the suction point (the exit from the high-pressure nozzle) causes the driving water to cool by evaporation, thereby reducing its effective temperature. By examining the evaporator water temperature response for various masses of evaporator water, it was possible to estimate performance for a continuously operating system. It appears that the lowest practically achievable evaporator temperature would be the effective temperature of the motive water after expansion through the nozzle, depending on the residence time in the evaporator, since the rate of cooling decreases at temperatures lower than this. This Ôsub-coolingÕ effect should be confirmed by further tests using a continuously operating ejector system.

Acknowledgements This work was carried out as part of the research programme of the Council for Scientific and Industrial Research (CSIR) Division of Mining Technology. The assistance of Mr. K. Stanton in the experimental work is particularly acknowledged.

References [1] P. Raynerd, Ejectors, selection and use of vacuum equipment, Institute of Chemical Engineers, North Western Branch Papers 1987, No. 1, 3.1–3.16, London, 1987. [2] J.H. Witte, Efficiency and design of liquid–gas ejectors, British Chemical Engineering 10 (9) (1965) 602–607. [3] J.H. Witte, Mixing shocks in two-phase flow, Journal of Fluid Mechanics 36 (4) (1969) 639–655. [4] L.D. Berman, G.I. Efimochkin, Design equations for water ejectors, Thermal Engineering 11 (7) (1964) 57–62. [5] Y. Takashima, Studies on liquid-jet gas pumps, Journal of the Scientific Research Institute 46 (December) (1952) 230–246. [6] K. Mangnall, A Technical Guide to Vacuum/Pressure Producing Machines and Associated Equipment, Hick Hargreaves & Co. Ltd., Bolton, UK, 1989. [7] R.D.C. Shone, An investigation into the use of water–vapour refrigeration for cooling mine service water, Journal of the Mine Ventilation Society of South Africa 34 (7) (1981) 121–143.

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[8] E. Spencer, New developments in steam vacuum refrigeration, ASHRAE Transactions 67 (June) (1961) 339–353. [9] S.T. Bonnington, A guide to jet pump design, British Chemical Engineering 9 (3) (1964) 150–154. [10] B.D. Vyas, S. Kar, Standardisation of water jet pumps, in: Proceedings of Symposium on Jet Pumps and Ejectors, Paper 10, BHRA Fluid Engineering, Cranfield, UK, 1972, pp. 155–170. [11] Spraying Systems Company, Industrial Spray Products Catalogue 55M, 6-14, 1996.

[12] J.T. Munday, D.F. Bagster, A new ejector theory applied to steam jet refrigeration, Industrial and Engineering Chemistry Process Design and Development 16 (4) (1977) 442–449. [13] T.J. Sheer, S.R. Mitchley, Vacuum boiling in a water vapour refrigeration system, in: Proceedings of IIR-Gustav Lorentzen Conference ‘‘Natural Working Fluids Õ98’’, International Institute of Refrigeration, Oslo, Norway, 2–5 June 1998, pp. 53–62.