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Simultaneous desalination and power generation using solar energy
Renewable Energy 34 (2009) 401–408
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Simultaneous desalination and power generation using solar energy Yuchun Zhao*, Aliakbar Akbarzadeh, John Andrews School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, PO Box 71, Bundoora, Vic. 3083, Australia
a r t i c l e i n f o
a b s t r a c t
Article history: Available online 7 July 2008
Using solar energy to produce fresh water and electricity simultaneously is a prospective way to solve the problems combining fresh water shortage, energy crisis and farm land degradation in Northern Victoria. This paper records the process of calculating the performance of the nozzle applying homogenous equilibrium model, designing and testing the prototype of such system using three different types of the nozzles in static and rotary systems. The research on the project is divided into two steps: first is about static system in which the spray nozzle is proved to be the best in both production of fresh water and power generation; while on the second stage, the convergent–divergent (C–D) nozzles are the best in rotary system. Some data were analyzed theoretically based on the test and the results found that the percentage of fresh water measured by experiment is consistent with the calculation using homogenous equilibrium expansion model (HEM), however, there is big difference in power generation between theory and experiments. Based on our experimental figures and analysis, the reasons for low power generation are found and a new model is proposed. According to the new model, a different reaction turbine using curve length C–D nozzles is designed to overcome the problems which were encountered in the previous prototype. After analyzing the efficiency of the cycle by T–s diagram, the evacuated tube solar collector integrated heat pipe is suggested to be applied on this system. Ó 2008 Elsevier Ltd. All rights reserved.
Keywords: Desalination Power generation Solar energy Convergent–divergent nozzle Flashing flow modeling CDP (combined desalination and power generation)
1. Introduction These days, the limited resources that are usable energy, fresh water and arable land are pestering human being sustainable existences. Firstly, based on the investigation of World Energy Council, although the increase of energy consumption is estimated about 1.7% per year in next 20 years, the situation is still crucial, because the demand of crude oil increases dramatically while the reserves fell by 2.7% [1], especially in China, the demand rate of increase reached 13.21% in 2003 [2]. Secondly, for fresh water, according to the report of UN in 2003, it has been estimated that today more than 2 billion people are affected by water shortages in over 40 countries: 1.1 billion do not have sufficient drinking water and 2.4 billion have no provision for sanitation and the problem is often worst that the population of developing countries living in water poverty at present will increase to 60% by 2020 [3]. At the same time, when humanity has constructed a huge global ecological engineering project to solve the shortage of fresh water and energy crisis, the intervention on ecosystems always results in the negative effects on biodiversity [4], such as the dam of Three Gorges of Yangzi River in China. Lastly, the arable land is decreased due to the saline, deserted and overgrassed. The consultants hired by The
* Corresponding author. E-mail address: [email protected] (Y. Zhao). 0960-1481/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2008.05.018
Australian Conservation Foundation and the National Farmers Federation predict in a report that Australia is facing the loss of 15.5 million hectares – equivalent to 70% of Victoria – to salinity. The report continues ‘‘the estimated total cost of resource degradation is to be more than 2 billion dollars, about half the net annual value of farm production which was 3.9 billion dollars during 1998–1999 – Unless action is taken to address the problems, the annual cost of dry land salinity alone could increase to 670 million dollars in 2020’’ [5]. For example, in Northern Victoria, the local forests are being killed and grasslands are being degraded due to salting; the deposition of salt was the result of overdrawing underground water for farming and other industrial or household use (Fig. 1). Furthermore, with the development of the industry and the increasing demand, more fresh water and power are needed, while the situation is that the resource is limited. Therefore, finding the sustainable method to satisfy the demand of the fresh water and energy should be one of the most important tasks in the agenda of both the government and researchers alike. Based on theoretical investigation along with some preliminary experiments it would be possible to simultaneously produce fresh water and power from saline water heated by renewable sources [6]. The project focuses on two aspects: fresh water production and power generation. The principle is that when the hot salt water heated by the solar pond passes through the rotary nozzles driven by the difference of atmospheric pressure and the pressure of the vacuumed chamber, it will vaporize and then condenses into the
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Nomenclature A D F R V p x Cd E P T h s _ m
area (m2) diameter of the nozzle thrust (N) radius (m) velocity (m/s) pressure (kPa) vapour quality in the mixture (%) drag coefficients energy (kJ) power (W) temperature ( C), torque (N m) specific enthalpy (kJ/kg) specific entropy (kJ/kg K) mass flow rate (kg/s)
n specific volume (m3/kg) r density (kg/m3) u angular velocity (rad/s) Subscripts 1, 2, . arbitrary position c critical condition g gaseous phase k kinetic o outlet s system a absolute d drag i inlet l liquid phase r relative t throat
Greek symbols efficiency (%)
h
fresh water, and the mixture exiting the nozzles at high velocity will exert an anti-force on the nozzles, making them rotate which will increase the pressure further, as a result, the velocity of the mixture will increase further and the rotation of nozzles can thus generate more power. Fig. 2 gives the designs of principle system and the actual model is shown in Fig. 3. In the system, the chamber can be vacuumed by an eductor which is connected to cooling water pipe. This paper mainly contains three types of information. 1. Calculating the performance of the nozzle using homogenous equilibrium model and tests on the static nozzle system engaged to obtain preliminary results for the design and construction of CDP rig. 2. Investigation on the flash flow through the nozzles, conducted by measuring the trust exacted on different shapes and sizes in diameter of throat, and comparing them with the theoretical
calculations. Previously many models were set up to solve the safety problems in nuclear power plants [7,8] and to improve the efficiency of two-phase nozzle employed in geothermal turbine [9]; however, as the parameters in our case are different, first-hand research was needed to ascertain the most suitable model to optimize the performance in low temperature and pressure conditions. 3. The test on production of fresh water and electricity generation will be carried out to find out which nozzle is mostly suitable for both stationary and rotary systems. Standards of evaluation will be mainly on power generation and percentage of fresh water production. During the test, results will be compared with experiments and factors affecting the performance will be addressed.
2. Basic calculation and analysis of relative experiments’ figures 2.1. The experimental instruments The schematic of the stationary test system is demonstrated in Fig. 4.
Fig. 1. Trees dying due to the saline coming from the underground water in Pyramid Hill, Victoria.
Fig. 2. The principle and the practical system with the fixed nozzles.
Y. Zhao et al. / Renewable Energy 34 (2009) 401–408
403
Fig. 3. The practical system with the fixed nozzles.
The parameters of main components are Load cell (Model UU18-K002): 2 kgf, accuracy 0.03%. Pressure transducer (PMP1400): 1 bar, 0.25%. Data acquisition (MV200): 30 channels, 0.15%. The apparatus used for force measurement and calibration in static nozzle and the measurement about rotation of shaft in rotational nozzles are shown in Fig. 5.
2.2. The preliminary calculation of fresh water percentage and comparison with test In the system, the following parameters are assumed to the performance of solar pond. Basically, the temperature of saline can be heated to 77.5 C by solar pond; therefore, we can calculate the performance as follows. The flow of the fluid in the nozzle is illustrated in Fig. 6(a) and the T–s diagram in Fig. 6(b). In the situation of the system, the percentage of fresh water depends on the difference of temperature between cooling and heated solar pond when the saline water vaporizes completely. Fig. 7(a) demonstrates the percentage of the fresh vs. temperature by the solar pond when cooling temperature is 25 C and Fig. 7(b) illustrates the effect on the fresh water percentage of the cooling temperature. The experimental figures show the variation is less around 1.0% than theoretical calculation. And in fact, the cooling water temperature cannot exactly describe the actual situation because the air concentration in the saline solution can affect the evaporation itself, some more precise assumptions will be of assistance, but the experiment shows this rig is reliable for the practical application. Based on the results of static test, the nozzles adopted in rotary nozzle system are spray nozzles and C–D nozzles which are installed on the rotational arms (Fig. 8). The results are depicted in Fig. 9. From the picture, it can be found that there is no obvious difference in different nozzles, but all of the nozzles can produce more fresh water than theoretical prediction, this is due to the
Fig. 4. The schematic test of rig. (a) Static nozzle system. (b) The rotary system.
reaction between the high speed mixture and surrounding vapour around the nozzles. 2.3. The preliminary calculation of the diameter of nozzles, power generation The homogenous equilibrium expansion model (HEM) assumes that: 1. 2. 3. 4.
the flow through the nozzle is isentropic process; velocities in two phases are equal; properties’ data correspond to those of a static, equilibrium; the flow is one-dimensional flow.
Known:
To ¼ 25 C; so ¼ 1:0753 kJ=ðkg KÞ _ o ¼ 0:05 kg=s ho ¼ 315:94 kJ=kg; m po ¼ 3:169 Kpa ;
Ti ¼ 77:5 C; si ¼ 1:0753 kJ=ðkg KÞ _ i ¼ 0:10 kg=s hi ¼ 334:89 kJ=kg; m
pi ¼ 42:86 Kpa ;
And vi and vnozzle are nearly zero when the nozzle is assumed to be static.
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Y. Zhao et al. / Renewable Energy 34 (2009) 401–408
a
b
Generator V
Reflective Sheet
Coupling AC 220
Rotation (rpm)
Tachometer
Driving Motor
Shaft rotation vs. voltage Linear (Shaft rotation vs. voltage)
4000 3000 2000
R= 249.61V
1000 0
0
2
4
6
8
10
12
14
16
Voltage (V) Fig. 5. The measurement systems and calibration. (a) The force measure system and calibration in static nozzle. (b) The calibration of rotation of shaft in rotary nozzles.
To obtain the Vo: It is assumed that the flow is adiabatic from the centre of the nozzles to the exit of the nozzle; the following equations can be obtained:
1 1 hi þ Vi2 ¼ ho þ Vo2 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Vo ¼ Vi2 þ 2ðhi ho Þ Vo ¼ 194:67 m=s sffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffi _ _ m 4A 4m A ¼ and Do ¼ D ¼ rVo p o prVo
(1)
From the value of heated saline temperature of 77.5 C and cooling temperature, we can calculate the outlet diameter of the nozzles. For the rotary nozzles, the pressure will increase and when the arm is 0.4 m, the value of Dt be obtained by (1), taking the density of saturated water at 77.5 C, Dt can be calculated. The relationship between the pressure inside the nozzles, velocity of exit from the nozzles vs. shaft rotation is given in Fig. 10(a) and the throat diameter of the nozzles vs. the responsive u of the shaft can be found in Fig. 10(b). During the test, three designs of nozzles were experimented; spray nozzle in production of fresh water is the most efficient and convergent–divergent nozzle (Fig. 10(b)) is comparatively the same in trust, but orifice is not suitable for CDP system. Therefore, most of the later experimenting efforts were focused on the spray nozzle. However, because of the existence of friction of the nozzle, this design possesses its limitations, Fig. 6(b) gives the typical process and Fig. 11 gives the ratio of thrust of test to the theory. It can be found that the extension of 20 mm is good but 40 mm would not make a promising improvement. According to the results of the
experiment, the nozzles selected in the next stage on the rotary CPD will be focused on spray nozzles with 20 mm length. And at the same time, a length of 20 mm convergent–divergent nozzle will be tested for comparison. At point 1 (Fig. 6(b)), the pressure is about 101 kPa, when the fluid flows to the end of arms, the pressure will climb to the peak point 2 due to the centrifugal force (1–2 is thought as isentropic compression). From point 2 to point 3s, with the decrease of the pressure, the sub-cooled saline will reach its saturated point 3s and 3, and then begin to vaporize until to the point 4s. For the piratical application, it will reach point 4 (point 4r means the actual entropy due to the reaction with the surrounding vapors in the chamber). If the efficiency of nozzle is ht we have
ht ¼
h1 h4 h1 h4s
(2)
where h4 ¼ h1 (h1 h4s)/ht. Then the specific kinetic energy is
Ek ¼ ðh1 h4 Þht ¼ 18:95ht pffiffiffiffiffi Vo ¼ 194:7 ht
(3)
When the nozzles are in the constant rotary, we can calculate the power (P) produced by the steam according to the following formula:
_ m _ i hi 2m _ o ho ht i ðVo uRÞ2 Td u Tf P ¼ m 2
(4)
In the system, drag torque Td by vapour is proportional to the rotation, while the power loss to friction is fixed – less than 5% of the
Y. Zhao et al. / Renewable Energy 34 (2009) 401–408
a
405
Fresh water percentage vs. temperature of spray nozzle (cooling temperature 25°C) 12
Fresh water percentage(%)
11 10 9 8 7 6 5
without extension 20mm extension 40mm extension theory without extention
4 3 2 50
60
70
80
90
100
Input temperature (°C)
Fresh Water Percentage (%)
b
Fig. 6. The flow in the nozzles (a) and the T–s diagram (b).
Fresh Water Percentage vs. Cooling Temperature 9 8
Theory test
7 6 5 4 3 20
25
30
35
40
45
50
Cooling Temperature (C) total power throughout experiment. Drag force Fd can be expressed as: Fd ¼ 1/2(CdrV2A) [10], therefore
Td
¼ 2
Fig. 7. (a) The percentage of the fresh vs. inlet temperature on static nozzle. (b) The percentage of the fresh vs. cooling temperature on static nozzle.
RR
0 r dFd Rr 1 2 0 2rCd rðr uÞ Da dr RR ¼ Cd rDa u2 0 r 3 dr
ð5Þ
¼ 2
where Da ¼ 10 mm, Td ¼ 1.64 105u2.
Cd ¼ 0.0808,
R ¼ 0.4 m,
r ¼ 3.169 kg/m3,
pffiffiffiffiffi P ¼ 1895ðht 5%Þ 0:05ð194:7 ht 0:4uÞ2 1:64 105 u3 (6) Fig. 12 shows the relation between power generation and rotation on different ht. According to the results on the static nozzles and the limitations of the system design, three different throat diameters (0.5 mm, 1.0 mm and 2 mm) in C–D nozzles and a diameter of 1 mm spray nozzles have been tested. The experimental data prove the C–D nozzle of 1 mm throat diameter is the best in generating electricity, but the result is much less than the theoretical calculation. Fig. 13 gives diagram about the optimal power generated and rotation by system vs. input temperature. After comparing the results with theory, a simple test was carried out in which a DC power was supplied to make the shaft rotate in the same condition, and it is shown that more than 105 W was needed to reach 1000 rpm, that means the drag is too big and the drag coefficient Cd needs to be measured based on the system, therefore, more test needs to be done using different arms with section area. Another factor affecting the power generation is the
nozzle efficiency, it seems the efficiency is much less than that of one-phase nozzle flow, which can be attributed to the velocity slip between the two phases and abrupt expansion outside of the nozzles. 2.4. The modified modeling on the flashing flow in C–D nozzle According to Eqs. (5) and (6), it can be written as
pffiffiffiffiffi P ¼ 1895ðht 5%Þ 0:05ð194:7 ht 0:4uÞ2 2:03 104 Cd u3
(7)
Based on Eq. (7), Fig. 14 describes the trends for different Cd, from these figures, it can be found that the test results are in the range of low efficiency and big drag coefficients. Therefore, for the new modeling, two factors should be considered, one is Cd, another is nozzle efficiency. In fact, when comparing theory with test results in Fig. 13, the efficiency lies in the curves of less 10% in Fig. 14. There is a good method to reduce the coefficient that is using two wheel sheet to cover the nozzles and arms, which will be considered with the new nozzle design. As for the low efficiency of the nozzles, generally the time-delay in bubble nucleation in flash flow was of 1 ms [11], that means the length of nozzle at least more than 20 cm if the speed more than 200 m/s. Obviously, in CDP system, it is not content due to the dimension limitation. Furthermore, the velocity slip also contributes to the loss of efficiency; hence new modeling
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Fig. 8. The nozzles in the test. (a) Spray nozzle. (b) Convergent–divergent nozzle.
will take the assumptions that the velocities in different phases are different. As a result, the new design about the nozzles will look like that in Fig. 15. There are two advantages in the new design. Firstly, the drag will drop dramatically because there is no section to cause resistance; the only drag is coming from the shear of the vapour between the surfaces of the wheel and surrounding vapour and it is very small. Secondly, the length of new curve nozzle is sufficient for bubble to vaporize and to make acceleration smoother, then to improve the efficiency of the nozzle.
than 8.0% fresh water using 20 mm long extension spray nozzles when the input temperature is 77.5 C, and the results of the test are a litter bigger than the theoretical calculation, especially in rotary nozzle system. (4) The drag of vapour and un-fully expansion are the main reasons for low efficiency in power generation, hence the new design of nozzle needs to be done in the future work.
4. Future work and discussion 4.1. Modeling of the nozzles
(1) According to our calculation and preliminary experiments on the fixed and rotary nozzles, it is possible to use renewable energy to produce fresh water, desalinize the salt and generate the electricity simultaneously. The concept has been conformed by the experiment. (2) The homogenous equilibrium model can be applied in the static nozzle system to calculate the percentage of fresh water, but there is big difference in power generation. In the static nozzle system, the variation of the force measurement is in the same order; while in rotary system, it is between 10 and 100 orders, therefore, a new model in predicting the power needs to be developed. (3) Spray nozzle with a 20 mm extension is suitable for the production of fresh water and power generation in stationary nozzle, but the convergent–divergent nozzle has been proved to suit in rotary system both in production of fresh water and power generation. As for the desalination, it is a premise to use CDP to prevent the saline water deteriorating the farm land in Australia. In our previous tests, it is reliable to produce more
In the system, the nozzle is an important component which not only affects the percentage of fresh water, but also influences the power generation. When the heated water passes through the
Percentage of fresh water vs. input temperature in rotary nozzles 12
Theory
Spray nozzles
C-D nozzles
10 8 6 4
Pressure (bar) or Velocity (m/s)
Pressure, Velocity vs. Rotation
250 200 150 100 50 0 1000
3000
5000
7000
Rotation of Arms (RPM) Pressure in the Nozzles vs. Rotation of Arms Velocity from the Nozzles vs. rotation of Arms
b 1.2
Throat Diameter of Nozzles vs. Rotation of Arms
1 0.8 0.6 0.4 1000
2 0 10.0
a
Throat Diameter (mm)
Percentage of fresh water (%)
3. Conclusions
2000
3000
4000
5000
6000
Rotation or Arms (RPM) 20.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
Throat Diameter of Nozzles vs. Rotation of Arms
Input temperature (°C) Fig. 9. Percentage of fresh water in different nozzles.
Fig. 10. (a) The pressure, velocity vs. the rotation of shaft. (b) The relationship between throat diameter and rotation.
Y. Zhao et al. / Renewable Energy 34 (2009) 401–408
The rate of force of test to theory (%)
20
The rate of the thrust of test to theory due the extention
18 16 14 12 10 8
without extention
6
20mm extention
4
40mm extention
2 0 50
60
70
80
90
Fig. 13. Optimal power and rotation vs. input temperature.
100
Temperature (°C) Fig. 11. The relations between the ratio of thrusts and input temperature.
nozzle it will flash due to the decreasing of pressure and to deduce the suitable modeling of flow is crucial. In the last 50 years, there had been hundreds of models proposed on the calculation of the critical flow rate of a two-phase, one component flow. Some models have no theoretical support and are based on the semi-empirical formulas, this is because the process is too complicated in which when the flash happens, there will be different types of pattern during the process, therefore, the traditional mass, momentum and energy conservation equations have been exerted more complicated relations, such as two-phase interaction, fluid and gas properties and the friction of the wall of the nozzles and based on the different situations and assumptions many models have been proposed. Ideally, with suitable simplifying assumptions from complex theories (e.g. based upon all of the six balance equations in which, three for fluid and three for gas) and equations on the properties, the solution can be solved, especially using the CPU [13–15]. Recently, a trend is seen of using computer software to generate vivid pictures and/or animations to illustrate the process to the readers, but concerning the assumption, modeling is more or less arbitrary. Generally, the modeling on the two-phase flow can be classified into two main categories [15]: theories which assume
Power vs. Rotation for Different Efficiency of the Nozzles
1200
Power Generation (Watts)
407
100%
1000
4.2. The way to produce vacuum in chamber Another important component is the vacuumed system. At present, we apply vacuum pump to create about 4 kPa of pressure and running on electricity may not be practical in some regional/ rural areas. In this project, there are two alternatives to solve this problem. One is to use eductor installed in cooling system to replace the vacuum pump. Here more tests on the suitable pressure in the chamber need to be done; not only does it affect the cooling temperature, critical flow, but it also links to the efficiency of the system as well, and if we can use eductor to replace the vacuum pump, this system will be more economical. Therefore, more experiments are to be conducted to make sure the eductor can sustain the demand of extracting the air due to the leakage and solution in the salty water. Another alternative is to choose solar collector that consists of evacuated glass tube combined with heat pipe to heat the saline to 130 C and pressure up to 300 kPa. Before the CDP starts to work, blowing out the air in the chamber through the pressurized steam creates the vacuum by operating the condenser. This technology is successfully applied in the production of heat pipe. The principle of the idea can be seen in Fig. 16 and the total efficiency of the system can reach 35%.
90% 80%
800
4.3. The effect by vapour drag on the rotary nozzles and new design nozzles
70% 60%
600
50% 400 200 0
thermodynamic equilibrium throughout the expansions which can be further divided into homogeneous theories and non-homogeneous theories; and non-equilibrium theories. Here homogeneous theories based on the thermodynamic equilibrium are adopted because the model is relatively simple while it can still provide an accurate and satisfactory prediction. Many practical applications have taken it as basic model, especially in the calculation on the safety of water-cooled nuclear power plant.
0
100
2000
30000
4000
5000
Rotation of Arms (RPM) Fig. 12. The relations between power, rotation and efficiency.
6000
Vapour density and rotor shape are the main factors to the drag; the former is determined by the cooling temperature, making it also determines fresh water production. Because the shape to the drag is complicated, it concerns with nozzles, chamber and demister system, the balance of the fresh water production and power generation has to be taken into consideration. For example, when the rotary nozzles exerted a drag force upon, it brings the vapour in the chamber to rotate, which in turn helps the liquid droplet separation with the vapour; this is beneficial to the fresh water production, but it is disadvantageous to the power
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Y. Zhao et al. / Renewable Energy 34 (2009) 401–408
Power vs. rotation in different effciency (CD=0.0808)
1200
Power (W)
1000
100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 7% 6%
800 600 400 200 0
0
500
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000
Rotation (rpm) Power vs. rotation in different effciency (Cd=0.10)
1200
Power (W)
1000
100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 7%
800 600 400 200 0
0
1000
2000
3000
4000
5000
Fig. 16. The principle of the new idea.
generation. These aspects will be researched and evaluated as a whole in the next phase on the new design of the nozzles. 6000
Acknowledgements
Rotation (rpm) Power vs. rotation in different effciency (Cd=0.15)
1200 1000
100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 7%
Power (W)
800 600 400 200 0
0
500
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000
Rotation (rpm) Fig. 14. Optimal power vs. rotation in different drag coefficients.
I would like to take this opportunity to thank the financial support by Australian Greenhouse Office. Also, I would like to give my thanks to Goodie David who helped the team to construct the prototype in RMIT. Many thanks should be to the members in our Renewable Energy Care Group in RMIT. References [1] [accessed 01.12.06]. [2] Zhi-Yong Han, Ying Fan, Jian-Ling Jiao, Ji-Sheng Yan, Yi-Ming Wei. Energy structure, marginal efficiency and substitution rate: an empirical study of China. Energy 2007;32(6):935–42. [3] Water for people – water for life. The United Nations World Water Development Report 1. ISBN 92-3-103881-8. Tokyo, Japan: UNESCO Publishing; 2003. p. 10–1. [4] Water: a shared responsibility. The United Nations World Water Development Report 2. ISBN 92-3-104006-5. Mexico: UNESCO Publishing; 2006. p. 17–20. [5] [accessed 26.07.05]. [6] Akbarzadeh A, Dixon C, Johnson P. Parametric analysis of a simple reaction water turbine and its application for power production from low head reservoirs; 2002. [7] Xu Jijun. Boiling heat transfer and gas–liquids two-phase flow. Beijing, China: Nuclear Energy Publishing Press; 1996. [8] Fauske HK. Contribution to the theory of two-phase, one-component critical flow, ANL-6633; 1962. [9] Alger TW. The performance of two-phase nozzles for total flow geothermal impulse turbines, UCRL-76417. Livermore, CA; 1975. [10] Lin Taylor. Preliminary design and calculation on the mill rotor. Unpublished investigation; 2005. [11] Riznic JR, Ishii M. Bubble number density and vapour generation in flashing flow. International Journal of Heat and Mass Transfer 1989;32(10):1821–33. [12] Fabris G. Two phase flow turbine for cogeneration, geothermal, solar and other applications. FAS Engineering; May 2006. [13] Henry RE. A study of one- and two-component, two-phase critical flows at low qualities, ANL-7430; 1968. [14] Wallis GB. The separated flow model of two-phase flow, EPRI NP-275; 1976. [15] Dauria F, Vigni P. Two-phase critical flow models, CSNI Report No.49. Roma; 1980.
Further Reading
Fig. 15. New design of the nozzles [12].
Incropera Frank P, David P. Dewitt Fundamentals of heat and mass transfer. John Wiley & Sons; 2002
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Simultaneous desalination and power generation using solar energy Yuchun Zhao*, Aliakbar Akbarzadeh, John Andrews School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, PO Box 71, Bundoora, Vic. 3083, Australia
a r t i c l e i n f o
a b s t r a c t
Article history: Available online 7 July 2008
Using solar energy to produce fresh water and electricity simultaneously is a prospective way to solve the problems combining fresh water shortage, energy crisis and farm land degradation in Northern Victoria. This paper records the process of calculating the performance of the nozzle applying homogenous equilibrium model, designing and testing the prototype of such system using three different types of the nozzles in static and rotary systems. The research on the project is divided into two steps: first is about static system in which the spray nozzle is proved to be the best in both production of fresh water and power generation; while on the second stage, the convergent–divergent (C–D) nozzles are the best in rotary system. Some data were analyzed theoretically based on the test and the results found that the percentage of fresh water measured by experiment is consistent with the calculation using homogenous equilibrium expansion model (HEM), however, there is big difference in power generation between theory and experiments. Based on our experimental figures and analysis, the reasons for low power generation are found and a new model is proposed. According to the new model, a different reaction turbine using curve length C–D nozzles is designed to overcome the problems which were encountered in the previous prototype. After analyzing the efficiency of the cycle by T–s diagram, the evacuated tube solar collector integrated heat pipe is suggested to be applied on this system. Ó 2008 Elsevier Ltd. All rights reserved.
Keywords: Desalination Power generation Solar energy Convergent–divergent nozzle Flashing flow modeling CDP (combined desalination and power generation)
1. Introduction These days, the limited resources that are usable energy, fresh water and arable land are pestering human being sustainable existences. Firstly, based on the investigation of World Energy Council, although the increase of energy consumption is estimated about 1.7% per year in next 20 years, the situation is still crucial, because the demand of crude oil increases dramatically while the reserves fell by 2.7% [1], especially in China, the demand rate of increase reached 13.21% in 2003 [2]. Secondly, for fresh water, according to the report of UN in 2003, it has been estimated that today more than 2 billion people are affected by water shortages in over 40 countries: 1.1 billion do not have sufficient drinking water and 2.4 billion have no provision for sanitation and the problem is often worst that the population of developing countries living in water poverty at present will increase to 60% by 2020 [3]. At the same time, when humanity has constructed a huge global ecological engineering project to solve the shortage of fresh water and energy crisis, the intervention on ecosystems always results in the negative effects on biodiversity [4], such as the dam of Three Gorges of Yangzi River in China. Lastly, the arable land is decreased due to the saline, deserted and overgrassed. The consultants hired by The
* Corresponding author. E-mail address: [email protected] (Y. Zhao). 0960-1481/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2008.05.018
Australian Conservation Foundation and the National Farmers Federation predict in a report that Australia is facing the loss of 15.5 million hectares – equivalent to 70% of Victoria – to salinity. The report continues ‘‘the estimated total cost of resource degradation is to be more than 2 billion dollars, about half the net annual value of farm production which was 3.9 billion dollars during 1998–1999 – Unless action is taken to address the problems, the annual cost of dry land salinity alone could increase to 670 million dollars in 2020’’ [5]. For example, in Northern Victoria, the local forests are being killed and grasslands are being degraded due to salting; the deposition of salt was the result of overdrawing underground water for farming and other industrial or household use (Fig. 1). Furthermore, with the development of the industry and the increasing demand, more fresh water and power are needed, while the situation is that the resource is limited. Therefore, finding the sustainable method to satisfy the demand of the fresh water and energy should be one of the most important tasks in the agenda of both the government and researchers alike. Based on theoretical investigation along with some preliminary experiments it would be possible to simultaneously produce fresh water and power from saline water heated by renewable sources [6]. The project focuses on two aspects: fresh water production and power generation. The principle is that when the hot salt water heated by the solar pond passes through the rotary nozzles driven by the difference of atmospheric pressure and the pressure of the vacuumed chamber, it will vaporize and then condenses into the
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Nomenclature A D F R V p x Cd E P T h s _ m
area (m2) diameter of the nozzle thrust (N) radius (m) velocity (m/s) pressure (kPa) vapour quality in the mixture (%) drag coefficients energy (kJ) power (W) temperature ( C), torque (N m) specific enthalpy (kJ/kg) specific entropy (kJ/kg K) mass flow rate (kg/s)
n specific volume (m3/kg) r density (kg/m3) u angular velocity (rad/s) Subscripts 1, 2, . arbitrary position c critical condition g gaseous phase k kinetic o outlet s system a absolute d drag i inlet l liquid phase r relative t throat
Greek symbols efficiency (%)
h
fresh water, and the mixture exiting the nozzles at high velocity will exert an anti-force on the nozzles, making them rotate which will increase the pressure further, as a result, the velocity of the mixture will increase further and the rotation of nozzles can thus generate more power. Fig. 2 gives the designs of principle system and the actual model is shown in Fig. 3. In the system, the chamber can be vacuumed by an eductor which is connected to cooling water pipe. This paper mainly contains three types of information. 1. Calculating the performance of the nozzle using homogenous equilibrium model and tests on the static nozzle system engaged to obtain preliminary results for the design and construction of CDP rig. 2. Investigation on the flash flow through the nozzles, conducted by measuring the trust exacted on different shapes and sizes in diameter of throat, and comparing them with the theoretical
calculations. Previously many models were set up to solve the safety problems in nuclear power plants [7,8] and to improve the efficiency of two-phase nozzle employed in geothermal turbine [9]; however, as the parameters in our case are different, first-hand research was needed to ascertain the most suitable model to optimize the performance in low temperature and pressure conditions. 3. The test on production of fresh water and electricity generation will be carried out to find out which nozzle is mostly suitable for both stationary and rotary systems. Standards of evaluation will be mainly on power generation and percentage of fresh water production. During the test, results will be compared with experiments and factors affecting the performance will be addressed.
2. Basic calculation and analysis of relative experiments’ figures 2.1. The experimental instruments The schematic of the stationary test system is demonstrated in Fig. 4.
Fig. 1. Trees dying due to the saline coming from the underground water in Pyramid Hill, Victoria.
Fig. 2. The principle and the practical system with the fixed nozzles.
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Fig. 3. The practical system with the fixed nozzles.
The parameters of main components are Load cell (Model UU18-K002): 2 kgf, accuracy 0.03%. Pressure transducer (PMP1400): 1 bar, 0.25%. Data acquisition (MV200): 30 channels, 0.15%. The apparatus used for force measurement and calibration in static nozzle and the measurement about rotation of shaft in rotational nozzles are shown in Fig. 5.
2.2. The preliminary calculation of fresh water percentage and comparison with test In the system, the following parameters are assumed to the performance of solar pond. Basically, the temperature of saline can be heated to 77.5 C by solar pond; therefore, we can calculate the performance as follows. The flow of the fluid in the nozzle is illustrated in Fig. 6(a) and the T–s diagram in Fig. 6(b). In the situation of the system, the percentage of fresh water depends on the difference of temperature between cooling and heated solar pond when the saline water vaporizes completely. Fig. 7(a) demonstrates the percentage of the fresh vs. temperature by the solar pond when cooling temperature is 25 C and Fig. 7(b) illustrates the effect on the fresh water percentage of the cooling temperature. The experimental figures show the variation is less around 1.0% than theoretical calculation. And in fact, the cooling water temperature cannot exactly describe the actual situation because the air concentration in the saline solution can affect the evaporation itself, some more precise assumptions will be of assistance, but the experiment shows this rig is reliable for the practical application. Based on the results of static test, the nozzles adopted in rotary nozzle system are spray nozzles and C–D nozzles which are installed on the rotational arms (Fig. 8). The results are depicted in Fig. 9. From the picture, it can be found that there is no obvious difference in different nozzles, but all of the nozzles can produce more fresh water than theoretical prediction, this is due to the
Fig. 4. The schematic test of rig. (a) Static nozzle system. (b) The rotary system.
reaction between the high speed mixture and surrounding vapour around the nozzles. 2.3. The preliminary calculation of the diameter of nozzles, power generation The homogenous equilibrium expansion model (HEM) assumes that: 1. 2. 3. 4.
the flow through the nozzle is isentropic process; velocities in two phases are equal; properties’ data correspond to those of a static, equilibrium; the flow is one-dimensional flow.
Known:
To ¼ 25 C; so ¼ 1:0753 kJ=ðkg KÞ _ o ¼ 0:05 kg=s ho ¼ 315:94 kJ=kg; m po ¼ 3:169 Kpa ;
Ti ¼ 77:5 C; si ¼ 1:0753 kJ=ðkg KÞ _ i ¼ 0:10 kg=s hi ¼ 334:89 kJ=kg; m
pi ¼ 42:86 Kpa ;
And vi and vnozzle are nearly zero when the nozzle is assumed to be static.
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a
b
Generator V
Reflective Sheet
Coupling AC 220
Rotation (rpm)
Tachometer
Driving Motor
Shaft rotation vs. voltage Linear (Shaft rotation vs. voltage)
4000 3000 2000
R= 249.61V
1000 0
0
2
4
6
8
10
12
14
16
Voltage (V) Fig. 5. The measurement systems and calibration. (a) The force measure system and calibration in static nozzle. (b) The calibration of rotation of shaft in rotary nozzles.
To obtain the Vo: It is assumed that the flow is adiabatic from the centre of the nozzles to the exit of the nozzle; the following equations can be obtained:
1 1 hi þ Vi2 ¼ ho þ Vo2 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Vo ¼ Vi2 þ 2ðhi ho Þ Vo ¼ 194:67 m=s sffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffi _ _ m 4A 4m A ¼ and Do ¼ D ¼ rVo p o prVo
(1)
From the value of heated saline temperature of 77.5 C and cooling temperature, we can calculate the outlet diameter of the nozzles. For the rotary nozzles, the pressure will increase and when the arm is 0.4 m, the value of Dt be obtained by (1), taking the density of saturated water at 77.5 C, Dt can be calculated. The relationship between the pressure inside the nozzles, velocity of exit from the nozzles vs. shaft rotation is given in Fig. 10(a) and the throat diameter of the nozzles vs. the responsive u of the shaft can be found in Fig. 10(b). During the test, three designs of nozzles were experimented; spray nozzle in production of fresh water is the most efficient and convergent–divergent nozzle (Fig. 10(b)) is comparatively the same in trust, but orifice is not suitable for CDP system. Therefore, most of the later experimenting efforts were focused on the spray nozzle. However, because of the existence of friction of the nozzle, this design possesses its limitations, Fig. 6(b) gives the typical process and Fig. 11 gives the ratio of thrust of test to the theory. It can be found that the extension of 20 mm is good but 40 mm would not make a promising improvement. According to the results of the
experiment, the nozzles selected in the next stage on the rotary CPD will be focused on spray nozzles with 20 mm length. And at the same time, a length of 20 mm convergent–divergent nozzle will be tested for comparison. At point 1 (Fig. 6(b)), the pressure is about 101 kPa, when the fluid flows to the end of arms, the pressure will climb to the peak point 2 due to the centrifugal force (1–2 is thought as isentropic compression). From point 2 to point 3s, with the decrease of the pressure, the sub-cooled saline will reach its saturated point 3s and 3, and then begin to vaporize until to the point 4s. For the piratical application, it will reach point 4 (point 4r means the actual entropy due to the reaction with the surrounding vapors in the chamber). If the efficiency of nozzle is ht we have
ht ¼
h1 h4 h1 h4s
(2)
where h4 ¼ h1 (h1 h4s)/ht. Then the specific kinetic energy is
Ek ¼ ðh1 h4 Þht ¼ 18:95ht pffiffiffiffiffi Vo ¼ 194:7 ht
(3)
When the nozzles are in the constant rotary, we can calculate the power (P) produced by the steam according to the following formula:
_ m _ i hi 2m _ o ho ht i ðVo uRÞ2 Td u Tf P ¼ m 2
(4)
In the system, drag torque Td by vapour is proportional to the rotation, while the power loss to friction is fixed – less than 5% of the
Y. Zhao et al. / Renewable Energy 34 (2009) 401–408
a
405
Fresh water percentage vs. temperature of spray nozzle (cooling temperature 25°C) 12
Fresh water percentage(%)
11 10 9 8 7 6 5
without extension 20mm extension 40mm extension theory without extention
4 3 2 50
60
70
80
90
100
Input temperature (°C)
Fresh Water Percentage (%)
b
Fig. 6. The flow in the nozzles (a) and the T–s diagram (b).
Fresh Water Percentage vs. Cooling Temperature 9 8
Theory test
7 6 5 4 3 20
25
30
35
40
45
50
Cooling Temperature (C) total power throughout experiment. Drag force Fd can be expressed as: Fd ¼ 1/2(CdrV2A) [10], therefore
Td
¼ 2
Fig. 7. (a) The percentage of the fresh vs. inlet temperature on static nozzle. (b) The percentage of the fresh vs. cooling temperature on static nozzle.
RR
0 r dFd Rr 1 2 0 2rCd rðr uÞ Da dr RR ¼ Cd rDa u2 0 r 3 dr
ð5Þ
¼ 2
where Da ¼ 10 mm, Td ¼ 1.64 105u2.
Cd ¼ 0.0808,
R ¼ 0.4 m,
r ¼ 3.169 kg/m3,
pffiffiffiffiffi P ¼ 1895ðht 5%Þ 0:05ð194:7 ht 0:4uÞ2 1:64 105 u3 (6) Fig. 12 shows the relation between power generation and rotation on different ht. According to the results on the static nozzles and the limitations of the system design, three different throat diameters (0.5 mm, 1.0 mm and 2 mm) in C–D nozzles and a diameter of 1 mm spray nozzles have been tested. The experimental data prove the C–D nozzle of 1 mm throat diameter is the best in generating electricity, but the result is much less than the theoretical calculation. Fig. 13 gives diagram about the optimal power generated and rotation by system vs. input temperature. After comparing the results with theory, a simple test was carried out in which a DC power was supplied to make the shaft rotate in the same condition, and it is shown that more than 105 W was needed to reach 1000 rpm, that means the drag is too big and the drag coefficient Cd needs to be measured based on the system, therefore, more test needs to be done using different arms with section area. Another factor affecting the power generation is the
nozzle efficiency, it seems the efficiency is much less than that of one-phase nozzle flow, which can be attributed to the velocity slip between the two phases and abrupt expansion outside of the nozzles. 2.4. The modified modeling on the flashing flow in C–D nozzle According to Eqs. (5) and (6), it can be written as
pffiffiffiffiffi P ¼ 1895ðht 5%Þ 0:05ð194:7 ht 0:4uÞ2 2:03 104 Cd u3
(7)
Based on Eq. (7), Fig. 14 describes the trends for different Cd, from these figures, it can be found that the test results are in the range of low efficiency and big drag coefficients. Therefore, for the new modeling, two factors should be considered, one is Cd, another is nozzle efficiency. In fact, when comparing theory with test results in Fig. 13, the efficiency lies in the curves of less 10% in Fig. 14. There is a good method to reduce the coefficient that is using two wheel sheet to cover the nozzles and arms, which will be considered with the new nozzle design. As for the low efficiency of the nozzles, generally the time-delay in bubble nucleation in flash flow was of 1 ms [11], that means the length of nozzle at least more than 20 cm if the speed more than 200 m/s. Obviously, in CDP system, it is not content due to the dimension limitation. Furthermore, the velocity slip also contributes to the loss of efficiency; hence new modeling
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Fig. 8. The nozzles in the test. (a) Spray nozzle. (b) Convergent–divergent nozzle.
will take the assumptions that the velocities in different phases are different. As a result, the new design about the nozzles will look like that in Fig. 15. There are two advantages in the new design. Firstly, the drag will drop dramatically because there is no section to cause resistance; the only drag is coming from the shear of the vapour between the surfaces of the wheel and surrounding vapour and it is very small. Secondly, the length of new curve nozzle is sufficient for bubble to vaporize and to make acceleration smoother, then to improve the efficiency of the nozzle.
than 8.0% fresh water using 20 mm long extension spray nozzles when the input temperature is 77.5 C, and the results of the test are a litter bigger than the theoretical calculation, especially in rotary nozzle system. (4) The drag of vapour and un-fully expansion are the main reasons for low efficiency in power generation, hence the new design of nozzle needs to be done in the future work.
4. Future work and discussion 4.1. Modeling of the nozzles
(1) According to our calculation and preliminary experiments on the fixed and rotary nozzles, it is possible to use renewable energy to produce fresh water, desalinize the salt and generate the electricity simultaneously. The concept has been conformed by the experiment. (2) The homogenous equilibrium model can be applied in the static nozzle system to calculate the percentage of fresh water, but there is big difference in power generation. In the static nozzle system, the variation of the force measurement is in the same order; while in rotary system, it is between 10 and 100 orders, therefore, a new model in predicting the power needs to be developed. (3) Spray nozzle with a 20 mm extension is suitable for the production of fresh water and power generation in stationary nozzle, but the convergent–divergent nozzle has been proved to suit in rotary system both in production of fresh water and power generation. As for the desalination, it is a premise to use CDP to prevent the saline water deteriorating the farm land in Australia. In our previous tests, it is reliable to produce more
In the system, the nozzle is an important component which not only affects the percentage of fresh water, but also influences the power generation. When the heated water passes through the
Percentage of fresh water vs. input temperature in rotary nozzles 12
Theory
Spray nozzles
C-D nozzles
10 8 6 4
Pressure (bar) or Velocity (m/s)
Pressure, Velocity vs. Rotation
250 200 150 100 50 0 1000
3000
5000
7000
Rotation of Arms (RPM) Pressure in the Nozzles vs. Rotation of Arms Velocity from the Nozzles vs. rotation of Arms
b 1.2
Throat Diameter of Nozzles vs. Rotation of Arms
1 0.8 0.6 0.4 1000
2 0 10.0
a
Throat Diameter (mm)
Percentage of fresh water (%)
3. Conclusions
2000
3000
4000
5000
6000
Rotation or Arms (RPM) 20.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
Throat Diameter of Nozzles vs. Rotation of Arms
Input temperature (°C) Fig. 9. Percentage of fresh water in different nozzles.
Fig. 10. (a) The pressure, velocity vs. the rotation of shaft. (b) The relationship between throat diameter and rotation.
Y. Zhao et al. / Renewable Energy 34 (2009) 401–408
The rate of force of test to theory (%)
20
The rate of the thrust of test to theory due the extention
18 16 14 12 10 8
without extention
6
20mm extention
4
40mm extention
2 0 50
60
70
80
90
Fig. 13. Optimal power and rotation vs. input temperature.
100
Temperature (°C) Fig. 11. The relations between the ratio of thrusts and input temperature.
nozzle it will flash due to the decreasing of pressure and to deduce the suitable modeling of flow is crucial. In the last 50 years, there had been hundreds of models proposed on the calculation of the critical flow rate of a two-phase, one component flow. Some models have no theoretical support and are based on the semi-empirical formulas, this is because the process is too complicated in which when the flash happens, there will be different types of pattern during the process, therefore, the traditional mass, momentum and energy conservation equations have been exerted more complicated relations, such as two-phase interaction, fluid and gas properties and the friction of the wall of the nozzles and based on the different situations and assumptions many models have been proposed. Ideally, with suitable simplifying assumptions from complex theories (e.g. based upon all of the six balance equations in which, three for fluid and three for gas) and equations on the properties, the solution can be solved, especially using the CPU [13–15]. Recently, a trend is seen of using computer software to generate vivid pictures and/or animations to illustrate the process to the readers, but concerning the assumption, modeling is more or less arbitrary. Generally, the modeling on the two-phase flow can be classified into two main categories [15]: theories which assume
Power vs. Rotation for Different Efficiency of the Nozzles
1200
Power Generation (Watts)
407
100%
1000
4.2. The way to produce vacuum in chamber Another important component is the vacuumed system. At present, we apply vacuum pump to create about 4 kPa of pressure and running on electricity may not be practical in some regional/ rural areas. In this project, there are two alternatives to solve this problem. One is to use eductor installed in cooling system to replace the vacuum pump. Here more tests on the suitable pressure in the chamber need to be done; not only does it affect the cooling temperature, critical flow, but it also links to the efficiency of the system as well, and if we can use eductor to replace the vacuum pump, this system will be more economical. Therefore, more experiments are to be conducted to make sure the eductor can sustain the demand of extracting the air due to the leakage and solution in the salty water. Another alternative is to choose solar collector that consists of evacuated glass tube combined with heat pipe to heat the saline to 130 C and pressure up to 300 kPa. Before the CDP starts to work, blowing out the air in the chamber through the pressurized steam creates the vacuum by operating the condenser. This technology is successfully applied in the production of heat pipe. The principle of the idea can be seen in Fig. 16 and the total efficiency of the system can reach 35%.
90% 80%
800
4.3. The effect by vapour drag on the rotary nozzles and new design nozzles
70% 60%
600
50% 400 200 0
thermodynamic equilibrium throughout the expansions which can be further divided into homogeneous theories and non-homogeneous theories; and non-equilibrium theories. Here homogeneous theories based on the thermodynamic equilibrium are adopted because the model is relatively simple while it can still provide an accurate and satisfactory prediction. Many practical applications have taken it as basic model, especially in the calculation on the safety of water-cooled nuclear power plant.
0
100
2000
30000
4000
5000
Rotation of Arms (RPM) Fig. 12. The relations between power, rotation and efficiency.
6000
Vapour density and rotor shape are the main factors to the drag; the former is determined by the cooling temperature, making it also determines fresh water production. Because the shape to the drag is complicated, it concerns with nozzles, chamber and demister system, the balance of the fresh water production and power generation has to be taken into consideration. For example, when the rotary nozzles exerted a drag force upon, it brings the vapour in the chamber to rotate, which in turn helps the liquid droplet separation with the vapour; this is beneficial to the fresh water production, but it is disadvantageous to the power
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Power vs. rotation in different effciency (CD=0.0808)
1200
Power (W)
1000
100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 7% 6%
800 600 400 200 0
0
500
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000
Rotation (rpm) Power vs. rotation in different effciency (Cd=0.10)
1200
Power (W)
1000
100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 7%
800 600 400 200 0
0
1000
2000
3000
4000
5000
Fig. 16. The principle of the new idea.
generation. These aspects will be researched and evaluated as a whole in the next phase on the new design of the nozzles. 6000
Acknowledgements
Rotation (rpm) Power vs. rotation in different effciency (Cd=0.15)
1200 1000
100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 7%
Power (W)
800 600 400 200 0
0
500
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000
Rotation (rpm) Fig. 14. Optimal power vs. rotation in different drag coefficients.
I would like to take this opportunity to thank the financial support by Australian Greenhouse Office. Also, I would like to give my thanks to Goodie David who helped the team to construct the prototype in RMIT. Many thanks should be to the members in our Renewable Energy Care Group in RMIT. References [1]
Further Reading
Fig. 15. New design of the nozzles [12].
Incropera Frank P, David P. Dewitt Fundamentals of heat and mass transfer. John Wiley & Sons; 2002