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Experimental investigation on the characteristics of flash evaporation from superheated water jets for desalination
Desalination 251 (2010) 103–111
Contents lists available at ScienceDirect
Desalination j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / d e s a l
Experimental investigation on the characteristics of flash evaporation from superheated water jets for desalination Sami Mutair a,1, Yasuyuki Ikegami b,⁎ a b
Graduate School of Science and Engineering, Saga University, 1-Honjo-machi, Saga city, Saga Prefecture, 840-8502, Japan Institute of Ocean Energy, Saga University, 1-Honjo-machi, Saga city, Saga Prefecture, 840-8502, Japan
a r t i c l e
i n f o
Article history: Received 11 September 2008 Accepted 19 September 2009 Available online 14 November 2009 Keywords: Flash evaporation Low temperature thermal desalination (LTTD) Superheated jet
a b s t r a c t A promising method of desalination suitable for low-populated islands and remote areas is experimentally investigated at a small desalination plant capable of producing 15.2 tons of fresh water per day based on the flash evaporation from superheated water jets. In this method, water at a temperature ranging from 24 to 40 °C is brought to superheat condition through the injection into a depressurized chamber maintained below the boiling pressure that corresponds to the injected water temperature. A part of the injected water quickly evaporates in order to regain equilibrium at the reduced pressure, and the generated steam is condensed on a surface condenser supplied with the cold water. Even at very low degrees of superheat, flash evaporation from the superheated jets has shown high efficiency in converting the latent heat of the liquid water into vapor within the jet residence time which does not exceed a fraction of a second. An exponentially decaying curve model that simulates the temperature decline curves at the centerline of the upward flowing jet is developed and found matching the experimental data considerably. Influence of flow conditions on the characteristics of the flashing jet and on the intensity of the flash evaporation is also clarified. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Water scarcity on the earth and its uneven distribution with population forced mankind to develop alternative water resources; thermal desalination is the most widely installed technique to substitute the water shortage, but the high capital and running costs are major challenges limit its applications; this high cost arises from the complexity of the devices involved in the conventional thermal desalination processes, containing the cost of feed water heating up to more than 100 °C to produce the steam, in addition to the large volume required for evaporating the seawater in long series of stages or effects. The estimated thermal energy required to evaporate the seawater by MSF and ME desalination processes is huge and can be very expensive if it is obtained directly from boilers (not extracted from steam turbine) and for this reason, thermal desalination is limited to places where energy resources are plenty at low cost. Great efforts have been spent towards the utilization of the renewable energy resources in driving the desalination process; among the promising techniques is the utilization of the ocean thermal energy whereas the obtainable temperature difference between the warm water at the surface of the ocean and the cold water at a depth of 1000 m is as high as 20 °C at many places. Many researches have been ⁎ Corresponding author. Tel.: +81 952 28 8624; fax: +81 952 28 8595. E-mail address: [email protected] (Y. Ikegami). 1 Tel.: + 81 952 28 8624; fax: +81 952 28 8595. 0011-9164/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2009.09.136
conducted for the implementation of this temperature difference in producing fresh water through the injection of the warm surface water of the ocean in a depressurized chamber maintained at a pressure lower than the boiling pressure that corresponds to the injected water temperature; the injected water then becomes superheated; hence, a part of the injected water turns to steam in order to regain the equilibrium condition. The generated steam is then condensed on a surface condenser that is supplied with the cold water drawn from the deep layers of the ocean. This process is environment-friendly as it requires no preheating of the feed water and is commonly referred to as low temperature thermal desalination (LTTD). A mini-sized plant based on this concept is under operation in Kavaratti (one of the Indian Lakshadweep islands), since 2005, the plant was developed by the national institute of ocean technology and produces fresh water at a rate of 100 tons/day, the warm water is drawn from the surface layers of the ocean at a temperature ranging from 28 to 30 °C while the cold water is sucked from the depth of 350 m at a temperature ranging from 7 to 15 °C, another barge-based LTTD plant with a capacity of 1000 tons/day was designed and commissioned 40 km off Chennai in 2007, the plant was successfully run for over 3 weeks. As the process has demonstrated sustainability in several places, implementation of this technique more widely is expected; therefore, deep understanding of the flash evaporation phenomenon that occurs in the superheated water jets after being injected into the depressurized environment is vital for the efficient design of the flash evaporator and for the selection of the plant's
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operational conditions as well. Miyatake et al. [1] has experimentally investigated the flash evaporation phenomenon that occurs when the sub-cooled water undergoes a sudden reduction of the surrounding pressure below its boiling pressure. Experiments were done using circular nozzles of different diameters and issue the water downward at an initial temperature of 60 °C. Through this study, water temperature was found to undergo two exponential decays after the elapsing of a period of time named delay time; variation of water temperature with time was correlated by an empirical equation assuming constant flow velocity of the jet. Through comparison, it was observed that the rate of flash evaporation from superheated water jets is extremely faster than that from superheated water pools, and also from superheated water flowing in channels as in the MSF evaporators. Miyatake et al. [2] extended the study and investigated the influence of water temperature on the flash evaporation at temperatures of 40 and 80 °C and derived a more comprehensive empirical equation suitable for predicting the variation of the water temperature at the centerline of the jet with time. However, Uehara et al. [3] have shown that the correlations proposed by Miyatake et al. [2] is not applicable for jets at initial temperatures lower that 40 °C and developed a new correlation for this purpose. Ikegami et al. [4] have investigated the influence of injection direction and showed that the upward flowing jets have better performance and faster evaporation than those flowing downward. Sasaki et al. [5] studied the phenomenon of flash evaporation from the superheated water jets that flow upward and classified the flow in the jet into four different patterns based on the velocity of the flow and the degree of superheat. Brown et al. [6] studied the mechanism of spray formation by the flashing of cylindrical jets of both water and Freon-11 and the spray formed by this process, analysis for drop sizes, drop velocities and spray patterns was carried out with the assistance of the high speed photography of the breakup zone and of the spray. Most of the data were collected for superheated water injected into the room atmosphere and a critical superheat was found, above which the jet is shattered by the rapid bubble growth within it. However, works that report on flash evaporation from superheated water jets flowing upward are few; in addition, influence of flow conditions on the intensity of flash evaporation is not clarified thoroughly, especially for jets of large diameters. This paper reports on the results of experimental investigations on flash evaporation from superheated water jets flowing vertically upward from round straight nozzles of large diameters. Temperature variation at the centerline of the flashing jet is simulated by the Boltzmann sigmoid model and particular attention is focused on the location of the curve's infection point as it implies the highest rate of flash evaporation, and the influencing factors reflect strongly on its location. The physical reasoning for the manner in which each experimental variable affects the flash evaporation phenomenon is also discussed. 2. Experimental plant and procedure A small desalination plant was constructed for research purposes at the institute of ocean energy, one of the research centers of Saga University in Japan and located in Imari city on the coast of the Sea of Japan. The plant is designed to work with the seawater as most of its parts are made of stainless steel while the heat exchange surfaces are made of titanium, the plant is equipped with seawater intake line and was intensively experimented using the seawater. The process has demonstrated sustainability in terms of quantity as the actual amount of distilled water has so far reached the maximum theoretical amount, and also in terms of quality whereas the electrical conductivity of the produced water is less than 0.0005 Siemens per meter (S/m) indicating a higher purity than the common drinking water (0.005–0.05 S/m). The chemical composition of the produced water fulfills the criteria for the drinking water as the high concentrations of Na+, C1− and the other ions in the seawater are almost completely removed. Details about the quality of the produced water are given by Ikegami et al. [7].
Fig. 1 shows a simplified schematic of the plant. After a sufficient de-aeration period, the test water is continually heated up to the desired temperature in the heater and circulated in the evaporator where the water undergoes sudden reduction of the surrounding pressure below its boiling pressure and the flash evaporation occurs, the generated steam is drawn to the condenser and then to the aftercondenser where the greater portion of the steam is condensed in a vertical plate type condenser and the little remaining steam is condensed in the after-condenser. The after-condenser is a shell-andtube type condenser installed in order to maintain annular flow in the main condenser and to prevent flooding. The resulting distilled water is released from the depressurized environment by falling several meters below the condenser level. The distilled water is then either collected in the fresh water tank or recycled in the evaporator according to the purpose of the experiment. Two vacuum pumps connected to the evaporator through the condenser and the aftercondenser work at full capacity to attain the desired vacuum in the evaporator at the beginning of each experiment and then, the vacuum is maintained constant by regulating the valves. Two separate loops of hot and cold water feed the heater and the condenser, respectively. The cold water simulates the seawater temperature at the deep layers and is prepared by a huge refrigerator of a capacity of 2532 kW set to maintain the water temperature at the cold water tank at about 8 °C. The hot water is prepared by six boilers each of a capacity of 930 kW; the boilers are operated automatically according to the necessary heat flow and are set to maintain the hot water tank at a temperature around 60 °C. Temperature distribution in the flashing jet is measured in the r–z plane perpendicular to the nozzle exit and divides the jet into two symmetrical halves by 20 platinum resistance thermometers (PRTs) (Hayashi electric engineering, SR1, accuracy: ±0.1 °C) fixed at intervals of 25 mm on a horizontal holding steel bar. The PRTs are directed vertically downward facing the flow, and the temperature is measured at the lower free end of each PRT; the holding bar is movable in the z direction and the temperature is measured at 26 stations located at different intervals from 0 to 700 mm starting from the nozzle exit. Fig. 2 shows details of the flash evaporator and Table 1 shows the investigated parameters and their experimented range. 2.1. Experimental considerations Several points are taken in consideration when performing the experiment such as the existence of the non-condensable gases in the test water which are found to significantly affect the flash evaporation. This fact is deducted from the comparison between temperature profiles at the centerline of the jet at various experiments of different deaeration periods. To avoid the effect of the non-condensable gases and to obtain reliably comparable results, test water is completely de-aerated before each experiment and the resulting distilled water is continually recycled in the evaporator until the whole test water becomes distilled with these non-condensable gases so far removed. The returning of the distilled water leads to constancy of water level in the evaporator and prevents the depletion of the test water during the experiments. As it is hard to prevent the intrusion of small contamination materials to the test water which originate either in an imperfectly cleaned evaporator or from the feed water when seawater is used, pure water is used instead throughout this work. Degree of superheat ΔTs is defined in Eq. (1) while the dimensionless temperature, θ introduced in Eq. (2) indicates the ratio of the superheat degree at a given location, to the initial superheat degree ΔTs; however, θ will be used to express temperature in the jet throughout this paper. ΔTs = T0 Tb
θðr;zÞ =
Tðr;zÞ Tb T0 Tb
ð1Þ
ð2Þ
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Fig. 1. Schematic diagram of the experimental plant.
where T0 is initial water temperature measured in the compressed liquid region by the same type of PRTs mentioned above, Tb is the boiling temperature that corresponds to the pressure inside the flash evaporator, measured at the far-field vapor by an absolute pressure sensor (Toshiba, AP3051CA, accuracy: ±15 Pa). z is the vertical
distance measured from the nozzle exit level, and r is the radial distance measured from the center of the nozzle. 3. Results and discussion 3.1. The mass evaporated by flashing Under adiabatic flow conditions, all the sensible heat consumed in the evaporation chamber is converted into latent heat of vaporization to produce steam of a temperature that is equal to the equilibrium temperature; therefore, the maximum amount of evaporated water achieved when the liquid temperature decreases to the equilibrium temperature is calculated from the heat balance Eq. (3), and the maximum ratio of evaporated-to-flashing mass is calculated by Eq. (4). mE =
mFE cpl ΔTs hfg
cpl ΔTs mE = mFE hfg
ð3Þ
ð4Þ
where mE is the mass flow rate of evaporated water and mFE is the mass flow rate of the water entering the evaporator measured by an Table 1 Influencing factors and their experimented range.
Fig. 2. Details of the flash evaporator.
Parameter
Experimented range
Nozzle diameter, d [mm] Velocity, u [m/s] Initial temperature, T0 [°C] Superheat, ΔTs [°C]
54.4, 81.3, 107 0.8, 1.25, 2.21, 3.56 24, 30, 35, 40 1–13
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electromagnetic flow meter (Tokyo Keiso, MGM1010K, accuracy: ±0.5% of reading). The actual mass flow rate of distilled water is measured by a positive displacement flow meter (Ultra Oval LUS50C11-A312, accuracy: ±0.5% of reading) installed at the distilled water recycling line that connects between the after-condenser and the evaporator. As shown in Fig. 3, evaporation ratio increases linearly with the increase of superheat degree and it is so far equal to the maximum theoretical ratio indicated by the solid line, even at degrees of superheat as low as 1 °C; however, several points are seen to lie above the solid line indicating higher evaporation ratio than the maximum, this error is attributed to the uncertainty in measuring the flow rate of the distilled water, and in measuring the temperatures and hence the exact value of the superheat degree. A maximum yield of 15.2 tons/day of distilled water is obtained at a flow rate of test water of 1586 tons/day from a nozzle of 81.3 mm diameter and at a superheat degree of 6 °C. The yield corresponds to an evaporation ratio of about 0.96%; however, the maximum theoretical amount of the distilled water when calculated by Eq. (3) at this condition is about 16.54 tons/day, the two values lie within a margin of error less that 10%. 3.2. Flow patterns Through a variety of experiments investigating the temperature variation at the centerline of the jet, three flow zones are designated in the jet, each of different characteristics: 1-Potential core zone: this zone exists near the nozzle exit and mainly characterized by unshattered flow and negligible temperature decline, the time elapsed by the flow in this zone is commonly referred to as delay time. 2-Spray zone: through this zone, the jet shatters and diffuses in conical shape so that the interface area extends and the water temperature declines rapidly. 3-Saturation zone through which the flow becomes greatly dispersed in the form of water drops surrounded by the rising vapor, the temperature in this zone is so far constant near the equilibrium temperature. Temperature readings taken in the potential core zone and in the spray zone refer to a great degree of certainty to the liquid phase temperature whereas the PRTs are continually accessed and wetted by the flowing liquid in these two zones; however, as the vertical distance z increases (as it is the case in the saturation zone), the flow spreads in a wider area and subsequently the fraction of the liquid that reaches the PRTs decreases; therefore, the temperature readings in this zone might be influenced by the surrounding vapor temperature. Fig. 4a shows the temperature profile at the jet centerline at an arbitrary condition with the three flow zones
Fig. 4. a. Dimensionless temperature profile at the centerline of the jet. b. Isothermal diagram shows the dimensionless temperature distribution in the jet.
indicated, while the isothermal diagram in Fig. 4b shows the corresponding temperature distribution at the area of influence near the nozzle exit; each flow zone in Fig. 4a has a correspondent thermal behavior in Fig. 4b, the potential core zone, spray zone and saturation zone in Fig. 4a are represented by the continuous area near the nozzle exit, the following adjacent isothermal lines and the following widespread area in Fig. 4b respectively. 3.3. Modeling of temperature variation at the centerline It is observed that the temperature decline at the centerline of the jet draws similar profiles at all the investigated conditions, and each centerline temperature plot is found to lie on a part of Boltzmann sigmoid curve that decays exponentially. A typical sigmoid curve model is represented by Eq. (5) and drawn in Fig. 5. ðA1 A2 Þ h io θ = A2 + n ðzz Þ 1 + exp δzip
Fig. 3. Variation of the evaporated mass ratio with superheat degree.
ð5Þ
where θ is the dimensionless temperature at the centerline of the jet, A1 and A2 are the initial and final θ values, zip is the center of curve and also represents the height of the inflection point between the two curvatures of different signs, and δz is the approximate range width of z
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Fig. 5. Typical Boltzmann sigmoid model.
variable through which θ value changes drastically. Fig. 6 shows the suitability of the Boltzmann model for the simulation of four sets of randomly selected experiments where the dots are the experimental readings and the solid lines are the simulation curves by the Boltzmann sigmoid model. Fig. 7 shows a generalization of the data fitting by Boltzmann model for the all investigated conditions whereas the actual distance z(exp) at which the water attains values of θ ranging from 0.1 to 0.9 is plotted on the x-axis against the corresponding distance z(cal) obtained from the proposed sigmoid curve and plotted on the y-axis. At higher values of θ, data are matching so well and uncertainty lies within 5% while at θ = 0.1, the uncertainty is higher. With the knowledge that experimental readings at low values of θ are subjected to high uncertainty due to their presence in the saturation zone which so often consists of vapor and some water mists of variable temperatures due to the explosive bubble growth accompanied with spraying from
Fig. 7. Experimental and calculated values of the height z at which θ attains several values.
the jet, the distance z(cal) at which θ attains the value 0.1 becomes more reliable than z(exp) at the same value of θ. Though the liquid temperature must decline to the equilibrium temperature for the flash evaporation to become complete, it is worth mentioning that the value of A2 which simulates θ value at the end height of the jet is found to range between 0 and 0.1 for the majority of the experiment runs; moreover, in a few cases A2 is found higher than 0.1, particularly when the superheat degree or the initial water temperature is the lowest. However, this behavior does not contradict with the fact that the actual evaporated mass is equal to the maximum theoretical amount as discussed in Section 3.1 because the temperature measurements are taken during the upward flight of the jet while the liquid undergoes further evaporation during its falling.
Fig. 6. Suitability of the Boltzmann model for the simulation of temperature decline curves.
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3.4. Influence of experimental variables Although it is easy to recognize the three mentioned flow zones in Fig. 4, it is quite difficult to determine a distinct and representative point at which every zone is initiated. As the slope of the curve at any location is an indicator for the local rate of evaporation, location of the curve's inflection point is an object of interest in this study as it implies the highest rate of evaporation, and the variation of experimental conditions reflects strongly on it. The location of the inflection point of each centerline temperature decline curve is calculated from its corresponding sigmoid curve equation obtained using fitting software. In Fig. 8, the calculated values of the inflection are plotted on the y-axis against the points locations z(cal) ip values obtained from the experimental readings corresponding z(exp) ip at the equivalent θ values. This figure shows that the inflection point can be estimated with a margin of error less that 5%. 3.4.1. Influence of flow velocity In Fig. 9a through c, the temperature variation at the centerline of the jet is plotted at various velocities and initial temperature of 30, 35 and 40 °C, respectively while the superheat degree is maintained constant. As shown in these figures, jets of higher flow velocity attain larger θ values at the same downstream distance due to the shorter elapsed time in the depressurized environment. However, the most significant influence of the flow velocity appears at the potential core zone where the increase of velocity is shown to increases the length of this zone. This behavior is attributed to the increase of the inertia of the jet which represents the retarding force that tends to maintain the jet un-shattered so that the coherent liquid column near the nozzle exit extends to longer downstream distance resulting in the suppression of the evaporation due to the increase of the static pressure at the nozzle exit and subsequently, the increase of the overall distance required to complete the evaporation. Fig. 10 shows the relationship between the flow velocity and the height of each curve's inflection point. The height of the inflection point seems to increase in a logarithmic-like relationship with the increase of flow velocity.
Fig. 9. Variation of θ with distance at various flow velocities.
3.4.2. Influence of the initial temperature Through a variety of experiments conducted in an effort to investigate the influence of water temperature, an increase of the initial water temperature T0 is found to enhance the flash evaporation linearly. Fig. 11 shows four sets of temperature variation profiles at the centerline of the jet, each set is obtained at various initial water
temperatures while the other conditions are kept constant. At relatively low flow velocities as in Fig. 11a through c, the potential core zone tends to disappears behind the vertical axis due to the initiation of the flash evaporation within the nozzle, so that θ attains a value less than 1 at the nozzle exit, this value is also influenced by the initial liquid temperature whereas it decreases with the increase of T0. However, on increasing the flow velocity as in Fig. 11d, the liquid temperature at the nozzle exit remains unchanged until a certain distance is elapsed by the flow before the bubbling starts at a further downstream distance; this delay distance decreases with the increase
Fig. 8. Uncertainty in the prediction of inflection point location by Boltzmann model.
Fig. 10. Relationship between the inflection point height and flow velocity.
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Fig. 11. Variation of θ with distance at various initial temperatures.
of the liquid temperature. Moreover, a common behavior is seen in Fig. 11a through d concerning the final θ value whereas it decreases linearly with an increase of T0. For better understanding of influence of temperature, the location of the inflection point zip is plotted against the initial water temperature at various experimental conditions in Fig. 12. As shown in this figure, the increase of the initial water temperature hastens the flash evaporation and linearly reduces the height of the inflection point. This behavior is thought to be attributed to the decrease of the latent heat of vaporization with the increase of water temperature, whereas the latent heat of vaporization is an interpretation of the energy required to increase the mean separation distance between molecules from the distance in the liquid to that several times larger in the vapor. The ratio of the distance between
molecules in the two phases can be taken as the cubic root of the ratio of specific volumes of saturated liquid and vapor as in Eq. (6). Lv = Ll
vv 1 =3 vl
ð6Þ
where Lv and Ll are the mean separation distance between molecules in the vapor and liquid phases, while vv and vl are the specific volumes of vapor and liquid respectively; evaluating this ratio at temperatures of 24 and 40 °C implies that the spacing between molecules in the bulk vapor should be 36.26 and 26.25 times that in the bulk liquid at the temperatures 24 and 40 °C respectively. In addition to the previous argument, for the nucleation process to proceed at nucleation cavity, a certain pressure difference should exist between the inner and outer surface of the bubble embryo to overcome the surface tension forces according to Eq. (7). PB Ps =
2σ rB
ð7Þ
where PB is the inner bubble pressure, Ps is the surrounding liquid pressure, σ is the surface tension, and rB is the bubble radius, referring to Fig. 13, the degree of superheat ΔTsat required to maintain this pressure difference decreases with the increase of the saturation temperature.
Fig. 12. Relationship between the inflection point height and the initial temperature.
3.4.3. Influence of Superheat degree Fig. 14 shows three sets of temperature profiles at the centerline of the jet obtained at different flow velocities, each set is plotted at several degrees of superheat while the initial water temperature is held constant. As shown in this figure, at relatively low degree of superheat, a certain increase of the degree of superheat hastens the flash evaporation markedly and results in an increase of the slope of the curve particularly in the spray zone, and shortens the distance δz through which the majority of the sensible heat is consumed by evaporation, while at higher degrees of superheat, the same increment
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Fig. 13. Variation of the saturation pressure with temperature.
will have less pronounced influence. Fig. 15 clarifies the nature of the superheat effect whereas the vertical distances z at which the water attains θ values from 0.2 to 0.9 are plotted at different degrees of superheat. The curves are seen to have steep inclinations between the superheat degrees of 2 and 4 while the trend of these curves tends to be horizontal with further increment of superheat degree. In Fig. 16, the height of each curve's inflection point, zip is plotted against the superheat degrees at various flow conditions. As shown in this figure, the height of the inflection point decreases in an exponential-like relationship with the increase of superheat degree. The enhancement of flash evaporation by the increase of superheat degree is thought to be attributed to the mean droplet size produced via atomization, whereas
Fig. 15. Relationship between superheat degree and the vertical distance at which θ attains several values.
it decreases as the degree of superheat increase due to the greater vapor release from the body of the jet. For this reason, degree of superheat is considered the driving force that controls the intensity of flash evaporation. 4. Conclusion Experiments on flash evaporation from superheated jets that issue the water upward from large nozzles were conducted and the following points were concluded: ■ Flash evaporation from superheated jets has shown efficiency in absorbing the latent heat of the liquid water for the generation of vapor within the very short residence time in the flash evaporator, even at low degrees of temperature and superheat. ■ Temperature variation at the centerlines of the superheated jets was simulated by Boltzmann sigmoid model. The model was found considerably appropriate and enables estimating the jet temperature at any height z; however, the four parameters that appear in Boltzmann equation should be correlated for this purpose. ■ Intensity of the flash evaporation was found to increase with an increase of the initial water temperature and the superheat degree,
Fig. 14. Variation of θ with distance at various superheat degrees.
Fig. 16. Variation of the height of the inflection point with superheat degree.
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and the highest evaporation rate is attained at a downstream distance that decreases linearly or exponentially with an increase of the initial water temperature or superheat degree respectively while it increases in a logarithmic-like relationship with the increase of flow velocity. Acknowledgment This research is supported by the COE program of Advanced Science and Technology for Utilization of Ocean Energy. References [1] O. Miyatake, T. Tomimura, Y. Ide, T. Fujii, An experimental study of spray flash evaporation, Desalination 36 (2) (1981) 113–128.
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[2] O. Miyatake, T. Tomimura, Y. Ide, M. Yuda, T. Fujii, Effect of liquid temperature on spray flash evaporation, Desalination 37 (3) (1981) 351–366. [3] H. Uehara, Y. Ikegami, N. Hirota, Experimental study of spray flash evaporation for desalination and otec, Joint Solar Eng. Conference, ASME, 1993, pp. 197–201. [4] Y. Ikegami, H. Sasaki, T. Gouda, H. Uehara, Experimental study on a spray flash desalination (influence of the direction of injection), Desalination 194 (1–3) (2006) 81–89. [5] H. Sasaki, Y. Ikegami, M. Monde, H. Uehara, Experimental study of flash desalination with upward spray (flow pattern and temperature distribution), Bulletin of the Society of Sea Water Science, Japan 59 (5) (2005) 354–360 Japanese. [6] R. Brown, J. Lois York, Sprays formed by flashing liquid jet, AIChE Journal 8 (2) (1962) 149–153. [7] Y. Ikegami, T. Wajima, H. Sasaki, Experimental study on desalination of seawater in Imari bay using an upward spray flash desalination plant, Bulletin of the Society of Sea Water Science, Japan 60 (2) (2006) 137–138.
Contents lists available at ScienceDirect
Desalination j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / d e s a l
Experimental investigation on the characteristics of flash evaporation from superheated water jets for desalination Sami Mutair a,1, Yasuyuki Ikegami b,⁎ a b
Graduate School of Science and Engineering, Saga University, 1-Honjo-machi, Saga city, Saga Prefecture, 840-8502, Japan Institute of Ocean Energy, Saga University, 1-Honjo-machi, Saga city, Saga Prefecture, 840-8502, Japan
a r t i c l e
i n f o
Article history: Received 11 September 2008 Accepted 19 September 2009 Available online 14 November 2009 Keywords: Flash evaporation Low temperature thermal desalination (LTTD) Superheated jet
a b s t r a c t A promising method of desalination suitable for low-populated islands and remote areas is experimentally investigated at a small desalination plant capable of producing 15.2 tons of fresh water per day based on the flash evaporation from superheated water jets. In this method, water at a temperature ranging from 24 to 40 °C is brought to superheat condition through the injection into a depressurized chamber maintained below the boiling pressure that corresponds to the injected water temperature. A part of the injected water quickly evaporates in order to regain equilibrium at the reduced pressure, and the generated steam is condensed on a surface condenser supplied with the cold water. Even at very low degrees of superheat, flash evaporation from the superheated jets has shown high efficiency in converting the latent heat of the liquid water into vapor within the jet residence time which does not exceed a fraction of a second. An exponentially decaying curve model that simulates the temperature decline curves at the centerline of the upward flowing jet is developed and found matching the experimental data considerably. Influence of flow conditions on the characteristics of the flashing jet and on the intensity of the flash evaporation is also clarified. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Water scarcity on the earth and its uneven distribution with population forced mankind to develop alternative water resources; thermal desalination is the most widely installed technique to substitute the water shortage, but the high capital and running costs are major challenges limit its applications; this high cost arises from the complexity of the devices involved in the conventional thermal desalination processes, containing the cost of feed water heating up to more than 100 °C to produce the steam, in addition to the large volume required for evaporating the seawater in long series of stages or effects. The estimated thermal energy required to evaporate the seawater by MSF and ME desalination processes is huge and can be very expensive if it is obtained directly from boilers (not extracted from steam turbine) and for this reason, thermal desalination is limited to places where energy resources are plenty at low cost. Great efforts have been spent towards the utilization of the renewable energy resources in driving the desalination process; among the promising techniques is the utilization of the ocean thermal energy whereas the obtainable temperature difference between the warm water at the surface of the ocean and the cold water at a depth of 1000 m is as high as 20 °C at many places. Many researches have been ⁎ Corresponding author. Tel.: +81 952 28 8624; fax: +81 952 28 8595. E-mail address: [email protected] (Y. Ikegami). 1 Tel.: + 81 952 28 8624; fax: +81 952 28 8595. 0011-9164/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2009.09.136
conducted for the implementation of this temperature difference in producing fresh water through the injection of the warm surface water of the ocean in a depressurized chamber maintained at a pressure lower than the boiling pressure that corresponds to the injected water temperature; the injected water then becomes superheated; hence, a part of the injected water turns to steam in order to regain the equilibrium condition. The generated steam is then condensed on a surface condenser that is supplied with the cold water drawn from the deep layers of the ocean. This process is environment-friendly as it requires no preheating of the feed water and is commonly referred to as low temperature thermal desalination (LTTD). A mini-sized plant based on this concept is under operation in Kavaratti (one of the Indian Lakshadweep islands), since 2005, the plant was developed by the national institute of ocean technology and produces fresh water at a rate of 100 tons/day, the warm water is drawn from the surface layers of the ocean at a temperature ranging from 28 to 30 °C while the cold water is sucked from the depth of 350 m at a temperature ranging from 7 to 15 °C, another barge-based LTTD plant with a capacity of 1000 tons/day was designed and commissioned 40 km off Chennai in 2007, the plant was successfully run for over 3 weeks. As the process has demonstrated sustainability in several places, implementation of this technique more widely is expected; therefore, deep understanding of the flash evaporation phenomenon that occurs in the superheated water jets after being injected into the depressurized environment is vital for the efficient design of the flash evaporator and for the selection of the plant's
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operational conditions as well. Miyatake et al. [1] has experimentally investigated the flash evaporation phenomenon that occurs when the sub-cooled water undergoes a sudden reduction of the surrounding pressure below its boiling pressure. Experiments were done using circular nozzles of different diameters and issue the water downward at an initial temperature of 60 °C. Through this study, water temperature was found to undergo two exponential decays after the elapsing of a period of time named delay time; variation of water temperature with time was correlated by an empirical equation assuming constant flow velocity of the jet. Through comparison, it was observed that the rate of flash evaporation from superheated water jets is extremely faster than that from superheated water pools, and also from superheated water flowing in channels as in the MSF evaporators. Miyatake et al. [2] extended the study and investigated the influence of water temperature on the flash evaporation at temperatures of 40 and 80 °C and derived a more comprehensive empirical equation suitable for predicting the variation of the water temperature at the centerline of the jet with time. However, Uehara et al. [3] have shown that the correlations proposed by Miyatake et al. [2] is not applicable for jets at initial temperatures lower that 40 °C and developed a new correlation for this purpose. Ikegami et al. [4] have investigated the influence of injection direction and showed that the upward flowing jets have better performance and faster evaporation than those flowing downward. Sasaki et al. [5] studied the phenomenon of flash evaporation from the superheated water jets that flow upward and classified the flow in the jet into four different patterns based on the velocity of the flow and the degree of superheat. Brown et al. [6] studied the mechanism of spray formation by the flashing of cylindrical jets of both water and Freon-11 and the spray formed by this process, analysis for drop sizes, drop velocities and spray patterns was carried out with the assistance of the high speed photography of the breakup zone and of the spray. Most of the data were collected for superheated water injected into the room atmosphere and a critical superheat was found, above which the jet is shattered by the rapid bubble growth within it. However, works that report on flash evaporation from superheated water jets flowing upward are few; in addition, influence of flow conditions on the intensity of flash evaporation is not clarified thoroughly, especially for jets of large diameters. This paper reports on the results of experimental investigations on flash evaporation from superheated water jets flowing vertically upward from round straight nozzles of large diameters. Temperature variation at the centerline of the flashing jet is simulated by the Boltzmann sigmoid model and particular attention is focused on the location of the curve's infection point as it implies the highest rate of flash evaporation, and the influencing factors reflect strongly on its location. The physical reasoning for the manner in which each experimental variable affects the flash evaporation phenomenon is also discussed. 2. Experimental plant and procedure A small desalination plant was constructed for research purposes at the institute of ocean energy, one of the research centers of Saga University in Japan and located in Imari city on the coast of the Sea of Japan. The plant is designed to work with the seawater as most of its parts are made of stainless steel while the heat exchange surfaces are made of titanium, the plant is equipped with seawater intake line and was intensively experimented using the seawater. The process has demonstrated sustainability in terms of quantity as the actual amount of distilled water has so far reached the maximum theoretical amount, and also in terms of quality whereas the electrical conductivity of the produced water is less than 0.0005 Siemens per meter (S/m) indicating a higher purity than the common drinking water (0.005–0.05 S/m). The chemical composition of the produced water fulfills the criteria for the drinking water as the high concentrations of Na+, C1− and the other ions in the seawater are almost completely removed. Details about the quality of the produced water are given by Ikegami et al. [7].
Fig. 1 shows a simplified schematic of the plant. After a sufficient de-aeration period, the test water is continually heated up to the desired temperature in the heater and circulated in the evaporator where the water undergoes sudden reduction of the surrounding pressure below its boiling pressure and the flash evaporation occurs, the generated steam is drawn to the condenser and then to the aftercondenser where the greater portion of the steam is condensed in a vertical plate type condenser and the little remaining steam is condensed in the after-condenser. The after-condenser is a shell-andtube type condenser installed in order to maintain annular flow in the main condenser and to prevent flooding. The resulting distilled water is released from the depressurized environment by falling several meters below the condenser level. The distilled water is then either collected in the fresh water tank or recycled in the evaporator according to the purpose of the experiment. Two vacuum pumps connected to the evaporator through the condenser and the aftercondenser work at full capacity to attain the desired vacuum in the evaporator at the beginning of each experiment and then, the vacuum is maintained constant by regulating the valves. Two separate loops of hot and cold water feed the heater and the condenser, respectively. The cold water simulates the seawater temperature at the deep layers and is prepared by a huge refrigerator of a capacity of 2532 kW set to maintain the water temperature at the cold water tank at about 8 °C. The hot water is prepared by six boilers each of a capacity of 930 kW; the boilers are operated automatically according to the necessary heat flow and are set to maintain the hot water tank at a temperature around 60 °C. Temperature distribution in the flashing jet is measured in the r–z plane perpendicular to the nozzle exit and divides the jet into two symmetrical halves by 20 platinum resistance thermometers (PRTs) (Hayashi electric engineering, SR1, accuracy: ±0.1 °C) fixed at intervals of 25 mm on a horizontal holding steel bar. The PRTs are directed vertically downward facing the flow, and the temperature is measured at the lower free end of each PRT; the holding bar is movable in the z direction and the temperature is measured at 26 stations located at different intervals from 0 to 700 mm starting from the nozzle exit. Fig. 2 shows details of the flash evaporator and Table 1 shows the investigated parameters and their experimented range. 2.1. Experimental considerations Several points are taken in consideration when performing the experiment such as the existence of the non-condensable gases in the test water which are found to significantly affect the flash evaporation. This fact is deducted from the comparison between temperature profiles at the centerline of the jet at various experiments of different deaeration periods. To avoid the effect of the non-condensable gases and to obtain reliably comparable results, test water is completely de-aerated before each experiment and the resulting distilled water is continually recycled in the evaporator until the whole test water becomes distilled with these non-condensable gases so far removed. The returning of the distilled water leads to constancy of water level in the evaporator and prevents the depletion of the test water during the experiments. As it is hard to prevent the intrusion of small contamination materials to the test water which originate either in an imperfectly cleaned evaporator or from the feed water when seawater is used, pure water is used instead throughout this work. Degree of superheat ΔTs is defined in Eq. (1) while the dimensionless temperature, θ introduced in Eq. (2) indicates the ratio of the superheat degree at a given location, to the initial superheat degree ΔTs; however, θ will be used to express temperature in the jet throughout this paper. ΔTs = T0 Tb
θðr;zÞ =
Tðr;zÞ Tb T0 Tb
ð1Þ
ð2Þ
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Fig. 1. Schematic diagram of the experimental plant.
where T0 is initial water temperature measured in the compressed liquid region by the same type of PRTs mentioned above, Tb is the boiling temperature that corresponds to the pressure inside the flash evaporator, measured at the far-field vapor by an absolute pressure sensor (Toshiba, AP3051CA, accuracy: ±15 Pa). z is the vertical
distance measured from the nozzle exit level, and r is the radial distance measured from the center of the nozzle. 3. Results and discussion 3.1. The mass evaporated by flashing Under adiabatic flow conditions, all the sensible heat consumed in the evaporation chamber is converted into latent heat of vaporization to produce steam of a temperature that is equal to the equilibrium temperature; therefore, the maximum amount of evaporated water achieved when the liquid temperature decreases to the equilibrium temperature is calculated from the heat balance Eq. (3), and the maximum ratio of evaporated-to-flashing mass is calculated by Eq. (4). mE =
mFE cpl ΔTs hfg
cpl ΔTs mE = mFE hfg
ð3Þ
ð4Þ
where mE is the mass flow rate of evaporated water and mFE is the mass flow rate of the water entering the evaporator measured by an Table 1 Influencing factors and their experimented range.
Fig. 2. Details of the flash evaporator.
Parameter
Experimented range
Nozzle diameter, d [mm] Velocity, u [m/s] Initial temperature, T0 [°C] Superheat, ΔTs [°C]
54.4, 81.3, 107 0.8, 1.25, 2.21, 3.56 24, 30, 35, 40 1–13
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electromagnetic flow meter (Tokyo Keiso, MGM1010K, accuracy: ±0.5% of reading). The actual mass flow rate of distilled water is measured by a positive displacement flow meter (Ultra Oval LUS50C11-A312, accuracy: ±0.5% of reading) installed at the distilled water recycling line that connects between the after-condenser and the evaporator. As shown in Fig. 3, evaporation ratio increases linearly with the increase of superheat degree and it is so far equal to the maximum theoretical ratio indicated by the solid line, even at degrees of superheat as low as 1 °C; however, several points are seen to lie above the solid line indicating higher evaporation ratio than the maximum, this error is attributed to the uncertainty in measuring the flow rate of the distilled water, and in measuring the temperatures and hence the exact value of the superheat degree. A maximum yield of 15.2 tons/day of distilled water is obtained at a flow rate of test water of 1586 tons/day from a nozzle of 81.3 mm diameter and at a superheat degree of 6 °C. The yield corresponds to an evaporation ratio of about 0.96%; however, the maximum theoretical amount of the distilled water when calculated by Eq. (3) at this condition is about 16.54 tons/day, the two values lie within a margin of error less that 10%. 3.2. Flow patterns Through a variety of experiments investigating the temperature variation at the centerline of the jet, three flow zones are designated in the jet, each of different characteristics: 1-Potential core zone: this zone exists near the nozzle exit and mainly characterized by unshattered flow and negligible temperature decline, the time elapsed by the flow in this zone is commonly referred to as delay time. 2-Spray zone: through this zone, the jet shatters and diffuses in conical shape so that the interface area extends and the water temperature declines rapidly. 3-Saturation zone through which the flow becomes greatly dispersed in the form of water drops surrounded by the rising vapor, the temperature in this zone is so far constant near the equilibrium temperature. Temperature readings taken in the potential core zone and in the spray zone refer to a great degree of certainty to the liquid phase temperature whereas the PRTs are continually accessed and wetted by the flowing liquid in these two zones; however, as the vertical distance z increases (as it is the case in the saturation zone), the flow spreads in a wider area and subsequently the fraction of the liquid that reaches the PRTs decreases; therefore, the temperature readings in this zone might be influenced by the surrounding vapor temperature. Fig. 4a shows the temperature profile at the jet centerline at an arbitrary condition with the three flow zones
Fig. 4. a. Dimensionless temperature profile at the centerline of the jet. b. Isothermal diagram shows the dimensionless temperature distribution in the jet.
indicated, while the isothermal diagram in Fig. 4b shows the corresponding temperature distribution at the area of influence near the nozzle exit; each flow zone in Fig. 4a has a correspondent thermal behavior in Fig. 4b, the potential core zone, spray zone and saturation zone in Fig. 4a are represented by the continuous area near the nozzle exit, the following adjacent isothermal lines and the following widespread area in Fig. 4b respectively. 3.3. Modeling of temperature variation at the centerline It is observed that the temperature decline at the centerline of the jet draws similar profiles at all the investigated conditions, and each centerline temperature plot is found to lie on a part of Boltzmann sigmoid curve that decays exponentially. A typical sigmoid curve model is represented by Eq. (5) and drawn in Fig. 5. ðA1 A2 Þ h io θ = A2 + n ðzz Þ 1 + exp δzip
Fig. 3. Variation of the evaporated mass ratio with superheat degree.
ð5Þ
where θ is the dimensionless temperature at the centerline of the jet, A1 and A2 are the initial and final θ values, zip is the center of curve and also represents the height of the inflection point between the two curvatures of different signs, and δz is the approximate range width of z
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Fig. 5. Typical Boltzmann sigmoid model.
variable through which θ value changes drastically. Fig. 6 shows the suitability of the Boltzmann model for the simulation of four sets of randomly selected experiments where the dots are the experimental readings and the solid lines are the simulation curves by the Boltzmann sigmoid model. Fig. 7 shows a generalization of the data fitting by Boltzmann model for the all investigated conditions whereas the actual distance z(exp) at which the water attains values of θ ranging from 0.1 to 0.9 is plotted on the x-axis against the corresponding distance z(cal) obtained from the proposed sigmoid curve and plotted on the y-axis. At higher values of θ, data are matching so well and uncertainty lies within 5% while at θ = 0.1, the uncertainty is higher. With the knowledge that experimental readings at low values of θ are subjected to high uncertainty due to their presence in the saturation zone which so often consists of vapor and some water mists of variable temperatures due to the explosive bubble growth accompanied with spraying from
Fig. 7. Experimental and calculated values of the height z at which θ attains several values.
the jet, the distance z(cal) at which θ attains the value 0.1 becomes more reliable than z(exp) at the same value of θ. Though the liquid temperature must decline to the equilibrium temperature for the flash evaporation to become complete, it is worth mentioning that the value of A2 which simulates θ value at the end height of the jet is found to range between 0 and 0.1 for the majority of the experiment runs; moreover, in a few cases A2 is found higher than 0.1, particularly when the superheat degree or the initial water temperature is the lowest. However, this behavior does not contradict with the fact that the actual evaporated mass is equal to the maximum theoretical amount as discussed in Section 3.1 because the temperature measurements are taken during the upward flight of the jet while the liquid undergoes further evaporation during its falling.
Fig. 6. Suitability of the Boltzmann model for the simulation of temperature decline curves.
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3.4. Influence of experimental variables Although it is easy to recognize the three mentioned flow zones in Fig. 4, it is quite difficult to determine a distinct and representative point at which every zone is initiated. As the slope of the curve at any location is an indicator for the local rate of evaporation, location of the curve's inflection point is an object of interest in this study as it implies the highest rate of evaporation, and the variation of experimental conditions reflects strongly on it. The location of the inflection point of each centerline temperature decline curve is calculated from its corresponding sigmoid curve equation obtained using fitting software. In Fig. 8, the calculated values of the inflection are plotted on the y-axis against the points locations z(cal) ip values obtained from the experimental readings corresponding z(exp) ip at the equivalent θ values. This figure shows that the inflection point can be estimated with a margin of error less that 5%. 3.4.1. Influence of flow velocity In Fig. 9a through c, the temperature variation at the centerline of the jet is plotted at various velocities and initial temperature of 30, 35 and 40 °C, respectively while the superheat degree is maintained constant. As shown in these figures, jets of higher flow velocity attain larger θ values at the same downstream distance due to the shorter elapsed time in the depressurized environment. However, the most significant influence of the flow velocity appears at the potential core zone where the increase of velocity is shown to increases the length of this zone. This behavior is attributed to the increase of the inertia of the jet which represents the retarding force that tends to maintain the jet un-shattered so that the coherent liquid column near the nozzle exit extends to longer downstream distance resulting in the suppression of the evaporation due to the increase of the static pressure at the nozzle exit and subsequently, the increase of the overall distance required to complete the evaporation. Fig. 10 shows the relationship between the flow velocity and the height of each curve's inflection point. The height of the inflection point seems to increase in a logarithmic-like relationship with the increase of flow velocity.
Fig. 9. Variation of θ with distance at various flow velocities.
3.4.2. Influence of the initial temperature Through a variety of experiments conducted in an effort to investigate the influence of water temperature, an increase of the initial water temperature T0 is found to enhance the flash evaporation linearly. Fig. 11 shows four sets of temperature variation profiles at the centerline of the jet, each set is obtained at various initial water
temperatures while the other conditions are kept constant. At relatively low flow velocities as in Fig. 11a through c, the potential core zone tends to disappears behind the vertical axis due to the initiation of the flash evaporation within the nozzle, so that θ attains a value less than 1 at the nozzle exit, this value is also influenced by the initial liquid temperature whereas it decreases with the increase of T0. However, on increasing the flow velocity as in Fig. 11d, the liquid temperature at the nozzle exit remains unchanged until a certain distance is elapsed by the flow before the bubbling starts at a further downstream distance; this delay distance decreases with the increase
Fig. 8. Uncertainty in the prediction of inflection point location by Boltzmann model.
Fig. 10. Relationship between the inflection point height and flow velocity.
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Fig. 11. Variation of θ with distance at various initial temperatures.
of the liquid temperature. Moreover, a common behavior is seen in Fig. 11a through d concerning the final θ value whereas it decreases linearly with an increase of T0. For better understanding of influence of temperature, the location of the inflection point zip is plotted against the initial water temperature at various experimental conditions in Fig. 12. As shown in this figure, the increase of the initial water temperature hastens the flash evaporation and linearly reduces the height of the inflection point. This behavior is thought to be attributed to the decrease of the latent heat of vaporization with the increase of water temperature, whereas the latent heat of vaporization is an interpretation of the energy required to increase the mean separation distance between molecules from the distance in the liquid to that several times larger in the vapor. The ratio of the distance between
molecules in the two phases can be taken as the cubic root of the ratio of specific volumes of saturated liquid and vapor as in Eq. (6). Lv = Ll
vv 1 =3 vl
ð6Þ
where Lv and Ll are the mean separation distance between molecules in the vapor and liquid phases, while vv and vl are the specific volumes of vapor and liquid respectively; evaluating this ratio at temperatures of 24 and 40 °C implies that the spacing between molecules in the bulk vapor should be 36.26 and 26.25 times that in the bulk liquid at the temperatures 24 and 40 °C respectively. In addition to the previous argument, for the nucleation process to proceed at nucleation cavity, a certain pressure difference should exist between the inner and outer surface of the bubble embryo to overcome the surface tension forces according to Eq. (7). PB Ps =
2σ rB
ð7Þ
where PB is the inner bubble pressure, Ps is the surrounding liquid pressure, σ is the surface tension, and rB is the bubble radius, referring to Fig. 13, the degree of superheat ΔTsat required to maintain this pressure difference decreases with the increase of the saturation temperature.
Fig. 12. Relationship between the inflection point height and the initial temperature.
3.4.3. Influence of Superheat degree Fig. 14 shows three sets of temperature profiles at the centerline of the jet obtained at different flow velocities, each set is plotted at several degrees of superheat while the initial water temperature is held constant. As shown in this figure, at relatively low degree of superheat, a certain increase of the degree of superheat hastens the flash evaporation markedly and results in an increase of the slope of the curve particularly in the spray zone, and shortens the distance δz through which the majority of the sensible heat is consumed by evaporation, while at higher degrees of superheat, the same increment
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Fig. 13. Variation of the saturation pressure with temperature.
will have less pronounced influence. Fig. 15 clarifies the nature of the superheat effect whereas the vertical distances z at which the water attains θ values from 0.2 to 0.9 are plotted at different degrees of superheat. The curves are seen to have steep inclinations between the superheat degrees of 2 and 4 while the trend of these curves tends to be horizontal with further increment of superheat degree. In Fig. 16, the height of each curve's inflection point, zip is plotted against the superheat degrees at various flow conditions. As shown in this figure, the height of the inflection point decreases in an exponential-like relationship with the increase of superheat degree. The enhancement of flash evaporation by the increase of superheat degree is thought to be attributed to the mean droplet size produced via atomization, whereas
Fig. 15. Relationship between superheat degree and the vertical distance at which θ attains several values.
it decreases as the degree of superheat increase due to the greater vapor release from the body of the jet. For this reason, degree of superheat is considered the driving force that controls the intensity of flash evaporation. 4. Conclusion Experiments on flash evaporation from superheated jets that issue the water upward from large nozzles were conducted and the following points were concluded: ■ Flash evaporation from superheated jets has shown efficiency in absorbing the latent heat of the liquid water for the generation of vapor within the very short residence time in the flash evaporator, even at low degrees of temperature and superheat. ■ Temperature variation at the centerlines of the superheated jets was simulated by Boltzmann sigmoid model. The model was found considerably appropriate and enables estimating the jet temperature at any height z; however, the four parameters that appear in Boltzmann equation should be correlated for this purpose. ■ Intensity of the flash evaporation was found to increase with an increase of the initial water temperature and the superheat degree,
Fig. 14. Variation of θ with distance at various superheat degrees.
Fig. 16. Variation of the height of the inflection point with superheat degree.
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and the highest evaporation rate is attained at a downstream distance that decreases linearly or exponentially with an increase of the initial water temperature or superheat degree respectively while it increases in a logarithmic-like relationship with the increase of flow velocity. Acknowledgment This research is supported by the COE program of Advanced Science and Technology for Utilization of Ocean Energy. References [1] O. Miyatake, T. Tomimura, Y. Ide, T. Fujii, An experimental study of spray flash evaporation, Desalination 36 (2) (1981) 113–128.
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[2] O. Miyatake, T. Tomimura, Y. Ide, M. Yuda, T. Fujii, Effect of liquid temperature on spray flash evaporation, Desalination 37 (3) (1981) 351–366. [3] H. Uehara, Y. Ikegami, N. Hirota, Experimental study of spray flash evaporation for desalination and otec, Joint Solar Eng. Conference, ASME, 1993, pp. 197–201. [4] Y. Ikegami, H. Sasaki, T. Gouda, H. Uehara, Experimental study on a spray flash desalination (influence of the direction of injection), Desalination 194 (1–3) (2006) 81–89. [5] H. Sasaki, Y. Ikegami, M. Monde, H. Uehara, Experimental study of flash desalination with upward spray (flow pattern and temperature distribution), Bulletin of the Society of Sea Water Science, Japan 59 (5) (2005) 354–360 Japanese. [6] R. Brown, J. Lois York, Sprays formed by flashing liquid jet, AIChE Journal 8 (2) (1962) 149–153. [7] Y. Ikegami, T. Wajima, H. Sasaki, Experimental study on desalination of seawater in Imari bay using an upward spray flash desalination plant, Bulletin of the Society of Sea Water Science, Japan 60 (2) (2006) 137–138.