## Abstract

A novel system combining dynamic flash evaporation and vapor separation for desalination has been investigated in this work. The feed water passes through injection tubes which are connected to injector passages installed tangentially onto a separator tube. Flashing in the injection tubes is initiated from pressure drop due to friction and acceleration resulting in a two-phase mixture. Centrifugal force from tangential injection separates the two-phase mixture. In this compact system, vapor production and phase separation occur on the order of several milliseconds. Tap water and seawater were used as inlet feed water for the system. Thermal conversion efficiency to analyze the vapor production efficacy and phase separation efficiency to evaluate the purity of the condensate were investigated to evaluate the system. Thermal conversion and phase separation efficiencies up to 98% were obtained with the single stage system. Further improvement in purity of condensate was achieved with a two-stage system. In the two-stage system, the vapor captured along with some entrained droplets from the first stage was directed to a second set of injector passages connected in series to the first stage retrieval tube. With a two-stage system and seawater with salt concentration by mass of 2.5%, collected condensate with salt concentrations lower than 0.02% by mass was achieved, which is comparable to that of potable water. Thus, the novel dynamic flash evaporation and vapor separation system have been demonstrated to be very effective in producing potable water.

## 1 Introduction

The growing scarcity of freshwater resources is one of the most pressing issues for human development. According to a recent study, by 2030, the demand for water is expected to expand by 40% and more than 160% of the total available water volume in the world will be needed to satisfy the global water requirements [1]. With population growth, economic development, pollution, and climate change accelerating the depletion of the planet's freshwater resources, the need to produce fresh water from unconventional water sources becomes imperative. Unconventional water sources such as seawater and brackish ground water typically have high salinities. The process of removing the salts to utilize these water sources is known as desalination. With the vast amount of seawater available, pursuing desalination of seawater near coastal regions becomes a logical choice. Developing scalable, energy-efficient, and cost-effective desalination systems becomes a priority.

To address the issue of water scarcity, there has been constant effort to provide potable water by desalination. The size and number of desalination plants globally have been on the increase at an average annual rate of about 6.8% since 2010. As of the middle of February 2020, the global installed desalination capacity for freshwater production stood at 97.2 × 106$m3/day$ [2]. Two of the major desalination approaches are thermal-based systems and membrane-based systems. In thermal-based systems, fresh water is produced by evaporation and subsequent condensation. The required energy is strongly dependent on the magnitude of latent heat of evaporation and the extent of heat recovery which can be achieved. Multistage flash evaporation (MSF) and multi-effect distillation (MED) are two of the widely used thermal desalination processes. Membrane-based systems such as reverse osmosis (RO) use a semipermeable membrane to separate salts for producing freshwater. Reverse osmosis accounts for over 72% of the global desalination capacity largely due to its energy efficient process but it requires significant electric power [3].

Energy usage and the cost of implementation are the primary factors that drive the cost of desalinated water. The major desalination technologies such as MSF, MED, and RO have seen significant cost reduction due to technological advancements in the past few decades. However, further advancements in these technologies are likely to be incremental and significant reduction in cost is not expected. Most of the current advancements focus on energy and cost efficiency through advanced materials, and on improving system components such as high-pressure pumps and heat recovery devices [3]. When considering costs, the size of the desalination plant, design and configuration of the desalination process contribute significantly to the cost of desalinated water [4]. The capital costs, which include land and construction costs, that utilize MSF, MED, and RO typically account for 30–50% of the total cost of desalination since they require relatively large land areas [5]. Therefore, implementing a process that is compact and requires less area could significantly reduce the cost of desalination. A novel system as proposed in this work that combines both flash evaporation and phase separation through tangential injection is expected to lead to an energy efficient, compact, and scalable approach for desalination.

Flash evaporation is a common process that is utilized in thermal desalination systems. Flash evaporation is achieved by reducing the system pressure below saturation pressure resulting in the production of vapor from superheated water. MSF process involves a series of stages with decreasing chamber pressure. Sea water enters each chamber with temperature above saturation resulting in flash evaporation until temperature reaches equilibrium corresponding to the pressure. Produced vapor is condensed to create fresh water. MED is similar to MSF with effects maintained at pressure lower than saturation for flashing. MED differs from MSF in the way the vapor is utilized to recover heat. Part of the produced vapor is used to preheat the feed water in the subsequent effect while it condenses inside the tubes [6]. These are batch type processes with huge chambers for flashing to occur. Pool or spray type flashing is commonly used. Pool type or static pool flashing involves a liquid pool in a chamber. When the chamber pressure drops below saturation the liquid flashes until it achieves equilibrium temperature. Static flashing is a relatively slow process taking several seconds to achieve equilibrium with the surrounding or for complete evaporation. It is shown to be influenced by the liquid level, degree of superheat, etc. Spray flash evaporation uses liquid injection into a low-pressure chamber for vapor production. Upon injection, the liquid is atomized and flashes to produce vapor. This process is influenced by the injection pressure which also affects the morphology of the sprayed jet. This is a faster process with equilibrium achieved in the order of milliseconds [7]. Higher injection pressures and superheats result in complete evaporation within short distance from the nozzle. The produced vapor from the above processes is often separated by means of gravity and this requires large chamber sizes.

Tangential injection has been used as a method for producing swirl flows which is shown to enhance heat transfer compared to purely axial flows [8]. In addition, swirl flows experience centrifugal forces which aid in separation of phases with different densities which can work independent of gravity [9]. Valentekovich et al. [10] demonstrated phase separation based on swirl flow produced by tangential injection for microgravity application. Valentekovich and Dhir [11] used tangential injection for phase separation under low gas to liquid volume ratios. They reported 0.999 volume-based dryness fraction for the separated gas.

In this work, a novel system for desalination that utilizes dynamic flash evaporation and vapor separation through tangential injection as was used in Ref. [12] has been investigated. Parameters for analyzing the purity of the produced condensate, the efficiency of vapor production and collection have been defined and studied. Parametric effects of variables such as flowrate and superheat are investigated with respect to the performance of the system. Single- and two-stage configurations of the system are studied.

## 2 Experiments

The experimental setup used for the single-stage configuration of the dynamic flash evaporation and vapor separation system is shown in Fig. 1. The setup is similar to that used in the work reported by the current authors [12]. The apparatus consists of primary and secondary tanks made of stainless steel with a capacity of 50 gal each, a centrifugal pump (MTH pumps-Model: T41B-AB, Plano, IL), 2.66 cm ID and 12 m long stainless-steel pipeline, tape heaters (power density: 2 W/cm2), immersion heaters, a flowmeter (Blue-White F-450), test section, pressure transducers, thermocouples, and a condenser. The test section consists of an injection block made of aluminum, a 30.48 cm long and 2.06 cm ID borosilicate glass tube as the separator tube, an exit block made of aluminum through which a retrieval tube made of stainless steel is carried. The injector and exit blocks are placed at the two ends of the separator tube. The injection block has two injector passages which are each 6.35 mm ID and are tangential to the separator tube. The injector passage configuration is also shown in Fig. 1. The retrieval tube is mounted coaxially with the separator tube. Two injection tubes which are each 30.48 cm long and 6.35 mm ID connect the water supply line to the injector passages in the injection block.

Fig. 1
Fig. 1
Close modal

Inlet feed water is stored in the primary tank at atmospheric pressure and maintained at a temperature of about 90 °C. Water from the primary tank is pumped using the centrifugal pump through the stainless-steel pipeline which is covered with a series of tape heaters. The tape heaters are used to raise the temperature of the feed water as it flows through the pipe mimicking solar heating while recognizing that in a solar heated system temperatures and pressures will be lower. In solar heating, seawater from a solar pond at atmospheric pressure will directly flow into the tubes connected to the injector passages with condenser pressure much lower than one atmosphere. In the current experiments, the pressurized feed water is heated to a higher temperature while still maintained in a subcooled state as it passes through the pipe. Subcooled pressurized feed water is then distributed to the injector passages through two injection tubes. The flow area of the injection tubes is smaller as such pressure drop due to friction is higher than in the heater section. As the heated water flows through the injection tubes, pressure drop occurs due to friction causing the initially subcooled liquid to a superheated state. The excess temperature drops as liquid flows through the tubes and flashing occurs to produce vapor. The produced vapor flows along with the liquid resulting in further increase in pressure drop due to two-phase friction and acceleration through the tubes. This in turn leads to further flashing. This process continues in the injector passages. As such a liquid vapor mixture flows out of the injector passages which connect tangentially into the separator tube. The two-phase mixture tangentially injected into the test section experiences centrifugal force. Centrifugal force pushes the heavier liquid toward the wall and vapor being lighter stays in the inner core region. A stable vapor core with an annulus form in the separator tube. A photograph showing the vapor core formation is shown in Fig. 2. Vapor from the core is extracted using the retrieval tube placed at the center of the separator tube. The extracted vapor is directed to a condenser where condensation occurs at atmospheric pressure to produce potable water. After liquid from the condenser is collected for a period of time, it is weighed and sampled for salt concentration. The liquid from the annulus exits through the liquid exit port in the exit block and is stored to the secondary tank and is later recirculated back to the primary tank. Pressure and temperature measurements are taken at various locations to monitor the flashing process and to perform energy balance for calculating vapor production rate. Experiments were conducted with tap water and seawater as inlet feed water.

Fig. 2
Fig. 2
Close modal

## 3 Results and Discussion

The system involves flashing of the inlet feed water and the centrifugal separation of the produced two-phase mixture. Three parameters are defined to study the effectiveness of the process.

Thermal conversion efficiency ($ηt$) represents the utilization of available superheat for vapor production. It is defined as the ratio of superheat of liquid utilized for vapor production to the maximum available superheat. The superheat utilized for vapor production is calculated as the temperature drop of the liquid prior to entering the injection tubes and at the exit of injector passages. The maximum available superheat is determined by the temperature of the liquid prior to flashing and the saturation temperature corresponding to the exit pressure (condenser pressure)
$ηt=ΔTinjectorΔTs(Pexit)$
(1)
$ΔTinjector= Ti−Tinjector$
(2)
$ΔTs(Pexit)=Ti−Tsat(Pexit)$
(3)

Phase separation efficiency ($ηs$) is defined to represent the purity of the produced condensate as it is expected that there is a possibility of liquid from the annulus getting entrained into the vapor core in the form of droplets.

Vapor mass flowrate is calculated from energy balance with the aid of temperature measurements. The mass flowrate of produced vapor is represented as
$m˙v,produced=m˙l(cpΔTinjectorhfg)$
(4)
Phase separation efficiency is defined as the ratio of the mass flowrate of pure vapor that is condensed in the condenser to the total mass flowrate of the condensed vapor and the entrained liquid
$ηs=m˙condensatem˙condenser=m˙condensatem˙condensate+m˙entrained$
(5)

where $m˙condensate$ represents the mass flowrate of vapor that goes into the condenser and $m˙condenser$ represents the mass flowrate of water measured at the exit of the condenser.

In case of tap water experiments, it was not possible to distinguish between condensed vapor and the entrained liquid that is in the condenser since salt concentration for tap water is very low. A mass-based approach was taken, and it was assumed that all the produced vapor is removed through the retrieval tube and is condensed in the condenser. Therefore, $m˙v,produced$ was used for $m˙condensate$.

For saltwater experiments, the salt concentrations in the primary tank and the condenser which includes both condensed vapor and liquid entrainment are measured. Unlike in tap water experiments, the use of saltwater allows for a differentiation between the mass of condensed pure vapor and the mass of liquid entrainment in the condenser. The salt concentrations of both the condenser and the primary tank as well as the total mass of liquid collected in the condenser are used to find the amount of liquid entrainment. By performing a mass balance in the condenser, we get
$m˙condenser = m˙condensate+m˙entrained$
(6)
By performing a mass balance of salt in the condenser, we get
$m˙condenser Cs,c=m˙condensateCs,v+m˙entrainedCs,e$
(7)
$C$ is the measured salt concentration which represents the percentage of mass of salt in a given fluid. Mass concentrations $Cs,c$, $Cs,v$, and $Cs,e$ are the measured salt concentrations in the liquid in the condenser, the condensate, and the entrained liquid, respectively. Mass concentration $Cs,v$ is 0 since there is no salt in pure vapor, $Cs,e$ is the salt concentration in the primary tank since liquid entrainment is due to liquid droplets of the feed water entering into the retrieval tube along with vapor. The presence of salt in the condenser is purely as a result of entrained liquid. Mass flowrate of the entrained liquid is expressed as
$m˙entrained= m˙condenser Cs,cCs,e$
(8)
With $m˙entrained$ known, the mass flowrate of pure vapor that is condensed is expressed as
$m˙condensate=m˙condenser −m˙entrained$
(9)
It is important to note that $m˙condensate$ is not the same as $m˙v,produced$ and it will be less than $m˙v,produced$. As some vapor from the core leaks into the liquid exit resulting in lesser amount of the produced vapor entering the condenser. The collection efficiency $(ηc)$ is defined as the ratio of the mass flowrate of vapor entering the condenser to the mass flowrate of vapor produced
$ηc= m˙condensatem˙v,produced$
(10)

The performance of the system is evaluated by studying the effects of flowrate and superheat on these parameters.

The uncertainty ($σR)$ in a quantity R (x1, x2,…, xn) depending on variables x1, x2,…, xn is calculated as
$σRR=1R2((∂R∂x1)2σx12+(∂R∂x2)2σx22+⋯+(∂R∂xn)2σxn2)$
(11)
where $σx1,σx2, …, σxn$ are the uncertainties associated with measurement of each variable x. Using the above approach, the uncertainties in thermal conversion, phase separation, and collection efficiencies can be calculated as follows:
$σηtηt=(σΔTinjectorΔTinjector)2+ (σΔTs(Pexit)ΔTs(Pexit))2$
(12)
$σηsηs=(σm˙condensatem˙condensate)2+ (σm˙condenserm˙condenser)2$
(13)
$σηcηc=(σm˙condensatem˙condensate)2+ (σm˙v,producedm˙v,produced)2$
(14)

The uncertainty in $m˙v,produced$ depends on the uncertainties in the inlet flowrate and temperature readings. It is assumed that there is no uncertainty associated with the properties as such they are taken from respective property tables. The uncertainty in $m˙condenser$ depends on the mass of liquid measured at the condenser exit as well as the time measurements from stopwatch. The uncertainty in $m˙condensate$ depends on uncertainties in salt concentration and mass of liquid measured at the condenser exit. All the measurement uncertainties are given in Table 1.

Table 1

Measurement uncertainties

ParameterAbsolute uncertainty
Flowrate0.2 GPM
$ΔTinjector$0.7 °C
$Cs,c$0.02%
$Cs,e$0.05%
$ηt$1.8–7.2%
$ηs$0.2–14.6%
$ηc$9.4–27.5%
ParameterAbsolute uncertainty
Flowrate0.2 GPM
$ΔTinjector$0.7 °C
$Cs,c$0.02%
$Cs,e$0.05%
$ηt$1.8–7.2%
$ηs$0.2–14.6%
$ηc$9.4–27.5%

### 3.1 Dynamic Flash Evaporation in Injection Tubes and Injector Passages.

Dynamic flashing has been studied extensively with applications to nuclear industry in literature such as flashing flows through nozzles [1315]. In present concept, occurrence of dynamic flashing in the injection tubes and injector passages leads to vapor production. Pressure drop through these sections varies nonlinearly along the length of the section. An effort to predict the pressure drop was made with simplifying assumption of thermal equilibrium even though flashing is a nonequilibrium process. Frictional pressure drop was calculated with a two-phase friction factor based on average viscosity. Void-quality relation with a constant slip factor of 1.5 was used to calculate the acceleration pressure drop. The tube was subdivided into smaller sections. Based on local pressure, temperature drop across each subsection was assumed for calculating the local quality. Using the assumed local quality and void-quality relation, the friction and acceleration pressure drops through the subsection were calculated. The total pressure drop through the section was used to recalculate the local quality based on equilibrium assumption. The calculated quality was compared with the initially assumed local quality. The process was repeated until the assumed and calculated qualities matched closely. Once they matched, the calculation was advanced to the next subsection. The procedure was continued until the end of the tube section. Various parameters were calculated as
$xz=cp(Ti−Tsat(Pz))hfg$
(15)
$αz=(1+1−xzxz(vfvg)S)−1$
(16)
$Pz=Pi−ΔPz$
(17)
$ΔPz =(ΔPf+ ΔPa)z$
(18)
$ΔPf= 2ftpΔzG2vfD(1+xz2(vfgvf))$
(19)
$ΔPa= G2vf(xz2αz(vgvf)+(1−xz)2(1−αz)−1)$
(20)

The calculated and experimental values for pressure and temperature at a flowrate of 1.75 GPM are shown in Fig. 3. The calculated quality and void fraction across the length of the section is shown in Fig. 4. The continuous solid and dotted lines show the predicted pressure and temperature through injection tubes and injector passages. Although the process is highly nonlinear, calculated pressure and temperatures obtained from a simple model compare favorably with experimental data. For the case shown in Fig. 3, the residence time is around 175 ms in the injection tubes and 14 ms in the injector passages resulting in a rate of temperature drop in the injection tubes of up to 102.85 °C/s and up to 750 °C/s in the injector passages showing a highly nonlinear and efficient process.

Fig. 3
Fig. 3
Close modal
Fig. 4
Fig. 4
Close modal

For the flowrates that were investigated, total residence time in the injection tubes and injector passages ranged from 189 ms to 331 ms and separation time in the separator tube ranged from 390 ms to 680 ms. Thus, in just under a second, vapor production and separation are completed. With these two processes occurring in such short amount of time and short distance, a compact system for desalination can be achieved.

### 3.2 Single-Stage System.

Single-stage experiments were conducted to demonstrate the proof of concept. In these experiments, tap water was used as the test fluid. The detailed results for the single-stage system can be found in our previous work [12]. Important results for thermal conversion and phase separation efficiency are summarized here.

#### 3.2.1 Thermal Conversion and Phase Separation Efficiency.

In single-stage experiments, inlet liquid flowrate was varied from 1.75 GPM (110 mL/s) to 2.25 GPM (142 mL/s) and available superheat varied from 16 °C to 18 °C. The retrieval tube used in these experiments had an ID of 1.09 cm and length of 30.48 cm. Thermal conversion and phase separation efficiencies were studied to assess the performance of the system. Figure 5 shows the thermal conversion and phase separation efficiencies for different flowrates at two available superheats. Phase separation and thermal conversion efficiencies as high as 98% were obtained. It can be seen that for a given superheat, increase in flowrate decreases both thermal conversion efficiency and phase separation efficiency though the effect on thermal conversion efficiency is smaller in comparison to phase separation efficiency. The utilization of available superheat is affected by backpressure or pressure drop through the liquid exit tube section as well as the retrieval tube section. For a given superheat, increase in flowrate increases vapor flowrate in the retrieval tube section and consequently increases liquid flowrate in the liquid exit section. This in turn increases the pressure at the exit of the injector passages which increases the saturation temperature at the exit of the injector passages. The amount of available superheat that is utilized decreases and as a result, thermal conversion efficiency drops. As seen from Fig. 5, the changes in thermal conversion efficiency when increasing superheat at a given flowrate were negligible. Although higher superheat results in higher vapor flowrate, additional pressure drop through both vapor and liquid exits was small.

Fig. 5
Fig. 5
Close modal

For phase separation efficiency, as flowrate is increased at a constant available superheat, phase separation decreases. When flowrate is increased, liquid and vapor tangential momentums increase but the ratio of liquid to vapor tangential momentum increases much more. Pressure drops through liquid and vapor exits also increase. This causes the vapor core to shrink and droplets from the liquid annulus enter into the retrieval tube along with vapor. For the same flowrate, it can be seen that increase in superheat results in higher phase separation efficiency. Increasing superheat increases vapor production which then increases vapor core length thereby reducing entrainment of liquid. As mentioned earlier, single-stage experiments are based on tap water as test fluid. An assumption was made that all the produced vapor is captured through the retrieval tube and condensed. However, in cases where the vapor core extends well past the retrieval tube inlet, part of the vapor leaves through the liquid exit instead of through the retrieval tube. As such, the measured phase separation efficiency was based on more condensate than that was actually present in the condenser. This can be noticed in a data point in Fig. 5 for 1.75 GPM at $ΔTs$ = 18 °C which resulted in phase separation efficiencies greater than 100%. This does not represent the actual phase separation efficiency since a value of over 100% is not possible. However, one can expect the actual phase separation efficiency to be high for this case since the vapor core extended past and covered the retrieval tube inlet. A vapor core that goes beyond the retrieval tube inlet is crucial for obtaining high phase separation efficiency as with increase in core length, there is less entrained liquid in the vapor that is entering into the retrieval tube.

One seawater experiment with 4.9% salt concentration in the primary tank was also conducted for the best case obtained for the single-stage system. With seawater as the test fluid, the amount of condensed vapor and liquid entrainment was quantified. The experiment resulted in collected condensate salt concentration of 0.12%. This gave a phase separation efficiency of about 98% corroborating the results from tap water experiments. While the obtained phase separation and thermal conversion efficiencies are attractive, the goal is to achieve potable water quality which has a salt concentration of less than 0.02%. This requires phase separation efficiency greater than 99%. Further improvement with a two-stage system was carried out to achieve this goal.

### 3.3 Two-Stage System.

In a two-stage system, a second stage is connected in series to the first stage. The setup used for the two-stage system is shown in Fig. 6. The vapor retrieved from the first stage contains droplets entrained from the liquid annulus. To improve the purity of the condensate, these droplets need to be separated. As such vapor from the retrieval tube of the first stage is tangentially injected into a second separator tube through two injector passages. The injector arrangement is similar to that of the first stage as shown in Fig. 6. Since the fluid entering the second stage is mostly vapor with some droplets, lesser momentum is sufficient to separate the entrained liquid. Thus, larger sized injection tubes and injector passages were used to reduce pressure drop through the second stage. The injection tubes in second stage are 1.59 cm ID and 30.48 cm long. The injector passages are each 9.53 mm ID. Because of droplets of liquid entering the second stage, the liquid film is expected to be very thin. As such a larger sized retrieval tube is used to maximize the capture of vapor with minimal pressure drop while minimizing liquid entrainment. The retrieval tube is of 1.76 cm ID and 30.48 cm long. The separator tube in the second stage is 30.48 cm long with 2.06 cm ID the same as that in the first stage.

Fig. 6
Fig. 6
Close modal

Two-stage system's performance was studied with respect to thermal conversion, phase separation, and collection efficiencies. Sea water was used as the inlet feed in these experiments. The results from the two-stage system are described below. In the two-stage experiments, liquid mass flowrate was varied over a narrow range from 1 GPM (63 mL/s) to 1.75 GPM (110 mL/s). The inlet tank salt concentration in these experiments varied from 0.9% to about 2.5%.

#### 3.3.1 Effect of Retrieval Tube Position.

The effect of retrieval tube position in the first stage was investigated. Four different positions were studied. The retrieval tube inlet was located at distances of 9 cm, 12.9 cm, 20.5 cm, and 28 cm from the location of injection of the two-phase mixture. The retrieval tube position in the second stage was fixed at a distance of 20.5 cm from the injector passages. Effect of retrieval tube position in the first stage on thermal conversion, phase separation, and collection efficiencies at 1.25 GPM and $ΔTs$ = 31 °C is shown in Fig. 7. It can be observed that the effect of retrieval tube position is not appreciable on thermal conversion efficiency and thermal conversion efficiency remains constant around 95% for all the positions shown. Even with changing retrieval tube position, total flow length remains the same as such the pressure drop through the liquid and vapor exit sections does not change. This results in similar temperatures at the exit of the injector passages and hence similar thermal conversion efficiencies. From the figure, it is observed that there is an optimum distance from injection location which maximizes phase separation efficiency. From 9 cm to 12.9 cm phase separation efficiency increases and then it drops as the retrieval tube is moved farther from injection location. Depending on the inlet momentum, the optimum distance for phase separation efficiency changes. For the 1.25 GPM case, the optimum distance is about 12.9 cm from the injection passage exit. Moving closer or farther away from the optimum distance reduces the efficacy of the separation process.

Fig. 7
Fig. 7
Close modal

In the first stage, part of vapor from the core can get pulled into the liquid exiting the separator tube. In addition, in a two-stage system because of the presence of very thin liquid film in the second stage some of the vapor leaves through the second stage liquid exit. To quantify the percentage of vapor captured for condensation, collection efficiency is used as defined earlier. The effect of first stage retrieval tube position on collection efficiency is also shown in Fig. 7. Because the retrieval tube position in the second stage was fixed, changes in collection efficiency were mainly due to the effect of retrieval tube position in the first stage. The collection efficiency initially increases and then drops as the retrieval tube is moved farther from the injector passage exit. It can be observed that there is an optimum in the collection efficiency with respect to the position of the retrieval tube in the first stage. When the retrieval tube lies too close to the injector passage exit, blobs of vapor get carried by the separated liquid. This could be due to the high liquid momentum ripping the vapor from the core near the retrieval tube inlet. On the contrary, when the retrieval tube is placed too far from the injectors, the tangential momentum decays with distance causing the core to collapse and part of the vapor gets carried toward the liquid exit. The pressure drop in the second stage liquid exit can be increased slightly to reduce the mass flowrate of vapor leaving through the liquid exit such that most of vapor goes to the condenser, thereby improving the collection efficiency. However, increasing the second stage liquid exit pressure drop was not pursued because it would force the thin film of liquid to entrain into the second stage retrieval tube thereby sacrificing the improvement in phase separation efficiency. Since the goal is to achieve high purity condensate, a slight sacrifice in the collection efficiency was deemed acceptable. As such in the cases discussed later, the retrieval tube position in the first stage is fixed at a distance of about 12.9 cm from the injection location and the retrieval tube position in the second stage was kept at 20.5 cm from the injector passage exit. Similar effects on other flowrate-superheat combinations were observed.

#### 3.3.2 Effect of Flowrate.

The effect of liquid flowrate on two-stage thermal conversion efficiency is similar to that of single-stage and is shown in Fig. 8. In these experiments, flowrate was varied from 1 GPM to 1.75 GPM for three available superheats of 18 °C, 24 °C, and 31 °C. Thermal conversion efficiency as high as 99% was obtained for 1 GPM at available superheats of 18 °C and 24 °C. Thermal conversion efficiency is the lowest at 83% for 1.75 GPM with an available superheat of 18 °C. For constant superheat, increase in liquid flowrate decreases thermal conversion efficiency. As mentioned earlier for the single-stage system, thermal conversion efficiency depends on the pressure drops experienced in both the vapor and liquid exit. When liquid flowrate is increased, pressure drop through both the vapor and liquid exit increases with liquid exit pressure drop being the dominant factor. This in turn increases the pressure at the exit of the injector passage and lowers the thermal conversion efficiency. When comparing two-stage thermal conversion efficiencies to that of the single-stage system for the same flowrate and superheat, it can be seen that thermal conversion efficiency for the two-stage system is lower. For 1.75 GPM and available superheat of 18 °C, thermal conversion efficiency is 94% for the single-stage system as seen in Fig. 5 and 83% for the two-stage system. This drop in thermal conversion efficiency for the two-stage system is due to the added pressure drop from the additional injection tubes and injector passages in the second stage. In the single-stage system, the pressure drop from the injection location to the exit was about 3.7 kPa. While for the two-stage system, the pressure drop from first stage injection location to exit was about 14.3 kPa.

Fig. 8
Fig. 8
Close modal

Despite a small decrease in thermal conversion efficiency when compared to the single-stage system, the two-stage system achieved higher phase separation efficiencies. The effect of liquid flowrate on two-stage phase separation efficiency is shown in Fig. 9. The main goal of obtaining phase separation efficiency above 99% was achieved for the two-stage system. With a superheat of 31 °C, phase separation efficiency is above 99% across all flowrates except for 1.75 GPM which resulted in a phase separation efficiency of 96%. A phase separation efficiency of 99% resulted in salt concentration of the collected condensate as low as 0.02% with tank concentrations of 2.5%. Salt concentration of 0.02% is comparable to that for tap water. This demonstrates that with a two-stage system, potable water quality can be achieved.

Fig. 9
Fig. 9
Close modal

It should be noted that the phase separation efficiency for 1.75 GPM at a superheat of 18 °C is much lower for the two-stage system compared with that of the single-stage system shown in Fig. 5. The is due to a larger retrieval tube diameter of 1.41 cm ID in the two-stage system compared with 1.09 cm ID used in the single-stage system. The effect of retrieval tube size is discussed in our earlier work [12]. Since the retrieval tube diameters are not the same, a proper comparison of phase separation efficiencies between the single-stage and two-stage system cannot be made.

From Fig. 9, it can be seen that at high superheats such as 31 °C, the changes in phase separation efficiency with flowrate are not significant. However, at the lowest superheat of 18 °C, increase in flowrate from 1.25 GPM to 1.75 GPM decreases the phase separation efficiency substantially. As the flowrate increases at low superheats, there is a relative increase in liquid tangential momentum and pressure drop through the liquid exit. These act to reduce the length of the core causing more liquid to entrain into the retrieval tube, thereby decreasing phase separation efficiency. For 1 GPM at 18 °C of superheat, there is an initial drop in phase separation efficiency. This could be due to both the liquid and vapor tangential momentums being too low to maintain a stable core thereby causing higher liquid entrainment. Changes in the vapor core due to flowrate can be observed from the photographs in Fig. 10 for an available superheat of 24 °C. It can be seen that for 1 GPM the vapor core extends and covers the retrieval tube inlet while for 1.75 GPM the vapor core collapses right at the retrieval tube inlet. For 1.75 GPM, phase separation efficiency drops to about 52%. This is an indicator of the importance of the retrieval tube inlet lying inside the vapor core to reduce liquid entrainment and the tangential momentum ratio of vapor to liquid.

Fig. 10
Fig. 10
Close modal

In addition to the thermal conversion and phase separation efficiency, the collection efficiency was also investigated. Knowledge of collection efficiency is important to determine the fraction of produced vapor that is condensed. Figure 11 shows the effect of flowrate on collection efficiency. It can be seen that the collection efficiency follows a similar trend to that of phase separation efficiency. At high superheats such as 31 °C, the collection efficiency shows little change with flowrate with values close to 90%. When the superheat is lower, the collection efficiency tends to decrease with increase in flowrate. Increase in flowrate increases the liquid tangential momentum which causes some of the vapor from edge of the vapor core to get carried away with liquid through the first stage liquid exit. In addition, part of the vapor is lost through the second stage liquid exit due to the presence of thin liquid film. As a result, the collection efficiency decreases. A different behavior is observed for 1 GPM especially at lower superheats. This could be that in the case of 1 GPM, both liquid and vapor momentum are too low to maintain a stable core which results in the breakage of vapor core and vapor getting carried with the liquid. Collection efficiency is influenced by vapor leaving with liquid in both stages. No effort has been made to separate the contribution from each stage. Nevertheless, it is important to note for the cases studied, 80–90% of the produced vapor is converted into potable water.

Fig. 11
Fig. 11
Close modal

#### 3.3.3 Effect of Superheat.

The effect of available superheat for the two-stage system was studied for different flowrates. Available superheats were varied in the range of 12–47 °C. The effect of available superheat on thermal conversion efficiency is shown in Fig. 12. Thermal conversion efficiencies as high as 99% were achieved for 1 GPM and 1.25 GPM at low superheats. It can be seen that with increase in superheat the thermal conversion efficiency drops across all the flowrates. Increase in superheat results in more vapor production rate. First, this increases the vapor flowrate through the retrieval tube causing an increase in the pressure drop through the vapor exit. Second, with increased vapor production rate the retrieval tube gets covered with a longer vapor core resulting in leakage of vapor through the first stage liquid exit. This causes the two-phase mixture flowing through the liquid exit to experience a higher pressure drop through the liquid exit. Both of these factors reduce the utilization of available superheat consequently reducing the thermal conversion efficiency. A different trend is observed for 1.75 GPM. For 1.75 GPM, at low superheats, the vapor production rate is relatively small. As such the vapor core is unstable and significant liquid is entrained in the vapor leading to substantial increase in pressure drop through the retrieval tube. Thus, the thermal conversion efficiency goes down.

Fig. 12
Fig. 12
Close modal

The effect of available superheat on phase separation efficiency is shown in Fig. 13. It can be seen that for all the flowrates, initially the phase separation efficiency increases with superheat and reaches close to 100%, e.g., at about 23.5 °C for 1.25 GPM and about 33 °C for 1.5 GPM, and then plateaus. Increase in superheat increases the vapor production rate for a given flowrate. This causes the vapor core to grow longer and cover the retrieval tube which reduces the chance of liquid entrainment and improves phase separation efficiency. At higher superheats, the vapor core is long enough to cover majority of the retrieval tube which continues to maintain very low entrainment thereby sustaining phase separation efficiencies close to 100%.

Fig. 13
Fig. 13
Close modal

Current work was primarily focused on developing a novel desalination approach involving compact dynamic flashing and phase separation. Complete energy and mass balance involving heat recovery from the cooling water used in the condenser to make the process energy efficient will be investigated in a future work.

#### 3.3.4 Correlation of Data.

A simple correlation for dependence of thermal conversion efficiency and phase separation efficiency on various independent variables would be valuable in terms of practical applications. With the limited data obtained from the experiments, a correlation for thermal conversion and phase separation efficiency has been attempted. Thermal conversion efficiency is correlated with nondimensional groups involving available superheat ($ΔTs$) and inlet flowrate ($m˙l$). In experiments, the pressure drop through the liquid exit tends to dominate the determination of thermal conversion efficiency so the superficial velocity through the liquid exit is used in the correlation.

The experimental data are correlated in the form $y=a−bxc$ as
$ηt=100−1.584×105(cpΔTshfg)0.48(Pexitρl(m˙lρlAl)2)−1.66$
(21)

in the range: $0.02≤(cpΔTshfg)≤0.088$; $138≤(Pexitρl(m˙lρlAl)2)≤424$

For these experiments, the exit pressure $(Pexit)$ has not been changed and kept at atmospheric pressure. $Al$ is the cross-sectional area of the liquid exit tube. The correlated data for thermal conversion efficiency is shown in Fig. 14. It should be noted that the correlation presented is valid only for the ranges given. The experimental data are correlated to within ±10%. Further experiments with changing exit pressures would enhance the validity of the correlation.

Fig. 14
Fig. 14
Close modal

Phase separation efficiency is affected by both flowrate and available superheat. The flowrate and superheat affect the morphology of the vapor core which has a strong influence on the phase separation efficiency. It is expected that the vapor core is maintained by the forces originating from tangential momentum. The correlated data for phase separation efficiency is shown in Fig. 15.

Fig. 15
Fig. 15
Close modal

It is correlated with the dimensionless group, $(cpΔTs/(m˙lρlAi)2)$ which is a ratio of available sensible energy for producing vapor and the rate of liquid momentum through the injectors. $Ai$ is the area of injectors. As such, this ratio can be viewed like swirl number used in single phase swirl flows.

With the available data, phase separation efficiency has been correlated as
$ηs=100−2.542×105(cpΔTs(m˙lρlAi)2)−4.162$
(22)

in the range $6.9≤ cpΔTs(m˙lρlAi)2≤35$

It should be noted that the outliers in Fig. 15 correspond to 1 GPM which showed anomalous behavior at low superheats. The separator and retrieval tube diameters are also expected to play a role in determining phase separation efficiency. In present work, they were not changed and remained constant.

## 4 Conclusions

In this study, viability of a novel dynamic flash evaporation and phase separation system for desalination has been shown.

1. Single-stage system and an improved two-stage system were studied.

2. Role of independent variables such as mass flowrate, superheat, and position of retrieval tube was investigated with respect to phase separation, thermal conversion, and collection efficiencies for a two-stage system.

3. With sea water having a mass-based salinity as high as 2.5%, a condensate purity acceptable for drinking water is obtained. Phase separation efficiencies above 99% with salt concentrations of condensate below 0.02% were achieved, which is comparable to that of tap water.

4. Correlations for phase separation and thermal conversion efficiencies with the available experimental data have been obtained.

## Funding Data

• NSF (No. 2002699; Funder ID: 10.13039/100000001).

• Division of Chemical, Bioengineering, Environmental, and Transport Systems (No. 2002699; Funder ID: 10.13039/100000146).

## Nomenclature

$Ai$ =

cross-sectional area of the injector passage (m2)

$Al$ =

cross-sectional area of the liquid exit tube (m2)

$cp$ =

specific heat capacity of water (kJ/kg K)

$Cs,c$ =

salt concentration in liquid exiting the condenser (%)

$Cs,e$ =

salt concentration in primary tank (%)

$hfg$ =

latent heat of vaporization (kJ/kg)

$m˙condensate$ =

mass flowrate of condensed vapor (kg/s)

$m˙condenser$ =

mass flowrate of liquid exiting the condenser (kg/s)

$m˙entrained$ =

mass flowrate of entrained liquid (kg/s)

$m˙l$ =

inlet mass flowrate of liquid (kg/s)

$m˙salt$ =

rate of salt accumulation in the condenser (kg/s)

$m˙v,produced$ =

mass flowrate of produced vapor (kg/s)

$Texit(Pexit)$ =

saturation temperature at exit pressure (°C)

$Ti$ =

temperature of water before flashing (°C)

$Tinjector$ =

temperature of water at exit of injector passage (°C)

$ΔTinjector$ =

temperature change due to flashing (°C)

$ΔTs(Pexit)$ =

maximum available superheat based on exit pressure (°C)

$ηc$ =

collection efficiency (%)

$ηs$ =

phase separation efficiency (%)

$ηt$ =

thermal conversion efficiency (%)

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