Thermal Science and Engineering Progress 20 (2020) 100710
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Thermal Science and Engineering Progress
journal homepage: www.elsevier.com/locate/tsep
Investigation of steam jet flash evaporation with solar thermal collectors in
water desalination systems
T
Akram W. Ezzata, , Eric Hub, Hussein M. Taqi Al-Najjarc, Zihui Zhaob, Xin Shub
⁎
a
Department of Mechanical Engineering, University of Baghdad, Iraq
School of Mechanical Engineering, The University of Adelaide, Adelaide, SA 5005, Australia
c
Department of Energy Engineering, University of Baghdad, Iraq
b
ARTICLE INFO
ABSTRACT
Keywords:
Flash evaporation
Desalination system
Subsonic ejector
Solar collector
Entrainment ratio
Experimental validation
Experimental and theoretical studies were carried out to investigate the depressurization induced by steam jet
using subsonic steam ejector with flat-plate solar thermal collector. Saline water flash evaporation could be
realized by such depressurization in water desalination systems. The most critical component in such systems is
the steam ejector nozzle where the Mach number within the ejector is highly influenced by its geometry. The
main objective of the research is to evaluate the effect of different operating parameters on evaporation performance which can be specified by two factors; first is the subsonic ejector efficiency governed by the steam
entrainment ratio, and second is the percentage gain of distilled water productivity. That goal served an innovative drive for the present work. The experimental test rig was designed and constructed with primary steam
pressure (1.25–2.5) bar and temperature (106–127) °C using a controlled boiler, while condenser pressure
ranged (0.974–1.0) bar. It was found that ejector efficiency increased up to 53% however the efficiency is
saturated beyond primary steam pressure of 2.0 bar due to the sonic velocity limitation. Also, it was noticed that
the percentage gain of distilled water productivity using steam ejectors with respect to that using conventional
evaporation ranged between 1.0%–5.5%. Based on current collector design considerations implemented in the
mathematical model, about 34% of the total thermal energy required for water heating and evaporation during
the desalination process can be covered by the solar collector. The error analysis for experimental validation
indicated an average value of 22.9%. Finally, it was concluded that the present research could be considered as a
good basis for further investigations of solar steam jet flash evaporation in desalination systems.
1. Introduction
Freshwater became one of the world's biggest needs due to the increase in population. Water desalination contributed effectively in
solving this problem. Flash evaporation of seawater is one of the wellknown technologies which are greatly improved recently. Solar heating
of saline water using Sun heat absorbed by solar thermal collectors is
one of the efficient ways. Normally, direct and indirect desalination
processes are related to the energy transferred to freshwater. Direct
solar desalination uses solar energy in solar stills, while indirect solar
desalination systems utilize solar energy via solar collectors. Two alternatives are simply implemented in such systems; the first is using
thermal collectors for heat collection while the second depends on
photovoltaic panels to convert the electromagnetic radiation into
electricity [1]. Though, a number of desalination plants around the
world are still under continuous research and development.
⁎
Fig. 1 shows the existing desalination methods according to the type
of energy used. Conventional energy sources such as non-thermal and
electricity are being used to operate high capacity thermal desalination
processes. The most technically applicable methods in water desalination are RO, MVC, MSF, MED, TVC and ED/EDR [2]. However, the
shortcomings of conventional desalination technologies are mainly laid
in the complexity of treatment process and the high energy consumption. The combination of different technologies can integrate their expected advantages to decrease the energy consumption, the cost and to
improve the desalination performance. In fact, analysis of energy consumption of different desalination technologies was taken much attention. At present, of the total production capacity, Reverse Osmosis is
contributed up to 63%, multi-stage flash evaporation around 23% and
only 8% by MED [3]. Actually, newly developed desalination technologies are still in lab-scale and need further improvement.
Different comparisons and analysis have been conducted for four
Corresponding author.
E-mail address: akramwahbi@yahoo.ie (A.W. Ezzat).
https://doi.org/10.1016/j.tsep.2020.100710
Received 13 May 2020; Received in revised form 27 August 2020; Accepted 28 August 2020
2451-9049/ © 2020 Published by Elsevier Ltd.
Thermal Science and Engineering Progress 20 (2020) 100710
A.W. Ezzat, et al.
Nomenclature
Subscripts
x
T
ΔT
P
m
M
ṁ
G
A
Ac
h
hfg
s
UL
v
S
IT
Qu
FR
a
Ambient
i
Inlet
n
Nozzle
d
Diffuser
f
Liquid phase
g
Vapor phase
i
Inlet
av
Average
s
Isentropic
1,2,…,7,8 Section designation numbers in steam ejector
Steam quality, kg/kg
Temperature, °C
Temperature difference, °C
Pressure, kpa
Mass, kg
Mach number
Steam mass flow rate, kg/s
Gain in water productivity, kg/kJ
Cross sectional area, m2
Collector area, m2
Enthalpy, kJ/kg
Latent heat of evaporation, kJ/kg
Entropy, kJ/kg °K
Overall heat loss coefficient, W/m2.°C
Steam velocity, m/s
Absorbed solar radiation, W/m2
Incident solar radiation, W/m2
Thermal gain, W
Heat removal factor
Abbreviations
ABVC
ADVC
MSF
MED
ED
EDR
TVC
RO
MVC
COP
MD
H/D
Greek symbols
α
β
η
ρ
μ
Effective absorptance of collector plate with glazing, 0.9
Water productivity, kg/ kJ
Efficiency
Density, kg/m3
Entrainment ratio
different types of single-effect evaporator desalination systems [4]. The
systems were operated by vapour compression heat pumps including
thermal (TVC), mechanical (MVC), absorption (ABVC) and adsorption
(ADVC). The parameters used for the analysis are: specific power consumption, performance ratio, specific cooling water flow rate and
specific heat transfer area. The performance ratio related to the thermal
vapour compression system has been proved to be inversely proportional to boiling pressure and temperature. A suitable steady-state
mathematical model has been developed for a single-effect thermal
vapour compression (TVC) desalination process [5]. The model was
used to study system performance due to variations of the physical
properties through the demister with fluid temperature and salinity,
pressure drop, boiling-point rise, specific heat transfer area and cooling
Absorption vapor compression
Adsorption vapor compression
Multi stage flash
Multi effect desalination
Electro-dialysis
electro-dialysis reversal
Thermal vapor compression
Reverse Osmosis
Mechanical vapor compression
Coefficient of performance
Membrane distillation
Humidification–Dehumidification
water rate.
Another study proved that MED method does not require additional
heat for evaporation at all levels and can be operated at lower temperatures (~70 °C) than MSF [6]. It has been demonstrated that a
higher thermal efficiency could be obtained by increasing evaporator
and generator temperatures or decreasing condenser saturated temperature. Whereas, the exergy efficiency would be greater at higher
evaporator and generator temperatures as well as condenser saturated
temperatures. The performance of a steam ejector with the condensation phenomenon has been investigated for desalination applications
[7]. It has been noticed that, in the chocking section, the liquid droplets
could be vaporized by increasing the superheat degree of the vapour to
35 K in the inlet section. On the other hand, the results showed that the
irreversibility of a steam ejector could occur in the mixing process. The
irreversible loss in the mixing process has been estimated to be 73% of
the total irreversible losses of the ejector when the inlet vapours are
saturated. One dimensional model has been implemented to study the
efficiency of solar-assisted refrigeration systems using the supersonic
ejector technique [8]. Research outcomes proved that the generator
temperature should basically exceed 90 °C in order to obtain an acceptable performance coefficient. Evaporator temperatures have been
limited to values below 10 °C and condenser temperatures above 35 °C.
Constant pressure mixing ejector theory has been used to estimate the
ejector dimensions.
Flash evaporation of saline water has been used on a small-scale
system to conduct experiments for the purpose of investigating the effect of operating parameters on flash evaporation enhancement [9]. A
suitable vacuum pump has been implemented to create low pressure in
the evaporator to ensure flash evaporation. A freshwater production
rate of 4 l/h has been reached as the maximum value when 56 °C
temperature and 0.08 bar pressure have been ensured in the evaporator, while the flash rate of the feed water was limited to 3.6 l/min.
A testing rig has been designed and used for simulating water desalination systems to study the effect of seawater inlet temperature and
Fig. 1. Flow sheet of the existing desalination methods according to type of
energy used.
2
Thermal Science and Engineering Progress 20 (2020) 100710
A.W. Ezzat, et al.
mass flow rate on system performance [10]. It has been concluded that
the performance falls with the inlet temperature of the seawater.
An experimental study has been realized using a steam ejector in a
desalination system with thermal vapour compression (TVC) approach
[11]. The system showed that steam ejector can work effectively when
operated below 100 °C. It has been also proved that coefficient of
performance (COP) of the steam ejector is proportional to secondary
steam temperature and inversely proportional to primary steam temperature. Moreover, steam ejectors are found to work at critical condensation temperatures higher than that based on typical operating
conditions. Ejector assisted passive solar desalination system has been
investigated using detailed CFD analysis complemented by experiments
for both open and closed ejectors [12]. The research concentrated on
the capability of the new design to reduce the consumed energy of the
process. The configuration related to closed ejectors showed reliable
performance. The results proved the possibility of energy reduction by
reducing the feed water water flow rate.
The prime motive behind the present research was designated as to:
1) Improve knowledge of the fluid flow and thermodynamics inside and
around the subsonic steam ejector. 2) Validate theoretical results based
on an experimental approach. 3) Investigate subsonic ejector efficiency
according to operating parameters. 4) Estimate the enhancement in the
distilled water productivity by both prime and induced evaporation
using subsonic ejector in comparison with that realized due to evaporation at atmospheric pressure. 5) Calculate the effectiveness of incorporating solar thermal collector within the system.
In the experimental part of the present research, the solar collector
is simulated by a variable power heat source to control primary steam
pressure and temperature. While both primary and secondary steam
condensation processes are realized by open-loop condensation in
which the condensed steam is collected at the outlet of the condenser.
The water inside the evaporator is preheated using an electrical heater
during the experiments.
primary steam generation in the mathematical model. Saline water is
added to the feed tank for heating purpose by the solar thermal collector. The pre-heated water is then heated up to the saturation temperature in the stem boiler to generate primary steam at design pressure
and temperature. Portion of the pre-heated water in solar thermal
collector is fed to the evaporator. The pre-heated water in the evaporator is heated to evaporator temperature using immersed electrical
heater. The primary and secondary steam are condensed in the condenser, and then collected in distilled water tank.
A single nozzle steam ejector is used in the present research as
shown in Fig. 3. The ejector is the most critical component in this
system because it realizes system function during desalination process
[13]. The shape of the ejector nozzle, convergent or convergent-divergent, directly influences the Mach number within the ejector. In the
current research, the Mach number is controlled to be less than 1
(subsonic) by selecting the convergent shape for ejector nozzle. The
high pressure and temperature of the saturated steam produced by the
boiler are allowed to flow through the ejector nozzle to the subsequent
parts. The primary steam flow into the convergent nozzle of the ejector
depressurizes the evaporator entrance area due to the conversion of
primary steam potential energy into kinetic energy and ejects the steam
evaporated from the evaporator to the mixing area of the ejector. This
steam flow from the evaporator is nominated as secondary flow. The
ratio of secondary steam flow rate to that of primary could be controlled through the design of the ejector and choosing the operating
parameters such as pressure and temperature in its primary, secondary
and outlet ports. Mathematical modelling of the system includes the
solar thermal collector and flash evaporation process.
2.2. Thermal design of flat-plate solar collector
A solar thermal collector is incorporated within the mathematical
modelling of the system to back up both boiler and evaporator with
appropriate portion of thermal energy at certain prerequisite temperature, see Fig. 2. A flat-plate collector is designed for that purpose
following the method of [14] using four specific collector factors with
the local solar radiation and the ambient temperature of Baghdad, Iraq.
The basic equation of flat-plate collector is given by [14] as:
2. Theoretical approach
2.1. Physical modelling of the system
The block diagram of Fig. 2 shows the contribution of both solar
thermal collector and steam boiler to the total energy required for
Qu = Ac FR [S
UL (Ti
Ta )]
Fig. 2. Block diagram of the desalination system used in the present research.
3
(1)
Thermal Science and Engineering Progress 20 (2020) 100710
A.W. Ezzat, et al.
Fig. 3. (A) 3D geometry of the ejector. (B) Ejector sections.
The heat removal factor FR includes parameters of collector piping
design, fluid properties and its heat transfer coefficient, and mass flow
rate.
The absorbed solar radiation S is found by [14] as:
The pressure of steam into the suction chamber P3 is the same at
nozzle outlet (P2 = P 3); therefore, s2f = s 3f and s2g = s 3g. Assuming
isentropic process between states at the sections 1 and 2, then s1 = s2s.
Therefore, the steam quality at position 2 could be calculated as:
(2)
S = IT
x2 = (s1
Collector design should provide the required fluid temperature with
reasonable partial energy for water heating and evaporation during
desalination process. The incident solar radiation IT was calculated
according to the isotropic model using beam, diffuse, and reflected
components for tilted collector due south [14–16]. The annual average
hourly solar radiation was found to be 480 W/m2 for a good atmospheric condition at the optimum collector tilt angle [16]. The annual
average daily ambient high temperature is 30 °C [16].
The design of the thermal collector for the present study is accomplished using a computer program that is specially developed for that
purpose. The main input and output parameters of the program, as
hourly average values, are shown in Table 1.
n
s2f )
= (h1
h2)/(h1
(5)
h2s )
Accordingly, steam density and enthalpy at state 2 could be calculated. Based on above assumptions, the expanding and accelerating
process of the primary fluid in the primary nozzle should meet energy
and mass conservation. The mass conservation equation between section 1 and section 2 as ṁ 1= ṁ2, could be written as:
1 A1 v1
=
(6)
2 A2 v 2
While the energy equation between the same sections could be
written as:
(7)
h1 + v12/2 = h2 + v22/2
The design pressure and temperature of primary steam are ranged
from (1.25–2.5) bar and (106–127) °C respectively, while those related
to condenser pressure and temperature ranged (0.974–1.0) bar and
(97–100) °C respectively. The estimated thermal energy for water
heating and evaporation is 4 kW for one hour. The simplified diagram
of the process flow of the studied case and its related p-h diagram are
shown in Fig. 4. The following assumptions are considered in the
mathematical model: The pressure losses in the condenser, evaporator
and connection pipeline of system components are ignored, no heat
exchange between system parts and the environment, an isenthalpic
process in the throttling process: state 1 to 2, state 3 to 4 and state 7 to
8, the fluid in the ejector is one-dimensional homogeneous flow, steam
flow from sections 1, 7 and 4 are considered as a saturated vapour,
primary and secondary steam is assumed to be entirely mixed and
further compressed in the subsonic diffuser and then discharged to the
condenser, the pressure of both primary and secondary steam into the
mixing chamber at section 3 is the same. The pressure in sections 1 and
4 corresponds to design pressure, while the pressure in section 3 is a
pre-assumed value. This value is cross-checked and corrected using part
2 of process 2 + 7–4. The mathematical model for flash evaporation is
based on simple thermodynamic equations that track water evaporation
and condensation processes at different sections [17–20]. The percentage salinity for water physical properties in the evaporator is ignored
due to its minor effect [21].
The steam quality at state 2 is found as:
s2f )/(s2g
(4)
s3f )
The isentropic enthalpy at state 2, h2s could be calculated based on
the relationship between the relative vapor quality and the nozzle efficiency ηn = 0.7.
2.3. Mathematical modelling of flash evaporation
x2 = (s2s
s3f )/(s3g
The velocity at state 1 and 2 can be calculated by solving Eqs. (6)
and (7) together.
Moreover, the mass flow rate at state 1 and 2 can be calculated by
Eqs. (8) and (9):
m1 =
1 A1 v1
(8)
m2 =
2 A2 v 2
(9)
Process 7–8:
There is an isentropic process between state 7 to state 8, therefore,
s8 = s7s = s7g. The steam quality at state 8 is found as:
x 8 = (s8
s8f )/(s8g
s8f ) = (s7g
s3f )/(s3g
(10)
s3f )
Therefore, the relative property of the steam in state 8, such as ρ8
Table 1
Thermal collector design parameters.
no
parameter
value
no
parameter
value
1
tilt angle
30°
6
2
3
inlet temperature
overall heat loss
coefficient
mass flow rate
collector area
30 °C
7 W/m2.
°C
7.2 g/s
6 m2
7
8
heat transfer
coefficient
outlet temperature
collector
temperature
thermal efficiency
thermal gain
270 W/m2.
°C
75 °C
60 °C
4
5
(3)
4
9
10
52%
1.35 kW
Thermal Science and Engineering Progress 20 (2020) 100710
A.W. Ezzat, et al.
Fig. 4. (A) Process flow of the studied case. (B) P-h diagram of the system.
and h8 can be calculated based on x8.
Process 3–4:
The process from 3 to 4 is similar to the process from 1 to 2. The
vapor quality in state 3 needs to be known by:
x3 = (s3s
s3f )/(s3g
s3f )
1. The mixing process of the primary and secondary steam streams
in the mixing chamber satisfies both energy and mass conservation
equations respectively as follows:
m4 (h4 + v42/2) = m2 (h2 + v22/2) + m8 (h8 + v82 /2)
(11)
4 A 4 v4
where s3s = s4s = s4g, since there is an isentropic process from state 3 to
4. Therefore, Eq. (11) could be transformed as x3 = (s4g − s3f)/(s
3g − s3f), ρ3 and h3 could be calculated based on the relative vapor
quality x3.
The diffuser efficiency ηd = 0.8, is represented as follows:
d
= (h4s
h3)/(h4
h3)
=
2 A2 v 2
+
8 A8 v 8
(13)
(14)
whereṁ 4 is the sum of the primary and secondary mass flow rates.
Eqs. (13) and (14) could be solved together in order to find the
velocity at state 4 and state 8 (ν4 and ν 8).
The mass flow rates at section 8 and section 4 could be calculated by
Eqs. (15) and (16) respectively as follows:
(12)
where h3 is enthalpy at state 3 and h4s is isentropic enthalpy at state 4.
Then h4 could be calculated by Eq. (12).
Process 2 + 7–4:
m8 =
8 A8 v 8
(15)
m4 =
4 A 4 v4
(16)
2. Check the assumed value of P3
Fig. 5. The conceptual design of experimental test rig.
5
Thermal Science and Engineering Progress 20 (2020) 100710
A.W. Ezzat, et al.
%G = [1/hfg, T 7
1/(hfg ,100 + Cp (100
T7 )]/[1/(hfg,100 + Cp (100
T7)]
(22)
3. Experimental approach
3.1. Experimental test rig
Flash evaporation of water in sub-cooled phase depends on the
technique used for depressurization. Some of these techniques are
based on static depressurization of the upward flowing fluid in the test
section [22,23]. Other techniques depend on the depressurization induced by steam jet using steam ejectors.
Testing rig is designed and constructed to validate the mathematical
model according to the operating pressures, temperatures and thermal
power consumed during desalination process using flash evaporation
induced by steam jet in subsonic ejector. The conceptual design of the
testing rig simulated the solar collector by variable power boiler which
is used to heat up the water to produce primary steam pressure of
(1.25–2.5) bar and temperature of (106–127) °C. The configured test rig
ensures water evaporation in the evaporator using an electric heater
and open-loop condenser cooling that covers the operational conditions. Fig. 5 illustrates the schematic diagram of the test rig. The
pressure control valve 1 is used to regulate steam pressure and flow rate
according to the design limits. The primary steam for the subsonic
ejector actuates the secondary flow of steam from the evaporation tank
due to the low-pressure condition created in the mixing area at the
upstream of nozzle outlet which also ensures water evaporation at
temperatures ranging (75–95) °C. The initial water temperature in the
evaporator is controlled by the electrical power of the preheating
heater. The mixed primary and secondary steam flow are drafted
through ejector divergent area to the condenser. The mixed steam
flowing inside the condenser is condensed after cooling by the water
coil fixed inside. A properly designed cooling coil is used in the condenser to remove heat from collected steam and condense it to the
operating temperature of (25–50) °C. Valve 4 is used to drain water
from the evaporator at the end of the experiments. The following design
criteria are considered for the test rig:
Plate 1. Experimental test rig.
The mixing process of the two fluids in the mixing chamber satisfies
momentum conservation equation:
m4 v4 = P3 A3 + m2 v2 + m8 v8
P4 A 4
(17)
where ν4 and ν7 refer to the velocity at state 4 and 7; P4 and P2 refer to
the pressure at state 4 and 2, and A3 is the area directly after mixing
primary and secondary flow. Eq. (17) can be arranged to find P3 as:
P3 = (m4 v4
m2 v2
m8 v8 + P4 A 4 )/ A3
(18)
Eq. (18) can be solved using iteration procedure by replacingṁ
with ṁ7.
The entrainment ratio of the ejector μ is defined as:
8
(19)
µ = m7 / m1
The coefficient of performance COP for subsonic ejector could be
represented by steam entrainment μ as the enthalpy difference along
primary steam path is almost equal to enthalpy difference along secondary steam path, as given by:
COP = m7 (h7
h 4)/m1 (h1
h 4) = µ
1- Sizing of the subsonic steam ejector is complied with the design
parameters of the system by selecting a typical ejector that ensures
nozzle replacement capability.
2- Condenser design ensures the range of the ejector back pressure
implemented during the experiments by using a proper cooling coil
for the steam condensation process.
3- The evaporation tank has the capability to keep the water temperature within specified limits by pre-heating due to solar collector
design.
4- Use of distilled water instead of saline water due to the minor effect
of water salinity on the physical properties [21].
(20)
Distilled water productivity β is estimated based on the steam mass
generated during evaporation process per thermal energy unit consumed during this process, according to the following equation:
= 1/ hfg
(21)
The percentage gain %G of distilled water productivity using flash
evaporation at the evaporator temperature T7 corresponding to the
evaporator pressure P7 with respect to that produced by the evaporation process at the atmospheric pressure Pa is estimated according to
following equation:
Plates 1 and 2 show the test rig and the steam ejector used in the
Plate 2. Manufacturing process for two ejector models.
6
Thermal Science and Engineering Progress 20 (2020) 100710
A.W. Ezzat, et al.
experiments.
Table 3
Experimental results.
4. Results and discussion
Table 2 illustrates the results obtained using the mathematical
model while Table 3 shows the experimental results, where ṁ1 is the
primary steam mass flow rate and ṁ7 is the secondary steam mass flow
rate.
The mathematical model used for the present research assumes that
the steam mass flow rate at position 7, ṁ7 is equal to that at position 8,
ṁ8 ignoring the connection area between these positions. This assumption is justified based on the continuity equation between these
two points as there is no mass addition or subtraction among them. The
theoretical values of steam velocity at the outlet of the ejector nozzle, ν2
is cross-checked based on the chocking condition at the nozzle outlet
when this velocity approaches sound velocity, M2 = 1. Primary steam
mass flow rate ṁ1 behavior versus variable primary steam pressure at
position 1, P1 is shown in Fig. 6. The theoretical results illustrate the
saturation of primary flow rate due to the sonic condition in the nozzle
outlet. However, there is a significant gap between the model results
and the experimental results which reach its maximum value at primary
steam pressure of 2 bar. This gap is related to the collection of distilled
water produced from the primary steam condensation process. The
underestimation in theoretical values is justified due to neglecting the
vapor compressibility in the mathematical model for its dependency on
the relative vapor speed to sound speed along the vapor path within
ejector sections. The analytical solution of the mathematical model can
only verify vapor speed at specified areas while ignoring this effect
along the vapor path.
The secondary steam mass flow rate showed an increase in its trend
versus primary steam pressure, see Fig. 7. Steam velocity saturation in
the nozzle outlet affects evaporator depressurization and then subsequently saturates the mass flow rate of secondary steam. However,
there is an underestimate in the model results with respect to experimental results at low primary steam pressure. While, overestimation is
noticed as primary steam pressure increased. These differences are due
to neglecting of irreversibility. The experimental validation for the
mathematical model is executed using error analysis between theoretical and experimental values of entrainment ratio. The error in entrainment ratio has been chosen as it represents the effect of the most
operating conditions in both mathematical model and experimental
approach. The average value of this error was 22.9% due to the effect of
theoretical assumptions on the mathematical results. This error could
be narrowed using CFD model for the theoretical calculations. Moreover, ejector and test rig design could be modified such that to eliminate the condensed droplets in the evaporator which affects the experimental results of entrainment ratio.
Steam entrainment ratios versus steam pressures at nozzle inlet,
evaporator and condenser are plotted using their average values μav of
the experimental and theoretical results; see Table 3. Entrainment ratio
trend increases with primary steam pressure P1, as shown in Fig. 8. The
average to mainstream value of the secondary steam mass flow rate
affects this increase. However, this increase is restricted as notified
early due to the limitation of the primary steam velocity to subsonic
values, as noticed from Table 2.
Steam line
pressure,
P1 (bar)
Condenser
pressure, P4
(bar)
Evaporator
pressure, p7
(bar)
ṁ1 (g/s)
ṁ7 (g/s)
μ
1.250
1.500
1.750
2.000
1.0
0.998
0.980
0.976
0.940
0.928
0.908
0.886
0.533
0.90
1.05
1.20
0.185
0.197
0.212
0.275
0.347
0.219
0.202
0.229
exp
μ
av
0.247
0.205
0.279
0.38
Fig. 6. Primary steam mass flow rate versus primary steam pressure.
Fig. 9 illustrates the influence of the evaporator pressure P7 on the
average entrainment ratio. The evaporator pressure P7 is proportional
to the steam pressure at nozzle outlet P2, which in turn inversely affects
Table 2
Mathematical Modelling results.
Steam line pressure, P1 (bar)
Condenser pressure, P4 (bar)
Evaporator pressure, p7 (bar)
ṁ1 (g/s)
ṁ
1.250
1.500
1.750
2.0
2.25
2.5
1.0
0.998
0.980
0.976
0.974
0.974
0.940
0.928
0.908
0.886
0.878
0.878
0.485
0.596
0.659
0.718
0.743
0.746
0.071
0.114
0.235
0.381
0.394
0.396
7
7
(g/s)
μ
th
0.146
0.191
0.357
0.531
0.533
0.531
v2 (m/s)
311.7
390.6
437.8
476.8
493.2
495.4
Thermal Science and Engineering Progress 20 (2020) 100710
A.W. Ezzat, et al.
proportional to the entrainment ratio, as both of them are influenced by
the additional evaporation induced by depressurization in the evaporator. This additional steam using subsonic ejector increases the
steam mixture mass flow rate to the condenser.
Fig. 12 shows the comparison between average entrainment ratios
obtained from present research in comparison to that obtained by Liu
research [17] versus primary steam superheat degree. The comparison
proves reliable agreement despite the different range in primary steam
superheat degree and primary steam temperature. The latter is ranged
(106–127) °C for the present research and 140 °C for Liu research [17].
Fig. 13 illustrates the pressure and velocity profiles along the ejector
sections based on the results obtained from the mathematical model.
The figure shows that the highest velocity occurs at the outlet of ejector
nozzle, Section 2, which is close to the sonic velocity but never exceeds
it. The lowest pressure occurs at the mixing chamber, Section 3 so that
the secondary flow could be sucked in. The model proved that velocity
and pressure profiles do not change significantly in the diffuser.
Therefore, in the subsonic velocity ejector, the diffuser could be designed as a constant cross-section with a minor effect on pressure and
velocity profile downstream the nozzle section of the ejector.
Fig. 7. Secondary steam mass flow rate versus primary steam pressure.
5. Conclusions
Experimental and mathematical studies were performed on steam
jet flash evaporation for desalination system using subsonic ejector and
incorporating solar thermal collector. The effects of primary steam
pressure, evaporator and condenser pressures on system performance
were investigated at the primary steam pressure ranging from 1.25 bar
to 2.5 bar and condenser pressures ranging from 0.974 bar to 1.0 bar. A
mathematical model was developed and validated against the experimental data generated by the steam ejector desalination system experiments conducted on a well-designed testing rig. The model is then
applied to estimate the effects of operating parameters on secondary
steam entrainment ratio and the percentage gain of water productivity.
The following outcomes are concluded from the present research:
Fig. 8. Average entrainment ratio versus primary steam pressure.
1) Steam ejector efficiency represented by entrainment ratio showed
an increase of 53% when the primary steam pressure changed from
1.25 bar to 2.0 bar. However, beyond 2 bar this ratio saturates due
to the limitation of the primary steam velocity to subsonic values.
2) The entrainment ratio is inversely proportional to evaporator pressure ranged from 0.898 bar to 0.94 bar.
3) The tendency of ejector efficiency decreases as the condenser pressure increases from 0.974 bar to 1.0 bar.
4) The percentage gain of distilled water productivity at selected evaporator temperature with respect to that produced during the classical evaporation process ranged (1.0–5.5)%.
5) Based on a sensitivity study, the mathematical model could be applied to correlate between ejector geometry, operating parameters
and ejector performance. The best combination could be selected for
the highest ejector efficiency at different conditions.
6) According to the present solar collector design, 34% of the total
Fig. 9. Average entrainment ratio versus evaporator pressure.
the secondary steam mass flow rate. This inverse proportionality justifies the trend of entrainment ratio with evaporator pressure. In conclusion, evaporator pressure P7 is another important parameter that
influences ejector efficiency.
Additionally, Fig. 10 proves that the average entrainment ratio is
inversely proportional to condenser pressure P4 and that the trend of
proportionality saturates due to the saturation of condenser pressure P4
at 0.974 bar. This relationship demonstrates that condenser pressure
has another role in controlling the ejector and the efficiency of the
whole process. However, there is a critical condenser pressure for each
ejector [24]. The influence of condenser pressure on the entrainment
ratio is restricted to such nominated critical pressure, which means that
condenser pressure P4 should not be set smaller than the critical pressure to avoid the reduction of ejector efficiency. Steam ejector efficiency governed by the entrainment ratio showed an average increase
of 53% when the primary steam pressure changed from 1.25 bar to
2.0 bar.
Fig. 11 shows that the percentage gain of distilled water productivity at selected evaporator temperature with respect to that produced during the classical evaporation process, T7 = 100 °C, ranged
(1.0–5.5)%. The figure proves that water productivity is directly
Fig. 10. Average entrainment ratio versus condenser pressure.
8
Thermal Science and Engineering Progress 20 (2020) 100710
A.W. Ezzat, et al.
condensation process for water pre-heating in the evaporator. The authors also recommend implementing solar energy in the experimental
part. The heat gain from the collector could be shared for heating up the
water inside evaporator and for ensuring the primary steam production
rate.
CRediT authorship contribution statement
Akram W. Ezzat: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Software,
Supervision, Validation, Visualization, Writing - original draft, Writing review & editing. Eric Hu: Conceptualization, Formal analysis, Funding
acquisition, Investigation, Methodology, Project administration,
Resources, Supervision. Hussein M. Taqi Al-Najjar: Data curation,
Formal analysis, Investigation, Methodology, Software, Writing - review & editing. Zihui Zhao: Data curation, Formal analysis, Resources,
Investigation, Software, Visualization. Xin Shu: Data curation, Formal
analysis, Resources, Investigation, Validation, Visualization.
Fig. 11. Percentage gain in distilled water productivity versus evaporator
temperature.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors acknowledge the support of the Adelaide University
workshop and RAB engineering services in Adelaide- Australia for their
support to fabricate the ejectors used in the test rig to validate the
mathematical model. This acknowledgment is extended to appreciate
the support of Chemical Engineering School in Adelaide University
–Australia to utilize the steam boiler in the distillation Lab. during
conduction the validation experiments.
Fig. 12. Average entrainment ratio versus primary steam superheat degree.
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Thermal Science and Engineering Progress 20 (2020) 100710
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