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Expander-Based Atmospheric Water Harvesting in the Tropics
Alison Subiantoro, Ph.D.
Department of Industrial Engineering, Krida Wacana Christian University (UKRIDA)
Jl. Tanjung Duren Raya 4, West Jakarta, Indonesia 11470
Tel: +62 21 5645762, E-mail: alison.subiantoro@ukrida.ac.id.
Note: This is the accepted version of the manuscript. The final publication is available at IOS
Press through http://dx.doi.org/10.3233/AJW-170020
Abstract
A novel concept of using an expander to harvest atmospheric water is explored. The main
advantages of this concept are its compactness and simplicity. Mathematical models were
developed in this project to study the concept. The benchmark system had a crank and piston radii
of 5 cm, rod length of 20 cm, operational speed of 60 rev/min, atmospheric temperature of 30°C
and relative humidity of 80%. The expander was designed to expand the air to 0.7 bar and 0°C at
the end of the expansion process. Because of the expansion, around 11.5 g of water was condensed
for every 1 kg of air expanded. Most of the expander power was consumed during expansion to
overcome the pressure difference across the two sides of the piston. The average power per cycle
was 3.374 W. Therefore, the ratio of energy consumed and condensed water volume produced is
117 kWh/m3.
The parametric study found that the ratio of energy and water volume decreased slightly as the
operational speed increased, increased linearly as the ambient air was hotter, decreased with
ambient relative humidity, unaffected by the expander size, increased with dead volume and was
practically unaffected by the piston mass.
Keywords: water, vapour, humidity, condensation, expander, tropics
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1. Introduction
Clean water is a basic necessity for all life. However, due to the growing demand from industry
and the increasing human population, it is important to get alternative sources of clean water. Some
of the most popular solutions already in use include desalination (Shrivastava, 2016) and
wastewater treatment (Deng & Wheatley, 2016). The challenges facing these methods are the cost
and complexity of the system. Moreover, a liquid water source/reservoir is required, hence, limiting
the choice of location of implementation.
In the tropics, the air is constantly humid throughout the year. For illustration, in Singapore,
which is located in South East Asia, the relative humidity is always above 60% and is often more
than 90% (Singapore’s National Environment Agency, 2016). The humid condition means that a
lot of water is available in the air in the form of water vapour. This can be condensed to liquid water
to provide an alternative clean water source. This is particularly attractive for places with high
humidity but limited accessible clean water source, like in many coastal areas and small islands in
South East Asia.
Cooling is arguably the most well-known mode of atmospheric water harvesting. However,
there are other ways to collect water from the atmosphere. In general, the methods can be classified
into three types (Wahlgren, 2001):
1. To cool a surface below the dew-point of the ambient air.
a. With an artificial refrigeration / heat pump system
b. With radiative cooling
2. To concentrate water vapour through use of desiccants.
a. With absorption in liquid desiccant
b. With adsorption on solid desiccant
3. To induce and control convection in a tower structure.
The strengths and limitations of the three types of methods are tabulated in Table 1 (Harriman,
1990, Khalil, 1993, Meytsar, 1997, Wahlgren, 2001). Type 1a, which is the artificial refrigeration
system, is the most common method for artificial condensation. However, this system involves a
lot of components because even in its most basic form, a typical refrigeration system consists of at
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least four main components (a compressor, an evaporator, an expansion device and a condenser).
A much simpler solution is to get cold temperature by directly expanding the air in an expander.
This method involves only one component, i.e. an expander. In an expander, air is expanded and its
temperature decreases. This low temperature of the expanded air will induce condensation.
The oldest, most common and most reliable machine design is the reciprocating mechanism.
The schematic is shown in Figure 1. It consists of a stationary cylinder, a piston that moves in a
reciprocating motion in the cylinder chamber, an intake port with its valve and an exhaust port with
its valve. The piston is linked to a crank mechanism that causes it to move up and down in the
cylinder. Reciprocating machine is known to be very reliable and has been used for expanders
before (Baek et al., 2002).
The working cycle starts with the piston at the bottom dead centre (BDC), which is the furthest
point of the piston from the cylinder’s top wall. The fluid inside the chamber is currently low in
pressure and temperature. The intake valve is shut while the exhaust valve is opened. The piston
then begins to move up, towards the cylinder’s top wall, pushing the low pressure fluid to flow out
of the chamber through the exhaust port. This process continues until the piston reaches the top
dead centre (TDC). This is the closest the piston can reach with respect to the cylinder’s top wall.
A narrow gap between the piston and the top wall remains for practical reasons. However, this gap
should be made as narrow as possible for better performance. At this moment, the exhaust valve is
shut while the intake valve is opened. The piston then moves away from the top wall, increasing
the volume of the working chamber. This induces high pressure fluid to flow into the chamber
through the intake port. This process continues until the piston reaches the designed location of
expansion (LOE) at which the intake valve is immediately shut, stopping the intake flow.
Meanwhile, the piston continues to move down, increasing the chamber volume further. This causes
the fluid pressure in the chamber to decrease. This expansion process continues until the piston
reaches the BDC location again. At this moment, the fluid pressure is at its lowest and the cycle is
completed.
Currently, expanders are mostly used to generate useful power, like in Rankine cycles (Badr
et al., 1985a, 1985b). Expanders have also been recently proposed for increasing energy efficiency
of refrigeration and heat pump systems (Tamura et al., 1997, Henderson et al., 2000, Robinson et
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al., 1998, Lorentzen, 1994). In this study, a reciprocating expander was used to harvest atmospheric
water by directly expanding the air to reduce its temperature to induce condensation. The focus is
on the feasibility of the concept. The issue of energy requirement and effects of various parameters
to the performance were also investigated.
2. Mathematical Models
2.1. Expander
The mathematical model of the expander was derived based on the crank mechanism schematic
and the free body diagram shown in Figure 2. It was assumed that the upper side of the piston was
exposed to the working chamber while the lower side was exposed to atmosphere.
The definitions and force balance equations of the piston mechanism are expressed in
Equations (2.1-2.4). The masses of the crank and connecting rod were ignored in this model.
( )
p
atmf
p
A
pp
F−
=
(2.1)
nfric
FF
η
=
(2.2)
nPN
FF =
ϕ
sin
(2.3)
ppiston
fricp
PN
a
m
FF
F=+
−
−
ϕ
cos
(2.4)
where Fp is the pressure force (N), pf is pressure of fluid in the working chamber (Pa), patm is
atmospheric pressure (Pa), Ap is piston’s cross sectional area (m2), Fn is the piston side contact force
(N), Ffric is the piston side friction force (N),
η
is the friction coefficient, FPN is the force provided
by the link PN to push the piston (N),
ϕ
is the connecting rod angle (rad) and mpiston is the piston
mass (kg).
The torque acting at the crank centre, TO, is calculated according to Equation (2.5) and the
power required at the crank centre is calculated according to Equation (2.6).
( ) ( )( )
p
atmfppistonpO
AppamrxT −+
−
+= 1tan
tan
ϕη
ϕ
η
(2.5)
ω
OO
TP =
(2.6)
where
ω
is angular speed of the crank (rad/s) and rp is the piston radius (m).
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2.2. Thermo-physics of the Fluid
The working fluid in this project was humid air. It was assumed that throughout the process,
the fluid was in thermodynamics equilibrium and can be treated as a homogenous mixture. It was
also assumed to behave as an ideal gas. Therefore, the properties of the fluid are according to
Equation (2.7).
ffff RT
m
Vp =
(2.7)
where pf is fluid pressure (Pa), Vf is fluid volume (m3), mf is fluid mass (kg), R is specific gas
constant (287 J/kg·K for air), Tf is fluid temperature (K).
The location of expansion (LOE) needs to be defined beforehand. This was done by first
defining the final expansion temperature. In this project, this was set to be 0°C to avoid frosting.
During expansion, the process was modelled according to the polytropic model as expressed in
Equation (2.8). The working fluid’s pressure is reduced together with its temperature.
γγ
221
1
VpVp =
(2.8)
where
γ
is the polytropic index, which is around 1.4 for air (Moran et al., 2000).
The enthalpy change because of the expansion is calculated according to Equation (2.9). This is the
available thermal energy to be used for condensation process. Specific heat of air can be estimated
according to Equation (2.10) (Moran et al., 2000).
∫
=− 2
1
12
T
TpdTchh
(2.9)
()
4
12
392
63
,102763
.010
913.110
294.
310
337.1653
.3287 TT
TTc airp−−
−− ×
+×−×
+×
−=
(2.10)
where: h is the specific enthalpy (J/kg), cp is specific heat at constant pressure (J/kg·K).
Enthalpy of humid air can be computed following the step-by-step procedure developed by
Devres (1994), resulting in Equation (2.11).
( ) ( )
( )
15
.273805.
1250115
.273 −
++−=
airairair
TWTh
(2.11)
where: T is dry-bulb temperature (K) and
W
is humidity ratio of humid air (kg/kg),
Finally, mass of condensed water produced is calculated with Equation (2.12).
evapcondevap
hmQ =
6
evap
cond
air h
mh
m=∆
→exp
(2.12)
3. Results and Discussion
The results gathered from the models are presented and discussed in this section. A benchmark
system is first discussed. Later, a parametric study is presented.
Throughout the study, the following assumptions were adopted:
• Working fluid was air
• Air was ideal gas
• Adiabatic expansion
• Air was expanded to 0°C
• Valves opened and closed instantaneously
• The port sizes were large enough such that the fluid flows did not affect the thermodynamics of
the fluid in the chamber.
• Suction and discharge reservoirs were always at the ambient pressure and temperature
• Perfect sealing (no leakage)
• Heat caused by frictions of expander components was negligible
• Constant crank rotational speed
• Weights of the crank and connecting rod were ignored
3.1. Benchmark system
The dimensions and operating conditions of the benchmark system are tabulated in Table 2.
The movement of the piston and the valve dynamics varied the fluid mass in the working
chamber as shown in Figure 3. At the beginning of the cycle, air was induced into the chamber
through the open suction valve, increasing the fluid mass in the expander. The discharge valve was
shut during the process. When the piston reached the location of expansion (LOE), the suction valve
was shut, stopping the flow of air into the expander. Hence, the fluid mass was constant during this
expansion process. This continued until the piston reached its bottom dead centre at a crank angle
of 180°. At this moment, the discharge valve was opened while the suction valve was kept shut. Air
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from the discharge reservoir gushed into the working chamber because the pressure inside the
chamber was lower than the reservoir. Therefore, the fluid mass in the chamber increased rapidly.
As the piston moved up, the fluid in the chamber was gradually discharged out through the discharge
valve. This process continued until the end of the cycle. The amount of air mass expanded in the
expander per cycle was around 0.7 g. Since the angular speed was 60 rev/min, the expanded air
mass flow rate was equal to 0.7 g/s.
The variation of fluid pressure and temperature in the chamber with crank angle is shown in
Figure 4. At the beginning of the cycle, as the volume was increasing, ambient air was flowing into
the chamber. The pressure and temperature inside the chamber were constant at 101325 Pa and
30°C, respectively. When the piston reached the LOE, the pressure and temperature gradually
dropped because no more air was added into the chamber while the volume was still increasing.
This decrease in pressure and temperature continued until the volume reached its maximum at the
bottom dead centre position. The minimum pressure and temperature were 70359 Pa and 0°C,
respectively. The pressure was then increasing rapidly at the beginning of the discharge because of
the sudden flow of air into the chamber when the discharge valve was opened. After the pressures
in the chamber and the ambient were in equilibrium, it stayed constant throughout the discharge
process until the whole cycle was completed.
The low temperature caused by expansion was the cause of the condensation of the water
vapour in the expander and indirectly, at the outer wall of the expander. Using the psychrometric
equations by Devres (1994), the dew point temperature of air at 30°C and 80% is 26.2°C and the
absolute humidity is around 21 g of water per every kg of air. The enthalpy difference provided by
the expansion process of air from the dew-point temperature of 26.2°C to 0°C was 26.4 kJ/kg of
air. Considering that 0.7 g of air was expanded every cycle, there was 18.4 J of enthalpy to be used
for water condensation. The latent heat of vaporization of water at 0.7 bar is 2283.3 kJ/kg of water
while the specific heat capacity is around 1.86 kJ/kg·K at room temperature. Therefore, assuming
that the available enthalpy was used to first cool the water vapour to the dew point temperature and
then to condense it, 0.008 g of water was condensed per cycle. This was equal to 29 g of water per
hour because the rotational speed was 60 rev/min here. This also meant that around 11.5 g of water
was condensed for every 1 kg of air expanded.
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The variation of expander power requirement with crank angle is plotted in Figure 5. It can be
seen that most of the power was consumed during the expansion. This power was mostly used to
overcome the pressure difference across the two sides of the piston. The average power per cycle
was 3.374 W. It is interesting to observe that the curve is continuous, unlike those of mass, pressure
and temperature. Moreover, the maximum power was not at crank angle of 180°. This is because
power was affected by not only pressure difference across the piston, but also the angle of the
connecting rod and the acceleration of the piston. As the piston was approaching the bottom dead
centre, the connecting rod angle was decreasing and hence, the required power was also decreasing.
It had been calculated above that 0.008 g of water was condensed every cycle. Therefore, the
ratio between energy usage and amount of water produced was found to be 0.117 kWh/kg of water.
Assuming that the water density was 1000 kg/m3, the ratio between the energy usage and volume
of water was 117 kWh/m3. This was around 17% of the standard ratio of 681 kWh/m3 (Wahlgren,
2001).
The gathered benchmark data are summarised in Table 3.
3.2. Parametric study
After discussing the benchmark data, parametric study is presented in this section. The focus
of the analysis is on the ratio of energy and condensed water volume. The varied parameters include
the followings and the results are shown in Figure 6.
• Rotational speed
• Atmospheric temperature
• Atmospheric relative humidity
• Expander size
It was found that the ratio decreases slightly as the operational speed was increased. This was
because the amplitude of piston acceleration and the piston side force were larger as the speed was
higher, which increased the power requirement. On the other hand, the rate of water condensation
was unchanged.
The ratio increased significantly as the ambient air was hotter. From the figure, it can be seen
that the increase is linear with a gradient of around 4 kWh/m3/°C. The reason was because less air
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can be expanded in every cycle if the ambient air was hotter because the final expansion temperature
has been fixed at 0°C. Moreover, the fluid had to be expanded more to achieve the desired expanded
temperature.
The ratio was found to decrease with a higher relative humidity. Air flow rate and required
power were unchanged here. However, more humid air had a higher dew point temperature and
therefore, was easier to condense the moisture.
Lastly, the ratio was unaffected by the expander size. This was because with a bigger expander,
more air was processed per cycle. However, at the same time, more power was required, cancelling
out the increase in air mass.
4. Conclusions
In this study, an expander is used to induce condensation to harvest atmospheric water. The
main advantages of this concept are its compactness and simplicity.
Mathematical models were developed and employed to study a benchmark expander system.
The system had a crank and piston radii of 5 cm, rod length of 20 cm, operational speed of 60
rev/min, atmospheric pressure of 101325 Pa, atmospheric temperature of 30°C and relative
humidity of 80%. The followings were found:
• The amount of air mass expanded in the expander per cycle was around 0.7 g. Since the
angular speed was 60 rev/min, the expanded air mass flow rate was equal to 0.7 g/s.
• The fluid temperature was constant during suction and discharge. During expansion, it
decreased to 0°C. From the process, around 11.5 g of water was condensed for every 1 kg of
air expanded.
• Most of the power was consumed during expansion to overcome the pressure difference
across the two sides of the piston. The average power per cycle was 3.374 W.
• The ratio of energy consumed and condensed water volume produced was 117 kWh/m3. This
was around 17% of the standard ratio of 681 kWh/m3 in the literature.
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A parametric study was conducted to complete the analysis. The focus of the analysis was on
the ratio of energy and condensed water volume. From the parametric study, the followings were
found:
• The ratio decreased slightly as the operational speed was increased.
• The ratio increased linearly with the ambient air temperature.
• The ratio decreased with a higher relative humidity.
• The ratio was unaffected by the expander size.
5. References
Badr, O., O’Callaghan, P. W. and Probert, S. D. (1985a). Multi-Vane Expanders: Geometry and
Vane Kinematics. Applied Energy, 19: 159-182.
Badr, O., Probert, S. D. and O’Callaghan, P. (1985b). Multi-Vane Expanders: Vane Dynamics
and Friction Losses. Applied Energy, 20: 253-285.
Baek, J. S., Groll, E. A. and Lawless, P. B. (2002). Development of a Piston-Cylinder Expansion
Device for the Transcritical Carbon Dioxide Cycle. International Refrigeration and Air
Conditioning Conference at Purdue, R11-8: 1-10.
Deng, Y. and Wheatley, A. (2016). Wastewater Treatment in Chinese Rural Areas. Asian Journal
of Water, Environment and Pollution, 13(4): 1-11.
Devres, Y. O. (1994). Psychrometric Properties of Humid Air: Calculation Procedures. Applied
Energy, 48: 1-18.
Harriman III, L. G. (1990). The Dehumidification Handbook (2nd Edition), Munters Cargocaire:
Amesbury, USA.
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Henderson, P. C., Hewitt, N. J. and Mongey, B. (2000). An Economic and Technical Case for a
Compressor/Expander Unit for Heat Pumps. International Journal of Energy Research, 24: 831-
842.
Khalil, A. (1993). Dehumidification of Atmospheric Air as a Potential Source of Fresh Water in
the UAE. Desalination, 34: 587-596.
Lorentzen, G. (1994). Revival of Carbon Dioxide as a Refrigerant. International Journal of
Refrigeration, 17: 292-301.
Meytsar, J. (1997). Method and Device for Producing Water by Condensing Atmospheric
Moisture. World Intellectual Property Organization Patent WO 97/41937.
Moran, M. J. and Shapiro, H. N. (2000). Fundamentals of Engineering Thermodynamics (4th
Edition). John Wiley & Sons, Inc.: New York, USA.
Robinson, D. M. and Groll, E. A. (1998). Efficiencies of Transcritical CO2 Cycles With and
Without an Expansion Turbine. International Journal of Refrigeration, 21:577-589.
Shrivastava, B. K. (2016). Technological Innovation in the Area of Drinking Water for Treatment
of Saline Water. Asian Journal of Water, Environment and Pollution, 13(3): 37-44.
Singapore’s National Environment Agency - http://www.nea.gov.sg/weather-
climate/climate/weather-statistics. (accessed: November 2, 2016)
Tamura, I., Taniguchi, H., Sasaki, H., Yoshida, R., Sekiguchi, I. and Yokogawa, M. (1997). An
Analytical Investigation of High-Temperature Heat Pump System with Screw Compressor and
Screw Expander for Power Recovery. Energy Conversion Management, 38: 1007-1013.
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Wahlgren, R. V. (2001). Atmospheric Water Vapour Processor Designs For Potable Water
Production: A Review. Water Research, 35(1): 1-22.
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Table 1 – Strengths and limitations of various methods of atmospheric water harvesting
STRENGTHS
LIMITATIONS
Type 1: Cooled surface
Heat pump
1. Technology is mature
1. Frost may form and degrade the cooling
process
2. Efficient when condenser air temperature is
low and cooling coil air temperature is high
2. There is mixing of dried and unprocessed
air within the processor
3. Easy maintenance
3. High power requirement
4. Refrigerants may affect the environment
negatively
Radiative cooling
1. No external energy source is needed
1. Existing technology depends on radiation
into a clear night sky
2. Simple mechanical requirements
Type 2: Desiccants
1. Well-developed technology
1. Energy requirement is fairly high
2. Able to dry air to a low relative humidity
2. Liquid absorbents can concentrate
contaminants from the atmosphere
Type 3: Convection induced or controlled in a structure
1. Adiabatic cooling has the lowest energy
requirements of the three design strategies 1. Large structure is required
2. Engineering experience in removal of
water from industrial compressed air systems
is well-developed
2. No existing prototype is known yet
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Table 2 – Dimensions and operating conditions of the benchmark system
Item
Value
Crank radius
5 cm
Rod length
20 cm
Crank angular velocity
60 rev/min
Dead volume
39.3 cm3
Maximum volume
824.7 cm3
Location of expansion
115°
Piston radius
5 cm
Piston thickness
0.2 cm
Piston density
2700 kg/m3
Piston mass
42.4 g
Friction coefficient
0.1
Atmospheric pressure
101325 Pa
Atmospheric temperature
30°C
Atmospheric relative humidity
0.8
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Table 3 – Summary of gathered benchmark data
Item
Value
Air mass / cycle
0.7 g of air
Air mass flow rate
7 g/s of air
Available enthalpy difference
26.4 kJ/kg of air
Available enthalpy diff. / cycle
18.4 J
Condensed water mass / cycle
0.008 g of liquid water
Condensed water mass / hour
29 g of liquid water
Ratio of energy and condensed water mass
0.117 kWh/kg of liquid water
Ratio of energy and condensed water volume
117 kWh/m3 of liquid water
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Figure 1 – Schematics of a reciprocating expander
Figure 2 - Crank mechanism schematic and free body diagrams of a reciprocating machine
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Figure 3 – Variation of fluid mass with crank angle
Figure 4 – Variation of fluid pressure and temperature with crank angle
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Figure 5 – Variation of expander power requirement with crank angle
Figure 6 – Variation of ratio of energy and water volume with operational speed, ambient air
temperature, ambient relative humidity and piston radius (expander size)
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