006 - theoretical study of a new thermodynamic power cycle for thermal water pumping application

8/11/2019 006 - Theoretical Study of a New Thermodynamic Power Cycle for Thermal Water Pumping Application

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Theoretical study of a new thermodynamic power cycle for thermalwater pumping application and its prospects when coupled to a solarpond

Abhijit Date*, Aliakbar Akbarzadeh

School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, PO Box 71, Bundoora, Victoria 3083, Australia

h i g h l i g h t s

Proposed a new power cycle to drive a thermal water pump.Examined the performance of an ideal thermal water pump based on new power cycle.Examined the prospects of this thermal water pump coupled with solar pond.

a r t i c l e i n f o

Article history:

Received 12 January 2013Accepted 2 May 2013Available online 13 May 2013

Keywords:

Thermal energy

Water pumpLow temperature heatSolar pond

a b s t r a c t

This is an introductory theoretical work on the new thermodynamic power cycle for thermal waterpumping. This paper describes the new thermodynamic power cycle with help ofPevand Pehcurvesand the operation of a thermal water pump based on this cycle with acetone as working uid. Furtherideal thermal performance of this water pump for different heat source and heat sink temperatures isdiscussed. The proposed thermal water pump has an ideal overall efciency equal to about 40% of Carnotcycle efciency for driving temperature difference of 60 C with acetone as working uid. This paperpresents the ideal theoretical performance predictions of such thermal water pump coupled with a solar

pond located on a salt farm at Pyramid Hill in north Victoria, Australia. Most salt farms around the worlduse electric pumps to draw saline water from ground or sea. The proposed thermal water pump canprovide an alternative to these electric pumps.

2013 Elsevier Ltd. All rights reserved.

1. Introduction and background

The solar water pump concept to pump ground water foragricultural irrigation, industry and residential water re-quirements has been proposed and investigated by many re-searchers in past[1e3]. Similarly concept of the wind driven waterpumps has been proposed and investigated by many researchers

in past[4e6], but due to reasons like lack of government supportand variable nature of wind energy the diffusion of this technol-ogy has been very slow [7]. Most common method used forpumping ground water has been conversion of solar energy toelectricity with PV panels and then using electric water pumps.But the PV pumping system can be relatively expensive and wouldneed battery based system for use during cloudy days and nights.Additionally plenty of low temperature thermal energy is available

around the world in form of waste heat, shallow geothermal andsolar thermal etc. For these reasons researchers around the worldhave developed few thermally driven water pump that directlyconvert thermal energy to mechanical energy. Most researchpublications have investigated thermal pumps based on thermo-dynamic Rankine cycle and are directly connected to at plate orevacuated tube solar collectors without thermal energy storage

system for 24 h of pumping[3,8e13].In 1975, Rao and Rao had proposed and investigated a design of

thermal water pump that would use pentane or petroleum fractionhaving boiling temperature of 35e40 C. In this publication theyhave discussed that at least 100 C is required to create enoughsuction pressures for water pumping. Further they have suggestedthat secondary working uid is needed to prevent direct contactbetween the vapour of the primary working uid and the waterthat is being pumped. The conguration of this thermal pump isvery complex to construct and operate[3].

In 1979, Sharma and Singh had proposed a thermal water pumpbased on Rankine cycle that used Freon as working uid in a

* Corresponding author. Tel.: 61 3 9925 0612; fax: 61 3 9925 6108.E-mail addresses: [email protected], [email protected] (A. Date),

[email protected](A. Akbarzadeh).

Contents lists available atSciVerse ScienceDirect

Applied Thermal Engineering

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m/ l o c a t e / a p t h e r m e n g

1359-4311/$e see front matter 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.applthermaleng.2013.05.004

Applied Thermal Engineering 58 (2013) 511e521
mailto:[email protected]:[email protected]:[email protected]:[email protected]://www.sciencedirect.com/science/journal/13594311http://www.elsevier.com/locate/apthermenghttp://dx.doi.org/10.1016/j.applthermaleng.2013.05.004http://dx.doi.org/10.1016/j.applthermaleng.2013.05.004http://dx.doi.org/10.1016/j.applthermaleng.2013.05.004http://dx.doi.org/10.1016/j.applthermaleng.2013.05.004http://dx.doi.org/10.1016/j.applthermaleng.2013.05.004http://dx.doi.org/10.1016/j.applthermaleng.2013.05.004http://www.elsevier.com/locate/apthermenghttp://www.sciencedirect.com/science/journal/13594311http://crossmark.dyndns.org/dialog/?doi=10.1016/j.applthermaleng.2013.05.004&domain=pdfmailto:[email protected]:[email protected]:[email protected]


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diaphragm type water pump. This pump had a very low lift and thevery low energy conversion efciency of around 0.4%[9].

Picken, Seare and Goto have proposed a simple design of athermal water pump using water piston. This pump is driven bywater vapour and hence needs heat source at temperatures morethan 100 C[14].

Klppel and Gurgel have used expansion and compression ofgas similar to air in their liquid piston pump. The working gas andthe liquidwere not separated andthe experiments have shown thatafter 1 h of operation some of the gas was dissolved in the waterand lost. They have suggested of using oil oatinglm over the top

of water to prevent mixing or providing a working gas rechargingchamber. The second approach would be practical if the pump wasoperated with air as workinguid, similar to a Stirling engine[10].

Solovey and Frolov have suggested in their research to usehydrogen stored in metal hydrides for water pumping. Hydrogengas that is released by elevating the temperature of metal hydride isused forpumping waterthrough pistoncylinder system. They claimtheir system can pump 1 m3 of water with an average suction headof 3e4 m and delivery head of 20e30 m in 11 h and consumearound 2.6 kWh thermal energy. Their system has an overall ef-ciency of around 4%. This type of pump system can be very slowdepending upon the heating of metal hydrides for dissociation andcooling of the metal hydrides for hydrogen adsorption. Additionallythis system needs a retracting spring to assist the piston in the

return or suction stroke. Part of the energy from the forward stroke

is stored in the spring to be used for return stroke and this reducesthe overall efciency[11].

Wong and Sumathy have proposed a thermal water pump de-signs with ethyl ether and pentane. They have discussed theimportance of the evaporation and condensation time in the solarthermal water pump that is coupled with a at plate solar collector.In case of a at plate or evacuated tube solar collector directlycoupled with a solar water pump the overall system efciency isvery much dependent on the number of pumping cycles achievedduring the peak sun hours. This type of system can only operateduring the day; hence the cycle time must be reduced [12,13,15].

Here attempt have been made to proposea newthermodynamiccycle for thermal water pumping to simplify the thermal waterpump design and operation. This paper describes the workingprinciple of the new thermal water pump with help of pumpschematics and thermodynamic curves (PevandPeh). Theoreticalanalysis of the new thermal water pump is carried out to predict itsthermal performance.

In 2010 about 280 Mt of sodium chloride salt was producedaround the world while Australia produced 11.5 Mt out of this andmajority of the salt was produced by evaporation of saline groundwater or sea water [16]. At present electric pumps are being used tomove large volumes of salinewaterfrom itssource to the salt farms.Solar ponds could be built on salt farms as all the raw materials arereadily available. Solar ponds can provide necessary heat to drive

thermal water pumps and the biggest advantage is their thermal

Nomenclature

db bore diameter (m)dp1 working uid piston diameter (m)dp2 water piston diameter (m)D diameter of heat exchanger tube (m)foC fraction of Carnotg acceleration due to gravity (m/s2)GrLHE Grashof number for heat exchanger with lengthLHEHd delivery head (m of water)Hs suction head (m of water)h specic enthalpy of working uid (J/kg)hfg specic latent heat of evaporation or condensation of

working uid (J/kg)k thermal conductivity of workinguid (W/m C)kHE thermal conductivity of heat exchanger material (W/

m C)LHE length of the heat exchanger tube (m)mwf mass of workinguid per stroke (kg)P absolute pressure of workinguid (Pa)Patm local atmospheric pressure (Pa)Pwf,d absolute pressure of workinguid during delivery

stroke (Pa)Pwf,s absolute pressure of workinguid during suction

stroke (Pa)Pd absolute delivery pressure on water side (Pa)Ps absolute suction pressure on water side (Pa)PR pressure ratio_QA available heat ux (J/m

2/day)QS total heat consumed per stroke (J/stroke)_QE heatux extracted from solar pond per day (J/m

2/day)Qin_S sensible heat input per stroke (J/stroke)Qin_L latent heat input per stroke (J/stroke)Qcc cooling capacity (J/stroke)_Qcc rate of heat transfer in cooling coil (W)_

QHE rate of heat transfer in heat exchanger/evaporator (W)

Ds stroke length (m)_V volume ow rate of water pumped/m2 of solar pond/

day (m3/m2/day)DV discharge volume per stroke (m3)DVp1 change in volume of workinguid per stroke for piston

1 (m3)DVp

2

volume of water pumped per stroke for piston 2 (m3)NS number of strokes per m2 of solar pond per day

(strokes/m2/day)y specic volume of working uid (m3/kg)td time for single delivery stroke to complete (s)ts time for single suction stroke to complete (s)T temperature of workinguid (C)THE,i temperature of inner wall surface of heat exchanger

(C)Tcc,i temperature of inner wall surface of cooling coil (C)Wd delivery work per stroke (J)Ws suction work per stroke (J)Wt total work done per stroke (J)xHE heat exchanger tube wall thickness (m)m dynamic viscosity of workinguid (N s/m2)n kinematic viscosity of workinguid (m2/s)a thermal diffusivity of workinguid (m2/s)b thermal expansion coefcient of working uid (1/C)rw density of liquid water (kg/m

3)r density of workinguid (kg/m3)ho overall theoretical efciency (%)ht thermodynamic efciency (%)

Subscript

1 thermodynamic property of working uid at point 12 thermodynamic property of working uid at point 23 thermodynamic property of working uid at point 330 thermodynamic property of working uid at point 30

4 thermodynamic property of working uid at point 4

A. Date, A. Akbarzadeh / Applied Thermal Engineering 58 (2013) 511e521512


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energy storage capacity. So theoretical performance of the newthermal water pump coupled with a solar pond located at PyramidHill in north Victoria, Australia is investigated. This paper hopes todevelop interest in further research on the proposed thermal waterpump coupled with solar pondsas means of continuous heat source.Wind energy driven water pump needs reliable nature of wind foroptimum utilisation. Wind energy cannot be stored easily and hasvery moderate energy density. While solar energy is comparativelyeasy to store as thermal energy in solar ponds. And a thermal waterpumpcoupledwith solar pondthat has achieved equilibriumwouldhave the capability to operate at any time no matter if it cloudy oreven night. Although this type of thermal water pumpe solar pondsystem has some disadvantages like the time required in achievingsteady state condition, land required for solar pond and waterconsumption of solar pond due to evaporation.

2. Working principle

Fig.1 shows workingof the newthermalwater pumpthrough thesystem schematic. Here the new thermodynamic power cycle iscalled as Thermal Power Pump cycle (TPP cycle) or Dates cycle. Thepump consists of following components: a well-insulated pistone

cylinder arrangement withbore diameterofdb and the stroke lengthDs, suction line (SL) and delivery line (DL) with non-return valves,heat exchanger with very small volume to evaporate the workinguid (HE), working uid pump (Pwf) with a non-return valve tocharge the HE, inlet valve (A) to start the delivery stroke, exhaustvalve (B)to start thesuctionstroke,cooling coil (CC) to condense thesaturated vapour of workinguidwhich is present in the cylinder atthe end of delivery stroke, workinguid reservoir (R).

As shown inFig. 1,initially the cylinder is lled with feed waterwhile the piston sits on the bottom end stop (BES). The HE has avery small volume compared to the piston displacement volume.Initially the HE contains a small amount of saturated vapour ofworking uid at the heat exchanger temperature from the previouscycle.

Just before the delivery stroke starts and while valve A is stillclosed all of the condensed workinguidfrom theprevious strokeispumped into the HE, this process is shown in Fig. 2 from points 4e1.

The mass of compressed liquid working uid that is introduced isequal to total volume displaced during the deliverystrokedivided bythe change in the specic volume of working uid during deliverystroke as is explained with the aid of equations in the next section.

Immediately after the compressed liquid working uid ispumped into the HE, valve A, as shown in Fig. 1,is opened and theworking uid is allowed to expand at constant pressure from point1 to point 3 as shown inFig. 2. Sensible heat Qin_Sand latent heatQin_L are added during the constant pressure expansion process,whilst delivery workWdis extracted as shown inFig. 2. Expansionis complete when the liquid working uid from the HE is fullyevaporated and the piston hits the TES.

Immediately after the piston hits the TES, valve A is closed andthe valve B is opened as shown inFig. 1. At this point a very smallamount of saturated vapour working uid remains in the HE.Opening valve B allows the saturated vapour working uid in thecylinder to enter the cooling coil, cool and condense. The vapourpressure will fall at constant specic volumeduring the initial stageof cooling, until the workinguid pressure is lower than the salinefeed water pressure, at which point the piston will start to movedown with the workinguid at constant pressure. While the pistonmoves down water from the feed water source is pulled into the

cylinder and this process represents the suction stroke. When all ofthe saturated vapour from the cylinder is condensed and the pistonis on the BES, the suction stroke is considered to be completed. Thework done on the workinguid by the water from the ground boreis termed suction work Ws. At the end of the suction stroke thecylinder is lled with water ready for the next delivery stroke. Thenvalve B is closed and immediately the working uid pump is acti-vated to allow a massmwfof compressed liquid working uid to bepumped into the HE for the next delivery stroke. Thereafter theprocess is repeated to achieve continuous operation of the pump. Ina practical application, the opening and closing of the valves wouldbe automatic.

In a Rankine cycle, the working uid is heated at constantpressure to saturated vapourand then this saturated vapour further

expands in an expander (turbine) to generate work output. In theproposed TPP cycle the work is extracted as the working uid isbeing heated/evaporated at constant temperature (2e3). The feed

DL

Water

SL

TES

PBES

s

db

AB

HE CC

OpenClosed

R

Pwf

Delivery stroke

A Working fluid flow control valve

B Working fluid flow control valve

BES Bottom End Stop

TES Top End Stop

P Piston

SL Suction Line

DL Delivery Line

HE Heat Exchanger

CC Condenser / cooling coil

R Reservoir

Pwf Working Fluid Pump

s Stroke length

db Bore diameter

Suction stroke

SLDL

TES

P

BES

Saturated

Vapour of

Working

Fluid

db

AB

HE CC

Closed Open

R

Pwf

s

Fig. 1. Working strokes of the thermal water pump.

A. Date, A. Akbarzadeh / Applied Thermal Engineering 58 (2013) 511e521 513


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water adds work to the working uid during the condensationprocess (3e30e4) as shown inFig. 2.

This type of thermal pump should be designed depending onthe application and available heat source and sink. If the suctionand delivery head is very critical then the selection of the heatsource, heat sink and working uid can be such that it providesenough working pressure. On the other hand if the available heatsource and sink were meant to be used then selection of workinguid is the only option to determine the suction and delivery head.

3. Theoretical analysis

In this section attempts have been made to offer governingequation for the proposed thermal water pump based on the TPPcycle with help of the pump schematic and the Pevand Pehdia-grams shown inFigs. 1and2.

The mass of the workinguid required per cycle depends on thedischarge volume per stroke and the specic volume of the satu-rated vapour of workinguid under the requireddelivery head. Themass of working uid required per cycle can be calculated from thefollowing equation.

mwf DV

y3y2 (1)

Here the discharge volume is proportional to the cylinder borediameterdband the stroke length Ds.

To start the rst cycle it is assumed that the piston is resting onthe BES and the cylinder is lled with water. Valve A and B areclosed and the HE is charged with the working uid. The constantpressure heating process from point 1e2 represents sensibleheating of the working uid without any phase change and thistakes place before the valve A is opened. The amount of sensibleheat added to the working uid from point 1e2 can be calculatedfrom the following equation.

Qin S mwf h2 h1 (2)

For the purpose of calculation the specic enthalpy of the

working

uid at point 1 can be assumed to be equal to the speci

c

enthalpy of the working uid at point 4, as shown by PehdiagraminFig. 2.

Before the valve A is opened the working uid pump is turnedoff. Once the valve A is opened the working uid starts to evaporateat constant temperature, this caused the piston to rise and push thewater out through DL. The amount of latent heat added to theworking uid during the constant temperature expansion process2e3 can be calculated using the following equation.

Qin L mwf h3h2 (3)

The total heat supplied to the thermal water pump during asingle cycle is the sum of the sensible and latent heats.

The delivery head is directly proportional to the saturationpressure of the working uid for the constant temperature pro-cess 2e3.

Hd

Pwf;dPatm

rwg

P2Patm

rwg (4)

Work done in pushing water during the delivery stroke 2e3 canbe calculated from following equation.

Wd DV Pwf;dPatm

DV P2 Patm (5)

To start the suction stroke valve A is closed and valve B isopened. The amount of cooling required for completing the suctionstroke 3e4 can be calculated using the following equation.

Qcc mwf h3h4 (6)

The amount of suction work done can be calculated from thefollowing equation.

Ws DV

Pwf;sPatm

DV P4Patm (7)

The suction head is directly proportional to the saturationpressure of the workinguid at point 4 and can be calculated fromfollowing equation. The value obtained fromthe following equation

is negative as it is less than the local atmospheric pressure.

P

(kPa)

v (m/kg)

1

23

4

Wd

Ws

v3v4

P4

P1,2,3

Qin_S

Win

Constant pressure heat addition to liquid working fluid

Delivery Stroke Constant temperature heat addition

Suction Stroke Condensation

Cold liquid working fluid at initial temperature is

pressurised reversiblyto a high pressure by a pump. In

this process, the volume changes slightly.

1 2

2 3

3 3 4

4 1

P

(kPa)

h (kJ/kg)

1

2 3

4

Wd

Ws

Qin_L

h3h1 h4

Win

P4

P1,2,3Qin_L

Qin_S

Valve A Open

Valve B Closed

P OFF

Valve A Closed

Valve B Closed

P ON

Valve A Closed

Valve B Open

P OFF

33

Fig. 2. Idealised thermodynamic power cycle on a Pevand Peh diagram.



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Although the suction head is shown as positive in graphs in thediscussion section of this paper.

Hs

Pwf;sPatm

rwg

P4Patm

rwg (8)

The total work output of the thermal water pump is the sum ofthe suction work and the delivery work.

Wt WsWd (9)

The work input in pumping the condensed working uid intothe HE can be calculated from following equation.

Win mwf y4 P1P4 (10)

The total heat that is consumed per stroke is the sum of sensibleheat, latent heat.

QS Qin SQin L (11)

The ideal thermodynamic efciency of the high pressure ther-mal water pump can be calculated from the following equation.

ht Wt

QS(12)

The theoretical overall efciency of the thermal water pump canbe calculated from the following equation.

ho Wt Win

QS(13)

The fraction of Carnot factor can be calculated using thefollowing equation.

foC hthCarnot

WtQS

T1T4T1 273

(14)

Number of strokes per m2 of solar pond per day depends on theamount of available heat ux per day and can be calculated fromthe following equation.

NS _QAQS

_QE

QS(15)

Now the volume owrateof water pumped per m2 of solar pondper day is calculated from the following equation.

_V NS DV (16)

In the present study acetone is used as the working uid and the

thermo-physical saturation properties of acetone have been takenfrom the appendix of the heat pipes book by Dunn and Reay [17].Fig. 3shows the ideal thermal performance of the proposed ther-mal water pump with acetone as a working uid. The heatexchanger and cooling coil are assumed to have heat transfereffectiveness equal to 1, i.e. the workinguid is assumed to be heatto the temperature of heat source and cooled to the temperature ofheat sink. In this case the heat sink temperature is assumed to the20 C and the heat source temperature is varied. So a suction headof about 7.7 m of water (gauge) could be achieved, when the localatmospheric pressure is assumed to be 100 kPa.

It can be seen from Fig. 3 that for an ideal case with well-insulated frictionless pistonecylinder device the theoretical over-all efciency of the proposed pump ranges from 8% to 17% for a heat

source temperature range of 65

Ce

100

C and heat sink

temperature maintained constant at 20 C. Further it can be seenthat the ideal overall efciency of the thermal water pump is about60% of the ideal Carnotcycleefciency for the working temperaturerange under consideration. An ideal case of the proposed thermalwater pump is several times more efcient than the thermal waterpumps investigated by other researchers in the past [2,3,9,13,14,18].

Ideal efciency of trilateral cycle can be calculated usingfollowing correlation as discussed by Fischer and Johann[19],

hTLC 1 T4 ln

T3T4

T3T4

(17)

Fig. 4shows the comparison of fraction of Carnot factor for thethermal water pump cycle and ideal trilateral cycle. It can be seenthat for a driving temperature difference of 60 C the foC factor forideal trilateral cycle is about 0.53 while that for the thermal water

pump cycle is about 0.40. The foC factor for thermal water pumpcycle is improved by reducing the driving temperature. While thefoC factor of an ideal trilateral cycle decreases when the drivingtemperature difference is reduced. This characteristic is unique astraditionally very low driving temperature difference (DT< 40 C)have always been considered non-practical for work generation[20e22].

In reality the proposed thermal water pump would have moreinefciency due to: heat loss during the delivery stroke from thesaturated vapour of the workinguid to the surroundings, pressureleakage from the piston, energy loss due to friction between piston

0%

3%

6%

9%

12%

15%

18%

21%

24%

0

5

10

15

20

25

30

35

40

60 65 70 75 80 85 90 95 100

Efficiency(%)

DeliveryHead

(mofwater)

Temperature of heat source ( C)

Delivery Head

Overall Efficiency

Carnot Cycle Efficiency

Ideal performance of a thermal water pump with Acetone as working fluid.

Heat sink is maintained at constant at 20 C which corresponds to a suction head of 7.7m of water

Fig. 3. Ideal thermal performance of the thermal water pump with acetone as working

uid.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

20 30 40 50 60 70

FractionofCarnot(foC)

Driving temperature difference ( C) - (Th - Tc)

New thermal cycle

Trilateral Cycle

Fraction of Carnot fractor for thermal water pump cycle and ideal trilateral cycle.

Acetone as working fluid and heat source is maintained at constant at 80 C

Fig. 4. Comparison of new thermal water pump cycle with ideal trilateral cycle.



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and cylinder. The effect of some of these causes of inefciency canbe reduced if not eliminated with smarter design of the pump. Athermal water pump with exible bellows or diaphragm thatreplace the piston would reduce frictional and leakage losses. Anoptimised design of HE could reduce the time for the deliverystroke and hence help reduce the heat losses during this stroke.

3.1. Pressure boosting

When the available heat source temperature is too low and theavailable heat sink temperature is too high pressure boosting tomeet the requirement of suction and delivery head can achievedwith modied expander design as shown in Fig. 5. The pressureratio to estimate the relation between the change in volume ofworking uid and the water during the suction and delivery strokecan be calculated using the following equation. Here the strokelength Dsis assumed to be equal on both working uid and watersides.

PR Pd Patm

Pwf;dPatm

PsPatm

Pwf;s Patm

DVp1DVp2

Ds

dp12

Ds dp22

dp12

dp22

(18)

With this modication the total volume of water that is pumpedper stroke is reduced to compensate for the increase in the suctionand delivery pressure.

3.2. Heat transfer analysis

Following the basic thermodynamic analysis as discussed aboveit is very important to analyse the heat transfer between theworking uid and heat source and sink. To analyse the rate of heat

transfer in the heat exchanger it is very critical to know the heattransfer limits along the heat source, heat exchanger wall andworking uid.

The amount of working uid required per cycle is calculatedusing Equation(1)and the total amount of heat that is required toevaporate this amount of working uid is calculated using Equa-tions (2) and (3) representing sensible portion and latent portion ofthe total heat respectively. It should be noted that the amount ofworking uid required per cycle is very small due to large volu-metric expansion during phase change.

When designing any device that utilises low temperature heatsource it is very important to have a minimum temperaturegradient between heat source/sink and bulk working uid at theevaporator/condenser respectively. Further in the present studyacetone is used as the working uid and according to Rao andBalakrishnan[23] acetone needs minimum 9 C of superheat tostart nucleate boiling. This means the temperature of the heatexchanger (evaporator) inner wall should be 9 C higher than thebulk working uid and the heat source would have to be couple ofdegrees higher than the heat exchanger inner wall, i.e. a minimumDTof 11 Ce12 C between heat source and working uid. For lowtemperature utilisation this might not be practical and hence hereit is assumed that the mode of heat transfer between heatexchanger inner wall and the working uid will be limited to nat-ural convection boiling and would never reach nucleate boiling.

Here the heat transfer limit due to natural convection boiling iscalculated using the Nusselt number correlation provided byChurchill and Chu for vertical plate[24], it is assumed that the heatexchanger is a vertical copper tube with large diameter (D) andshort length (L) that satises D=L 35=Gr1=4L [25]. Further it isassumed that the heat exchanger is immersed in the large pool ofhot water (i.e. LCZ) and the walls of the heat exchanger areisothermal.

_QHE k2LHE

0BBB@

0:68

0:67

gb2

T3 THE;i

L3HE

a2n2

!1=4

1 0:492 a2=n2

9=16

4=9

1CCCA

AHE

T3 THE;i

(19)

pd

pd

Pwf

pd

pd

p2

Saline

ground

water /

sea water

Connecting rod

Open to atmosphere

Working fluid

Fig. 5. Schematic of pressure boosted thermal water pump.



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The time required for a single delivery stroke to complete can becalculated using the following equation.

td QS_QHE

(20)

To analyse the rate of heat transfer in the cooling coil(condenser) it is very important to know the conguration of the

condenser. For the present thermal water pump the cooling coil isassumed to be immersed in a large pool of cold water or similarheat sink. So it is reasonable to assume that the cooling coil surfaceis isothermal. Further it is assumed that the working uid vapourenters the cooling coil at very low velocity i.e. Reynolds numberlessthan or equal to 35,000. The correlation for condensation of organicuids at low velocities inside horizontal tubes is used to calculatethe condensation heat transfer limit[25].

_Qcc k4Acc

T4Tcc;i

0:555

r4 r4 r3 gk

34h

0fg;3

m4Dcc

T4 Tcc;i

!1=4(21)

Here the modied enthalpy of vaporisation is given by

h0fg;3 hfg;3 0:37 cp;4 T4Tcc;i[25].The time required for a single suction stroke to complete can be

calculated using the following equation.

td QS_Qcc

(22)

4. Solar pond coupled thermal water pump

Noone hasexplored theidea of couplinga solarpondto a thermalwater pump. In past solar ponds have been used to supply heat forseveral industrial application and one of the recent application ofsolar pond in Australia was at Pyramid Hill in State of Victoria[26].Also researchers around the world have used solar ponds to produce

power using organic Rankine cycle heat engines[27,28].Large areasof northernVictoriain Australiahave beensalt affectedland withthesalinity of the water in the aquifer of the affected region ranges fromseveral hundred to several thousands of ppm (25,000e30,000 ppmin the area of this study) and the water table is only a few metersbelow the ground surface as stated in the report on the trends of theground water in Mallee region (north Victoria) [29]. This offers analmost innite source of low saline water for construction andmaintenance of salinity gradient solar ponds. Also, landin thisregionis relativelyat and receives sunshine at a yearly global average rateof approximately 19 MJ/m2/day on horizontal surfaces. These char-acteristics have been identied as providing favourable conditionsfor construction and operation of solar ponds as sources of industrialprocess heat for the salt industry which operates in northern Vic-

toria. Onthis basis a 3000 m2

solar pond was constructed in PyramidHill as part of the facilities of the Pyramid Salt Company in northernVictoria. The 3000 m2 solar pond at Pyramid Hill was used to supplyindustrialprocess heat forsalt dryingprocess [26]. At present electricwater pumps are used to pump saline ground water to the evapo-ration ponds at Pyramid Salt Company. Using a thermal water pumpcoupled with a solar pond to pump the saline ground water wouldhave lots of advantages. In this section simple thermal performanceanalysis of a thermal water pump coupled with a solar pond locatedat Pyramid Hill in Victoria has been carried out.

4.1. Solar pond

A solar pond is a large body of saline water whose salinity in-

creases with depth. These ponds are used as solar thermal energy

collectors that can simultaneously store heat for long period, sothey are suitable for sessional solar thermal energy storage. In caseof fresh water ponds all the solar radiation that fall on the surface isabsorbed by top 3 m of fresh water and this thermal energy israpidly lost to the atmosphere through natural convection heattransfer. So the temperature of a fresh water pond never rises and isalmost constant throughout the fresh water pond depth.

A solar pond has three layers namely upper convective zone(UCZ), non-convective zone (NCZ) and lower convective zone (LCZ).The UCZ is made of almost fresh water and is about 0.3 m thick. TheNCZ is made of water with different salinity; at the top of NCZ thesalinity of water is similar to that of UCZ water while at the bottomof NCZ the water has salinity close to saturation, while the entireLCZ is made of water with salinity close to saturation. In case of thesolar pond the natural convection is suppressed by the presence ofthe salinity gradient in the NCZ and hence the solar energy that isabsorbed by the water in the LCZ is trapped and stored.

Practical heat extraction from LCZ for different applications isvery common. In past heat has been extracted from LCZ using twomethods, in the rst method hot saline water is extracted fromthe LCZ and passed through an external heat exchanger as used atKutch in India to supply heat to a dairy[30]and Beith Haarava in

Israel to supply heat for power production [28]. In the secondmethod an in-pond heat exchanger is used for heat extractionfrom the LCZ as used at Pyramid Hill, Victoria to supply heat forsalt drying [26] and Mashhad in Iran [31]. Tabor [32] has dis-cussed both of these methods in his review of solar pond tech-nology, and stressed that both methods have convenient practicalmerit.

Transient thermal performance analysis with a one dimensionalnumerical model as proposed by Wang and Akbarzadeh[33]hasbeen used to predict the temperature development proles of thesolar pond located at Pyramid Hill in Victoria for the present study.For this simulation the UCZ is assumed to be 0.3 m thick and isconsidered to be a single layer for the purpose of the nite differ-ence temperature estimation. The salinity of the water in the UCZ is

assumed to be 2% and the salt is sodium chloride. The temperatureof the UCZ is assumed to the equal to the monthly average localdaily temperature as suggested by Hull and Weinberger [34,35].This assumption has been made to simplify the solar pond analysis.For accurate performance prediction of the solar pond it is impor-tant to consider the energy balance between UCZ and the airinterface as discussed by Bansal and Kaushik [36]. The NCZ isassumed to be 1.2 m thick with salinity at the top interface equal to2% and at the bottom interface equal to 20%. The LCZ is assumed tobe 2.5 m thick with a constant salinity of 20%. So the solar pondunder investigation has a total depth of 4 m. A sinusoidal curve thatts the monthly average values of global solar radiation on hori-zontal surface and ambient temperature for north Victoria are usedin this simulations study.

The ground below the solar pond is assumed to have uniformthermal properties. As explained by previous studies the under-ground conditions have strong inuence on the thermal perfor-mance of the solar pond[33,37]. In this simulation it is assumedthat the solar pond is lined with plastic liner under which there is5 m of natural clay. The thermal properties of the clay underthe pond liner are assumed to be: thermal conductivitykg 1.28 W/m K; density rg 1460 kg/m

3; specic heat capacitycpg 880 J=kg K[38].

Fig. 6 shows the LCZ temperature development for the abovementioned solar pond conguration and UCZ temperatures overone year period. It is assumed that the solar pond operation startsin early spring (i.e. 1st October for southern hemisphere) and theheat extraction starts 60 days later (i.e. on 1st December). The

temperature pro

les used for the present study and as shown in



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Fig. 6are from the 1st October in the second year, this way the heatextraction can be from early spring. In region of interest the annualaverage global solar radiation received by horizontal surface isabout 18.7 MJ/m2/day.Fig. 6 also shows the daily average global

solar radiation received by the horizontal surface that is used fortemperature development simulation of the solar pond.

It can be seen fromFig. 6that the amount of heat extraction hasa large effect on the LCZ temperature. In the present study twoscenarios of heat extraction are examined, Case A: 10% heatextraction and Case B: 15% heat extraction of the annual averageglobal solar radiation received by horizontal surface. For Case A thetemperature development shows the maximum LCZ temperatureof 90 C and minimum temperature of 56 C. Further it can be seenthat with higher heat extraction rate for Case B the maximum andminimum LCZ temperature drops by almost 10 C as compared toCase A.

Further it can be seen fromFig. 6that the temperature of LCZfor Case A on 360th day is about 5 C higher than that on 1st

day. And for Case B the temperature of LCZ on 360th day is about

3 C higher than that on 1st day. The temperature of LCZ tends torise every year and this type of behaviour of the higher heatcapacity due to thicker LCZ as discussed by Wang and Akbarza-deh[33].

4.2. Thermal water pump coupled to solar pond

Fig. 7shows the schematic of the thermal water pump coupledwith a solar pond. The thermal water pump takes the water fromthe ground water bore close to the solar pond. For continuousoperation valve A and valve B are solenoid valves and their oper-ation is controlledby the sensors (proximity or contact) installedonthe BES and TES. The operation of the working uid pump is alsocontrolled by the sensor on the BES. All the auxiliary power for thevalves, sensors and working uid pump is supplied by a batteryconnected solar photovoltaic system which is not shown in theschematic.

The mode of heat transfer between the LCZ and the outer sur-face of HE wall would be natural convection, between the outersurface and the inner surface of HE wall would be conduction andfrom the inner surface of HE wall to the working uid will benatural convective boiling for low temperature difference (5 C). Although for the present study of ideal case it is assumedthat the HE has heat transfer effectiveness equal to 1. Similarly theCC is also assumed to have heat transfer effectiveness equal to 1.This means the working uid is assumed to be heated to LCZtemperature for delivery stroke and cooled to the UCZ temperaturefor suction stroke.

All the thermal performance characteristics of the thermal wa-ter pump coupled to a solar pond are estimated by using the solarpond LCZ and UCZ temperature proles as shown inFig. 6and thegoverning equations discussed in Section3of this paper.

Figs. 8e10show the ideal thermal performance of a thermalwater pump coupled to the solar pond for Case A and B. The suctionhead is more or less constant at about 8 m throughout the year for

both heat extraction scenarios.

0

3

6

9

12

15

18

21

24

27

30

0

10

20

30

40

50

60

70

80

90

100

0 30 60 90 120 150 180 210 240 270 300 330 360 DailyAvg.G

lobalSolarRadiationreceivedbyHorizontal

Surface(M

J/m/day)

Temperature(C)

Days

LCZ Temperature @ Case A - 10% Heat Extraction LCZ Temperature @ Case B - 15% Heat Extraction

UCZ Temperature Daily Avg Global Solar Rad Hori Surface

Fig. 6. Temperature prole of a solar pond for Case A and Case B.

Solar Pond

LCZ

NCZ

UCZ

Sun

Ground

Water

Bore

A

Evaporation

pond

CC

Suction

head

Delivery

head

Saturated

Vapour of

Working

Fluid

B

SL

DL

HE

A Working fluid flow control

valve (Hot Side)

B Working fluid flow control

valve (Cold Side)

BES Bottom End Stop

TES Top End Stop

P Piston

SL Suction Line

DL Delivery Line

HE Heat Exchanger

CC Condenser / Cooling coil

R Reservoir

P Working Fluid Pump

Pwf

BES

TES

Open Closed

R

P

Water

Fig. 7. Thermal water pump coupled to solar pond.



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For Case A the maximum delivery head produced is about 22 mand the useful delivery head is generated after 22nd day from thestart of the spring and this useful delivery head is maintained forrest of the year. This means for Case A the pump would operate for338 day in a year, i.e. the pump cannot be utilised for the wholeyear.

For Case B the maximum delivery head produced is about 9 mand the useful delivery head is generated after 75th day from thestart of the spring and is maintained till 260th day of that year. Thismeans for Case B the pump would operate for 185 day in a year, i.e.the pump can only be utilised for half the year.

Limit on pump utilisation is due to the available heat sourcetemperature and the saturation pressures of the working uid atthese temperatures. The present study uses acetone as the workinguid and this put the lower limit to the temperature of heat sourceto 56 C, as below this temperature saturation pressure dropsbelow local atmospheric pressure and make the delivery strokepressure useless. This shows the importance of appropriate selec-

tion of workinguid to match the available heat source for systemoptimisation.

Fig. 8shows that the maximum theoretical overall efciency ofthe pump for Case A is about 7.8% and the corresponding Carnotcycle efciency is about 19.5%, i.e. the maximum overall efciencyof TPP cycle for Case A is about 40% of the Carnot cycle efciency.The annual average efciency of the thermal water pump for theCase A is about 6.6% and the annual average Carnot cycle efciencyis about 16.9%, i.e. the annual average overall efciency of TPP cycle

for Case A is about 39% of the annual average Carnot cycleefciency.

Fig. 9shows that the maximum theoretical overall efciency ofthe pump for Case B is about 6.7% and the corresponding Carnotcycle efciency is about 16.5%, i.e. the maximum overall efciencyof TPP cycle for Case B is about 40% of the Carnot cycle efciency.The annual average efciency of the thermal water pump for theCase B is about 5.5% and the annual average Carnot cycle efciencyis about 13.4%, i.e. the annual average overall efciency of TPP cyclefor Case B is about 40% of the annual average Carnot cycle efciency.This performance of the thermal water pump based on TPP cycleshows potential to compete with Rankine cycle based thermalwater pumps as proposed by earlier researchers.

For Case A the amount of heat extracted per m2 of solar pond perday is equal to 10% of the annual average global solar radiationreceived by horizontal surface (18.7 MJ/m2/day), i.e. 1.87 MJ/m2/day. For Case B the amount of heat extracted per m2 of solar pondper day is equal to 15% of the annual average global solar radiationreceived by horizontal surface (18.7 MJ/m2/day), i.e. 2.8 MJ/m2/day.Even though the amount of heat extracted per day for the Case B ismore than that for Case A, the LCZ temperature for Case B is lowerthan that for Case A and this prevents optimum utilisation of the

available thermal energy in the pond with acetone driven thermalwater pump.

Fig. 10shows ideal volume of water pumped per unit area ofsolar pond per day (m3/m2/day) for Case A and B. The maximumvolume of water pumped per m2 of solar pond in a single day forCase A and Case B is same and equal to 1.28 m3. The minimumvolume of water pumped per m2 of solar pond in a single day forCase A is about 0.53 m3 and that for Case B is 0.78 m3. The sum ofvolume of water pumped per m2 ofsolarpond per yearfor CaseA isabout 270 m3/m2/year and for Case B it is about 177 m 3/m2/year.

4.3. Australian salt production

As discussed in the Introductionsection every year 11.5 Mt of

salt is produced in Australia from sea and ground water[16]. About400 Mt of saline water with 2.5%e3% salinity would be required toproduce 11.5 Mt of salt. Large amount of energy would be requiredto move such large amount of saline water from sea or aquifer tothe evaporation ponds. For example, if the total pumping head isassumed to be roughly 10 m including theuid frictional head, thenabout 40,000 GJ of mechanical energy would be required to move400 Mt of saline water from source to evaporation ponds.

If it is assumed that the thermal water pumpsoperates at annualaverage efciency of 5%, then the total thermal energy required to

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

22%

24%

0

2

4

6

8

10

12

14

16

18

20

22

24

0 30 60 90 120 150 180 210 240 270 300 330 360

Efficiency(%)

Wate

rHead(m)

Days

D el ive ry He ad Suc tion Head O veral l ef fi ci ency C arno t Cyc le Ef fi ci en cy

Thermal water pump coupled to solar pond with 10% heat extraction of annual average daily global solarradiation received on horizontal surface

Useful delivery headgenerated after 22 day

~19.5%

Maximum efficiency ~7.8%

Fig. 8. Ideal performance of thermal water pump coupled to solar pond for Case A.

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

22%

24%

0

2

4

6

8

10

12

14

16

18

20

22

24

0 30 60 90 120 150 180 210 240 270 300 330 360

Efficiency(%)

WaterHead(m)

Days

Delivery Head Suction Head Overall efficiency Carnot Cycle Efficiency

Thermal water pump coupled to solar pond with 15% heat extraction of annual average daily global solar

radiation received on horizontal surface

Useful delivery headgenerated after 75 day

Useful delivery head

available till 260 day

~16.5%

Maximum efficiency ~ 6.7%

Fig. 9. Ideal performance of thermal water pump coupled to solar pond for Case B.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

0 30 60 90 120 150 180 210 240 270 300 330 360

VolumeofWaterpumped/m/day(m/m/day)

Days

Volume of Water @ Case A Volume of Water @ Case B

Useful water flowavailable after 22 day

for 10% heat extraction

Useful water flow

available after 75 dayfor 15% heat extraction

Useful water flowavailable till 260 day

for 15% heat extraction

0.78m

0.53m

1.28 m

Fig. 10. Volume of water pumped per unit area of solar pond per day (m

3

/m

2

/day).



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produce 40,000 GJ of mechanical pumping energy would be800,000 GJ. On average annually 1 GJ/m2 of thermal energy isavailable from a solar pond with 15% heat extraction rate. Thismeans total 800,000 m2 or 80 Ha of solar pond oor e required tosupply enough thermal energy to pump the 400 Mt of saline waterfrom its source to evaporation.

4.4. Application of the thermal water pump at Pyramid Hill Salt

Companye an example

On average the ground water depth in northern Victoria liesbetween 2 m and 10 m[29],so the proposed thermal water pumpwould be suitable for water pumping in this region. For deeperaquifers modied pressure boosting or submersible thermal waterpump most be designed.

At the Pyramid Hill Salt Company site there are 12 bores thatsupply about 1500 m3/day of saline ground water to the evapora-tion ponds. Further about to west of the evaporation system thereare another 10 bores that supply about 1300 m3/day of additionalsaline water, this information has been supplied on the PyramidHill Salt Company website [39]. So the totalvolume of saline groundwater that is pumped into the evaporation pond system is about

2800 m3/day.As discussed in the previous sub-section a thermal water pump

based on the TPP cycle coupled to a solar pond with congurationof 0.3 m UCZ, 1.2 m NCZ and 2.5 m LCZ and Case A of 10% heatextraction can pump a minimum of 0.53 m3 of water per m2 of solarpond oor per day.So a solar pond withoor area of about 4700 m2

is required to pump the daily volume of water from these 22 bores.Number of small stroke volume capacity thermal water pumpswould be more practical from point of easy of manufacture andreliability of water supply.

Based on rough estimates for small thermal water pump withstroke volume of 20 L, the heat exchanger (copper tube) surfacearea of about 0.01 m2 would be require to achieve desired latentheat transfer. While 10 times larger condenser (copper tube) sur-

face area 0.1 m2 will be required to maintain the desired cold sidetemperature. Further based on these rough estimates the total timerequired to complete a suction and delivery stroke is calculated tobe 20 s. This means when this 20 L thermal water pump operatesfor 24 h it could pump a total volume of 140 m3/day, i.e. 20 of these20 L volume thermal water pumps coupled with 5200 m2 solarpond could pump 2800 m3 of water from the bores to the evapo-ration ponds per day. A thorough design of the heat exchanger andcondenser should be made in future for accurate economic com-parison of the thermal water pump system with and electric waterpump system.

The present solar pond at Pyramid Hill is 3000 m 2 and it is only2 m deep with LCZ thickness of about 0.8 m and this solar pond willnot be able to supply all the heat at required temperature. So either

the present solar pond must be redesigned and modied to theconguration used in the study or a new solar pond could beconstructed to supply the heat requirements of the thermal waterpumps.

5. Conclusion

The Thermal Power Pump cycle (TPP cycle) proposed andexamined in this paper is about 40% as efcient as a Carnot cycle fordriving temperature difference of 60 C with acetone as workinguid. The thermal water pump based on the TTP cycle could besimple to construct and operate as compared to some of the otherdesigns of the thermal water pumps proposed in the past. TTP cyclehas potential for water pumping applications with low temperature

heat sources. For an ideal thermal water pump acetone would be

suitable working uid candidate, it provides can provide sufcientwater suction head of about 7.7 m with the heat sink at 20 C anddelivery head of about 35 m of water with heat source at 100 C.Thermal water pump coupled to solar pond can help the salt pro-duction industry to reduce their electricity consumption. Forconguration of the solar pond used in the present study, the rate ofheat extraction must be limited to a maximum of 10% to providealmost all year operation of the pump. Increase in the heat extrac-tion from 10% to 15% reduces the temperature of LCZ by 10 C thatmakes acetone a less favourable workinguid for optimum energyutilisation. An alternative workinguid shouldbe selected forlowerLCZ temperatures. The proposed thermal pump coupled withsolar pond provides an alternative technology for application in thesalt industry in northern Victoria. Experimental investigation isrequired for validation of the theoretical analysis discussed in thispaper. The thermal water pump application is notlimited to the saltindustry. The proposedTPP cyclewith heat enginethat has pressureboosting feature could be used to pressurize saline feed water to areverse osmosis desalination system. Another application of TPPcycle could be to operate industrial hydraulic press using waste heatfrom industry. TPP cycle based driven heat engine could be used tocompress air or any other uid for specic industrial applications.

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006 - theoretical study of a new thermodynamic power cycle for thermal water pumping application

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