a salt gradient solar pond

7/29/2019 A Salt Gradient Solar Pond

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Commission of the European Communities

e n e r g y

A SALT GRADIENT SOLAR PONDFOR SOLAR HEAT COLLECTIONAND LONG TER M STORAGE

ReportEUR 9838 EN

Blow-up f rom mic ro f iche o r ig ina l


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Commission of the European Communities

e n e r g y

A SALT GRADIENT SOLAR PONDFOR SOLAR HEAT COLLECTIONAND LONG TERM STORAGE

P.J. UNSWORTH, N.AL-SALEH, V. PHILLIPS, B. BUTLINSchool of Engineer ing and Appl ied SciencesUnivers i ty of Sussex, Br ighton, BN1 9QTEast Sussex, U.K.

Contract No. ESA-S-038-UKFINAL REPORT

Solar Energy Appl ied to Dwel l ing - EC Solar Energy R&D Programme

Directorate-General for Sc ience, Research and Development

1985 EUR 9838 EN


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Published by theC OM MISSION OF TH E EU ROPEA N C OM MU N IT IESDirectorate-GeneralInformation Market and Innovation

Btiment Jean MonnetLU XEMB OU R G

LEGAL NOTICENeither the Com miss ion of the European Co mm unit ies nor any person act ing on behal fof the Commiss ion is responsib le for the use which might be made of the fo l lowingin fo rmat ion

ECSCEEGEAEC Brussels - Luxembourg, 1985


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IIISUMMARY

The solar pond project at the University of Sussex aims to studythe design, construction, filling, and operation of salt gradientsolar ponds, and to develop instrumentation for monitoringbehaviour and performance.This paper describes the construction, filling, and operation ofan outdoor pilot solar pond, and a simple means of maintainingsalt density gradient, as well as work on pond transparency.To obtain high overall operating efficiency we have sucessfullyexperimented with extracting heat from both the non-convectinginsulation layer and the convecting storage layer of the pond.This permits interception and extraction of heat flow in the non-convecting layer which would otherwise be lost at the surface. Wehave carried out laboratory and outdoor experiments to testwhether this causes unwanted convective mixing in the non-convective zone, and have measured heat transfer coefficientsachievable in that layer.Both steady-state and finite difference model calculations arepresented to indicate the improvements in operating efficiency andtemperature that are achievable with this method of heatextraction. Good applications and limitations are discussed.Pond salinity density readings have been taken by direct weighing,and by means of a direct reading instrument which we havedeveloped. This measures the Archimedean upthrust on a smalldisc-shaped float by balancing it against a downward magneticforce exerted by an external solenoid on a small permanent magnetattached to the float. The current required to stabilise thevertical position of the float gives a direct measure of theupthrust force and hence of the density. Resolution is to partsin lOV


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SYMBOLS USEDa solar absorption in mixing layeraj solar abso rpti on in mix ing and insu lati on layer sa,b constants in equations describing solar absorption in

waterCp specific heat, J kg~ 1K~ 1dd thickness of insulation layer, mD s thickness of storage layer, mD thickness of insulating material beneath pond, mDg thickness of ground, down to stratum at T a, mE heat extraction factor from insulation layer, fraction

of solar absorption in that layerH solar radiation incident on unit horizontal area, Jm - 2H yearly average of H, 102 Wm - 2h 1 # h 2 inner and outer surface heat transfer coefficients,Wm-^K- 1J t characteristic length in heat exchanger theory, mL total length of heat exchanger tubing, mm mass flow rate, kg s"1n division of insulation into n sub-layersNu Nusselt numberPr Prandlt numberQ heat transfer rate to heat exchanger fluid, WQ heat extraction rate per unit area, Wm - 2Q s heat extraction rate per unit area from storage layer ofpond, Wm~ 2Qig combined heat extraction rate per unit area from

insulation and storage layers, Wm - 2r solar angle of refraction in pond, 39.2 in London at2.00 p.m. on equinox

r,r2 inner and outer radii of heat exchanger tube, mRL heat loss thermal resistance, Km 2/WT temperature, Ct time, sT a ambient temperature, CT a mean annual ambient temperature, CU heat exchanger overall heat transfer coefficient,

Wm- 2K _ 1


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VI fluid velocity, ms " 1 distance below top of insulation layer in steady state

model, m distance below pond surface in finite difference model,

m distance along heat exchanger tubing, m stability parameter thickness of pond mixing layer, m thickness of sub-layer in finite difference model, m solar absorption, Wm - 2 pond operating efficiency Q/ or Q i s / Hn/Tlx defined in equation (12)rimax efficiency intercept in equation (12) flux of solar radiation at depth x, Wm - 2, solar fluxes at bottom of mixing layer, and bottom ofinsulation layer respectively, Witt-2 density, kg m~ 3 - T a, C9(3 temperature rise of storage layer, C surface coefficient of solar transmission (0.85)u viscosity


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VIIC O N T E N T S

Page

SUMMARY IIITABLE OF SYMBOLS USED V

Chapter 1 INTRODUCTION 11.1 The Idea of the Salt Gradient Solar Pond 11.2 Objectives of the Sussex Solar Pond Project 21.3 Phases of the Work 2

Chapter 2 THE SUSSEX PILOT SOLAR POND 42.1 Construction Criteria 42.2 The Sussex Pond 5

Chapter 3 INSTRUMENTATION 83.1 Water Temperature Measurement 83.2 Density Measurement 8

3.2.1 Direct weighing 83.2.2 Buoyancy densitometer 9

3.3 Optical Transmission 11Chapter 4 POND MAINTENANCE 12

4.1 Pond Clarity 124.2 Density Gradient' 134.2.1 Modification of density gradient 14

4.3 Pond Level 144.4 External Insulation 15


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VIIIPage

Chapter 5 HEAT EXTRACTION 165.1 Extraction from the Insulation Layer5.1.1 Laboratory tests

5.1.2 Outdoor tests5.2 Salt Mixing Effects5.3 Heat Transfer Rates

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Chapter 6 CALCULATION OF POND OPERATING EFFICIENCY 216.1 Heat Extraction from the Storage Layer6.2 Heat Extraction from Insulation and

Storage Layers6.3 Discussion

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Chapter 7 FINITE DIFFERENCE THERMAL MODEL 27Chapter 8 CONCLUSIONS 29

REFERENCES 31APPENDIX I Heat Exchanger TheoryAPPENDIX II: Finite Difference Thermal ModelFIGURES

333537


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1CHAPTER 1INTRODUCTION

1.1 The Idea of the Salt Gradient Solar PondA salt gradient solar pond is an open salt pond which combinessolar heat collection with long term storage. Its structureprovides an insulating action which enables water at the bottom ofthe pond to reach temperatures up to 100 degrees centigrade overthe summer whilst the surface temperature is close to ambient andto retain its heat for space heating or other purposes throughoutthe winter.When sunlight falls onto an ordinary pond of clear water, theenergy is absorbed mostly at the bottom where it heats the bottomlayer. This rises by convection to the surface where it releaseeits heat to the air so that little heat is retained.A solar pond, by contrast, contains one to three metres depth ofsalt water whose concentration increases steadily with depth fromfresh water at the surface to strong solution (e.g. 15% of salt)at the bottom. The increase in density of the solution with depthovercomes the buoyancy of the heated water and eliminatesconvection. Since water is also opaque to infra-red the saltgradient pond thus eliminates heat loss by both convection andradiation. Heat loss into the ground is partly recoverable andequivalent to extra storage, or may be minimised by insulation.Salt gradient solar ponds may occur in nature when a lake isformed over a natural salt base (1) . The first artificial solarponds were proposed and built by Tabor in 1959-65 (2) usingunlined ponds. He had large scale electric power production inmind but discontinued work when he found he could not compete withelectricity prices from cheap oil at that time. More recent ideashave simplified heat extraction (3 ), used a distinct pond layerfor heat storage (4) , and simplified maintenance on the saltgradient (5 ). Research into solar ponds is active in USA, Israel,Australia, and the Middle East.


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1.2 Objectives of the Sussex Solar Pond ProjectThe aim of this project was to obtain experience with operatingsolar ponds in the Northern climate of the UK, where the solarpond would have an advantage over other solar heat collectionmethods in being able to trap the diffuse component of solarradiation which is 50% of the total radiation incident in the UK.The project aims were to study the design, construction, filling,operation, and maintenance of salt gradient solar ponds, and todevelop instrumentation for monitoring behaviour and performance.To obtain high overall operating efficiency the project aimed toexperiment with extracting heat from both the non-convectinginsulation layer and the convecting storage layer of the pond.Two thermal models are described which give good agreement withthe observed performance of the pond and are useful as a designaid and to compare efficiency achievable by different methods ofheat extraction.1.3 Phases of the workThe work was carried out in three phases:Phase 1. Laboratory work. Instrumentation was developed fortemperature measurement and recording, and a new type ofdensitometer was developed to measure pond density at any depth.Experiments in small laboratory tanks were also carried out to tryout and verify procedures for pond filling and gradientestablishment. The effect of a heat exchanger placed in the saltgradient layer was investigated at this stage before being testedin the outdoor pilot pond.Phase 2. Outdoor experiments. The pond was constructed andfilled and then observations of temperature profile and densitydistribution were made throughout 1983 and 1984 for comparisonwith theory. Experiments on heat extraction from the insulationlayer and storage layer were conducted, and on their effect onsalt diffusion. Methods of pond maintenance and salt gradientcontrol were tried out.


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Phase 3. Analysis of results and thermal modelling. A finitedifference computer model was developed and compared and found toagree well with the measured performance. An analytic steadystate model was also used to show efficiency improvement by heat


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CHAPTER 2THE SUSSEX PILOT SOLAR POND

2.1 Construction CriteriaThe two principal criteria in the construction of a solar pond arecost, and guaranteed freedom from leakage. Over many years arelated technology has been developed for the construction oftanks, ponds, and lakes for the storage and containment of noxiouschemicals and wastes in the chemical industry. From the manyrecommendations for such storage schemes (ref (6)), the followingguidelines may be deduced. In particular, to ensure freedom fromleakage, some sort of lining to the pond is required subject tothe following constraints:(a) Liner integrity is critical - the pond cannot be emptied for

repairs to leaks due to the cost of salt.(b) Steel corrodes rapidly at high temperature, especially in

contact with soil acids and possibly lime.(c) Concrete is liable to crack on contraction, and expansion

joints often leak.(d) Plastic liners offer the most secure impervious lining

material over twenty years. Hypalon (chlorosulphonatedpolyethelene) and butile rubber are the most suitable atreasonable cost.

(e) The support structure must not crack if splits in the liningmaterial are to be avoided.

The pond walls may be vertical or sloping. Some uncertaintyexists as to whether the heating which occurs when sunlight isabsorbed at a sloping wall, may give rise to convectiveinstability in the salt gradient. However solar ponds withsloping walls have been successfully operated and must remainstrong contenders unless instability effects are too serious.


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The following points apply to sloping walls:(a) They can be self-supporting and support the liner.(b) They are simpler and cheaper to construct than vertical

walls.(c) If the slope is less than 1:3, people falling in can climb

out without help.(d) Less salt is needed than for a cylindrical hole.(e) The pond above the sloping walls acts as insulator for heat

stored in the ground beneath the pond and results in lessoverall heat loss.

(f) A greater area is needed for a given storage volume.2.2 The Sussex PondA diameter of only 4.5 metres was chosen for the pond, in orderthat any disastrous mistake during operation, which might requirethe pond to be refilled, would not be too expensive. As edgeeffects associated with the walls are proportionately larger for asmall pond, vertical walls were chosen to simplify the thermalmodelling of the pond. A commercial tank available for use infish farming was bought for the purpose and the outdoor solar pondwas constructed in September 1982. It was an above groundcylinder 4.5 metres in diameter and 1.2 metres high, formed bybolting together rectangular sheets of galvanised sheet steel.Earth was dug out and replaced by coarse sand to a depth of 0.6metres to give a stable smooth floor of low conductivity. Thermocouples sealed in closed stainless steel tubes were placed in theground at depths of 0, 13, 28, 58 and 81cm beneath the bottom ofthe pond. The tank was then lined with a flexible liner of blackbutile rubber 1 mm thick, sitting directly on the sand.To reduce heat losses from the sides of the pond, we added anouter jacket of vermiculite granules 30 cm thick between the steelwalls of the tank and an outer containing wall of thin hardboard.


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The pond was then filled to give a 0.80 metres non-convectinginsulation layer above a bottom storage layer of depth0.20 metres. The specific gravity in the storage layer was1.85 and the density in the insulation layer varied linearly from1.00 at the surface to 1.08 at the interface with the storagelayer.The method used to create the salt distribution was as follows.The full amount of salt required (1475 kg) was emptied into thebottom of the pond and water was added up to a depth equal to thestorage layer depth (0.20 metres) plus half the insulating layerthickness (0.80/2 metres), using a hosepipe connected to adomestic water supply. With all the salt dissolved and mixeduniformly, the density would then equal the planned value for thestorage layer.The agitation caused by the water entering was in fact inadequateto dissolve much of the salt, which was ICI Granular Salt. Forcedagitation was therefore used, by circulating the salt and watermixture through a 280 watt centrifugal pump with a flow rating of180 /min. This rapidly and easily dissolved and mixed all thesalt. The density and its uniformity were then checked byweighing samples. Some extra salt was found to be necessarybecause the degree of hydration of the salt was greater thanexpected.The linear salt gradient of the insulation layer was then createdby injecting water through a diffuser consisting of two parallelhorizontal semi-circular Perspex plates of radius 15 cm separatedby 3 mm. The injected water leaves the solution below the levelof the diffuser unaffected, but mixes with the solution aboveprogressively diluting it as the diffuser is raised and creates agradient of salt density. Fig. (9) shows a photograph of thisdiffusion process being tried in the laboratory, with water dyedwith potassium permanganate being diffused into salt solution.The diffuser was positioned initially at the desired position for


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the storage layer/insulation layer interface, and fresh water wasinjected whilst the diffuser was brought up to the rising surfacein steps of 5 cm for every 2.5 cm rise in the surface, so that itreached the surface as the pond reached its final level. A flowrate of 24 /min was used, which was the maximum available fromthe supply, and enabled the salt gradient layer to be completedwithin four hours.To prevent algae growth, 0.6 ppm of CuSO^ copper sulphate wasadded during filling, and NaOH was used to give a pH value ofbetween 5 and 6, to keep the CuSO^ in solution.Figs. (1) to (8) show photographs of the pond at various stages ofconstruction and on completion.


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CHAPTER 3INSTRUMENTATION

The three most important measurements required are of saltconcentration, water temperature, and optical transmission of thepond water. They were measured as follows.3.1 Water Temperature MeasurementThe vertical temperature distribution in the pond was measured bymeans of a fixed vertical array of thermocouples at 5 cmintervals. The thermocouples were of copper/constantan sealed inthin-walled stainless steel tubes 3 mm in diameter. Theirelectrical outputs were taken to a 32-way solid-state multiplexertogether with the ground thermocouples. The multiplexer outputwas taken to a thermocouple amplifier, and the temperature datawas recorded by a microprocessor-controlled data handling systemand outputted in digital form on a small tape recorder. Data fromthe tapes could then be read into an Apple II computer in thelaboratory for subsequent analysis and processing.3.2 Density MeasurementThe density changes by approximately 10% over the 1 m thickness ofthe insulation layer, i.e. by 0.1% per cm, so that measurement isrequired to parts in 10*4 . We used two methods of measurement -direct weighing of pond samples, and observation using adensitometer developed in our laboratory which electronicallymeasured the buoyancy upthrust on a small float. We mostly usedthe direct weighing technique because of operational problems withour own densitometer, and to ensure reliability of our data.3.2.1 Direct weighing

A vertical array of small plastic tubes at 5 cm intervals waspermanently installed in the pond (see Fig. (6)) to enable samples


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to be withdrawn from the pond to enable tests to be made on waterfrom any level in the pond. For density measurement, samples wereweighed in a standard specific gravity bottle using a precisionlaboratory balance. Under steady pond conditions, samples takenover a few days showed specific gravity reproduceable to withinthree parts in 101* with careful technique, the samples beingweighed at laboratory temperature.3.2.2 Buoyancy densitometerWe have developed a direct reading densitometer instrument (ref(9)) in which the upward buoyancy force on a small submerged buoyis balanced by the downward magnetic force on a small ferritepermanent magnet attached to the buoy and attracted downwardstowards a magnetic solenoid just below the buoy (see Fig. 15).The vertical position of the buoy is sensed by means of the beamfrom a light emitting diode (LED) which falls on a fixed light-sensitive resistor. If the buoy moves up or down it moves throughthe beam and alters the light falling on the resistor, whoseresistance then changes in response to the movement. This is usedto control electronically the current through the magneticsolenoid, so as to cause a fixed amount of light to fall on theresistor, and so to hold the buoy in equilibrium by servo control.The solenoid current required is a direct measure of the buoyancyforce and hence of the liquid density around the buoy, so thatdirect electronic readout is possible.For accuracy to parts in 1*, the temperature coefficient andageing of the LED/photo resistor combination must be balanced out.This is achieved by combining them with a second LED/resistor pair(with fixed geometry) in a balanced bridge arrangement. Othercomponents are chosen with careful attention to thermalcoefficients.The geometry is designed so that the magnet is seif-centring inthe field of the solenoid for exact reproducability, and iscontrolled at a position where the solenoid axial field gradient


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3 B / 3 Z is at a maximum, i.e. independent of axial position z. Thesolenoid current required for balance and hence the calibration isthen independent of the position where servo balance occurs.As convection instabilities in the insulating layer have beennoted to start in layers approximately 1 cm thick, to observe 1 cmsteps in the gradient, the buoy must sample vertical layers ofless than 1 cm, so that the buoy was chosen to be of a flatconical shape.The instrument was calibrated at 20C against solutions ofaccurately known specific gravity (by sample weighing) over therange 1.000 - 1.115, and gave the following relation betweenspecific gravity and solenoid current I:

SG 2 = 0.9900 + 0.001235 I2(mA)For measurements at temperatures other than 20, a temperaturecorrection is necessary

I 2 0 = i T - 0.219(T - 20 ), (I in mA) .This was due to thermal expansion of the plastic material selectedfor the buoy. Temperature measurement to 1C gives SG accuracy to.00027. This temperature error should be reduceable by almost anorder of magnitude by using a buoy machined from thin-walledstainless steel. The current I exhibited a peak-to-peak noise of0.0012 in SG at around 2 Hz. Integration over one minute reducesthis error to around 1 10_l+.Unfortunately in operation, measurement was often made whilst asignificant wind was blowing around the pond. The densitometerproved to be sensitive to the wind-induced vertical oscillatorymotion in the water of the pond which could easily increase thenoise tenfold. Because of this and the need to make temperaturecorrections to the readings, and because it was of the utmostimportance that complete reliance could be placed on the densityreadings, it was decided to use the direct weighing technique


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rather than rely on the results of a relatively unproven system.We nevertheless feel that the densitometer design can be made intoa convenient and accurate instrument.3.3 Optical TransmissionThe efficiency of the solar pond depends on the proportion of theincident solar radiation which is able to penetrate to the bottomof the pond. This depends on both the natural absorption whichoccurs in water and also on extraneous factors such as wind-blowndirt, algae growth, or even the products of corrosion of metalfixtures in the pond. Practical degrees of clarity achievable areclearly location dependent, so it is of some interest to see howclose the actual transparency of our pond was to the naturaltransparency of fresh water. We therefore measured the fractionof the radiation incident at the surface which reached any givendepth of the pond by using two pyranometers. One measured thesurface radiation, whilst the second recorded the radiation at anygiven depth in the pond. Fig. (14) shows the transmission curvefor the pond under typical operating conditions. Even though wehad not filtered the pond during the 18 months before taking thesereadings, and in spit of an early cloudiness due to corrosion (seeSection 4.1 ), the transmission curve is not significantlydifferent from the results in ref (7 ).


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CHAPTER 4POND MAINTENANCE

4.1 Pond ClarityOver two years of operation we have experienced no problem withalgae growth, except just at the topmost surface layer around theedge of the pond. This is presumably due to fresh rain waterdiluting the surface concentration of copper sulphate presentthroughout the pond to prevent algae growth. Spraying the surfacewith weak copper sulphate solution every six months controlledthis. It is necessary to keep the pH at between 5 and 6 tomaintain copper sulphate in solution. The pH value of samplestaken for density measurement indicated a tendency for the acidityto increase - presumably due to the effects of slightly acid rain.Calculated amounts of sodium hydroxide were therefore added byextracting solution from a particular level through the sampletube, dissolving some sodium hydroxide and then reinjecting thesolution.In the Autumn, large numbers of leaves were blown into the pond soa net was used to intercept the bulk of these. Large numbers ofleaves nevertheless entered the pond during gales at other timesof the year or just before or after the net was placed inposition. They would gradually sink to the bottom of the pondwhere they help to maintain a verv dark colour for good solarabsorption. No attempt was made to remove these leaves at anystage and they did not appear to give any adverse effect on thepond. They could presumably be removed by circulating water fromthe storage layer through a small filtration unit, but this hasnot yet been attempted. Large numbers of animal life such asbeetles, flies, moths and wasps flew into the pond - and manyspent a week or more at intermediate depths before finally sinkingto the bottom. At one stage when the surface was temporarilyseriously covered with blown leaves and airborne seeds, we did trycleaning the surface by using a vacuum cleaner of the wet and dry


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type with the nozzle placed on a floating platform a centimetre orso above the surface. This successfully removed the detritus. Ina large pond surface contamination tends to collect at one side ofthe pond, blown by the wind. A vacuuming or surface filtrationtechnique could clearly be adapted to remove this.In August 1984 we experienced a sudden and severe cloudiness inthe water, which developed rapidly over two weeks so that thewater appeared opaque to the eye beyond 50 cm depth. This provedto be due to copper hydroxide caused by a corrosive reactionbetween the bare copper metal heat exchanger we were using at thetime reacting with other metals present in the pond. Theseincluded the stainless steel thermocouple tubes, and a large lumpof lead which had been used to tension the support wire for thedensitometer when it was lowered into the pond. The heatexchanger and lead were removed and we were fortunately able todissolve the copper hydroxide by adding approximately 100 g of thechemical EDTA (ethylenediaminetetraacetic acid disodium salt).This was distributed throughout the depth of the pond by injectingit using the sample tubes. It dissolved the copper hydroxide byforming a soluble complex with copper ions.4.2 Density GradientOver the two years of pond operation we experienced no problemswith pond instability and so did not attempt to modify the saltgradient, except in the surface mixing layer, until otherexperiments were concluded. At the surface in times of extremeweather or wind or very strong diurnal temperature fluctuations,the thickness of the surface mixing layer tended to grow fromaround 10 to 20 cm and even 25 cm at one stage. Under calmerconditions this layer would then tend to shrink back to around 10cm but since the pond efficiency is reduced by the amount ofabsorption of solar radiation taking place in this layer, it wasclearly important to be able to minimise and control thisthickness if necessary. This we did by injecting fresh water witha diffuser in a manner similar to establishing the original salt


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gradient (see Section 2.2). The diffuser was initially placed5 cm below, the boundary between the insulation and mixing layer,with a good flow rate to encourage mixing, and was then slowlyraised to the surface of the pond, progressively diluting thesolution in the mixing layer to produce a linear gradient reachingunity at the surface.4.2.1 Modification of density gradientAfter completing all our heat transfer experiments, we tested outa technique of modifying the salt gradient at any depth. It wasbased on our experience with the sample tubes of being able towithdraw a sample, dissolve a small amount of chemical andreinject the solution at the same level. To modify the densitygradient of the whole pond we did this using two diffusers, one toextract the solution and the other to reinject the solution at thesame level at the opposite side of the pond after dissolving extrasalt. Water extracted from a given level in the insulation layerand then reinjected at the same level tends to slide in withoutmixing with the adjacent layers of solution. Dissolving sodiumchloride slowly in the process enabled us to increase the densityat any level in a controlled fashion starting from the bottom ofthe pond.4.3 Pond LevelTo prevent pond overflow onto the granular insulation around thepond during heavy rain, we used a simple static system toautomatically siphon water off if it rose above a pre-determinedlevel. This eliminated the need for overflow pipes and seals topenetrate the tank and the lining material below the surface. Attimes of regular and heavy rainfall the effect is to give analmost steady washing of the surface to maintain a surface densityequal to 1.00 and restrict the thickness of the surface mixinglayer to 10 cm.


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4.4 External InsulationWe encountered a serious problem with the external insulationcladding around the pond. This was formed from vermiculite(micafil) granules (see Section 2.2). Owing to leakage in theplastic sheeting over the top of the granules, rain was able toget in and resulted in the granules becoming soaked with moisture,We found that there was no way that we could dry the granulesout, even in the laboratory, without going to unrealistic lengths.The effect was to increase the thermal conductivity of theinsulation from 0.07 Wm - 1K - 1 to between 0.3 to 0.5 Wm _ 1K ~ l. Itwas clear that we should have chosen an insulator with closedcellular structure incapable of becoming saturated with moisture.


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CHAPTER 5HEAT EXTRACTION

5.1 Extraction from the Insulation LayerConventionally, heat from salt gradient solar ponds has beenextracted from the storage layer (lower convecting zone), which isthe hottest part of the pond (ref (3)). If less than maximumtemperature is required greater thermodynamic efficiency can beachieved by extracting heat from a suitable portion of the coolerinsulation layer (non-convecting zone), since a temperaturegradient exists across this layer. The heating of the insulationlayer occurs by direct absorption of solar insulation passingthrough the layer, and from the heat (loss) flow from the storageto the insulation layer. By extracting heat from the insulationlayer, this heat flow may be intercepted and utilised.Two potential problems arise in doing this:(a) Since the saline gradient inhibits free vertical convection,

the surface heat transfer coefficient between heat exchangerand the non-convection layer may be too small.

(b) Too large a temperature difference between the heat exchangerand the pond may induce unwanted convective mixing, andresult in increased upward diffusion of salt.

5.1.1 Laboratory testsA laboratory experiment was set up to investigate these points,using a 37 cm deep pond with a maximum specific gravity at thebottom of 1.16. A heat exchanger (Fig. (10)) made from 2.6 m of8 mm diameter glass tube was formed into a helix of 8 turns,0.23 m high by 0.07 m diameter. Cold water was fed in at the top,and the heated water removed at the bottom. The tank was heatedby an overhead 1 kW tungsten halogen lamp.


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17The effect on convection was observed by injecting fluorescene dyeclose to the heat exchanger coils. During heat extraction twoeffects were noticed:(a) Convective motion of the dye was essentially horizontal and

laminar in the non-convective layer (see Figs. (10) and(12)), but was turbulent with vertical motion (as would beexpected) in the upper mixing layer and bottom convectivelayer if these overlapped the heat exchanger. Heatextraction rates used were ~ 100 w/m of heat exchanger tube.

(b) There was evidence that the density gradient in the non-convective layer tended to break up in a step-wise fashion.The steps were observed as horizontal bands of depth ~ 1 cm,visible when looking horizontally through the glass ends ofthe tank due to the associated variation in refractive indexof the solution. They were self healing over an hour or twoafter heat extraction was stopped.

Subsequently, we found that water convective motion was made evenmore visible by dropping into the water a pinch of powderedanhydrous cupric sulphate. This caused a vertical white ribbon inthe solution which altered its shape with any convection (see Fig.(12)). Twelve hours later it had fallen to the bottom of thetank.Concerning the two potential problems (a) and (b) above, wemeasured a satisfactory external heat transfer coefficient of ~300 W m - 2k - 1 between the heat exchanger tubing and the non-convecting layer of the pond, and no measureable effect on densitydistribution after 24 hours of operation. We concludedtentatively that using heat exchanger tubes of diameter less thanthe ~ 1 cm thickness of the convection cells perhaps did not causesignificant mixing, and proceeded to outdoor testinq.5.1.2 Outdoor testsWe built a heat exchanger from 14.6 m of 8 mm diameter Cu andplaced it in the insulation layer as indicated in Fig. 8. Twosets of experiments were carried out.


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Heat extraction Cold water was fed in at the top and warm watercollected from the bottom outlet. The pond temperatures T p i andTpo at the same heights as the inlet and outlet were measured atthe beginning of the extraction period. (The pond temperatureclose to the heat exchanger changed during the extraction periodbut was very little affected a few metres away. Hence the initialtemperature, before circulating fluid through the heat exchanger,was used to specify the overall pond temperature, which variedessentially linearly with depth.) The flow rate was measureddirectly, and heat transfer coefficients determined from thisdata, according to the heat exchanger theory in Appendix I.Heat injection To give a greater control range in measurement ofheat transfer rates, closed circuit circulation was employed withelectrical heating of the water up to 3 kW before it entered theheat exchanger at T 0 (i.e. flow reversed to transfer its heat tothe pond.) The effect of fluid/pond temperature differences of upto 40C on pond mixing could then be observed.Mixing effects The effect on the density gradient was observed byplacing in the pond 6 mm diameter polythene tubes with inlets in avertical line at 5 cm intervals. The pond solution could then beextracted and its density determined with a specific gravitybottle and precision balance. Care had to be taken to allow thesamples all to reach the same steady temperature to avoid weighingerrors.Measurements were also taken using a heat exchanger with tubes of2.5 cm diameter.5.2 Salt Mixing EffectsThe degree of salt mixing in the insulation layer caused byoperating a heat exchanger within that layer was measured in aseries of experiments over a period of 78 days. This was done byregularly measuring the salt density profile of the pond asaccurately as possible and comparing the rate of change of this


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profile during periods when the heat exchanger was in operationwith the rate of change when the heat exchanger was not beingoperated. The factor could then be calculated by which saltdiffusion was increased to a heat exchanger traced in theinsulation layer. Fig. (17) shows the changes in salt profilewith depth which accompanied periods of operation of the heatexchanger and periods of inactivity. The changes in densityindicate an increase in the upper levels of the pond at theexpense of a decrease in the lower regions, corresponding to ageneral upward diffusion of salt. The effect of the heatexchanger in the insulation layer is seen to cause anapproximately sixfold increase in the rate of upward diffusion.This increase was measured with very high heat transfer rates ofaround 2 kW (5.5 kW per m 2 of heat exchanger surface), so thatlower transfer rates with heat exchangers of greater area shouldgive lower diffusion rates. Acceptability of the method willdepend on the cost effectiveness of the increase in operatingefficiency that may be possible set against the increase in saltconsumption by the pond.5.3 Heat Transfer RatesThe theory of the heat exchanger is given in Appendix I. It isassumed that the pond water gives rise to a linear gradient in thetemperature of the pond fluid over the length of the heatexchanger tubing. Values are not available in the literature forthe external surface heat transfer coefficient between the tubingof the heat exchanger and the pond liquid, which is a non-convecting fluid due to the effect of the salt gradient.Laboratory tests however indicate essentially free horizontalconvection within the pond layers which is able to draw heat fromregions of the pond remote from the heat exchanger. Figs. (10)and (12) show a photograph of laminar convection around a heatexchanger operated in a laboratory tank with a salt gradient.


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Performance of the heat exchanger was therefore measured in orderto obtain a value for this external heat transfer coefficient. Todo this, thermocouples were mounted at the inlet and the outlet ofthe heat exchanger. Before water was circulated through theexchanger, the thermocouples were used to measure the pondtemperature at the level of the inlet and of the outlet.Subsequently, during the transfer process, they recorded thewater inlet and outlet temperatures. These four temperatures,together with the water flow rate, are sufficient to enable theexternal heat transfer coefficient to be determined. A value of300 W m - 2 K - 1 was obtained and found to apply over a good range ofheat transfer rates.


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21

CHAPTER 6CALCULATION OF POND OPERATING EFFICIENCY

The mathematical modelling of solar ponds is complicated by thevery many parameters and factors influencing performance. Theseinclude:(a) The thicknesses of the mixing, insulation, and storage zones(b) ground conditions - soil type, depth of water table, and

whether insulation covering is added(c) the pond size and shape - small ponds need a 2-dimensionalheat flow model in the ground(d) the solar input and latitude of the site(e) degree of water transparency achievable(f) heating load profile(g) the long time constant of the transient response (- months

for the pond, ~ years for the ground).Wang and Akbarzadeh's steady state model (8 ) gives good insightinto parametric dependence and achievable efficiency. In thefollowing treatment, their model is adapted to show theimprovement by extracting heat from the insulation layer.6.1 Heat Extraction from the Storage LayerAssuming an infinite pond, permitting a one-dimensional treatment,and using their notation, the equation for steady state heat flowin the non-convecting insulation layer of the pond is

* (_ k dTj d m ( 1 )dx w dx dxwhere is the solar flux reaching depth x:_ y = b In , .? ]( + e)/cosr

(2)

is the mean annual solar insulation at ground level. is thesurface transmissivity, taken to be 0.85 to allow for Fresnel


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reflection and the effect of waves. is measured downwards fromthe top of the insulation layer. The temperature of the surfacemixing layer is taken to be equal to the mean ambient temperature,

(3).e. = T - T = = O a t x = 0Insul ating mater ial of thickness D may be placed between thestorage layer and the ground, and it is assumed that at a grounddepth Dg the temperature is steady and equal to the surface meanambient temperature, e.g. due to the presence of ground water.Thi s leads to a bou nda ry condi tion at = d in which the radiationflux entering and absorbed in the storage layer equals the sum ofthe heat out flo ws into the ground and into the insulation layer,tog eth er wit h the hea t Q being extrac ted from the storage layer:

= D. D_ i + _ 3k. k_ * gd_kw

+ * tir)w '-dx-' + Q (4)x=d

The hea t flow equat ion (1) may be integrated twice using (2) toelimi nate , and using boundary conditions ( 3 ), (4) to determinecons tant s of integra tion. The result may be written in the formQ =H" Tb +

-rb Jin (y cos r)(d + ) + D. D_i + _ak. kL I g

d_kw(5)H

which has the form of the Hottel-Whillier-Bliss linear plot forflat pl ate coll ecto rs of the operat ing efficiency of Q/ again stthe tem per atu re dif fer enc e 8


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equations (1) - (5). The modified solar absorption in theinsulation layer is then,x=d' = - d ' ('x=0 - *'d> * (* * *d> - ( - *d } (6)absorption extractionThe last two terms may be interpreted as the actual solarabsorption, together with an energy loss due to extracting afraction E of the absorbed energy directly via a heat exchangerplaced in the insulation layer. E is therefore an extractioncoefficient.Similarly, in the storage layer, the net solar absorption isreplaced by' d(l - E) - # d (7)d 'dx~ *" 'd ~'d

absorption extractioncorresponding to the actual solar absorption ^ less extractedenergy ^. Together with the variable extraction term Q in (5 ),the next extraction rate from the storage layer is

Qg = Q + The total extraction rate from both layers isQ I s ( -


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24This equation has the form

1 9d = (1 - E) ri + En - - . =^ (12)0 1 R L Hintercept n m a x slopewhere = xb + 3 n ,,

d (y cosr)oL(d + ) +

and is the intercept value when E = 0, i.e. with conventionalextraction from the storage layer only. 1 = tag =xbn [(y0 cosr)/] and is the intercept value when E = 1,i.e. when extraction from the insulation layer equals theradiation absorption in that layer.Equation (12) shows that the intercept increases linearly with E(in general > 0) . RL in the slope term is the thermalresistance for heat losses through the ground and through theinsulation layer of the pond, and is independent of E.The improvement effected by insulation layer extraction is shownin Table 1, and Fig. (16). Unless otherwise stated, data for thepond is: d = 2.5 m, = 0.2 m, D = 5 m, D = 0, ky, = 0.565W m _ 1 K - i , kg = 1.00 W m - 1 K - i , r = 39.2 (2.00 p.m. at equinox at 52latitude), k = 0.035 W m - 1K - i , = 0.85, b = 0.08, y0 = 90 m.Figure (16) shows plots of operating efficiency against storagelayer temperature for conventional extraction from the storagelayer only (lines 1 and 2 ) , and with extraction from both storageand insulation layers (lines 3 and 4 ) , which assume the extractionfactor E = 1. For other values of E, performance lines areparallel, but with a different efficiency intercept n m a x (fromTable 1 or equations (11) and (12)). Table 1 shows how theefficiency intercept and performance line slope vary with pondparameters according to equation (11). Figure 16 shows thatefficiency is more than doubled by the improved extractiontechnique when 63/H = 5.The heat extracted from the insulation layer expressed as afraction F of the total heat extraction is given by

(. - ,) (a. - a.)F = il = J _ (13)Ql s w h e r e aj = b n [ y 0 c o s r / ( + d ) ] .


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25TABLE 1 - Efficiencies 0 and , and slopes 1/RL for

different pond depths for use with equation (12)

(m)d (m) 0.22.5 0.42.5 0.62.5 0.21.5 0.41.5 0.61.5^o"i

0.2750.398

0.2630.351

0.2530.323

0.3010.398

0.2850.351

0.2720.323

I/RL(MJ/(dayc m 2))0.0368 0.0368 0.0368

(vfith no ground ir0.0498

sulation0.0498

Di =0.04980)

1 / R L(MJ/(dayOC m 2))0.0305(with

0.0305 0.030510 cm ground ins

0.0435ulation:

0.0435Di = 0

0.0435. 1 m)

6.3 DiscussionHeat extraction from both insulation and storage layers is seen togreatly increase operating efficiency. Since the whole of thepond volume is effectively used for heat storage and extraction,it is therefore possible to increase the thickness of theinsulation layer at the expense of the storage layer, since thisleads to greater operating efficiency. Storage layer volume hasthe effect of increasing the storage capacity and time constant ofthe pond. The optimum will depend on the variation in operatingtemperature that can be tolerated.If the heat exchanger inlet and output levels can be adjusted (bymoving the heat exchanger or by using a number of inlet or outputpoints selectable by valves) the pond may be matched to seasonalvariations in the requirements on fluid inlet and output temperatures . This method of heat extraction is particularly suited toapplications where the return flow temperature from the externalheating load is near ambient temperature, in order to be able toutilise the low temperature heat near the top of the insulationlayer. Such applications would include air heating systems,greenhouses, crop drying, swimming pool heating, and water preheating.


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27

CHAPTER 7FINITE DIFFERENCE THERMAL MODEL

A simple computer program has also been developed to model pondbehaviour under realistic (i.e. non-steady state) conditions, andgives good agreement with pond data measured over two years ofoperation. The program allows heat to be extracted from a storagelayer and/or from the insulation layer by modelling the behaviourof a heat exchanger placed in the pond, using the experimentallydetermined value for the surface heat transfer coefficient betweenthe pond and the heat exchanger. The program is written in BASICand is applicable to a wide variety of circumstances andapplications.For input data it uses daily or weekly mean values of ambienttemperature and radiation incident on a horizontal surface, andcalculates absorption at different depths in the pond afterallowing for latitude, and reflection and refraction at thesurface. Finite difference methods are used to calculate heatflow within the pond together with equations to allow for heatextraction from the storage layer (via external or internal heatexchangers) or from the insulation layer (via an internal heatexchanger). Bottom losses are calculated simply in terms of theheat conductivity of the ground and the depth above a stratumconsidered to be at mean ambient temperature. No attempt is madeto calculate ground storage effects. Side wall losses areconsidered to arise from the temperature excess of the pond wallsat each level above daily ambient mean. Pond surface temperatureis taken as equal to daily mean air temperature in the UK,although a more elaborate treatment may be used for countrieswhere evaporative losses are much greater. The thicknesses of thesurface mixing, insulation, and storage layers are inputparameters. Calculated and experimental data for a Sussex pond


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(4.5 m in diameter 1.05 m deep) is shown in Fig. (19) for theyear 1983 . Appendix II shows the finite difference equations usedin modelling the pond.Figure 18 shows efficiency plots for a solar pond in steady stateconditions with a heat exchanger extracting heat from the storagelayer only (curve a ) , from both the storage and insulation layers(curve b) and from the insulation layer only (curve c ) . Liquidflow rate through the heat exchanger is used in the modelling tocontrol the amount of heat being extracted in each case. The ponddata used is as follows: = 0.2, d = 1.5m. The lowerconvecting layer thickness affects storage time constant, but notsteady state performance. Di = 0.1 m, ki = 0.035 Wm~ 1k~ 1, Dg = 5m, kg = 1.0 W m - lk _ 1, kw 0.565 W m _ 1k - 1 , = 0.85, a = 0.36,b = 0.08, r = 39.2.For heat extraction from the insulation layer, the level of theheat exchanger inlet should ideally be at a height in the pondwhere the pond temperature equals the inlet temperature (seeSection 6.3).For the curves presented, the inlet temperature was taken to be atambient temperature, and the heat exchanger to span the wholedepth of the insulation layer. It is seen that extraction fromthe insulation layer alone gives the greatest improvement inefficiency. At the higher operating temperatures / " = 0.3, or0.4, the efficiency is improved by 70% and 88% respectively.Somewhat reduced improvement is obtained with higher inlettemperatures. However, a number of applications do involve inputtemperatures not much above ambient, e.g. crop drying, swimmingpool heating, greenhouse heating, in which case the efficiencyimprovements are considerable.


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29

CHAPTER 8CONCLUSIONS

A small 4.5 m diameter salt gradient solar pond has beenconstructed and operated successfully over two years withoutsuffering from gradient instability or algae growth problems.Experiments on heat extraction have shown that it is possible toplace a heat exchanger in either the insulation layer or thestorage layer of the pond without apparently causing instability.We have measured the surface heat transfer coefficient betweenheat exchanger tubing and the non-vertically convecting fluid ofthe insulation layer - a quantity basic to the design of asuitable heat exchanger. Modelling shows that significantimprovement in pond operating efficiency may be achieved by heatextraction from the insulation layer of the pond as opposed to themore normal storage layer extraction. The reason is that heatflowing through the insulation layer which would be lost at thesurface is intercepted by the heat exchanger.A dynamic (i.e. non-steady state) computer model of the pond hasbeen developed using finite difference techniques. This will givedetailed day-to-day predictions on pond performance using weatherdata as input and heat extraction from either the insulationand/or the storage layers of the pond. A steady state analyticalmodel is also presented which gives good insight into the effectsof varying pond design parameters on overall efficiency. Themodels indicated it to be worthwhile to consider using insulatingmaterial under the pond, both from the point of view of removinguncertainty due to limited data on soil conductivity and as ameans of improving overall efficiency.The importance of selecting materials for pond fixtures to avoidcorrosion was made apparent when the whole pond turned cloudy overa period of two weeks, due to an electrochemical reaction betweenthe copper of a heat exchanger in the pond and a lump of lead


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accidentally present in the pond. The strong horizontalconvective motion at all levels of the pond transported theproducts of corrosion throughout the pond and destroyed itsclarity. The copper hydroxide corrosion product was fortunatelytreatable chemically and enabled us to avoid having to refill thepond.A densitometer giving a direct electronic readout has also beendeveloped. It is based on measuring the downward magnetic forcenecessary to balance the upward Archimedean upthrust on a smallbuoy. Density values were linear to a few parts in IO1* in termsof the current readout and showed the basic principle to be good.However, thermal expansion of the plastic material selected forthe buoy led to a need to apply temperature corrections. Thisplus suscepibility to wave motion beneath the surface of the podunless wind conditions were light led us to make our densitymeasurements by direct weighing.The whole project has been encouraging in being able to build andoperate a pond under realistic conditions without serious problemsand to be able to produce a computer model giving good agreementwith observed performance. Though high storage temperatures werenot reached, due to edge losses in a small diameter pond, thepromising overall operating efficiencies and relativelyinexpensive cost of these ponds indicate that a full-scale pondshould be constructed in a suitable northern climate location.


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REFERENCES1. A.V. Kalecinsky, Ann.Physik IV, _ , 408, 19022. H. Tabor, Solar Ponds, Solar Energy T_, 189, 19633. F. Zangrando and H.C. Bryant, Heat Extraction from a Salt

Gradient Solar Pond, Int.Conf. on Alternative Energy Sources,Miami Beach, 2935, Dec 1977

4. A. Rabl and C.E. Nielson, Solar Ponds for Space Heating,Solar Energy 17, 1, 1975

5. C.E. Nielson, A flow system for maintenance of saltconcentration gradient in solar ponds, Solar Energy 19_, 763,1977

6. W.B. Kays, Construction of Linings for Reservoirs, Tanks andPollution Control Facilities, Wiley, 1977

7 H.C. Bryant and I. Colbeck, A solar pond for London?, SolarEnergy 19_, 321, 1977

8. Y.F. Wang and A. Akbarzadeh, A parametric study on solarponds, Solar Energy 30, 555, 1983

9. P.J. Unsworth, N. Al-Saleh, V. Phillips, Proc.Ec.Contractors, Solar Energy Applications to Dwellings, , 155,1982; A2_, 354, 1983; A4, 409, 1984

10. P.J. Unsworth and N. Al-Saleh, Salt gradient pond for solarheat collection and long term storage, First EC Conference orSolar Heating, 871, 1984 (Amsterdam), pubi. Reidel.

11. P.J. Unsworth, N. Al-Saleh and V. Phillips, Improving solarpond efficiency by heat extraction from the non-convectingzone, UK-ISES Conf. on Long Term Energy Storage in SolarSystems (C35), 44, 198412. F.J. Bayley, J.M. Owen and A.B. Turner, Heat Transfer, pubi.Nelson, London, 1972

13. G.D. Smith, Numerical Soluton of Partial DifferentialEquations: Finite Difference Methods, pubi. Oxford, 1978


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APPENDIX IHEAT EXCHANGER THEORY

The transfer rate from the pond into the heat exchanger fluid is0 = "V** - Tfi) (A1)

where T f 0, Tf are the fluid outlet and inlet temperatures, m theflow rate, c p the specific heat. Over a length dz of tubing, thetransfer rate isdQ = (Tp - Tf) U. 2nr 2dz (A2)where Tp, Tf are the pond and fluid temperatures, r 2 the heatexchanger tube outer radius, and U the overall heat transfer

coefficient per unit area for the heat exchanger given by . f t L + y y + i ( M ,U rL h A k h 2rA is the inner tube radius, k the tube material thermalconductivity and h 1, h 2 the inner and outer surface heat transfer

coefficients. hL is given byh = Nu = 0.023 Re 0 8 Pr 0 1* (A4)

2vr where Pr = , Re = - - , = -- (5) V irr zp(, , are fluid viscosity, velocity, and density).

Assuming the pond temperatue varies linearly with distance alongthe heat exchanger tubing (total length L)i.e. Tp = T p l + (Tp0 - T p l) z/L (A6)then equation (A2) may be integrated to give

T ^ - T - (^ - T ^ >e" L /* - 7 (T n - )(1 - e" L / )(A7)ro po ^i Pi L P Piwhere I = % . - (A8)irr2


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Experimentally h- was found from measurements of the temperaturesTpi Tpo Tfi Tfo a n d t n e flow rate m (T pl and Tp 0 beingmeasured in regions of the pond well away from the heat exchangerto avoid local temperature effects, or at the heat exchangerbefore fluid was circulated). The value of U was adjusted untilthe outflow temperature Tf 0 predicted by equation (A7) ageeed withthe experimental value. hA was calculated theoretically for thegiven flow rate m from equations (A4) and (A5), and equation (A3)then used to deduce h 2Once h 2 is known, equation (A7) and (Al) may be used to design theheat exchanger for given heat transfer rates and temperatures.


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35

APPENDIX IIFINITE DIFFERENCE THERMAL MODEL

The pond is treated one-dimensionally, and is divided into a topmixing layer of thickness (~ 20 cm), the non-convectinginsulation layer of thickness d, the bottom convecting storagelayer of thickness D s, a layer of insulating material of thicknessDi between the base of the pond and the ground, and the groundbeneath of thickness D g below which temperature is taken to be atmean annual ambient temperature.The solar flux reaching depth beneath the top surface of thepond is given by

() = TH{a - bn(x/cosr)}where = surface transmissivity (~ 0.85), is the solar fluxincident at the surface, r is the angle of refraction, a and b areconstants 0.36 and 0.08 to model the absorption of sunlight inwater (see ref (7)).The top layer is assumed to follow ambient temperature T a. Thisis true to within 1C normally in Sussex.The insulation layer is divided into thin layers of thickness which heat up according to

3T 3 _,_ . 3 2TP C P 9t = - 7* + k " a x " 2 " < * * - a

where = density, Cp specific heat, k thermal conductivity, and is the rate of side heat loss per unit pond area, and isthe rate of heat extraction per unit area from that layer ofthe insulation zone.Using finite difference techniques (ref (12,13)), with time steps t and with indices j, j+1 denoting time t, t+t, the temperaturechange at levels i [from 2 to (n-1)] during the time step 6t isgiven by


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36

Ti,j+1 - Tifj + ofCTi-i.j - 2Tifj + Ti+lfj] _ if X 3 X L t j^i,j + ^i,j)} (i-2ton-l). kotwhere o = pcpx2is a stability parameter which must be


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37

Figure 1. Preparing the 30 cm sand base to the pond.v.- ***' ... e

F i g u r e 2, I n s e r t i n g t h e r m o c o u p le s i n t o the g r o u n d .


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Figure 3. Bolting together the galvanised steel sheets.

Figure 4. Putting the 1 mir. thick butile rubber liner in place.


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39

Figure 5. The gantry over the pond surface.

Figure 6. Outlets of the syphon tube used to withdraw pond samples.


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Figure 7. The completed pond and instrument hut.

Figure 8. Heat exchanger in the insulation layer between25 and 75 cm over the bottom.


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41

Figure 9. Diffusing dyed water into salt solution to createa salt density gradient in a laboratory pond.

Figure 10. Heat exchanger in a laboratory pond showinghorizontal laminar convection in the insulatinglayer.


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Figure 11. Laboratory heat exchanger and sample syphon tub es .

Figure 12. Laminar convection in laboratory tank made visibleby dropping in anhydrous copper oxide powder.


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(cm)110100

90

80

70

60

50

40

30

20

10

J t r : (above >ottom) j ! .

. . . . . . . . . . . . . . . . . . . . . . . . .^ % . . . . . . . . . . - - > a a . . a . . . . a a a a . a . . . a; . . . a a a\ \ i"., i 1 i ! 1 1 1 i * , * .

i j f i1*: f i f ! ? ! ?* * * a a: : : B. : : : : : :* * , *: : : : : '. : : i : : :: : : : * : : : : :* . ! ! ! > - ! ! : l i l i l "vi l i l i! 1 i ! * i i* * * a1 i i I ! 1 ! V ! ; ! i" a a a ', ' . ' : ; i i i n ; i ; * I t1 : i i i i ; i i ; i

. D E N S I T Y ! ! * " a *0 : -rs*1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 ( k g / )

F i g u r e 13 . D e n s i t y p r o f i l e on 15 May 84


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1987 86543 82 81

. ^ ; .

.,.

->

>

. i- m

1 8 2 8 38 48 5 8 6 8 7 8 8 8 9 8 1 88 (cm)Figure 14. Percentage solar penetration (y) with depth (, cm) belowsurface of pond.


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DENSITOMETER

MAGNETICSOLENOID

F i g u r e 1 5 . B u o ya n cy d e n s i t o m e t e r .


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46

nis

0.40.30.2

0.1

0 2Figure 16.

Curve 1; Storage layer extractiononly. No ground insulation,E = 0.Curve 2 : Storage layer extractiononly. 0.1 m ground insulation,E = 0.Curve 3: Storage and insulationlayer extraction. No ground in-sulation, E = 1.Curve 4 ; Storage and insulationlayer extraction,insulation, E = 1.0 . 1 m g r o u n dT he d a s h e d p o r t i o n s of the c u r v e sc o r r e s p o n d t o h e a t b e i n g i n j e c t e di n t o t h e s t o r a g e l a y e r (Q


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47

EFFICIENCY0 .3

0 .2

0 .1

Ext rac t i on f rom:(a) storage layer only(b) storages-insulation layers(c) insulation layer only

( T s - T a m b ) / S ( C / W m " 2 )0 .6

F i g u r e 1 8 . P on d e f f i c i e n c i e s c a l c u l a t e d u n d e r s t e a d yc o n d i t i o n s w i t h t h e f i n i t e d i f f e n c e m o d e l ,a n d m o d e l l i n g t h e h e a t e x c h a n g e r p l a c e d i nt h e p o n d .


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Temperature/ c

60

50 -

measured temepraturescalculated by finitedifference model

JAN20 24 28

TIME/WEEKS32 36 40 44 48 52

DECFigure 19 Comparison of observed storage temper ature, and model Iiehaviour


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a salt gradient solar pond

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