Cubical Cavity Heat Loss

8/8/2019 Cubical Cavity Heat Loss

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An understanding of convective heatloss is essential to the design ofefficient solar central receivers.In solar central-receiversystems, an array of heliostatsreflects sunlight onto a receiver atopa tower. The receiver absorbs solarenergy and uses it to heat a workingfluid, which can be air, water, moltensalt, or liquid metal. This heated fluid

is used to provide process heat or togenerate electric power in a thermalpower plant (Figure 1).The receiver's efficiency inabsorbing and transferring solarenergy to the working fluid is criticalto the central-receiver concept sinceplant performance, capital cost,and, ultimately, the cost of energyproduced are significantly affectedby the receiver's efficiency. Inaddition to these economic

ramifications, errors in estimates ofenergy loss entail the risk ofperpetuating inefficient receiverdesigns and implanting incorrectreceiver technology for the future.To calculate receiver efficiencypredictions are required for energylosses from: Reflection of incoming solarenergy

Radiation from heatedsurfaces Heat conduction into thestructure that supports thereceiver and Convection (natural, forced,or mixed).

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Figure 1.Solar One, the 10-MWe Solar Thermal CentralReceiver Pilot Plant near Barstow, CA, is theworld's largest solar electric generatingstation. It is designed to produce 10 MW e ofelectric power for the Southern CaliforniaEdison Company utility grid (after supplyingthe plant's own power requirements) for 8hours on a clear summer-solstice day. Theflat-plate experiment described in this articlewas designed to obtain information on theconvective heat transfer that occurs onexternal-type receivers of the kind used inSolar One.

Located near Almeria, Spain, theInternational Energy Agency's Small SolarPower Systems Project is designed to testtwo types of solar-thermal power plants. Ourcavity experiment yielded information onconvective heat transfer typical of thecavity-type receiver used in this plant. Thefacility was designed to produce 50 0 kW ofeelectric power for 8 hours under the bestweather conditions.

Figure 2 is a schematic of thereceiver energy balance.While methods exist forestimating the first three lossmechanisms, information needed toestimate convective heat losses hasbeen, until recently, almostnonexistent. The large sizes, highsurface temperatures, and complexgeometries of central receivers haveplaced them in convective heattransfer regimes for which there hasbeen a dearth of experimental dataand predictive methods.

Because of this lack ofinformation, in 1979 we initiated theCentral Receiver Convective EnergyLoss Program, a research effort toestablish a convective heat-lossdata base, involving a number ofuniversities and private firms. As partof the program, we were directlyinvolved in two large-scale heattransfer experiments: A flat-plateexperiment to obtain information forexternal-type receivers such as theSolar Thermal Central Receiver PilotPlant (Solar One) at Barstow, CA,and an experiment coveringcavity-type receivers like theInternational Energy Agency's SmallSolar Power Systems Project nearAlmeria, Spain.

Since scaling is difficult, weconducted the experiments"near-full-scale" and attemperatures that closely simulatedactual receiver operating conditions.Despite the large sizes, high power

I requirements (up to 525 kW), andhigh temperatures involved, weconducted the experiments in acontrolled, laboratory-typeenvironment.

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3mx3m60C to 650C0-6 m/s

Size of sides: 2. 2 mSurface temp: 800CNatural convection

ii ~ E m l t t e d : Radiant Energy

/Figure 2.The receiver of a solar centralreceiver power plant absorbs 90%to 95% of incoming concentrated

Isolar energy; the remainder isreflected. A large portion of theabsorbed energy is carried awayby the working fluid in the receiverto generate power or processheat. The rest is re-emitted asthermal radiation, lost byconduction to the receiverstructure, or lost by convection tothe environment.

Figure 3.We conducted two large heat-transfer experiments, one on alarge flat plate (a) and the other on a cubical cavity (b).

:? : / '~ ~ ConcentratedSolar Energy; /' ! f1?llqr~ , . .

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Vertical Flat Plate ExperimentConvective heat transfer fromexternal receivers can occur either ina forced-convection mode(wind-driven), a natural-convectionmode (buoyancy-driven), or acombined forced and naturalconvection mode (mixedconvection) In addition, the surfacetemperature of a receiver is high inrelation to ambient air temperature,so property variations in the air nearthe receiver surface resulting fromlarge temperature gradients havesignificant effects on the convectiveheat-transfer process We designedthis experiment to obtain informationprimarily on mixed-convection heattransfer and the effects of propertyvariations on both mixed andnatural-convection heat transfer forregions of boundary-layer flow onexternal receivers.The experimental apparatusconsists of a large (3 m x 3 m),electrically heated, vertical flat plateplaced parallel to the horizontal flowof air in a wind tunnel (Figure 3a).

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Wind velocities in the tunnelrange up to 6 m/ s and the plate isheated to temperatures as high as650C. Depending on thecombination of surface temperatureand wind velocity, the mode of heattransfer from the vertical plate iseither natural convection, mixedconvection, or forced convection. Inthe mixed-convection mode, theboundary-layer flow on the verticalplate is similar to that for mixedconvection from an external receiveror a skewed three-dimensionalboundary layer, as shownschematically in Figure 4.Figure 5 shows the domain ofnew data from this experiment ascompared to existing data in theliterature in terms of the Grashofnumber, Gr (a measure of thenatural-convection driving force),and the Reynolds number, Re (ameasure of the forced-convectiondriving force) (Box A). Regionsdominated by natural, mixed, andforced-convection heat transfer areindicated. The region for which data

Figure 4.When air is forced parallel to andhorizontally over a heated verticalsurface, the air near the surface(the boundary layer) is heated andrises due to buoyancy as it movesdownstream. Away from thesurface, in the unheated freestream, the flow remainshorizontal. This flow patternresults in a skewed three-dimensional boundary layer on thevertical flat plate. Air flow near thewall arcs upward, while air flow inthe free stream remains horizontal.

exist in the literature is shown in darkgray, and is composed mainly ofpure natural- and forced-convectiondata. The unshaded area shows thelarge region where knowledge hasbeen added to existing information.In addition, there was littleinformation in the literature on theeffects of significant fluid propertyvariations at high temperatures onnatural-convection or mixedconvection heat transfer forreceiver-like geometriesExperiments conducted forconditions on which data alreadyexist, such as low-temperature purenatural convection and pure forcedconvection, were used as baselinetests to verify the design of theexperiment.

We measured both heat transferfrom the plate and the boundarylayer profiles of velocity,temperature, and flow angle. Theoverall or average heat transfer interms of the Nusselt number (adimensionless measure of heattransfer-see Box A) is shown in

NaturalConvection Flow

Figure 6 as a function of Reynoldsand Grashof numbers. From theseheat-transfer measurements weestablished relationships for mixedconvection and high-temperaturenatural convection. The mixedconvection relationship wedeveloped was one of theexperiment's most importantfindings (Box B)Our measurements showed anunexpected result in the turbulentmixed-convection boundary layerthe existence of a region of constantflow angle with respect to distancefrom the wall. This region occursvery near the surface of the plate.We expect that the constant-angleregion is a feature of the flow thatturbulence models, being developedas a part of detailed efforts to modelthese types of flows, will need topredict in order to accurately predictheat transfer.

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Figure 6.Experimental heattransfer data show the conditionsfor which forced, mixed, and natural convectiondominate heat transfer from the test surface. Themeasured overall or average heat transfer is plottedas the Nusselt number (a dimensionless measure ofheat-transfer rate) against the Reynolds and Grashonumbers.

Figure 5.A significant body of new information on convective Currently, data exist primarily for pure forcedheat transfer has been added to the literature convection and low-temperature pure natural(represented by the white region). The Grashof convection (dark gray regions). Our experimentsnumber, Gr, is a measure of the natural-convection provided data for high-temperature turbulent-flowdriving force, while the Reynolds number, Re, is a conditions-the first data available for both naturalmeasure of the forced-convection driving force. The and mixed convection relevant to external receiverillustration shows the regions dominated by natural, geometries.mixed, and forced convective heat transfer.

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Large Cubical-CavityExperimentWe designed this experiment(Figures 3b and 7) to produceconvective heat-transfer processessimilar to those that occur incavity-type solar central receivers.The cubical geometry was chosenbecause it is representative of actualreceivers and lends itself totheoretical modeling of flow andheat transfer. Interior surfaces wereheated electrically as high as 750Cto simulate typical receivertemperatures.We used two methods to obtainour data: (1) we determined the heatleaving the interior surfaces of thecavity from measured surface

temperatures, and (2) we measuredvelocity, temperature, and radiantheat flux distributions in the apertureplane to determine the heat leavingthe opening in the cavity. Asexpected, losses from the surfaceswere equal to losses through theopening, thus providing a check ofthe experimental methods.Air temperature and velocitydistributions in the aperture plane(Figure 8) indicate that most of theheat is convected outward from thecavity's top center, with only afraction escaping at the uppercorners. Flow-visualization studies,shown schematically in Figure 8,confirmed this finding.As shown in Figure g, flowpatterns are caused by air being

drawn into the bottom of the cavity,being heated by the surfaces, andrising rapidly to the top of the cavity.The air must then turn and flowhorizontally along the cavity ceiling.The air flows from each side wallmeet in the middle of the ceiling and,having nowhere else to go, flowdownward. Air from the back wallturns along the ceiling and pushesthe mass of air near the ceiling out ofthe cavity.We added lips to the top andbottom of the opening. While the lipschanged the flow pattern, they didnot reduce the vigor of the flow orgreatly decrease heat transfer.Remarkably, we found that heattransfer from the large cavity wasgreater than for natural convection

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Figure 7.In the cubical-cavity experiment,the traverse containingthermocouples and othermeasurement instrumentation ismounted on the exterior buildingwall. The traverse is a horizontalbeam self-cooled by an enclosedwater channel on the side facingthe cavity. In the back of the beam,sheltered from thermal radiationemitted from the cavity, is astepping motor that drives thetransducer mounting plate in thehorizontal direction.

from a flat plate of the same height,total interior surface area, andtemperature. This finding is againstintuition until it is realized that naturalconvection inside the cavityenhances heat transfer by impingingon several surfaces in a situationthat more nearly resembles mixedconv

We found that the heat f lux-thheat rate per unit area-from thecavity depends only upon thetemperature difference between thcavity and ambient air. Theconsequence is that smaller,less-expensive, scale models ofreceivers may now be tested withconfidence, particularly in caseswhere the geometry differs greatlfrom previous experiments.

Box AGrashof, Reynolds, and Nusselt Numbers

The Grashof number, a dimensionless parameter used in the study ofnatural convection caused by a hot body, is

where a is the fluid's coefficient of thermal expansion, LiT is the temperaturedifference between the hot body and the fluid, g is the acceleration of gravity,d is a characteristic length of the system, p is the density of the fluid, and !J. isthe fluid viscosity. The Grashof number is proportional to the ratio of thebuoyant forces caused by heating to the viscous drag on the heated surface.

The Reynolds number, a dimensionless parameter used in the study offorced convection where the effects of viscosity are important, is

where p is the density of the fluid, V is its velocity, d is a characteristic length,and J.L is the fluid viscosity. The Reynolds number is the ratio of the inertialforces to viscosity.

The Nusselt number, a dimensionless parameter used in the study offorced convection, isNu = {3 dk

where {3 is the heat-transfer coefficient, d is a characteristic length of thesystem, and k is the thermal conductivity of the surrounding fluid. The Nusseltnumber is the ratio of the convective heat transfer to the conductive heattransfer.

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Box BCalcUlating Mixed-ConvectionHeat Transfer

The experiment shows that theaverage mixed-convection heattransfer, 0mlxed' can be estimated bycombining two simpler estimates ofconvective-heat transfer for aproblem: one based on theassumption that only forcedconvection is occurring and theother on the assumption of natural

convection for a given problem:o 32 0 32 + 0 32mixed = forced naturalThis relationship predicts themeasured average mixedconvection heat transfer from thevertical plate within a smallpercentage.

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Figure 8.The temperature difference distribution in theaperture plane (a) shows that the highesttemperatures are found in the boundary layerexiting from the top surface of the cavity, with thehighest at the center and then the two corners. Theorientation of the temperature surface to the cavityaperture is as follows: the left axis is the bottomedge, the right axis (not shown) is the top edge, andthe nearly horizontal axes are the sides.

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The outflow velocity distribution (b) indicatessimilar trends. We found inflow velocities to benearly uniform, in the order of 1.0 mis, over thelower portion of the cavity. The samecharacteristics as reported for temperature areapparent here; velocities are greatest in theboundary layer, especially in the center and thenthe corners. The roughness of the surface near thezero-inflow location is due to fluctuations in the flowand inaccuracies in measuring the low velocities.

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ConclusionOur experiments have given us abetter understanding of convectivelosses from receivers. This newunderstanding is guiding thedevelopment of detailed numericalmodels for predicting localconvective losses, and has allowedus to develop a simplified

Figure 9.In a cubical cavity, flow patternsare the result of air being drawninto the bottom of the cavity whereit is heated by the surfaces, andthen rising rapidly to the top of thecavity. The air must then turn and

mathematical model to predict theoverall or average convective lossesfrom receivers. This model providesthe designer with a practical,easy-to-use tool for estimating thetotal convective energy loss from areceiver and the uncertainty in thatestimate.

flow horizontally along the cavityceiling. Air flowing from each sidewall meets in the middle of theceiling and flows downward. Airfrom the back wall turns along theceiling and pushes air out of thecavity.

For more information, callJohn Kraabel (415) 422-3408 orDennis Siebers (415) 422-2078.l.. (5" 10 2 ~ l e -207

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Cubical Cavity Heat Loss