PERFORMANCE ANALYSIS FOR V-GROOVE ABSORBER · Hottel-Whillier-Bliss equation (Duffie and Beckman,...

PERFORMANCE ANALYSIS FOR V-GROOVE ABSORBER

Introduction

Solar air heaters form the major component ofsolar energy utilization systems which absorbthe incoming solar radiation, converting it intothermal energy at the absorbing surface, andtransferring the energy to a fluid flowing throughthe collector. Solar air heaters, because of theirinherent simplicity, are cheap and the mostwidely used collection device (Momin et al.,2002). It has a wide range of applications indrying agricultural products, industrial processheating in textile and papers, space heating andgreenhouse heating. Several designs of solar aircollectors have been studied over the years,hence the design of suitable air collectors is oneof the most important factors controlling the

economics of solar drying. Therefore extensiveinvestigations have been carried out on theoptimum design of conventional and modifiedsolar air heaters, in order to search for efficientand inexpensive designs suitable for massproduction for different practical applications.Previous researchers have focused on the effectsof design and operational parameters, type offlow passes, number of glazing and types ofabsorbers flat, corrugated or finned, on thethermal performance of solar air heaters (Vermaet al., 1991; Verma et al., 1992; Choudhuryet al., 1995 and Karim et al., 2004). SopianSupranto et al. (1999) studied the use of porousmedia in doublepass solar air heaters and

Department of Mechanical and Manufacturing Engineering, Faculty of Engineering University PutraMalaysia, 43400 UPM Serdang, Selangor, Malaysia. Tel.: 0060-126771656; E-mail: [email protected]

* Corresponding authorSuranaree J. Sci. Technol. 14(1):39-52

Bashria Abdrub alrasoul Abdallah Yousef* and Nor Mariha Adam

Received: Mar 31, 2006; Revised: Nov 8, 2006; Accepted: Nov 11, 2006

Abstract

This paper concerns theoretical study to investigate the effect of mass flow rate, flow channel depthand collector length on the system thermal performance and pressure drop through the collector, onV-groove absorber at single and double flow mode. This study has been conducted by using a developedinternet based mathematical simulation. It concludes that in V-groove absorbers types, the double flowmode is 4 - 5% more efficient than the single mode. On the other hand the use of porous media in doubleflow increases the air heater efficiency to be 7% more efficient than an air heater in single mode, and2 - 3% more efficient in double flow mode without porous media. The analysis and the graphs obtainedin this paper can be a helpful tool for a design engineer to construct economical and efficient solar airheaters with technical dimensions.

Keywords: Single and double flow V-groove absorber, porous media, thermal performance, pressure

drop, flow channel depth

40 Performance Analysis for V-groove Absorber

found that the use of porous media in the secondchannel of solar air heaters increases the heattransfer area. In addition, this type of air heaterhas a higher thermal performance comparedto the conventional single-pass solar air heater.An internet based mathematical simulationhas been conducted and developed by Bashriaet al. (2004a, 2004b) to predict the thermalperformance for different designs of solar airheaters with flat or V-groove absorbers, single,double or triple glass covers, in single passor double pass double ducts with or withoutporous media.

This study uses the aforementioneddeveloped program by Bashria et al. (2004a,2004b) to find the effect of different parameters,such as mass flow rate, flow channel depthand collector length on the system thermalperformance and pressure drop through thecollector, for V-groove absorbers in single anddouble passes with and without using a porousmedia.

Theoretical Analysis

To model the solar air types and obtain theirrelative equations, a number of simplifyingassumptions has been made to lay thefoundation without obscuring the basic physicalsituation. These assumptions are as follows:

1. Performance is steady state.2. There is no absorption of solar energy

by a cover insofar as it affects lossesfrom the collector.

3. Heat transfer fluid is considered anon-participating medium.

4. The radiation coefficient between thetwo air duct surfaces is found byassuming a mean radiant temperatureequal to the mean fluid temperature.

5. Loss through front and back are to thesame ambient temperature.

In single pass V-groove absorber,energy is transferred from the plate to thebottom of the cover through both the radiationheat transfer coefficient h

r and the convection

heat transfer coefficient h1, and to the fluid at a

temperature at Tf through the convection heat

transfer coefficient h2. Energy is transferred from

the fluid to the ambient air at Ta through the

back loss coefficient Ub. Energy is lost to the

ambient air through the combined convectionand radiation coefficient U

t. Schematic

drawings for single pass V-groove absorberand thermal net work are shown in Figure 1(a).The steady-state energy equations yield thefollowing equations (Bashria et al., 2004a):

Collector cover

h1 (Tp -Tc )+hr (Tp -Tc ) = Ut (Tc -Ta ) (1)

V-groove absorber

h2 (Tp -Tf )+h1 (Tp -Tc ) + hr (Tp -Tc ) =Ιτα (2)

Fluid medium

h2 (Tp -Tf )+Ub (Ta -Tf ) = (______) (______) (3)

In double pass double duct energy istransferred from the plate at T

P to the cover

through the radiation heat transfer coefficienth

r1 and the convection heat transfer h

1, and to

the fluid in the upper duct flowing throughthe V-groove at a temperature T

f1 through

the convection heat transfer coefficient h2, and

to the fluid in the lower duct flowing betweenthe absorber plate and the base plate at atemperature T

f2 through the convection heat

transfer coefficient h3. Also energy is transferred

to the base plate through the radiation heattransfer coefficient h

r2. Energy is transferred from

the fluid flowing in the lower duct at Tf2 to the

base plate through convection heat transfercoefficient h

4. Finally, energy is lost to the

ambient air through the combined convectionand radiation coefficient U

t through the cover

glass. Figure 1(b) illustrates the double passdouble duct V-groove absorber and the thermalnet work. The steady-state energy balance onthe cover, the plate and the fluid in the upperand lower ducts (with the assumption thatthe heat transfer fluid is a non participatingmedium) gives the following equations:

mCp

W

dT f

dx

41Suranaree J. Sci. Technol. Vol. 14 No. 1; January - March 2007

Fluid medium in the upper passage

h2 (Tp -Tf1 ) = (_______) (_______) (11)

Fluid medium in the lower duct

h3 (Tp -Tf2 ) + h4 (Tpr -Tf2 ) +

h5 (Tf2 -Tr ) = (_______) (_______) (12)

Porous media

hr2 (Tp -Tpr ) + h6 (Tpr -Tr ) = h4 (Tpr -Tf2 ) (13)

Bottom plate

h5 (Tf2 -Tr ) + h6 (Tpr -Tr ) = Ub (Tr -Ta ) (14)

The thermal efficiency which is definedas the ratio of the useful energy to the totalincident solar radiation is expressed by theHottel-Whillier-Bliss equation (Duffie andBeckman, 1991).

(15)

Heat Transfer Coefficients

In order to solve the models, the convectiveheat transfer coefficient for air flowing overthe outside surface of the top glass cover andinside channel are needed. The followingcorrelation proposed by McAdams (1954)for air flowing over the outside surface of theglass cover is used to predict the convective heattransfer coefficient

ha = 5.7 + 3.8V (16)

where ha is the convective heat transfercoefficient, and V is the wind velocity.

The radiation heat transfer coefficientfrom the absorber to the glass cover can be statedas follows using Duffie and Beckman, (1991)and Verma et al. (1992)

Collector cover

h1 (Tp -Tc )+hr (Tp -Tc ) = Ut (Tc -Ta ) (4)

V-groove absorber

h2 (Tp -Tf1 ) + h1 (Tp -Tc ) + hr (Tp -Tc )

+ h3 (Tp -Tf2 ) + hr2 (Tp -Tr )= Ιτα (5)

Fluid medium in the upper passage

h2 (Tp -Tf1 ) = (_______) (_______) (6)

Fluid medium in the lower duct

h3 (Tp -Tf2 ) = (_______) (_______) + h4 (Tf2 -Tr ) (7)

Bottom plate

h4 (Tf2 -Tr ) + hr2 (Tp -Tr ) = Ub (Tr -Ta ) (8)

In case of double flow double duct packedwith porous media (glass-wool of 0.8 porosity)energy is transferred from the plate at Tp to theporous media through the radiation heat transfercoefficient h

r2. Energy is transferred from the

porous media to the fluid in the lower ductthrough the convective heat transfer coefficienth

4 and from the fluid at T

f2 to the bottom plate

through convection heat transfer coefficienth

5.

Also energy is transferred from the

porous media to the bottom plate through theconvection heat transfer coefficient heattransfer coefficient h

6. Figure 1(c) illustrates

the double pass double duct V-groove absorberwith porous media in the lower duct and thethermal net work. The steady-state energybalance gives the following equations

Collector cover

h1 (Tp -Tc ) + hr (Tp -Tc ) = Ut (Tc -Ta ) (9)

V-groove absorber

h2 (Tp -Tf1 ) + h1 (Tp -Tc ) +hr (Tp -Tc ) +

h3 (Tp -Tf2 )+ hr2 (Tp -Tpr) = Ιτα (10)

mCp2

W

dT f2

dx

mCp1

W

dT f1

dx

mCp2

W

dT f2

dx

mCp1

W

dT f1

dx


Ta

Tc

1/Ut

1/h1

1/h2Tf qu

1/hr

1/Ub

TpI

Tc

Tph1

Insulation

h2

UbFluid flow

Tf

CoverUtI

1/h41/hr2

1/h3

1/h2

Tp

Tc

1/h1

1/Ut

1/hr1

I

Ta

Tf1 qu1

Tf2 qu2

Tr

Cover Ut

hr1

Fluid inlet

h2h1

Tp Ub

h4

Ub Insulation

h3

hr2

Tf1

I

Fluid outlet Tf2

I

Cover Ut

hr1

h2

h6

Ub Insulation

Fluid inlet

Tr1 h1 Tp

h4

h3 h5hr2

Tr

I

Floid outlet T2 1/hr2

1/hr1 1/h1

1/Ut

1/Ub

Tpr

1/h6 1/h5

1/h4

1/h3

1/h2

Tp

Tc

Ta

Tf2

Tf1 qu1

qu2

Tr

Figure 1. Schematic diagram of V-groove solar air heaters with thermal network


(17)

In the V-groove the radiation is reflectedseveral times in the grooves, each timeabsorbing a fraction of the beam. This multipleabsorption gives an increase in the solarabsorptance but at the same time increases thelong-wavelength emittance (Ruslan et al., 2003).

(18)

The convective heat transfer coefficientsare calculated using the following relations

(19)

where Nu is Nusselt number, k is the air thermalconductivity and D

h is the equivalence diameter

of the channel. Nusselt number for laminar flowregion (Re < 2300), transition flow region (2300< Re < 6000), and turbulent flow regionrespectively as mentioned by (Naphon, 2005) are:

(20)

Nu = 0.116(Re _125) Pr 2 / 3 1 / 3

(1+ (___) 2 / 3

)(___) 0.14Dh

L w

(21)

(22)

where Re is the Reynolds number, Pr is PrandtlNumber

(23)

Dh = 4 _________________________ (24)

For the V-groove absorber it is found thatthe hydraulic diameter equals (Bashria et al.,2004a):

Dh = _____________ (25)

Pressure Drop

When the air flows through the channel inthe air heater, due to friction the air pressuredrops along the length of the flow channel. Thispressure drop across the flow duct is given bythe following expression (Verma et al., 1992):

(26)

(27)

The values of fo and y are

fo = 24 / Re, y = 0.9for laminar flow (Re < 2550)

fo = 0.0094, y = 2.92Re -0.15

for transitional flow (2550 < Re < 104)fo = 0.059Re-0.2, y = 0.73

for turbulent flow (104 < Re < 105)

Simulation Procedure

A prototype internet-based computer programwas developed to be used as a tool to supportthe design of solar air heaters used for dryingagricultural products in Malaysia. Dream-weaverTM combined with the Active Server Pages

Cross sectional area of the flowwetted perimeter

2Hv sin (φ / 2)1 + sin (φ / 2)


(ASP) as an extension environment, have beenchosen as a development software tool. Theprogrammatic code was written by VBScript asscripting language to execute commands on acomputer (Bashria et al., 2004a). Rules havebeen used to specify a set of actions performedfor a given situation. The required data areclassified into three groups, the general inputdata concerning metrological conditions, thecollector characteristics data that contain allspecific manufacturing attributes related to thecollector and the energy characteristics datawhich contain measured data about inlettemperature and mass flow rate related to thetransfer media inside the collector (Bashriaet al., 2004b). The aforementioned internet basedcomputer program is in the process of continualdevelopment but it can be accessed through thewebsite http://www.eng.upm.edu.my/home/bashria/public_html/default.asp

Initial work for simulation was based ondetermining the types and components ofsolar air heaters, its use, advantages anddisadvantages. In developing the numericalprocedure, several steps and processes areinvolved. The primary task can be categorizedinto five steps, as follows: Identification andcharacterization of the problem, conceptualiza-tion, mathematical model, implementation andtesting. The flow cart of such developmentprocesses is shown in Figure 2. The numericalalgorithm and mathematical model that used tocalculate the thermal performance were basedon Hottel-Wrillier-Bliss equation and on thedeveloped energy balance equations at variouscomponents of the collector models, along withthe different heat transfer coefficients at theirsurfaces which have mentioned previously in thetheoretical analysis section. These equations havebeen transferred to syntax code and implantedinto the developed computer program.

Numerical values of different para-meters such as outlet temperature, efficiencyand the pressure drop were computedcorresponding to an ambient temperature 33oC,solar radiation 500 W/m2, air velocity 1.5 m/sec,inlet temperature of 35oC and different valuesof mass flow rate.

Validation

Validation and verification focus on thecom-parison between the predicted output andthe experimental results for each type of solarair heater. The experimental results have beencarried out by Karim et al. (2004), for V-grooveabsorber in single and double pass mode. Theoutput from the mathematical simulation hasbeen run according to the same configuration andparameters used in experimental work done byKarim et al. (2004). A great correlation hasoccurred between the experimental and thepredicted efficiencies (R2 = 99.5%, P < 0.001)for single flow mode as shown in Figure 3. Alsoa good correlation (R2 = 98.7%, P < 0.001) and(R2 = 97.5%, P < 0.001) has been found betweenthe experimental and predicted efficiencies andoutlet temperature respectively as shown inFigure 4.

This study of double pass V-grooveabsorber with porous media has notbeen conducted before either theoretically orexperi-mentally. The theoretical study has beenconducted by using the program developedin this study.

Results and Discussion

Figure 5 shows the variation of efficiency withmass flow rate for V-groove absorber in singlepass, double pass and double pass mode withporous media. From the figures, it can be seenthat the efficiency of the air heater is stronglydependent on the air flow rate. The efficienciesof all three air heaters increased constantly, thentended to approach a constant value. This figureclearly shows that the double flow mode is4 - 7% more efficient than the single flow mode.This increase in efficiency in double pass modeis due to the increased heat removal from twoflow channels compared to one flow channel insingle pass operation. On the other hand, the useof porous media in double flow increases the airheater efficiency to 7% more efficiency than theair heater in single mode and more than 2 - 3%efficiency in double flow mode without porousmedia. Hence, the use of porous media increasesthe heat transfer area which contributed to


Figure 2. Simulation procedure flow chart

Conceptualization Phase

Knowledge representationKnowledge acquisition


the higher efficiency.Hence, the outlet temperature is an

important parameter for drying applications; theoutlet temperature was investigated for a widerange of flow rates. Figure 6 shows the variationof outlet temperature with flow rate. As expectedthe outlet temperature of the flowing air throughthe collector decreased with increased flow rate,but after a flow rate of about 0.05 kg/sec forsingle flow mode, and a flow of about 0.065kg/sec for double flow mode the rate of thetemperature drop became lower. Figure 7

illustrates the variation of the pressure dropwith mass flow rate; it shows that the pressuredrop is a function of the mass flow rate; hence itis increased by increasing the mass flow rate.The figure clearly shows that the value of thepressure drop in double flow mode almostdoubles the value of the pressure drop in singleflow. At the same time the use of porous mediain the double flow V-groove absorber increasesthe pressure drop from 3 to 25 Pa more than thepressure drop in the double flow V-grooveabsorber without the porous media.

Predicted efficiencyExperimental efficiency

Mass flow rate (kg/s)

Eff

icie

ncy

Predicted TemperatureExperimental TemperaturePredicted EfficiencyExperimental Efficiency


Eff

icie

ncy

oute

t te

mpe

ratu

re (

o C)

Figure 4. Experimental and predicted output for double flow mode

Figure 3. Experimental and predicted output for single flow mode


Eff

icie

ncy


Single passDouble passDouble pass with porous media

Figure 5. Efficiency variation with mass flow rate for single pass, double pass and doublepass with porous media in V-groove absorber



Out

let

tem

pera

ture

(o C

)

Figure 6. Outlet temperature variation with mass flow rate for single pass, double passand double pass with porous media in V-groove absorber

The variation in efficiency and pressuredrop with flow channel depth for singlepass mode in V-groove absorber at differentcollector lengths (1.8 m, 1.5 m, and 1 m.) isdisplayed in Figures 8 - 9 respectively at a fixedmass flow rate of 0.034 kg/sec. Figure 8indicates that at a fixed mass flow rate theefficiency decreases with the increase of the flowchannel depth. Science the deep air channel depthreduces the heat transfer to the flowing air whichresulting in low efficiency of the system, and thiseffect is more predominant for a longer flow

channel. Figure 9 illustrates that the pressuredrop increases with a decrease in the flow depth,and this increase is greater for a longer channelflow. The variation in outlet temperature with theflow channel depth is displayed in Figure 10,which indicates that the outlet temperatureincreases with the decrease in the flow depth.

The effect of a different upper channeldepth on the pressure drop, efficiency and theoutlet temperature for double pass mode with andwithout porous media is conducted, for a fixedmass flow rate of 0.03 kg/sec, a constant lower


flow depth of 0.025 m channel and two differentchannel lengths of 1.0 m and 1.5 m. It is found thatwith the increase of the flow depth the pressuredrop decreases and also the efficiency and theoutlet temperature decreases and by increasingthe duct length, the efficiency decreases but theoutlet temperature and the pressure dropincreases as illustrated in Figures 11 - 13. Itappears from Figures 11 - 13 that the use of theporous media increases the system efficiencyby 3 - 7%, but the rise in outlet temperature isfaintly low at 2 - 3oC.

Conclusion

A mathematical simulation to predict the effectof different parameters on system thermalperformance and pressure drop, for V-grooveabsorbers in single and double flow modes withand without using a porous media have beenconducted. It is found that increasing the massflow rate through the air heaters results in higherefficiency but also pressure drop is increased.On the other hand, decreasing the channel flowdepth results in increasing the system efficiency


Pre

ssur

e dr

op (

Pa)


Figure 7. Pressure drop variation with mass flow rate for single pass, double pass and doublepass with porous media in V-groove absorber

Flow depth (m)

Eff

icie

ncy

mm

m

Figure 8. Efficiency variation with flow channel depth for single pass in V-groove absorber


Flow depth (m)

Out

let

tem

prat

uer

(o C)

Figure 10. Outlet temperature drop variation with flow channel depth for single pass inV-groove absorber

and outlet temperature at the same time as itincreases the pressure drop.

The channel length also has an effect onthe thermal efficiency, hence the efficiency ofthe system is increases more for a shortchannel length than for a long one, while thepressure drop is less than the pressure drop fora long channel length.

The double flow is more efficient thanthe single flow mode and the use of porousmedia increases the system efficiency and the

outlet temperature. This increment will result inan increase in the pressure drop thus increasingthe pumping power expanded in the collector.

Finally the adoption of the aforemen-tioned mathematical simulation that has beendeveloped to predict the thermal performanceof solar air heaters, and to find the influence ofdifferent parameters seems to be promising, as itis capable of predictive a reasonable resultsaccording to chosen parameters with design rulesthat incorporate human expertise in this field.

Figure 9. Pressure drop variation with flow channel depth for single pass in V-grooveabsorber

Flow depth (m)

Pre

ssur

e dr

op (

Pa)

mm

m


Upper channel depth (m)

Eff

icie

ncy

With porous media L = 1mWith porous media L = 1.5mWithout porous media L = 1mWithout porous media L = 1.5m

Figure 12. The variation of efficiency with upper channel depth


Without porous media L = 1mWithout porous media L = 1.5mWith porous media L = 1mWith porous media L = 1.5m

Pre

ssur

e dr

op (

Pa)

Figure 11. The variation of pressure drop with upper channel depth

Figure 13. The variation of outlet temperature with upper channel depth


Out

let

tem

pera

ture

(o C

)

With porous media L = 1mWith porous media L = 1.5mWithout porous media L = 1mWithout porous media L = 1.5m


Furthermore, the use of the internet will helpin sharing and distributing this knowledge.

This process should be of interestto designers and engineers who would like tocompare the cost effectiveness of solar airheaters.

Notations

A Area of collector that absorb solarradiation, m2

CP

Specific heat of working fluid, J/kg KD Collector Width, mDh Hydraulic diameter, mf Friction factorFR Heat removal factorh Fluid heat transfer coefficient, W/m2 Khr Radiation heat transfer coefficient,

W/m2 KH

VV-groove height, m

I Solar radiation, W/m2

L Collector length, mm Collector flow rate, kg/secN u Nusselt numberP Pressure drop across the duct, PaQ u Rate of useful energy gain, WRe Reynolds numberT a Ambient air temperature, KT c Cover temperature, KT f Fluid temperature, KT i Fluid inlet temperature, KT p Absorber plate surface temperature, KT pr Porous media temperature, KT r Bottom plate temperature, KU Overall heat loss coefficient, W/m2 KU b Back loss coefficient, W/m2 KU t Top loss coefficient, W/m2 KW Collector width, m

Greek symbols

ε p Emittance of absorber plateε c Emittance of glass coverρ Air density, kg/m3

σ Stephen-Boltzman constantτ Solar transmittance of glazingα Solar absorptance of collector plateφ V-groove angleµ Dynamic viscosity, Pa.sec

Subscripts

a ambientb backc coverf fluidh hydraulicp plateu useful

References

Momin, A-M.E., Saini, J.S., and Solanki, S.C.(2002). Heat transfer and friction insolar air heater duct with V-shaped ribroughness on absorber plate. Int. J.H.M.T.,945:3,383-3,396.

Verma, R., Chandra, R., and Garg, H.P. (1991).Parametric studies on the corrugatedsolar air heaters with and without cover.Renewable Energy, 1(3/4):361-371.

Verma, R., Chandra, R., and Garg, H.P. (1992).Technical note-optimization of solar airheaters of different designs. RenewableEnergy, 2(4/5):521-531.

Choudhury, C., CHauhan, P.M., and Garg, H.P.(1995). Performance and cost analysisof two–pass solar air heaters. HeatRecovery System &CHP., 15(8):755-773.

Karim, M.A., and Hawlader, M.N.A. (2004).Development of solar air collectors fordrying applications. Energy Conversionand Management, 45:329-344.

Sopian Supranto, K., Daud, W.R.W., Othman,M.Y., and Yatim, B. (1999). Thermalperformance of double pass solarcollector with and without porous media.Renewable Energy, 18:557-564.

Bashria, A.A., Adam, N.M., Sapuan, S.M., Daud,M., Omar, H., Megat, H.M., and Abas, F.(2004a). Prediction of thermal perfor-mance of solar air heaters by internet-basedsimulation. Proc. Instn. Mech. Engrs. PartA: J. Power and Energy, 218:579-587.

Bashria, A.A. Yousef, Adam, N.M., Daud, M.,Omar, H., Ahmed, M.H.M., and ElradiA. Musa. (2004b). Expert system basedprediction of the performance of solarair collectors in Malaysia. JEE, 3:91-101.


Duffie, J.A., and Beckman, W.A. (1991). SolarEngineering of Thermal Processes. 2nd ed.John Wiley& Sons, Inc. Toronto, 919 p.

McAdams, W.H. (1954). Heat Transmission.3rd ed. McGraw-Hill, NY, 532 p.

Ruslan, M.H., Othman, M.Y., Yatim, B., Sopian,K., and Ibrahim, Z. (2003). Force convec-tion solar drying system. Proceedingsof the International Symposium on

Renewable Energy: Environment Protec-tion and Energy Solution for SustainableDevelopment; 14-17 September; KualaLumpur, p. 671-680.

Naphon, P. (2005). On the performance andentropy generation of the double passsolar air heater with longitudinal fins.Renewable Energy, 30:1,345-1,357.

PERFORMANCE ANALYSIS FOR V-GROOVE ABSORBER · Hottel-Whillier-Bliss equation (Duffie and Beckman,...

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