Effect of the variable porosity on the heat transfer process in solar air receiver

Transcription

1 Engineering Conerences International ECI Digital Archives Sixth International Conerence on Porous Meia an Its Alications in Science, Engineering an Inustry Proceeings Eect o the variable orosity on the heat transer rocess in solar air receiver Pei Wang Hohai University, rancisw2012@163.com D. Y. Liu Hohai University Changzhou Follow this an aitional works at: htt://c.engconintl.org/orous_meia_vi Part o the Engineering Commons Recommene Citation Pei Wang an D. Y. Liu, "Eect o the variable orosity on the heat transer rocess in solar air receiver" in "Sixth International Conerence on Porous Meia an Its Alications in Science, Engineering an Inustry", Es, ECI Symosium Series, (2016). htt://c.engconintl.org/orous_meia_vi/17 This Conerence Proceeing is brought to you or ree an oen access by the Proceeings at ECI Digital Archives. It has been accete or inclusion in Sixth International Conerence on Porous Meia an Its Alications in Science, Engineering an Inustry by an authorize aministrator o ECI Digital Archives. For more inormation, lease contact ranco@beress.com.

2 Proceeings o the 6th International Conerence on Porous Meia an Its Alications in Science an Engineering ICPM6 July 3-8, 2016, Waikoloa, Hawaii EFFECT OF THE VARIABLE POROSITY ON THE HEAT TRANSFER PROCESS IN SOLAR AIR RECEIVER P. Wang Deartment o Renewable Energy Science an Engineering, Hohai University, Nanjing, China; ABSTRACT Solar air receiver is the core comonent o central receiver system (CRS) in solar thermal ower lants ue to the unique eature o some orous meium like silicon carbie oam ceramic an so on. In the air receiver, the orous material receives the concentrate sunlight rom the heliostat iel an heats u the ume inlet air by convection an raiation. The incient raiation is istribute in the inner sace o the orous meium rather than locate on the bounary o the heate ace in the ront o the receiver. Aiming at this henomenon which calle volumetric eect, we roose a novel solar air receiver using the orous meium with variable orosity along the incient irection to otimize its heat transer rocess an increase the thermal eiciency o the receiver. For this kin o orous meium, the eect o the variability o the orosity on the temerature an raiative heat lux istributions an also the thermal eiciency o the air receiver will be analyze systematically. Our analysis emonstrate that the structure with variable orosity will enhance the transer o raiative energy into the orous meium, consequently ecreases the thermal raiative loss at the inlet an increases the thermal eiciency o the air receiver. INTRODUCTION Porous meia is wiely utilize in many moern inustrial alications involving heat transer rocesses such as solar thermal utilization, nuclear waste reository, heat ies, combustion, heat transer enhancement etc. One area o utilization is the receiver (Aacutevila AL 2011) o a central receiver system (CRS) in solar thermal ower lants ue to the unique eature o silicon carbie (SiC) oam ceramic, such as large seciic area, high conuctivity an thermal shock resistance. In CRS, the orous material receives the concentrate sunlight rom the heliostat iel an heats u the ume inlet air by convection an raiation. Investigate on variants in local thermal non-equilibrium moel was given by (Alazmi B, Vaai K 2000) consiering the eect o non-darcy, isersion, non-equilibrium an variable orosity. The eect o ierent bounary conitions uner LTNE conitions was given by (Yang K, Vaai K 2010). However or the high temerature over thousans, thermal raiation behavior can not be neglecte. Its imact on conuctive heat transer in a acke be has been analyze by (Singh BP, Kaviany M 1991). Aim at the raiation transer in the orous meia in some tyical inustrial evice, (Wang P, Vaai K, an Liu DY 2014) erorme a numerical analysis ocus on the LTNE moel coule with raiation transer. The mechanism o the inluence o the raiation transer on the coule heat transer rocess with conuction an convection in the meia was reveale; (Flamant G, Olale G 1983) ocus on the raiation heat transer rocess in a ouble layers structure (glass be an SiC orous layer) exerimentally. When consiering the collimate incient raiation, the istribution o raiative energy changes in the incient irection shoul be taken into account simultaneously with convection rocesses. Hence, the urose o this stuy is to unerstan the role o the collimate incient raiation on the convective heat transer in air receiver uner LTNE conitions. In this work, the temerature iels or the soli matrix an lui hases will be analyze while incororating the local thermal nonequilibrium along with the ierential aroximation (P- 1 moel). The eect o intrinsic roerties an otic arameters will be iscusse resectively. NOMENCLATURE c Seciic heat o lui at constant ressure [J kg -1 K -1 ] Pore iameter [m] Eb Blackboy emissive ower F Inertial coeicient G Incient raiation h v Volumetric heat transer coeicient [W m -2 K] J Raiosity K Permeability [m 2 ] L a Thickness o a absorber [m] Mass low rate [kg/s/m 2 ]

3 P Pressure [Pa] Pr Prantl number q 0 Initial heat lux [W/m -2 ] q Heat lux ŝ Unit vector in the irection o lui low T Temerature [K] u Velocity[m/s] V Velocity vector [m s -1 ] Greek symbols: s Seciic surace area o the orous meium [m -1 ] ε Emissivity φ Porosity λ Thermal conuctivity [W m -1 K -1 ] μ Dynamic viscosity [kg m -1 s -1 ] Extinction coeicient [m -1 ] Otic thickness Single scattering albeo Dimensionless heat lux subscrits a Average/absorber b Back c Collimate/cavity Diuse e Eective/environment Flui hase r Raiative s Soli hase t Total v Voi w Wall 2 Moel escrition 2.1 Physical moel an assumtions Figure 1 shows the schematic structure o a SiC ceramic oam air receiver or volumetric receiver is use to receive concentrate lux on its surace which is coole irectly by the ume air. As can be seen the receiver s surace area (y irection) is much larger than its thickness (x irection). As such a one imensional aroximation in the irection o the thickness is invoke. We will also assume that the soli matrix is homogeneous an isotroic, an the variations o the thermal roerties o soli an lui hases are neglecte. Furthermore the low is consiere to be steay an ully eveloe. Figure 1: Schematic o the SiC ceramic oams air receiver 2.2 Mathematical moel Governing Equations Continuum equation: V 0 (1) Momentum equation: 2 P F K K (2) where the ermeability K, emirical unction F which eens rimarily on the microstructure o the orous meium can be reresente as: K F an V V V V V V J 3 2 (3) (4) P is the gauge ressure an the local volume average o a quantity can be eine as 1 V V, J is a unit vector oriente V along the velocity vector. Energy equations: lui hases: c V T e T hs as Ts T soli hases: se s r s s s (5) 0 T q h a T T (6) where:

4 e (7) se s (8) The seciic surace area o orous be with aears in both energy equation 5 an 6 is eveloe base on geometrical consierations: 61 (9) The lui-to-soli hase heat transer coeicient in this stuy was base on the emirical correlation establishe by (Wang P, 2015) is resente as ollows: hs (10) Pr Re 10s The raiation arameters that is the extinction, absortion an scattering coeicients s are strongly eenent on the exerimental test. (Hsu P, Howell JR 1992) resente a metho o simultaneously inverting conuctivity an extinction coeicient rom the exerimental ata. The tren o the change o extinction coeicient ha goo agreement the geometric otics limit reiction (Tien CL 1988) when ore size greater than 0.6mm: 1 1 (11) where the value o is given as, other test results shows that shoul be change to base on oam ceramic orous meia. (Mohanraj R et. al. 1996) also resente the exerimental test ocus on the RPC material, the result shows that raiation roerties is not sensitive to the temerature at the range o 1200K-1400K, etaile arameters is given as ollow: 3 = (12) 3 s = Raiation transer Uner the assumtion o collimate irraiation, a moiie ierential aroximation (P-1 Moel) is alie to aress this roblem here. We have the exress or the iuse raiative lux q an the incient raiation G as ollow: 4 4 s s c q T G G (14) q 1 G (15) 3 Then the ierential equation or G is obtaine as: G 4 Ts G sgc (16) 3 Meanwhile qc, the remnant collimate beam ater artial extinction, by absortion an scattering, along its ath in the irection which erenicular to the horizontal bounary is given by the exact solution: c c 0 q G q e x (17) Variable orosity The variation o the orosity in the low irection are eine by a linear unction: a = A + B L x (18) where the coeicient A an B control the variation o the orosity. When the B is negative, it means that the orosity ecreases along the low irection, however it increase when B is ositive Bounary conitions The incient raiation lux qin which is concentrate by a heliostat iel can be resente by: 2 qin 1MW/m (19) Raiation heat loss between the receiver s surace an environment can be reresente by: 4 4 loss s,in e q T T (20) The temerature o the inlet lui, T,in is the same as the environment temerature Te which is taken as T,in Te 300K (21) For the outlet bounary, an aiabatic bounary conition is use: T s x T x xl xl 0 0 (22) (23) the iuse raiative lux can be neglecte hence the raiative bounary conitions or the

5 inlet an outlet are as ollows: G x x0 G x xl 0 3 Numerical roceure (24) Using a Finite Volume Metho, Governing equations are iscretize using a SIMPLE algorithm. The iscretization scheme is base on a uniorm gri set u an a cell centere scheme. Furthermore, 1st orer uwin ierencing metho is emloye to iscretize the convective terms. The convergence is consiere to have been reache when the relative variation o temerature between consecutive iterations is smaller than 10-8 or all the gri oints in the comutational omain. 4 Results an iscussion irraiation attenuation ecreases sharly along the incient irection o the orous meia. This art can be taken as the volumetric energy source istribute in the orous meia. Hence, with its ecrease the heat lux absorbe by the orous meia ecreases. However the iuse raiative q increases irst an then ecrease slightly, this is because the iuse raiative lux q eenent on not only the soli temerature Ts but also the istribution o the incient irraiation qc. For the conuctive heat lux qs in the soli hase (see Fig. 3a, 3b), the eect o the orosity on its istribution has a reverse rule comare to that on the iuse raiative lux. This shows the limiting interactions between thermal raiation an conuction. When comaring the Fig 3a, 3b we can also oun that the conuctive heat lux qs ecreases slightly at the irraiate surace. 4.1 Increasing orosity Fig. 2 eicts the istribution o lui an soli temerature T an Ts an heat lux q or ierent value o orosity with constant ore iameter =2mm, inlet air velocity Uin=0.5m/s an incient raiation q0=1mw. As execte in the Fig. 2a an 2b, the temerature Ts along the x irection or the soli hase is ecrease in the incient irection, however, or the lui hase temerature, it increases along the x irection. It can be seen that the soli temerature Ts at the irraiate surace greatly ecreases when using the variable orosity material along the x irection. Ts ecreases nearly 50K when the control arameters A =0.9 an B =-0.3. The outlet air temerature at the back wall o the absorber increases when using the variable orosity material, this is because that the lower surace temerature ecreases the raiative loss, consequently the eiciency increase accoringly. Fig. 3a, an 3b resent that both o the variation value o the extinct collimate raiative lux qc, iuse raiative lux q an conuctive heat lux qs along the x irection. It can be seen that the incient raiative energy here we assume as the graient o the collimate (a) Variable orosity (b) Constant orosity Fig. 2: Eect o the orosity on the temerature an heat lux in the x irection (A =0.9, B =-0.3)

6 Fig. 4: Eect o the orosity on the temerature an heat lux in the X irection (A =0.9, B =-0.3) (a) Variable orosity (b) Constant orosity Fig. 3: Eect o the orosity on the heat lux in the x irection (A =0.9, B =-0.3) 4.2 Decreasing orosity (a) Variable orosity (b)constant orosity (a) Variable orosity (b) Constant orosity Fig. 5: Eect o the orosity on the heat lux in the X irection (A =0.9, B =-0.3) Fig. 4 an 5 eicts the istribution o lui an soli temerature T an Ts an heat lux q or ierent arrangement o orosity with constant ore iameter =2mm, inlet air velocity Uin=0.5m/s an incient raiation q0=1mw. For this case, in the Fig. 4a an 4b, It can be seen that the soli temerature Ts at the irraiate surace greatly increases when using the variable orosity material along the x irection. Ts increases nearly 20K when the control arameters A =0.6 an B =0.3. The outlet air temerature at the back wall o the absorber ecreases when using the variable orosity material, this is because that the lower surace temerature increases the raiative loss, consequently the eiciency ecrease accoringly. When comaring the Fig 5a an 5b we can also oun that the conuctive heat lux qs ecreases more slightly at the irraiate

7 surace or the variable orosity, which is ue to the high temerature graient o the soli hase with variable orosity eect. CONCLUSIONS Convective an raiative transort in a air receiver using orous meia in the resence o collimate irraiation an local thermal nonequilibrium is analyze in this work. A moiie P-1 aroximation with collimate irraiation was introuce to incororate the raiative transer. We analyze the istribution o the temerature o the lui an soli hase, also the heat lux in the incient irection was resente. Base on our analysis, it can be seen that the incient raiative energy i.e. the collimate irraiation attenuation sharly along the incient irection o the orous meia. The temerature Ts along the x irection is ecrease or the soli hase but increases or the lui hase temerature along the x irection. The iuse raiative q increases irst an then ecrease, this is because the iuse raiative lux not only eenent on the soli temerature but also the istribution o the incient irraiation i.e. the extinction art o collimate irraiation qc. Lower soli temerature can be achieve by using a variable orosity. The orosity an ore iameter has a non-monotonic eect on the thermal eiciency o the receiver, otimization can be achieve by urther arameters analysis. ACKNOWLEDGEMENT The suort o the National Natural Science Founation o China (No ), Natural Science Founation o Jiangsu Province (No.BK ). The authors also grateully acknowlege the inancial suort rom the National High-tech R&D Program o China (863 Program) o Chinese Science an Technology Deartment uner Project Numbers No. 2007AA05Z445. Flamant G, Olale G "High temerature solar gas heating comarison between acke an luiize be receivers I," Solar Energy, vol. 31, Hsu P, Howell JR 1992."Measurement o thermal conuctivity an otical roerties o orous artially stabilize zirconia," Exerimental Heat Transer, vol. 5, Mohanraj R et. al "Measurements o raiative roerties o cellular ceramics at high temeratures," Journal o Thermohysics an Heat Transer, vol. 10, Singh BP, Kaviany M "Ineenent theory versus irect simulation o raiation heat transer in acke bes," International Journal o Heat an Mass Transer, vol. 34, Tien CL "Thermal-Raiation in Packe an Fluiize-Bes," Journal o Heat Transer ASME, vol. 110, Wang P, Vaai K, an Liu DY "Analysis o Raiative Eect uner Local Thermal Non- Equilibrium Conitions in Porous Meia- Alication to a Solar Air Receiver," Numerical Heat Transer Part a-alications, vol. 65, Wang P, Vaai K, an Liu DY 2015 "Analysis o collimate irraiation uner local thermal nonequilibrium conition in a acke be," International Journal o Heat an Mass Transer, vol. 80, Yang K, Vaai K "Analysis o temerature graient biurcation in orous meia - An exact solution," International Journal o Heat an Mass Transer, vol. 53, REFERENCES Aacutevila AL "Volumetric receivers in Solar Thermal Power Plants with Central Receiver System technology: A review," Solar Energy, vol. 85, Alazmi B, Vaai K "Analysis o Variants Within the Porous Meia Transort Moels," Journal o Heat Transer, vol. 122,