An Air-Based Cavity-Receiver for Solar Trough Concentrators

Transcription

1 An Air-Based Cavity-eceiver for Solar Trough Concentrators oman Bader 1, Maurizio Barbato, Andrea Pedretti 3, Aldo Steinfeld 1,4,* 1 Department of Mechanical and Process Engineering, ETH Zurich, 809 Zurich, Sitzerland Department of Innovative Technologies, SUPSI, 698 Manno, Sitzerland 3 Airlight Energy Holding SA, 6710 Biasca, Sitzerland 4 Solar Technology Laboratory, Paul Scherrer Institute, 53 Villigen PSI, Sitzerland Abstract A cylindrical cavity-receiver containing a tubular absorber that uses as the heat transfer fluid is proposed for a novel trough concentrator design. A numerical heat transfer model is developed to determine the receiver s absorption efficiency and pumping poer reuirement. The D steady-state energy conservation euation coupling radiation, convection and conduction heat transfer is formulated and solved numerically by finite volume techniues. The Monte Carlo ray-tracing and radiosity methods are applied to establish the radiation distribution and radiative exchange ithin the receiver. Simulations ere conducted for a 50 m-long and 9.5 m-ide collector section ith 10 C inlet temperature, and mass flos in the range kg/s. Outlet temperatures ranged from 60 to 601 C, and corresponding absorption efficiencies varied beteen 60 and 18 %. Main heat losses integrated over the receiver length ere due to reflection and spillage at the receiver s indoed aperture, amounting to 13% and 9% of the poer input, respectively. The pressure drop along the 50 m module as in the range 0.3 to mbar, resulting in isentropic pumping poer reuirements of % % of the poer input. 1 Introduction Tubular receivers are typically used in line-focusing concentrator systems (e.g. parabolic troughs) to efficiently absorb incident radiation through the application of selective coatings and vacuum insulations. Hoever, hen the heat transfer fluid (HTF) has lo volumetric heat capacity and thermal conductivity, as it is usually the case for gases, cavity-receivers are an interesting alternative to conventional tube receivers, as they offer the potential for larger heat transfer area and flo cross-section ithout significantly affecting the reradiation losses from the absorber. Cylindrical cavity-receivers have been previously analyzed for an annular flo cross-section [1], and for a cavity containing a single absorber tube or an array of absorber tubes [-4]. Air is used as the HTF in the present case. The advantages are four-fold: 1) performance loss and operating temperature constraints due to chemical instability of the HTF are avoided; ) operating pressure can be close to ambient, eliminating the need for sophisticated sealing; 3) a packed-bed thermal storage can be incorporated to the system and heated directly by, eliminating the need for a heat exchanger beteen HTF and thermal storage medium; and 4) costs for the heat transfer fluid are removed. Further, by employing conventional materials of construction and avoiding selective absorber coatings, vacuum insulation, or getters, significantly loer fabrication costs per unit receiver length are expected than those for existing receivers. On the other hand, the disadvantages of -receivers are associated ith the larger mass flo rates and surface area needed due to the loer volumetric heat capacity and thermal conductivity of as compared to those of thermo-oils, molten salts, sodium, or other heat transfer fluids proposed. These drabacks translate into higher pressure drops and concomitant energy penalties. In this paper, a numerical heat transfer model of an -based cylindrical cavity-receiver is developed and applied to investigate the * Corresponding author: aldo.steinfeld@ethz.ch

2 influence of mass flo rate on outlet temperature, receiver s absorption efficiency, pumping poer reuirements, and thermal losses [5]. eceiver design The cavity-receiver configuration is shon schematically in Fig. 1. It consists of a cylindrical cavity containing an eccentric absorber tube. Cavity and absorber are made of stainless steel, and separated by an annular gap at ambient pressure. The cavity is lined by a layer of mineral ool insulation, encapsulated in a thin aluminum shell. The rectangular cavity aperture area matches the focal plane of the trough concentrator and is closed by a uartz indo to reduce reradiation and convection heat losses. The receiver dimensions are listed in Table 1. Fig. 1: Cross-sectional vie of the cavity-receiver configuration: 1-absorber inner surface, -absorber outer surface, 3-cavity inner surface, 4-indo inner surface, 5-indo outer surface, 6-shell outer surface. absorber inner radius cavity inner radius absorber all thickness d absorber cavity inner all thickness d I absorber 0.15 cavity insulation thickness d II 0.1 shell thickness d III cavity aperture idth b aperture 0.1 indo thickness d indo eccentricity ε Table 1: Cavity-receiver dimensions shon in Fig. 1 in (m). 3 Heat transfer model Steady-state energy conservation is given by: γ Q Ql,reflection Ql,reradiation Ql,convection Quseful = 0 (1) here Q is the concentrated radiation incident on the receiver, γ is the intercept factor defined as the ratio of radiation intercepted by the receiver aperture to that incident on the receiver, Q is the l,reflection

3 radiation lost to the environment after one or multiple reflections at surfaces -5, Q l,reradiation is the energy loss by radiation emitted by surfaces, 3, 5 and 6, Q l,convection is the convective heat loss from surfaces 5 and 6, and Q useful is the energy gain, carried aay by the heat transfer fluid. Conductive heat transfer D steady-state energy conservation applied to the solid domains (absorber, cavity, and indo) of the receiver reduces to: ( k T) 0 = () The boundary condition at the surfaces of the solid domains reuires: k T nˆ = + (3) s convection radiation here ˆn denotes the surface normal vector, and convection and radiation are the net surface energy fluxes by convection and radiation. Finite volume techniues are applied to solve the energy euation. [6] Temperature dependent thermal conductivities are used for AISI430 stainless steel [7], for mineral ool insulation material and fused silica [8], and for commercial aluminum alloy Al-6061-T6 [9]. Convective heat transfer Pertinent Nu-correlations from literature are applied to calculate the convective heat transfer coefficients for turbulent pipe flo [10], natural convection beteen nested cylinders [11], and natural convection around horizontal cylinders [1]. adiative heat transfer adiative exchange results from: i) absorbed radiation at surfaces, 3 and indo, and ii) net radiative heat exchange among surfaces 1-6 and the environment. Hence, the boundary heat flux by radiation is: radiation = reradiation (4) Concentrated radiation focused onto the receiver is obtained by a trough concentrator based on aluminized polymer mirror foils mounted on a precast concrete frame [13]. The mirror foils are pneumatically spanned to form a concentrator profile as shon schematically in Fig. a, consisting of an array of adjacent circular segments that approximates a parabola. The resulting radiative flux distribution at the focal plane of this compound circular trough (CCT) concentrator is shon in Fig. b, and compared to that of the underlying ideal parabolic trough concentrator. Both distributions are determined by Monte Carlo ray-tracing, neglecting mirror surface errors and reflection losses. Fig. a) Half profile of the compound circular trough (CCT) concentrator, b) Simulated radiative flux distribution at the focal plane of CCT and ideal parabolic trough concentrators. Focal length f = m, rim angle φ rim = concentrator 3.5

4 Monte Carlo ray-tracing is applied to determine intercept factor γ, reflection losses Q l,reflection, and radiation absorbed by surfaces, 3, and the indo [14]. Surfaces 1 to 3, and 6 are assumed gray-diffuse ith uniform surface properties and temperature on each segment. Spectral directional transmittance T, λ, reflectance, λ and absorptance B, λ of the uartz indo are calculated based on the spectral complex refractive index [14-15]. adiative heat exchange among surfaces 1-4 and the environment is calculated by applying the enclosure theory (radiosity method) comprising opaue surfaces and semi-transparent indos [14]: here: N reradiation, N i i ( δ ) ( ( ) ) 4 Fk ii = Fk i T, i 1 + δ σti (5) B i= 1 i i= 1 1, if k = i δ = 0 otherise E B i reradiation,i is the radiosity, indices k and i denote surface segments on surfaces 1-4, Fk iis the configuration factor from segment k to segment i, determined ith Monte Carlo ray-tracing, σ is the Stefan-Boltzmann constant. For opaue surface segments T,i = 0. Hemispherical total indo transmittance T, reflectance, absorptance B, and emittance E used in E. (5) are calculated by integrating directional spectral uantities [14]. adiative heat losses from surfaces 5 and 6 are calculated from: l,reradiation,5,6 4 4 ( sky ) = Eσ T T (6) here E and T are surface emissivity and temperature. Pumping poer reuirement Pressure drop calculated from [8]: p of the flo beteen receiver inlet and outlet is l receiver receiver p 1 p = dx = f ρ ( T ( x) ) U ( T ( x) ) dx x 4 0 absorber 0 l (7) here f is the friction factor (Moody diagram), ρ is the density, U is the mean flo velocity, T is the local temperature, and l receiver is the receiver length. The mechanical poer W p,s reuired for compression of from atmospheric pressure p to receiver inlet pressure p,in = p + p is calculated assuming isentropic compression of an ideal gas. Absorption efficiency The absorption efficiency of the receiver is defined as: Q useful η absorption = (8) Q 4 Simulation results The baseline parameters are given in Table 4. For the receiver dimensions of Table 1, Q = 89 kw. The ideal radiative flux at the receiver aperture, shon in Fig. b, is reduced by 13.4% due to incidence angle θ ske = 30, by 8.5% due to transmission losses introduced by the concentrator top membrane, and by an additional 6.3% due to reflection losses on the mirrors. Peak concentration is reduced to 135 suns. End effects due to ske radiation and other concentrator imperfections are omitted from consideration. Air mass

5 flo rates ere varied in the range kg/s. The integration step along the receiver axis is 1 m. Energy balance, E. (1), is used as the convergence criterion in each D simulation step, ith maximum residuum < 1 %. Direct normal insolation sun ( Wm) Solar incidence angle ( deg) ske I 850 θ 30 Air inlet temperature T,in ( C) 10 Air inlet pressure p,in ( bar) 1.0 Ambient temperature T ( C) * 60 Apparent sky temperature T sky ( C) 1.85 Emissivity surface 1 ε Emissivity surface ε 0.9 Emissivity surface 3 ε Emissivity surface 6 ε Concentrator length l concentrator ( m) 50 Net concentrator aperture area A ( concentrator m ) 475 * The receiver is contained in the gas tight chamber of an inflated polymer membrane concentrator containing at elevated temperature. Table 4: Baseline parameters. The outlet temperature T,out, receiver absorption efficiency η absorption, and mechanical pumping poer reuirement W p,s are shon as a function of the mass flo rate m in Fig. 3. As m increases from 0.1 to 1. kg/s, T,out decreases from 601 to 60 C, η absorption increases from 17.6 to 59.7%, and W p,s increases 3 from 1.9 W to 1.14 kw ( Wp,s U ). Fig. 4 shos the thermal losses from the receiver, normalized by Q = 89 kw. The hite portions of the bars represent η absorption. Temperature independent losses are: 8.7 % incoming radiation spilled at the aperture, 1.7 % reflection losses at the indo, and 3.4 % reflection losses from surfaces and 3 to the environment. As m is reduced from 1. to 0.1 kg/s, temperature dependent losses change in the folloing ranges: reradiation losses from surfaces and 3 to the environment: %, reradiation from surface 6 to the environment: %, reradiation from the indo to the environment: %, convection losses at the receiver outer surface: %, convection losses at the indo outer surface: %. Overall, the temperature dependent losses increase from 15.8 % at m = 1. kg/s to 57.4 % at m = 0.1kg/s. The local absorption efficiency η absorption,local = Q useful Q as a function of local temperature is shon in Fig. 5 for mass flo rates in the range kg/s, and compared to that of a commercial Schott PT70 receiver. [16] The decrease in absorption efficiency ith decreasing mass flo rate is due to the decreasing convective heat transfer beteen absorber tube and. The absorption efficiency of the current non-optimized receiver falls short by % points compared to the Schott receiver.

6 Fig. 3: Air outlet temperature T,out, receiver absorption efficiency η absorption, and mechanical pumping poer reuirement W, for are mass flo rates in the range kg/s. p,s Fig. 4: Heat flos by modes in %, normalized by the total concentrated incident poer Q ; the diagram reports the useful energy gain and specifies the different contributions to energy losses for mass flo rates in the range kg/s. Fig. 5: Local absorption efficiency as a function of the local temperature; parameter is the mass flo rate; for comparison, the absorption efficiency of a commercial Schott PT70 receiver is shon. [17]

7 5 Summary and Outlook We examined a ne design of an -based receiver for trough concentrators that features a tubular absorber contained in an insulated cavity, ith a rectangular aperture closed by a uartz indo. Numerical heat transfer simulations ere conducted for a 50 m-long and 9.5 m-ide collector section, ith fixed inlet temperature 10 C. As the mass flo rate as varied in the range kg/s, outlet temperatures decreased from 601 to 60 C, absorption efficiencies increased from 18 to 60 %, and isentropic pumping poer reuirements increased from 1.9 W to 1.14 kw. Main energy losses ere caused by incoming radiation being spilled and reflected at the receiver aperture. With decreasing mass flo rates and, conseuently, increasing receiver temperatures, convection losses at the cavity outer surface and reradiation losses became predominant. Higher receiver s absorption efficiency is achievable by optimizing the receiver geometry, improving the cavity insulation, applying selective coatings to the aperture indo, and by incorporating a secondary concentrator at the cavity aperture. Acknoledgments This study has been funded by Airlight Energy Holding SA. Nomenclature A concentrator net concentrator aperture area ( m ) aperture cavity aperture idth m b ( ) B absorptance (-) di cavity inner all thickness ( m) dii cavity insulation thickness ( m) diii shell thickness ( m) d absorber absorber all thickness ( m) d indo indo thickness ( m) dx receiver length increment ( m) E emittance (-) f Moody friction factor (-) f concentrator focal length of concentrator ( m) Fk i configuration factor from surface segments k to i (-) i index (-) I sun direct normal insolation ( Wm) k thermal conductivity ( W mk) ; index (-) l length ( m) m mass flo rate ( kg s) N total number of surface segments on surfaces 1-4 (-) ˆn unit surface normal vector (-) p pressure ( Pa)

8 p pressure drop in flo beteen receiver inlet and outlet ( Pa) p x local pressure gradient in receiver ( Pa m) convection surface heat flux by convection ( Wm) l energy loss per unit time and per unit surface area ( Wm) Q energy loss per unit time from the receiver ( W) l radiation surface heat flux by radiation ( Wm) reradiation radiosity ( Wm ) energy absorbed by surface ( Wm) Q total concentrated poer incident onto the receiver ( W) Q useful total energy gain by the heat transfer fluid per unit time ( W) reflectance (-) absorber absorber inner radius ( m) specific gas constant of ( J kgk) cavity cavity inner radius ( m) T temperature ( C,K) T transmittance (-) U mean flo velocity ( ms ) W pumping poer reuirement ( W) p xyz,, x Cartesian coordinates dummy variable Greek symbols δ δ = 1 if k = i, else δ = 0 Dirac function, (-) ε eccentricity; ( m) emissivity (-) φ rim concentrator rim angle ( deg) γ intercept factor (-) η absorption receiver absorption efficiency (-) θ incidence angle ( deg) ske 3 ρ density ( kg m ) 4 σ Stefan-Boltzmann constant ( WmK ) Subscripts 1,,... surfaces a annulus in inlet s isentropic; surface indo ambient λ spectral

9 Superscript ' Abbreviations CCT HTF directional; energy flo per unit receiver length compound circular trough heat transfer fluid eferences [1] Boyd D.A., Gajes., 1976, Sift., A cylindrical blackbody energy receiver, Solar Energy, 18, pp [] Melchior T., Steinfeld A., 008, adiative transfer ithin a cylindrical cavity ith diffusely/specularly reflecting inner alls containing an array of tubular absorbers, ASME Journal of Solar Energy Engineering, 130, pp [3] Melchior T., Perns C., Weimer, A.W., Steinfeld A., 008, A cavity-receiver containing a tubular absorber for high-temperature thermochemical processing using concentrated energy, Int. Journal of Thermal Sciences, 47, pp [4] Barra O.A., Franceschi L., 198, The parabolic trough plants using black body receivers: Experimental and theoretical analyses, Solar Energy, 8, pp [5] Bader., Barbato M., Pedretti A., Steinfeld A., An Air-Based Cavity-eceiver for Solar Trough Concentrators, ASME Journal of Solar Energy Engineering, in press. [6] Patankar S.V., 1980, Numerical Heat Transfer and Fluid Flo, Hemisphere Publishing Corp. [7] [8] Incropera F.P., and DeWitt D.P., 00, Fundamentals of Heat and Mass Transfer, 5th ed., John Wiley & Sons. [9] Mills K.C., 00, ecommended Values of Thermophysical Properties for Selected Commercial Alloys, Woodhead Publishing Ltd, Cambridge. [10] Gnielins, V., 1976, Int. Chemical Engineering, 16, p [11] Kuehn T.H., and Goldstein.J., 1978, An Experimental Study of Natural Convection Heat Transfer in Concentric and Eccentric Horizontal Cylindrical Annuli, ASME Journal of Heat Transfer, 100, pp [1] Churchill S.W., and Chu H.H.S., 1975, Correlating euations for laminar and turbulent free convection from a horizontal cylinder, Int. Journal of Heat and Mass Transfer, 18, pp [13] Bader., Haueter P., Pedretti A., Steinfeld A., Optical design of a novel to-stage trough concentrator based on pneumatic polymeric structures, ASME Journal of Solar Energy Engineering, 131, (009). [14] Siegel., and Hoell J., 00, Thermal adiation Heat Transfer, 4th ed., Taylor&Francis, Ne York. [15] Palik E.D., 1998, Handbook of Optical Constants of Solids, Academic Press. [16] Burkholder F., Kutscher C., 009, Heat Loss Testing of Schott's 008 PT70 Parabolic Trough eceiver, Tech. eport NEL/TP