An Air-Based Cavity-Receiver for Solar Trough Concentrators

Roman Bader1, Maurizio Barbato2, Andrea Pedretti3, Aldo Steinfeld1,4,* 1 Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland

2 Department of Innovative Technologies, SUPSI, 6928 Manno, Switzerland 3 Airlight Energy Holding SA, 6710 Biasca, Switzerland

4

Solar Technology Laboratory, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland

Abstract

A cylindrical cavity-receiver containing a tubular absorber that uses air as the heat transfer fluid is proposed for a novel solar trough concentrator design. A numerical heat transfer model is developed to determine the receiver’s absorption efficiency and pumping power requirement. The 2D steady-state energy conservation equation coupling radiation, convection and conduction heat transfer is formulated and solved numerically by finite volume techniques. The Monte Carlo ray-tracing and radiosity methods are applied to establish the solar radiation distribution and radiative exchange within the receiver. Simulations were conducted for a 50 m-long and 9.5 m-wide collector section with 120°C air inlet temperature, and air mass flows in the range 0.1 – 1.2 kg/s. Outlet air temperatures ranged from 260 to 601 °C, and corresponding absorption efficiencies varied between 60 and 18 %. Main heat losses integrated over the receiver length were due to reflection and spillage at the receiver’s windowed aperture, amounting to 13% and 9% of the solar power input, respectively. The pressure drop along the 50 m module was in the range 0.23 to 11.84 mbar, resulting in isentropic pumping power requirements of 46.45 10−⋅ % - 0.395 % of the solar power input.

1 Introduction

Tubular receivers are typically used in line-focusing solar concentrator systems (e.g. parabolic troughs) to efficiently absorb incident solar radiation through the application of selective coatings and vacuum insulations. However, when the heat transfer fluid (HTF) has low 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 flow cross-section without significantly affecting the reradiation losses from the absorber. Cylindrical cavity-receivers have been previously analyzed for an annular flow cross-section [1], and for a cavity containing a single absorber tube or an array of absorber tubes [2-4].

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; 2) 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 air, eliminating the need for a heat exchanger between 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 lower fabrication costs per unit receiver length are expected than those for existing receivers. On the other hand, the disadvantages of air-receivers are associated with the larger mass flow rates and surface area needed due to the lower volumetric heat capacity and thermal conductivity of air as compared to those of thermo-oils, molten salts, sodium, or other heat transfer fluids proposed. These drawbacks translate into higher pressure drops and concomitant energy penalties. In this paper, a numerical heat transfer model of an air-based cylindrical cavity-receiver is developed and applied to investigate the

* Corresponding author: aldo.steinfeld@ethz.ch

influence of air mass flow rate on outlet air temperature, receiver’s absorption efficiency, pumping power requirements, and thermal losses [5].

2 Receiver design

The cavity-receiver configuration is shown 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 air gap at ambient pressure. The cavity is lined by a layer of mineral wool insulation, encapsulated in a thin aluminum shell. The rectangular cavity aperture area matches the focal plane of the solar trough concentrator and is closed by a quartz window to reduce reradiation and convection heat losses. The receiver dimensions are listed in Table 1.

Fig. 1: Cross-sectional view of the cavity-receiver configuration: 1-absorber inner surface, 2-absorber outer surface, 3-cavity inner surface, 4-window inner surface, 5-window outer surface, 6-shell outer

surface.

absorber inner radius absorberR 0.125 cavity inner radius cavityR 0.3 absorber wall thickness absorberd 31.5 10−⋅ cavity inner wall thickness Id 31.5 10−⋅ insulation thickness IId 0.1 shell thickness IIId 31 10−⋅ cavity aperture width apertureb 0.1 window thickness windowd 35.43 10−⋅ eccentricity ε 0.03

Table 1: Cavity-receiver dimensions shown in Fig. 1 in (m).

3 Heat transfer model

Steady-state energy conservation is given by:

solar l,reflection l,reradiation l,convection useful 0Q Q Q Q Qγ − − − − = (1)

where solarQ is the concentrated solar radiation incident on the receiver, γ is the intercept factor defined as the ratio of solar radiation intercepted by the receiver aperture to that incident on the receiver, l,reflectionQ is the

solar radiation lost to the environment after one or multiple reflections at surfaces 2-5, l,reradiationQ is the energy loss by radiation emitted by surfaces 2, 3, 5 and 6, l,convectionQ is the convective heat loss from surfaces 5 and 6, and usefulQ is the energy gain, carried away by the heat transfer fluid.

Conductive heat transfer – 2D steady-state energy conservation applied to the solid domains (absorber, cavity, and window) of the receiver reduces to:

( ) 0k T∇⋅ =∇ (2)

The boundary condition at the surfaces of the solid domains requires:

convection radiationsˆk T n q q∇ ⋅ = + (3)

where n̂ denotes the surface normal vector, and convectionq and radiationq are the net surface energy fluxes by convection and radiation. Finite volume techniques are applied to solve the energy equation. [6] Temperature dependent thermal conductivities are used for AISI430 stainless steel [7], for mineral wool 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 flow [10], natural convection between nested cylinders [11], and natural convection around horizontal cylinders [12].

Radiative heat transfer – Radiative exchange results from: i) absorbed solar radiation at surfaces 2, 3 and window, and ii) net radiative heat exchange among surfaces 1-6 and the environment. Hence, the boundary heat flux by radiation is:

radiation reradiation solarq q q= − (4)

Concentrated solar 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 shown schematically in Fig. 2a, 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 shown in Fig. 2b, 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. 2a) 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

concentrator 3.5f = m, rim angle rim 73.6φ = ° .

Monte Carlo ray-tracing is applied to determine intercept factor γ , reflection losses l,reflectionQ , and solar radiation absorbed by surfaces 2, 3, and the window [14]. Surfaces 1 to 3, and 6 are assumed gray-diffuse with uniform surface properties and temperature on each segment. Spectral directional transmittance w,T λ′ , reflectance w,R λ′ and absorptance w,B λ′ of the quartz window are calculated based on the spectral complex refractive index [14-15]. Radiative heat exchange among surfaces 1-4 and the environment is calculated by applying the enclosure theory (radiosity method) comprising opaque surfaces and semi-transparent windows [14]:

( ) ( )( )reradiation, 4w,

1 11

N Ni i

ki k i i k i i ki ii ii i

q EF R F T T

B Bδ δ σ− −

= =

− = − +∑ ∑ (5)

where:

1, if

0 otherwiseki

k iδ

==

reradiation,iq is the radiosity, indices k and i denote surface segments on surfaces 1-4, k iF − is the configuration factor from segment k to segment i , determined with Monte Carlo ray-tracing, σ is the Stefan-Boltzmann constant. For opaque surface segments w,iT = 0. Hemispherical total window transmittance wT , reflectance

wR , absorptance wB , and emittance wE used in Eq. (5) are calculated by integrating directional spectral quantities [14]. Radiative heat losses from surfaces 5 and 6 are calculated from:

( )4 4l,reradiation,5,6 skyq E T Tσ= − (6)

where E and T are surface emissivity and temperature.

Pumping power requirement – Pressure drop airp∆ of the air flow between receiver inlet and outlet is calculated from [8]:

( )( ) ( )( )receiver receiver

2airair air air air air

absorber0 0

14

l lpp dx f T U T dxx xx R

ρ∂

∆ = =∂∫ ∫ (7)

where f is the friction factor (Moody diagram), airρ is the air density, airU is the mean air flow velocity,

airT is the local air temperature, and receiverl is the receiver length. The mechanical power p,sW required for compression of air from atmospheric pressure p∞ to receiver inlet pressure air,in airp p p∞= + ∆ is calculated assuming isentropic compression of an ideal gas.

Absorption efficiency – The absorption efficiency of the receiver is defined as:

usefulabsorption

solar

QQ

η = (8)

4 Simulation results

The baseline parameters are given in Table 4. For the receiver dimensions of Table 1, solar 289Q = kW. The ideal radiative flux at the receiver aperture, shown in Fig. 2b, is reduced by 13.4% due to solar incidence angle skew 30θ = ° , 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 skew radiation and other concentrator imperfections are omitted from consideration. Air mass

flow rates were varied in the range 0.1 1.2− kg/s. The integration step along the receiver axis is 1 m. Energy balance, Eq. (1), is used as the convergence criterion in each 2D simulation step, with maximum residuum

1< %.

Direct normal insolation ( )2sun W mI 850

Solar incidence angle ( )skew degθ 30 Air inlet temperature ( )air,in °CT 120 Air inlet pressure ( )air,in barp 1.0 Ambient air temperature ( )°CT∞ * 60 Apparent sky temperature ( )sky °CT 1.85 Emissivity surface 1 1ε 0.8 Emissivity surface 2 2ε 0.9 Emissivity surface 3 3ε 0.1 Emissivity surface 6 6ε 0.1 Concentrator length ( )concentrator ml 50 Net concentrator aperture area ( )2

concentrator mA 475 * The receiver is contained in the gas tight chamber of an inflated polymer

membrane concentrator containing air at elevated temperature.

Table 4: Baseline parameters.

The outlet air temperature air,outT , receiver absorption efficiency absorptionη , and mechanical pumping power requirement p,sW are shown as a function of the air mass flow rate airm in Fig. 3. As airm increases from 0.1 to 1.2 kg/s, air,outT decreases from 601 to 260 °C, absorptionη increases from 17.6 to 59.7%, and p,sW increases from 1.9 W to 1.14 kW ( 3

p,s airW U∝ ). Fig. 4 shows the thermal losses from the receiver, normalized by

solar 289Q = kW. The white portions of the bars represent absorptionη . Temperature independent losses are: 8.7 % incoming radiation spilled at the aperture, 12.7 % reflection losses at the window, and 3.4 % reflection losses from surfaces 2 and 3 to the environment. As airm is reduced from 1.2 to 0.1 kg/s, temperature dependent losses change in the following ranges: reradiation losses from surfaces 2 and 3 to the environment: 0.83 - 14.7 %, reradiation from surface 6 to the environment: 2.8 - 6.4 %, reradiation from the window to the environment: 5.5 - 15.7 %, convection losses at the receiver outer surface: 4.9 - 16.4 %, convection losses at the window outer surface: 1.8 - 4.2 %. Overall, the temperature dependent losses increase from 15.8 % at

air 1.2m = kg/s to 57.4 % at air 0.1m = kg/s. The local absorption efficiency absorption,local useful solarQ Qη ′ ′= as a function of local air temperature is shown in Fig. 5 for air mass flow rates in the range 0.2 – 1.2 kg/s, and compared to that of a commercial Schott PTR70 receiver. [16] The decrease in absorption efficiency with decreasing mass flow rate is due to the decreasing convective heat transfer between absorber tube and air. The absorption efficiency of the current non-optimized air receiver falls short by 14.6 – 48.6 % points compared to the Schott receiver.

Fig. 3: Air outlet temperature air,outT , receiver absorption efficiency absorptionη , and mechanical pumping power requirement p,sW , for are mass flow rates in the range 0.1 – 1.2 kg/s.

Fig. 4: Heat flows by modes in %, normalized by the total concentrated incident solar power solarQ ; the diagram reports the useful energy gain and specifies the different contributions to energy losses

for air mass flow rates in the range 0.1-1.2 kg/s.

Fig. 5: Local absorption efficiency as a function of the local air temperature; parameter is the air mass flow rate; for comparison, the absorption efficiency of a commercial Schott PTR70 receiver is shown.

[17]

5 Summary and Outlook

We examined a new design of an air-based receiver for solar trough concentrators that features a tubular absorber contained in an insulated cavity, with a rectangular aperture closed by a quartz window. Numerical heat transfer simulations were conducted for a 50 m-long and 9.5 m-wide collector section, with fixed inlet air temperature 120°C. As the air mass flow rate was varied in the range 0.1 – 1.2 kg/s, outlet air temperatures decreased from 601 to 260 °C, absorption efficiencies increased from 18 to 60 %, and isentropic pumping power requirements increased from 1.9 W to 1.14 kW. Main energy losses were caused by incoming solar radiation being spilled and reflected at the receiver aperture. With decreasing mass flow rates and, consequently, 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 window, and by incorporating a secondary concentrator at the cavity aperture.

Acknowledgments

This study has been funded by Airlight Energy Holding SA.

Nomenclature

concentratorA ( )2m net concentrator aperture area

apertureb ( )2m cavity aperture width

B ( )- absorptance

Id cavity inner wall thickness ( )m IId cavity insulation thickness ( )m IIId shell thickness ( )m absorberd ( )m absorber wall thickness

windowd ( )m window thickness

dx ( )m receiver length increment

E ( )- emittance

f Moody friction factor ( )-

concentratorf ( )m focal length of concentrator

k iF − k configuration factor from surface segments to i ( )-

i ( )- index

sunI ( )2W m direct normal insolation

k ( )W mK thermal conductivity ;

( )- index

l ( )m length

airm ( )kg s air mass flow rate

N ( )- total number of surface segments on surfaces 1-4

n̂ ( )- unit surface normal vector

p ( )Pa pressure

airp∆ ( )Pa pressure drop in air flow between receiver inlet and outlet

airp x∂ ∂ local pressure gradient in receiver ( )Pa m

convectionq surface heat flux by convection ( )2W m

lq ( )2W menergy loss per unit time and per unit surface area

lQ ( )Wenergy loss per unit time from the receiver

radiationq surface heat flux by radiation ( )2W m

reradiationq radiosity ( )2W m

solarq solar energy absorbed by surface ( )2W m

solarQ ( )Wtotal concentrated solar power incident onto the receiver

usefulQ ( )Wtotal energy gain by the heat transfer fluid per unit time

R ( )- reflectance

absorberR ( )mabsorber inner radius

airR ( )J kgK specific gas constant of air

cavityR ( )mcavity inner radius

T temperature ( )°C,K

wT ( )-transmittance

airU mean air flow velocity ( )m s

pW ( )W pumping power requirement , ,x y z Cartesian coordinates

x∗ dummy variable Greek symbols

kiδ 1 if , else 0ki kik iδ δ= = = Dirac function, ( )- ε ( )m eccentricity;

( )- emissivity

rimφ ( )deg concentrator rim angle

γ ( )- intercept factor

absorptionη receiver absorption efficiency ( )-

skewθ ( )deg solar incidence angle

airρ ( )3kg m air density

σ Stefan-Boltzmann constant ( )2 4W m K

Subscripts 1,2,... surfaces a annulus in inlet s isentropic; surface w window ∞ ambient λ spectral

Superscript ' directional; energy flow per unit receiver length Abbreviations CCT compound circular trough HTF heat transfer fluid

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