Band-approximated Radiative Heat Transfer Analysis Of A Solar Chemical Reactor For The Thermal Dissociation Of Zinc Oxide

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Solar Energy 81 (2007) 1285–1294 www.elsevier.com/locate/solener

Band-approximated radiative heat transfer analysis of a solar chemical reactor for the thermal dissociation of zinc oxide Reto Mu¨ller a, A. Steinfeld b

a,b,*

a Solar Technology Laboratory, Paul Scherrer Institute, 5232 Villigen, Switzerland Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland

Received 27 April 2006; received in revised form 11 December 2006; accepted 26 December 2006 Available online 14 February 2007 Communicated by: Associate Editor Claudio Estrada-Gasca

Abstract A solar chemical reactor for the thermal dissociation of ZnO is modeled by means of a detailed heat transfer analysis that couples radiative transport to the reaction kinetics. An extended band-approximated radiosity method enables the analysis of directional and wavelength depended radiation exchange. Boundary conditions included the incident concentrated solar radiation, determined by the Monte Carlo ray-tracing technique, and the hemispherical and band-approximated optical properties derived for the quartz window. Validation was accomplished by comparing the numerically modeled and experimentally measured window temperatures, reaction rates, and energy conversion efficiencies. The experimentally measured solar-to-chemical energy conversion efficiency increased with temperature, peaked at 14% for a reactor temperature of 1900 K and ZnO dissociation rate of 12 g/min, and decreased as the reactor approached its stagnation temperature. The conditions for which this efficiency can be augmented are discussed.  2007 Elsevier Ltd. All rights reserved. Keywords: Solar; Hydrogen; Thermochemical cycle; Zinc; Zinc oxide; Radiation; Radiosity; Heat transfer

1. Introduction Solar hydrogen production by the 2-step water-splitting thermochemical cycle via ZnO/Zn redox reactions can be represented by: 1st step ðsolarÞ : ZnO ! Zn þ 0:5O2 2nd step ðnon-solarÞ : Zn þ H2 O ! ZnO þ H2

ð1Þ ð2Þ

The net reaction is H2O = H2 + 0.5O2, but since H2 and O2 are formed in different steps, the need for high-temperature gas separation is thereby eliminated. This cycle has been identified as a promising path for solar hydrogen production because of its potential of reaching energy conversion * Corresponding author. Address: Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland. Tel.: +41 44 6327929; fax: +41 44 6321065. E-mail address: [email protected] (A. Steinfeld).

0038-092X/$ - see front matter  2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2006.12.006

efficiencies exceeding 40%, and consequently, the potential of economic competitiveness (Perkins and Weimer, 2004; Steinfeld, 2005). Several chemical aspects of the thermal dissociation of ZnO have been previously investigated (Palumbo et al., 1998, and literature cited therein). At 2340 K, DG = 0 kJ/mol and DH = 395 kJ/mol. Activation energies determined by thermogravimetry were reported in the range 310–350 kJ/mol (Weidenkaff et al., 2000a). The reaction rate law and the corresponding Arrhenius parameters were also derived for directly irradiated ZnO pellets (Moeller and Palumbo, 2001a). The condensation of zinc vapor in the presence of O2 was studied by fractional crystallization in a temperature-gradient tube furnace (Weidenkaff et al., 1999). It was found that the oxidation of Zn is a heterogeneous process and, in the absence of nucleation sites, Zn(g) and O2 can coexist in a meta-stable state. Otherwise, they need to be quenched to avoid their recombination. In particular, the quench efficiency is sensitive to

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Nomenclature A A b A A C Cmax e C ek C E EA Fi,j Fb i;j F T m ;Dk F T s ;Dk DGR H DHR I? IR MF Mr,ZnO MC Nu P R R b R R R Re T T Tb T T0

surface area (m2) total hemispherical overall absorption total pseudo-hemispherical overall absorption for concentrated solar radiation total pseudo-hemispherical overall absorption for diffuse radiation on inner window surface solar concentration ratio maximal solar concentration ratio average solar concentration ratio over aperture average solar concentration ratio over surface element k total hemispherical overall emission activation energy (J/mol) view factor between finite surfaces i and j – diffuse radiation view factor between finite surfaces i and j – nondiffuse radiation fraction of blackbody emissive power at Tm in the spectral range Dk fraction of blackbody emissive power at Ts = 5780 K in the spectral range Dk Gibbs free enthalpy change of reaction (J/mol) enthalpy (J/mol) enthalpy change of reaction (J/mol) normal solar irradiation (W/m2) infrared mass of ZnO fed (kg) molecular weight of ZnO, Mr,ZnO = 0.0814 kg mol1 Monte Carlo Nusselt number power (W) gas constant, R = 8.314 J mol1 K1 total hemispherical overall reflection total pseudo-hemispherical overall reflection for concentrated solar radiation total pseudo-hemispherical overall reflection for diffuse radiation on inner window surface reaction rate (mol/m2 s) Reynolds number temperature (K) total hemispherical overall transmission total pseudo-hemispherical overall transmission for concentrated solar radiation total pseudo-hemispherical overall transmission for diffuse radiation on inner window surface ambient temperature, T0 = 300 K

the dilution ratio of Zn(g) in an inert gas flow and to the temperature of the surface on which the products are quenched (Palumbo et al., 1998; Steinfeld, 2005). Alternatively, electrothermal methods for in situ separation of

Tstagnation stagnation temperature (K) UV ultraviolet VIS visible a absorption coefficient (m1) cP heat capacity (J/mol K) k0 frequency factor (kg/m2 s) n refractive index n_ molar flow (mol/s) q heat flux (W/m2) qc conductive flux at window (W/m2) qchem chemical heat sink (W/m2) qcon convective and conductive flux at cavity (W/m2) qcv convective flux at window (W/m2) ^ qe incoming non-diffuse radiative flux of concentrated solar radiation (W/m2) qi incoming diffuse radiative flux (W/m2) ^ qi incoming non-diffuse radiative flux (W/m2) ql diffuse radiative flux leaving the window (W/m2) qm net heat flux at opaque wall with index m (W/ m 2) qo outgoing diffuse radiative flux (W/m2) ^ qo outgoing non-diffuse radiative flux (W/m2) r radial dimension (m) Subscripts c convective/conductive cavity cavity chem chemical max maximal R reactor solar solar k spectral depended property h directional depended property i, j, k, m surface indices Symbols e emissivity eapp apparent emissivity g energy conversion efficiency j extinction coefficient k wavelength (m) h angle of incidence q reflectivity r Boltzmann constant r = 5.67 · 108 W m2 K4 rG spatial standard deviation of Gaussian distribution, m s transmissivity

Zn(g) and O2 at high temperatures have been experimentally demonstrated to work in small scale reactors (Fletcher et al., 1985; Palumbo and Fletcher, 1988; Parks et al., 1988; Fletcher, 1999). Nevertheless, high-temperature separation

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of Zn vapor and O2 remains a technological challenge. Various exploratory tests on the dissociation of ZnO were carried out in solar furnaces (Bilgen et al., 1977; Elorza-Ricart et al., 1999; Weidenkaff et al., 2000b; Lede et al., 2001; Moeller and Palumbo, 2001b). The reaction temperature can be significantly lowered and the recombination avoided by using carbonaceous materials as reducing agents (Wieckert and Steinfeld, 2002). The solar carbothermic reduction of ZnO has been experimentally demonstrated using C(s) (Murray et al., 1995; Adinberg and Epstein, 2004; Osinga et al., 2004a) and CH4 (Steinfeld et al., 1995; Kra¨upl and Steinfeld, 2003) as reductants. Based on the chemical thermodynamic and kinetic constrains of the ZnO dissociation reaction, a solar chemical reactor was designed and a 10 kW prototype was fabricated and tested in a high-flux solar furnace (Haueter et al., 1999a; Mu¨ller et al., 2006). This solar reactor features a windowed rotating cavity-receiver lined with ZnO particles that are held by centrifugal force. With this arrangement, ZnO is directly exposed to high-flux solar irradiation and serves simultaneously the functions of radiant absorber, thermal insulator, and chemical reactant. The direct irradiation of particles provides an efficient means of heat transfer to the reaction site, bypassing the limitations imposed by indirect transport of high-temperature heat, as corroborated in previous experimental studies (Kra¨upl and Steinfeld, 2003). This paper is focused on the modeling aspects of such a high-temperature chemical reactor, with emphasis in analyzing the coupling of radiative transfer with the chemical kinetics. Previous pertinent studies involving gas–solid heterogeneous reactions include reactor models based on the Monte Carlo method for coal gasification (Lipin´ski and Steinfeld, 2005; Lipin´ski et al., 2005; Zedtwitz et al., 2007) and the thermal decomposition of methane (Hirsch and Steinfeld, 2004), and on the Rosseland approximation for the carbothermal reduction of ZnO (Osinga et al., 2004b) and the thermal decomposition of limestone (Lipin´ski and Steinfeld, 2004). 2. Analysis 2.1. Solar reactor configuration A schematic of the 10 kW solar reactor prototype is shown in Fig. 1. It has been previously described in detail (Mu¨ller et al., 2006); only the main features will be highlighted here. Its main component is a rotating drum composed of a cylindrical cavity (#1) impervious to gas diffusion and packed within high-temperature resistant ceramic insulation (#6). The cavity is built from metallic hafnium and has a thin inner HfO2 layer. It contains a 6cm diameter aperture (#2) to let in concentrated solar radiation through a 20-cm diameter 3-mm thick quartz window (#3). The rotational movement along the horizontal axis generates a centripetal acceleration that forces the ZnO particles to cover the cavity wall, thereby creating an efficient use of the cavity space for radiation heat transfer

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Fig. 1. Schematic of the solar reactor configuration: 1 = cavity, 2 = aperture, 3 = quartz window, 4 = rotating drum, 5 = actuation, 6 = insulation, 7 = dynamic feeder, 8 = product outlet port, 9 = rotary joint, 10 = cooling fluids.

and reducing the thermal load on the cavity wall materials. The reactor has a dynamic feeding system (#7) that extends and contracts within the cavity, and enables to evenly spread out a layer of ZnO of a desired thickness along the entire cavity. 2.2. Solar power input The incoming solar radiation is determined by the optical characteristics of PSI’s solar furnace (Haueter et al., 1999b). The Monte Carlo (MC) ray-tracing technique was applied to calculate the distribution of the solar concentration ratio C at the focal plane of the solar furnace, defined as the solar flux at the focal plane normalized by the direct normal solar irradiance I?. This was necessary due to geometrical imperfections of the parabolic concentrator and flat heliostat. The MC results can be approximated by a Gaussian curve:   r2 CðrÞ ¼ C max exp  2 ð3Þ 2rG with Cmax = 4500 and rG = 3.9 cm. Integration of Eq. (3) over a circular target of radius r yields the solar power input, Z r P ðrÞ ¼ 2pI ? CðrÞr dr ð4Þ 0

Fig. 2 shows the spatial distribution of the solar concentration ratio at the focal plane of the solar furnace and the corresponding solar power input for I? = 900 W/m2 as a function of the target’s radius. The data points correspond to the experimentally measured values, as recorded by a

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mann et al., 1975; Neuer and Jaroma-Weiland, 1998). The quartz window optical properties are approximated in three bands, as listed in Table 1 (Heraeus, 1994; Lide, 2004). They are assumed to be independent of temperature – a reasonable assumption in the absence of devitrification (nucleation of the cristobalite phase), which generally does not occur below 1300 K. Overall spectral–directional absorption Ak,h, reflection Rk,h, and transmission Tk,h of the single-layer quartz window are given in terms of its surface reflectivity q and transmissivity s by (Siegel and Howell, 2002): T k;h ¼ s

1  q 1  q2  1 þ q 1  q 2 s2 2

Rk;h Fig. 2. Left axis: numerically calculated solar concentration ratio at the focal plane of PSI’s solar furnace. Right axis: measured (data points) and calculated solar power input for I? = 900 W/m2.

calibrated CCD camera on a water-cooled Al2O3-coated Lambertian target. For I? = 900 W/m2, the solar power input through the 6-cm diameter aperture is Psolar = 9.9 kW. A scheme of the aperture, the window (divided into three ring segments), and the connecting Al2O3 frustum is shown in Fig. 3. Each of these five surfaces is assumed isothermal. A finer segmentation would increase accuracy at the expense of added complexity and computational time. The temperature of the virtual surface 1 at the aperture is assumed equal to the nominal cavity temperature. Its emissivity is set equal to the apparent emissivity of the cavity, as calculated by Monte Carlo, eapp = 0.95 (Mu¨ller, 2005). The emissivity of the Al2O3-frustum is taken equal to 0.2 in the 0–4.5 lm range, and 0.9 in the 4.5–1 lm range (Hage-

ð1  qÞ s2 ¼q 1þ 1  q2 s 2

Ak;h ¼

ð5Þ ! ¼ qð1 þ sT k;h Þ

ð6Þ

ð1  qÞð1  sÞ 1  qs

ð7Þ

with q and s being spectral and directional depended. q is calculated as a function of the incident angle and the refractive index by the Fresnel’s equations, while refraction at the window boundaries is calculated by Snell’s law (Siegel and Howell, 2002). Hemispherical and band-approximated overall properties of the window can be readily calculated by integrating Tk,h, Rk,h, and Ak,h over all solid angles and over the spectral bands (denoted by Dk). For example, Z Z p=2 ADk ¼ 2 Ak;h cos h sin h dh dk ð8Þ Dk

0

The expressions for TDk and RDk are analogous. The computed values are listed in Table 2 for the three spectral bands of Table 1. Pseudo-hemispherical and band-approximated properties of the window for incoming solar radiation (denoted by a ‘‘hat’’) can be calculated by integrating Tk,h, Rk,h, and Ak,h over the spectral bands (denoted by Dk) and the corresponding range of solid angles (denoted by Dh), Table 1 Optical properties of the 3 mm-thick quartz window Band label

k (lm)

n (–)

j (–)

a (m1)

UV VIS IR

0–0.17 0.17–3.5 3.5–1

1.50 1.46 1.80

101 0 103

108 8.4 108

Table 2 Hemispherical band-approximated overall absorption, reflection, and transmission of the quartz window

Fig. 3. Scheme of the front part of the solar reactor, containing the aperture (1), frustum (2), and window elements (3–5). The origin of the coordinate system is located at the center of the aperture.

A (%) R (%) T (%)

UV

VIS

IR

90.6 9.4 0.0

2.8 13.6 83.5

86.6 13.4 0.0

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weighed by the solar concentration ratio distribution C(r). For example, R R Ak;h  CðrÞ cos h dh dk b A Dk ¼ DkR DhR ð9Þ CðrÞ cos h dh dk Dk Dh b Dk are analogous. The comThe expressions for Tb Dk and R puted values of the pseudo-hemispherical and band-approximated properties are listed in Table 3 for the three spectral bands of Table 1. Normal impinging radiation is given as a reference value. Interestingly, the overall reflectivity is about 7–11% higher – depending on the spectral range – for concentrated solar radiation coming from the solar furnace than that for normal impinging radiation. For the central window element (element 5), the relative deviation from the results for normally impinging radiation is small. However, it increases rapidly at larger distances from the center (element 3), which may be of concern when scaling up. Finally, properties are required for diffuse radiation impinging on the inner surface of the quartz window, where the source of such radiation is by emission or reflection from the cavity or frustum. They can be calculated by integrating Tk,h, Rk,h, and Ak,h over the spectral bands and the corresponding range of solid angles. For example, for two generic surfaces i and j: Z Z Z 1 cos h1 cos h2 ADk ¼ Ak;h dh1 dh2 dk ð10Þ Ai F i;j Dk Dh1 Dh2 pL2 where h1 and h2 are the angles between a generic ray connecting the two surfaces and the normal to the surfaces, and L is the path length of the generic ray. The computed values of the pseudo-hemispherical and band-approximated overall optical properties for diffuse radiation impinging on the inner quartz window are given in Table 4, for the three bands of Table 1, and for the three window segments of Fig. 3. Table 3 Pseudo-hemispherical and band-approximated overall absorption, reflection, and transmission for concentrated solar radiation impinging on the quartz window, for the three bands of Table 1, and for the three window segments of Fig. 3 Band

Element

Optical properties in % b A

b R

Tb

Relative deviation from normally impinging radiation in % bA bR b T A?  1 R?  1 T?  1

UV

3 4 5 ?

95.4 95.8 95.8 95.8

4.6 4.2 4.2 4.2

0.0 0.0 0.0 0.0

0.50 0.04 0.00

+11.47 +0.97 +0.01

– – –

VIS

3 4 5 ?

2.7 2.6 2.5 2.5

7.3 6.6 6.6 6.6

90.0 90.8 90.9 90.9

+9.66 +3.00 +0.30

+10.13 +0.79 +0.00

1.00 0.14 0.01

3 4 5 ?

91.3 91.8 91.8 91.8

8.7 8.2 8.2 8.2

0.0 0.0 0.0 0.0

0.60 0.05 0.00

IR

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Table 4 Pseudo-hemispherical and band-approximated overall absorption, reflection, and transmission for diffuse radiation impinging on the inner surface of the quartz window, for the three bands of Table 1, and for the three window segments of Fig. 3 Band

UV

VIS

IR

Start

Target Window element 3

Window element 4

Window element 5

Element 1

AUV ð%Þ RUV ð%Þ T UV ð%Þ

94.4 5.59 0.00

95.6 4.36 0.00

95.8 4.19 0.00

Element 2

AUV ð%Þ RUV ð%Þ T UV ð%Þ

90.4 9.54 0.00

89.9 10.1 0.00

89.5 10.5 0.00

Element 1

AVIS ð%Þ RVIS ð%Þ T VIS ð%Þ

2.84 8.66 88.5

2.62 6.88 90.5

2.55 6.64 90.8

Element 2

AVIS ð%Þ RVIS ð%Þ T VIS ð%Þ

2.75 14.0 83.2

2.89 14.5 82.5

2.92 15.1 82.0

Element 1

AIR ð%Þ RIR ð%Þ T IR ð%Þ

90.3 9.75 0.00

91.6 8.40 0.00

91.8 8.20 0.00

Element 2

AIR ð%Þ RIR ð%Þ T IR ð%Þ

86.4 13.5 0.00

85.9 14.1 0.00

85.5 14.5 0.00

2.3. Extended band-approximated radiosity method The band-approximated radiosity method – also called the enclosure theory – is applied (Siegel and Howell, 2002). In order to account for the directional distribution of radiation, the radiosity method is extended for non-diffuse radiation. Fig. 4 shows the schematic of a generic cavity with partially transparent and opaque walls. Indicated are the radiative fluxes. Non-diffuse radiative fluxes are denoted with a hat. Energy conservation on generic surface m for the spectral band Dk yields. qi;m;Dk þ ^ qi;m;Dk ¼ qm;Dk þ qo;m;Dk

ð11Þ

Here, the incoming radiation is separated into diffuse and directional components. Since reflected and emitted radiation are diffuse, no directional outgoing radiation is considered on the right hand side of Eq. (11). q1 is the net power into the cavity. Analogous to the standard radiosity method, the incoming radiative flux is expressed in terms of the ‘‘diffuse’’ view factors, qi;m;Dk ¼

5 X

F m;j qo;j;Dk

ð12Þ

j¼1

+6.71 +0.59 +0.01

Normally impinging radiation is given as reference value.

– – –

The matrix F of view factors is computed analytically. An equivalent formulation of Eq. (12) is required for the directional component. The corresponding ‘‘directional’’ view factors are established by ray tracing. Note that the

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Applying energy conservation on the inner window surface gives:

partly transparent window

ql ,k

qo;k;Dk ¼ Ek;Dk F k;Dk rT 4k þ

qˆo ,k

qˆe ,k

qo ,k

qc ,k

qi ,k qˆi ,k

qo ,m

qo;k ¼

qm

opaque wall

Fig. 4. Scheme of a generic cavity with two partly transparent and three opaque walls. Indicated are the radiative, conductive, and convective heat fluxes. Symbols are listed in the nomenclature.

reciprocity relation does not hold ðAi Fb i;j 6¼ Aj Fb j;i Þ, which prevents surface areas from canceling in Eq. (13): 5 X j¼1

Aj Fb j;m ^qo;j;Dk Am

ð13Þ

Thus, the outgoing radiative flux for surface m is: em;Dk F m;Dk rT 4m

ð20Þ

qo;k;Dk

þ ð1  em;Dk Þðqi;m;Dk þ ^qi;m;Dk Þ

ð14Þ

qo;k;Dk þ ^qo;k;Dk þ ql;k;Dk þ qc;k;Dk þ qcv;k;Dk ¼ qi;k;Dk þ ^qi;k;Dk þ ^qe;k;Dk

Note that qc and qcv in Eq. (15) denote the convective heat flux to the surrounding air and the conductive heat flux to the neighboring window element, respectively. The convective term is determined using the Nusselt correlation of Eq. (21) (VDI, 1994), with the window diameter as characteristic length: Nu ¼ 0:332  Re0:5

Finally, the net power into the reactor’s cavity is used to drive the endothermic chemical reaction assumed to take place at the cavity’s inner surface covered with ZnO, and to compensate for the heat loss by convection and conduction through the cavity’s insulation:

On the outside (see Fig. 4), the leaving radiative flux is ð16Þ

Substituting Eqs. (12), (13) and (16) in Eq. (15) yields: 5 X ¼ qc;k;Dk  qcv;k;Dk þ ð1  T j;k;Dk ÞF k;j qo;j;Dk j¼1

b k;Dk ^qe;k;Dk  Ek;Dk F k;Dk rT 4 þA k

ð17Þ

Hemispherical and band-approximated properties of the quartz window are given in Table 2; pseudo-hemispherical band-approximated properties for concentrated solar radiation impinging on the quartz window are given in Table 3; pseudo-hemispherical and band-approximated properties for diffuse radiation impinging on the inner surface of the quartz window are given in Table 4. External concentrated radiation impinging on the outer window surface ^qe is calculated from the known normal solar irradiance I? in the specific spectral band, and from the mean solar concentration ratio on the corresponding window segment as determined by MC ray tracing of the solar furnace: ð18Þ

ð22Þ

qcon is estimated by means of an experimentally established combined heat transfer coefficient of 64 W/m2 K. qchem includes the energy required to heat the reactants and to supply for the enthalpy change of the reaction,   Z T qchem ¼ Rchem ðT Þ  DH R ðT Þ þ cp;ZnO ðT ÞdT ð23Þ T0

ð15Þ

b k;Dk ^qe;k;Dk þ T k;Dk qi;k;Dk þ Ek;Dk F k;Dk rT 4 ql;k;Dk ¼ R k

ð21Þ

q1  A1 ¼ ðqchem þ qcon Þ  Acavity

where Fm,Dk is the fraction of blackbody emissive power at Tm in the spectral range considered. For the partially transparent window k, energy conservation yields:

e k  I ?  F T ;Dk ^ qe;k;Dk ¼ C S

4 X Dk¼1

qˆi ,m

qo;k;Dk

ð19Þ

Summing up the shares of heat fluxes over the spectral bands yields the total outgoing radiative flux qo, qi ,m

qo;m;Dk ¼

Rj;k;Dk qo;j;Dk F k;j

j¼1

qcv ,k

^ qi;m;Dk ¼

5 X

where the reaction rate is well described by a zero-order Arrhenius-type law:   k0 EA Rchem ðT Þ ¼ exp ð24Þ M r;ZnO RT and EA = with k0 = 1.356 · 1012 kg m2 s1 328 kJ Æ mol1, experimentally determined for samples of ZnO directly irradiated in a solar furnace (Moeller and Palumbo, 2001a). The nominal cavity temperature is set as boundary condition for the aperture (element 1). Conductive heat flux is set as boundary condition for the frustum (element 2). Convective heat fluxes are set as boundary conditions for the three window segments (elements 3, 4, and 5). The resulting system of 53 nonlinear equations is solved numerically with Maple (2003, Maple). The results are checked for energy conservation within spectral bands as well as for the complete spectral range. Relative errors in the values of the heat fluxes are in the order of 108. 3. Results The experimentally measured and modeled temperatures of the reactor cavity, the aperture’s frustum, and

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Fig. 5. Experimentally measured and numerically modeled temperature profiles during the heating and cooling phases of the solar reactor. (a) Heating phase with shutter opened stepwise; the average solar concentration ratio over the aperture is shown on the left ordinate, temperatures on the right. (b) Cooling phase with shutter closed.

the quartz window segments are shown in Fig. 5 for the heating and cooling phases. The cavity and frustum temperatures were measured by a solar blind-pyrometer1; the window temperature was measured by an IR pyrometer.2 During heating, the shutter of the solar furnace was opened stepwise, as indicated by the average solar concentration ratio over the aperture (see left ordinate of Fig. 5a). During the cooling phase, the shutter was closed. Peak cavity temperature observed was 1970 K. The window temperature varied between 550 and 995 K as the solar concentration

1

The blind-pyrometer is not affected by the reflected solar irradiation because it measures in a narrow wavelength interval around the 1.4 lm wavelength where solar irradiation is mostly absorbed by the H2O in the atmosphere. 2 The IR pyrometer measures in a narrow wavelength interval around the 8 lm wavelength where the quartz window approaches an opaque surface.

ratio was increased from 980 to 2720. It should be noted that, during ZnO feeding, the cavity and window should be maintained above the saturation point of zinc vapor for avoiding its condensation and subsequent re-oxidation. The net power into the reactor’s cavity A1 Æ q1 is shown in Fig. 6 as a function of its temperature and the average e for a fully solar concentration ratio over its aperture, C, opened shutter. Negative values imply net power being lost from the cavity through the aperture during cooling. For e ¼ 3900, the maximal solar power into the cavity is C 12 kW, which compares well with the experimentally measured value. The cavity’s stagnation temperature, Tstagnation, is defined as the temperature for which q1 = 0 (assuming perfectly insulated cavity, no convection or conduction losses, no chemical reaction). For example, for e ¼ 3700, Tstagnation = 2950 K. However, the measured C cavity temperature for the case of no chemical reaction was 2000 K – indicated by the star symbol – because of

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Fig. 6. Left axis: variation of the net power into the reactor’s cavity as a function of the cavity temperature. The parameter is the average solar concentration ratio over the aperture. Right axis: variation of the ZnO dissociation rate as a function of cavity temperature. Indicated (circles) are the experimentally measured rates.

convection heat losses by the flowing Ar used for sweeping the gaseous products and keeping the window clear and of conduction heat losses through the insulation, the sum of which amounts to 8.8 kW. Also shown in Fig. 6 are the numerically calculated and experimentally measured rates of ZnO dissociation as a function of cavity temperature. The maximum measured rate was 12 g/min. For the maximum achievable average solar concentration ratio of e ¼ 3900, the predicted rate is 75 g/min. C The solar reactor performance is characterized by its solar-to-chemical energy conversion efficiency, defined as the enthalpy change of the reaction divided by the solar power input through the reactor’s aperture: g¼

n_ products H products ðT R Þ  n_ reactants H reactants ðT 0 Þ P solar

ð25Þ

Note that Eq. (25) accounts for the reaction process heat and the sensible/latent heat of the hot products exiting the reactor. Additionally, g is based on the rate of ZnO dissociation, i.e. re-oxidation of Zn occurring downstream of the reactor’s exit is omitted from consideration. The numerically calculated (solid curves) and experimentally established (data points) energy conversion efficiencies are shown in Fig. 7 as a function of the nominal cavity temperature. For the data points, the error bars were calculated for a pyrometer error of ±20 K. g increased with temperature because of the enhanced reaction kinetics, reached maximum values at 1900 K, and decreased as the cavity approached its stagnation temperature. Peak efficiency recorded was 14%, which implies a reasonable good performance for a prototype reactor at a power level of 10 kW. Energy losses are mainly due to re-radiation through the aperture, conduction through the insulation,

Fig. 7. Experimentally determined (data points) and numerically predicted (solid curves) solar-to-chemical energy conversion efficiency as a function of the nominal cavity temperature. Indicated is the mass of the ZnO fed. The parameter is the percentage of power loss by conduction and convection heat transfer.

and convection by the Ar carrier gas. The use of Ar should be minimized to avoid the energy penalty associated with its separation and recycling. Higher efficiencies are expected for a scale-up reactor because of the improved reaction surface area to wall area ratio, and consequently, reduced relative conductive losses (responsible for up to 60% of the total heat losses), as demonstrated experimentally for a 5–300 kW scale-up of a solar reactor for the carbothermic reduction of ZnO (Wieckert et al., in press). An additional efficiency increase could be realized by increasing the solar concentration ratio at the aperture, for example by means of a CPC in tandem with the primary solar concentrator, enabling the use of smaller apertures and, consequently, reducing re-radiation losses (responsible for about 25% of the total heat losses). Indicated in Fig. 7 is the mass of the ZnO fed, either MF < 45 g or MF > 45 g, since 45 g is the minimal mass required to fully cover the cavity’s surface area. g increases with temperature for both data sets, but it is significantly lower for MF < 45 g. At above 1900 K, the reactor was operating close to its stagnation temperature and not enough power was left for sustaining the endothermic reaction. Consequently, only relatively low feeds were possible without drastically decreasing the reactor temperature, resulting in slower reaction rates and lower energy conversion efficiencies. Also shown in Fig. 7 is the energy conversion efficiency e over all predicted by the reactor model for the mean C e ¼ 3430. The parameter is the percentexperimental runs, C age of power loss by conduction and convection heat transfer [qcon in Eq. (22)], with 0% corresponding to the

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ideal perfectly insulated adiabatic cavity with only re-radiation losses through the aperture, and 100% corresponding to the experimentally established qcon = 64 W/m2 K Æ (T1  T0). The model predicts an increase of g with temperature, a peak of 5.7% at 1894 K, and a decrease to zero at the stagnation temperature, which compares well with the experimentally data set obtained for MF < 45 g. However, the predicted g underestimates the data set obtained for MF > 45 g (where the peak g is 14%), because of the conservative assumption of the reaction taking place only at the cavity’s inner surface covered with ZnO. It was qualitatively observed that, for large feeds, the reaction surface is larger than Acavity. The portion of incoming solar power that is re-radiated increases from 11% at 1600 K to 37% at 2200 K; which demands a reduction in the feeding batch and, consequently, a reduction of the chemical heat sink. Evidently, reducing conductive and convective heat losses results in higher g and a shift of the peaks to higher temperatures, as well as a shift of the stagnation temperatures to higher values. A reduction of 50% should result in a solarto-chemical energy conversion efficiency exceeding 30%. 4. Summary and conclusions We have formulated a radiative heat transfer model to compute heat fluxes, temperatures, reaction rates, and solar-to-chemical energy conversion efficiencies of a solar chemical reactor for ZnO dissociation. The numerically modeled window temperatures compared well with the experimentally measured ones, and vary between 550 and 995 K as the solar concentration ratio was increased from 980 to 2720. The maximum measured mean solar concentration ratio over the 6 cm-diameter aperture was e ¼ 3900, which corresponds to a solar power input of C 12 kW. The theoretical stagnation temperature for e ¼ 3700 is 2950 K, while the experimentally measured C maximum temperature without reaction was 2000 K as a result of the convective and conductive heat losses, amounting to 8.8 kW for this operational state. The maximum measured rate of ZnO dissociation was 12 g/min. The peak solar-to-chemical energy conversion efficiency was 14% for a nominal cavity temperature of 1900 K; an efficiency exceeding 30% is predicted by halving the conductive and convective heat losses. Further augmentation in the energy conversion efficiency is expected for a scale-up reactor because of the improved reaction surface area to wall area ratio, and by increasing the solar concentration ratio at the aperture, enabling the use of smaller apertures and, consequently, reducing re-radiation losses. Acknowledgements Project funded by the BFE-Swiss Federal Office of Energy under grant Nr. 46693/86759. We thank P. Ha¨berling, D. Wuillemin and S. Kra¨upl for technical support during the experimental campaign at PSI’s solar furnace, and

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