Author's Accepted Manuscript

Heat transfer and fluid flow analysis of a 4 kW solar thermochemical reactor for ceria redox cycling

Philipp Furler, Aldo Steinfeld

www.elsevier.com/locate/ces

PII: S0009-2509(15)00396-6

DOI: http://dx.doi.org/10.1016/j.ces.2015.05.056

Reference: CES12391

To appear in: Chemical Engineering Science

Received date: 23 February 2015 Revised date: 7 May 2015 Accepted date: 10 May 2015

Cite this article as: Philipp Furler, Aldo Steinfeld, Heat transfer and fluid flow analysis of a 4 kW solar thermochemical reactor for ceria redox cycling,

Chemical Engineering Science, http://dx.doi.org/10.1016/jxes.2015.05.056

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Heat transfer and fluid flow analysis of a 4 kW solar thermochemical reactor for ceria redox cycling

Philipp Furlera and Aldo Steinfelda

a Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland Abstract

A solar reactor consisting of a cavity-receiver containing a reticulated porous ceramic (RPC) foam made of CeO2 is considered for effecting the splitting of H2O and CO2 via a thermochemical redox cycle. A transient 3D heat and mass transfer model of the reduction step is formulated and solved using Monte-Carlo ray-tracing coupled to computational fluid dynamics. Experimental validation is accomplished in terms of measured temperatures and O2 evolution rates obtained with a solar reactor prototype tested under high-flux radiative power inputs in the range 2.8 - 3.8 kW and mean solar concentration ratios up to 3024 suns. Critical temperatures of up to 2250 K induced CeO2 sublimation, which in turn affected detrimentally the solar reactor performance. The model is applied to analyze an improved geometrical design with alternative flow configuration, enabling more uniform radiative absorption and temperature distributions, and resulting in a higher solar-to-fuel energy conversion efficiency.

1. Introduction

Solar thermochemical cycles based on metal oxide redox reactions can split CO2 and H2O to produce a mixture of CO and H2 (syngas), which can be further processed to liquid hydrocarbon fuels.1-4 Non-stoichiometric cerium oxide has emerged as an attractive redox active material because of its relatively high oxygen solid-state conductivity, contributing to fast redox kinetics5

and because of its crystallographic stability over a wide range of oxidation states. ' The two-step H2O/CO2-splitting solar thermochemical cycle based on oxygen-deficient ceria is represented by:

High-temperature reduction: CeO2 —+AH > CeO2.^ + (1)

Low-temperature oxidation with H2O: CeO2-^ + SH2O —AH > CeO2 + SH2 (2a)

Low-temperature oxidation with CO2: CeO2-^ + SCO2 —~AH > CeO2 + SCO (2b)

In the first, high-temperature endothermic step, ceria is thermally reduced to a non-stoichiometric state using concentrated solar energy. In the subsequent, lower temperature exothermic step, ceria

is re-oxidized with H2O and/or CO2 to produce H2 and/or CO, respectively. Solar reactors for

effecting this cycle include cavity-receivers with rotating or stationary structures, glass dome reactors,11 aerosol flow reactors,12 and moving and fluidized bed reactors.13' 14 We have developed a solar reactor that features a cavity-receiver containing porous ceria and demonstrated experimentally the production of H2 from H2O,15 and CO from CO2,15-17 as well as the coproduction of H2 and CO by simultaneous splitting a mixture of H2O and CO2 using the solar cavity-receiver reactor.18

In this work, we present a transient 3D heat and mass transfer model of the solar reactor for

performing the high-temperature solar reduction step (Eq. 1). The model couples Monte-Carlo

(MC) ray-tracing and computational fluid dynamics (CFD) techniques. Validation is accomplished by comparing numerically calculated and experimentally measured temperatures, O2-evolutions, and solar-to-fuel energy conversion efficiencies obtained with the 4-kW solar reactor prototype. The validated model is further applied to examine an improved geometrical design with alternative flow configuration and to identify the major sources of energy loss as well as strategies to minimize them.

2. Solar reactor configuration and experimental setup

The solar reactor configuration is shown schematically in Figure 1 (a). The engineering design has been presented previously in detail.16 The main features are briefly summarized here. The solar reactor consisted of a cavity-receiver with a 4 cm dia. circular aperture for the access of concentrated solar radiation. The aperture was closed by a 24 cm dia., 3 mm thick clear fused quartz disk window mounted on a frustum. A compound parabolic concentrator (CPC)19 was incorporated into the aperture to further boost the solar concentration ratiot to mean values of up to 3024 suns. The cavity contained a cylinder of reticulated porous ceramic (RPC) foam made of pure ceria composed of four 20 mm-tick, 60 mm-i.d., 100 mm-o.d. rings, and a single 20 mm-thick, 100 mm-o.d. disk. The total mass of the CeO2 cylinder was 1413 g. The cavity was insulated by a 10 mm-thick layer of CeO2 laminate surrounded by Al2O3-SiO2 and sheathed by an outer shell made of Inconel 600. An annular gap between RPC and insulation induced uniform radial flow across the RPC cylinder. Temperatures were measured at the outer surface of the RPC (B-type thermocouples), in the middle of the Al2O3-SiO2 insulation, and at the outer Inconel wall (K-type thermocouples). Argon (99.999% purity) flow rates were regulated by electronic mass flow controllers (Bronkhorst F-201C) and injected through four radial inlet ports and one axial

+ The solar concentration ratio, C, is defined as solar radiative power intercepted by the aperture. C is expressed in units of "suns" when normalized to 1 kW m-2.

nozzle located at the frustum close to the quartz window. Gases exited the reactor through an axial outlet port at the rear plate. The gas composition was monitored at the outlet by gas chromatography (Varian 490), supplemented by a paramagnetic alternating pressure based O2 detector (Siemens Oxymat 6). Experimentation was performed at the ETH's high flux solar simulator (HFSS): an array of seven Xe arc lamps, close-coupled to truncated ellipsoidal reflectors, provided an external source of intense thermal radiation (mostly in the visible and IR spectra) that closely approximated the heat transfer characteristics of highly concentrating solar systems, such as solar towers and dishes.20 The radiative flux distribution at the aperture plane was measured optically using a calibrated CCD camera focused on a water-cooled, Al2O3-plasma coated Lambertian (diffusely reflecting) target. The radiative power input through the aperture Psolar was obtained by integration of the radiative flux and verified with measurements using a water-calorimeter.

Ce02 Laminate

Al203 -Si02\ çeo, RPC Insulation

^convection

T = 293 K)

Inconel shell

Inlet (t = 293 K)

Al2O3-SiO2 insulat. laminate

Outlet pel = 0 Pa, fluid To = 293 K)

solid solid

gas-gap

CeO2-RPC

x x..x x x x x..x x x x...

Sksolar Se .reaction SC,O2

fVYvAYYvVVYYV'

(T=293 K)

Figure 1: (a) Schematic of the solar reactor configuration and (b) schematic of the fluid, solid, and porous domains. Also indicated are the boundary conditions and source terms.

A typical experimental run consisted of two consecutive stages: 1) the solar reactor was pre-

heated for 30 min at a radiative power input Psolar = 0.8 kW; 2) the radiative power input was

increased to 2.8, 3.4, or 3.8 kW to initiate thermal reduction. The corresponding mean solar concentration ratios over the aperture were 2228, 2706, and 3024. During both stages, the Ar flow rate was kept constant at 1.8 L min-1 (SLPM; mass flow rate calculated at 273.15 K and 101 325 pa) through the side inlets (uniformly distributed over the four radial inlets) and 0.2 L min-1 through the reactor front.

3. Heat and mass transfer analysis

Figure 1 (b) shows a schematic representation of the individual computational domains (fluid, solid, and porous) of the model. The reactor cavity, reactor front, gas-gap, inlets, and outlet are modeled as fluid domains, assumed to be a non-participating media for radiation. Laminar flow conditions (Re << 150 in all domains,21) and ideal gas mixtures are assumed. The Al2O3-SiO2 insulation, ceria laminate, and the inconel reactor shell are modeled as solid domains. The reactive ceria RPC is modeled as a homogeneous and radiative participating two-phase porous domain.

Governing equations — The continuity, species conservation, momentum, and energy conservation equations in the fluid domains are given respectively by:

(pU) = 0 (3)

d(p\ ) -

V 2/ + V (pUYn ) = 0 (4)

d ______/ _ _ t 2 = _^

—(pU) + V-[pUU) = -Vp + Vj VU + (VU) — I V• U + SM,buoy (5)

dt V 3 y

d(ph) + V\Uph) = V(kVT) (6)

where p is the density, U is the velocity vector, Y02 the concentration of 02 in the gas mixture, p is the dynamic viscosity, I the identity matrix, SM,buoy an external momentum source accounting for buoyancy, h is the enthalpy, and, k the thermal conductivity of the gas mixture. Gas diffusion is neglected in Eqs. (4) and (6) because Pemass > 1, thus advective mass transport is dominant compared to mass diffusion. Gas flows are modeled as Ar-02 mixtures of variable composition, determined by solving Eq. (4). Kinetic energy and viscous dissipation are neglected in Eq. (6) because U << 1 m s-1 and Br << 1.

Due to the absence of flows, the energy conservation equation in the solid domains is simplified to:

^p) =v.( kVT) (7)

The governing equations for the fluid phase of the RPC porous domain are:

^ + (pKU) = Sco W (8)

dt ' 2

d{peY0) =_

dt +V (pK. UYo2 ) = Sc ,o2 (9)

d(epU) v / , w . u |U

+ v.(p( ku )u ) = -v^ +

1 j (10)

r = ( - T 2= juK. VU + (VU)T — IV U

v 3 J j

+ S M,buoy + S M,porous

d(eph) dt

+ V (pK Uh) = V • (kVT) + SE,solar +Vqr + Qfs (11)

where 8 is the volume porosity, k the isotropic porosity tensor, Sc,o2 the O2 mass source accounting for oxygen evolution during thermal reduction, SM,porous a momentum source accounting for viscous losses and inertial drag forces imposed by the porous structure on the fluid according to the Dupuit-Forchheimer law, SE,solar accounts for incoming absorbed solar radiation from the HFSS, and Vqr is the radiative source term accounting for radiation exchange. The energy conservation equations of fluid and solid are coupled via the source term QfS = hfs • Afs (Ts - Tf), where hfs is the interphaseal heat transfer coefficient, Afs is the fluid-solid

area density, and TS and Tf the temperatures of the solid and fluid, respectively. Thermal equilibrium between both phases (Ts = Tf) is enforced by setting hfs artificially high (10 000 W m-1 K-1), which is reasonable in this case, as Peth < 1, thus thermal diffusion is dominant over advection.

The governing equation for the solid phase of the RPC porous domain is: d((1 -£)ph± = vl =

( kKs VT ) + S e,reaction + Qf (12)

where SE,reaction is the energy sink accounting for the endothermicity of the CeO2 reduction reaction.

The RPC is modeled as participating media. The radiative transfer equation for an isotropic, gray, absorbing-emitting-scattering participating media is given by:

dI (r, s)

r,s, __ _ —

-PI(r, s) + a Ib (r) + — f I (r, s (13)

d^ ■ ■ +a (r)+4,4,

where r is the position vector, s the direction vector, s the path length, fi , a and a the extinction, absorption, and scattering coefficients, respectively, I the radiation intensity depending on position r and direction s, Ib the blackbody radiation intensity depending on the local temperature T, and w the solid angle. The radiation source term in Eq. (11) is given by:

Vqr =a

4nIb - J Idœ

Material properties — Material properties are listed in Table 1. Heat capacities (cp) of CeO2 and Al2O3-SiO2 insulation have been measured by differential scanning calorimetry (DSC) using a Netsch DSC 404 C Pegasus in the temperature range 470-1100 K and 470-1400 K, respectively. The thermal conductivity (k) of CeO2 laminate was measured in the temperature range of 300973 K by laser flash analysis using a Netsch Laserflash-analyser LFA 457. The thermal

conductivity of the Al2O3-SiO2 insulation was taken from the manufacturer. The effective heat and mass transfer properties of the RPC structure have been determined by direct numerical porelevel simulation on the exact RPC geometry obtained by computer tomography.23-25 The effective extinction coeffcient of the RPC was determined by pore-level MC on its 3-D tomographic scans.23' 24 The scattering and absorption coefficients were calculated from cr = ps fi and

a = (1 -ps) • fi, where ps is the surface total reflectance weighted by the Planck blackbody

spectral emission in a temperature range 300-2500 K. ps of partially reduced ceria at S = 0.035 was measured with an integrating sphere using a monochromatic collimated beam of light emitted by a Xe-arc in a spectral range 300 - 1600 nm under three different incident angles (8,

40, and 60 degrees). The thermal conductivity of CeO2, the optical properties of the Al2O3-SiO2

insulation, polished aluminum frustum and CPC were taken from literature. - The quartz window is modeled as a partially transparent thin disc with ts of 0.94 and ps of 0.06.

Table 1: Material properties used in the CFD analysis

CeO2 RPC T (K) Ref.

Density (kg m-3) 7220 -

Porosity (%) 63 -

Total CeO2 mass (g) 1413 - 16

Permeability (m2) 4.63376-10"8 - 23

Dupuit-Forchheimer coefficient (m-1) 1616.7 - 23

Thermal conductivity solid (W m-1 K-1) (17.8004-0.02402-r+0.0000112032-7M .7-109 • T3)/(7.9799+0.00483384• T-9.3397 -10-6• T2+2.8 40-9 • T3) 0.4 280 - 2000 >2000 23, 27

Specific heat capacity (J kg-1 K-1) -0.0001271-7^ + 0.2697656T + 299.8695684 444.27 280- 1100 > 1000

Extinction coefficient (m-1) 497.8 - 23_ENR EF_129

Surface reflectance (at ô = 0.035) -3-10"5T+0.2866 300-2500

Absorption coefficient CeO1.965 (m-1) (l-(-0.00006T+0.411))-497.8 300-2500

Scattering coefficient CeO1.965 (m-1) (-0.00006T+0.411)-497.8 300-2500

Fluid-solid heat transfer coefficient (W m-2 K-1) 10000

Fluid-solid area density (m-1) 952 - 23

Al2O3-SiO2 Insultation

Density (kg m-3) 560.65 - 29

Specific heat capacity (J kg-1 K-1) 4-10"7-ri-1.3797-10"3-r2+1.5987289-r+477.6995948 1118.44 IV IA S S OO OO o o

Thermal conductivity (W m-1 K-1) 0.00012926T+0.019654 280-2200 22

Hemispherical total emittance 0.28 - 26

CeO2 Laminate

Density (kg m-3) 504.4 -

Specific heat capacity (J kg-1 K-1) -0.0001271 T2 + 0. 2697656T + 299.8695684 444.27 280- 1100 > 1000

Thermal conductivity (W m-1 K-1) 2.2-10"7-r2-2.8387-10"4-r+0.17678688 295 - 2000

Hemispherical total emittance 0.7 -

Inconel 600

Density (kg m-3) 8470 30

Specific heat capacity (J kg-1 K-1) 0.2827T+327.29 123 - 1173 30

Thermal conductivity (W m-1 K-1) 0.0158T+10.169 123 - 1073 30

Thermal conductivity (W m-1 K-1) 2.35332617 40-12 • T3-1.289997670118 40-8 • T2 + 4.837061371854420-10-5 • T+0.00483418574527758 290 - 2400 31

Dynamic viscosity (kg m-1 s-1) 3.51928-lT'^-f-2.0456Ï56372- \~&U~P+ 6.8496118733557110-8 • T+4.2066780036496440-6 290 - 2400 31

Boundary conditions and source terms — The boundary conditions and source terms are schematically indicated in Figure 1 (b). The radiative power input delivered by the HFSS and absorbed within the cavity-receiver was determined by MC ray tracing, yielding the energy sources SE,solar to the CFD code. At the outer reactor shell, natural convective heat transfer was modeled using Nusselt correlations for vertical flat surfaces32 and for horizontal cylinders.33 The water-cooled CPC and frustum were assumed to be at 293 K. 0.45 L min-1 of Ar containing an O2 mass fraction of 110-5 was injected at T = 293 K normally to the inlet surface through each of the four radial inlet ports. 0.2 L min-1 of Ar flow with PO2 = 110-5 atm was injected at T = 293 K

axially and uniformly distributed over the window surface. A the outlet, prelative = 0 Pa. The reduction of nonstoichiometric ceria was modeled based on thermodynamic equilibrium, as

previous work has shown that the overall kinetics were controlled by heat transfer.

Experimental data by Panlener et al. was fitted according to the procedure described by Scheffe

et al. and Ermanoski et al., yielding the following expressions of nonstoichiometry S and reaction enthalpy AH as a function of temperature and PO2 :

log (J) = a1 + a2 - log

+ a3 - log

+ a4 - log

+a6 - log

T + a7 - log

-T + a8 -log

1 O 2 P

V P0 y

P O 2 P

V P0 y

+ a5 - T

AH = b1 + b2 -S

The fitting parameters are listed in Table 2.

Table 2 Fitting parameters for S and AH

Fitting parameter Fitting parameter

value value

a1 -9.783687979325373 a7 0.000009111263871567086

__a_2___________________ 0.43818838204603383 3.04372591882286* 10"7

__a_3___________________ ~"-Ö"Öi7553628274Y87237 bi 969.4087154075294

a4 ""-"Ö700Ö4W9?3"3T26Tf84977"" b2 -503.7387449398726

as 0.004301105768218843

a6 ""-"Ö700Ö8744T89M869576

Numerical Solution — The MC simulations were performed using the in-house code VEGAS with 1010 rays. The CFD simulations were performed with ANSYS CFX 14.0. The discrete

transfer radiation model was applied to solve Eq. (13), ' which was transformed into a set of transport equations for I and solved for discrete solid angles along s. The governing equations are discretized both in space (284 411 - 3 277 176 tetrahedras) and time (time step = 2 s) and solved on the individual control volumes by the finite-volume method with a first order upwind and

second order backward Euler scheme. Simulations were performed on the central highperformance cluster Brutus of ETH Zurich.

4. Experimental validation

The MC simulation of the HFSS was experimentally validated with measurements of the radiative flux distribution at the focal plane. Figure 2 shows the radiative flux distribution for all seven Xe-arcs of the HFSS: a) measured with a calibrated CCD camera on a Lambertian target; b) simulated by MC, and c) measured and simulated along the vertical and horizontal axes. The mean relative difference between the measured and simulated values over the aperture size was 2.9% with a standard deviation of 0.045 MW m Deviations are attributed to non-ideal ellipsoidal geometry and misalignment.

(a) (b) (c)

Figure 2: Radiative flux distribution of the ETH's HFSS (7 Xe-arc lamps): (a) measured with a calibrated CCD camera; (b) simulated by MC, and (c) measured and simulated along the vertical and horizontal planes.

Experimental validation of the solar reactor model was accomplished by comparing its numerical outputs to experimental data obtained with the prototype solar reactor tested at the HFSS for a set of three experimental runs with Psolar = 2.8, 3,4, and 3.8 kW. A summary of the operating conditions is presented in Table 3.16 Figures 3 (a)-(c) show the experimentally measured (dashed curves) and numerically calculated (solid curves) temperatures at locations TB>1, Tb,2, Tk,1, Tk,2, and TK,3 (positions indicated in Figure 4) as a function of time for three runs with Psolar = 2.8, 3.4, and 3.8 kW. Also shown are the measured (dashed curves) and simulated (solid curve) O2 evolution curves at the outlet of the reactor as a function of time. The temperature of the ceria RPC rose rapidly with increasing Psolar, from the initial 1015 K (average of TB>1 and TB,2) after pre-heating at 0.8 kW to 1800 K at 2.8 kW, 1855 K at 3.4 kW, and 1899 K at 3.8 kW. Additionally, as Psolar increased from 2.8 to 3.8 kW, both the peak and average heating rates increased from 127 K min -1 / 36 K min-1 to 163 K min- / 56 K min- . As expected, higher heating rates and temperatures lead to higher O2 peak rates and higher total O2 evolution. This trend is captured by the reactor model which predicts a peak temperature (average of TB>1 and TB,2) and a total O2 evolution of 1793 K and 1.33 ml g-1ceO2 for 2.8 kW, 1837 K and 1.73 ml g-1ceO2 for 3.4

kW, and 1869 K And 1.93 ml g-1CeO2 for 3.8 kW, respectively. The temperature agreement between simulation and experiment is reasonably good at all locations for the three runs. Discrepancies are attributed to uncertainties in the positioning of the thermocouples and to the extrapolation of measured material properties to higher temperatures, such as the case for k of CeO2 laminate and Al2O3-SiO2 insulation. Good matching is also obtained between measured and simulated O2 evolution rates, especially in the cases of 2.8 kW and 3.4 kW, considering the uncertainties with thermodynamic data at above 1773 K.

Time (min) Time (min) Time (mitl)

Figure 3: (Top) Numerically calculated (solid lines) and experimentally measured (dashed lines) temperatures at locations indicated in Figure 4 and (bottom) numerically calculated and measured O2 evolution rate at the outlet of the reactor as a function of time for the experimental run performed at: (a) Psolar = 2.8 kW, (b) Psolar = 3.4 kW, and (c) Psolar = 3.8 kW.

AI2O3 insulation RPC

aperture

symmetry axis ^

"•"Tb.1

•Tk,2 • Tk,1

shell laminate

Figure 4: Schematic cross-section of the solar reactor showing the measurement locations of the type-B and type-K thermocouples: TB,i and TB>2 at the outer surface of the ceria RPC; TK>1 and TK>2 in the middle of the Al2O3-SiO2 insulation; and TKf3 at the outer reactor shell.

Table 3: Operating conditions used during the experimental campaign and applied for the model validation

Power input during reduction, Psoiar, (kW) 2.8 3.4 3.8

Duration of pre-heating (min) 30 30 30

Power input during pre-heating (kW) 0.8 0.8 0.8

Duration of reduction step (min) 22 Ï 18 16

Ar flow rate front (L min-1) éBhâ 0.2 0.2

Ar flow rate radial inlets (L min-1) 1.8 1.8 1.8

CeO2 mass loading (g) 1413 1413 1413

The solar-to-fuel energy conversion efficiency is defined as

_ AH fuel Jrfueldt

^solar-to-fuel _ ""p p (17)

J Psolar dt + Einert J rinert dt

where rfuel is the molar rate of fuel production, AHfuel is the heating value of the fuel, Psolar is the solar radiative power input, rinert is the flow rate of the inert gas, and Einert is the energy required

to separate the inert gas (assumed 20 kJ mol" inert gas). Assuming stoichiometric fuel production (rfuel = 2rO2) according to Eq. (2b) and accounting for 15 min of pre-heating, the

experimentally determined values of efficiency were: %olar-to-fuel = 1.16%, 1.42%, and 1.73% for 2.8 kW, 3.4 kW, and 3.8 kW, respectively. These are slightly higher than the numerically simulated values: //solar-to-fuel = 1.06%, 1.39%, and 1.55% for 2.8 kW, 3.4 kW, and 3.8 kW, respectively, attributed to the slight under-prediction of the total O2 yield. Note that the sensible heat of solids and gases was not recovered during the experimental runs.

5. Modelling results and discussion

Incoming thermal radiation — Figure 5 shows the radiative flux distribution at Psolar = 3.8 kW that is: (a) impinging on the exposed ceria RPC surface; (b) absorbed on the exposed top Al2O3-SiO2 insulation; and (c) absorbed on the water-cooled cooper-ring (part of reactor front), as determined by MC. Both axial and radial non-uniformity is observed. The front parts of the RPC and the Al2O3-SiO2 insulation are more strongly irradiated than locations towards the rear end because of the large rim angle of the HFSS (>45 degree) combined with the optical design of the

CPC (outlet angle = 90 degrees) which directs the incoming radiation mostly onto areas close to

the reactor front. This resulted in an average radiative flux of 122 kW m on the RPC side walls

-2 -2 and 250 kW m on the RPC back plate compared to peak 690 kW m at locations close to the

reactor front. The radial non-uniformity in flux distribution is attributed to partial misalignment

of the Xe-arcs. In total, 2.3 kW of radiative power (60.5% of Psolar) is volumetrically absorbed

within the RPC structure.

Figure 5: Radiative heat flux at Psoiar = 3.8 kW: (a) impinging on the innermost exposed RPC surface, (b) absorbed by the exposed Al2O3-SiO2 insulation, and (c) absorbed by the water-cooled copper ring close to the reactor's aperture.

The Al2O3-SiO2 insulation receives an average and peak radiative flux of 210 and 393 kW m , respectively, resulting in 0.93 kW (24.5% of Psolar) absorbed radiative power. The water-cooled copper ring which is placed directly after the CPC absorbs 0.19 kW (5% of Psolar).

Temperature distribution and flow analysis — Figure 6 (a) shows the temperature distribution

and normalized velocity vectors of the flow field in the vertical cross-section of the solar reactor

after 30 min pre-heating with Psolar = 0.8 kW and 16 min reduction with Psolar = 3.8 kW. The O2

concentration at peak O2 evolution is depicted in Figure 6 (b). As expected, locations exposed to

high radiative fluxes exhibit higher temperatures. The model predicts a peak and average ceria

temperature of 2258 K and 1915 K, respectively. The highest temperature is achieved close to the

reactor front where the RPC is exposed to a radiative flux exceeding 650 kW m . Such high temperatures are undesired as it causes ceria sublimation and mechanical failure of the RPC

structure, as experimentally observed. ' Due to the very high ceria temperatures, the O2 concentration reaches a peak value of 17% at these locations. The temperature difference across the RPC is 145 K on average. For the Al2O3-SiO2 insulation, the model predicts temperatures above 2200 K at certain locations close to the aperture, which exceeds the melting temperature (2143 K) as experimentally verified. The contact surface of the Al2O3-SiO2 and CeO2 laminate is maintained below 1700 K to prevent undesired side reactions.40 The mean gas temperature in the cavity and at the outlet are 1798 K and 1767 K, respectively. In the reactor front, the mean gas temperature is only 488 K due to the injected flows at T = 293 K and the water-cooled surfaces. Free convection is dominating the flow pattern, causing internal circulations and forcing the radially incoming gases to flow into the reactor front. This situation has a detrimental effect on 7solar-to-fuel because O2 is not efficiently purged from the reactor, limiting the ceria reduction according to Eq. (1). Furthermore, ceria vapor derived by sublimation of the overheated RPC is carried out by the gas flow and condenses on the water-cooled specular CPC, lowering its reflectivity and consequently the radiative power input through the aperture by up to 15%, as experimentally observed. 18

02 Mass fraction Contour [%]

14.5 13.7 13.0 12.2 11.4

10.6 9.9

9.1 S3 7.5 6.8 6.0

5.2 4.4 3.7 2.9 2.1

1.3 0.6 0.001

Gas-gap

Figure 6: (a) Normalized velocity vectors and temperature distribution in the vertical cross-section after 30 min pre-heating with Psolar = 0.8 kW and 16 min reduction with Psolar = 3.8 kW and (b) Normalized velocity vectors and O2-concentration in the vertical cross-section of the cavity-receiver at peak O2-evolution (t = 38 min) at Psolar = 3.8 kW.

These gas circulations can be avoided by increasing the purge gas flow and reversing the flow

direction. Figure 7 shows a contour plot of the velocity and normalized velocity vectors of the

flow field in the vertical cross section for Psolar = 2.8 kW and an Ar flow rate of 12.5 L min-1

provided tangentially through 6 nozzles around the window circumference. The flow direction is

reversed by operating the radial openings as additional outlets instead of inlets. For simplicity, the reduction chemistry is omitted. The tangential injection of Ar causes a swirl flow pattern preventing back flow of gases from the cavity into the reactor front, thus depositions of sublimated CeO2 at the CPC surface. In contrast, providing the Ar flow radially or axially did not prevent the back flow of gases below Ar flow rates of 15 L min-1.

Figure 7: Velocity contour plot and normalized velocity vectors in the vertical cross-section for a stationary simulation performed at Psolar = 2.8 kW. Argon purge gas is provided tangentially through 6 nozzles at the window circumference and exits the reactor through 4 radial and one axial outlet ports.

Energy Flows — Figure 8 shows the instantaneous energy balance as a function of time for the

reduction stage performed with Psolar = 3.8 kW. Indicated is the heat consumed by the

endothermic reaction, the sensible heat content of reactor components, and the heat losses by

conduction, convection, and radiation (reflected and re-emitted). Heating of the reactor

components (reactor shell, Al2O3-SiO2 insulation, CeO2 laminate, CeO2 RPC) consumed 31% of

Psolar on average, but account for 17% of Psolar at the end of reduction (t = 46 min). Conductive

losses to the water-cooled front and through the insulated walls were significant and accounted

for 16% of Psolar on average. Radiative losses, the dominant source of irreversibility, increased considerably with reduction time due to the increasing cavity temperature and accounted for 48% of Psolar on average and 57 % of Psolar peak. Sensible heat loss by the out-flowing gas (Ar/O2 mixture) and convection losses at the window and water-cooled surfaces were less significant and amounted to 1% each. The remaining fraction of energy, about 2.9% of Psolar, was consumed by the endothermic reduction of CeO2.

□ Sensible heat of reactor components

□ Chemical reaction ■ Out-flow heat loss

□ Convection

□ Conduction

□ Radiation

Figure 8: Instantaneous energy balance based on the numerical model for Psoiar = 3.8 kW. Indicated are the heat consumed by the endothermic reaction (Chemical reaction), the sensible heat of the reactor components, and the heat losses by conduction, convection, and radiation (reflected-and re-radiated).

There is room for optimization of the aperture's size to maximize the absorption of Psolar and minimize re-radiation losses.41 The cavity's ability to capture Psolar is given by the apparent absorptivity, aapparent, defined as the fraction of radiative flux across the aperture that is absorbed by the cavity walls. aapparent, determined by MC, is only 0.85 because of 10% reflection losses escaping through the aperture and 5% absorption losses on water-cooled surfaces inside the cavity. Selective coatings for quartz windows with high transmissivity in the visible region of the

solar spectrum and high surface reflectivity in the IR region around the 1.5 ¡um (Wien's displacement law for Planck's blackbody radiation at 2000 K) can help re-capture some of the reflected and emitted radiation by the hot cavity, provided these coatings withstand the high

temperatures. Energy required for heating the reactor components can be reduced by using thermal insulation materials with lower specific heat capacities. Further, minimizing AT between the reduction and oxidation steps of the cyclic process or operation under pressure-swing isothermal conditions43-45 (not discussed in this study) can eliminate this energy penalty. Conduction losses can be obviously reduced by improving the insulation and by avoiding the heat bridges created by water-cooled surfaces, but the Al-made CPC and frustum require active cooling because of the exposure to radiative fluxes exceeding 2000 W/m . Alternative cooling fluids (e.g. oil) should be assessed to minimize AT between the hot cavity and actively cooled reactor front. Operation under vacuum pressures could further reduce heat losses to the surrounding, reduce usage of purge gas, and achieve lower O2 partial pressures.13 The radiative properties of the ceria RPC, especially the optical thickness, can be optimized for efficient radiative penetration and absorption by adjusting the pore size and porosity.23

To increase %olar-to-fuel an alternative solar reactor design depicted in Figure 9 is proposed. The cavity has a conical shape to enable a more uniform distribution of absorbed incoming radiation and to avoid hot spots. A 6i - 0o secondary concentrator46 with acceptance angle 0-= 45° and exit angle 6o= 60° is incorporated to reduce the aperture diameter to 3.5 cm, boost the solar concentration ratio, and prevent direct high-flux irradiation of the insulation close to the aperture. This element is actively cooled but maintained at T = 573 K to lower conduction losses. The ceria mass loading is increased to 2500 g to enhance the ratio of reactive to inert material (insulation, shell). Purge and reactant gases are provided tangentially via 6 radially arranged injection nozzles

located close to the quartz window. Product gases exit the reactor through four radial and one axial outlet port.

CeO.RPC

Al203-Si02 insulation

Ce02 laminate

Outlet |

Inconel shell

secondary concentrator Figure 9: Schematic of the conical solar reactor configuration.

Quartz window

Figure 10 shows the numerically calculated average temperatures of the ceria RPC, Al2O3-SiO2 insulation, and reactor shell along with the O2 evolution rate during a redox cycle at Psolar = 2.0 kW. The non-solar oxidation step was modeled assuming a 20 min cooling phase with Psolar = 0 kW. During thermal reduction, an average ceria heating rate of 18.0 K min-1 is predicted leading to peak average ceria temperature of 1963 K min-1. Similar to the cylindrical cavity, O2 evolution starts immediately after increasing Psolar and reaches peak and average rates of 0.15 and 0.1155 mL min-1 g-1 CeO2, respectively. The total predicted O2 evolution is 3 times higher than the one experimentally achieved with the cylindrical cavity.

Time (min)

Figure 10: Numerically calculated average temperatures of the ceria RPC, Al2O3-SiO2 insulation, and reactor shell and (bottom) numerically calculated O2 evolution rate at the reactor outlets for a redox cycles with Psolar = 2 kW during reduction and Psolar = 0 kW during oxidation.

Figure 11 shows the temperature distribution (a) and the O2-concentration (b) along with the normalized velocity vectors of the flow field in the vertical cross-section of the solar reactor at the end of the reduction step (t = 40 min) and at peak O2 evolution (t = 20 min) performed at Psolar = 2.0 kW, respectively. The conical cavity design coupled to the 0i - 6o secondary concentrator results in a more homogeneous temperature distribution within the RPC, on average 52 K across the structure, and prevents hot spots and melting of the Al2O3-SiO2 insulation. The tangential injection of purge gas close to the window circumference at flow rates > 7 L min-1 induces a

swirl flow which prevents backflow of gases into the reactor front and thereby CeO2 depositions on the secondary concentrator, consistent with the results of Figure 7. Furthermore, it also hinders

Figure 11: (a) Normalized velocity vectors and temperature distribution in the vertical cross-section of the cavity-receiver at the end of the reduction step (t = 40 min) performed with Psolar = 2.0 kW and (b) normalized velocity vectors and O2-concentration in the vertical cross-section at peak O2-evolution (t = 20 min).

O2 from circulating into the reactor front which enhances purging. This can be seen in Figure 11 (b) which shows a clear difference in O2 concentration between the reactor front and the reactor cavity. Assuming stoichiometric oxidation with CO2 (rCO = 2-rO2), the new solar reactor design reaches nsolar-to-fuel = 5.4% (without heat recovery).

The superior performance compared to the cylindrical cavity is attributed to lower radiation and conduction losses (on average 57% lower), to a more uniform temperature distribution within the reactor cavity (av. AT across RPC: cylindrical reactor = 145 K, conical reactor = 52 K), to more effective purging of O2 from the cavity by the Ar flow (av. PO2 at peak O2-evolution: cylindrical reactor = 0.0999 atm, conical reactor = 0.0185 atm), and to a higher mass loading of ceria (mcylindrical = 1413 g, mconical = 2500 g). Further increase of nsolar-to-fuel to 6.4% is feasible by recovering the sensible heat of gases and solids during the temperature swing between reduction and oxidation steps.

7. Summary and conclusions

We have presented a dynamic numerical model of a high-temperature solar reactor that couples Monte-Carlo ray-tracing to computational fluid dynamics. Experimental validation of the model was accomplished by comparing temperatures and O2 evolution rates with experimentally measured data obtained with a 4-kW solar reactor prototype for a set of experimental runs conducted at ETH's high-flux solar simulator facility. Radiation losses due to reflection and reemission and conduction losses through water-cooled components were identified as the major heat losses, accounting for 48% and 16% of the total solar radiative power input, respectively. Temperature distribution inside the cavity was observed to depend on the distribution of absorbed

incoming radiation and reached peak values of 2250 K at highly exposed regions close to the aperture. Such high temperatures induce ceria sublimation and cause local melting of the Al2O3-SiO2 insulation. Further complication aroused from the buoyancy-driven natural convection flow carrying CeO2(g) towards the actively-cooled reactor front where it eventually condensed, thereby reducing the CPC's surface reflectance and consequently the radiative power input through the aperture. Increasing the purge gas flow rate and reversing the flow direction by providing the gas tangentially through 6 nozzles close to the window circumference is found to prevent the backflow of gas to the reactor front.

An alternative reactor design featuring a conical cavity shape coupled to QrQo secondary concentrator enabled a more uniform distribution of absorbed incoming radiation and prevented hot spots on the insulation. Lower radiation/conduction losses, higher ceria mass loading, and effective purging of evolved O2 resulted in nsolar-to-fuel of 5.4% (without heat recovery). Further increase of nsolar-to-fuel to 6.4% is feasible by recovering the sensible heat of gases and solids during the temperature swing between reduction and oxidation steps. Other improvements include the use of selective coatings for quartz windows, RPC with optimized pore size and porosity, and operation under pressure-swing isothermal conditions.

Nomenclature

Symbols

Afs ai bi C

convection

fluid-solid area density (m-1) fitting parameter fitting parameter solar concentration ratio

heat capacity(J mol-1 K-1)

energy for inert gas separation from the air (J mol-1) enthalpy (J kg-1)

convective heat transfer coefficient (W m K- ) interphaseal heat transfer coefficient (W m K ) higher heating value of the fuel (J mol-1)

reaction enthalpy (J mol-1) radiation intensity (W m )

blackbody radiation emission intensity (W m )

identitiy matrix

isotropic porosity tensor thermal conductivity (W m-1 K-1) radiation power input (W)

pressure (atm) fluid-solid heat source (W) position vector

molar fuel production rate (mol s-1) molar oxygen evolution rate (mol s-1)

rinert

SE,solar Se ,reaction

SM,buoy Sm , porous

T Ts Tf AT t

Greek symbols a

^apparent

flow rate of inert gas (mol s-1) path length (m) direction vector

oxygen mass source (mol m s )

radiation source (W m- / W m- )

reaction energy source (W m )

buoyancy momentum loss vector (kg m s-1)

porous momentum loss vector (kg m s-1)

temperature (K)

solid temperature (K)

fluid temperature (K)

temperature difference (K)

time (s)

velocity vector (m s-1) O2 concentration

absorption coefficient (m-1) apparent cavity absorptance extinction coefficient (m-1) scattering coefficient (m-1) nonstoichiometry porosity

surface emittance dynamic viscosity (kg m-1 s-1)

density (kg m- )

Ps Ts W

surface total reflectance

transmittance

solid angle (degree)

nsoiar-to-fuei solar-to-fuel energy conversion efficiency

V qr radiation source term (W)

Dimensionless Groups

Br Birkman number

Pe Péclet number

Pemass Péclet number for mass transport

Peth Péclet number for heat trasfer

Re Reynolds number

Abbreviations

CCD charge-coupled device

CFD computational fluid dynamics

CPC compound parabolic concentrator

ETH Swiss Federal Institute of Technology

GC gas chromatography

HFSS High-Flux Solar Simulator

MC Monte-Carlo method

RPC reticulated porous ceramic

SLPM standard liters per minute at 273.15 K and 1 atm

Acknowledgements

We gratefully acknowledge the financial support by the Swiss Competence Center Energy & Mobility, the Helmholtz-Gemeinschaft Deutscher Forschungszentren (Virtuelles Institut SolarSyngas), and the European Research Council under the European Union's ERC Advanced Grant (SUNFUELS □ n° 320541).

References

(1) Steinfeld, A., Solar thermochemical production of hydrogen—a review. Solar Energy, 2005, 78, (5), 603-615.

(2) Perkins, C.; Weimer, A. W., Likely near-term solar-thermal water splitting technologies. International Journal of Hydrogen Energy, 2004, 29, (15), 1587-1599.

(3) Smestad, G. P.; Steinfeld, A., Review: Photochemical and Thermochemical Production of Solar Fuels from H2O and CO2 Using Metal Oxide Catalysts. Industrial & Engineering Chemistry Research, 2012, 51, 11828-11840.

(4) Miller, J. E.; McDaniel, A. H.; Allendorf, M. D., Considerations in the Design of Materials for Solar-Driven Fuel Production Using Metal-Oxide Thermochemical Cycles. Advanced Energy Materials, 2013, 4, (2), 1300469.

(5) Chueh, W. C.; McDaniel, A. H.; Grass, M. E.; Hao, Y.; Jabeen, N.; Liu, Z.; Haile, S. M.; McCarty, K. F.; Bluhm, H.; El Gabaly, F., Highly Enhanced Concentration and Stability of Reactive Ce3+on Doped CeO2 Surface Revealed In Operando. Chemistry of Materials, 2012, 24, (10), 1876-1882.

(6) Chueh, W. C.; Haile, S. M., A thermochemical study of ceria: exploiting an old material for new modes of energy conversion and CO2 mitigation. Philos Transact A Math Phys Eng Sci, 2010, 368, (1923), 3269-94.

(7) Zinkevich, M.; Djurovic, D.; Aldinger, F., Thermodynamic modelling of the cerium-oxygen system. Solid State Ionics, 2006, 177, (11-12), 989-1001.

(8) Lapp, J.; Davidson, J. H.; Lipinski, W., Heat Transfer Analysis of a Solid-Solid Heat Recuperation System for Solar-Driven Nonstoichiometric Redox Cycles. Journal of Solar Energy Engineering, 2013, 135, (3), 031004-031004.

(9) Diver, R. B.; Miller, J. E.; Allendorf, M. D.; Siegel, N. P.; Hogan, R. E., Solar Thermochemical Water-Splitting Ferrite-Cycle Heat Engines. Journal of Solar Energy Engineering, 2008, 130, (4), 041001-8.

(10) Kaneko, H.; Miura, T.; Fuse, A.; Ishihara, H.; Taku, S.; Fukuzumi, H.; Naganuma, Y.; Tamaura, Y., Rotary-Type Solar Reactor for Solar Hydrogen Production with Two-step Water Splitting Process. Energy & Fuels, 2007, 21, (4), 2287-2293.

(11) Abanades, S.; Flamant, G., Thermochemical hydrogen production from a two-step solar-driven water-splitting cycle based on cerium oxides. Solar Energy, 2006, 80, (12), 1611-1623.

(12) Scheffe, J. R.; Welte, M.; Steinfeld, A., Thermal Reduction of Ceria within an Aerosol Reactor for H2O and CO2 Splitting. Industrial & Engineering Chemistry Research, 2014, 53, (6), 2175-2182.

(13) Ermanoski, I.; Siegel, N. P.; Stechel, E. B., A New Reactor Concept for Efficient Solar-Thermochemical Fuel Production. Journal of Solar Energy Engineering, 2013, 135, (3), 031002031002.

(14) Kodama, T.; Enomoto, S.-i.; Hatamachi, T.; Gokon, N., Application of an Internally Circulating Fluidized Bed for Windowed Solar Chemical Reactor with Direct Irradiation of Reacting Particles. Journal of Solar Energy Engineering, 2008, 130, (1), 014504.

(15) Chueh, W. C.; Falter, C.; Abbott, M.; Scipio, D.; Furler, P.; Haile, S. M.; Steinfeld, A., High-Flux Solar-Driven Thermochemical Dissociation of CO2 and H2O Using Nonstoichiometric Ceria. Science, 2010, 330, (6012), 1797-1801.

(16) Furler, P.; Scheffe, J. R.; Gorbar, M.; Moes, L.; Vogt, U.; Steinfeld, A., Solar thermochemical CO2 splitting utilizing a reticulated porous ceria redox system. Energy & Fuels, 2012, 26, 70517059.

(17) Furler, P.; Scheffe, J.; Marxer, D.; Gorbar, M.; Bonk, A.; Vogt, U.; Steinfeld, A., Thermochemical CO2 splitting via redox cycling of ceria reticulated foam structures with dual-scale porosities. Physical Chemistry Chemical Physics, 2014.

(18) Furler, P.; Scheffe, J. R.; Steinfeld, A., Syngas production by simultaneous splitting of H2O and CO2 via ceria redox reactions in a high-temperature solar reactor. Energy & Environmental Science, 2012, 5, (3), 6098.

(19) Welford, W. T.; Winston, R., High Collection Nonimaging Optics. Academic Press, San Diego, 1989.

(20) Petrasch, J. r.; Coray, P.; Meier, A.; Brack, M.; HaDberling, P.; Wuillemin, D.; Steinfeld, A., A Novel 50kW 11,000 suns High-Flux Solar Simulator Based on an Array of Xenon Arc Lamps. Journal of Solar Energy Engineering, 2007, 129, (4), 405.

(21) Seguin, D.; Montillet, A.; Comiti, J.; Huet, F., Experimental characterization of flow regimes in various porous media—II: Transition to turbulent regime. Chemical Engineering Science, 1998, 53, (22), 3897-3909.

(22) Zircar Zirconia, Inc., Thermal Conductivity of Zircar Zirconia Fibrous Insulation. http://zircarzirconia.com/technical-documents/thermal-conductivity-zircar-zirconia-fibrous-insulation/, January 2014.

(23) Suter, S.; Steinfeld, A.; Haussener, S., Pore-level engineering of macroporous media for increased performance of solar-driven thermochemical fuel processing. International Journal of Heat and Mass Transfer, 2014, 78, (0), 688-698.

(24) Haussener, S.; Coray, P.; Lipinski, W.; Wyss, P.; Steinfeld, A., Tomography-Based Heat and Mass Transfer Characterization of Reticulate Porous Ceramics for High-Temperature Processing. Journal of Heat Transfer, 2010, 132, (2), 023305.

(25) Petrasch, J.; Meier, F.; Friess, H.; Steinfeld, A., Tomography based determination of permeability, Dupuit-Forchheimer coefficient, and interfacial heat transfer coefficient in reticulate porous ceramics. International Journal of Heat and Fluid Flow, 2008, 29, (1), 315-326.

(26) Touloukian, Y.; Dewitt, D., Thermal Radiative Properties Nonmetallic Solids. IFI/Plenum, New York, Washington, 1972, Vol. 8.

(27) Touloukian, Y., Thermophysical properties of high temperature solid materials: Oxides and their solutions and mixtures. Part I: Simple oxygen compunds and theire mixtures. Thermophysical Properties Research Center, Purdue University, 1967.

(28) Siegel, R.; Howell, J., Thermal Radiation Heat Transfer. Taylor&Francis, 2002.

(29) Zircar Zirconia, Aluminium Boards, Discs & Cylinders, TYPE Buster. http://www.zircarzirconia.com/doc/GA-B.pdf, January 2014.

(30) Special Metal Corporation, Physical Constants and Thermal Properties Inconel 600. http://www.specialmetals.com/documents/Inconel alloy 600 (Sept 2008).pdf, January 2014.

(31) Zimmermann, D., Flow Modeling of a Solar Thermogravimeter. Master Thesis ETH Zurich, 2012.

(32) Churchill, S. W.; Chu, H. H. S., Correlating equations for laminar and turbulent free convection from a vertical plate. International Journal of Heat and Mass Transfer, 1975, 18, (11), 13231329.

(33) Churchill, S. W.; Chu, H. H. S., Correlating equations for laminar and turbulent free convection from a horizontal cylinder. International Journal of Heat and Mass Transfer, 1975, 18, (9), 10491053.

(34) Panlener, R. J.; Blumenthal, R. N.; Garnier, J. E., A thermodynamic study of nonstoichiometric cerium dioxide. Journal of Physics and Chemistry of Solids, 1975, 36, (11), 1213-1222.

(35) Scheffe, J. R.; Steinfeld, A., Thermodynamic Analysis of Cerium-Based Oxides for Solar Thermochemical Fuel Production. Energy & Fuels, 2012, 26, (3), 1928-1936.

(36) Petrasch, J., A Free and Open Source Monte Carlo Ray Tracing Program for Concentrating Solar Energy Research. In ASME Conf. Proc., 2010; pp 125-132.

(37) Lockwood, F. C.; Shah, N. G., A new radiation solution method for incorporation in general combustion prediction procedures. Symposium (International) on Combustion, 1981, 18, (1), 1405-1414.

(38) Ansys Inc., Ansys CFX-Solver Theory Guide, Release 14.5. 2012.

(39) Haering, H.-W., The Air Gases Nitrogen, Oxygen and Argon. Wiley-VCH Verlag GmbH, 2008.

(40) Mizuno, M.; Berjoan, R.; Coutures, J.-P.; Foex, M., Phase Diagram of the System Al2O3-CeO2 at Liquidus Temperature. Journal of the Ceramic Association, Japan, 1975, 83, (954), 90-96.

(41) Steinfeld, A.; Schubnell, M., Optimum aperture size and operating temperature of a solar cavity-receiver. Solar Energy, 1993, 50, (1), 19-25.

(42) Maag, G.; Falter, C.; Steinfeld, A., Temperature of a Quartz/Sapphire Window in a Solar Cavity-Receiver. Journal of Solar Energy Engineering, 2011, 133, (1), 014501.

(43) Bader, R.; Venstrom, L. J.; Davidson, J. H.; Lipinski, W., Thermodynamic Analysis of Isothermal Redox Cycling of Ceria for Solar Fuel Production. Energy & Fuels, 2013.

(44) Hao, Y.; Yang, C.-K.; Haile, S. M., High-temperature isothermal chemical cycling for solar-driven fuel production. Physical Chemistry Chemical Physics, 2013, 15, (40), 17084-17092.

(45) Muhich, C. L.; Evanko, B. W.; Weston, K. C.; Lichty, P.; Liang, X.; Martinek, J.; Musgrave, C. B.; Weimer, A. W., Efficient Generation of H2 by Splitting Water with an Isothermal Redox Cycle. Science, 2013, 341, (6145), 540-542.

(46) Rabl, A.; Winston, R., Ideal concentrators for finite sources and restricted exit angles. Applied Optics, 1976, 15, (11), 2880-2883.

Highlights manuscript "Heat transfer and fluid flow analysis of a 4 kW solar thermochemical reactor for ceria redox cycling"

• Splitting of H2O and CO2 is performed using a solar thermochemical redox cycle.

• The solar reactor features a reticulated porous ceramic foam made of CeO2.

• A heat/mass transfer model coupling Monte-Carlo ray tracing to CFD is developed.

• Experimental validation is accomplished with a 4-kW solar reactor prototype.

• The model is applied to identify irreversibilities and improve the reactor design.