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International Journal of Heat and Mass Transfer

journal homepage: www.elsevier.com/locate/ijhmt

Reticulated porous ceria undergoing thermochemical reduction with high-flux irradiation

Simon Ackermann a, Michael Takacs a, Jonathan Scheffe b, Aldo Steinfeld a'*

a Department of Mechanical and Process Engineering, ETH Zürich, Sonneggstrasse 3, 8092 Zürich, Switzerland b Department of Mechanical and Aerospace Engineering, University of Florida, USA

i CrossMark

ARTICLE INFO

Article history:

Received 10 June 2016

Received in revised form 31 October 2016

Accepted 7 November 2016

Keywords: Solar

Thermochemistry Redox cycle Porous ceria

ABSTRACT

A numerical and experimental analysis is performed on the solar-driven thermochemical reduction of ceria as part of a H2O/CO2-splitting redox cycle. A transient heat and mass transfer model is developed to simulate reticulated porous ceramic (RPC) foam-type structures, made of ceria, exposed to concentrated solar radiation. The RPC features dual-scale porosity in the mm-range and im-range within its struts for enhanced transport. The numerical model solves the volume-averaged conservation equations for the porous fluid and solid domains using the effective transport properties for conductive, convective and radiative heat transfer. These in turn are determined by direct pore-level simulations and Monte-Carlo ray tracing on the exact 3D digital geometry of the RPC obtained from tomography scans. Experimental validation is accomplished in terms of temporal temperature and oxygen concentration measurements for RPC samples directly irradiated in a high-flux solar simulator with a peak flux of 1200 suns and heated to up to 1940 K. Effective volumetric absorption of solar radiation was obtained for moderate optically thick structures, leading to a more uniform temperature distribution and a higher specific oxygen yield. The effect of changing structural parameters such as mean pore diameter and porosity is investigated.

© 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://

creativecommons.org/licenses/by/4.0/).

1. Introduction

Solar-driven thermochemical cycles for splitting H2O and CO2 comprise an endothermic step for the reduction of a metal oxide using concentrated sunlight followed by an exothermic step for the oxidation of the reduced metal oxide with H2O and CO2 to form the basic components of syngas, H2 and CO [1]. Syngas can then be further processed to conventional liquid hydrocarbon fuels (e.g. kerosene, diesel) via Fischer-Tropsch synthesis or other gas-to-liquid technologies. Ceria-based oxides have emerged as highly attractive redox materials [2-14] because of their relatively high oxygen exchange capacities [15-19], fast oxygen-ion transport [20-22] and high oxidation rates [23-27]. The redox reactions with pure ceria are represented by:

High - temperature reduction : CeO2 ! CeO2-d + 2 O2 (1)

Low - temperature oxidation with H2O :

CeO2-d + dH2O ! CeO2 + dH2 (2a)

* Corresponding author. E-mail address: aldo.steinfeld@ethz.ch (A. Steinfeld).

Low - temperature oxidation with CO2 : CeO2-d + dCO2 ! CeO2 + dCO (2b)

where the non-stoichiometry d denotes the reduction extent.

In a previous paper [14], we proposed the use of reticulated porous ceramic (RPC) foam-type structures having dual-scale porosity: mm-size pores with struts containing micron-size pores. The mm-size pores enable volumetric absorption of concentrated solar radiation [28] and thus effective heat transfer during the reduction step, while the micron-size pores within the struts offer increased specific surface area leading to enhanced reaction kinetics during the oxidation step. The thermochemical redox cycle is performed under a temperature/pressure-swing operational mode; thus, the cyclic process is inherently of transient nature and the reduction step, Eq. (1), proceeds as the RPC is heated to the desired upper temperature. It was experimentally shown that these ceria RPC structures with dual-scale porosity remain morphologically stable over 227 consecutive redox cycles in a solar reactor [14]. A representative 3D rendering of a computer tomography (CT) scan of a RPC sample is shown in Fig. 1, along with the scanning electron micrograph (SEM) of the strut's cross section.

Optimization of the RPC structure demands the development of numerical simulation models for heat and mass transfer [13,29,30].

http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.11.032 0017-9310/© 2016 The Authors. Published by Elsevier Ltd.

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Nomenclature

Symbols

Adomain area of the volume-averaged domain [m2]

Asf fluid-solid interfacial area relevant for the convective

transport [m-1]

cp,(.) heat capacity [J kg-1 K-1]

dm,(.) mean pore diameter [m]

DAr02 binary gas diffusion coefficient [m2 s-1]

Fd Dupuit-Forchheimer coefficient [m-1]

hsf interfacial heat transfer coefficient [W m-2 K-1]

H(.) Enthalpy [J kg-1]

HVco heating value of CO [J kg-1]

AH02 reaction enthalpy [kJ mol-1]

I intensity of radiative flux [Wm-2 sr-1]

Ib blackbody radiation intensity [W m-2sr-1]

Isolar flux of incident solar radiation [W m-2]

keff effective thermal conductivity [W m-1 K-1]

k(.) thermal conductivity [W m-1 K-1]

K permeability [m2]

L length of domain [m]

mO2 oxygen mass [kg]

M molar mass [kg mol-1]

nppi number of pores per inch [-]

n normal vector [-]

p pressure [Pa]

Dp pressure drop [Pa]

P02 oxygen partial pressure [Pa]

qout radiative heat flux leaving the solid domain [W m-2]

Qco Combustion heat of CO [J]

Qsolar cumulative energy of the incident solar radiation [J]

r position vector

r total hemispherical reflectance of ceria [-]

r02 oxygen evolution rate [kg s-1]

s path length of a ray [m]

s direction vector

s' scattering direction vector

SMD momentum source for porous media [kg m-2 s-2]

Sradiative source term for the radiative net flux [W m-3]

Sreradiation source term for the reradiated flux [W m 3]

Ssolar source term for the absorbed high-flux irradiation

[W m-3]

t time [s]

T(.) temperature [K]

Ud superficial velocity [m s-1]

u velocity vector

Vcell cell volume [m3]

Y02 oxygen concentration [-]

Greek symbols

a(.) absorption coefficient [m-1]

b effective extinction coefficient of RPC [m-1]

d nonstoichiometry [-]

e(.) porosity [-]

eemit total hemispherical emittance of ceria [-]

g solar-to-fuel energy conversion efficiency [%]

i(.) dynamic viscosity [Pa s]

Is cosine of the scattering angle [-]

p(.) density [kg m-3]

r scattering coefficient [m-1]

Ö"S Stefan-Boltzmann constant [W m-2 K-4]

U scattering phase function [-]

X' solid angle [rad]

Dimensionless numbers Nu Nusselt number [-] Pr Prandtl number [-]

Re Reynolds number [-]

Operator

<. > superficial average Subscripts

amb ambient conditions Ar argon

CeO2 ceria f fluid phase

O2 oxygen

RPC-dual morphological property of RPC with porous struts (dual-scale porosity)

RPC-single morphological property of RPC with non-porous

struts

s solid phase

strut morphological property of the porous strut Abbreviations

CFD computational fluid dynamics

CT computed tomography

DPLS direct pore level simulation

ETH Swiss Federal Institute of Technology in Zurich

FV finite volume

HFSS high flux solar simulator

MC Monte Carlo

ppi pores per inch

RPC reticulated porous ceramic

The effective transport properties can be determined by applying direct pore-level simulations (DPLS) on the exact 3D digital representation of the RPC, including the im-size pores of the struts, obtained by high-resolution synchrotron CT [31-37]. Since the numerical solution of the governing unsteady Navier-Stokes equations at the pore scale is computational expensive, the volume-averaging theory for porous media is applied for the fluid and solid domains [38-42] by incorporating the effective transport properties determined by DPLS. In this paper, we follow this methodology to develop a heat and mass transfer model of the ceria RPC with dual-scale porosity and investigate its transient behaviour during the reduction step. The model is validated with experimental data obtained from temporal measurements of temperature and reduction extents on RPC samples exposed to high-flux irradiation. To guide the optimization of the RPC structure, virtual samples with a wide range of porosities and mean pore diameters are numeri-

cally engineered based on the CT scan of a real RPC sample and their performance is studied by applying the heat and mass transfer model.

2. Experimental methods

Ceria RPC samples with dual-scale porosities were manufactured of cylindrical shape, 30 mm-diameter and 15mm-height, following the recipe described previously [14]. Two mm-size porosities were selected: 10 and 35 pores per inch (ppi) foams with a corresponding porosity of 0.825 and 0.867, respectively, and mean pore diameter of 2.3 and 0.7 mm, respectively. The strut porosity was 0.26 with a mean pore diameter of 10 im [37].

The experimental setup is schematically shown in Fig. 2. Experimentation was carried out at ETH's High-Flux Solar Simulator (HFSS) [43], which comprises an array of high-pressure Xenon arcs,

mm-sized pores

Concentrated solar radiation

Gas flow

p,m-sized pores

Fig. 1. A 3D rendering of a computer tomography (CT) scan of the RPC structure, along with the scanning electron micrograph (SEM) of the strut's cross section. The RPC features dual-scale porosity: the mm-size pores enable efficient volumetric absorption of concentrated solar radiation during the reduction step while the lm-size interconnected pores within the struts provide enhanced kinetic rates during the oxidation step.

each closed-coupled with truncated ellipsoidal specular reflectors, and provides a source of intense thermal radiation - mostly in the visible and IR spectra - that closely approximates the heat transfer characteristics of highly concentrating solar systems. The radiative flux distribution at the focal plane was measured optically using a calibrated CCD camera focused on a Lambertian (diffusely reflect-

ing) target and verified with a water calorimeter. A 45°-mirror is used to re-direct the radiation beam towards the sample. The ceria RPC sample was placed on top of a ZrO2 flat porous crucible, laterally lined with Al3O2 insulation, and positioned with its top surface at the HFSS's focal plane. The radiative flux distribution was continuous and uniform over the sample surface. A transparent quartz envelope provided the reaction chamber for controlled gas atmosphere and access to direct irradiation. A water-cooled metallic jacket protected the quartz for the thermal load and spilled radiation. Three thermocouples were placed inside the RPC along its axis: in the front, bulk, and back at 2, 8, and 14 mm below the top surface, respectively. The outlet gas composition was monitored on-line with a nondispersive infrared sensor coupled with an O2 electrochemical sensor (Siemens Ultramat 23: frequency 2 Hz) and a gas chromatograph (Varian, CP-4900 Micro GC; frequency 0.0073 Hz). The reduction extent was calculated based on the O2 evolution. For each run, three heating and cooling cycles were performed to ensure reproducibility.

Micrometer and sub-micrometer CT were conducted on ceria RPC samples with 10 ppi and various strut porosities [37,44]. The scan specifications and the morphological analysis were documented in an earlier publication [37]. The scans of this RPC are used as a corner stone for the numerical engineering of RPCs with different ppi and porosities.

3. Numerical methods

RPC geometries with a wide range of porosities and mean pore diameters (mm-size) were digitally engineered on the basis of the CT scans by dilation/erosion of the struts with spherical structuring elements on the fluid-solid interface and by scaling of the actual scan voxel size [45], as schematically shown in Fig. 3. The relevant morphological properties are the strut porosity estrut, the foam porosity £Rpc-single, the total (dual-scale) porosity eRpC-dual, and amount of pores per inch nppi [37]. Note that dilation/erosion of the struts changes eRPC-single while keeping nppi constant, while the opposite is true for scaling. A correlation for the specific surface area as a function of eRPC-single and nppi is listed in Table 1. The strut morphology was kept constant with estrut = 0.3 and a mean pore

ceria RPC

45°-tilted mirror

quartz dome --—gas inlet

Insulation

water-cooled jacket

_ gas outlet / to gas analysis

front/bulk/back thermocouples

Fig. 2. Schematic of the experimental setup.

Table 1

List of correlations for the morphological and effective heat/mass transport properties of the ceria RPC with dual-scale porosity.

Correlation

Morphology Porosity

Mean pore diameter

Specific surface area (relevant for convective heat and mass transport)

Heat transport

Effective thermal conductivity [37]

eRPC -dual — eRPC -single — eRPC-single) ' estrut

dm,RPC — (5:3022 ' 10-5 ' eRpC-single + 2:1549 -10-5) -357

A =__nppi _

sf ^ IFns^ficTîrF^^ ' . -1 -Vi'^ii:. 1 n

- — 0:6223 ' eRPC-dual '

-+(1 - 0:6223 ' SRPC-dual)

Heat transfer coefficient Dimensionless numbers

Extinction coefficient Scattering phase function

Mass transport Permeability

Dupuit-Forchheimer coefficient CeO2

Specific heat capacity [13] Thermal conductivity [57] Reduction enthalpy [13] Equilibrium thermodynamics [15]

Hemispherical total emittance [13,57] Total hemispherical reflectance

for 5780 K [46] Total hemispherical reflectance

for 1773 K [46] Binary gas diffusivity [58]

'(1:0548 ' ÊRPC-dual ' ¡¿^ + 1 - 1:0548 ' £RPC-dual)

h — JNui 2

Nu — 4:173 + 2:359 ' £RPC-single + (0:3772 ' ^-single - 0:7479 ' %PC-single + 0:4849)

Re1:0953-0:2239'EEPC-singie Pr0671-0:0213'ERPC-singie Re _ Pf UD 'dm.RPC

Pr — Cpk' 11

-630:674eRJ>C-single-120:060eÏPC-single+1229:36 b 1000'dm.RPC

U — 0:63 ' 12 - 1:43 ' 1s + 0:79

1:46'10-6 n357-1:198'10-6

Cp,Ce02 — -0:000127069 ' T2 + 0:2697656 ' T + 299:8696 Cp,Ce02 = 444.27 for T > 1100 K

kce02 — -1:7234232 ' 10-9 ' T3 + 1:1203174 ' 10-5 ' T2 - 0:024019964 ' T + 17:800409 -DHo ,mol — 969:408715407529 - 503:738744939872 ' d0 5

d — 10-(2 14591 10-s T2 -9 88196 10-3 T+12 21108) ' ^po^x 1:25424'10-7't2-3:09807'10-4T-1 83281'10-2

V Pû y

with T in °C

- — 0:7

r(d)|;

0315600

(5+10-10) '

1:748573 ' d 3:106837 d

T3 + 1:2229562900 ' 10-10 ' T2

+4:8414771319 ' 10-8 ' T - 6:2970340089 ' 10-

K _ KPC-single

5:4685 Ai

DAr02 — -6:7617280958 ' 10

diameter of 10 im, which was shown to provide fully interconnected pore network and relatively high mass loading [37,11].

Governing conservation equations: A 1D volume-averaged heat and mass transfer model of the RPC was implemented in a commercial CFD software (ANSYS® Academic Research, release 15.0). The governing energy conservation equations of the solid and fluid phases were modelled separately on two spatially congruent cell zones. For the solid phase:

((1 - £RPC-dual)(Ps>(Hs» = V ' (eff V<Ts}) + Sradiative

+ rO2 M DHO2 (d) + hsfAsf (<Tf }-<T.})

M02 V cell

where qs is the density of the solid, Hs is the enthalpy of the solid per unit mass, keff is the effective thermal conductivity, d is the oxygen nonstoichiometry of ceria, rO2 (Dd) =/ (@<pOi} >@§r) is the oxygen mass release rate, DHO2 is the reaction enthalpy, hsf is the interfacial heat transfer coefficient determined by DPLS, Asf is the pore specific surface area for the mm-size pores, MO2 the molar mass of oxygen, and Ts and Tf the temperatures of the solid and fluid domains, respectively. Eq. (3) contains the rate of enthalpy change, the conduction term, and three source terms for the spatially-dependent volumetric net radiative source Sradiative, the reaction enthalpy and the convective heat transfer between the solid and fluid domains. Sradiative is found by solving the radiative heat transfer equation

along path s for an absorbing, emitting, and anisotropically scattering medium:

s ' VI(r, s) + bI(r, s) — aIb(r) + — J I(r, s')U(s', s)dX

where I is the radiation intensity, Ib is the blackbody radiation intensity depending on the local temperature, r is the position vector, s is the direction vector, s' is the scattering direction vector, b the extinction coefficient, a is the absorption coefficient, r is the scattering coefficient, and U is the scattering phase function. In addition, Sradiative accounts for the incident concentrated solar radiation (Ssolar) absorbed in each volumetric cell as it penetrates the RPC and undergoes attenuation. Thus, Sradiative = SSolar + Sreradiation with Sreradiation = a(4p/b - f4p ZdX'). Ssolar is determined as a function of the reflectivity (which in turn depends on d, see Table 1 [46]), eRPC-single, dm,RPC and the radiation penetration depth by applying an in-house Monte Carlo ray tracing code [47]. Refraction is neglected because the surface of the struts is assumed opaque. For the geometric optics regime, a = b (1 - r) and r = b ■ r, where b is determined by MC, and r is the reflectivity of CeO2.

For the fluid phase:

I (£rpC-dual hPf }<Hf }) + V'«u)(Pf }<Hf })

— V ' (£rpc-dual<kf }V<Tf}) + hsf Asf (<Ts} - <Tf})

where qf is the fluid density, Hf is the fluid enthalpy per unit mass and kf is the fluid thermal conductivity for the mole-weighted

species composition of the fluid. Eq. (5) contains the rate of enthalpy change, the convection term, the conduction term, and the convective heat transfer between the solid and fluid domains. The fluid phase was modelled as a binary O2/Ar mixture, assumed a Newtonian incompressible ideal gas with pfRgas7"f = pM. Note that coupling between the fluid and solid domains is through the con-vective heat transfer term. Additionally for the fluid phase, the mass, momentum, and species conservation equations are given by:

dSRPC-dual (Pf > dt

+ V • (ËRPC-dualhPf >(u» =

ro2 (Ad)

V cell

d(eRPC-dual (Pf >(Y o2 >) dt

+ V • (£RPC-dual (u>(Pf >(YO2 >)

ro2 (Ad)

= V • (ÊRPC-dualDArO2 V((Pf >(Yo2 >)) +

V cell

dt (eRPC-dual (Pf >(u>) + V • (ËRPC-dual(Pf >(u>(u>) = -V(P>+Smd

where YO2 is the mass fraction of O2 in Ar, and DArO2 the binary gas diffusion coefficient. Eq. (6) contains the rate of mass change, the advection term, and the source term. Eq. (7) contains the rate of species change, the advection term, the diffusion term, and the source term accounting for the oxygen evolution. Eq. (8) contains the rate of momentum change, the advection term, the pressure drop term, and the source term accounting for the additional pressure drop induced by the porous solid phase, as described by Darcy's law:

smd = —

(1f > K

(u>-FD(Pf >(u>|(u>|

where K and FD are the effective permeability and Dupuit-Forchheimer coefficients, determined by DPLS.

Boundary conditions: Boundary conditions at the topside and backside are shown in Eqs. (10) and (11), respectively:

CtLo = (! - eRPC-single)eemitffs (T(0)4 - T^b) + / /(t, s)s ■ ndX

Jo snpo

qo'utlz=L =(1

<■ 4p

- £RPC-smgle)£emitffs (T(Lf - TímbR / ¡(T; S)S ' °dX

snpO (11)

where eemit is the total hemispherical emittance of ceria, rS the Stefan-Boltzmann constant and Iamb the ambient temperature. Radiation leaving topside and backside boundary surfaces, either emitted from the solid fraction at the boundary surface (first term in the boundary conditions) or emitted and/or back-scattered from the inner domain (second term in the boundary conditions), is assumed lost to the environment. The lateral walls are adiabatic. The incident solar radiation, /solar = 900 kW m-2, impinges at the topside and is attenuated as it travels along the z-direction. The inlet flow gas has a temperature of 300 K, an oxygen partial pressure of 210-4 atm, and a specific mass flow rate of 0.01183 kg s-1 m-2. A grid refinement and time step sensitivity study verified independency of the grid and time resolution.

Effective heat and mass transport properties: Table 1 lists the empirical correlations for describing the morphological and effective heat/mass transport properties of the ceria RPC with dual-scale porosity, as computed by DPLS on the digitally engineered 3D geometries based on the CT scan (see Fig. 3).

Conduction: The effective thermal conductivity is determined by solving Fourier's law at the pore scale within the solid and fluid phase by the finite volume (FV) technique [37,44,48-51]. Table 1 lists the effective thermal conductivity keff as a function of the

dual-scale porosity eRPC-dual and the fluid and solid thermal conductivities kf and ks (=kCeO2) [37]. For eRPC-dual = eRPC-single, keff is for an RPC structure with single-scale porosity (estrut = 0).

Convection: The fluid flow across an RPC's duct geometry is solved at the pore scale by the FV technique [34,52,53]. Fig. 4a shows the flow streamlines across a RPC calculated by DPLS for eRPC = 0.459, dm,RPC = 1.64 mm, estmt = 0.3 and dm,strut =10 im, where the white color indicates the void spaces of the resolved mm-size pores and the grey color indicates the volume-averaged porous struts (im-size pores not resolved). Less than 1% of the fluid mass flows through the porous struts. Fig. 4b shows the absolute pressure drop Dp versus the mean strut pore diameter dm strut across a RPC with eRPC-single = 0.459 and 0.823. For dmstrut

a) Geometrically resolved mm-size pores

Volume-averaged p,m-size pores

Fig. 4. a) Flow streamlines across a RPC with eRPC-single = 0.459, dmRPC = 1.64 mm and estrut = 0.3, dm,strut = 10 im. The white color indicates the void spaces of the resolved mm-size pores and grey color indicates the volume-averaged porous struts (im-size pores not resolved). b) Absolute pressure drop as a function of dm,strut across a RPCs with eRPC-single = 0.459 and 0.823.

6 100 im, Dp is unaffected as the flow bypasses the struts, regardless of £RPc-single- The same observation applies for the convective heat transferred from the solid to the fluid. Therefore, for structures with dmstrut « 10 im which are mainly relevant for this work, the strut pores do not affect the convective transport properties. Fig. 5a-c shows the Nusselt number as a function of Reynolds number, Prandtl number, and eRPC-single, the effective permeability K as a function of eRPC-single for a RPC with varying ppi, and the Dupuit-Forchheimer coefficient FD as a function of eRPC-single for a RPC with varying nppi. Table 1 lists the corresponding least-square fitted empirical correlations. Nu increases with Re, Pr, and decreasing eRPC_single. K increases with eRPC_single and decreasing nppi, while the opposite is true for FD.

Radiation: The effective radiative heat transfer properties are computed by applying a collision-based Monte Carlo (MC) ray-tracing method at the pore level using an in-house Fortran code [54]. Fig. 6a shows b as a function of dmRPC for various eRPC_single. The least-squared correlation is listed in Table 1. For the porous struts, bstrut ~ 150,000 m-1. Because of the high optical thickness, the porous struts are assumed opaque. Fig. 6b shows U as a function of the cosine of the scattering angle, is. A second order polynomial function is least-squared fitted to describe the anisotropic forward and backward scattering and U was practically independent of eRPC_single or ppi. The least-squared correlation is listed in Table 1. The spectral reflectivity of ceria was measured as a function of its reduction extent in a spectroscopic goniometric system [55,56]. Correlations of the total hemispherical reflectance as a function of d, weighted according to Planck's law for blackbody temperatures of 5780 K (incident solar spectrum) and 1773 K (reduction temperature), are given in Table 1.

Equilibrium thermodynamics of ceria: Equilibrium composition is assumed, as justified by the fast intrinsic kinetics compared to transport phenomena observed in previous runs with RPC directly exposed to high-flux solar irradiation [7]. The equilibrium d as a function of the temperature and oxygen partial pressure is listed Table 1, obtained by applying the oxygen defect model to thermo-gravimetric relaxation runs [19].

4. Experimental validation

Two RPC samples of nppi = 10 and 35 ppi underwent heating and

thermal reduction by subjecting them to /solar= 1200 kWm-2, an oxygen partial pressure of 210-4 atm, and a volumetric purge flow rate of 0.5 l min-1. Fig. 7a and b shows the numerically calculated (curves) and the experimentally measured (markers) of the temporal variation of the front, bulk, and back temperatures and of the cumulative oxygen evolution during a representative run. For the

near front region, the simulation model agrees well with the temperature measurement. For the bulk and back side, the model initially under predicts the temperature measurements but matches well once steady state is achieved. The 35 ppi sample exhibits a higher temperature gradient than that of the 10 ppi sample because of the higher optical thickness of the structure. The model is able to predict well the measured oxygen evolution for both RPC samples, justifying the assumption of thermodynamic equilibrium. For t < 20 s, the model predicts a slightly higher rate of the oxygen yield compared to the measurement, attributed to downstream dispersion until the detection unit.

5. Modelling results

A cubic RPC sample of 0.025 x 0.025 x 0.025 x m3, eRPC-single = 0.75 and dmRPC = 2.19 mm is considered. Fig. 8a-d shows the profiles of the fluid and solid temperatures, the intensity of the internal radiative flux integrated over the solid angles, the nonstoichiometry, and the oxygen partial pressure pO2 along the sample depth at various times. Initially, the topside temperature near the irradiated front surface increases to 1500 K in the first 10 s while the backside remains cool. After 150 s, the temperature profile reaches approximate steady state with a maximum of 1850 K around 0.004 m from the top and 1050 K at the backside (Fig. 8a). Such large temperature gradients are the result of the emitted and back-scattered radiation being lost at the boundaries. The solution of the flux intensity conservation equation integrated over the solid angles is shown in Fig. 8b. As expected, the integrated intensity field strongly correlates to the solid temperature and peaks at 2.7106 W m~2. Radiation penetration and volumetric absorption is confirmed. As for the reduction extent, d achieves 0.039 towards the irradiated front while at the backside the structure remains unreacted. pO2 peaks at 0.047 atm after t = 25 s and decreases as the temperature approaches steady state.

In a further step, the heating rate and thermal reduction of RPC samples of different nppi was investigated by keeping the mass constant, i.e. volume and porosity constant at 0.025 x 0.025 x 0.025 m3 and 0.75, respectively. Additionally, a structure was investigated with large pores (dm,RPC = 2.2 mm) for the front side half and small pores (dm RPC = 0.6 mm) for the backside half of the structure. The morphological information of the RPC is listed in Table 2a.

Fig. 9a and b shows the temporal temperature and cumulative oxygen evolution mO2. The volume-averaged and backside temperatures increase with dm RPC for all times. In contrast, the front side temperature and the temperature gradients decrease with dm,RPC because of the decreasing optical thickness. For t > 100 s, the struc-

Fig. 5. a) Nu as a function of Re for various Pr and £RPC-si„gle; b) Permeability as a function of £RPC-si„gle for a RPC with varying ppi: c) Dupuit-Forchheimer coefficient as a function of eRPC-single for a RPC with varying nppi.

Fig. 6. a) Effective extinction coefficient, b, as a function of the mean pore diameter for several porosities; b) scattering phase function as a function of the cosine of the scattering angle.

Fig. 7. Numerically calculated (curves) and the experimentally measured (markers) of the temporal variation of: a) the front, bulk, and back temperatures; and b) the cumulative oxygen evolution during a representative run with two RPC samples of 10 and 35 ppi.

ture with two different mean pore size regions achieves the highest volume-averaged temperature because of the improved volumetric absorption at the front side half and the lower radiation losses at the backside due to the smaller pores which serve as radiation shield and thermal insulator. Initially (t < 50 s), the RPC sample with the smaller dm,RPC shows a slightly higher mO2 because of overheating of the irradiated near front region, as shown in Fig. 9b. For t > 50 s, mO2 increases with increasing pore size and peaks for dm,RPC = 2.2 mm. As expected, mO2 for the structure with two different pore size regions is significantly higher than that for the mono-dm,RPC structures because of the superior volumetric absorption and lower radiation losses at the backside.

In a next step, the heating and reduction behaviour of RPC with different porosities was investigated by keeping volume and nppi constant at 0.025 x 0.025 x 0.025 m3 and 10, respectively. Additionally, a structure was investigated with two different porosity zones: the front side half with eRPC-single = 0.75 while the backside half with eRPC-single = 0.6. The morphological information of the RPC is listed in Table 2b. Fig. 10a and b shows the temporal temperature and mO2. The volume-averaged, front side and backside

temperatures increase with eRPC-single for all times. In contrast, the temperature gradients decrease with eRPC-single because of lower specific mass and slightly decreasing optical thickness. Initially, mO2 increases with eRPC-single, but decreases for t > 50 s because of the higher ceria mass densities. For the structure with two porosity regions, the volume-averaged, front side and backside temperatures are between those of the structure with eRPC-single = 0.6 and eRPC-single = 0.75 for all times because the optical thickness changed only slightly.

Performance: The performance of various RPC samples was characterised by calculating the solar-to-fuel energy conversion efficiency g as defined:

g(t) =

Qco(t) _ 2 • HVco • R0 fvr02 (z, t)dVdt

Q solar (t)

^solar ' t ' Adomain

where QCO is the heating value of the CO that would be produced by assuming complete oxidation of the reduced ceria by CO2, Qsolar the cumulative incident solar radiation, HVCO the specific heating value of CO and Adomain the irradiated domain area. Fig. 11a and b show g

Table 2

Morphological information of RPC samples with: a) varying nppi and constant £RPC-single; b) varying £RPC-single and constant nppi.

nppi [ppi]

dm,RPc [mm]

eRPC-single [-] estrut [-]

nppi [ppi]

dm,RPc [mm] 1.9

eRPC-single [-] °.6

estrut [-] 0.3

as a function of time for the RPC samples of Table 2a and b, respectively. For all cases, g increases with time, peaks, and decreases once the reduction approaches completion. For the RPC samples of varying dm,RPC and constant eRPC-single, g peaks at earlier times for samples with smaller dm,RPC or smaller eRPC-single because of higher radiation losses at the overheated front region. For t > 40 s, the structure with the two pore size regions (dmRPC = 0.6/2.2 mm) leads to higher g, as expected from mO2 shown in Fig. 9b. In contrast, a lower g is observed for the RPC consisting of two porosity

0.6/2.2

2.2 2.5 1.9/2.2

0.75 0.9 0.6/0.75

0.3 0.3 0.3

zones (£RPc-single = 0.6/0.75) because of the relatively lower temperatures of the backside zone and higher radiation losses from the front side zone.

The time when the g peaks is critical. Afterwards, the reduction approaches completion and the evolution of additional oxygen decreases significantly, even though Jsolar is maintained constant. Thus, for maximizing g, reduction should be stopped after g peaks. Fig. 12 shows the peak g as a function of dmRPC for various eRPC-single. For eRPC-single = 0.75, the peak g increases from 0.6% for

Fig. 10. Profiles as a function of time for various £RPC-single for: a) volume-averaged, front side and backside temperature; and b) cumulative oxygen yield.

1 1 1 1 1

0.9 - o

0.8 - ♦

0.7 - • • • -

0.6 - • « <3

0.5 - -

0.4 - « . , =0.60 RPC-single

0.3 — • SRPC-single = 075

0.2 - ♦ ^PC-single = 0-90

0.1 - o <] W=iJ5'Vc=u,2J™ e„_ . . =0.60/075 RPC-single

0.0 i 1 ^ 1 1 1

" m.RPC

3.0 10"3

Fig. 12. Peak solar-to-fuel energy conversion efficiency as a function of the mean pore diameter for various porosities (morphological information see Table 2a and b).

dmiRpC = 0.6 mm to 0.7% for dmRPC = 2.2 mm and slightly decreased for dm RPC = 2.7 mm. The RPC with the two different pore size regions reached the highest peak g of 0.9% due to the reduced radiation losses at the backside, consistent with mO2 shown in Fig. 9b.

6. Summary and conclusions

A transient heat and mass transfer model was implemented to characterise the thermochemical reduction of RPC structures made of ceria with dual-scale porosity exposed to concentrated radiation. The numerical model was validated with measured data of temperatures and O2 evolution obtained in experiments using a high-flux solar simulator. RPC samples with a wide range of porosities and mean pore diameters were investigated, as these two morphological properties determine the optical thickness and, consequently, the capability of the RPC structure to absorb radiation efficiently and volumetrically, leading to a more uniform heating across the structure and to higher oxygen yield. A porosity of 0.75 and pore size of 2.2 mm exhibited a good trade-off between high specific mass, moderate optical thickness, and permeability and thus, showed the largest specific oxygen yield per ceria mass. RPC structure with two pore size regions, namely with large pores (dm,RPC = 2.2 mm) for the front side half and small pores (dm,RPC = 0.6 mm) for the backside half, reached the highest solar-to-fuel energy conversion efficiency. The results obtained in this study guide the design of the RPC structures for their use in a solar chemical reactor [6-8].

Acknowledgements

We gratefully acknowledge the financial support by the European Union under the 7th Framework Program (Project SFERA II — No. 312643) and the European Research Council under the ERC Advanced Grant (Project SUNFUELS — No. 320541).

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