Analysis of radiation heat transfer and temperaturedistributions of solar thermochemical reactor for syngas production

Abstract

This paper investigated radiation heat transfer and temperaturedistributions of solar thermochemical reactor for syngas productionusing the finite volume discrete ordinate method (fvDOM) and P1 approximationfor radiation heat transfer. Different parameters including absorptivity,emissivity, reflection based radiation scattering, and carrier gasflow inlet velocity that would greatly affect the reactor thermalperformance were sufficiently investigated. The fvDOM approximationwas used to obtain the radiation intensity distribution along thereactor. The drop in the temperature resulted from the radiation scatteringwas further investigated using the P1 approximation. The results indicatedthat the reactor temperature difference between the P1 approximationand the fvDOM radiation model was very close under different operatingconditions. However, a big temperature difference which increasedwith an increase in the radiation emissivity due to the thermal non-equilibriumwas observed in the radiation inlet region. It was found that theincident radiation flux distribution had a strong impact on the temperaturedistribution throughout the reactor. This paper revealed that thetemperature drop caused by the boundary radiation heat loss shouldnot be neglected for the thermal performance analysis of solar thermochemicalreactor.

Keywords

solar thermochemical reactor / incident radiation flux / temperature distribution / radiation absorptivity / radiation emissivity / thermal performance analysis

Introduction

Currently, heat transfer analysisof solar thermochemical reactor using concentrated solar energy asa heat source to drive high-temperature chemical reaction is an attractingresearch area in the general context of solar fuels and specificallyfor syngas production [1–3].The technologyof thermochemical solar energy-to-fuel conversion using concentratedsolar energy is mostly considered as an interesting option for CO₂ depletion which promotes carbon recycling, therebydecreasing the dependence extent on fossil fuels [4,5]. However, the thermal performance of solar thermochemical reactordecreases the syngas yield and the syngas efficiency.

The solar thermochemical reactorfor syngas production is an enclosure thermal receiver directly coupledto the concentrated solar energy [6,7]. Inside the reactor,the mechanism of chemical processes consist of cyclical series ofendothermic and exothermic chemical reactions. The precursor materialis constantly reduced at high thermal temperatures and subsequentlyoxidized to regenerate the pristine oxide for the next step [8–11]. However, the optimal operating conditions for convertingconcentrated solar radiation into syngas that can be used as sustainableenergy mainly depend on the thermal behavior of the reactor [12–15]. Since metal oxides are better suited to the solarenergy application [16–19], an efforthas been made to determine the optimal operating temperature leadingto high chemical species conversion efficiency. Most of the studieshave suggested that the peak solar flux intensities between 1000 kW/m² and 10000 kW/m² wouldreach a sufficient efficiency of thermochemical processes [20,21].This has led researchers to mainly focus on high-temperaturethermochemical receiver and thermal performance analysis of solarreactor that pose great challenges to applications in the conversionof concentrated solar energy into chemical energy. Therefore, increasingimprovements have been done in the solar thermochemical application.The solar reactor geometry optimization has been conducted to providean efficient heat transfer to the reactant [22,23]. Besides, a small aperture radius has been designedand different inlet/outlet configurations have been optimized andused in order to minimize thermal losses and achieve high absorptionefficiencies for different operating conditions [23–25]. However, the high radiation heat flux distributioninside the solar receiver is the most important factor in the processof solar thermochemical for syngas production. Thus, numerical simulationsand experimental measurements have been conducted to properly investigatethe concentrated solar irradiance distribution throughout the reactor.Numerical simulation methods generally focus on appropriate radiationmodels to analyze the thermal performance of solar cavity receiver.Most of the studies are based on the Monte-Carlo ray-tracing (MCRT)method to investigate the radiation performance and predict the temperaturedistribution inside the solar cavity receiver [26–28]. In addition, researchers have also developed numericalmethods coupled to the fluid flow, heat and mass transfer to predictthe thermal behavior of the reactor under different operating conditions.In several cases of radiation heat transfer, the P1 radiation modelhas been coupled to the enthalpy equation to solve the phenomenonrelated to the radiation heat transfer, considering the incident powerflux as a Gaussian distribution or non-fluctuating heat flux [29–32]. Note that, the P1 approximation is derived fromthe simplification of radiative transfer equation and seems to greatlypredict the incident radiation flux distribution. The Rosseland approximationand the study on a comparison between the P1 approximation and Rosselandapproximation have been performed by several researchers [33–35] to obtain more accuracy in the temperature predictionfrom the solar irradiance flux distribution. Moreover, Trépanieret al. [36] have investigatedthe predictive capabilities of finite volume method (RTE-FVM) andthe P1 model for a possible improvement of radiation heat transfer.For real applications, some researchers have focused on experimentalmeasurement to investigate the temperature distribution throughoutthe reactor. The main purpose is to show an agreement between thecomputational and the experimental results [37]. However, most of the literaturehas revealed that the heat flux distribution has a significant influenceon temperature distribution throughout the reactor. Therefore, fora substantial improvement in solar energy-to-fuel conversion technology,an effort should be made regarding the thermal performance of solarthermochemical reactor.

This paper has investigated irradianceheat flux transfer and temperature distributions throughout the solarthermochemical reactor for syngas production. Besides, it has developedthe P1 approximation and finite volume discrete ordinate method (fvDOM)approximation for more accuracy in the prediction of temperature distributionfrom the radiation flux distribution. Moreover, it has analyzed thethermal performance of the reactor, considering different parametersincluding absorptivity, emissivity, reflection based radiation scattering,and carrier gas flow inlet velocity.

Physical models

Reactor model

Figure 1 shows the 2D schematic diagramof the proposed solar thermochemical reactor used for the numericalsimulation [32]. The boundaryfields of the reactor are characterized by the inlets, the wall, andthe reactor outlet. The inner cavity wall of the reactor is made ofthe ceramic material (Al₂O₃). The internal field of the reactor is assumed to be gray diffuseradiation, absorbing, diffusely reflecting, emitting and scatteringmedia. The concentrated solar energy is considered as the heat sourcefor the reaction to enter into the reactor through the inlet at the(x) direction protected by transparentquartz glass window. The reactor is initially filled with the mixedgas at 300 K. The solar irradiance, once entering into the reactor,is impinging throughout the inner cavity of the reactor. The heatflux diffused from the inlet is highly concentrated in the internalfield of the reactor extended over 75 mm at the (x) direction, prompting the rise of reactor inner temperatureup to the desired reaction temperature. During the process, two oppositeinlet ports at the (y) directionclose to the quartz window lead the mixture gas into the inner cavityof the reactor. The carrier gas considered in this paper as a mixtureof gas is injected in the (y) directionto sweep and keep the quartz window clean and safe from solid depositionand carry the reactant species into the internal field of the reactorthrough the aperture. The product exits from the outlet of the reactorin the (x) direction. To reducethe conduction heat losses and achieve a high-temperature stability,the inner wall is protected by a well-insulating layer (aluminum silicatefiber (Al₂Si₂O₅(OH)₄) and calcium oxide fiber(CaO)). The reactor is enclosed by a stainless steel housing.

Governing equation

The continuity conversation equation,momentum conservation equation and energy conservation equation forthe solar thermochemical reactor are numerically calculated, respectivelyby

(1)\nabla \cdot (\rho u)=\mathrm{0},

(2)\nabla \cdot (\rho uu)=-\nabla P+\rho g+\nabla \cdot (\mathrm{2}{\mu }_{\mathrm{eff}}D(u))-\nabla (\mathrm{2}/\mathrm{3}{\mu }_{\mathrm{eff}}(\nabla \cdot u)),

(3)\nabla \cdot (\rho uh)+\nabla \cdot (\rho uK)-{\displaystyle \frac{\mathrm{\partial }P}{\mathrm{\partial }t}}=\nabla \cdot ({\alpha }_{\mathrm{eff}}\nabla h)+\rho u\cdot g-\nabla q_r,

where ρ is the density, u is the velocity, μ_eff is the molecular viscosity, P is the total pressure of the gas, g is the gravitational acceleration, D(u) isthe rate of strain tensor, h isthe specific enthalpy, K is thekinetic energy, α_eff is the effective thermal diffusivity, and \nabla q_r is the radiation source.

The rate of strain tensor D(u) isdefined as

(4)D(u)=\mathrm{1}/\mathrm{2}(\nabla u+{(\nabla u)}^T).

The total pressure is calculatedby

(5)P=P_{\mathrm{rgh}}+\rho \cdot gh+P_{\mathrm{ref}},

where P_rgh is the dynamic pressure, ρ·gh is the static pressure, gh is the gravity force, and P_ref is the referencepressure (atmospheric).

The kinetic energy is calculatedby

(6)K=m{\displaystyle \frac{{\left|u\right|}^{\mathrm{2}}}{\mathrm{2}}},

where m is the mass.

The effective thermal diffusivity α_eff can beexpressed by

(7){\alpha }_{\mathrm{eff}}={\displaystyle \frac{\mu }{Pr}}={\displaystyle \frac{k}{c_P}},

whereμis the dynamicviscosity, Pr is the Prandtl number, k is the thermal conductivity, and c_P is the specificheat capacity at constant pressure.

The radiative source \nabla q_r is calculated from theradiation intensity using P1 and fvDOM approximations for radiationheat transfer to solve the radiative heat transfer equation as expressedby [38,39]

(8){\displaystyle \frac{d{I}_{r,s}}{d{s}^{\text{'}}}}=\nabla (I_{r,s})=\epsilon I_{\mathrm{b,}r}-(\kappa +{\sigma }_{r,s})I_{r,s}-{\displaystyle \frac{{\sigma }_{r,s}}{\mathrm{4}\pi }}{\displaystyle \underset{\mathrm{4}\pi }{\int }{I}_{r,s^{*}}\Phi (s^{*},s)}d{\Omega }^{\ast },

where I_r,s is the radiation intensity at the r point that propagates along the s direction, s^{\text{'}} is the coordinate along that direction, s* is the scattering direction vector, I_b,r is the blackbody radiationintensity at r point, \kappa is the absorptioncoefficient, ε is the emissioncoefficient, σ_r,s is the scatteringcoefficient, φ(s*, s) is the scattering phase function, andΩ* is the solid angle.

Due to the difficulty associatedwith the solution to the radiative heat transfer Eq. (8), substantialsimplifications have been made. In the case of P1 approximation forradiative heat transfer, it is assumed that the radiative intensitycan be solved as a partial differential equation in which the directionaldependence in radiative transfer equation is integrated out [38].This can result in a diffusionequation for incident radiation flux intensity as expressed by

(9)\nabla \cdot \left({\displaystyle \frac{\mathrm{1}}{\mathrm{3}\alpha +{\sigma }_s(\mathrm{3}-C)}}\nabla G\right)=(\alpha G-\mathrm{4}\pi \epsilon I_b+E),

where G is the incident radiation flux, α is the radiation absorptivity, E is the emissivity contribution, and C is a linear anisotropic phase functioncoefficient.

The total amount of radiation ofall point can be calculated by

(10)I_b={\displaystyle {\int }_{\mathrm{0}}^{\infty }{I}_{\mathrm{b,}r}\mathrm{d}r}={\displaystyle \frac{\sigma }{\pi }}{T}^{\mathrm{4}},

where σ is theStefan-Boltzmann constant, T isthe radiation temperature, and r is the coordinate. The value of Stefan-Boltzmann constant consideredin this paper is 5.67×10^-8 W/(m²·K⁴). For the P1 approximation, the radiation heat transfer equationfor a gray diffuse medium is simplified to [39].

(11)\nabla \cdot \left({\displaystyle \frac{\mathrm{1}}{\mathrm{3}\alpha +{\sigma }_s(\mathrm{3}-C)}}\nabla G\right)=\alpha G-\mathrm{4}\epsilon \sigma T^{\mathrm{4}}+E.

The fvDOM radiation model solvesfor a discrete number of finite solid angles where the radiative transferEq. (8) is directly solved for r points and s directions in aparticipating media [40]. The radiative source \nabla q_r in the enthalpy Eq. (3) is calculated consideringthe transport equation for the total radiation flux (G) and the divergent of radiative flux vector(q_r) [39]. The relation between the incidentradiation flux and the radiation flux vector can be obtained by integratingthe radiation intensity over all possible directions and across allpossible points [39].

(12)q_r=-{\displaystyle \frac{\mathrm{1}}{\mathrm{3}\alpha +{\sigma }_s(\mathrm{3}-C)}}\nabla G,

(13)-\nabla q_r=\alpha G-\mathrm{4}\epsilon \sigma T^{\mathrm{4}}.

Boundary conditions

The boundary and initial conditionsof the physical parameters of the reactor, including radiation boundaryconditions, are listed in Table 1. An appropriate physical conditionfor the radiation boundary condition can be the Marshak conditionexpressed by

(14)-{\displaystyle \frac{\mathrm{1}}{\mathrm{3}\alpha +{\sigma }_s(\mathrm{3}-C)}}\overrightarrow{n}\cdot \nabla G={\displaystyle \frac{{\epsilon }_{\mathrm{w}}}{\mathrm{2}(\mathrm{2}-{\epsilon }_{\mathrm{w}})}}(\mathrm{4}\sigma T_{\mathrm{w}}^{\mathrm{4}}-G_{\mathrm{w}}),

where ε_w is the wall emissivity, T_w is the calculated wall temperature, G_w is the incidentradiation flux at the wall, and \overrightarrow{n} is the unitnormal vector to the wall.

The radiation intensity boundaryconditions are defined for the fvDOM radiation model. The fvDOM coefficientsare defined as nPhi= 3 and nTheta= 0, the convergence criteria for radiationiteration is 10^-3, and maxIter= 4 for the maximum number of iterations. nPhi denotes the azimuthal angles in PI/2,indicating that the direction of the rays is on x-y plane (from y to x) direction and nTheta denotesthe polar angles in PI (from Z to x-y plane).However, only nPhi is consideredand the direction of the rays is on an x-y plane since the model is in2D geometry configuration. In this paper, according to the reactorgeometry model, fvDOM approximation allocates 12 rays varying from I₀ to I₁₁ with an averageorientation Omega of 1.0472 rad. The boundary condition for the fixedflux pressure is calculated as

(15)\nabla P={\displaystyle \frac{({\varphi }_{H/A}-\varphi )}{\left|S_f\right|D_P}},

where φ is the flux,φ_H|A is the predicted flux field, S_f is the patch face area vectors,and D_P isthe pressure diffusivity.

Other boundary conditions are thegeometric conditions as listed in Table 1.

Numerical solution methods

In this paper, all the calculationswere conducted under OpenFOAM . The analysis of solar radiation flux and radiation temperaturedistribution throughout the reactor was made based on the P1 and fvDOMapproximation for radiative heat transfer. The computational modelwas developed under a steady-state solver buoyant FoamSolar whichwas coupled to the Utility package and libraries through toolboxessuch as libraries of physical models . Figure 2 isthe flowchart indicating the sequence of calculations for the model.Before the calculation starts, the time, mesh, and field were created.Note that the geometry model including all the boundary fields wereperformed using the polyMesh utility. Besides, the pre-processingtasks including the setting of boundary conditions as defined in Table1, the selection of both species thermo-physical properties and appropriatethermodynamics package were done for the calculations. Then, the calculationproceeded by reading the velocity field U. The reactive particle was assumed to be compressible fluid.

The solar thermal energy transportand temperature distribution inside the reactor were calculated byselecting the defined radiation heat transfer model. The radiationproperties including the absorption and emission model were also selected.The scattering model was selected to further investigate the radiationlosses relative to the rays that were forced to deviate from theiroriginal path. As mentioned above, the P1 and fvDOM approximationfor radiation heat transfer were alternately selected. Note that thesetwo radiation models use the same scheme for calculating the incidentradiation flux. However, an additional boundary condition for radiationintensity was defined for the fvDOM radiation model. Moreover, thefvDOM model allocated a precise number of rays with an average orientationdepending on the fvDOM coefficients defined by the user in the radiationproperties utility. For the overall process, the initial temperaturethroughout the reactor including fluid and the temperature of theinner wall cavity of the reactor was considered to be 300 K and theconcentrated solar radiation from the solar simulator was assumednot to fluctuate. In addition, it was assumed that the incident radiationflux which was reflected and emitted from any walls was diffuselydistributed throughout the reactor. The solutions were converged beforeany corrections were done and according to the convergence criteriaset to 10^-8.The post-processing tasks were performed under ParaView to furtheranalyze the results obtained.

Results and discussion

Temperature distribution with different radiation heat transfermodels

Figure 3 demonstrates the temperaturedifference between P1 and fvDOM radiation models. The simulation wasconducted at 1600 K, a fluid inlet velocity of 0.006 m/s, and 19.738atm to predict the temperature distribution of P1 and fvDOM radiationheat transfer models. Figure 3(a) and (b) indicates the temperaturegradient inside the reactor at 3h and 50 min, respectively. It canbe seen that the diffused heat flux forward the inner cavity of thereactor is attenuated, thereby resulting in a gradual decrease intemperature with an increase in the axial length of the reactor. Thecomparison between these radiation models was further conducted, consideringthe condition under which the reactor was completely heated to thedesired reaction temperature at 6h 16 min for the fvDOM method and1h 43 min for the P1 method. According to the simulation cost in time,the results indicate that the P1 radiation model is more rapid thanthe fvDOM radiation model. This might result from the fact that theP1 model easily solves the radiative heat transfer equation with littleCPU demand [40]. Figure3(c) depicts the temperature distribution of each radiation modelas a function of the axial length of the reactor. Figure 3(d) displaysthe temperature difference between the temperatures predicted by theapplied radiation models with an increase in the axial length of thereactor. The horizontal line in Fig. 3(d) exhibits the equilibriumtemperature where the temperature predicted by the P1 model is equalto that predicted by the fvDOM model. As shown in Fig. 3(c) and (d),the temperature difference can be observed at the inlet of the reactorwhere an average increase of 0.5% in the temperature is obtained withthe fvDOM model. Then, an average increase of 0.45% in the temperatureis observed with the P1 model at the internal field of the reactor.For both radiation models, the temperature has a tendency to stabilizewith the axial length of the reactor. However, the temperature differenceis significantly increased to 122 K with an average increase of 4%obtained with the P1 model at the outlet of the reactor. The differencein the temperature prediction between these radiation models is stronglydependent on the boundary radiation, especially at the region wherethe reactor cross section is reduced. A similar tendency with a littlefluctuation of temperature is obtained inside the reactor with theapplied radiation models. Therefore, both P1 and fvDOM models canaccurately predict the temperature distribution inside the reactor.

Incident radiation flux and irradiance distribution along thereactor

Figure 4 shows the solar irradiancedistribution throughout the reactor based on the fvDOM model. Theincident radiation flux (G) isplotted for a better understanding of the radiation flux distributioninside the reactor. As depicted in Fig. 4(a), the incident radiationheat flux which enters into the reactor through the transparent quartzglass window is unevenly distributed within the reactor. It seemsthat the reactor is heated up by the radiation heat transfer as thethermal energy is diffused forward the internal field of the reactor[7,32,37]. Note that the incident radiation flux results inthe contribution of radiation intensity at overall possible directionsand across all possible points in the participating media. Therefore,it is necessary to investigate the radiation intensity distributionalong the reactor. Since the inner cavity of the reactor is assumedas gray diffuse radiation, as can be seen in Fig. 4(b)–(d),the radiation intensity is reflected and diffused throughout the internalfield of the reactor. The reactor is progressively heated up as theradiation heat flux is absorbed [7]. A possible explanation is that the radiative heat flux comingfrom the solar simulator is diffused in the reactor at 12 differentpositions from I₀–I_11, consisting of 12 rays with an average orientation of W =1.0472 rad and impinged along the innercavity of the reactor. The deviation of radiation intensity wouldbe attributed to the effect of absorption and reflection in the participatingmedia [32,36]. Some radiation intensities (I₇, I₉ and I₁₀), as shown inFig. 4(b) are significantly absorbed once entering into the reactorwhile certain radiation intensities (I₀, I₅, I₆ and I₁₁) in Fig. 4(c) have been reflected before being absorbed. The radiationintensities at the position of (I₁, I₂, I₃ and I₄) in Fig. 4(d) have not been immediately modified when entering intothe reactor. However, their modification begins from 0.02 to 0.055m where I₁, I₄, I₂ and I₃ are respectivelyabsorbed. The radiation intensity at position I₈ in Fig. 4(b) lower than thosedescribed above varies little as a function of the axial length ofthe reactor and drops dramatically afterwards, indicating that radiationintensity I₈ is absorbed significantly from 0.08 m. It seems that the higher absorptionin the radiation intensity would be the reason for radiation dispersion[10]. Furthermore, the radiation intensities are subsequently highlyconcentrated when the reactor is completely heated up and then graduallyattenuated at the outlet of the reactor. The sharp decrease in theradiation flux at the outlet of the reactor can be attributed to theradiation losses from the back wall where the reactor cross sectionis reduced [32]. Thus,the radiation intensity losses inside the reactor are caused by theabsorption of radiative energy in the medium.

Effect of absorption coefficients on thermal performance ofthe reactor

Figure 5 shows the effect of radiationabsorption on the temperature distribution as a function of the axiallength of the reactor. Different absorption coefficients were usedto investigate the change in radiation intensity throughout the reactor.As can be observed in Fig. 5(a), the variation in absorption coefficientgreatly affects the temperature distribution. For both the P1 andthe fvDOM radiation model, the temperature significantly increaseswith an increase in the absorption coefficient [7]. This indicates that as more irradianceis absorbed, more increase in temperature is predicted [32]. As mentioned in Fig. 4(b)–(d)above, it can be clearly seen that a higher temperature distributionresults in a huge absorption of radiation intensity. An additionalremark is that the temperature prediction is more uniform when theradiation intensity is highly concentrated inside the reactor. Moreover,the analysis of temperature distribution as a function of absorptioncoefficient suggests that there exist some disagreement between thesetwo models. The fvDOM model has a tendency to predict a higher temperaturedistribution than the P1 model at the inlet of radiation for an absorptioncoefficient smaller than 0.7. Alternatively, an over prediction oftemperature distribution is observed with the P1 model, leading toa big difference between these radiation models for an absorptioncoefficient greater than 0.7. However, a very similar temperaturedistribution is obtained at the inlet of radiation with a little differencewith the increasing axial length of the reactor when absorption andemission coefficients are 0.7 and 0.5 respectively. Thus, an absorptioncoefficient of 0.7 would lead to an agreement between these two radiationmodels at the inlet of radiation. Figure 5(b) further describes anaverage temperature drop for each radiation model as a function ofabsorption coefficients. As can be observed, the average temperaturedifference for each radiation model increases with an increase inradiation absorptivity. This led to the understanding that as moreirradiance is absorbed, more increase in temperature is predictedinside the reactor. However, the consistent temperature distributionbetween the P1 and the fvDOM approximation for irradiative transferdisappears with increasing absorption coefficient. This would resultin the fact that absorption coefficients have a strong impact on temperaturedistribution.

Effect of emissivity coefficients on thermal performance ofthe reactor

The temperature distribution varieswith emissivity coefficients, as shown in Fig. 6. The emissivity variationof the inner cavity of the reactor greatly affects the temperaturedistribution for both the P1 and the fvDOM radiation model. As canbe seen in Fig. 6(a), the temperature prediction significantly decreaseswith an increase in the emissivity coefficient [32,33]. Moreover, the effect of emissivity variation onthe thermal performance of the reactor has presented a similar trendas mentioned above in Fig. 6(a). It is observed that at the inletof radiation the temperature predicted by the P1 model is lower thanthat predicted by the fvDOM model. This might probably result in theaccuracy between the two models since the P1 model assumes that allsurfaces are diffuse and maybe result in a loss of accuracy due tothe complexity of the geometry if the optical thickness is small [38–40].Moreover, for the fvDOM model, the radiative heattransfer equation is solved for a discrete number of finite solidangles which would lead to a heat balance for a coarse discretization[40]. Figure 6(b) depictsthe average drop in the temperature for a better understanding ofthe effect of emissivity coefficient on each radiation model. Notethat low prediction of temperature distribution with increasing emissivitywould be ascribed to the boundary radiation heat loss due to the thicknessof thermal non-equilibrium at the inlet of radiation. As shown inFig. 6(b), the drop in the temperature increases with an increasein the emissivity. However, a greater drop is observed in the caseof the P1 radiation model due to the loss of accuracy in the temperatureprediction at the inlet of radiation which increases with increasingemissivity. Therefore, the radiation emissivity coefficients greatlyaffect the P1 radiation model at the inlet of radiation. An emissivityof 0.5 could lead to a higher temperature distribution inside thereactor.

Effect of reflection based radiation scattering coefficientson the temperature distribution

Figure 7 shows the temperature distributionwith the variation of the constant scattering of the inner cavityof the reactor. To simulate the effect of scattering on temperatureprediction, a constant scatter model was used assuming that the innercavity of the reactor was isotropic [40]. The aim of the use of scatter model is to investigatewhether some radiation could be forced to deviate from their originalpath in order to result in an interaction with one or more localizednon-uniformities in the medium. Although the temperature is predictedfrom the contribution of irradiance distribution at overall possibledirections and across all possible points in the medium of the reactor,yet, the scattering coefficient has no significant effect on the temperaturedistribution with the fvDOM radiation model as shown in Fig. 7. Apossible explanation is that scattering does not have any strong effecton the temperature distribution when the fluid considered in the mediumis gas [40]. Consequently,the change in the radiation from its original path would result ina similar effect. However, for the P1 model, the variation of scatteringcoefficient from 0 to 0.5 has forced the deviation of radiation fromtheir original path, thereby resulting in the heat loss of radiationsince the temperature is decreased as a function of the axial lengthof the reactor. Moreover, the increase in the scattering coefficientfrom 0.5 to 0.8 gradually decreases the temperature along the reactor.The drop observed in the temperature distribution would essentiallybe caused by the fact that some radiations are reflected based radiationscattering and would not be absorbed.

As shown in Fig. 8, a further analysiswas made to investigate, in detail, the effect of reflection basedradiation scattering considering linear-anisotropic phase functioncoefficients. The value of phase function coefficient was set to avalue in the interval of ] - 1;+ 1[. The minus (-) sign representsbackward scattering and the positive (+) values correspond to forwardscattering. As can be seen in Fig. 8(a), the effect of scatteringis mainly observed inside the reactor from 0.03 m and increases to0.1 m where the axial length of the reactor is reduced. The temperaturedrops with an increase in scattering coefficients. However, the dropin the temperature mainly depends on the scattering direction. Asshown in Fig. 8(b), the backward scattering leads to a greater dropin the temperature than the forward scattering [10]. Considering Fig. 8(a) and (b),the maximum average temperature drop to 23.97 K is attributed to thebackward scattering coefficient σ_s=0.8 and C=–0.8. Therefore, the reflection based radiation scatteringwould result inevitably in the radiation losses, leading to the dropin the temperature inside the reactor. The drop in the temperaturedue to the scattering effect can have an effect on the thermal performanceof the reactor. Consequently, the effect of reflection based radiationscattering could not be neglected for the thermal performance analysisof solar thermochemical reactor since a little drop in the temperaturecan greatly affect the syngas yield [11, 14, 20, 41, 42].

Effect of inlet velocity of carrier gas flow on temperaturedistribution

Figure 9 shows the effect of differentinlet velocities of carrier gas flow on the temperature distribution.To simulate the effect of injected carrier gas flow, the internalfield temperature of the reactor is considered to be uniform at 1400K and 19.738 atm. A selective gas radial velocity of 0.004, 0.005and 0.006 m/s at (y) directionwas applied to the reactor at each inlet of gas flow. Note that thecarrier gas flow was simultaneously injected into the reactor throughtwo radial inlet positions. As indicated in Fig. 9, the effect ofcarrier gas flow is remarked at the injection region for both theP1 and the fvDOM radiation model where the temperature decreases sharplybefore quickly increases to the maximal value due to the convectiveheat transfer between the fluid and the cavity walls. Moreover, ascan be seen, the effect of carrier gas is extended from 0.0 to 0.04m of the axial length of the reactor at (x) direction. This is essentially due to the position of gas injectionand indicates that the carrier gas which once enters the reactor throughthe radial inlets is roughly heated up before being converged to thefluid zone of the reactor through the aperture by convection heattransfer. However, as the inlet velocity of the injected carrier gasflow increases, the temperature drop also increases. For example,at an inlet velocity of 0.004 m/s, the temperature drops to 1232.2K and 1233.3 K for the P1 and the fvDOM models, respectively whileat an inlet velocity of 0.005 m/s the temperature drops to1261.1 Kand 1259.2 K for the P1 and the fvDOM models, respectively. The inletvelocity of carrier gas flow has a great impact on the temperaturedistribution [32, 35]. Therefore, a better controllingof the inlet velocity of carrier gas flow would avoid a significantdrop in the temperature during experimental processes.

Conclusions

The radiation heat transfer was analyzedand temperature distributions of solar thermochemical reactor forsyngas production were investigated. The P1 approximation and fvDOMapproximation for radiation heat transfer were adopted successfullyto obtain the radiation flux distribution and temperature predictioninside the reactor. The effects of radiation absorptivity, emissivity,reflection based radiation scattering, and inlet velocity of carriergas flow on the thermal performance of the reactor were investigated.It was found that the radiative heat transfer has a strong impacton accurate prediction of the temperature distribution throughoutthe reactor. For both the P1 and the fvDOM radiation model, the variationof radiation absorptivity and emissivity has greatly affected thetemperature distribution. As a result, the temperature significantlyincreased with an increase in the radiation absorptivity while a decreasein temperature distribution was observed with an increasing radiationemissivity. The consistent temperature distribution between the P1approximation and the fvDOM approximation disappeared at the inletof radiation due to the thickness of thermal non-equilibrium. A littledrop in the temperature was observed with the P1 approximation whenconsidering the reflection based radiation scattering inside the reactor.Thus, the radiation heat loss due to the radiation scattering shouldnot be neglected during the thermal performance analysis of solarthermochemical reactor. Moreover, the inlet velocity of carrier gasflow has a great impact on the temperature distribution. Therefore,a strong control of the inlet velocity of injected carrier gas flowwould have relevant effects on the thermal performance of the reactor.

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