# Experimental Evaluation and Modeling of Air Heating in a Ceramic Foam Volumetric Absorber by Effective Parameters

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}layers (CeO

_{2}/MPSZ) [17] and good rates of hydrogen production were obtained. From the thermal point of view, the absorber was instrumented to measure temperatures at the center of the front and rear sides. It was observed that the front temperature reached values in the range of 1373~1473 K, and the rear side 873~973 K. Such marked differences prevented reaction temperatures along the volume of the absorber. However, despite the importance of knowing the porous absorber’s thermal behavior, only a few studies report the temperature distributions in the material. Most studies assume the absorber’s global temperature corresponds to the measurement of one or two sensors, usually located on the absorber’s front face, and the durability of the absorber’s impregnation method after thermal cycling [30]. Moreover, the porous absorber selection criteria are usually not discussed, nor are the effect of changing porosity and gas flow rates. Recently, V.R. Patil et al. [31] performed an experimental analysis of several reticulated porous ceramic (RPC) absorbers with different porosities and RPC materials (silicon-infused silicon carbide, alumina, and ceria). The RPCs were exposed to various concentrated solar radiation ratios and airflow rates in order to determine the thermal efficiency and air outlet temperature. The main conclusions of this work indicate that larger pores size enhance heat transfer while variable porosity across the RPC absorber reduce temperature gradients. Also, the authors deduce that higher airflow rates increase heat transfer between the fluid and the solid. The highest experimental thermal efficiency was achieved with a Si–SiC (silicon-infused silicon carbide) RPC absorber with 10 PPI (pores per inch). The authors highlight the importance of convective heat exchange together with volumetric radiation absorption to achieve the volumetric effect [32]. Finally, the authors suggest that incident concentrated radiation penetrates the RPC and undergoes attenuation. The effective transport properties and thermal performance of different RPC absorbers exposed to high solar concentration ratios are usually investigated with simulation techniques that use ideal porous structures [33] or through experiments under highly controlled conditions such as constant radiative flux or temperature [34]. Either way, the goal of both techniques is to obtain the thermal and performance parameters to be applied in real operating conditions. The correct selection of these semi-empirical parameters is a very important issue in the homogeneous equivalent models [18]. Perfect knowledge of these parameters is critical when RPC absorbers are exposed to high solar concentration ratios. Porous absorber selection criteria is a difficult subject to approach due to it requiring a deep knowledge of the physical properties of the porous absorber the environment, and the working conditions where it will operate [35,36,37]. Absorbers selected must be capable of operating minimizing heat losses and favoring heat and mass transfer between the reactants. Furthermore, porous absorbers must have a long effective area to host the reactants [38]. In this work, we performed an experimental and numerical thermal analysis of three Partially Stabilized Zirconia (PSZ) foam-type absorbers with a pore density of 10, 20, and 30 PPI used as a volumetric absorber. A numerical model and an analytical approximation were developed to reproduce experimental results and calculate the thermal conductivity, as well as volumetric heat transfer coefficient. Values obtained for the volumetric heat transfer coefficient were 308 and 971 Wm

^{−3}K

^{−1}, for the 10 and 30 L/min

^{−1}in airflow, respectively; while the thermal conductivity values calculated were 1.4, 0.52, and 0.3 Wm

^{−1}K

^{−1}for the 10 PPI, 20 PPI, and 30 PPI absorbers, respectively. The results obtained in this work allow us to establish a selection criterion for porous absorbers that operate within solar reactors and, according to the results described above, we have found that the porous absorber with a pore density of 20 PPI is the most suitable to operate inside the reactor since its properties will favor the volumetric effect and mass and heat transfer inside the absorber.

## 2. Materials and Methods

#### 2.1. Volumetric Absorber and Solar Reactor

^{−3}. This foam-type ceramic was selected owing to its properties of high thermal shock resistance, low reactivity, high effective surface area, standardized pore sizes, and excellent high-temperature creep resistance. The selected absorbers were: 10, 20, and 30 PPI (Figure 1).

#### 2.2. Instrumentation and Operation

^{®}, (Okazaki Manufac-turing Company, Kobe city, Japan) mineral-insulated thermocouple) consisting of a thin tube (sheath) made of stainless steel or heat-resistant steel, thermocouple wires enclosed within the tube and an inorganic insulator (MgO) firmly packed around the wires. Figure 3 shows the probe locations: four on the absorber (directly irradiated) front face, four on the rear face, exactly opposing the position of the front thermocouples, four on the circular absorber edge, and one at the insulator-ceramic support interface. A high-temperature ceramic cement (OMEGABOND

^{®}, OB-600) protected the thermocouple’s contact area from measurement errors in probes exposed to concentrated radiative energy. An Infrared Thermometer (Impac IGA 140/23 Series, from LumaSense Technologies, Inc., Baleful, Denmark) located in front of the reactor window allowed measuring the temperature within the absorber’s central area. Finally, sheathed thermocouples were installed to measure the flowing gas temperature.

^{−1}. The solar furnace’s shutter is opened progressively to avoid thermal shocks by sudden irradiation of the absorber. The front-face thermocouple average reading is stabilized near the target temperature (close to 1110 K in the present study). A steady state is defined when temperature readings change by less than 3% within a timeframe of 5 min. After stabilization at 30 L/min

^{−1}, the flow rate is reduced to 10 L/min

^{−1}, and the temperature can stabilize again. The procedure is repeated for the three absorber pore densities (10, 20, and 30 PPI), Figure 4 shows the experimental configuration. Temperature and pressure data acquisition was performed with a data logger switch unit (model 34972A LXI, from Keysight Tech-nologies, Colorado Springs, CO, USA). The internal reactor pressure was monitored with a high-quality pressure transmitter (S-20, from WIKA Alexander Wiegand SE & Co., Klingenberg, Germany), with a two-second sampling interval, and followed in real-time through a graphical user interface (GUI).

#### 2.3. Numerical Methods

^{®}software version 5.2 (COMSOL, Inc., Burlington, MA, USA). This simulation was carried out to investigate the thermal fields present in the porous absorber from the experimental temperature measurements (thermocouples distributed according to Figure 3). The problem was addressed firstly considering the heat transfer conductivity coefficient non-dependent of temperature by solving the steady-state heat conduction equation:

^{−8}Wm

^{−2}K

^{−4}), and ${T}_{\mathrm{cav}}$ is the cavity temperature. The front surface of the absorber receives and loses energy in the form of radiation, which is represented by the boundary condition in the following equation:

#### 2.4. Analytical Approximation

_{2}can be adjusted from the work of Sun et al. (2013) [45] to:

## 3. Results

#### 3.1. Experimental

^{−1}, as can be appreciated in the graph. Nevertheless, the full stabilization required 1.0 h at least. When the steady-state is reached, the temperature difference between the two faces of the absorber is 338 K, this temperature difference remains constant if the solar irradiance is kept at a value close to 800 W m

^{−2}, even changing the airflow rate. The experiment continued with the flow rate of 10 L/min

^{−1}for 0.5 h to compensate for minor temperature oscillations due to solar irradiance variations. Then, the flow rate was reduced to 5 L/min

^{−1}, and the system was allowed to stabilize again. In the last segment, the flow rate was not changed, but the solar furnace shutter was closed and opened in intervals of 0.4 h, to simulate the system’s response to dispersed clouds. During the shutter’s closures, the absorber’s front face temperature decreased by 110 K, 209 K, and 315 K for the first, second, and third closures. Temperatures presented a delayed response to closures due to the reactor’s large thermal mass.

#### 3.2. Theoretical

^{−1}K

^{−1}. Comparing the RMS of the three absorbers, the absorber with 30 PPI presents the highest deviation, this is since the internal structure of porous absorbers with high pore density is more complex, which offers obstructions or physical barriers to airflow and thermal barriers to heat transfer.

^{−1}flowrates. As mentioned above, the absorber’s front and back temperatures and the air inlet temperatures were fixed to the experimental values (Figure 7). Meanwhile, the volumetric heat transfer coefficient ${h}_{V}$ (Equation (5)) was varied to fit the experimental air outlet temperature data. The fits were accurate to 0.5 K, and the values obtained for ${h}_{V}$ were 308 and 971 W K

^{−1}m

^{−1}, for the 10 and 30 L/min

^{−1}cases, respectively.

## 4. Discussion

^{−3}K

^{−1}, for 10 and 30 L/min

^{−1}flowrates, which could be compatible with a nearly linear scaling with Reynolds number [53]. The values calculated for thermal conductivity in the absorbers with 10 PPI, 20 PPI, and 30 PPI were, respectively, 1.4, 0.52, and 0.3 Wm

^{−1}K

^{−1}, and this trend is roughly inverse to pore density [54] (see Figure 11). However, this behavior is not attributable only to solid matrix conduction effects because, for media of the same material and type of geometry, the thermal conductivity depends essentially on the air volume fraction. As verified by weight, all the samples used in this work have nearly the same bulk density, within 3%, no matter their pore density in PPI. Also, all of them exhibit the same structure due to the fabrication method used. Thus, one can deduce that the variations on the total conductivity are due to radiative [55] and convective effects [56]. In the same way, radiative conductivity described by Equation (11) is inversely proportional to the extinction coefficient ${\beta}_{R}$, which in turn is inversely proportional to pore diameter [57]. Thus, if radiative heat transfer dominates within the absorber, then it is expected that total conductivity be inversely proportional to pore density. This assumption is confirmed in Figure 11 where the behavior of thermal conductivity follows an inverse scale trend with pore density, suggesting that radiation is the dominant heat transfer mechanism within the solid phase of the porous medium. Absorber selection criteria are usually not discussed because it is a difficult subject to approach due to it requiring a deep knowledge of the physical properties of the porous absorber, the environment, and the working conditions where it will operate, and the performance expected of it. In this way, porous absorbers selected must be capable to operate at high temperatures, minimizing heat losses, and favoring heat and mass transfer between the reactants. Furthermore, porous absorbers must have a long effective area to host the reactants [38]. Hence, it is desirable that heat distribution throughout the volume of the porous support be uniform and it is also desirable that the effective area of the porous support be very large to host as large an amount of reactant as possible. The first condition depends on the thermal properties of the porous support and the operating conditions of the reactor, while the second condition depends on the geometry (shape and pore size), the structure of the porous system (open porosity, interconnection of pores, etc.) and the number of pores (pore density and percentage of porosity). However, these two conditions are not always easy to meet, therefore, an absorber should be selected that meets both conditions in a higher percentage. Pore density is one of the determining parameters in the correct selection of porous absorbers, since it determines the amount of material that can be deposited within the porous medium. Generally, the porous absorber with higher pore density has more internal surface area available [58], and this is true only if the porous system is homogeneous. However, it should be considered that when the pore density increases, the concentrated energy does not penetrate in the deeper space in the absorber and is absorbed in areas close to the surface, therefore temperature gradients are created within the porous medium. On the other hand, the internal structure of porous absorbers with high pore density is more complex, which offers obstructions or physical barriers to air flow and thermal barriers to heat transfer, and additionally, the deposit of reactants could be less effective. After the considerations described above, we have found that the porous absorber with pore density of 20 PPI is the most indicated to operate inside the reactor, since its properties, widely described in this work, will favor the volumetric effect and mass and heat transfer inside the absorber.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Volumetric absorbers used in experimental tests. partially stabilized zirconia (PSZ) foam filters with pore density: (

**A**) 30 PPI (pores per inch), (

**B**) 20 PPI, and (

**C**) 10 PPI.

**Figure 2.**Reactor Cross-section. (1) Gas inlet manifold, (2) Reactor body, (3) Flat Glass Window, (4) Alumina thermal insulator, (5) Volumetric absorber, (6) Pyrometers, (7) Water-cooled aperture stop, (8) Window cooling nozzles.

**Figure 3.**Distribution of thermocouple probes in the porous absorber (1): front face (yellow), rear face (red), absorber edge (blue), and insulation interface (green) (2). The red line indicates the direction of pyrometer readings (3).

**Figure 4.**(

**a**) Solar reactor operation diagram showing the temperature (T) and pressure (P) sensors, the mass flow controllers (MF), and the gas inlet/outlet, also is illustrated the incoming radiation flux (1), the water reservoir (2), the compressed air tank (3), and the air extractor (4). (

**b**) The solar reactor installed in the high radiative flux solar furnace (HoSIER), the reactor (1), solar concentrator panel (2), and front pyrometer (3).

**Figure 5.**Temperature data for 10 PPI absorber obtained throughout the test. Values were averaged over the sensors located in the absorber body.

**Figure 6.**Front, back, and side face temperature data obtained during steady-state operation under different flow rates. Values were averaged over the sensors located in the absorber body.

**Figure 7.**Air inlet and outlet temperatures data obtained during steady-state operation under different flowrates. Values were averaged over the sensors located in the absorber body.

**Figure 8.**Isothermal surfaces corresponding to the 20 PPI absorber obtained from numerical simulations.

**Figure 9.**Isothermal surfaces on the z-y plane (perpendicular to thickness) of the absorber material. (

**a**) 10 PPI, (

**b**) 20 PPI, and (

**c**) 30 PPI.

**Figure 10.**Temperature of the solid and the gas as a function of depth, from the analytical model, for the 20 PPI absorber with different air flowrate. (

**a**) 30 L/min

^{−1}and (

**b**) 10 L/min

^{−1}.

**Figure 11.**Total conductivity (k

_{t}) obtained from the simulations for different linear pore densities (red squares) and a trendline for these values (red dotted line). The effective conductivity (k

_{e}) [43] for the 20 PPI absorber (black circles) with the expected scaling for this quantity (black dotted line) based on the assumption of radiation heat transfer dominance [57].

**Table 1.**Experimental (Exp) temperature data in the porous medium and simulations (Sim) predictions for the 10, 20, and 30 PPI absorbers, with 30 L/min

^{−1}in air flowrate. RMS refers to root-mean-square deviations.

Location | 10 PPI | 20 PPI | 30 PPI | |||||
---|---|---|---|---|---|---|---|---|

x (mm) | y (mm) | z (mm) | Exp (K) | Sim (K) | Exp (K) | Sim (K) | Exp (K) | Sim (K) |

27 | 0 | 27 | 1172 | 1196 | 1203 | 1204 | 1203 | 1108 |

27 | 23 | 27 | 786 | 795 | 685 | 681 | 685 | 603 |

−30 | 0 | 27 | 1108 | 1210 | 1103 | 1201 | 1103 | 1102 |

−30 | 23 | 27 | 795 | 804 | 642 | 688 | 642 | 609 |

−30 | 0 | −30 | 1107 | 1056 | 1086 | 1077 | 1086 | 994 |

−30 | 23 | −30 | 820 | 727 | 645 | 630 | 645 | 560 |

27 | 0 | −30 | 1101 | 1101 | 1063 | 1112 | 1063 | 1024 |

27 | 23 | −30 | 735 | 745 | 574 | 644 | 574 | 572 |

RMS | 5% | 6% | 7% |

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## Share and Cite

**MDPI and ACS Style**

Arreola-Ramos, C.E.; Álvarez-Brito, O.; Macías, J.D.; Guadarrama-Mendoza, A.J.; Ramírez-Cabrera, M.A.; Rojas-Morin, A.; Valadés-Pelayo, P.J.; Villafán-Vidales, H.I.; Arancibia-Bulnes, C.A. Experimental Evaluation and Modeling of Air Heating in a Ceramic Foam Volumetric Absorber by Effective Parameters. *Energies* **2021**, *14*, 2506.
https://doi.org/10.3390/en14092506

**AMA Style**

Arreola-Ramos CE, Álvarez-Brito O, Macías JD, Guadarrama-Mendoza AJ, Ramírez-Cabrera MA, Rojas-Morin A, Valadés-Pelayo PJ, Villafán-Vidales HI, Arancibia-Bulnes CA. Experimental Evaluation and Modeling of Air Heating in a Ceramic Foam Volumetric Absorber by Effective Parameters. *Energies*. 2021; 14(9):2506.
https://doi.org/10.3390/en14092506

**Chicago/Turabian Style**

Arreola-Ramos, Carlos E., Omar Álvarez-Brito, Juan Daniel Macías, Aldo Javier Guadarrama-Mendoza, Manuel A. Ramírez-Cabrera, Armando Rojas-Morin, Patricio J. Valadés-Pelayo, Heidi Isabel Villafán-Vidales, and Camilo A. Arancibia-Bulnes. 2021. "Experimental Evaluation and Modeling of Air Heating in a Ceramic Foam Volumetric Absorber by Effective Parameters" *Energies* 14, no. 9: 2506.
https://doi.org/10.3390/en14092506