Three-dimensional modelling and analysis of solar radiation absorption in porous volumetric receivers

Highlights

• Convergent incidence and large pores sizes creates a peak flux near the focal point.

• Higher absorption efficiencies are obtained for forward scattering in porous media.

• The wall properties are more important in the case of low optical thicknesses.

• A even distribution and high wall absorption are obtained by moving the focal plane.

• Higher slope errors of concentrator result in lower energy absorption.

Abstract

This work addresses the three-dimensional modelling and analysis of solar radiation absorption in a porous volumetric receiver using the Monte Carlo Ray Tracing (MCRT) method. The receiver is composed of a solid matrix of homogeneous porous material and isotropic properties, bounded on its side by a cylindrical wall that is characterized through a diffuse albedo. The Henyey-Greenstein phase function is used to model the radiation scattering inside the porous media. The effect of the angle of incidence, optical thickness (porosity, pores size and height of the receiver), asymmetry factor of the phase function and wall properties on the solar radiation absorption in the porous media is studied in order to obtain the receiver efficiency as a function of these parameters. The model was validated by comparing the results for a simple geometry composed of a long slab of finite thickness with the values available in the literature, and then tested with a cylindrical receiver using a parabolic dish as concentration system with a concentration factor of 500. A peak of absorbed solar radiation of 156 MW m⁻³ and an absorption efficiency of $90.55\%$ were obtained for a phase function asymmetry factor of $0.4$ (forward scattering) and scattering albedo and extinction coefficient of $0.54$ and 100 m⁻¹, respectively. The results for the diffuse reflectance, diffuse transmittance and absorption are also presented. The model developed in this work is useful to obtain and understand the energy absorption distribution in porous volumetric receivers coupled to solar concentration systems, when different porous structures and geometric parameters are used.

Introduction

Non-linear solar concentration systems are promising technologies to replace the conventional generation of electricity based on fossil fuels [1]. In recent years, a notable progress in concentrating solar thermal energy was achieved in terms of improving reflector designs, materials and heat transfer fluids, thermal to electric energy conversion and energy storage [2]. In these systems, two important components are the solar concentrators, which should concentrate the solar radiation on the thermal receiver, and the thermal receiver itself, where solar radiation is converted to thermal energy. In the recent work of Ho and Iverson [3], a description of typical configurations of solar thermal receivers is made and, according to that work, the volumetric thermal receivers present great challenges from the point of view of their numerical modelling and optimization. The volumetric receivers with solid matrix (porous media) have been under investigation, mainly due to their capability to achieve high values of temperature and thermal efficiency, being one of the most promising technologies to improve the thermal efficiency of solar concentration power systems [4], [5], [6], [7]. In the work of Ávila-Marín [8], a chronological review of volumetric receivers development associated with concentrating solar power (CSP) plants is presented. The author identified the various receiver configurations, materials, power plant configurations, advantages and main problems.

In terms of modelling porous volumetric receivers associated with CSP plants, the recent work of de la Beaujardiere and Reuter [9] presents a review of performance modelling of these systems, including the energy conversion system, the thermal energy storage and the receiver modelling. Regarding the receiver modelling, two different fields of study can be identified. One of them is the absorption of solar radiation in the porous media, in which the Monte Carlo Ray Tracing (MCRT) method [6], [10], [11] is used, and the other one is the integration of solar radiation absorption with fluid flow and heat transfer modelling in order to obtain the thermal performance of receivers [7], [12], [13]. The MCRT method used to describe the light transport in biological media [14], [15], [16] can be also used to solve the problem of light transport in porous media with solid matrix [6], [10], [11]. In this case, there are two possible approaches: one is the computation of the propagation of ray packages with a specified statistical weight [10], [11], [14], in which energy absorption occurs in every interaction point and their energy decreases gradually; and the other one is the modelling of propagation of each ray, one by one, until they are absorbed or exit the system [6].

Wang et al. [14] addressed the light transport in multi-layered tissues using MCRT method and presented the results of diffuse reflectance and transmittance as function of the exit angle, which were validated with data from the work of van de Hulst [17]. Gao et al. [18] modelled and studied the effect of incidence angle, optical thickness and asymmetry factor on the diffuse reflectance of a infinite slab turbid medium. They found that for large optical thickness and small incidence angles, the angular distribution of diffuse reflectance is similar to that of Lambertian surface. In the work of Cui et al. [10], solar radiation propagation in a pressurized volumetric receivers was modelled using the MCRT method and assuming a solar radiation flux in the front face of the receiver while a non-uniform cylindrical coordinate grid was employed in the statistical analysis of energy distribution. This technique reduces the number of cells and computation time compared to that for a uniform grid. He et al. [11] did a similar study but using a heliostat field as concentration system. In other works [10], [11], [14], the MCRT method was based on the propagation of ray packages while in the work of Chen et al. [6] the same method was implemented by computing the propagation of every single ray. They used a parabolic dish as the concentration system and studied the effects of porous structure parameters, slope error of the concentrator and receiver misalignment on the performance of the receiver. Zhao and Tang [19] used the MCRT method to determine the extinction coefficients of silicon carbide porous media based on the Fresnel and Beer laws in order to obtain the optical properties of the porous media. They concluded that the extinction coefficient of the silicon carbide strongly depends on the porosity and pores size. Gomez-Garcia et al. [20] modelled the radiation propagation in a porous volumetric receiver with a stack of thick square grids and also analysed the influence of geometric parameters in the receiver performance, such as the grid length and the gap between consecutive layers.

The thermal energy in the receiver is collected using a heat transfer fluid, which will transfer heat to a thermodynamic cycle that converts thermal to mechanical energy and then to electrical energy through an electric generator. Recently, Benoit et al. [21] did a review of current and future liquid, gas, supercritical, two-phase and particulate heat transfer fluids. Using air as heat transfer fluid in porous volumetric receivers offers significant advantages, such as high conversion efficiency, low environmental impact and the possibility of being used in deserts or other isolated regions with scarce water resources [22].

Regarding the heat transfer processes in the receiver, Capuano et al. [23] presented an overview of various numerical modelling approaches of solar radiation conversion when air is used as heat transfer fluid, developed at the German Aerospace Center (DLR), and results for different numerical models are compared with experimental measurements. Fuqiang et al. [24] studied the effect of using different radiative transfer models (P1 and Rosseland approximation) on the heat transfer modelling of a porous media solar receiver by combining the MCRT method and CFD modelling. They concluded that the difference in the maximum temperature in the solar receiver between these two approximations is small. According to the work of Smirnova et al. [25], the volumetric receivers are exposed to severe thermal loads, where maximum temperatures of more than 1000 $°$C are reached. These high thermal loads might reduce the lifetime of the receivers. In this way, Smirnova et al. [25] conducted a study where the effect of thermal loads in the receiver is quantified. They presented the mechanical stresses and the maximum thermal load up to which the receiver should be operated. Recently, Gomez-Garcia et al. [26] presented a review of thermal and hydrodynamic modelling of conventional ceramic volumetric absorbers. They identified the radiative and thermal properties that a good absorber must have, providing values of reference for the characteristics of ceramic volumetric receivers. Fend et al. [27] conducted an experimental study using a variety of porous materials and reported the measuring method and the results for the thermal conductivity, convective heat transfer coefficient and efficiency. Recommendations on the design of volumetric absorbers were also given.

As for the design of the porous volumetric receivers, high porosity or large pores means low pressure drop in the receiver, however this also implies a lower heat transfer coefficient between the porous material and the heat transfer fluid [13]. Therefore, an optimal thermal receiver should have a structure that causes low pressure drop and maintains good heat transfer characteristics. In this regard, Wu et al. [28] presented experimental and numerical studies on the pressure drop in ceramic foams for air receiver applications using two modified structures, and presented a empirical model to predict the pressure drop based on those results. Albanakis et al. [29] did an experimental assessment of the response of various foam materials, and the results showed that the efficiency of porous volumetric receivers depends on both materials characteristics and flow conditions. Roldán et al. [30] investigated the thermal performance of different configurations of volumetric receivers using Computational Fluid Dynamics. They carried out simulations for various values of porosity in order to find the optimal working configurations. Wang et al. [31] presented a novel design of gradient-porous heat sinks for volumetric receivers. They compared the receiver performance to that of an homogeneous porous receiver configuration and concluded that the gradient-porous arrangement can improve both pressure drop and thermal performance. Wu et al. [32] developed a correlation for the local convective heat transfer coefficient between the air flow and ceramic foams based on numerical simulations, and validated it with experimental data. Porous volumetric receivers still is an area of growing research, for example, in terms of radiation flux distribution and experimental study on the effect of differents geometrical parameters [33], determination of representative elementary volumes [34], techniques to improve its performance, such as volumetric solar receiver with structured packed bed [35], composite porous structure [36] and micro heat exchangers with multi-layered porous media which can be used in solar thermal receivers [37]. An interesting and recent study was presented by Zaversky et al. [38] where two different types of one-dimensional model of radiation propagation inside the foam were developed. Those models were checked for consistency against experimental data and then used to optimize the absorbed thermal efficiency by considering single, double and triple layer absorber configurations. They found that the optimized single-layer is the best absorber configuration while, if necessary, the second layer can be used to satisfy mechanical and stability requirements.

The absorption of solar radiation is a very important aspect in the performance of porous volumetric receivers because the spatial distribution of absorbed energy is the source of the heat transfer process. Thus, the first step to optimize the thermal efficiency of a volumetric receiver is understanding how solar radiation is distributed in the receiver and how this distribution and the absorption efficiency are affected by the different characteristic parameters of the receiver. The state of the art shows some gap in the detailed and parametric analysis of solar radiation absorption in porous volumetric receiver. For this reason, a detailed three-dimensional modelling and analysis of solar radiation absorption in a single layer porous media receiver is presented in this work, using the MCRT method to simulate the concentrated solar radiation flux incident in the front face (inlet) of the volumetric receiver. The model includes the effect of the incidence angle on the absorption of energy while the receiver wall is modelled as a diffuse surface. One of the main innovation of this work is using Henyey-Greenstein phase function to model light scattering inside the porous media. Other contributions of this work are the study of the effect of optical thickness (porosity, pore diameter and height of the receiver), asymmetry factor of the phase function, boundary wall properties and geometric parameters of the concentration system on the distribution and performance of solar radiation absorption in the receiver. Based on the results presented in this paper, a discussion on the distribution of absorbed solar radiation and absorption efficiency are conducted, and the conditions to improve the performance of the receiver are presented.