Experimental analysis of free convection heat loss in a bicylindrical cavity receiver

Highlights

• A novel bicylindrical cavity receiver was designed and experimentally investigated.

• The model cavity receiver shows maximum convective loss at about −30°.

• The data of the model were used to predict convective loss at higher temperatures.

• Nusselt number correlations were proposed for both upward-facing and downward-facing situations.

Abstract

Convection heat loss from solar cavity receivers in parabolic dish concentrators significantly reduces the performance of the system. In this paper, steady-state experiments were conducted to investigate heat losses from an electrically heated bicylindrical cavity receiver, which consists of two coaxial cylinders of diameters 0.06 and 0.09 m with an aspect ratio (length to diameter) of one. The cavity surface was exposed to constant heat fluxes from 785 W/m² to 1770 W/m² at different inclination angles from −90° (vertically upward-facing) to +90° (vertically downward-facing). The temperature distribution of the cavity surface depicts that due to the presence of a sharp corner between the two cylinders, the flow instability intensifies, and the temperature of the top surface rises. The results showed that the maximum convective loss occurs approximately at −30° that corresponds to 63% of the total heat loss while the minimum convective loss occurs at +90°, which accounts for about 19% of the total heat loss. A convective heat loss relation was developed for cavity surface temperatures up to 300 °C and used to estimate convective losses at higher temperatures. Flow visualization experiments were also performed to investigate heat losses from the cavity receiver. It was observed that increasing the inclination angle from 45° to 60° results in a decrease in the induced buoyant force. Empirical correlations were also developed for Nusselt number as a function of Rayleigh number, inclination angle, and the ratio of cavity surface temperature to the ambient temperature for both upward and downward-facing situations. Comparing correlated Nusselt numbers with experimental results for upward-facing positions shows ±5% deviation, while for downward-facing inclinations, the correlation predicts the experimental data by a deviation within ±12%. Moreover, a comparison of experimentally measured convective losses with literature shows discrepancy at lower inclinations but depicts good agreement when the inclination angle increases. For the vertically downward-facing situation, the experimental data shows a close fit where the effect of aperture size becomes negligible. The analyses also revealed that the relative combined standard uncertainty of convective Nusselt number varies between 2% and 14%, depending upon the cavity inclination and the heat flux applied.

Introduction

Solar cavity receivers are the key components of parabolic dish systems that absorb concentrated solar radiation and heat up the working fluid. The performance of a cavity receiver can appreciably be reduced by heat losses, including conductive loss through the insulation as well as convective and radiative losses to the ambient. Generally, conductive and radiative losses can easily be determined analytically, whereas the determination of convective loss is not a trivial task due to the complexity of flow and temperature fields in and around the cavity [1]. Experimental and numerical investigations of convective loss in cavity receivers have been the subject of many researches over the last years. A comprehensive review of convective loss mechanisms in cavity receivers with different geometries and under various boundary conditions can be found in Wu et al. [2]. Clausing [3], [4] was the first who proposed the analytical model of cavity receivers based on the understandings of the physics of the convective loss. He hypothesized that the convective loss depends on two factors: the ability to transfer mass and energy across the aperture and the ability to heat the air inside the cavity. The analytical results indicated that the capability to heat the air inside the cavity is of the greatest importance, and buoyancy effects dominate. A generalized model for both downward and upward-facing spherical and hemispherical receivers has been developed by Leibfried and Ortjohann [5]. They modified Clausing and Stine models for Nusselt number considering the influence of geometry on bulk flow temperature. Taumoefolau et al. [1] experimentally investigated natural convective loss from an electrically heated cylindrical cavity receiver. They found that convective loss has a higher value for a larger exposure ratio (ratio of aperture diameter to cavity diameter). Moreover, the inclination, which corresponds to maximum convective loss, increases with decreasing exposure ratio. In an experimental study, Abbasi-Shavazi et al. [6] investigated the effect of temperature distribution along the cavity walls on radiative loss. They showed that models using an average cavity temperature overestimate the radiative loss up to 20% compared with models that use experimental temperatures along the cavity surface. Also, it is noted that correlations based on the surface areas of the stagnation and convection zones would be able to predict experimental results better. Chakroun and coworkers [7], [8], [9] investigated the effects of aperture geometry, aspect ratio, and opening ratio on free convection heat loss in the upward-facing rectangular and semi-cylindrical cavities. They found that the increase in Nusselt number for the semi-cylindrical cavity over the rectangular cavity ranges from 50 to 200%, depending on the inclination angle. They showed that for the upward-facing cavity, the Nusselt number increases with a decreasing aspect ratio. Additionally, decreasing the opening ratio generally decreases the Nusselt number regardless of the inclination angle and aspect ratio. The effect of aperture size and position on convective loss from a solar heat-pipe receiver was investigated by Wu et al. [10]. They concluded that for downward-facing inclinations, moving the aperture upward increases the convective loss while for sideward and vertically downward inclinations, no significant increase in convective loss appears. The results also indicated that increasing convective loss mainly occurs for the initial upward moving of aperture, while increasing the aperture size results in a steady increase in convective loss. In another study, Wu et al. [11] and Shen et al. [12] showed through experiments that in a cylindrical cavity with different surface boundary conditions, the convection heat loss is more sensitive to the tilt angle compared with the radiative and conductive losses. Lovegrove et al. [13] conducted an experiment to study heat losses from an isothermal cylindrical cavity receiver. They proposed an improved correlation to predict a convective loss for cavity receivers on dish concentrators using a characteristic length scale combining geometric parameters. The correlation showed a considerably good prediction of convective loss for the model receiver and two actual receivers for 20 m² and 400 m² dishes. Tan et al. [14] experimentally investigated heat losses from a hemispherical cavity receiver considering factors such as inlet temperature of the working fluid, inclination, and aperture size. They proposed a correlation for Nusselt number at low fluid temperature and extended it to high-temperature situations. Experimental findings of Azzouzi et al. [15] for a cylindrical cavity receiver revealed that the thermal performance of the receiver decreases with increasing aspect ratio for all inclination angles. They also noted that in a given inclination angle, the solar concentration ratio greatly influences the thermal efficiency. Moreover, the convective loss reaches a maximum for the aspect ratio of 2, independent from the solar concentration ratio. Pavlovic et al. [16] compared thermal, optical, and exergy efficiencies of spiral and conical cavity receivers and found that the conical design leads to higher thermal and exergy efficiencies for all operating conditions.

Besides experimental studies of convective loss, numerical investigations mainly based on computational fluid dynamics (CFD) have also been developed. Paitoonsurikarn et al. [17] presented a numerical study investigating the convective loss from four cavity receivers of different geometries and scales. They proposed a new correlation based on the concept of the ensemble cavity length scale to account for the combined effects of cavity geometry and inclination angle. In numerical analysis, Sendhil Kumar and Reddy [18] compared the natural convection loss from three types of receivers, namely cavity, semi-cavity, and modified cavity receivers for solar dish collectors. Their numerical results indicated that the modified cavity receiver experiences lower convective loss. While the inclination angle greatly influences convective loss for cavity and modified cavity receivers, the effect of inclination on the semi-cavity receiver seems to be of minor importance.

According to Clausing [3], the interior volume of the cavity can be divided into two zones, namely a convective zone and a stagnant zone. The boundary between these zones can be approximated by a free shear layer passing through the upper lip of the aperture (Fig. 1). The convective loss mainly occurs in the convective zone and decreases by decreasing the extent of this zone. The inclination angle and the cavity geometry significantly influence the amount of the stagnant and convective zones. As the cavity receiver rotates from 0° (side-facing) to +90° (vertically downward-facing), the extent of the stagnant zone increases and reaches the maximum while the convective zone reduces and roughly vanishes. This was supported by both experimental and numerical studies [1], [5], [6], [19], [20]. In the vertically downward-facing situation, the hot air rises and covers the entire cavity with a temperature close to that of the walls and temperature gradient forms as stable strata. Although the flow configuration and the zones depend mainly on the cavity geometry and wall temperature, however, a higher bulk air temperature can be achieved as the ratio of the aperture to the inner surface area of cavity reduces [5]. Hence, for a given surface temperature of the cavity, minimizing the aperture area results in a decrease in convective loss.

By summarizing the various designs of cavity receivers, it can be concluded that generally, two key parameters are of utmost importance in the effectiveness of the design: the aperture size, which controls the flow of air entering and leaving the cavity, and the presence of sharp corners in the cavity, which affects flow instability and rate of heat transfer. The effect of sharp corners on buoyancy-driven flows was studied by Vafai and Ettefagh [21]. Sharp corners significantly affect the flow field and heat transfer in open-ended cavities through the formation of flow instabilities. Depending upon the geometry of the cavity, these alter the extent of the stagnant zone and flow circulation, which in turn change the convective loss. Accordingly, this paper addresses the design and investigation of a bicylindrical cavity receiver that accounts for the aforementioned parameters. The receiver consists of two coaxial cylindrical cavities with different diameters and the same aspect ratios. The new design was investigated for convective loss compared with traditional single-cylinder cavities. Empirical correlations were also proposed for Nusselt number and convective loss, which can be used to estimate the convective loss at higher temperatures.