Elsevier

Chemical Engineering Science

Volume 81, 22 October 2012, Pages 298-310
Chemical Engineering Science

Computational modeling and on-sun model validation for a multiple tube solar reactor with specularly reflective cavity walls. Part 1: Heat transfer model

https://doi.org/10.1016/j.ces.2012.06.064Get rights and content

Abstract

A three-dimensional, steady state computational model coupling radiative transfer with convective and conductive heat transfer is developed to describe a solar receiver consisting of an array of five tubes enclosed within a specularly reflective cylindrical cavity with a windowed aperture. Ray trace modeling of the concentrating system provides the magnitude and direction of solar energy incident on the aperture. Transport of solar radiation in the cavity space is decoupled from all other transport processes occurring in the receiver and profiles of the absorbed solar energy are determined via a Monte Carlo technique requiring only the receiver geometry, solar profile at the aperture, and spectral directional optical properties. A finite volume method is utilized to account for thermal radiation emitted by heated surfaces and implemented in conjunction with a computational fluid dynamics model. Maximum temperatures of 1820 K, 1355 K and 1536 K are predicted for the center, front, and back tubes, respectively for a solar power input of 6 kW though temperature gradients as high as 340 K develop between the front and back sides of the center tube. More than 79% of the solar energy is absorbed by tube surfaces. Emission losses account for 11–25% of the solar input whereas conductive heat losses account for 55–69% of the solar input and arise predominantly from conduction along the tube length to cooled cavity walls. Average discrepancies between theoretically predicted and experimentally measured temperatures are 44 K (4%) for silicon carbide tubes and 21 K (2%) for Inconel tubes over temperature ranges of, respectively, 600–1700 K and 700–1400 K.

Highlights

► A heat transfer model is developed for a reflective cavity solar receiver. ► Radiative transfer is incorporated via a combined Monte Carlo/finite volume scheme. ► Detailed descriptions of solar flux produced by a realistic concentrator are included. ► Temperatures up to 1820 K are achieved with 6 kW solar power. ► Model results match experimentally measured temperature profiles within 44 K (4%).

Introduction

Concentrated solar energy can be used to provide the heat necessary to drive various highly endothermic chemical reactions for renewable fuel production including direct thermolysis of water, reduction of metal oxides for thermochemical water splitting cycles, and gasification of cellulosic biomass, coal or other carbonaceous materials to produce synthesis gas (Kodama, 2003, Steinfeld, 2005). Metal oxide cycles and biomass gasification, when powered by the clean energy of the sun, are theoretically entirely renewable and carbon neutral. Numerous solar reactor concepts have been proposed (Abanades et al., 2007, Lichty et al., 2010, Melchior et al., 2008, Rodat et al., 2009, Palumbo et al., 2004, Wieckert et al., 2004, Z'Graggen and Steinfeld, 2008, Kogan et al., 2007) with most consisting of cavity-receiver type designs in which concentrated solar radiation enters into a closed cavity through a small aperture or window. Directly irradiated designs theoretically offer rapid and efficient heating owing to direct absorption of solar energy by reactant particles, and these designs have the potential to minimize solar load on the receiver walls (Abanades et al., 2007, Hirsch and Steinfeld, 2004, Kogan et al., 2007, Moller and Palumbo, 2001, Palumbo et al., 2004, Z'Graggen and Steinfeld, 2008). Indirectly irradiated designs can eliminate the necessity of a transparent window by enclosing reactants in either opaque absorbing tubes or a separate cavity (Dahl et al., 2004, Lichty et al., 2010, Melchior et al., 2008, Rodat et al., 2009, Wieckert et al., 2004). Receiver cavities are typically constructed from strongly absorbing materials and insulated heavily so as to minimize radiative absorption and conduction losses. Reflective cavity receivers are subject to comparatively larger conduction losses as walls must remain sufficiently cool to maintain the quality of the reflective surface, and are only practically feasible in indirectly-irradiated designs without the possibility of particle-wall contact. Nevertheless, the small thermal mass of reflective cavity receivers makes them amenable to laboratory scale experimental operation.

Computational models are used to characterize receiver performance and accurate descriptions of relevant transport phenomena involve coupling typical momentum, continuity, and energy equations with the complex integro-differential equations describing radiative transfer. Finite volume or discrete ordinates (Abanades et al., 2007, Haussener et al., 2009, Rodat et al., 2010, Siegel et al., 2010), radiosity (Palumbo et al., 2004, Wieckert et al., 2004), and Monte Carlo (Hirsch and Steinfeld, 2004, Maag and Steinfeld, 2010, Melchior et al., 2008, Z'Graggen and Steinfeld, 2008) methods are commonly employed to solve the radiative transfer problem. Finite volume (FV) (Chui and Raithby, 1993, Raithby and Chui, 1990) and discrete ordinates (DO) (Fiveland, 1987) methods retain compatibility with a control-volume based computational fluid dynamics (CFD) modeling approach and thus FV/DO radiation models are commonly implemented in conjunction with highly complex three-dimensional fluid flow and heat transfer models including, for instance, discrete particle models, turbulence, and the effects of buoyancy (Abanades et al., 2007, Siegel et al., 2010). However, previous studies indicated inadequacies in solutions obtained via the finite volume method for solar energy in the receiver cavity due to ray concentration and false scattering errors (Martinek, 2012). Similar deficiencies have been detailed in the literature for isolated heat sources, non-participating media, highly reflective boundary surfaces, and collimated radiative energy (Byun et al., 2000, Chai et al., 1993, Coelho, 2002, Raithby, 1999).

In the current study a computational heat transfer model which couples both Monte Carlo and finite volume descriptions of radiative transfer with a three-dimensional computational fluid dynamics (CFD) model describing convective heat transfer, conductive heat transfer, and fluid flow is developed and experimentally validated for the 10 kW prototype solar receiver described by Lichty et al. (2010). The solar receiver is depicted schematically in Fig. 1 and consists of a reflective cylindrical outer cavity constructed of polished aluminum with an inner diameter of 18.3 cm. A rectangular quartz window (5.7 cm by 9.8 cm) sits at the front of the cavity and is surrounded by a nickel-plated copper cooling plate. The receiver may be operated either open to the external atmosphere with a windowless aperture, or sealed from the surrounding environment by means of a quartz panel in order to prevent oxidation of the tube material. The cavity encloses five interchangeable 2.54 cm outer-diameter, 0.356 m long flow tubes arranged in the staggered pattern shown in Fig. 1. Tube positions are provided in detail by Lichty et al. (2010) and wall thicknesses are 0.32 cm. Each tube extends 3.8 cm above and below the vertical extent of the cavity. Five distinct cooling zones encircle the receiver to prevent overheating or oxidation of polished aluminum cavity walls.

Section snippets

Characterization of the solar flux profile

The solar flux incident on the aperture or window surface is produced by the High Flux Solar Furnace (HFSF) at the National Renewable Energy Laboratory (NREL). The HFSF (Lewandowski et al., 1991) consists of a single flat heliostat, a primary concentrator comprised of an array of 25 mirrored hexagonal facets, and a vertically-opposing two plate attenuator utilized to control the total power incident on the receiver with a maximum achievable solar input of approximately 9 kW. The secondary

Absorption of solar energy

Profiles of solar energy flux absorbed around the circumference of each tube surface in a horizontal plane aligned with the aperture centroid are illustrated in Fig. 6(a) for 6 kW solar power produced with a 50% attenuator opening. Fig. 6(b) shows the solar energy flux absorbed by the center tube, front east tube, and back east tube in the horizontal plane aligned with the aperture centroid after at least one reflection at the cavity wall. The angle β is measured counterclockwise from the

Conclusions

A theoretical heat transfer model is developed for a reflective cavity solar receiver. Radiative energy is separated into two components: (1) solar energy introduced at the aperture and (2) energy emitted by heated surfaces within the receiver. Solar energy is directly mapped from a profile at the window surface onto all tube and cavity wall surfaces by means of a statistically-based Monte Carlo technique. Emitted energy is approximated with a finite volume radiation model solved simultaneously

Nomenclature

    aλ

    spectral absorption coefficient (m-1)

    As

    surface area (m2)

    Ac

    cross-sectional area (m2)

    Cp

    heat capacity (J/kg/K)

    eλb

    blackbody spectral emissive power (W/m2/μm)

    Fi−j

    radiation configuration factor between surfaces i and j

    g

    gravitational acceleration (m/s2)

    h

    enthalpy (J/kg); convective heat transfer coefficient (W/m2/K)

    Iλ

    spectral radiation intensity (W/m2/sr/μm)

    Iλb

    spectral blackbody radiation intensity (W/m2/sr/μm)

    k

    thermal conductivity (W/m/K)

    l

    index denoting finite solid angle

    L

    length between thermocouple

Acknowledgements

The authors appreciate financial support from the DOE-EERE Fuel Cell Technologies Program for Sandia National Laboratory/University of Colorado-Boulder R&D on solar thermochemical production of hydrogen, from the USDA Grant 2009-10001-05114, and from the U.S. Department of Education Graduate Assistance in Areas of National Need Program.

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