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Research Papers

Radiation Boundary Conditions for Computational Fluid Dynamics Models of High-Temperature Cavity Receivers

[+] Author and Article Information
Siri Sahib S. Khalsa1

Sandia Staffing Alliance, Under Contract to Sandia National Laboratories, Concentrating Solar Technologies Department, P.O. Box 5800, Albuquerque, NM 87185-1127sskhals@sandia.gov

Clifford K. Ho

Sandia National Laboratories, Concentrating Solar Technologies Department, P.O. Box 5800, Albuquerque, NM 87185-1127ckho@sandia.gov

1

Corresponding author.

J. Sol. Energy Eng 133(3), 031020 (Aug 05, 2011) (6 pages) doi:10.1115/1.4004274 History: Received May 12, 2011; Accepted May 17, 2011; Published August 05, 2011; Online August 05, 2011

Rigorous computational fluid dynamics (CFD) codes can accurately simulate complex coupled processes within an arbitrary geometry. CFD can thus be a cost-effective and time-efficient method of guiding receiver design and testing for concentrating solar power technologies. However, it can be computationally prohibitive to include a large multifaceted dish concentrator or a field of hundreds or thousands of heliostats in the model domain. This paper presents a method to allow the CFD code to focus on a cavity receiver domain alone, by rigorously transforming radiance distributions calculated on the receiver aperture into radiance boundary conditions for the CFD simulations. This method allows the incoming radiation to interact with participating media such as falling solid particles in a high-temperature cavity receiver. The radiance boundary conditions of the CFD model can take into consideration complex beam features caused by sun shape, limb darkening, slope errors, heliostat facet shape, multiple heliostats, off-axis aberrations, atmospheric effects, blocking, shading, and multiple focal points. This paper also details implementation examples in ansys fluent for a heliostat field and a dish concentrator, which are validated by comparison to results from delsol and the ray-tracing code asap , respectively.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Illustration of a solid particle receiver, which uses a curtain of falling particles as the absorption medium for concentrated solar radiation from a heliostat field. Receiver illustration from Ref. [1].

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Figure 2

The union of emissions from all micro-elements within one boundary surface macro-element produces the nonuniform radiation distribution along the entire solid angle irradiated by the macro-element

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Figure 3

Map of the heliostat field that will be represented as a CFD boundary condition. The receiver is located at the origin of the map, 300 m above the heliostat pivot points.

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Figure 4

Contour plot of the flux distribution on the cavity receiver aperture. The flux at each vertex (intersection of white dashed lines) is prescribed to one macro-element. East is positive along the horizontal axis. Upward is positive along the vertical axis. Note that the corners and edges of the plot also represent flux values for macro-elements.

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Figure 5

Illustration of the vectors used to calculate the weighting factors for a heliostat beam. The unit normal n∧h to a heliostat surface bisects the sun vector s∧ and the specular vector t∧h, which points from the heliostat to the aim point. The vector n∧a is the unit normal to the cavity receiver aperture.

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Figure 6

Illustration of a cavity receiver irradiated by a heliostat field. The aperture is discretized into 11 × 11 macro-elements. The entire solid angle irradiated by the heliostat field, through a macro-element on the aperture, is projected onto a hemisphere based on the aperture. The angles ΔΘ (polar) and ΔΦ (azimuthal) denote the angular widths of the irradiated solid angle. This solid angle is discretized into 5 × 5 smaller solid angles, each of which will be irradiated by one micro-element per macro-element.

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Figure 7

Contour plot of the normalized weighting factors for the directional distribution of radiation from the heliostat field. The weight at each vertex (intersection of white dashed lines) is prescribed to one micro-element per macro-element. Note that the corners and edges of the plot also represent solid angles irradiated by micro-elements.

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Figure 8

Left: Cavity receiver aperture discretized into 11 × 11 macro-elements (one macro-element is highlighted). Right: One macro-element discretized into 5 × 5 micro-elements (micro-elements are highlighted).

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Figure 9

A radiation beam emitted from a micro-element is an elliptic cone defined by two angular beam widths, Δθ and Δφ, and is pointed in the beam direction b̂ (from Ref. [8])

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Figure 10

Flux distributions on a plane located 5.45 m from the aperture, inside the cavity receiver, calculated using different methods. Left: delsol . Right: ansys fluent with rigorous boundary conditions (example 1). West is positive along the horizontal axis. Upward is positive along the vertical axis.

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Figure 11

Contour plot of the flux magnitudes (W/m2 ) prescribed to the macro-elements (circular annuli) on the aperture of the cavity receiver irradiated by the dish concentrator.

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Figure 12

Comparison between ansys fluent (using the method described in this work) and asap . Middle and back planes are located 6.35 cm and 12.7 cm, respectively, from the focal plane.

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