Reduction of false scattering in arbitrarily specified discrete directions of the discrete ordinates method

Li, Hongshun

doi:10.1016/j.jqsrt.2003.08.005

Cited by 10 publications

(18 citation statements)

References 9 publications

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“…Nevertheless, the DO method has two major shortcomings due to its FV nature, namely the "ray effect" and "false scattering", which affect result accuracy (Brunner, 2002;Chai and Patankar, 2006). The former is also known as "ray concentration" (Martinek and Weimer, 2013), and the latter as "numerical scattering" (Li, 2004), "numerical smearing" (Jessee and Fiveland, 1997) or "false diffusion" in CFD communities (Hachicha, 2013). Before using DO as a ray-tracing method in a solar field, the ability of reducing these shortcoming effects must be checked.…”

Section: Overcoming Do Shortcomings In Ray Tracingmentioning

confidence: 99%

“…Before using DO as a ray-tracing method in a solar field, the ability of reducing these shortcoming effects must be checked. Various methods were suggested by different researchers (Li, 2004;Jessee and Fiveland, 1997;Hachicha, 2013), but their implementation in ANSYS Fluent due to its closed-source specification is almost impossible. Therefore, in the following paragraphs, the origin of these errors and their alleviation are discussed.…”

Section: Overcoming Do Shortcomings In Ray Tracingmentioning

confidence: 99%

“…To illustrate the interaction between FV mesh density and the angular discretisation of the DO in reducing both the ray effect and false scattering, a test case from literature (Li, 2004) with an available Monte Carlo ray-tracing result is used. The domain (illustrated in Figure 1) has oblique collimated radiation entering into a black square enclosure filled with a pure isotropical scattering and homogeneous medium ( )…”

Section: Test Case For Oblique Collimated Radiationmentioning

confidence: 99%

“…The oblique angle is defined by θ = -90°, φ = -60°and enters through a Monte Carlo solution (Li, 2004) transparent section of the top wall (…”

Section: Test Case For Oblique Collimated Radiationmentioning

confidence: 99%

“…Moghimi et al (2014Moghimi et al ( , 2015 used the same package for simulating a thermal model of a multi-tube trapezoidal cavity receiver and its optimisation, but the optical modelling of the domain and inclusion of the mirror field were not considered in their optimisation. After an introduction to the Radiative Transfer Equation (RTE) and its solution using the Discrete Ordinates (DO) method on a finite volume (FV) mesh, the accuracy of the optical simulation method is illustrated for a test case from literature (Li, 2004;Hachicha, 2013). The recommended settings are then applied to an implementation of an LFC receiver for the FRESDEMO (Mertins, 2009;Bernhard et al, 2008) mirror field layout to illustrate the benefit of a combined FV RTE solution and heat transfer modelling.…”

Section: Introductionmentioning

confidence: 99%

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A novel computational approach to combine the optical and thermal modelling of Linear Fresnel Collectors using the finite volume method

2015

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A computational approach is presented, which uses the finite volume (FV) method in the Computational Fluid Dynamics (CFD) solver ANSYS Fluent to conduct the ray tracing required to quantify the optical performance of a line concentration Concentrated Solar Power (CSP) receiver, as well as the conjugate heat transfer modelling required to estimate the thermal efficiency of such a receiver. A Linear Fresnel Collector (LFC) implementation is used to illustrate the approach. It is shown that the Discrete Ordinates method can provide an accurate solution to the Radiative Transfer Equation (RTE) if the shortcomings of its solution are resolved appropriately in the FV CFD solver. The shortcomings are due to false scattering and the socalled ray effect inherent in the FV solution. The approach is first evaluated for a 2-D test case involving oblique collimated radiation and then for a more complex 2-D LFC optical domain based on the FRESDEMO project. For the latter, results are compared with and validated against those obtained with the Monte Carlo ray tracer, SolTrace. The outcome of the FV ray tracing in the LFC optical domain is mapped as a non-uniform heat flux distribution in the 3-D cavity receiver domain and this distribution is included in the FV conjugate heat transfer CFD model as a volumetric source. The result of this latter model is the determination of the heat transferred to the heat transfer fluid running in the collector tubes, thereby providing an estimation of the overall thermal efficiency. To evaluate the effectiveness of the phased approach in terms of accuracy and computational cost, the novel 2-D:3-D phased approach is compared with results of a fully integrated, but expensive 3-D optical and thermal model. It is shown that the less expensive model provides similar results and hence a large cost saving. The novel approach also provides the benefit of working in one simulation environment, i.e. ANSYS Workbench, where optimisation studies can be carried out to maximise the performance of linear CSP reflector layout and receiver configurations.

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Section: Overcoming Do Shortcomings In Ray Tracingmentioning

confidence: 99%

Section: Overcoming Do Shortcomings In Ray Tracingmentioning

confidence: 99%

Section: Test Case For Oblique Collimated Radiationmentioning

confidence: 99%

“…The oblique angle is defined by θ = -90°, φ = -60°and enters through a Monte Carlo solution (Li, 2004) transparent section of the top wall (…”

Section: Test Case For Oblique Collimated Radiationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A novel computational approach to combine the optical and thermal modelling of Linear Fresnel Collectors using the finite volume method

2015

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Analysis of Conduction and Radiation Heat Transfer in a Differentially Heated 2‐D Square Enclosure

Sasmal

Mishra

2016

Heat Trans. Asian Res.

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Radiative heat transfer with and without conduction in a differentially heated 2-D square enclosure is analyzed. The enclosure with diffuse gray boundaries contains radiating and/or conducting gray homogeneous medium. Radiatively, the medium is absorbing, emitting and scattering. On the south boundary, four types of discrete heated regions, viz., the full boundary, the left one-third, left two third and middle one third, are considered. In the absence of conduction, distributions of heat flux along the south boundary are studied for the effect of extinction coefficient. In the presence of conduction, distributions of radiation, conduction and total heat fluxes along the south boundary are analyzed for the effects of extinction coefficient, scattering albedo, conduction-radiation parameter, and south boundary emissivity. Effects of these parameters on centerline temperature distribution are also studied. To assess the performance of three commonly used radiative transfer methods, in all cases, the radiative transfer equation is solved using the discrete ordinate method (DOM), the conventional discrete ordinate method (CDOM) and the finite volume method (FVM). In the combined mode problem, with volumetric radiative information known from one of the three methods, viz., DOM, CDOM, and FVM, the energy equation is solved using the finite difference method (FDM). In all cases, the results from FDM-DOM, FDM-CDOM, and FDM-FVM are in good agreement. Computationally, all three sets of methods are equally efficient. C⃝ 2016 Wiley Periodicals, Inc. Heat Trans Asian Res, 0(0): 1-25, 2016; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj).

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Finite-volume ray tracing using Computational Fluid Dynamics in linear focus CSP applications

et al. 2016

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The modelling of solar irradiation in concentrated solar power (CSP) applications is traditionally done with ray-tracing methods, e.g. the Monte Carlo method. For the evaluation of CSP receivers, the results from ray-tracing codes are typically used to provide boundary conditions to Computational Fluid Dynamics (CFD) codes for the solution of conjugate heat transfer in the receivers. There are both advantages and disadvantages to using separate software for the irradiation and heat transfer modelling. For traditional ray-tracing methods, advantages are the cost-effectiveness of the Monte Carlo method in modelling reflections from specular surfaces; the ability to statistically assign a sun shape to the rays; the statistical treatment of reflectivity and optical errors (e.g. surface slope errors), to name a few. When considering a complex mirror field and a complex receiver with secondary reflective surfaces, especially with selective coatings to enhance absorption and limit re-radiation losses, standard ray tracers may be limited in specifying emissivity and absorptivity, which are both specular and temperature dependent, and are hence not suitable as radiation analysis tool. This type of scenario can be modelled accurately using CFD, through the finite volume (FV) treatment of the radiative transfer equation (RTE) and a banded spectrum approach at an increased computational cost. This paper evaluates the use of CFD in the form of the commercial CFD code ANSYS Fluent v15 and v16 to model the reflection, transmission and absorption of solar irradiation from diffuse and specular surfaces found in linear CSP applications. 2-D CFD solutions were considered, i.e. line concentration. To illustrate and validate the method, two sources were used. The first source was test cases from literature with published solutions and the second a combined modelling approach where solutions were obtained using both FV and ray tracing (with SolTrace). For all the test cases, good agreement was found when suitable modelling settings were used to limit both ray-effect and false scattering errors.

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Reduction of false scattering in arbitrarily specified discrete directions of the discrete ordinates method

Cited by 10 publications

References 9 publications

A novel computational approach to combine the optical and thermal modelling of Linear Fresnel Collectors using the finite volume method

A novel computational approach to combine the optical and thermal modelling of Linear Fresnel Collectors using the finite volume method

Analysis of Conduction and Radiation Heat Transfer in a Differentially Heated 2‐D Square Enclosure

Finite-volume ray tracing using Computational Fluid Dynamics in linear focus CSP applications

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