scholarly journals Ray Effect Mitigation Through Reference Frame Rotation

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
John Tencer
Keyword(s):  
Reference Frame ◽  
Discrete Ordinates ◽  
Property A ◽  
Major Drawback ◽  
Discrete Ordinates Method ◽  
Versatile Technique ◽  
Undesirable Property ◽  
Ray Effects ◽  
Combined Mode ◽  
Global Reference Frame

The discrete ordinates method is a popular and versatile technique for solving the radiative transport equation, a major drawback of which is the presence of ray effects. Mitigation of ray effects can yield significantly more accurate results and enhanced numerical stability for combined mode codes. When ray effects are present, the solution is seen to be highly dependent upon the relative orientation of the geometry and the global reference frame. This is an undesirable property. A novel ray effect mitigation technique of averaging the computed solution for various reference frame orientations is proposed.

scholarly journals The Impact of Reference Frame Orientation on Discrete Ordinates Solutions in the Presence of Ray Effects and a Related Mitigation Technique

2014 ◽  
Author(s):  
John Tencer
Keyword(s):  
Reference Frame ◽  
Invariant Solution ◽  
Discrete Ordinates ◽  
Discrete Ordinates Method ◽  
Multiple Materials ◽  
Rotationally Invariant ◽  
Ray Effects ◽  
The Impact ◽  
Combined Mode ◽  
Mitigation Technique

The discrete ordinates method is a popular and versatile technique for deterministically solving the radiative transport which governs the exchange of radiant energy within a fluid or gas mixture. It is the most common ‘high fidelity’ technique used to approximate the radiative contribution in combined-mode heat transfer applications. A major drawback of the discrete ordinates method is that the solution of the discretized equations may involve nonphysical oscillations due to the nature of the discretization in the angular space. These ray effects occur in a wide range of problems including those with steep temperature gradients either at the boundary or within the medium, discontinuities in the boundary emissivity due to the use of multiple materials or coatings, internal edges or corners in non-convex geometries, and many others. Mitigation of these ray effects either by increasing the number of ordinate directions or by filtering or smoothing the solution can yield significantly more accurate results and enhanced numerical stability for combined mode codes. When ray effects are present, the solution is seen to be highly dependent upon the relative orientation of the geometry and the global reference frame. This is an undesirable property. A novel ray effect mitigation technique is proposed. By averaging the computed solution for various orientations, the number of ordinate directions may be artificially increased in a trivially parallelizable way. This increases the frequency and decreases the amplitude of the ray effect oscillations. As the number of considered orientations increases a rotationally invariant solution is approached which is quite accurate. How accurate this solution is and how rapidly it is approached is problem dependent. Uncertainty in the smooth solution achieved after considering a relatively small number of orientations relative to the rotationally invariant solution may be quantified.

Improved Discrete Ordinates Method for Ray Effects Mitigation

2009 ◽  
Author(s):  
Zhi-Feng Huang ◽  
Huai-Chun Zhou ◽  
Pei-feng Hsu
Keyword(s):  
Three Dimensional ◽  
Computation Time ◽  
Computational Time ◽  
Discrete Ordinates ◽  
Emissive Power ◽  
Participating Media ◽  
Discrete Ordinates Method ◽  
Time Requirements ◽  
The Difference ◽  
Ray Effects

A new and improved method based on the discrete ordinates scheme with infinitely small weights (DOS+ISW) is developed for radiative heat transfer in three-dimensional participating media. To demonstrate the effectiveness of the method, ray effects caused by 1) abrupt step changes in the boundary conditions and 2) the stepwise variation of the medium emissive power are discussed. In this work, angular quadrature sets with large number of discrete ordinate directions are chosen to mitigate ray effects, while at the same time keeping the computational time increase to a minimum. Comparing with the conventional discrete ordinates method, the difference is that intensities in these directions are calculated by DOS+ISW. Intensity with fine directional resolution calculated by this method is validated by comparing with that of Reverse Monte Carlo method. The large number of discrete ordinates directions used in the new method becomes computationally prohibitive in discrete ordinates method due to the increased computer memory and computation time requirements.

Hybrid SN-PN Solution of the Radiative Transfer Equation in Multi-Dimensional Media

2011 ◽  
Author(s):  
Maathangi Sankar ◽  
Sandip Mazumder
Keyword(s):  
Radiative Transfer ◽  
Transfer Equation ◽  
Complex Geometry ◽  
Radiative Transfer Equation ◽  
Discrete Ordinates ◽  
Differential Approximation ◽  
Discrete Ordinates Method ◽  
Surface Exchange ◽  
New Formulation ◽  
Ray Effects

The Modified Differential Approximation (MDA) was originally proposed for solution of the radiative transfer equation (RTE) in order to remove the shortcomings of the P1 approximation in scenarios where the radiation intensity is strongly directionally dependent. In the original MDA approach, the wall-emitted component of the intensity is determined using a surface-to-surface exchange formulation that makes use of geometric viewfactors. Such an approach is computationally very expensive for complex geometry and/or inhomogeneous media. This article presents a new formulation in which the wall-emitted component is solved using the Discrete Ordinates Method (SN approximation), while the medium-emitted component is solved using the P1 approximation, resulting in a hybrid SN-PN RTE solver. Results show that the hybrid Discrete Ordinates-P1 method (DOM-P1) is computationally very efficient, but its accuracy is poor in optically thin situations where ray effects, inherent in the Discrete Ordinates Method, are pronounced. To circumvent this problem, the control-angle Discrete Ordinates Method (CADOM) is finally employed, and the accuracy of the hybrid CADOM-P1 method is found to be far superior to the hybrid DOM-P1 method.

Application of Modified Discrete Ordinates Method With the Concept of Blocked-Off Region Method to Radiative Heat Transfer Problems in Irregular Geometries

2010 ◽  
Author(s):  
H. Amiri ◽  
S. H. Mansouri ◽  
A. Safavinejad
Keyword(s):  
Heat Transfer ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Curvilinear Coordinates ◽  
Discrete Ordinates ◽  
Test Problems ◽  
Discrete Ordinates Method ◽  
Irregular Geometries ◽  
Transfer Problems ◽  
Ray Effects

The discrete ordinates method (DOM) for the solution of radiative heat transfer problems have received significant attention and development owing to their good compromise between accuracy, flexibility and moderate computational requirement. However, the DOM suffers from the ray effects related to the discretization of the angular distribution of the radiation intensity. The modified discrete ordinate method (MDOM) proved to significantly mitigate ray effects originated from discontinuities or abrupt changes of the wall temperature. This article presents blocked-off region treatment of irregular geometries using a modified discrete ordinates method in Cartesian coordinates. The Cartesian based 2D algorithm can be used to solve radiative heat transfer in irregular geometries by dividing the region into active and inactive regions. It is easier and convenient way of handling 2D irregular geometries than to write an algorithm in curvilinear coordinates. It is capable of handling participating (absorbing, emitting and isotropic or anisotropic scattering) or non participating gray media enclosed by gray diffuse walls. Both radiative and non-radiative equilibrium situations are considered. The walls of the enclosures can have either heat flux or temperature boundary conditions. Cases with curved and obstacle and radiation shield are considered. Some test problems are considered and results are validated with the available results in the literature. Results are found to be accurate for all kinds of situations.

Radiation, Conduction, and Convection From a Sphere in an Absorbing, Emitting, Gray Medium

1992 ◽  
Vol 114 (1) ◽  
pp. 250-254 ◽  
Author(s):  
P. D. Jones ◽  
Y. Bayazitoglu
Keyword(s):  
Radiative Transfer ◽  
Radiative Transfer Equation ◽  
Infinite Medium ◽  
Discrete Ordinates ◽  
Discrete Ordinates Method ◽  
Transfer Equations ◽  
Gray Medium ◽  
Intensity Field ◽  
Radiative Transfer Equations ◽  
Combined Mode

Combined mode heat transfer is solved for an emitting, reflecting sphere in low Peclet number motion through a gray, nonscattering, absorbing, emitting, and conducting infinite medium. The coupled formulation of the energy and radiative transfer equations is solved numerically. The radiative transfer equation is expressed in a unique spatial/directional coordinate system, whose object is to exploit the axisymmetry of the problem. The radiation intensity field is solved using the discrete ordinates method. Results are presented in terms of the Planck and Peclet numbers, and serve as a combined radiation/convection analog to the well-known Nusselt number result for a radiatively nonparticipating medium.

scholarly journals Ray Effects and False Scattering in Improved Discrete Ordinates Method

Energies ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6839
Author(s):  
Yong Cheng ◽  
Shuihua Yang ◽  
Zhifeng Huang
Keyword(s):  
Heat Flux ◽  
Radiative Transfer ◽  
Radiative Heat ◽  
Anisotropic Scattering ◽  
Radiative Heat Flux ◽  
Discrete Ordinates ◽  
Discrete Ordinates Method ◽  
Computation Efficiency ◽  
Scattering Phase ◽  
Ray Effects

The improved discrete ordinates method (IDOM) developed in our previous paper is extended to solve radiative transfer in three-dimensional radiative systems with anisotropic scattering medium. In IDOM, radiative intensities in a large number of new discrete directions are calculated by direct integration of the conventional discrete ordinates method (DOM) results, and radiative heat flux is obtained by integrating radiative intensities in these new discrete directions. Ray effects and false scattering, which tend to compensate each other, are investigated together in IDOM. Results show that IDOM can mitigate both of them effectively with high computation efficiency. Finally, the effect of scattering phase function on radiative transfer is studied. Results of radiative heat flux at boundaries containing media with different scattering phase functions are compared and analyzed. This paper indicates that the IDOM can overcome the shortages of the conventional DOM well while inheriting its advantages such as high computation efficiency and easy implementation.

MITIGATION OF RAY EFFECTS IN THE DISCRETE ORDINATES METHOD

2003 ◽  
Vol 43 (5) ◽  
pp. 445-466 ◽  
Author(s):  
Hong-Shun Li ◽  
Gilles Flamant ◽  
Ji-Dong Lu
Keyword(s):  
Discrete Ordinates ◽  
Discrete Ordinates Method ◽  
Ray Effects

Improved Discrete Ordinates Method for Ray Effects Mitigation

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Zhi-Feng Huang ◽  
Huai-Chun Zhou ◽  
Pei-feng Hsu
Keyword(s):  
Three Dimensional ◽  
Computation Time ◽  
Computational Time ◽  
Discrete Ordinates ◽  
Discrete Ordinate ◽  
Emissive Power ◽  
Participating Media ◽  
Discrete Ordinates Method ◽  
The Difference ◽  
Ray Effects

A new and improved method based on the concept of discrete ordinates scheme with infinitely small weights (DOS+ISW) is developed for modeling radiative heat transfer in three-dimensional participating media. To demonstrate the effectiveness of the method in mitigating ray effects, the ray effects caused by (1) abrupt step changes in the boundary conditions and (2) the stepwise variation of the medium emissive power are considered. In this work, angular quadrature sets with large number of discrete ordinate directions are chosen to mitigate ray effects while at the same time keeping the computational time increase to a minimum. Comparing with the conventional discrete ordinates method, the difference is that intensities in these directions are calculated by DOS+ISW method. Intensity with fine directional resolution calculated by this method is validated by comparing with that of reverse Monte Carlo method. The large number of discrete ordinate directions used in the new method becomes computationally prohibitive in the conventional discrete ordinates method due to the increased computer memory and computation time requirements.

Application of Modified Discrete Ordinate Method to Combined Conductive and Radiative Heat Transfer Problems in Irregular Geometry

2010 ◽  
Author(s):  
H. Amiri ◽  
S. H. Mansouri ◽  
A. Safavinejad
Keyword(s):  
Heat Transfer ◽  
Radiative Heat ◽  
Discrete Ordinates ◽  
Discrete Ordinates Method ◽  
Flux Boundary Conditions ◽  
The Media ◽  
Transport Problems ◽  
Volume Method ◽  
Transfer Problems ◽  
Ray Effects

A blocked-off region concept is implemented with the modified discrete ordinates method (MDOM) to solve combined conductive and radiative heat transport problems in irregular geometries. The media analyzed are absorbing, emitting and isotropically or anisotropically scattering. The walls have temperature or flux boundary conditions. The finite-volume method is used to solve the energy equation and the modified discrete ordinates method is employed to solve the radiative transfer equation. The SDOM and MDOM are compared in all cases, and the accuracy of the results is assessed by comparing the results with those obtained by other researchers. The results confirm the capability of the MDOM to minimize the anomalies due to ray effects in combined mode heat transfer problems.

Sign in / Sign up

Export Citation Format

Share Document