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.

Discrete Ordinates Method for Transient Radiation Transfer in Cylindrical Enclosures

2003 ◽  
Author(s):  
Kyunghan Kim ◽  
Zhixiong Guo
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Radiative Heat ◽  
Radiation Transfer ◽  
Radiation Heat Transfer ◽  
Discrete Ordinates ◽  
Radiation Heat ◽  
Discrete Ordinates Method ◽  
Transient Radiation ◽  
Tissue Welding

The Discrete Ordinates Method (DOM) for solving transient radiation transfer equation in cylindrical coordinates is developed for radiation heat transfer in participating turbid media in pico-scale time domain. The application problems addressed here are laser tissue welding and soldering. The novelty of this study lies with the use of ultrashort laser pulses as the irradiation source. The characteristics of transient radiation heat transfer in ultrafast laser tissue welding and soldering are studied with the DOM developed. The temporal distribution of radiative energy inside the tissue cylinder as well as the radiative heat flux on the tissue surface is obtained. Comparisons are performed between laser welding without use of solder and laser soldering with use of solder. The use of solder is found to have highly concentrated radiation energy deposition in the solder-stained region and reduce the surface radiative heat flux accordingly. Comparisons of transient radiation heat transfer between the spatially square-variance and Gaussian-variance laser inputs and between the temporally Gaussian and skewed input profiles are also conducted.

scholarly journals EFFECTS OF TURBULENCE-RADIATION INTERACTIONS IN A NON-PREMIXED TURBULENT METHANE-AIR FLAME

2018 ◽  
Vol 17 (1) ◽  
pp. 63
Author(s):  
L. D. Lemos ◽  
F. R. Centeno ◽  
F. H. R. França
Keyword(s):  
Heat Flux ◽  
Radiative Heat ◽  
Turbulent Flame ◽  
Chemical Species ◽  
Radiative Heat Flux ◽  
Discrete Ordinates ◽  
Low Velocity ◽  
Ansys Fluent ◽  
Methane Flame ◽  
Steady Laminar

This work studied a turbulent flame and analyzed the interaction between turbulence and radiation (TRI). The problem consists of a non-premixed turbulent methane flame surrounded by a low-velocity air coflow identified as Flame DLR-A. The steady laminar diffusion flamelet (SLDF) model is used to solve the chemical kinetics. To generate the flamelet library, turbulence-chemistry interaction is taken into account through previously assumed probability density functions (PDF) of mean scalars. Radiative heat flux is calculated with the discrete ordinates method, considering the Gray Gas model (GG). Turbulence is solved with k-ε Standard model and TRI methodology is based on temperature self-correlation. The solution is obtained using ANSYS/Fluent code coupled with user-defined functions (UDFs). Results indicated that the temperature and chemical species predictions are little affected by TRI, while the radiative quantities (radiative heat flux on the domain wall) are importantly affect by TRI effects.

Angular False Scattering in Radiative Heat Transfer Analysis Using the Discrete-Ordinates Method With Higher-Order Quadrature Sets

2013 ◽  
Author(s):  
Brian Hunter ◽  
Zhixiong Guo
Keyword(s):  
Monte Carlo ◽  
Radiative Transfer ◽  
Phase Function ◽  
Radiative Heat ◽  
Higher Order ◽  
Heat Transfer Analysis ◽  
Discrete Ordinates ◽  
Equal Weight ◽  
Participating Media ◽  
Discrete Ordinates Method

The SN quadrature set for the discrete-ordinates method is limited in overall discrete direction number in order to avoid physically unrealistic negative directional weight factors. Such a limitation can adversely impact radiative transfer predictions. Directional discretization results in errors due to ray effect, as well as angular false scattering error due to distortion of the scattering phase function. The use higher-order quadrature schemes in the discrete-ordinates method allows for improvement in discretization errors without an overall directional limitation. In this analysis, four higher-order quadrature sets (Legendre-Equal Weight, Legendre-Chebyshev, Triangle Tessellation, and Spherical Ring Approximation) are implemented for determination of radiative transfer in a 3-D cubic enclosure containing participating media. Radiative heat fluxes, calculated at low direction number, are compared to the SN quadrature and Monte Carlo predictions to gauge quadrature accuracy. Additionally, investigation into the reduction of angular false scattering with sufficient increase in direction number using higher-order quadrature, including heat flux accuracy with respect to Monte Carlo and computational efficiency, is presented. While higher-order quadrature sets are found to effectively minimize angular false scattering error, it is found to be much more computationally efficient to implement proper phase function normalization for accurate radiative transfer predictions.

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.

Consideration of the Scattering Effects in the Glass As a Participating Medium Using the Discrete Ordinates Method

2001 ◽  
Author(s):  
S. Coutin Rodicio ◽  
B. Restrepo Torres
Keyword(s):  
Heat Flux ◽  
Radiative Heat ◽  
Three Dimensional ◽  
Discrete Ordinates ◽  
Radiative Heat Exchange ◽  
Scattering Medium ◽  
Discrete Ordinates Method ◽  
Radiant Intensity ◽  
Scattering Coefficients ◽  
Scattering Effects

Abstract Three-dimensional radiative heat exchange in a commercial type of glass as a participating medium is predicted using the discrete ordinates method. The radiative transfer equation (RTE) is analyzed for an absorbing, re-emitting, and scattering medium enclosed by gray walls. The main objective of this work is to formulate the RTE in a three-dimensional enclosure represented by a rectangular glass furnace where scattering effects are considered in the prediction of the radiant intensity, temperature distribution, incident and emitted energy, and heat flux at the glass surface. A comparative study is performed for glass under scattering and non-scattering conditions. The influence of scattering effects in the radiant intensity will provide further understanding of their impact in the glass thermal behavior. Additionally, the results of a parametric study on the glass for different scattering coefficients, surface heat flux, wall emissivity, and the forward scattering are discussed. The S4 approximation of the discrete ordinates method is employed in this model.

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.

Solving Radiative Transfer Equation in Scattering Plane-Parallel Medium Using Wavelets Approximation

2002 ◽  
Author(s):  
Oguzhan Guven ◽  
Bryan Y. Wang ◽  
Yildiz Bayazitoglu
Keyword(s):  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Heat ◽  
Numerical Solutions ◽  
Radiative Transfer Equation ◽  
Anisotropic Scattering ◽  
Wavelet Approximation ◽  
Plane Parallel ◽  
Scattering Phase ◽  
Scattering Phase Function

Wavelet analysis is presented for solving the radiative transfer equation for a scattering medium in a one-dimensional plane-parallel geometry. Some properties of the wavelet transform for numerical approximation of radiative heat transfer are demonstrated. The governing equations are reduced to a system of first-order ordinary differential equations. Linear anisotropic scattering is assumed in order to compare the results with the previous researchers. The method of analysis is quite general since it only requires that the scattering phase function is square integrable. The numerical solutions indicate that wavelet approximation is promising.

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.

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