A Simpler Formulation for Radiative View Factors From Spheres to a Class of Axisymmetric Bodies

1982 ◽  
Vol 104 (1) ◽  
pp. 201-204 ◽  
Author(s):  
B. T. F. Chung ◽  
M. H. N. Naraghi
Keyword(s):  
Numerical Integration ◽  
View Factor ◽  
View Factors ◽  
New Formulation ◽  
Axisymmetric Bodies

A simpler formulation is developed for radiative view factor from a sphere to a class of axisymmetric bodies. The new formulation is semianalytical in nature and only requires a single numerical integration at most.

Radiation Configuration Factors Between Disks and a Class of Axisymmetric Bodies

1982 ◽  
Vol 104 (3) ◽  
pp. 426-431 ◽  
Author(s):  
M. H. N. Naraghi ◽  
B. T. F. Chung
Keyword(s):  
Numerical Integration ◽  
Analytical Solutions ◽  
Coaxial Cylinder ◽  
Present Approach ◽  
Shape Factors ◽  
Present Technique ◽  
Analytical Formulae ◽  
View Factors ◽  
Axisymmetric Bodies

A general formulation is developed for the radiation shape factors between a disk and a class of coaxial axisymmetric bodies such as cylinder, cone, ellipsoid, and paraboloid. In certain cases, the view factors can be derived analytically directly from the present technique, while in others, they can be generated from a single numerical integration. The analytical solutions for view factors from a disk to a coaxial cylinder based on the present approach are found to agree with those published earlier. The analytical formulae of view factors from disks or annular rings to circular cones, truncated cones, ellipsoid, paraboloids, and truncated praboloid are herein presented.

scholarly journals A modified numerical integration method to calculate the view factor between finite and infinite cylinders in arbitrary array

2020 ◽  
Vol 142 ◽  
pp. 107358
Author(s):  
Chuan Jiang ◽  
Jun Wang ◽  
Omar Behar ◽  
Cyril Caliot ◽  
Yaoming Zhang ◽  
...  
Keyword(s):  
Numerical Integration ◽  
Integration Method ◽  
View Factor ◽  
Numerical Integration Method

View Factors to Grounds of Photovoltaic Collectors

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
J. Appelbaum
Keyword(s):  
Global Radiation ◽  
Appreciable Amount ◽  
View Factor ◽  
Solar Pv ◽  
Mathematical Expressions ◽  
Inclination Angles ◽  
View Factors ◽  
Solar Field ◽  
Analytical Expressions ◽  
General Configuration

Ground reflected radiation is one component of the global radiation on photovoltaic collectors in a solar field. This component depends on the view factor of the collector to ground, hence depends on the relative position of the collectors to each other. General analytical expressions and numerical values for the view factor to the ground were developed between flat-plate collectors positioned in a general configuration. Based on the general expression, the view factors to ground for particular collector configurations were derived. For deployment of photovoltaic collectors in multiple rows with common inclination angles, the view factor to ground is rather small, and hence, the reflected radiation from the ground on the collectors may be neglected compared to the direct beam and the diffuse components. However, in some cases the reflected radiation from the ground may constitute an appreciable amount as in snowy area. Bifacial photovoltaic (PV) panels can absorb solar radiation by both the front and the rear sides and are usually deployed vertically. In this case the reflected radiation from the ground on the panels may be appreciable depending on the ground albedo. The mathematical expressions of the different view factors may be used by the solar field designer to estimate the amount of reflected radiation from the ground reaching the collectors for different configurations of solar PV plants.

View Factors of Flat Solar Collectors Array in Flat, Inclined, and Step-Like Solar Fields

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Nassar Yasser Fathi ◽  
Alsadi Samer
Keyword(s):  
Solar Radiation ◽  
Diffuse Radiation ◽  
Dynamic Parameter ◽  
Incident Radiation ◽  
Appreciable Amount ◽  
Design Parameters ◽  
View Factor ◽  
Solar Radiation Incident ◽  
View Factors ◽  
Reflecting Surfaces

Solar radiation consists of direct beam, sky diffuse, and reflected radiations from the ground and adjacent surfaces. The amount of diffuse radiation falling on solar collector depends on the view factor of the collector to sky. The reflected radiation striking the collector's surface depends on the reflectivity of the surface, as well as on view factors and the amount of solar radiation reaching the reflecting surfaces. The amount of reflected radiation coming from the ground can be of an appreciable amount, and can be amplified using special reflector surfaces. This study develops general analytical expressions for the sky's view factors as well as factors related to the ground and those between collectors for the deployment of collectors in multiple rows, in three types of solar fields: flat, inclined, and steplike solar fields. All parameters presented in these expressions are measurable (edge-to-edge dimension). The effects of the design parameters such as the tilt of the angle of the collector, the distance between the collectors, the height of the collector, the position of the collector above the ground (as in the case of step-like field), and the inclination of the land of the field (as in the case of an inclined field) on the view factors are numerically demonstrated. The current study also specifies new terms such as the sunny zone and the shadow zone; these zones control the amount of solar radiation reflected onto the collector. As a result, the ground-view factor that depends on the altitude of the solar angle is considered to be a dynamic parameter. The results obtained may be used to estimate the solar radiation incident on all types of solar fields, with the possibility of increasing the incident radiation on a collector by using planar reflectors.

A New Semianalytical Algorithm for Calculating Diffuse Plane View Factors

1998 ◽  
Vol 120 (1) ◽  
pp. 279-281 ◽  
Author(s):  
A. Mavroulakis ◽  
A. Trombe
Keyword(s):  
Exact Solutions ◽  
View Factor ◽  
View Factors ◽  
Plane View

A new semianalytical algorithm for calculating diffuse plane view factors which is based on an extension of Nusselt’s sphere method is presented. For simple cases of view factor calculations where exact solutions exist, the accuracy of the algorithm is tested and compared with the accuracy of others.

Horizontal Tubular Microalgae Photobioreactor Plant View Factors and Diffuse Radiation

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
T. Maor ◽  
J. Appelbaum
Keyword(s):  
Solar Radiation ◽  
Present Article ◽  
Diffuse Radiation ◽  
Design Parameters ◽  
View Factor ◽  
Diffuse Solar Radiation ◽  
Horizontal Tubes ◽  
Vertical Walls ◽  
View Factors

Different view factors and different components of the diffuse solar radiation impinging on a photobioreactor plant for cultivating microalgae products are formulated and calculated in the present article. The outdoor plant consists of multiple horizontal tubes arranged in multiple vertical walls. The diffuse radiation on a tube may come from three directions of the sky: from the aperture between the walls (from the sky above), from the penetration of the diffuse radiation between the tubes, and from the plant edges. Each component of the diffuse radiation is associated with a different view factor. For design parameters of a practical plant, the largest component of the diffuse radiation comes from the sky above the plant.

View Factors of Samples Tested in Cone and Cylinder Calorimeters

2012 ◽  
Vol 134 (9) ◽  
Author(s):  
Marcos J. A. Gemaque ◽  
Fernando S. Costa
Keyword(s):  
Thermal Radiation ◽  
Heat Input ◽  
Blackbody Radiation ◽  
View Factor ◽  
Exposed Surface ◽  
Solid Materials ◽  
Input Distribution ◽  
Total View ◽  
Flammability Characteristics ◽  
View Factors

Cone and cylinder calorimeters are devices used to determine flammability characteristics of solid materials under prescribed heat inputs. Temperature and heat input distribution on the exposed surface of a specimen in a calorimeter can be affected by variations of position or size of the specimen. This work analyzes the thermal radiation view factors of slabs and cylinders tested in cone and cylinder calorimeters, respectively. Blackbody radiation thermal interchange is assumed and reflections of neighbor objects are not considered. Uniformity of view factor distributions and total view factors are compared for slabs and cylinders tested in calorimeters, considering positioning and size variations.

View Factors in Radiation Between Two Parallel Oriented Cylinders of Finite Lengths

1982 ◽  
Vol 104 (2) ◽  
pp. 384-388 ◽  
Author(s):  
N. H. Juul
Keyword(s):  
Line Source ◽  
Closed Form Solution ◽  
Diffuse Radiation ◽  
Form Solution ◽  
View Factor ◽  
Double Integral ◽  
Integral Expression ◽  
View Factors ◽  
Limiting Case ◽  
Analytical Expressions

A simple double-integral expression for the diffuse radiation view factor, F12, between two parallel cylinders of finite lengths is derived. No closed-form solution appears possible except for the limiting case of infinite long cylinders for which an analytical expression for the view factor F12∞ is derived by applying the crossed string method. The accuracies of the line source approximations are evaluated, and the regions for which they are accurate to one percentage or better are identified. The view factor F12 between two opposing cylinders of equal length is computed by numerical integration and normalized by F12∞. The results are presented. Analytical expressions, which approximate the view factors between two opposite cylinders of finite length, are derived and their accuracy is evaluated over a useful parameter range. The range of their applications corresponds approximately to that for the line source approximation. This result is expected, because the errors are caused in part by blockage of radiation which is similar.

scholarly journals Accuracy of view factor calculations for digital terrain models of comets and asteroids

2020 ◽  
Vol 642 ◽  
pp. A167
Author(s):  
L. Rezac ◽  
Y. Zhao
Keyword(s):  
Thermal Evolution ◽  
View Factor ◽  
Loop Transformation ◽  
Practical Applications ◽  
Critical Elements ◽  
Digital Terrain ◽  
Average Accuracy ◽  
Order Of Magnitude ◽  
View Factors ◽  
Shared Edge

Context. Detailed shape and topographic models coupled with sophisticated thermal physics are critical elements to proper characterization of surfaces of small bodies in our solar system. Calculations of self-heating effects are especially important in the context of thermal evolution of non-convex surfaces, including craters, cracks, or openings between “rocks”. Aims. Our aim is to provide quantitative comparisons of multiple numerical methods for computing view factors for concave geometries and provide a more rigorous criteria for the validity of their application. Methods. We contrasted five methods of estimating the view factors. First, we studied specific geometries, including shared-edge facets for a reduced two-facet problem. Then, we applied these methods to the shape model of 67P/Churyumov-Gerasimenko. Nevertheless, the presented results are general and could be extended to shape models of other bodies as well. Results. The close loop transformation of the double area integration method for evaluating view factors of nearby or shared-edge facets is the most accurate, although computationally expensive. Two methods of facet subdivision we evaluate in this work provide reasonably accurate results for modest facet subdivision numbers, however, may result in a degraded performance for specific facet geometries. Increasing the number of subdivisions improves their accuracy, but also increases their computational burden. In practical applications, a trade-off between accuracy and computational speed has to be found, therefore, we propose a combined method based on a simple metric that incorporates a conditional application of various methods and an adaptive number of subdivisions. In our study case of a pit on 67P/CG, this method can reach average accuracy of 2–3% while being about an order of magnitude faster than the (most accurate) line integral method.

Numerical Determination of Radiative View Factors Using Ray Tracing

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
T. Walker ◽  
S.-C. Xue ◽  
G. W. Barton
Keyword(s):  
Ray Tracing ◽  
Unit Area ◽  
Three Dimensional ◽  
Setup Time ◽  
View Factor ◽  
Ray Tracing Method ◽  
Ray Density ◽  
View Factors ◽  
Tracing Method

A ray-tracing method is presented for numerically determining radiative view factors in complex three-dimensional geometries. This method uses a set of “primitive” shapes to approximate the required geometry together with a Monte Carlo simulation to track the fate of randomized rays leaving each surface. View factors were calculated for an operational fiber drawing furnace using both numerical integration and ray-tracing methods. Calculated view factor profiles were essentially identical above a ray density of 105 per unit area. Run times for the ray-tracing method were considerable longer, although the setup time to describe a new geometry is very short and essentially independent of system complexity.

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