Schemes and Applications of First and Second-Order Discrete Ordinates Interpolation Methods to Irregular Two-Dimensional Geometries

1997 ◽  
Vol 119 (4) ◽  
pp. 730-737 ◽  
Author(s):  
H.-M. Koo ◽  
K.-B. Cheong ◽  
T.-H. Song
Keyword(s):  
Exact Solutions ◽  
Second Order ◽  
Heat Fluxes ◽  
Discrete Ordinates ◽  
Analysis Tool ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Emissive Power ◽  
Square Enclosure ◽  
Good Agreement

This paper presents numerical schemes and comparison of predictions of radiative heat transfer for the first and the second order discrete ordinates methods (DOM1 and DOM2) using an interpolation scheme. The formulations are followed by derivation of numerical schemes for two-dimensional body fitted grids. With varying the optical depths and the numbers of grids and ordinates, radiative wall heat fluxes by DOM1 and DOM2 are calculated to compare with the exact solutions for three kinds of two-dimensional enclosures (square, quadrilateral, and J-shaped) containing absorbing/emitting and nonscattering media of known temperature with cold black walls. Emissive power and radiative wall heat fluxes by DOM1 and DOM2 are calculated to compare with zonal results for two-dimensional square enclosure containing absorbing/emitting and isotropically scattering medium of known uniform heat source with cold black walls. The results of DOM1 and DOM2 are in good agreement with the exact solutions or the zonal results. DOM1 gives more accurate results than DOM2 for most of the tested optical depths and the numbers of grids and ordinates. These methods appear as powerful candidates of very versatile radiation analysis tool. Their grid and ordinate dependencies are also discussed in depth.

Surface Radiation Exchange for Two-Dimensional Rectangular Enclosures Using the Discrete-Ordinates Method

1992 ◽  
Vol 114 (2) ◽  
pp. 465-472 ◽  
Author(s):  
A. Sa`nchez ◽  
T. F. Smith
Keyword(s):  
Weighting Factor ◽  
Heat Fluxes ◽  
Surface Radiation ◽  
Discrete Ordinates ◽  
Two Dimensional ◽  
Discrete Ordinates Method ◽  
Radiation Exchange ◽  
Radiant Exchange ◽  
Irregular Geometries ◽  
Good Agreement

The purpose of this study is to develop a model based on the discrete-ordinates method for computing radiant exchange between surfaces separated by a transparent medium and to formulate the model so that arbitrary arrangements of the surfaces can be accommodated. Heat fluxes from the model are compared to those based on the radiosity/irradiation analysis. Three test geometries that include shadowing and irregular geometries are used to validate the model. Heat fluxes from the model are in good agreement with those from the radiosity/irradiation analysis. Effects of geometries, surface emittances, grid patterns, finite-difference weighting factor, and number of discrete angles are reported.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

Numerical Modeling of Radiative and Reactive Flow Field Around a Blunt Body at Hypersonic Regimes

2010 ◽  
Author(s):  
Morteza Rahmanpour ◽  
Reza Ebrahimi ◽  
Mehrzad Shams
Keyword(s):  
Flow Field ◽  
Differential Equations ◽  
Heat Fluxes ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Implicit Time ◽  
Discrete Ordinates ◽  
Two Dimensional ◽  
Fully Implicit ◽  
Time Marching

A numerical method for calculation of strong radiation for two-dimensional reactive air flow field is developed. The governing equations are taken to be two dimensional, compressible Reynolds-average Navier-Stokes and species transport equations. Also, radiation heat flux in energy equation is evaluated using a model of discrete ordinate method. The model used S4 approximation to reduce the governing system of integro-differential equations to coupled set of partial differential equations. A multiband model is used to construct absorption coefficients. Tangent slab approximation is assumed to determine the characteristic parameters needed in the Discrete Ordinates Method. The turbulent diffusion and heat fluxes are modeled by Baldwin and Lomax method. The flow solution is obtained with a fully implicit time marching method. A thermochemical nonequilibrium formulation appropriate to hypersonic transitional flow of air is presented. The method is compared with existing experimental results and good agreement is observed.

A Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion

1988 ◽  
Vol 32 (02) ◽  
pp. 83-91
Author(s):  
X. M. Wang ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Model ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Potential Flow Model ◽  
Good Agreement

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.

Two-Dimensional Radiation in Absorbing-Emitting Media Using the P-N Approximation

1983 ◽  
Vol 105 (2) ◽  
pp. 333-340 ◽  
Author(s):  
A. C. Ratzel ◽  
J. R. Howell
Keyword(s):  
Separation Of Variables ◽  
Second Order ◽  
Radiative Energy ◽  
Two Dimensional ◽  
Differential Approximation ◽  
Relaxation Methods ◽  
Emissive Power ◽  
Diffusion Solution ◽  
Emitting Media ◽  
Successive Over Relaxation

Radiative energy transfer in a gray absorbing and emitting medium is considered in a two-dimensional rectangular enclosure using the P-N differential approximation. The two-dimensional moment of intensity partial differential equations (PDE’s) are combined to yield a single second-order PDE for the P-1 approximation and four coupled second-order PDE’s for the P-3 approximation. P-1 approximation results are obtained from separation of variables solutions, and P-3 results are obtained numerically using successive-over-relaxation methods. The P-N approximation results are compared with numerical Hottel zone results and with results from an approximation method developed by Modest. The studies show that the P-3 approximation can be used to predict emissive power distributions and heat transfer rates in two-dimensional media with opacities of unity or greater. The P-1 approximation is identical to the diffusion solution and is thus applicable only if the medium is optically dense.

Flow through non-uniform gauze screens

1973 ◽  
Vol 59 (4) ◽  
pp. 737-743 ◽  
Author(s):  
J. L. Livesey ◽  
E. M. Laws
Keyword(s):  
Experimental Investigation ◽  
Velocity Profiles ◽  
Second Order ◽  
Two Dimensional ◽  
Measured Velocity ◽  
Flow Through ◽  
Good Agreement

An experimental investigation into flow through shaped gauze screens in two-dimensional and axisymmetric situations has shown that there is disagreement between measured velocity profiles and those computed from the method developed by Elder (1958). This disagreement has been shown to be attributable to the retention of a term of second order in the basic linearization and comparisons between experimental and theoretical profiles omitting this term are in good agreement.

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

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