A Laplace transform exponential method for monoenergetic three-dimensional fixed source discrete ordinates problems in Cartesian geometry

2010 ◽  
Vol 5 (1) ◽  
pp. 80 ◽  
Author(s):  
Eliete Biasotto Hauser ◽  
Marco Tullio Vilhena ◽  
Ricardo C. Barros
Keyword(s):  
Laplace Transform ◽  
Three Dimensional ◽  
Discrete Ordinates ◽  
Cartesian Geometry ◽  
Exponential Method

The Error Bounds for Three-Dimensional Nodal LTSN Method

2008 ◽  
Author(s):  
Eliete Biasotto Hauser ◽  
Ruben Panta Pazos ◽  
Marco T. M. B. Vilhena ◽  
Ricardo C. Barros
Keyword(s):  
Spectral Analysis ◽  
Analytical Solution ◽  
Laplace Transform ◽  
Error Bounds ◽  
Three Dimensional ◽  
Discrete Ordinates ◽  
Exponential Functions ◽  
Decay Constants ◽  
The Laplace Transform ◽  
Cartesian Geometry

In this paper we present a proof about the convergence of the 3D Nodal-LTSN Method in order to solve the transport problem in a parallelepiped domain. For that, we define functions associated to the errors, one in the approximated flux, another in the quadrature formula and establish a relation between them. We present a Nodal-LTSN method to generate an analytical solution for discrete ordinates problems in three-dimensional cartesian geometry. We first transverse integrate the SN equations and then we apply the Laplace transform. The essence of this method is the diagonalization of the LTSN transport matrices and the spectral analysis garantees this. The transverse leakage terms that appear in the transverse integrated SN equations are represented by exponential functions with decay constants that depend on the characteristics of the material of the medium the particles leave behind. We present numerical results generated by the offered method applied to typical shielding model problems.

scholarly journals Radial Turbine Design for Solar Chimney Power Plants

Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 674
Author(s):  
Paul Caicedo ◽  
David Wood ◽  
Craig Johansen
Keyword(s):  
Power Plants ◽  
Reference Frames ◽  
Three Dimensional ◽  
Discrete Ordinates ◽  
Large Area ◽  
Solar Chimney ◽  
Cfd Simulations ◽  
Radial Turbine ◽  
Design Changes ◽  
Turbine Design

Solar chimney power plants (SCPPs) collect air heated over a large area on the ground and exhaust it through a turbine or turbines located near the base of a tall chimney to produce renewable electricity. SCPP design in practice is likely to be specific to the site and of variable size, both of which require a purpose-built turbine. If SCPP turbines cannot be mass produced, unlike wind turbines, for example, they should be as cheap as possible to manufacture as their design changes. It is argued that a radial inflow turbine with blades made from metal sheets, or similar material, is likely to achieve this objective. This turbine type has not previously been considered for SCPPs. This article presents the design of a radial turbine to be placed hypothetically at the bottom of the Manzanares SCPP, the only large prototype to be built. Three-dimensional computational fluid dynamics (CFD) simulations were used to assess the turbine’s performance when installed in the SCPP. Multiple reference frames with the renormalization group k-ε turbulence model, and a discrete ordinates non-gray radiation model were used in the CFD simulations. Three radial turbines were designed and simulated. The largest power output was 77.7 kW at a shaft speed of 15 rpm for a solar radiation of 850 W/m2 which exceeds by more than 40 kW the original axial turbine used in Manzanares. Further, the efficiency of this turbine matches the highest efficiency of competing turbine designs in the literature.

Denovo: A New Three-Dimensional Parallel Discrete Ordinates Code in SCALE

2010 ◽  
Vol 171 (2) ◽  
pp. 171-200 ◽  
Author(s):  
Thomas M. Evans ◽  
Alissa S. Stafford ◽  
Rachel N. Slaybaugh ◽  
Kevin T. Clarno
Keyword(s):  
Three Dimensional ◽  
Discrete Ordinates

An Efficient Sparse Finite Element Solver for the Radiative Transfer Equation

2009 ◽  
Author(s):  
Gisela Widmer
Keyword(s):  
Linear System ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Degrees Of Freedom ◽  
Radiative Transfer Equation ◽  
Three Dimensional ◽  
Discrete Ordinates ◽  
Five Dimensions ◽  
Computational Costs ◽  
Dimensional Domain

The stationary monochromatic radiative transfer equation (RTE) is posed in five dimensions, with the intensity depending on both a position in a three-dimensional domain as well as a direction. For non-scattering radiative transfer, sparse finite elements [1, 2] have been shown to be an efficient discretization strategy if the intensity function is sufficiently smooth. Compared to the discrete ordinates method, they make it possible to significantly reduce the number of degrees of freedom N in the discretization with almost no loss of accuracy. However, using a direct solver to solve the resulting linear system requires O(N3) operations. In this paper, an efficient solver based on the conjugate gradient method (CG) with a subspace correction preconditioner is presented. Numerical experiments show that the linear system can be solved at computational costs that are nearly proportional to the number of degrees of freedom N in the discretization.

Solution of the three-dimensional one-group discrete ordinates problems by the LTSn method

1995 ◽  
Vol 22 (2) ◽  
pp. 131-134 ◽  
Author(s):  
J. Zabadal ◽  
M. Vilhena ◽  
L. Barichello
Keyword(s):  
Three Dimensional ◽  
Discrete Ordinates
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