1,720,965 research outputs found
VOF evaluation of the surface tension by using variational representation and Galerkin interpolation projection
No full textIn this work we propose a variational approach with cell-to-point Galerkin projections for studying two-phase interface advection problems dominated by surface tension. A Volume Of Fluid (VOF) algorithm is used for tracking and locating the evolution of the two-phase interface on a Cartesian grid and a finite element numerical scheme for solving the velocity-pressure state. The velocity field that drives the evolution of this interface is computed from the weak form of the Navier-Stokes equation where the surface tension force is represented in variational form by the continuous surface force (CSF) and continuous surface stress (CSS) methods. Standard numerical approaches solve the strong form of the Navier-Stokes equations and define the CSS term by taking the divergence of the surface tension tensor. This computation of the divergence term results in a singular force which is difficult to compute when the grid is refined since the tensor is computed in a discontinuous cell-by-cell way. In this work we use the variational formulation of the Navier-Stokes equation and avoid differentiation. The tensor, which is a function of the unit normal, is evaluated over regular Sobolev spaces by using a cell-to-point Galerkin projection. This allows a regular piece-wise continuous representation of the surface tensor and the unit normal based on the VOF reconstruction. In standard approaches the CSF surface force is computed by using the curvature, which is the divergence of the unit normal. In this paper we recover the curvature with point-wise Galerkin projection avoiding direct differentiation. Tests on convergence for two and three-dimension in the static and dynamical cases are reported to show the correct representation in the desired spaces. This method is also natural for coupling non uniform grid computation of the fluid with Cartesian grid of the VOF algorithm
A logarithmic turbulent heat transfer model in applications with liquid metals for Pr = 0.01-0.025
Full text linkThe study of turbulent heat transfer in liquid metal flows has gained interest because of applications in several industrial fields. The common assumption of similarity between the dynamical and thermal turbulence, namely, the Reynolds analogy, has been proven to be invalid for these fluids. Many methods have been proposed in order to overcome the difficulties encountered in a proper definition of the turbulent heat flux, such as global or local correlations for the turbulent Prandtl number and four parameter turbulence models. In this work we assess a four parameter logarithmic turbulence model for liquid metals based on the Reynolds Averaged Navier-Stokes (RAN) approach. Several simulation results considering fluids with Pr = 0.01 and Pr = 0.025 are reported in order to show the validity of this approach. The Kays turbulence model is also assessed and compared with integral heat transfer correlations for a wide range of Peclet numbers
Numerical validation of a four parameter logarithmic turbulence model
No full textComputational Fluid Dynamics codes are used in many industrial applications in order to evaluate interesting physical quantities, such as the heat transfer in turbulent flows. Commercial CFD codes use only turbulence models with an imposed constant turbulent Prandtl number Prt, which can give accurate results only for simulations when a strong similarity between the velocity field and the temperature field can be assumed. For fluids with a low Prandtl number, as for heavy liquid metals, a constant turbulent Prandtl number leads to an overestimation of the heat transfer, so experimental results and Direct Numerical Simulation cannot be reproduced. In this work we propose a new k-Ω-kθ-Ωθ turbulence model as an improvement of the k-ω-kθ-ωθ turbulence model, already validated by the authors, where Ω and Ωθ are calculated as the natural logarithm of the variables ω and ωθ. With this reformulation of the previous turbulence model we obtain some important advantages in numerical stability and robustness of the code. Results for the simulations of fully developed turbulent flows in two and three dimensional geometries are reported and compared with experimental correlations and DNS data, when available
Numerical simulation of a turbulent Lead Bismuth Eutectic flow inside a 19 pin nuclear reactor bundle with a four logarithmic parameter turbulence model
No full textComputational Fluid Dynamic allows scientists and engineers to investigate fluid flow in complex geometries and evaluate heat transfer between a solid body and a fluid. In the present paper we study the heat transfer of a Lead Bismuth Eutectic (LBE) turbulent flow in a bare 19 pin nuclear reactor bundle. When dealing with low Prandtl number fluids, like LBE for which Pr = 0.025, proper turbulence models are needed to improve the prediction of heat transfer. We use here a four logarithmic parameter turbulence model in order to calculate Reynolds stresses and turbulent heat flux. In particular, an equation for temperature fluctuations and one for their dissipation are solved. These variables are used to model thermal characteristic time scales. The results are reported for different values of the Peclet number and a fixed value of the pitch to diameter ratio. The obtained values of the Nusselt number are compared with experimental correlations, that can be found in literature, and with the ones obtained using a Simple Eddy Diffusivity model, where the eddy thermal diffusivity is calculated as proportional to eddy viscosity through a modeled turbulent Prandtl number
A computational 3D model for the multiscale analysis of nuclear reactors assembly
No full textIn this work we propose a multiscale model for the evaluation of the temperature field in a nuclear assembly. In particular the zone where the coolant flows is represented as a three dimensional (3D) domain while the fuel rods are taken into account as one-dimensional (1D) inclusion. In this framework the 3D domain is not conformal with the complex fuel rod grid resulting in a small computational cost of the problem. An interesting aspect of this multiscale approach is, as we show in the numerical results section, that by a proper average of the solution we can retrieve the results obtained with the homogeneous model
A new surface tension VOF evaluation by using variational representation and Galerkin interpolation projection
No full textIn this work we propose a new algorithm for studying two-phase interface advection problems dominated by surface tension. We use a Volume Of Fluid (VOF) algorithm for studying the evolution of the two-phase interface on a Cartesian grid and a finite element numerical scheme for the velocity-pressure state. The velocity field that drives the evolution of this interface is obtained by solving the weak form of the Navier-Stokes equation where the surface tension force is not defined in a singular way. With standard numerical approaches that solve the strong form of the Navier-Stokes equations the surface force is determined by taking the divergence of the surface tension tensor. The computation of the divergence term results in a force which is non-convergent when the grid is refined since the tensor is computed in a discontinuous cell-by-cell way. In the past this approach was proposed with artificial different smoothing schemes in order to compute such a singular force. In this work we use the variational formulation of the Navier-Stokes equation and avoid differentiation. The tensor which is a function of the unit normal is evaluated by a Galerkin projection over regular Sobolev spaces. This allows the piece-wise continuous representation of the surface tensor and the unit normal based on the VOF reconstruction. Tests on convergence for two and three-dimension in the static and dynamical cases are reported to show the correct representation in the desired spaces. This method is also natural for coupling non uniform grid computation of the fluid with Cartesian grid of the VOF algorithm
Numerical simulation of a liquid sodium turbulent flow over a backward facing step with a four parameter logarithmic turbulence model
No full textIn recent years a great interest has grown around liquid metals. These fluids are characterized by much higher thermal conductivity, if compared with standard fluids like air and water and can be used in applications where large heat fluxes are present while being subjected to small temperature gradients. In the present paper we simulate a turbulent flow of liquid sodium, with a Prandtl number equal to 0.0088, over a vertical backward-facing step. A uniform heat flux is applied on the vertical wall next to the change of cross section. Reynolds stresses and turbulent heat flux are modeled with a four logarithmic parameter turbulence model. We investigate the cases of purely forced convection, where the temperature field is just a passive scalar, and of mixed convection, where temperature has an impact on the fluid behavior through a buoyancy term that is introduced in the momentum equation with the Boussinesq approximation. The results are reported for various values of the Richardson number, i.e. Ri=0 for the purely forced convection and Ri>0 for the mixed convection case, and compared with data coming from Direct Numerical Simulations that are available in literature
A multiscale heat transfer model for nuclear reactor assemblies
No full textWe develop a new multiscale approach to investigate the heat transfer in a nuclear assembly. Fuel rods are represented as mono-dimensional (1D) inclusions into a three-dimensional (3D) bulk domain representing the coolant. More precisely, the interaction between the fuel rod grid and the coolant is modeled by means of projection operators that couple the 1D and 3D problem taking into account the actual dimension of the rods together with the cladding layers. Due to the dimensional reduction, the inclusions do not need to conform with the bulk computational grid. As a result, the computational challenges of the numerical discretization, due to the high geometrical complexity of the problem, are significantly reduced, as confirmed by the numerical simulations presented in this work
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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