A unified finite element algorithm for two-equation models of turbulence

Ilinca, F.; Tu, Jiyuan; Pelletier, Dominique

doi:10.1016/s0045-7930(97)00039-x

Cited by 34 publications

(30 citation statements)

References 27 publications

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“…For details on the benefits of a logarithmic turbulence model and on the formulation of the eddy viscosity and eddy thermal diffusivity on can refer to [6], [7], [8], [9] and [10]. In the present turbulence model we adopt a realizability constrain where the eddy viscosity is limited from above by a value that depends on the local values of the mean strain rate tensor modulus and of the turbulent kinetic energy k [11], [12].…”

Section: Numerical Modellingmentioning

confidence: 99%

A multiscale numerical algorithm for heat transfer simulation between multidimensional CFD and monodimensional system codes

Chierici

Chirco

Vià

et al. 2017

J. Phys.: Conf. Ser.

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Abstract. Nowadays the rapidly-increasing computational power allows scientists and engineers to perform numerical simulations of complex systems that can involve many scales and several different physical phenomena. In order to perform such simulations, two main strategies can be adopted: one may develop a new numerical code where all the physical phenomena of interest are modelled or one may couple existing validated codes. With the latter option, the creation of a huge and complex numerical code is avoided but efficient methods for data exchange are required since the performance of the simulation is highly influenced by its coupling techniques. In this work we propose a new algorithm that can be used for volume and/or boundary coupling purposes for both multiscale and multiphysics numerical simulations. The proposed algorithm is used for a multiscale simulation involving several CFD domains and monodimensional loops. We adopt the overlapping domain strategy, so the entire flow domain is simulated with the system code. We correct the system code solution by matching averaged inlet and outlet fields located at the boundaries of the CFD domains that overlap parts of the monodimensional loop. In particular we correct pressure losses and enthalpy values with source-sink terms that are imposed in the system code equations. The 1D-CFD coupling is a defective one since the CFD code requires point-wise values on the coupling interfaces and the system code provides only averaged quantities. In particular we impose, as inlet boundary conditions for the CFD domains, the mass flux and the mean enthalpy that are calculated by the system code. With this method the mass balance is preserved at every time step of the simulation. The coupling between consecutive CFD domains is not a defective one since with the proposed algorithm we can interpolate the field solutions on the boundary interfaces. We use the MED data structure as the base structure where all the field operations are performed, allowing the algorithm to be used with all the numerical codes where a MED duplicate of the field solution can be created. The MEDmem libraries come with the Salome platform and include basic methods for handling meshes and fields. We provide results that show the consistency of the proposed algorithm.

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Section: Numerical Modellingmentioning

confidence: 99%

A multiscale numerical algorithm for heat transfer simulation between multidimensional CFD and monodimensional system codes

Chierici

Chirco

Vià

et al. 2017

J. Phys.: Conf. Ser.

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“…The formulation of this new turbulence model is based on [12] in which the various k-ε, k-ω and k-τ models for dynamic turbulence are analyzed in their formulation with logarithmic variables. The introduction of logarithmic variables brings important advantages to the turbulence model, in particular the fact that the original variables are always kept positive because they are calculated as the exponential values of the new logarithmic variables, so this ensures an increased numerical stability.…”

Section: The Logarithmic Turbulence Modelmentioning

confidence: 99%

“…The introduction of logarithmic variables brings important advantages to the turbulence model, in particular the fact that the original variables are always kept positive because they are calculated as the exponential values of the new logarithmic variables, so this ensures an increased numerical stability. Another important feature is that the logarithmic variables have profiles that are smoother than the ones of the natural variables [12]. In this new turbulence model we use the logarithmic forms of the specific dissipations ω and ω θ Ω = ln(ω) ,…”

Section: The Logarithmic Turbulence Modelmentioning

confidence: 99%

Numerical Validation of a Four Parameter Logarithmic Turbulence Model

Cerroni¹,

Vià²,

Manservisi³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. Computational 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 P r t , 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-k θ -Ω θ turbulence model as an improvement of the k-ω-k θ -ω θ turbulence model, already validated by the authors, where Ω and Ω θ are calculated as the natural logarithm of the variables ω and ω θ . 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.

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“…The discretization is space is performed by an unstructured grid finite element method. The incompressible Navier-Stokes equations are discretized using the nonconforming 10 QQelement pair, whereas standard 1 Q elements are employed for k and For our purposes, it is worthwhile to introduce an auxiliary parameter k   , which makes it possible to decouple the transport equations (19) and (20) as follows [21][22][23]:…”

Section: Iterative Solution Strategymentioning

confidence: 99%

“…This representation provides a positivity-preserving linearization of the sink terms, whereby the parameters T  and  evaluated using the solution from the previous outer iteration [21,22,24]. The iterative solution process is based on the following hierarchy of nested loops (see Fig.…”

Section: Iterative Solution Strategymentioning

confidence: 99%

Nonlinear analysis of the pressure field in industrial buildings with curved metallic roofs due to the wind effect by FEM

Díaz¹,

Nieto²,

Vilán³

et al. 2013

Applied Mathematics and Computation

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In this paper, an evaluation of distribution of the air pressure is determined throughout the laterally closed industrial buildings with curved metallic roofs due to the wind effect by the finite element method (FEM). The non-linearity is due to Reynolds-averaged Navier-Stokes (RANS) equations that govern the turbulent flow. The Navier-Stokes equations are non-linear partial differential equations and this non-linearity makes most problems difficult to solve and is part of the cause of turbulence. The RANS equations are time-averaged equations of motion for fluid flow. They are primarily used while dealing with turbulent flows. Turbulence is a highly complex physical phenomenon that is pervasive in flow problems of scientific and engineering concern like this one. In order to solve the RANS equations a two-equation model is used: the standard k   model. The calculation has been carried out keeping in mind the following assumptions: turbulent flow, an exponential-like wind speed profile with a maximum velocity of 40 m/s at 10 m reference height, and different heights of the building ranging from 6 to 10 meters. Finally, the forces and moments are determined on the cover, as well as the distribution of pressures on the same one, comparing the numerical results obtained with the Spanish CTE DB SE-AE, Spanish NBE AE-88 and European standard rules, giving place to the conclusions that are exposed in the study.

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A unified finite element algorithm for two-equation models of turbulence

Cited by 34 publications

References 27 publications

A multiscale numerical algorithm for heat transfer simulation between multidimensional CFD and monodimensional system codes

A multiscale numerical algorithm for heat transfer simulation between multidimensional CFD and monodimensional system codes

Numerical Validation of a Four Parameter Logarithmic Turbulence Model

Nonlinear analysis of the pressure field in industrial buildings with curved metallic roofs due to the wind effect by FEM

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