1,720,974 research outputs found
S. Manservisi, D. Cerroni and F. Menghini , Simulations of the four parameter κ-e-κt-et heat transfer turbulence model in rod bundle geometries
No full textIn heavy liquid metals such as sodium, lead and Lead-Bismuth Eutectic (LBE) with low Prandtl number (Pr approx 0.025) the time scales of temperature and velocity fields are rather different, because heat transfer is due mainly to molecular diffusion. In these fluids a standard constant turbulent Prandtl number model fail to reproduce correlations build from experimental data and predict too high a heat transfer. Heavy liquid metals are promising coolant fluids for achieving the necessary requirements of fast nuclear reactors and many European projects have been started with the purpose to develop CFD codes able to correctly predict turbulent heat transfer for these fluids. The present work addresses an effort to improve the prediction of turbulent heat transfer for liquid metal flows in plane and cylindrical geometries assessing a k-e-kt-et four parameter turbulence model. In particular the simulations aim to reproduce fully developed thermal and velocity profiles by using a standard finite element implementation of the Navier-Stokes equations coupled with the energy and momentum turbulence models. The standard k-e system with low-Reynolds model functions is employed to compute the turbulent velocity field while a kt-et system is employed to compute the turbulent thermal field. The results of the simulations are compared with Direct Numerical Simulations (DNS) data and with heat transfer experimental correlations in order to validate the four parameter turbulence model. Different uniform heat flux boundary conditions with zero and constant temperature fluctuations at the wall are presented
A CFD Four Parameter Heat Transfer Turbulence Model for Engineering Applications in Heavy Liquid Metals
No full textIn ordinary fluids, such as water or air, similarity between thermal and dynamical fields holds and it is commonly accepted that implementing a Computational Fluid Dynamics (CFD) code for a two-equation turbulence model with the hypothesis of a constant turbulent Prandtl number in the range 0.85-0.9 is sufficient to obtain reliable results both for velocity and temperature fields. In heavy liquid metals such as sodium, lead and Lead-Bismuth Eutectic (LBE) with low Prandtl number (Pr ≈ 0.025) the time scales of temperature and velocity fields are rather different, because heat transfer is due mainly to molecular diffusion. In these fluids a standard constant turbulent Prandtl number model fails to reproduce correlations build from experimental data and predicts a too high heat transfer. Heavy liquid metals are promising coolant fluids for achieving the necessary requirements of fast nuclear reactors and many European projects have been started with the purpose of developing CFD codes able to correctly predict turbulent heat transfer for these fluids. The present work addresses an effort to improve the prediction of turbulent heat transfer for liquid metal flows in plane and cylindrical geometries assessing a k-e-kt-et four parameter turbulence model. In particular the simulations aim to reproduce fully developed thermal and velocity profiles by using a standard finite element implementation of the Navier Stokes equations coupled with the energy and momentum turbulence models. A modified κ-â̂Š system with low-Reynolds model functions is used for the turbulent velocity field while a κθ- â̂Šθ system is employed to compute the turbulent temperature field. The results of the simulations are compared with Direct Numerical Simulations (DNS) data and with heat transfer experimental correlations in order to validate the four parameter turbulence model. Different uniform heat flux boundary conditions with zero and constant temperature fluctuations at the wall are presented
Four Parameter Heat Transfer Turbulence Models for Heavy Liquid Metals
No full textIn advanced Gen IV nuclear reactors heavy liquid metals are considered as coolant for their high conductivity and specific neutronic properties. These fluids have a very low Prandtl number and show a peculiar heat transfer where conduction can be the dominant mechanism at very high Reynolds numbers. In ordinary fluids various turbulence models are available to match the experimental data: Similarity between velocity and thermal turbulent fields is assumed in almost all commercial Computational Fluid Dynamics codes and the simple eddy diffusivity model with constant turbulent Prandtl number is implemented. In low Prandtl number fluids this model fails to reproduce standard correlations build from experimental data. Therefore it is important to develop new heat transfer turbulence models that are able to reproduce numerically the physical behavior. In this work we present different turbulence models to study the heat transfer in heavy liquid metal turbulent flows. Results obtained with the simple eddy diffusivity model are reported. More complex four parameter turbulence models are also presented and numerical results in simple geometries are reported. For a large range of forced flows with no similarity between velocity and thermal fields a four parameter turbulence model is a powerful tool for predicting the heat transfer
Numerical simulations of the four parameter k-w-kt-et heat transfer turbulence model in single rod and rod bundle geometries with LBE coolant
No full textAbstract: Low Prandtl number fluids, such as heavy liquid metals, may be used as coolant for Generation IV nuclear power plants for their high conductivity and neutronic properties. These fluids show a rather different convective heat transfer behavior compare with that of ordinary fluids, such as water or gas. In such ordinary fluids various turbulence models are available to match the experimental data for flow and temperature fields. In particular it is well known that a two-equation turbulence model, for example k-e or k-w, can be used to simulate many experiments and for fluid with approximately unit Prandtl number the thermal exchange can be reproduced by considering complete similarity between velocity and thermal field. Nowdays the similarity hypothesis is assumed in almost all Computational Fluid Dynamics (CFD) codes where simple eddy diffusivity models (SED) with constant turbulent Prandtl number is implemented. In low Prandtl number fluids, the standard constant turbulent Prandtl number model fails to reproduce standard correlations build from experimental data. Nevertheless these standard correlations are commonly used by engineers to predict heat transfer in generation IV nuclear reactor cores. For this it is important to develop new heat transfer turbulent models that are able to reproduce numerically the desired behavior. The present work addresses a new effort to improve the prediction of turbulent heat flux in vertical annular and rod bundle geometries by applying the four parameter k-w-kt- et model. These numerical cases are investigated by using an in-house finite element code. The k-w turbulence model is employed for simulating the turbulent flow field right up to the wall with no wall functions since they are available only for ordinary fluids. The thermal eddy heat diffusivity can be expressed in a definite manner similar to the viscous eddy diffusivity as a function of the square temperature fluctuation kt and its dissipation rate et . These variables can be computed by solving two new transport equations. Results obtained from the four parameter k-w-kt-et model are compared with standard experimental correlations when available
Numerical comparison of different solution methods for optimal boundary control problems in thermal fluid dynamics
No full textIn this paper we propose and compare different methods for the solution of the control-adjoint-state optimality system which minimizes an objective functional in temperature. The minimization is constrained by the energy convection-diffusion equation with velocity field defined by the incompressible Navier- Stokes system. Three methods, based on different solution spaces, for solving the adjoint-state optimality system are compared. In the first one, as in the standard approach, the controlled temperature field is assumed to belong to a regular class of solutions with smooth derivatives and the resulting control-adjoint-state optimality system is solved in a segregated way. In the second one we introduce a fully coupled solution approach, where, in order to obtain a more robust numerical algorithm, the boundary control is extended to the interior and Dirichlet conditions are implicitly enforced through a volumetric force term. In the last approach we introduce Discontinuous Galerkin formulation for the energy equation in order to seek discontinuous solutions. Numerical two and three-dimensional test cases arenreported in order to show the validity of the proposed approaches. The results are compared in term of solution smoothness and achievement of low values of the objective functional
An improved monolithic multigrid Fluid-Structure Interaction solver with a new moving mesh technique
No full textFluid-Structure Interaction simulations have gained popularity in the research community because of their applications in several industrial and biological fields. In such problems mesh movement is necessary in order to clearly evaluate the deformed solid state and the stresses. In many cases, especially when large displacement occurs, the movement of the mesh nodes can reduce accuracy and convergence properties of the solver. In this paper we present an improved fluid structure interaction solver with a new moving mesh algorithm based on a multilevel Arbitrary Lagrangian Eulerian method to be used in the computation of the arbitrary fluid displacement field. This algorithm is used together with a multigrid, monolithic, fluid structure interaction solver for large displacement problem in which the mesh overlapping is more likely to happen. Numerical simulations in two and three-dimension for both hexahedral and tetrahedral meshes are reported in order to better investigate the capabilities of this solver
NUMERICAL SIMULATIONS OF THE FOUR PARAMETER κ-ω-κt-εt HEAT TRANSFER TURBULENCE MODEL FOR LIQUID METALS
No full textLow Prandtl number fluids, such as heavy liquid metals, may be used as coolant for nuclear power plants for their high conductivity and neutronic properties. These fluids show a rather different convective heat transfer behavior to that of ordinary fluids, such as water or gas. In such ordinary fluids various turbulence models are available to match the experimental data for flow fields and thermal fields are computed based on similarity between velocity and thermal fields. This is assumed in almost all Computational Fluid Dynamics codes where the simple eddy diffusivity model with constant turbulent Prandtl number is implemented. In low Prandtl number fluids the standard constant turbulent Prandtl number model fails to reproduce standard correlations build from experimental data. Therefore it is important to develop new heat transfer turbulent models that are able to reproduce numerically the desired behavior. The present work addresses a new effort to improve the prediction of turbulent heat flux in vertical annular geometry by applying the four parameter κ-ω-κt-εt model. The thermal eddy heat diffusivity can be expressed in a definite manner similar to the viscous eddy diffusivity as a function of the square temperature fluctuation κt and its dissipation rate εt. These variables can be computed by solving two new transport equations. In this work a simple case is investigated using the κ-ω turbulence model for simulating the turbulent flow field right up to the wall with no wall functions. Results obtained from the four parameter κ-ω-κt-εt model are compared with the standard algebraic turbulent heat flux approximations, namely, the simple eddy diffusivity. For large range of forced flows a four parameter κ-ω-κt-εt model is a powerful tool for predicting the heat transfer in flows with no similarity between velocity and thermal fields
EVALUATION OF A FOUR PARAMETER HEAT TRANSFER TURBULENCE MODEL FORCED LBE FLOWS IN DIFFERENT GEOMETRIES.
No full textThe present work addresses an effort to improve the prediction of turbulent heat transfer for LBE coolant flows in plane, simple cylindrical rod and bundle rod geometries. In particular the simulations aim to reproduce fully developed thermal and velocity profiles by using a standard finite element implementation of the Navier Stokes equations coupled with the energy and momentum turbulence models. κ-ε system with low-Reynolds model functions is employed in order to compute the turbulent flow with a near-wall approach. The turbulent heat flux is approximated by an isotropic diffusion gradient model where its eddy diffusivity αt is a function of the ratio R between the temperature and velocity turbulent time scales. In order to compute the turbulent time scale of temperature two new variables are defined, the mean square temperature fluctuation κθ and its dissipation εθ , which are calculated by solving two transport equations. Results obtained from the four parameter κ-ε-κθ -εθ model are compared with DNS data available in literature for plane and cylindrical geometries. Finally forced fully developed flows in cylindrical rod and bundle rod geometry are compared with heat transfer correlations extracted by experimental data
Numerical validation of a k-w-kt-wt heat transfer turbulence model for low Prandtl number fluids
No full textIIn ordinary fluids with Pr~1 it is well known that a two equation turbulence model with a constant turbulent Prandtl number Prt~0.85 is usually sufficient to correctly predict heat transfer in fully turbulent flows. On the contrary, in heavy liquid metals the simple hypothesis of constant P rt cannot reproduce experimental data and the turbulent Prandtl number P rt has to be introduced as a function of state variables. In this work we introduce a four parameter turbulence model that may improve heat transfer prediction in fully developed heavy liquid metal flows. The turbulent heat flux transport equation is solved algebraically and an expression for the thermal eddy diffusivity αt is obtained. This quantity depends on the thermal and dynamical time scales of turbulence and their ratio. A four parameter turbulence model κ-e-κt-et for low-Prandtl number fluids has been already presented by the authors with satisfactory results. The main problem of the κ-e models is the stability of the system since e is a function of κ on the boundary. The introduction of the κ-w system allows to calculate directly the time scale of turbulence as τ =1/w and to achieve a more stable and robust solution near the wall. Numerical results are obtained by using an in-house code with a standard finite element implementation of Navier-Stokes equations coupled with the four parameter turbulence model. The code allows multiple refinement of the mesh in order to improve the solution and to correctly impose the boundary conditions with a near-wall approach. Results from simulations of fully developed turbulent flows of heavy liquid metals are reported for the plane and cylindrical geometries, in particular for the heat transfer between a wall heated with uniform heat flux and the liquid metal flow. The results are compared with DNS data when available and with experimental heat transfer correlations for the prediction of the Nusselt number in order to evaluate the turbulence model
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