1,720,978 research outputs found
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
Analysis and Computations of Optimal Control Problems for Boussinesq Equations
Full text linkThe main purpose of engineering applications for fluid with natural and mixed convection is to control or enhance the flow motion and the heat transfer. In this paper, we use mathematical tools based on optimal control theory to show the possibility of systematically controlling natural and mixed convection flows. We consider different control mechanisms such as distributed, Dirichlet, and Neumann boundary controls. We introduce mathematical tools such as functional spaces and their norms together with bilinear and trilinear forms that are used to express the weak formulation of the partial differential equations. For each of the three different control mechanisms, we aim to study the optimal control problem from a mathematical and numerical point of view. To do so, we present the weak form of the boundary value problem in order to assure the existence of solutions. We state the optimization problem using the method of Lagrange multipliers. In this paper, we show and compare the numerical results obtained by considering these different control mechanisms with different objectives
A New Anisotropic Four-Parameter Turbulence Model for Low Prandtl Number Fluids
Full text linkDue to their interesting thermal properties, liquid metals are widely studied for heat transfer applications where large heat fluxes occur. In the framework of the Reynolds-Averaged Navier– Stokes (RANS) approach, the Simple Gradient Diffusion Hypothesis (SGDH) and the Reynolds Analogy are almost universally invoked for the closure of the turbulent heat flux. Even though these assumptions can represent a reasonable compromise in a wide range of applications, they are not reliable when considering low Prandtl number fluids and/or buoyant flows. More advanced closure models for the turbulent heat flux are required to improve the accuracy of the RANS models dealing with low Prandtl number fluids. In this work, we propose an anisotropic four-parameter turbulence model. The closure of the Reynolds stress tensor and turbulent heat flux is gained through nonlinear models. Particular attention is given to the modeling of dynamical and thermal time scales. Numerical simulations of low Prandtl number fluids have been performed over the plane channel and backward-facing step configurations
An adjoint-based temperature boundary optimal control approach for turbulent buoyancy-driven flows
No full textThis paper deals with the adjoint optimal control for turbulent buoyancy-driven flows. The aim of this optimal control problem is to obtain a desired velocity profile and enhance the turbulence intensity in a well defined region by controlling the fluid temperature on domain boundaries and consequently the buoyancy forces. The fluid is assumed to be incompressible within the Boussinesq approximation, while turbulence is considered by coupling the Wilcox k-ω model with the Reynolds Averaged energy and Navier Stokes equations. The state, adjoint and control equations are derived by employing the Lagrangian multipliers method. The optimality system is solved with a finite elements code where a steepest descent algorithm has been implemented in order to find the optimal boundary control parameter. Numerical results are reported to show the robustness of the method in solving strongly-coupled optimality systems with a large number of unknowns
ANALYSIS AND NUMERICAL RESULTS FOR BOUNDARY OPTIMAL CONTROL PROBLEMS APPLIED TO TURBULENT BUOYANT FLOWS
No full textIn this work, we introduce the mathematical analysis of the optimal control for the Navier-Stokes system coupled with the energy equation and a k-ω turbulence model. While the optimal control of the Navier-Stokes system has been widely studied in past works, only a few works are based on the analysis of the turbulent flows. Moreover, the optimal control of turbulent buoyant flows are usually not taken into account due to the difficulties arising from the analysis and the numerical implementation of the optimality system. We first prove the existence of the solution of the boundary value problem associated with the studied system. Then we use an optimization method that relies on the Lagrange multiplier formalism to obtain the first-order necessary condition for optimality. We derive the optimality system and we solve it using a gradient descent algorithm that allows uncoupling state, adjoint, and optimality conditions. Some numerical results are then reported to validate the presented theoretical analysis
VALIDATION ON A NEW ANISOTROPIC FOUR-PARAMETER TURBULENCE MODEL FOR LOW PRANDTL NUMBER FLUIDS
No full textThis work aims to validate a new anisotropic four-parameter turbulence model for low-Prandtl number fluids in forced and mixed convection. Traditional models based on the gradient-diffusion hypothesis and Reynolds analogy are inadequate to simulate the turbulent heat transfer in low-Prandtl number fluids. Additional transport equations for thermal variables are required to predict the characteristic thermal time scale. In a four-parameter turbulence model, two additional transport equations are solved for the temperature variance and its dissipation rate. Thus, it is possible to formulate appropriate characteristic time scales to predict the near-wall and bulk behaviour of mean and turbulent variables. The isotropic version of the four-parameter model has been widely studied and validated in forced and mixed convection. We aim to extend the model validity by proposing explicit algebraic models for the closure of Reynolds stress tensor and turbulent heat flux. For the validation of the anisotropic four-parameter turbulence model, low-Prandtl number fluids are simulated in several flow configurations considering buoyancy effects and numerical results are compared with DNS data
A multigrid local smoother approach for a domain decomposition solver over non-matching grids
No full textIn this paper we consider a multigrid approach for solving elliptic equations over non-matching grids with domain decomposition methods. The domain is partitioned into subdomains with different mesh levels that do not match at the interface. The proposed algorithm searches for the global solution over different levels by projecting the residuals on the overlap region. This method is used in conjunction with a domain decomposition solver which only requires, in each iteration step, the solutions of several small local subproblems over finite element blocks. This algorithm is shown to converge to the solution of the corresponding Lagrange multiplier problem for non-matching grids. The convergence properties of the algorithms are analyzed and numerical examples are presented. When the multigrid and domain decomposition approaches are combined, the method is shown to be reliable and easy to implement. Furthermore the local nature of the solver allows for a straightforward implementation on multiple parallel computers and graphics processing unit (GPU) clusters
A multiscale fluid structure interaction model derived from Koiter shell equations
No full textIn this work we propose the numerical simulation of fluid structure interaction (FSI) problem by using a membrane model, derived from the Koiter shell equations. With this approach the thickness of the solid wall can be neglected, with a meaningful reduction of the computational cost of the numerical problem. The fluid structure problem is then reduced to the fluid equations on a moving mesh together with a particular Robin boundary condition imposed on the surface corresponding to the solid moving wall. Furthermore an artificial absorbing outflow boundary condition has been implemented in order to reduce the damping and reflections of the pressure waves at the domain's outlet. This model is implemented and solved with an in-house finite elements code, and tested through axisymmetric cases that show the robustness of the developed algorithm. Finally, we report a comparison of the implemented model with results of a FSI monolithic model, based on non-linear incompressible structure
THERMAL-HYDRAYULICS AND NEUTRONICS CODES COUPLING FOR THE ANALYSIS OF A LEAD FAST REACTOR
No full textIn this work the thermal-hydraulics and neutronics behavior of a Lead Fast Reactor (LFR) core is investigated evaluating the power generation distribution taking into account the local temperature field. The temperature field is evaluated using the CFD finite element code FEMuS and exchanged with the multiscale neutron code DONJON-DRAGON, which interpolates the macroscopic cross-sections according to the local temperature field and local lead density distribution. As a result, the neutron flux changes and defines a new power density distribution which is used to update the temperature field into the CFD code. The coupling between neutron and CFD codes is achieved through their inclusion into the numerical platform SALOME. The numerical libraries MED, included into the SALOME platform, are used to exchange data run-time between FEMuS and DONJON
Numerical simulation of a low Prandtl number flow over a backward facing step with an anisotropic four-equation turbulence model
No full textIn recent years the use of liquid metals has become more and more popular for heat transfer applications in many fields ranging from IV generation fast nuclear reactors to solar power plants. Due to their low Prandtl number values, the similarity between dynamical and thermal fields cannot be assumed and sophisticated heat turbulence models are required to take into account the anisotropy of the turbulent heat transfer involving liquid metals. In the present work, we solve an anisotropic four-equation turbulence model coupled with the Reynolds Averaged Navier Stokes system of equations to simulate a turbulent flow of liquid sodium over a vertical backward-facing step. We implement an explicit algebraic model for Reynolds stress tensor and turbulent heat flux that takes into account flow anisotropic behavior. We study forced and mixed convection regimes when a uniform heat flux is applied on the wall behind the step. Linear isotropic approximations for eddy viscosity and eddy thermal diffusivity underestimate the turbulent heat flux components while this anisotropic model shows a better agreement with DNS results
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