The 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 not valid 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 or four parameter turbulence models. In this work we assess a four parameter logarithmic turbulence model for liquid metals based on RANS 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.

This work focuses on the well-known issue of mass conservation in the context of the finite element technique for computational fluid dynamic simulations. Specifically, non-conventional finite element families for solving Navier-Stokes equations are investigated to address the mathematical constraint of incompressible flows. Raviart-Thomas finite elements are employed for the achievement of a discrete free-divergence velocity. In particular, the proposed algorithm projects the velocity field into the discrete free-divergence space by using the lowest-order Raviart-Thomas element. This decomposition is applied in the context of the projection method, a numerical algorithm employed for solving Navier-Stokes equations. Numerical examples validate the approach’s effectiveness, considering different types of computational grids. Additionally, the presented paper considers an interface advection problem using marker approximation, in the context of multiphase flow simulations. Numerical tests, equipped with an analytical velocity field for the surface advection, are presented to compare exact and non-exact divergence-free velocity interpolation.

The volume of fluid (VOF) method is a popular technique for the direct numerical simulations of flows involving immiscible fluids. A discrete volume fraction field evolving in time represents the interface, in particular, to compute its geometric properties. The height function method (HF) is based on the volume fraction field, and its estimate of the interface curvature converges with second-order accuracy with grid refinement. Data-driven methods have been recently proposed as an alternative to computing the curvature, with particular consideration for a well-balanced input data set generation and symmetry preservation. In the present work, a two-layer feed-forward neural network is trained on an input data set generated from the height function data instead of the volume fraction field. The symmetries for rotations, reflections, and the anti-symmetry for the phase swapping have been considered to reduce the number of input parameters. The neural network, establishing a correlation between curvature and height function values, can efficiently predict the local interface curvature. We compare the trained neural network to the standard Height Function method to assess its performance and robustness.

This paper investigates a numerical code coupling technique to tackle multi-physics and multi-scale simulations using state-of-the-art software packages that typically address some specific modeling domain. The coupling considers the in-house FEM code, FEMuS, and the FVM code OpenFOAM, by exploiting the MED library from the SALOME platform. The present approach is tested on a buoyancy-driven fluid flow within a square cavity, where the buoyancy force constitutes the coupling term. In uncoupled scenarios, momentum and temperature equations are solved both in FEM and FVM codes without data exchange. In the coupled setting, only the OpenFOAM velocity and the FEMuS temperature fields are solved separately and shared at each time step (or vice versa). The MED library handles the coupling with the addition of suitable ad-hoc data structures that perform the field transfer between codes. Different Rayleigh numbers are investigated, comparing the outcomes of coupled and uncoupled cases with reference literature results. Additionally, a boundary data transfer application is presented to extend the capabilities of the coupling algorithm to coupled applications with separate domains. In this problem, the two domains share interfaces and boundary values on specific fields as fluxes are exchanged between the two numerical codes.

This study introduces numerical advancements in an alternative design for the SPS Beam Dump Facility (BDF) at CERN. The design envisions a high-power operation target made of flowing liquid lead. The BDF is a proposed versatile facility at CERN, intended for both beam-dump-like and fixed-target experiments. The target behavior is assessed, assuming a proton beam with a momentum of 400 GeV/c, a pulse frequency of 1/7.2 Hz, and an average beam power of 355 kW. An evaluation is conducted using various Computational Fluid Dynamics (CFD) codes to analyze the behavior of liquid lead and to predict the thermal stress on the target vessel induced by the pulsed heat source generated by the charged particle beam. The comparison increases the reliability of the results, investigating the dependencies on the CFD modeling approach. The beam is modeled as a volumetric heat source with data coming from beam-lead interaction simulations provided by CERN and obtained with the Monte-Carlo code FLUKA. The velocity field and stress profiles are utilized to enhance the design of the lead loop and verify its viability and safety when operated with a liquid metal target.