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Publication# Direct numerical simulation of phase change in the presence of non-condensable gases

Résumé

This paper describes a new numerical method for the simulation of phase change phenomena between a liquid and a vapour in the presence of non-condensable gases. The method is based on an interface-tracking approach in the framework of single-fluid modelling. The principal innovative feature represented is the capability of simulating a mixture of the condensable gas (vapour) and non-condensable gases with different densities. The formulation and subsequent discretization of the governing equations for the species transport are discussed in detail. In particular, a volume-averaged velocity field is introduced into the species transport equation in combination with a mass-averaged velocity field approach for the momentum equations. The resulting algorithm has been implemented into the incompressible Navier-Stokes solver, PSI-BOIL, which features a finite-volume approach based on a fixed, rectangular, Cartesian grid. Several verification cases have been undertaken to ensure the code modifications have been correctly implemented. These include simulation of the Stefan problem, involving evaporation and condensation in a 1 D configuration, and an evaporating droplet under forced convective flow. In all cases, very good agreement has been obtained with analytical solution. A simulation of direct-contact condensation of a practical application is also presented, which serves to demonstrate the potential capability of the new approach to a wider range of engineering problems, including pressure suppression pools in nuclear reactors. (C) 2020 Elsevier Ltd. All rights reserved.

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Chargement

Chargement

Chargement

We present a numerical model for the simulation of 3D mono-dispersed sediment dynamics in a Newtonian flow with free surfaces. The physical model is a macroscopic model for the transport of sediment based on a sediment concentration with a single momentum balance equation for the mixture (fluid and sediments).
The model proposed here couples the Navier-Stokes equations, with a
volume-of-fluid (VOF) approach for the tracking of the free surfaces between the liquid
and the air, plus a nonlinear advection equation for the sediments (for the transport, deposition, and resuspension of sediments).
The numerical algorithm relies on a splitting approach to decouple diffusion and advection phenomena such that we are left with a Stokes operator, an advection operator, and deposition/resuspension operators.
For the space discretization, a two-grid method couples a finite element discretization for the resolution of the Stokes problem, and a finer structured grid of small cells for the discretization of the advection operator and the sediment deposition/resuspension operator.
SLIC, redistribution, and decompression algorithms are used for post-processing to limit numerical diffusion and correct the numerical compression of the volume fraction of liquid.
The numerical model is validated through numerical experiments.
We validate and benchmark the model with deposition effects only for some specific experiments, in particular erosion experiments. Then, we validate and benchmark the model in which we introduce resuspension effects. After that, we discuss the limitations of the underlying physical models.
Finally, we consider a one-dimensional diffusion-convection equation and study an error indicator for the design of adaptive algorithms. First, we consider a finite element backward scheme, and then, a splitting scheme that separates the diffusion and the convection parts of the equation.

Dynamics of nucleate boiling are strongly affected by the formation and behaviour of the microlayer, a layer of liquid underneath growing bubbles. As a result of its minute thickness, very high heat fluxes occur within the microlayer and its evaporation contributes significantly to the overall heat transfer. Microlayer formation is, however, not guaranteed and the transition from the contact-line to the microlayer regime of nucleate boiling is not fully understood. The difficulty of experimental investigation of the microlayer and the uncertainties surrounding its formation and subsequent evolution motivate the use of Direct Numerical Simulation (DNS) to model its behaviour. In this work, a computational strategy for utilising DNS to model nucleate boiling by resolving explicitly the microlayer is developed. The numerical method is based on the resolution of continuum conservation equations for incompressible two-phase flows in Cartesian and axisymmetric cylindrical coordinates. The phasic interface is tracked by means of the geometric Volume-of-Fluid (VOF) method and the algorithm is applicable both to adiabatic and volatile flows. Online, implicit coupling of the fluid and solid domains for the solution of the conjugate heat-transfer problem is included and closure models for the treatment of the interfacial heat-transfer resistance and the dynamic contact angle are introduced. A rigorous verification and validation exercise is performed to evaluate the efficacy of the numerical algorithm. Subsequently, a theoretical criterion for modelling the transition between contact-line and microlayer regimes is derived, and tested. Very good agreement is found with the reference experimental and simulation data and the predictive power of the criterion is demonstrated with the aid of DNS results. The computational procedure is then validated for simulations of nucleate boiling with resolved microlayer using relevant experimental data recently measured at the Massachusetts Institute of Technology; it is shown that the main observed growth features and surface heat-transfer characteristics are well-reproduced using the overall method. A sensitivity study of the dependence of the initial microlayer thickness on the growth conditions is performed and a universal equation describing the thickness distribution is proposed with liquid properties and bubble expansion rate being the governing parameters. Finally, the computational method is extended to coarse-mesh problems by introducing several reduced-order models and the full bubble-growth cycle from nucleation to detachment is simulated. Good agreement with reference measurements is again achieved and the experimental findings regarding the force balance during nucleate boiling are confirmed.

Carlo Fiorina, Andreas Pautz, Stefan Radman

A porous medium-based representation of nuclear reactors and complex engineering systems more in general can significantly reduce simulation and modelling costs, while preserving a reasonable degree of accuracy via regime map-based correlations for modelling physical interactions. This paper presents a segregated algorithm for the simulation of dispersed two phase flows in such systems treated as porous media in an Eulerian framework. The global algorithm pertaining to the coupling between the mass, momentum and energy conservation equations solution is discussed and implemented via the finite volume OpenFOAM programming library. In the context of pressure–velocity coupling, a novel implementation of the Partial Elimination Algorithm for the treatment of the inter-phase momentum transfer term is developed. It is found to perform better than existing implementations for a number of cases with important momentum coupling between phases. A conclusive verification of the overall solution algorithm is performed with the Method of Manufactured Solutions and order-of-accuracy testing. From an implementation perspective, the performance of the algorithm in parallel strong scaling up to 4096 cores is assessed and proves to be in line with OpenFOAM-based code standards.

2021