A symmetry-preserving second-order time-accurate PISO-based method

A new conservative symmetry-preserving second-order time-accurate PISO-based pressure-velocity coupling for solving the incompressible Navier-Stokes equations on unstructured collocated grids is presented in this paper. This new method for implicit time stepping is an extension of the conservative symmetry-preserving incremental-pressure projection method for explicit time stepping and unstructured collocated meshes of Trias et al. [35]. In order to assess and compare both methods, we have implemented them within one unified solver in the open source code OpenFOAM where we use a Butcher array to prescribe the Runge-Kutta method. Thus, by changing the entries of the Butcher array, explicit and diagonally implicit Runge-Kutta schemes can be combined into one solver. We assess the energy conservation properties of the implemented discretisation methods and the temporal consistency of the selected Runge-Kutta schemes using Taylor-Green vortex and lid-driven cavity flow test cases. Finally, we use a more complex turbulent channel flow test case in order to further assess the performance of the presented new conservative symmetry-preserving incremental-pressure PISO-based method. Although both implemented methods are based on a symmetry-preserving discretisation, we show they still produce a small amount of numerical dissipation when the total pressure is directly solved from a Poisson equation. When an incremental-pressure approach is used, where a pressure correction is solved from a Poisson equation, both methods are effectively fully-conservative. For high-fidelity simulations of incompressible turbulent flows, it is highly desirable to use fully-conservative methods. For such simulations, the presented numerical methods are therefore expected to have large added value, since they pave the way for the execution of truly energy-conservative high-fidelity simulations in complex geometries. Furthermore, both methods are implemented in OpenFOAM, which is widely used within the CFD community, so that a large part of this community can benefit from the developed and implemented numerical methods

Heat Transfer Mechanism In Particle-Laden Turbulent Shearless Flows

Particle-laden turbulent flows are one of the complex flow regimes involved in a wide range of environmental, industrial, biomedical and aeronautical applications. Recently the interest has included also the interaction between scalars and particles, and the complex scenario which arises from the interaction of particle finite inertia, temperature transport, and momentum and heat feedback of particles on the flow leads to a multi-scale and multi-physics phenomenon which is not yet fully understood. The present work aims to investigate the fluid-particle thermal interaction in turbulent mixing under one-way and two-way coupling regimes. A recent novel numerical framework has been used to investigate the impact of suspended sub-Kolmogorov inertial particles on heat transfer within the mixing layer which develops at the interface of two regions with different temperature in an isotropic turbulent flow. Temperature has been considered a passive scalar, advected by the solenoidal velocity field, and subject to the particle thermal feedback in the two-way regime. A self-similar stage always develops where all single-point statistics of the carrier fluid and the suspended particles collapse when properly re-scaled. We quantify the effect of particle inertial, parametrized through the Stokes and thermal Stokes numbers, on the heat transfer through the Nusselt number, defined as the ratio of the heat transfer to the thermal diffusion. A scale analysis will be presented. We show how the modulation of fluid temperature gradients due to the statistical alignments of the particle velocity and the local carrier flow temperature gradient field, impacts the overall heat transfer in the two-way coupling regime

Depth-averaged and 3D Finite Volume numerical models for viscous fluids, with application to the simulation of lava flows

This Ph.D. project was initially born from the motivation to contribute to the depth-averaged and 3D modeling of lava flows. Still, we can frame the work done in a broader and more generalist vision. We developed two models that may be used for generic viscous fluids, and we applied efficient numerical schemes for both cases, as explained in the following. The new solvers simulate free-surface viscous fluids whose temperature changes are due to radiative, convective, and conductive heat exchanges. A temperature-dependent viscoplastic model is used for the final application to lava flows. Both the models behind the solvers were derived from mass, momentum, and energy conservation laws. Still, one was obtained by following the depth-averaged model approach and the other by the 3D model approach. The numerical schemes adopted in both our models belong to the family of finite volume methods, based on the integral form of the conservation laws. This choice of methods family is fundamental because it allows the creation and propagation of discontinuities in the solutions and enforces the conservation properties of the equations. We propose a depth-averaged model for a viscous fluid in an incompressible and laminar regime with an additional transport equation for a scalar quantity varying horizontally and a variable density that depends on such transported quantity. Viscosity and non-constant vertical profiles for the velocity and the transported quantity are assumed, overtaking the classic shallow-water formulation. The classic formulation bases on several assumptions, such as the fact that the vertical pressure distribution is hydrostatic, that the vertical component of the velocity can be neglected, and that the horizontal velocity field can be considered constant with depth because the classic formulation accounts for non-viscous fluids. When the vertical shear is essential, the last assumption is too restrictive, so it must relax, producing a modified momentum equation in which a coefficient, known as the Boussinesq factor, appears in the advective term. The spatial discretization method we employed is a modified version of the central-upwind scheme introduced by Kurganov and Petrova in 2007 for the classical shallow water equations. This method is based on a semi-discretization of the computational domain, is stable, and, being a high-order method, has a low numerical diffusion. For the temporal discretization, we used an implicit-explicit Runge-Kutta technique discussed by Russo in 2005 that permits an implicit treatment of the stiff terms. The whole scheme is proved to preserve the positivity of flow thickness and the stationary steady-states. Several numerical experiments validate the proposed method, show the incidence on the numerical solutions of shape coefficients introduced in the model and present the effects of the viscosity-related parameters on the final emplacement of a lava flow. Our 3D model describes the dynamics of two incompressible, viscous, and immiscible fluids, possibly belonging to different phases. Being interested in the final application of lava flows, we also have an equation for energy that models the thermal exchanges between the fluid and the environment. We implemented this model in OpenFOAM, which employs a segregated strategy and the Finite Volume Methods to solve the equations. The Volume of Fluid (VoF) technique introduced by Hirt and Nichols in 1981 is used to deal with the multiphase dynamics (based on the Interphase Capturing strategy), and hence a new transport equation for the volume fraction of one phase is added. The challenging effort of maintaining an accurate description of the interphase between fluids is solved by using the Multidimensional Universal Limiter for Explicit Solution (MULES) method (described by Marquez Damian in 2013) that implements the Flux-Corrected Transport (FCT) technique introduced by Boris and Book in 1973, proposing a mix of high and low order schemes. The choice of the framework to use for any new numerical code is crucial. Our contribution consists of creating a new solver called interThermalRadConvFoam in the OpenFOAM framework by modifying the already existing solver interFoam (described by Deshpande et al. in 2012). Finally, we compared the results of our simulations with some benchmarks to evaluate the performances of our model

Implicit and conventional large eddy simulation of flow around a circular cylinder at Reynolds number of 3900

The implicit Large Eddy Simulation (iLES) incorporating an unstructured 3rd-order Weighted Essential Non-Oscillatory (WENO) reconstruction method and the conventional Large Eddy Simulation with Wall Adapting Local Eddy-Viscosity (WALE) are investigated on the flow around a circular cylinder at a Reynolds number of 3900. Simulations are carried out in the framework of open-source package OpenFOAM with a 2nd-order Euler implicit time integration and Pressure-Implicit Splitting-Operator (PISO) algorithm is used for the pressure-velocity coupling. The results are compared to the high fidelity experiment and DNS data, and demonstrated a favourable performance for iLES with a 3rd-order WENO scheme on the instantaneous flow structure. The conventional LES on the prediction of mean surface pressure coefficient and velocity profiles on the wake can be beneficial by reducing the effect of Rhie-Chow interpolation. The spectral analysis reveals that the current simulations are also capturing Von Karman shedding frequencies and shear layer frequencies. Finally, distinct features of iLES and LES are discussed

LES stochastic modelling of cavitation with its applications in OpenFOAM

Cavitation is a vaporization process that commonly happens in high-pressure injector nozzles nowadays. It has been shown by previous studies that cavitation has a significant influence on the subsequent atomization process, the quality of which would in turn heavily affect the process of combustion. Injector nozzle designs nowadays are trending towards higher and higher injection pressure, making the knowledge on cavitation phenomena more and more relevant and necessary. Studies into cavitation phenomena have attracted a rapidly increasing amount of interest from both the academic and the industrial circle. However, due to the inherent difficulties, cavitation still renders itself a process that is hard to be quantified with the experimental facilities nowadays. On the computational side, some cavitation models have been developed and applied successfully. Lagrangian models have had much success in several studies. However, when it comes to applications of parallel computing, the inherent difficulty on computational load balancing could hinder the application of Lagrangian models in simulations of realistic injector nozzles. The Eulerian approach, on the other hand, is naturally conducive to a better computational load balance, for which a simple domain decomposition usually suffices. In the category of Eulerian modeling, the homogeneous equilibrium model (HEM) imposes less of a requirement to computational load, thus have been widely used in applications nowadays.As much as HEMs have been widely applied in both academic studies and commercial computational tools, the stochastic feature of cavitation phenomena has been missing in the single Eulerian field models nowadays. With only one Eulerian field, only one bubble radius associated with the volume fraction is solved in any spatial location. However, physically, the vapor bubble sizes are highly fluctuating, hence can better be described by a probability density function (PDF). In order to solve the evolution equation of the PDF, a Eulerian Stochastic Field (ESF) model is developed in this work. Multiple Eulerian fields are used to represent a distribution of cavitation bubble radii.The ESF method has been previously applied for cavitation simulations only in the context of a compressible flow solver. However, the solution of the compressible form of the Navier-Stokes equation is known to be computationally expensive for low Mach number flow. Therefore, whether the ESF model can be applied in combination with a pressure based solver became an interesting question. In this work, we coupled the ESF model to a pressure-based PISO algorithm, making the ESF model computationally efficient enough for studies of realistic injector nozzle geometries and standard operating conditions. Several simplified geometries, including one step-contraction throttle and two academic injector nozzle designs, are investigated using the novel cavitation model. Furthermore, we applied the ESF model on a realistic multi-hole injector geometry (spray G/G2 as defined by the Engine Combustion Network (ECN)) demonstrating that the ESF cavitation model can be applied in simulations of realistic nozzle injector geometries

Reduced order models for the incompressible Navier-Stokes equations on collocated grids using a 'discretize-then-project' approach

A novel reduced order model (ROM) for incompressible flows is developed by performing a Galerkin projection based on a fully (space and time) discrete full order model (FOM) formulation. This 'discretize-then-project' approach requires no pressure stabilization technique (even though the pressure term is present in the ROM) nor a boundary control technique (to impose the boundary conditions at the ROM level). These are two main advantages compared to existing approaches. The fully discrete FOM is obtained by a finite volume discretization of the incompressible Navier-Stokes equations on a collocated grid, with a forward Euler time discretization. Two variants of the time discretization method, the inconsistent and consistent flux method, have been investigated. The latter leads to divergence-free velocity fields, also on the ROM level, whereas the velocity fields are only approximately divergence-free in the former method. For both methods, stable and accurate results have been obtained for test cases with different types of boundary conditions: a lid-driven cavity and an open-cavity (with an inlet and outlet). The ROM obtained with the consistent flux method, having divergence-free velocity fields, is slightly more accurate but also slightly more expensive to solve compared to the inconsistent flux method. The speedup ratio of the ROM and FOM computation times is the highest for the open cavity test case with the inconsistent flux method