New Simplified Algorithm for the Multiple Rotating Frame Approach in Computational Fluid Dynamics

This paper deals with rotating effects simulation of steady flows in turbomachinery. To take into account the rotating nature of the flow, the frozen rotor approach is one of the widely used approaches. This technique, known in a more general context as a multiple rotating frame (MRF), consists on building axisymmetric interfaces around the rotating parts and solves for the flow in different frames (static and rotating). This paper aimed to revisit this technique and propose a new algorithm referred to it by a virtual multiple rotating frame (VMRF). The goal is to replace the geometrical interfaces (part of the computer-aided design (CAD)) that separate the rotating parts replaced by the virtual ones created at the solver level by a simple user input of few point locations and/or parameters of basic shapes. The new algorithm renders the MRF method easy to implement, especially for edge-based numerical schemes, and very simple to use. Moreover, it allows avoiding any remeshing (required by the MRF approach) when one needs to change the interface position, shape, or simply remove or add a new one, which frequently happened in practice. Consequently, the new algorithm sensibly reduces the overall computations cost of a simulation. This work is an extension of a first version published in an ASME conference, and the main new contributions are the detailed description of the new algorithm in the context of cell-vertex finite volume method and the validation of the method for viscous flows and the three-dimensional (3D) case which is of significant importance to the method to be attractive for real and industrial applications.BCAM-BALTOGAR CFD Platform for Turbomachinery Simulation and Design (BFA/DFB - 6/12/TK/2012/00020

Simulation of Water Entry and Exit of a Circular Cylinder Using the ISPH Method

Simulations of free surface flows, as well as flows with moving boundaries in general, are quite difficult to describe with the classic, mesh-based Eulerian methods, such as finite difference, finite volume, and finite element methods. Meshless Lagrangian methods or a combination of Eulerian-Lagrangian methods that have the ability to describe the free surface with large deformations have been developing in the past fifteen years. In this paper, the Lagrangian incompressible smoothed particle hydrodynamics (ISPH) method for simulating the dynamics of an incompressible viscous fluid flow is presented. The ISPH method is an attractive choice for the simulation of incompressible fluid flow because it is based on the simple SPH formulations, and it solves the pressure field implicitly using the projection scheme of solving the Navier-Stokes equations. A computer code for the simulation of the viscous incompressible fluid flow based on the ISPH method is developed. Water entry and water exit of a rigid body are very important phenomena in marine hydrodynamics and there have been many studies and experiments on the topic. The cases of two-dimensional water entry and water exit of a circular cylinder at a forced constant velocity were studied in order to verify and validate the method. Numerical simulations of a rigid circular cylinder falling onto initially calm water at a constant entry velocity were carried out. Also numerical simulation of the water exit of a circular cylinder, initially fully immersed, was performed. The obtained numerical results are in good agreement with the experimental and analytical ones found in the literature

Stable coupling of the Yee scheme with a linear current model

This work analyzes the stability of the Yee scheme for non stationary Maxwell's equations coupled with a linear current model. We show that the usual procedure may yield unstable scheme for physical situations that correspond to strongly magnetized plasmas in X-mode (TE) polarization. We propose to use first order clustered discretization of the vectorial product that gives back a stable coupling. We validate the schemes on some test cases representative of direct numerical simulations of X-mode in a magnetic fusion plasma

Adaptive time stepping approach for Phase-Field modeling of phase separation and precipitates coarsening in additive manufacturing alloys

In the present work, the capacity of phase field method to highlight microstructural changes during the spinodal decomposition of a given binary alloy basing on the Cahn-Hilliard equation is presented. Then, growth and coarsening of precipitates are studied using the KKS (Kim-Kim-Suzuki) model, which includes Cahn-Hilliard and Allen-Cahn equations. The implementation of time stepping algorithms to resolve Phase-Field equations is illustrated. Within Fourier space, using semi-implicit spectral method, it has been demonstrated that it allows faster computing than schemes based on finite difference method. First, spinodal decomposition of a given binary alloy under isothermal loading is implemented and three time stepping approaches are applied: constant time stepping, non- iterative and an iterative method. While the non-iterative method is faster than the constant time stepping scheme, the iterative one, although relatively more CPU consuming, can guarantee the convergence of the computing. These methods are combined in an innovative approach tested on 1D, 2D and 3D grids. The effectiveness of the adopted adaptive time-stepping algorithm allows resolving equations in reasonable CPU time. It predicts different physical phenomena, such as phase separation and growth and coarsening of precipitates induced by important interfacial energies

Differential formulation of discontinuous Galerkin and related methods for compressible Euler and Navier-Stokes equations

A new approach to high-order accuracy for the numerical solution of conservation laws introduced by Huynh and extended to simplexes by the current work is renamed CPR (correction procedure or collocation penalty via reconstruction). The CPR approach employs the differential form of the equation and accounts for the jumps in flux values at the cell boundaries by a correction procedure. In addition to being simple and economical, it unifies several existing methods including discontinuous Galerkin (DG), staggered grid, spectral volume (SV), and spectral difference (SD). The approach is then extended to diffusion equation and Navier-Stokes equations. In the discretization of the diffusion terms, the BR2 (Bassi and Rebay), interior penalty, compact DG (CDG), and I-continuous approaches are used. The first three of these approaches, originally derived using the integral formulation, were recast here in the CPR framework, whereas the I-continuous scheme, originally derived for a quadrilateral mesh, was extended to a triangular mesh. The current work also includes a study of high-order curve boundaries representations. A new boundary representation based on the Bezier curve is then developed and analyzed, which is shown to have several advantages for complicated geometries. To further enhance the efficiency, the capability of h/p mesh adaptation is developed for the CPR solver. The adaptation is driven by an efficient multi-p a posteriori error estimator. P-adaptation is applied to smooth regions of the flow field while h-adaptation targets the non-smooth regions, identified by accuracy-preserving TVD marker. Several numerical tests are presented to demonstrate the capability of the technique

Numerical Simulation Of Conventional Fuels And Biofuels Dispersion And Vaporization Process In Co-flow And Cross-flow Premixers

In order to follow increasingly strict regulation of pollutant emissions, a new concept of Lean Premixed pre-vaporized (LPP) combustion has been proposed for turbines. In LPP combustion, controlled atomization, dispersion and vaporization of different types of liquid fuel in the premixer are the key factors required to stabilize the combustion process and improve the efficiency. A numerical study is conducted for the fundamental understanding of the liquid fuel dispersion and vaporization process in pre-mixers using both cross-flow and co-flow injection methods. First, the vaporization model is validated by comparing the numerical data to existing experiments of single droplet vaporization under both low and high convective air temperatures. Next, the dispersion and vaporization process for biofuels and conventional fuels injected transversely into a typical simplified version of rectangular pre-mixer are simulated and results are analyzed with respect to vaporization performance, degree of mixedness and homogeneity. Finally, collision model has been incorporated to predict more realistic vaporization performance. Four fuels, Ethanol, Rapeseed Methyl Esters (RME), gasoline and jet-A have been investigated. For mono-disperse spray with no collision model, the droplet diameter reduction and surface temperature rise were found to be strongly dependent on the fuel properties. The diameter histogram near the pre-mixer exit showed a wide droplet diameter distribution for all the fuels. In general, pre-heating of the fuels before injection improved the vaporization performance. An improvement in the drag model with Stefan flow correction showed that a low speed injection and high cone angle improved performance. All fuels achieved complete vaporization under a iv spray cone angle of 140°. In general, it was found that cross-flow injection achieved better vaporization performance than co-flow injection. A correlation is derived for jet-A‟s total vaporization performance as a function of non-dimensional inlet air temperature and fuel/air momentum flux ratio. This is achieved by curve-fitting the simulated results for a broad range of inlet air temperatures and fuel/air momentum flux ratios. The collision model, based on no-time-counter method (NTC) proposed by Schmidt and Rutland, was implemented to replace O‟Rourke‟s collision algorithm to improve the results such that the unphysical numerical artifact in a Cartesian grid was removed and the results were found to be grid-independent. The dispersion and vaporization processes for liquid fuel sprays were simulated in a cylindrical pre-mixer using co-flow injection method. Results for jet-A and Rapeseed Methyl Esters (RME) showed acceptable grid independence. At relatively low spray cone angle and injection velocity, it was found that the collision effect on the average droplet size and the vaporization performance were very high due to relatively high coalescence rate induced by droplet collisions. It was also found that the vaporization performance and the level of homogeneity of fuel-air mixture could be significantly improved when the dispersion level is high, which can be achieved by increasing the spray cone angle and injection velocity. In order to compare the performance between co-flow and cross-flow injection methods, the fuels were injected at an angle of 40° with respect to the stream wise direction to avoid impacting on the wall. The cross-flow injection achieved similar vaporization performance as co-flow because a higher coalescence rate induced by droplet collisions cancelled off its higher heat transfer efficiency between two phases for cross-flow injections

IMMERSED BOUNDARY METHODS FOR COMPRESSIBLE FLOWS

Ph.DDOCTOR OF PHILOSOPH