Finite element simulation of compressible particle-laden gas flows

AbstractA macroscopic two-fluid model of compressible particle-laden gas flows is considered. The governing equations are discretized by a high-resolution finite element method based on algebraic flux correction. A multidimensional limiter of TVD type is employed to constrain the local characteristic variables for the continuous gas phase and conservative fluxes for a suspension of solid particles. Special emphasis is laid on the efficient computation of steady state solutions at arbitrary Mach numbers. To avoid stability restrictions and convergence problems, the characteristic boundary conditions are imposed weakly and treated in a fully implicit manner. A two-way coupling via the interphase drag force is implemented using operator splitting. The Douglas–Rachford scheme is found to provide a robust treatment of the interphase exchange terms within the framework of a fractional-step solution strategy. Two-dimensional simulation results are presented for a moving shock wave and for a steady nozzle flow

Recent advances in the simulation of particle-laden flows

A substantial number of algorithms exists for the simulation of moving particles suspended in fluids. However, finding the best method to address a particular physical problem is often highly non-trivial and depends on the properties of the particles and the involved fluid(s) together. In this report we provide a short overview on a number of existing simulation methods and provide two state of the art examples in more detail. In both cases, the particles are described using a Discrete Element Method (DEM). The DEM solver is usually coupled to a fluid-solver, which can be classified as grid-based or mesh-free (one example for each is given). Fluid solvers feature different resolutions relative to the particle size and separation. First, a multicomponent lattice Boltzmann algorithm (mesh-based and with rather fine resolution) is presented to study the behavior of particle stabilized fluid interfaces and second, a Smoothed Particle Hydrodynamics implementation (mesh-free, meso-scale resolution, similar to the particle size) is introduced to highlight a new player in the field, which is expected to be particularly suited for flows including free surfaces.Comment: 16 pages, 4 figure

Computational analysis of performance deterioration of a wind turbine blade strip subjected to environmental erosion

Wind-turbine blade rain and sand erosion, over long periods of time, can degrade the aerodynamic performance and therefore the power production. Computational analysis of the erosion can help engineers have a better understanding of the maintenance and protection requirements. We present an integrated method for this class of computational analysis. The main components of the method are the streamline-upwind/Petrov–Galerkin (SUPG) and pressure-stabilizing/Petrov–Galerkin (PSPG) stabilizations, a finite element particle-cloud tracking method, an erosion model based on two time scales, and the solid-extension mesh moving technique (SEMMT). The turbulent-flow nature of the analysis is handled with a Reynolds-averaged Navier–Stokes model and SUPG/PSPG stabilization, the particle-cloud trajectories are calculated based on the computed flow field and closure models defined for the turbulent dispersion of particles, and one-way dependence is assumed between the flow and particle dynamics. Because the geometry update due to the erosion has a very long time scale compared to the fluid–particle dynamics, the update takes place in a sequence of “evolution steps” representing the impact of the erosion. A scale-up factor, calculated in different ways depending on the update threshold criterion, relates the erosions and particle counts in the evolution steps to those in the fluid–particle simulation. As the blade geometry evolves, the mesh is updated with the SEMMT. We present computational analysis of rain and sand erosion for a wind-turbine blade strip, including a case with actual rainfall data and experimental aerodynamic data for eroded airfoil geometries

Inertial Coupling Method for particles in an incompressible fluctuating fluid

We develop an inertial coupling method for modeling the dynamics of point-like 'blob' particles immersed in an incompressible fluid, generalizing previous work for compressible fluids. The coupling consistently includes excess (positive or negative) inertia of the particles relative to the displaced fluid, and accounts for thermal fluctuations in the fluid momentum equation. The coupling between the fluid and the blob is based on a no-slip constraint equating the particle velocity with the local average of the fluid velocity, and conserves momentum and energy. We demonstrate that the formulation obeys a fluctuation-dissipation balance, owing to the non-dissipative nature of the no-slip coupling. We develop a spatio-temporal discretization that preserves, as best as possible, these properties of the continuum formulation. In the spatial discretization, the local averaging and spreading operations are accomplished using compact kernels commonly used in immersed boundary methods. We find that the special properties of these kernels make the discrete blob a particle with surprisingly physically-consistent volume, mass, and hydrodynamic properties. We develop a second-order semi-implicit temporal integrator that maintains discrete fluctuation-dissipation balance, and is not limited in stability by viscosity. Furthermore, the temporal scheme requires only constant-coefficient Poisson and Helmholtz linear solvers, enabling a very efficient and simple FFT-based implementation on GPUs. We numerically investigate the performance of the method on several standard test problems...Comment: Contains a number of corrections and an additional Figure 7 (and associated discussion) relative to published versio

Numerical simulation of compressible multiphase flows

The present work is motivated by the pervasive nature of compressible multiphase flow in practical applications. These flows often feature particles (i.e. solid particles, droplets or bubbles) and develop rich dynamics as particles interact with different flow features such as shock waves. These interactions present unique challenges for numerical methods. The underlying primary motivation is to judiciously exploit shock-particle interaction in different flow topology, e.g. in gas-solid and gas-liquid systems, with proper and efficient methods. In the first part, the interaction of shock wave with a particle cloud in dense gas-solid regime is investigated through a particle resolved direct numerical simulation to quantify the unsteadiness and velocity fluctuations, arising from this interaction, in the particle cloud and the wake behind that. This investigation is performed using a Particle-Resolved Direct Numerical Simulation (PR-DNS) by solving the compressible Navier-Stokes equations coupled with a compressible Immersed Boundary Method (IBM), to account for the particles, in the Parallel Adaptive Wavelet-Collocation Method (PAWCM) framework. The PAWCM is a finite difference framework that uses wavelets to dynamically adapt the grid used to represent the solution, which minimizes the overall computational cost and allows larger simulations to be performed. The quantification is performed in three steps. First the simulation of simplified case of the shock interaction with a transverse array of particles is performed to reveal the source of unsteadiness under the wave-wave and wave wake interaction of the neighboring particles and introduce the dilatation effect arise over the particle wake. Then the interaction of the shock wave with the particle cloud is investigated to replicate the experimental canonical multiphase shock tube problem of Wagner et al. (2011). The budget of the vorticity equation explains the sources of strong unsteadiness in the particle cloud that previously was observed by Regele et. al (2014). In the third step the particle cloud is exposed to a compression wave that gradually introduce the flow. A detailed analysis of the velocity fluctuation and kinetic energy in the fluctuating motion is performed for both cases to ascertain the importance of the velocity fluctuations that arise from the strong unsteadiness in the shock induced case. In the second part, a finite difference solver is developed for Parallel adaptive Wavelet Collocation method framework to investigate high-speed compressible gas-liquid flows with surface tension effects. This study is motivated by gaining deeper insight into the process of fuel atomization in a supersonic cross flow of supersonic combustors under the startup conditions. The solver is developed based on the five equation interface capturing scheme by solving compressible multiphase/multicomponent Navier-Stokes equations along with an advection equation for the material interface. An interface capturing scheme is applied to counter the numerical diffusion induced by shock capturing scheme and maintain the immiscibility condition at the material interface. The capillary force is modeled using a continuous surface approach. The gas phase is modeled as an ideal gas and the liquid phase is modeled using a stiffened-gas equation of state. Capability of the model is demonstrated by several one and two dimensional benchmark problem. In the third part a finite volume shock/interface capturing scheme is developed for two phase flows based on the extension of single phase all-speed simple low-dissipation AUSM (SLAU) scheme. SLAU is the latest version of the AUSM-family schemes with a new numerical flux function which features low dissipation without any tunable parameters in low Mach number regimes while maintaining the robustness of AUSM-family fluxes at high Mach numbers with a very simple formulation. To demonstrate the accuracy of the method, it has been tested on the well known two-fluid air/water flow benchmark problems and the results were compared with the two-phase AUSM+ and AUSM+-up schemes. Finally the scheme was applied for the problem of shock particle cloud interaction to solve the phasic averaged governing equations along with the k-ϵ model to attempt modeling the unclosed terms

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

An interface capturing method for liquid-gas flows at low-Mach number

Multiphase, compressible and viscous flows are of crucial importance in a wide range of scientific and engineering problems. Despite the large effort paid in the last decades to develop accurate and efficient numerical techniques to address this kind of problems, current models need to be further improved to address realistic applications. In this context, we propose a numerical approach to the simulation of multiphase, viscous flows where a compressible and an incompressible phase interact in the low-Mach number regime. In this frame, acoustics is neglected but large density variations of the compressible phase can be accounted for as well as heat transfer, convection and diffusion processes. The problem is addressed in a fully Eulerian framework exploiting a low-Mach number asymptotic expansion of the Navier-Stokes equations. A Volume of Fluid approach (VOF) is used to capture the liquid-gas interface, built on top of a massive parallel solver, second order accurate both in time and space. The second-order-pressure term is treated implicitly and the resulting pressure equation is solved with the eigenexpansion method employing a robust and novel formulation. We provide a detailed and complete description of the theoretical approach together with information about the numerical technique and implementation details. Results of benchmarking tests are provided for five different test cases