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Accurate models of the added mass force of a uniform random distribution of spherical particles or bubbles

The added mass force resulting from the acceleration of a body in a fluid is of fundamental and practical interest in dispersed multiphase flows. Euler–Lagrange (EL) and Euler–Euler (EE) simulations require closure terms for the added mass force in order to accurately couple the conserved variables between phases. Presently, a more thorough understanding of the added mass force in a multi-particle system is developed based on potential flow resulting in a resistance matrix formulation analogous to Stokesian dynamics. This formulation is then used to generate a dataset of added mass resistance matrices for large systems of randomly generated particles. This methodology is used to create a volume fraction corrected binary model for predicting the added mass force in large systems as well as generate statistics of the added mass force in such systems. This work provides clarification to the theory of the added mass force for particle clouds, and modelling options that may be implemented in existing EL and EE codes.

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The discrete Green's function paradigm for two-way coupled Euler–Lagrange simulation

We outline a methodology for the simulation of two-way coupled particle-laden flows. The drag force that couples fluid and particle momentum depends on the undisturbed fluid velocity at the particle location, and this latter quantity requires modelling. We demonstrate that the undisturbed fluid velocity, in the low particle Reynolds number limit, can be related exactly to the discrete Green's function of the discrete Stokes equations. In addition to hydrodynamics, the method can be extended to other physics present in particle-laden flows such as heat transfer and electromagnetism. The discrete Green's functions for the Navier–Stokes equations are obtained at low particle Reynolds number in a two-plane channel geometry. We perform verification at different Reynolds numbers for a particle settling under gravity parallel to a plane wall, for different wall-normal separations. Compared with other point-particle schemes, the Stokesian discrete Green's function approach is the most robust at low particle Reynolds number, accurate at all wall-normal separations. To account for degradation in accuracy away from the wall at finite Reynolds number, we extend the present methodology to an Oseen-like discrete Green's function. The extended discrete Green's function method is found to be accurate within 6% at all wall-normal separations for particle Reynolds numbers up to 24. Furthermore, the discrete Green's function approach is well suited to dilute systems with significant mass loading and this is highlighted by comparison against other Euler–Lagrange as well as particle-resolved simulations of gas–solid turbulent channel flow. Strong particle–turbulence coupling is observed in the form of turbulence modification and turbophoresis suppression, and these observations are placed in context of the different methods.

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Particle/fluid simulations of an eruptive flare: Identifying the field-aligned currents responsible for the hard x-rays

While magnetohydrodynamics (MHD) can provide a reasonable description of the overall magnetic reconnection that is believed to drive flares, additional, and often separate processes have to be envoked to in order to explain the electron acceleration that is responsible for many of the observed flare emissions. A new model that incorporates the dynamic coronal current sheets, the reconnection site, and possible electron acceleration processes is developed through the use of two-dimensional particle and modified two-fluid simulations. The specific example of an eruptive flare driven by the coalescence of flux tubes supported by prescribed photospheric current elements is evaluated. It is shown that the electrons and ions have differential trajectories through the coronal current sheet which leads to the development of additonal plasma currents that flow around the surface of the current sheet. These surface currents are explicitly neglected in MHD but they are vital to the flare dynamics because they divert current from the coronal current sheet into the chromosphere, producing an effective resistivity that aids the development of fast reconnection. Because the surface currents are in the plane of the magnetic field, electrons in them experience strong acceleration and can account for the observed hard X-ray emissions. Model predictions are compared with observed time profiles of hard X-ray emissions and Doppler shifts seen in soft X-ray line emissions and are able to account for such features as (1) the asymmetry in the rise and decay time of the hard X-rays, (2) the apparent delay between the largest Doppler shifts and the hard X-ray peak, and (3) the relatively low intensity of the blue-shifted component. The use of particle and fluid simulations is important because it provides different, but complementary treatments of the electron acceleration, the global magnetic morphology, and the flare current system.

Winglee, R. M.↗

Merging for Particle-Mesh Complex Particle Kinetic Modeling of the Multiple Plasma Beams

We suggest a merging procedure for the Particle-Mesh Complex Particle Kinetic (PMCPK) method in case of inter-penetrating flow (multiple plasma beams). We examine the standard particle-in-cell (PIC) and the PMCPK methods in the case of particle acceleration by shock surfing for a wide range of the control numerical parameters. The plasma dynamics is described by a hybrid (particle-ion-fluid-electron) model. Note that one may need a mesh if modeling with the computation of an electromagnetic field. Our calculations use specified, time-independent electromagnetic fields for the shock, rather than self-consistently generated fields. While a particle-mesh method is a well-verified approach, the CPK method seems to be a good approach for multiscale modeling that includes multiple regions with various particle/fluid plasma behavior. However, the CPK method is still in need of a verification for studying the basic plasma phenomena: particle heating and acceleration by collisionless shocks, magnetic field reconnection, beam dynamics, etc.

Lipatov, Alexander S.↗

SHIVA (Spaceflight Holography Investigation in a Virtual Apparatus)

This paper provides the description and results of a ground-based experiment designed to support the spaceflight program SHIVA, which started its flight definition in 1998. SHIVA will apply new diagnostic tools and experimental techniques to test the validity of a newly discovered analytical solution to the general equation of motion of a particle in a fluid. We have designed a spaceflight experiment with the help of the theoretical model that is optimized for testing the model, and for measuring g, g-jitter, and other microgravity phenomena. Our ongoing, ground-based particle/fluid experiment supports both the experimental and theoretical aspects of the project. The ultimate spaceflight experiment will be similar to the ground-based experiment. The "virtual spaceflight chamber" concept asserts that certain spaceflight experiments can be recorded in holograms in such a manner that having the holograms on earth is optically equivalent to being back in space with unlimited time to conduct the experiment. Properly exploited, this concept can save a significant amount of experiment time in space by effectively bringing the. experiment optically back to earth. SHIVA will accomplish the following: record a large number of holograms of particle fields in space under controlled conditions, extract the precise, three-dimensional position of all of the particles as a function of time, examine the effects of all parameters on the motion of the particles, and test these against predictions of the Coimbra-Range1 solution to the general equation of motion. Particle sizes will range from hundreds of microns up to about 2 mm in diameter and will cover a range of densities and fluid viscosities. Forcing functions will be introduced onto the particle field, including at least the following: a) No isolation in the Spacelab vibration environment. b) Isolation from Spacelab. c) Oscillatory motion from 1 to 100 Hz with amplitudes of a few millimeters. d) Convective fields to be introduced mechanically. The first objective of this research is to understand the physics of particle interactions with fluids and other particles in low Reynolds number flows in microgravity. Secondary objectives are to: (1) observe and quantify g-jitter effects and microconvection on particles in fluids, (2) validate an exact solution to the general equation of motion of a particle in a fluid, and (3) to characterize'the ability of isolating platforms to isolate experiments containing particles in liquids.

Trolinger, James D.↗