scholarly journals Fully Correlated Stochastic Inter-Particle Collision Model for Euler–Lagrange Gas–Solid Flows

2020 ◽  
Vol 105 (4) ◽  
pp. 935-963
Author(s):  
Berend van Wachem ◽  
Thomas Curran ◽  
Fabien Evrard
Keyword(s):  
Kinetic Energy ◽  
Particle Velocity ◽  
Fluid Velocity ◽  
Spherical Particles ◽  
Particle Collision ◽  
The Real ◽  
Real Particle ◽  
Collision Partner ◽  
Particle Kinetic Energy ◽  
Fictitious Particle

AbstractIn Lagrangian stochastic collision models, a fictitious particle is generated to act as a collision partner, with a velocity correlated to the velocity of the real colliding particle. However, most often, the fluid velocity seen by this fictitious particles is not accounted for in the generation of the fictitious particle velocity, leading to a de-correlation between the fictitious particle velocity and the local fluid velocity, which, after collision, leads to an unrealistic de-correlation of the real particle velocity and the fluid velocity as seen by the particle. This de-correlation, in turn, causes a spurious decrease of the particle kinetic energy, even though the collisions are assumed perfectly elastic. In this paper, we propose a new model in which the generated fictitious particle velocity is correctly correlated to both the real particle velocity and the local fluid velocity at the particle, hence preventing the spurious loss of the total particle kinetic energy. The model is suitable for small inertial particles. Two algorithms for integrating the collision frequency are also compared to each other. The models are validated using large eddy simulation (LES) of mono-dispersed particle-laden stationary homogeneous isotropic turbulence. Simulations are conducted with spherical particles with different turbulent Stokes number, $$St_t = [0.75 - 5.8]$$ S t t = [ 0.75 - 5.8 ] , and volume fractions, $$\alpha _p = [0.014 - 0.044]$$ α p = [ 0.014 - 0.044 ] , and are compared to the results of the LES using a deterministic discrete particle simulation model.

BLOOD FLOW IN CORONARY ARTERY BIFURCATION CALCULATED BY TURBULENT FINITE ELEMENT MODEL

2021 ◽  
Author(s):  
Aleksandar Nikolić ◽  
◽  
Marko Topalović ◽  
Milan Blagojević ◽  
Vladimir Simić
Keyword(s):  
Finite Element ◽  
Blood Flow ◽  
Kinetic Energy ◽  
Finite Element Model ◽  
Fluid Velocity ◽  
Fluid Pressure ◽  
Element Model ◽  
Viscous Sublayer ◽  
Flow Problems ◽  
Analysis Of Results

Simulation of blood flow in this paper is analyzed using two-equation turbulent finite element model that can calculate values in the viscous sublayer. Implicit integration of the equations is used for determining the fluid velocity, fluid pressure, turbulence, kinetic energy, and dissipation of turbulent kinetic energy. These values are calculated in the finite element nodes for each step of incremental- iterative procedure. Developed turbulent finite element model, with the customized generation of finite element meshes, is used for calculating complex blood flow problems. Analysis of results showed that a cardiologist can use proposed tools and methods for investigating the hemodynamic conditions inside bifurcation of arteries.

Interphasial energy transfer and particle dissipation in particle-laden wall turbulence

2013 ◽  
Vol 715 ◽  
pp. 32-59 ◽  
Author(s):  
Lihao Zhao ◽  
Helge I. Andersson ◽  
Jurriaan J. J. Gillissen
Keyword(s):  
Energy Transfer ◽  
Kinetic Energy ◽  
Stokes Equations ◽  
Mechanical Energy ◽  
Wall Turbulence ◽  
Spherical Particles ◽  
Velocity Versus ◽  
Wall Region ◽  
Carrier Fluid ◽  
Stokes Force

AbstractTransfer of mechanical energy between solid spherical particles and a Newtonian carrier fluid has been explored in two-way coupled direct numerical simulations of turbulent channel flow. The inertial particles have been treated as individual point particles in a Lagrangian framework and their feedback on the fluid phase has been incorporated in the Navier–Stokes equations. At sufficiently large particle response times the Reynolds shear stress and the turbulence intensities in the spanwise and wall-normal directions were attenuated whereas the velocity fluctuations were augmented in the streamwise direction. The physical mechanisms involved in the particle–fluid interactions were analysed in detail, and it was observed that the fluid transferred energy to the particles in the core region of the channel whereas the fluid received kinetic energy from the particles in the wall region. A local imbalance in the work performed by the particles on the fluid and the work exerted by the fluid on the particles was observed. This imbalance gave rise to a particle-induced energy dissipation which represents a loss of mechanical energy from the fluid–particle suspension. An independent examination of the work associated with the different directional components of the Stokes force revealed that the dominating energy transfer was associated with the streamwise component. Both the mean and fluctuating parts of the Stokes force promoted streamwise fluctuations in the near-wall region. The kinetic energy associated with the cross-sectional velocity components was damped due to work done by the particles, and the energy was dissipated rather than recovered as particle kinetic energy. Componentwise scatter plots of the instantaneous velocity versus the instantaneous slip-velocity provided further insight into the energy transfer mechanisms, and the observed modulations of the flow field could thereby be explained.

scholarly journals Formation of Particle Real Energy in the Bicubic Equation Limiting Particle Velocity Formalism with Possible Applications to Light Dark Matter

2019 ◽  
Vol 11 (2) ◽  
pp. 92
Author(s):  
Josip Soln
Keyword(s):  
Dark Matter ◽  
Particle Velocity ◽  
Dark Matter Particle ◽  
Particle Energy ◽  
Physical Parameters ◽  
The Real ◽  
Complex Particle ◽  
Particle Parameters ◽  
Real Value ◽  
Limiting Velocity

The complex particle energy, appearing in this article, with the suggestive choices of physical parameters,is transformed simply into the real particle energy. Then with the bicubic equation limiting particle velocity formalism, one evaluates the three particle limiting velocities, $c_{1},$ $c_{2}$\ and $% c_{3},$ (primary, obscure and normal) in terms of the ordinary particle velocity, $v$, and derived positive $m_{+}=m\succ 0$ \ and negative \ $% m_{-}=-m\prec 0$ \ \ particle masses with $m_{+}^{2}=m_{-}^{2}=$ $m^{2}$. In general, the important quantity in solving this bicubic equation is the real square value $\ z^{2}(m)$ of the congruent parameter, $z(m)$, that connects real or complex value of particle energy, $E,$ and the real or complex value of particle velocity squared, $v^{2}$, $2Ez(m)=3\sqrt{3}mv^{2}$% . With real $z^{2}(m)$ one determines the real value of discriminant, $D,$ of the bicubic equation, and they together influence the connection between $% E$ and $v^{2}.$ Hence, when $z^{2}\prec 1$ and \ $D\prec 0$ one has simply that $E\gg mv^{2}$. However,with $D\succeq 0$ and $z^{2}\succeq 1$ , both $E$ and $v^{2}$ may become complex simultaneously through connecting relation $% E=3\sqrt{3}mv^{2}/2z(m)$, with their real values satisfying \ Re $E\succcurlyeq m\left( \func{Re}v^{2}\right) $, keeping, however $z^{2}$ the same and real. In this article, this new situation with $D\succeq 0$ is discussed in detail.by looking as how to adjust the particle\ parameters to have $\func{Im% }E=0$ with implication that automatically also Im$v^{2}=0.$.In fact, after having adjusted the particle\ parameters successfully this way, one simply writes Re$E=E$ and Re$v^{2}=v^{2}$. \ \ This way one arrives at that the limiting velocities satisfy $c_{1}=c_{2}$\ $\#$ $c_{3}$, which shows the degeneracy of $c_{1}$ and $c_{2}$ as the same numerical limiting velocity for two particles. This degeneracy $c_{1}$ =$c_{2}$ is simply due to the absence of $\func{Im}E$. It would start disappearing with just an infinitesimal $\func{Im}E$. Now,while $c_{1}=c_{2}$ is real, $c_{3}$ is imaginary and all of them associated with the same particle energy, $E$. With these velocity values the congruent parameter becomes quantized as $% z(m_{\pm })=3\sqrt{3}m_{\pm }v^{2}/2E=\pm 1$ which, with the bicubic discriminant $D=0$ value, implies the quantization also of the particle mass, $m,$ into $m_{\pm }=\pm m$ values . The numerically equal energies,from $E=\func{Re}E$ can be expressed as $\ \ \ \ \ \ \ \ \ \ \ $$E(c_{1,2}($ $m_{\pm }))=E(c_{3}(m_{\pm }))$ either directly in terms of $% c_{1}(m_{\pm })=c_{2}(m_{\pm })$ and $c_{3}(m_{\pm })$ or also indirectly in terms of particle velocity, $v$, as well as in the Lorentzian fixed forms with $v^{2}\#$ $c_{1}^{2},$ $c_{2}^{2}$\ or $c_{3}^{2}$ assuring different from zero mass, $m$ $\#$ $0$. At the end, with here developed formalism, one calculates for a light sterile neutrino dark matter particle, the energies associated with $m_{\pm} $ masses and $c_{1,2}$and $c_{3}$ limiting velocities.

Investigation of Particle Kinetic Energy for EKF-CMP Process

2021 ◽  
Author(s):  
Phuoc-Trai Mai ◽  
Li-Shin Lu ◽  
Chao-Chang Arthur Chen ◽  
Yu-Ming Lin
Keyword(s):  
Kinetic Energy ◽  
Particle Kinetic Energy

Analysis of Dispersion of Small Spherical Particles in a Random Velocity Field

1990 ◽  
Vol 112 (1) ◽  
pp. 114-120 ◽  
Author(s):  
H. Ounis ◽  
G. Ahmadi
Keyword(s):  
Particle Velocity ◽  
Digital Simulation ◽  
Density Ratio ◽  
Spherical Particles ◽  
Theoretical Predictions ◽  
The Mean ◽  
Analysis Of Dispersion ◽  
Gradient Effects ◽  
Analytical Expressions ◽  
Good Agreement

The equation of motion of a small spherical rigid particle in a turbulent flow field, including the Stokes drag, the Basset force, and the virtual mass effects, is considered. For an isotropic field, the lift force and the velocity gradient effects are neglected. Using the spectral method, responses of the resulting constant coefficient stochastic integrao-differential equation are studied. Analytical expressions relating the Lagrangian energy spectra of particle velocity to that of the fluid are developed and the results are used to evaluate various response statistics. Variations of the mean-square particle velocity and particle diffusivity with size, density ratio and response time are studied. The theoretical predictions are compared with the digital simulation results and the available data and good agreement is observed.

scholarly journals On a pulsatile flow of a two-phase viscous fluid in a tube of elliptic cross-section

1990 ◽  
Vol 13 (4) ◽  
pp. 669-676 ◽  
Author(s):  
A. K. Ghosh ◽  
A. R. Khan ◽  
L. Debnath
Keyword(s):  
Viscous Fluid ◽  
Cross Section ◽  
Fluid Velocity ◽  
Small Time ◽  
Spherical Particles ◽  
Elliptic Cross Section ◽  
Two Phase ◽  
Elliptic Cross ◽  
Periodic Pressure ◽  
Small Times

A study is made of an unsteady flow of an incompressible viscous fluid with embedded small inert spherical particles contained in a tube of elliptic cross-section due to a periodic pressure gradient acting along the length of the tube. The solutions for the fluid velocity and the particle velocity are obtained for large and small times. It is shown that the effect of particles on the flow is significant in the small-time solution while the large-tlme solution shows no effect of the particles on the flow.

scholarly journals Particle Velocity and Concentration Profiles in Freeboard of Gas-solid Fluidized Bed and Proposal of a New Elutriation Model with Particle Collision.

2000 ◽  
Vol 37 (3) ◽  
pp. 168-175
Author(s):  
Hiroyuki KAGE ◽  
Hidekazu OGAWA ◽  
Takaya KUWAMOTO ◽  
Takuya SHIGEHIRO ◽  
Hironao OGURA ◽  
...  
Keyword(s):  
Fluidized Bed ◽  
Particle Velocity ◽  
Particle Collision ◽  
Concentration Profiles

scholarly journals Virtual motion of real particles

2010 ◽  
Vol 650 ◽  
pp. 1-4 ◽  
Author(s):  
G. TRYGGVASON
Keyword(s):  
Kinetic Energy ◽  
Numerical Simulations ◽  
Turbulent Kinetic Energy ◽  
Multiphase Flows ◽  
Isotropic Turbulence ◽  
Finite Size ◽  
Direct Numerical Simulations ◽  
Spherical Particles ◽  
Length Scale ◽  
Turbulent Eddies

Direct numerical simulations are rapidly becoming one of the most important techniques to examine the dynamics of multiphase flows. Lucci, Ferrante & Elghobashi (J. Fluid Mech., 2010, this issue, vol. 650, pp. 5–55) address several fundamental issues for spherical particles in isotropic turbulence. They show the importance of including the finite size of the particles and discuss how particles of a size comparable to the largest length scale at which viscosity substantially affects the turbulent eddies (i.e. the Taylor microscale) always increase the dissipation of turbulent kinetic energy.

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