A direct comparison of particle-resolved and point-particle methods in decaying turbulence

2018 ◽  
Vol 850 ◽  
pp. 336-369 ◽  
Author(s):  
M. Mehrabadi ◽  
J. A. K. Horwitz ◽  
S. Subramaniam ◽  
A. Mani
Keyword(s):  
Numerical Simulation ◽  
Particle Acceleration ◽  
Direct Numerical Simulation ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Point Particle ◽  
Particle Methods ◽  
Particle Model ◽  
Second Moment ◽  
Acceleration Model

We use particle-resolved direct numerical simulation (PR-DNS) as a model-free physics-based numerical approach to validate particle acceleration modelling in gas-solid suspensions. To isolate the effect of the particle acceleration model, we focus on point-particle direct numerical simulation (PP-DNS) of a collision-free dilute suspension with solid-phase volume fraction $\unicode[STIX]{x1D719}=0.001$ in a decaying isotropic turbulent particle-laden flow. The particle diameter $d_{p}$ in the suspension is chosen to be the same as the initial Kolmogorov length scale $\unicode[STIX]{x1D702}_{0}$ ($d_{p}/\unicode[STIX]{x1D702}_{0}=1$) in order to overlap with the regime where PP-DNS is valid. We assess the point-particle acceleration model for two different particle Stokes numbers, $St_{\unicode[STIX]{x1D702}}=1$ and 100. For the high Stokes number case, the Stokes drag model for particle acceleration under-predicts the true particle acceleration. In addition, second moment quantities which play key roles in the physical evolution of the gas–solid suspension are not correctly captured. Considering finite Reynolds number corrections to the acceleration model improves the prediction of the particle acceleration probability density function and second moment statistics of the point-particle model compared with the particle-resolved simulation. We also find that accounting for the undisturbed fluid velocity in the acceleration model can be of greater importance than using the most appropriate acceleration model for a given physical problem.

scholarly journals Flow topologies in bubble-induced turbulence: a direct numerical simulation analysis

2018 ◽  
Vol 857 ◽  
pp. 270-290 ◽  
Author(s):  
Josef Hasslberger ◽  
Markus Klein ◽  
Nilanjan Chakraborty
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Turbulent Flows ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Small Scale ◽  
Flow Topology ◽  
Two Phase ◽  
Local Flow ◽  
Interface Curvature

This paper presents a detailed investigation of flow topologies in bubble-induced two-phase turbulence. Two freely moving and deforming air bubbles that have been suspended in liquid water under counterflow conditions have been considered for this analysis. The direct numerical simulation data considered here are based on the one-fluid formulation of the two-phase flow governing equations. To study the development of coherent structures, a local flow topology analysis is performed. Using the invariants of the velocity gradient tensor, all possible small-scale flow structures can be categorized into two nodal and two focal topologies for incompressible turbulent flows. The volume fraction of focal topologies in the gaseous phase is consistently higher than in the surrounding liquid phase. This observation has been argued to be linked to a strong vorticity production at the regions of simultaneous high fluid velocity and high interface curvature. Depending on the regime (steady/laminar or unsteady/turbulent), additional effects related to the density and viscosity jump at the interface influence the behaviour. The analysis also points to a specific term of the vorticity transport equation as being responsible for the induction of vortical motion at the interface. Besides the known mechanisms, this term, related to surface tension and gradients of interface curvature, represents another potential source of turbulence production that lends itself to further investigation.

scholarly journals Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres

2016 ◽  
Vol 796 ◽  
pp. 40-85 ◽  
Author(s):  
A. W. Vreman
Keyword(s):  
Numerical Simulation ◽  
Kinetic Energy ◽  
Direct Numerical Simulation ◽  
Velocity Gradient ◽  
Dissipation Rate ◽  
Point Particle ◽  
Turbulence Kinetic Energy ◽  
Spherical Particles ◽  
Particle Model ◽  
Particle Simulations

A statistically stationary homogeneous isotropic turbulent flow modified by 64 small fixed non-Stokesian spherical particles is considered. The particle diameter is approximately twice the Kolmogorov length scale, while the particle volume fraction is 0.001. The Taylor Reynolds number of the corresponding unladen flow is 32. The particle-laden flow has been obtained by a direct numerical simulation based on a discretization of the incompressible Navier–Stokes equations on 64 spherical grids overset on a Cartesian grid. The global (space- and time-averaged) turbulence kinetic energy is attenuated by approximately 9 %, which is less than expected. The turbulence dissipation rate on the surfaces of the particles is enhanced by two orders of magnitude. More than 5 % of the total dissipation occurs in only 0.1 % of the flow domain. The budget of the turbulence kinetic energy has been computed, as a function of the distance to the nearest particle centre. The budget illustrates how energy relatively far away from particles is transported towards the surfaces of the particles, where it is dissipated by the (locally enhanced) turbulence dissipation rate. The energy flux towards the particles is dominated by turbulent transport relatively far away from particles, by viscous diffusion very close to the particles, and by pressure diffusion in a significant region in between. The skewness and flatness factors of the pressure, velocity and velocity gradient have also been computed. The global flatness factor of the longitudinal velocity gradient, which characterizes the intermittency of small scales, is enhanced by a factor of six. In addition, several point-particle simulations based on the Schiller–Naumann drag correlation have been performed. A posteriori tests of the point-particle simulations, comparisons in which the particle-resolved results are regarded as the standard, show that, in this case, the point-particle model captures both the turbulence attenuation and the fraction of the turbulence dissipation rate due to particles reasonably well, provided the (arbitrary) size of the fluid volume over which each particle force is distributed is suitably chosen.

scholarly journals Shock interaction with a deformable particle: Direct numerical simulation and point-particle modeling

2013 ◽  
Vol 113 (1) ◽  
pp. 013504 ◽  
Author(s):  
Y. Ling ◽  
A. Haselbacher ◽  
S. Balachandar ◽  
F. M. Najjar ◽  
D. S. Stewart
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Point Particle ◽  
Shock Interaction ◽  
Particle Modeling ◽  
Deformable Particle

Direct Numerical Simulation of Particle Heat and Mass Transfer in a Fluidized Bed

2014 ◽  
Author(s):  
Zhi-Gang Feng ◽  
Adam Roig
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Fluidized Bed ◽  
Immersed Boundary Method ◽  
Fluid Velocity ◽  
Temperature Fields ◽  
Immersed Boundary ◽  
Boundary Method ◽  
Study Heat Transfer

We have developed a Direct Numerical Simulation combined with the Immersed Boundary method (DNS-IB) to study heat transfer in particulate flows. In this method, fluid velocity and temperature fields are obtained by solving the modified momentum and heat transfer equations, which result from the presence of heated particles in the fluid; particles are tracked individually and their velocities and positions are solved based on the equations of linear and angular motions; particle temperature is assumed to be a constant. The momentum and heat exchanges between a particle and the surrounding fluid at its surface are resolved using the immersed boundary method with the direct forcing scheme. The DNS-IB method has been used to study heat transfer of 1024 of heated spheres in a fluidized bed. By exploring the rich data generated from the DNS-IB simulations, we are able to obtain statistically averaged fluid and particle velocity as well as overall heat transfer rate in a fluidized bed.

Direct numerical simulation of a turbulent core-annular flow with water-lubricated high viscosity oil in a vertical pipe

2018 ◽  
Vol 849 ◽  
pp. 419-447 ◽  
Author(s):  
Kiyoung Kim ◽  
Haecheon Choi
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Pipe Flow ◽  
Annular Flow ◽  
Volume Fraction ◽  
Phase Interface ◽  
High Viscosity ◽  
Vertical Pipe ◽  
The Core ◽  
High Viscosity Oil

The characteristics of a turbulent core-annular flow with water-lubricated high viscosity oil in a vertical pipe are investigated using direct numerical simulation, in conjunction with a level-set method to track the phase interface between oil and water. At a given mean wall friction ($Re_{\unicode[STIX]{x1D70F}}=u_{\unicode[STIX]{x1D70F}}R/\unicode[STIX]{x1D708}_{w}=720$, where $u_{\unicode[STIX]{x1D70F}}$ is the friction velocity, $R$ is the pipe radius and $\unicode[STIX]{x1D708}_{w}$ is the kinematic viscosity of water), the total volume flow rate of a core-annular flow is similar to that of a turbulent single-phase pipe flow of water, indicating that water lubrication is an effective tool to transport high viscosity oil in a pipe. The high viscosity oil flow in the core region is almost a plug flow due to its high viscosity, and the water flow in the annular region is turbulent except for the case of large oil volume fraction (e.g. 0.91 in the present study). With decreasing oil volume fraction, the mean velocity profile in the annulus becomes more like that of turbulent pipe flow, but the streamwise evolution of vortical structures is obstructed by the phase interface wave. In a reference frame moving with the core velocity, water is observed to be trapped inside the wave valley in the annulus, and only a small amount of water runs through the wave crest. The phase interface of the core-annular flow consists of different streamwise and azimuthal wavenumber components for different oil holdups. The azimuthal wavenumber spectra of the phase interface amplitude have largest power at the smallest wavenumber whose corresponding wavelength is the pipe circumference, while the streamwise wavenumber having the largest power decreases with decreasing oil volume fraction. The overall convection velocity of the phase interface is slightly lower than the core velocity. Finally, we suggest a predictive oil holdup model by defining the displacement thickness in the annulus and considering the boundary layer characteristics of water flow. This model predicts the variation of the oil holdup with the superficial velocity ratio very well.

Stochastic Lagrangian model for hydrodynamic acceleration of inertial particles in gas–solid suspensions

2016 ◽  
Vol 788 ◽  
pp. 695-729 ◽  
Author(s):  
Sudheer Tenneti ◽  
Mohammad Mehrabadi ◽  
Shankar Subramaniam
Keyword(s):  
Particle Acceleration ◽  
Particle Velocity ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Density Ratio ◽  
Granular Temperature ◽  
Solid Flow ◽  
Acceleration Model ◽  
The Mean ◽  
Solid Suspensions

The acceleration of an inertial particle in a gas–solid flow arises from the particle’s interaction with the gas and from interparticle interactions such as collisions. Analytical treatments to derive a particle acceleration model are difficult outside the Stokes flow regime, but for moderate Reynolds numbers (based on the mean slip velocity between gas and particles) particle-resolved direct numerical simulation (PR-DNS) is a viable tool for model development. In this study, PR-DNS of freely-evolving gas–solid suspensions are performed using the particle-resolved uncontaminated-fluid reconcilable immersed-boundary method (PUReIBM) that has been extensively validated in previous studies. Analysis of the particle velocity variance (granular temperature) equation in statistically homogeneous gas–solid flow shows that a straightforward extension of a class of mean particle acceleration models (drag laws) to their corresponding instantaneous versions, by replacing the mean particle velocity with the instantaneous particle velocity, predicts a granular temperature that decays to zero, which is at variance with the steady particle granular temperature that is obtained from PR-DNS. Fluctuations in particle velocity and particle acceleration (and their correlation) are important because the particle acceleration–velocity covariance governs the evolution of the particle velocity variance (characterized by the particle granular temperature), which plays an important role in the prediction of the core annular structure in riser flows. The acceleration–velocity covariance arising from hydrodynamic forces can be decomposed into source and dissipation terms that appear in the granular temperature evolution equation, and these have already been quantified in the Stokes flow regime using a combination of kinetic theory closure and multipole expansion simulations. From PR-DNS data we show that the fluctuations in the particle acceleration that are aligned with fluctuations in the particle velocity give rise to a source term in the granular temperature evolution equation. This approach is used to quantify the hydrodynamic source and dissipation terms of granular temperature from PR-DNS results for freely-evolving gas–solid suspensions that are performed over a wide range of solid volume fraction ($0.1\leqslant {\it\phi}\leqslant 0.4$), Reynolds number based on the slip velocity between the solid and the fluid phase ($10\leqslant \mathit{Re}_{m}\leqslant 100$) and solid-to-fluid density ratio ($100\leqslant {\it\rho}_{p}/{\it\rho}_{f}\leqslant 2000$). The straightforward extension of drag law models does not give rise to any source in the granular temperature due to hydrodynamic effects. This motivates the development of better Lagrangian particle acceleration models that can be used in Lagrangian–Eulerian formulations of gas–solid flow. It is found that a Langevin equation for the increment in the particle velocity reproduces PR-DNS results for the stationary particle velocity autocorrelation in freely-evolving suspensions. Based on the data obtained from the simulations, the functional dependence of the Langevin model coefficients on solid volume fraction, Reynolds number and solid-to-fluid density ratio is obtained. This new Lagrangian particle acceleration model reproduces the correct steady granular temperature and can also be adapted to gas–solid flow computations using Eulerian moment equations.

Sign in / Sign up

Export Citation Format

Share Document