Investigating Multiphase Turbulence Statistics of Large-Scale Two-Way Coupled Gravity-Driven Flows

2014 ◽  
Author(s):  
Jesse Capecelatro ◽  
Olivier Desjardins ◽  
Rodney O. Fox
Keyword(s):  
Kinetic Energy ◽  
Kinetic Theory ◽  
Turbulent Kinetic Energy ◽  
Particle Velocity ◽  
Volume Fraction ◽  
Constitutive Relations ◽  
Granular Temperature ◽  
Particle Phase ◽  
Simulation Results ◽  
Filtering Approach

Starting from the kinetic theory (KT) model for monodisperse granular flow, the exact Reynolds-average (RA) equations were recently derived for the particle phase in a collisional gas-particle flow by Fox [1]. The turbulence model solves for the RA particle volume fraction, the phase-average (PA) particle velocity, the PA granular temperature, and the PA particle turbulent kinetic energy (TKE). A clear distinction is made between the PA granular temperature, which appears in the kinetic theory constitutive relations, and the particle-phase turbulent kinetic energy, which appears in the turbulent transport coefficients. Mesoscale direct numerical simulation (DNS) can be used to assess the validity of the closures proposed for the unclosed terms that arise due to nonlinearities in the hydrodynamic model. In order to extract meaningful statistics from simulation results, a separation of length scales must be established to distinguish between the PA particle TKE and the PA granular temperature. In this work, we introduce an adaptive spatial filter with an averaging volume that varies with the local particle-phase volume fraction. This filtering approach ensures sufficient particle sample sizes in order to obtain meaningful statistics while remaining small enough to avoid capturing variations in the mesoscopic particle field. Two-point spatial correlations are computed to assess the validity of the filter in extracting meaningful statistics. The filtering approach is applied to fully-developed cluster-induced turbulence (CIT), where the production of fluid-phase kinetic energy results entirely from momentum coupling with finite-size inertial particles. Simulation results show a strong correlation between the local volume fraction and granular temperature, with maximum values located just upstream of clusters (i.e., where maximum compressibility of the particle velocity field exists), and negligible particle agitation is observed within clusters.

Effects of surface roughness on self-excited cavitating water jet intensity in the organ-pipe nozzle: Numerical simulations and experimental results

2019 ◽  
Vol 33 (27) ◽  
pp. 1950324
Author(s):  
Xiangdong Han ◽  
Yong Kang ◽  
Deng Li ◽  
Weiguo Zhao
Keyword(s):  
Numerical Simulation ◽  
Surface Roughness ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Energy Intensity ◽  
Volume Fraction ◽  
Water Jet ◽  
The Self ◽  
Simulation Results ◽  
Organ Pipe

This study was conducted to investigate effects of surface roughness on self-excited cavitating water jet intensity in an organ-pipe nozzle. Roughness average (Ra) values are 0.8, 1.6, 3.2, 6.3, 12.5, and 25 [Formula: see text]m, respectively. Numerical simulation results indicate that at inlet pressure of 10 MPa, the maximum, minimum, and real-time pressures in the self-excited oscillation chamber reach their respective peak values. The turbulent kinetic energy intensity in the external flow region is also most intense at this point, the vapor volume fraction in orifice is the highest, the vortex distribution scope in the orifice is the largest under [Formula: see text], and the self-excited cavitating water jet intensity is the strongest. The opposite variations emerge at [Formula: see text] compared to those of [Formula: see text], where the intensity is weakest. Pressure varies only slightly as Ra varies from 0.8 [Formula: see text]m to 6.3 [Formula: see text]m. Turbulent kinetic energy intensity behaves similarly as Ra increases from 0.8 [Formula: see text]m to 3.2 [Formula: see text]m. At [Formula: see text], it was weaker than at Ra = 0.8–3.2 [Formula: see text]m. Similarly, there are only slight differences in vapor volume fraction and vortex distribution scope with Ra from 0.8 [Formula: see text]m to 6.3 [Formula: see text]m. The intensities at Ra = 0.8–3.2 [Formula: see text]m are similar, and weaker at Ra = 6.3 [Formula: see text]m. Pressure values are maximal at inlet pressure of 20 MPa, turbulent kinetic energy intensity is most intense, vapor volume fraction is highest, vortex distribution scope is largest under [Formula: see text] [Formula: see text]m, and intensity is strongest. Distinctions among pressure, turbulent kinetic energy intensity, vapor volume fraction, and vortex distribution scope values with Ra from 0.8 [Formula: see text]m to 3.2 [Formula: see text]m are slight. Differences in the corresponding intensities are also slight; all decrease with Ra from 12.5 [Formula: see text]m to 25 [Formula: see text]m as the intensity gradually weakens. Numerical simulation results were validated by comparison against corresponding experimental phenomena.

On multiphase turbulence models for collisional fluid–particle flows

2014 ◽  
Vol 742 ◽  
pp. 368-424 ◽  
Author(s):  
Rodney O. Fox
Keyword(s):  
Kinetic Energy ◽  
Hydrodynamic Model ◽  
Volume Fraction ◽  
Turbulence Models ◽  
Fluid Particle ◽  
Granular Temperature ◽  
Particle Phase ◽  
Phase Volume ◽  
Phase Volume Fraction ◽  
Particle Flows

AbstractStarting from a kinetic theory (KT) model for monodisperse granular flow, the exact Reynolds-averaged (RA) equations are derived for the particle phase in a collisional fluid–particle flow. The corresponding equations for a constant-density fluid phase are derived from a model that includes drag and buoyancy coupling with the particle phase. The fully coupled macroscale/hydrodynamic model, rigorously derived from a kinetic equation for the particles, is written in terms of the particle-phase volume fraction, the particle-phase velocity and the granular temperature (or total granular energy). As derived from the hydrodynamic model, the RA turbulence model solves for the RA particle-phase volume fraction, the phase-averaged (PA) particle-phase velocity, the PA granular temperature and the PA turbulent kinetic energy of the particle phase. Thus, unlike in most previous derivations of macroscale turbulence models for moderately dense granular flows, a clear distinction is made between the PA granular temperature $\Theta _\textit {p}$, which appears in the KT constitutive relations, and the particle-phase turbulent kinetic energy $k_\textit {p}$, which appears in the turbulent transport coefficients. The exact RA equations contain unclosed terms due to nonlinearities in the hydrodynamic model and we briefly discuss the available closures for these terms. Finally, we demonstrate by comparing model predictions with direct numerical simulation results that even for non-collisional fluid–particle flows it is necessary to provide separate models for $\Theta _\textit {p}$ and $k_\textit {p}$ in order to correctly account for the effect of the particle Stokes number and mass loading.

scholarly journals A New Method to Determine the Impact of Individual Field Quantities on Cycle-to-Cycle Variations in a Spark-Ignited Gas Engine

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4136
Author(s):  
Clemens Gößnitzer ◽  
Shawn Givler
Keyword(s):  
Kinetic Energy ◽  
Flow Field ◽  
Turbulent Kinetic Energy ◽  
Negative Impact ◽  
Operating Conditions ◽  
Engine Operation ◽  
Gas Engine ◽  
Cycle Simulation ◽  
Simulation Results ◽  
The Impact

Cycle-to-cycle variations (CCV) in spark-ignited (SI) engines impose performance limitations and in the extreme limit can lead to very strong, potentially damaging cycles. Thus, CCV force sub-optimal engine operating conditions. A deeper understanding of CCV is key to enabling control strategies, improving engine design and reducing the negative impact of CCV on engine operation. This paper presents a new simulation strategy which allows investigation of the impact of individual physical quantities (e.g., flow field or turbulence quantities) on CCV separately. As a first step, multi-cycle unsteady Reynolds-averaged Navier–Stokes (uRANS) computational fluid dynamics (CFD) simulations of a spark-ignited natural gas engine are performed. For each cycle, simulation results just prior to each spark timing are taken. Next, simulation results from different cycles are combined: one quantity, e.g., the flow field, is extracted from a snapshot of one given cycle, and all other quantities are taken from a snapshot from a different cycle. Such a combination yields a new snapshot. With the combined snapshot, the simulation is continued until the end of combustion. The results obtained with combined snapshots show that the velocity field seems to have the highest impact on CCV. Turbulence intensity, quantified by the turbulent kinetic energy and turbulent kinetic energy dissipation rate, has a similar value for all snapshots. Thus, their impact on CCV is small compared to the flow field. This novel methodology is very flexible and allows investigation of the sources of CCV which have been difficult to investigate in the past.

Development and Validation of a Porous Medium Computational Fluid Dynamics Model for a Jet

2008 ◽  
Author(s):  
Timothy J. Drzewiecki ◽  
Brian L. Mount ◽  
Martin Lopez de Bertodano
Keyword(s):  
Porous Medium ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Transport Model ◽  
Constitutive Relations ◽  
Symmetric Domain ◽  
Jet Mixing ◽  
Negative Reactivity ◽  
An Array Of Cylinders ◽  
Development And Validation

The fast boron shutdown injection in a PHWR consists of a jet flowing through a very large moderator tank that contains an array of cylindrical coolant channels. The accurate prediction of the turbulent jet mixing is required to determine an accurate distribution of boron inside the moderator tank to model the insertion of negative reactivity into the reactor during fast shutdown. A CFD code is used to determine the distribution of boron in the moderator tank. The flow is analyzed with a porous medium model based on volume averaged momentum, turbulent kinetic energy, and turbulence dissipation equations. The additional source terms arise due to the averaging must be constituted. The constitutive relations that are implemented in the present model are: (i) the drag force on an array of cylinders for the momentum equations and (ii) the additional mixing effect of the cylinders which results in the sources of turbulent kinetic energy and turbulence dissipation transport model. The CFD analysis is performed on a porous, axis symmetric domain. The CFD results are finally compared with data for the boron concentration distribution obtained in a scaled geometrically similar experiment, demonstrating the validity of the approach.

Pseudo-turbulent gas-phase velocity fluctuations in homogeneous gas–solid flow: fixed particle assemblies and freely evolving suspensions

2015 ◽  
Vol 770 ◽  
pp. 210-246 ◽  
Author(s):  
M. Mehrabadi ◽  
S. Tenneti ◽  
R. Garg ◽  
S. Subramaniam
Keyword(s):  
Kinetic Energy ◽  
Phase Velocity ◽  
Turbulent Kinetic Energy ◽  
Gas Phase ◽  
Reynolds Stress ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Velocity Fluctuations ◽  
The Mean ◽  
Particle Assemblies

Gas-phase velocity fluctuations due to mean slip velocity between the gas and solid phases are quantified using particle-resolved direct numerical simulation. These fluctuations are termed pseudo-turbulent because they arise from the interaction of particles with the mean slip even in ‘laminar’ gas–solid flows. The contribution of turbulent and pseudo-turbulent fluctuations to the level of gas-phase velocity fluctuations is quantified in initially ‘laminar’ and turbulent flow past fixed random particle assemblies of monodisperse spheres. The pseudo-turbulent kinetic energy $k^{(f)}$ in steady flow is then characterized as a function of solid volume fraction ${\it\phi}$ and the Reynolds number based on the mean slip velocity $\mathit{Re}_{m}$. Anisotropy in the Reynolds stress is quantified by decomposing it into isotropic and deviatoric parts, and its dependence on ${\it\phi}$ and $Re_{m}$ is explained. An algebraic stress model is proposed that captures the dependence of the Reynolds stress on ${\it\phi}$ and $Re_{m}$. Gas-phase velocity fluctuations in freely evolving suspensions undergoing elastic and inelastic particle collisions are also quantified. The flow corresponds to homogeneous gas–solid systems, with high solid-to-gas density ratio and particle diameter greater than dissipative length scales. It is found that for the parameter values considered here, the level of pseudo-turbulence differs by only 15 % from the values for equivalent fixed beds. The principle of conservation of interphase turbulent kinetic energy transfer is validated by quantifying the interphase transfer terms in the evolution equations of kinetic energy for the gas-phase and solid-phase fluctuating velocity. It is found that the collisional dissipation is negligible compared with the viscous dissipation for the cases considered in this study where the freely evolving suspensions attain a steady state starting from an initial condition where the particles are at rest.

Development of Venturi-Tube With Spiral-Shaped Fin for Water Treatment

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Dong Ho Shin ◽  
Yeonghyeon Gim ◽  
Dong Kee Sohn ◽  
Han Seo Ko
Keyword(s):  
Water Treatment ◽  
Numerical Analysis ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Volume Fraction ◽  
Volume Flow Rate ◽  
Numerical Data ◽  
The Body ◽  
Venturi Tube ◽  
Type Water

Detailed numerical data were presented for the development of a venturi-type water purifier which had a cavitation nozzle to enhance turbulent kinetic energy and vapor volume fraction. Numerical analysis for cavitation was conducted in multiphase flow using the software, cfx. The numerical method used in this study was verified by the experimental data of pressure distribution in tube and the observation of cavitation from previous studies. From the result of the numerical analysis, a logarithmic relation between the vapor volume fraction and volume flow rate of water according to the area ratio between the throat and the entrance of a venturi-tube was derived. In addition, spiral-shaped fins were developed to enhance the turbulent kinetic energy in the body of a venturi-tube. Thus, it was confirmed that the volume fraction and turbulent kinetic energy of the developed water purifier were enhanced compared with the normal venturi-tube without the spiral-shaped fin. Finally, the improved water treatment performance of the advanced design of the venturi-tube was confirmed by the removal test of the representative solutions.

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.

Study on the Rheology of Foam Fracturing Fluid with Mixture Model

2012 ◽  
Vol 512-515 ◽  
pp. 1747-1752 ◽  
Author(s):  
Xiao Sun ◽  
Shu Zhong Wang ◽  
You Lian Lu
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Gas Phase ◽  
Mixture Model ◽  
Turbulent Viscosity ◽  
Bubble Diameter ◽  
Fracturing Fluid ◽  
Viscosity Increase ◽  
Change Trend ◽  
Simulation Results

Numerical simulation study on the rheology or foam fluid was carried through by treating inner phase as granular fluid with mixture model. The simulation results show that the gas phase is well distributed on cross-section. Besides, the higher the foam quality, the higher the velocity gradient near the wall. For turbulent properties, the turbulent kinetic energy and viscosity increase as the foam quality increases. With the same foam quality, the bigger the bubble diameter, the higher the turbulent viscosity and turbulent kinetic energy. What’s more, the foam quality 63% is a catastrophe point at which the rheology of foam fracturing fluid changes sharply. The change trend of turbulent viscosity along radial direction is different between the regions where the foam quality is below and over catastrophe point, and in the latter the change trend is flatter. From the simulation results it can be seen that the mixture model is more applicable and effective to the region where foam quality is over 63%.

Direct numerical simulation of turbulence modulation by particles in compressible isotropic turbulence

2017 ◽  
Vol 832 ◽  
pp. 438-482 ◽  
Author(s):  
Qi Dai ◽  
Kun Luo ◽  
Tai Jin ◽  
Jianren Fan
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Rotational Motion ◽  
Isotropic Turbulence ◽  
Volume Fraction ◽  
Stokes Number ◽  
Systematic Investigation ◽  
Turbulence Modulation ◽  
Physical Mechanisms ◽  
Preferential Concentration

In this paper, a systematic investigation of turbulence modulation by particles and its underlying physical mechanisms in decaying compressible isotropic turbulence is performed by using direct numerical simulations with the Eulerian–Lagrangian point-source approach. Particles interact with turbulence through two-way coupling and the initial turbulent Mach number is 1.2. Five simulations with different particle diameters (or initial Stokes numbers, $St_{0}$) are conducted while fixing both their volume fraction and particle densities. The underlying physical mechanisms responsible for turbulence modulation are analysed through investigating the particle motion in the different cases and the transport equations of turbulent kinetic energy, vorticity and dilatation, especially the two-way coupling terms. Our results show that microparticles ($St_{0}\leqslant 0.5$) augment turbulent kinetic energy and the rotational motion of fluid, critical particles ($St_{0}\approx 1.0$) enhance the rotational motion of fluid, and large particles ($St_{0}\geqslant 5.0$) attenuate turbulent kinetic energy and the rotational motion of fluid. The compressibility of the turbulence field is suppressed for all the cases, and the suppression is more significant if the Stokes number of particles is close to 1. The modifications of turbulent kinetic energy, the rotational motion and the compressibility are all related with the particle inertia and distributions, and the suppression of the compressibility is attributed to the preferential concentration and the inertia of particles.

On fluid–particle dynamics in fully developed cluster-induced turbulence

2015 ◽  
Vol 780 ◽  
pp. 578-635 ◽  
Author(s):  
Jesse Capecelatro ◽  
Olivier Desjardins ◽  
Rodney O. Fox
Keyword(s):  
Kinetic Energy ◽  
Volume Fraction ◽  
Finite Size ◽  
Fluid Phase ◽  
Particle Phase ◽  
Pressure Tensor ◽  
Production Term ◽  
Velocity Statistics ◽  
Gravity Driven ◽  
Momentum Coupling

At sufficient mass loading and in the presence of a mean body force (e.g. gravity), an initially random distribution of particles may organize into dense clusters as a result of momentum coupling with the carrier phase. In statistically stationary flows, fluctuations in particle concentration can generate and sustain fluid-phase turbulence, which we refer to as cluster-induced turbulence (CIT). This work aims to explore such flows in order to better understand the fundamental modelling aspects related to multiphase turbulence, including the mechanisms responsible for generating volume-fraction fluctuations, how energy is transferred between the phases, and how the cluster size distribution scales with various flow parameters. To this end, a complete description of the two-phase flow is presented in terms of the exact Reynolds-average (RA) equations, and the relevant unclosed terms that are retained in the context of homogeneous gravity-driven flows are investigated numerically. An Eulerian–Lagrangian computational strategy is used to simulate fully developed CIT for a range of Reynolds numbers, where the production of fluid-phase kinetic energy results entirely from momentum coupling with finite-size inertial particles. The adaptive filtering technique recently introduced in our previous work (Capecelatro et al., J. Fluid Mech., vol. 747, 2014, R2) is used to evaluate the Lagrangian data as Eulerian fields that are consistent with the terms appearing in the RA equations. Results from gravity-driven CIT show that momentum coupling between the two phases leads to significant differences from the behaviour observed in very dilute systems with one-way coupling. In particular, entrainment of the fluid phase by clusters results in an increased mean particle velocity that generates a drag production term for fluid-phase turbulent kinetic energy that is highly anisotropic. Moreover, owing to the compressibility of the particle phase, the uncorrelated components of the particle-phase velocity statistics are highly non-Gaussian, as opposed to systems with one-way coupling, where, in the homogeneous limit, all of the velocity statistics are nearly Gaussian. We also observe that the particle pressure tensor is highly anisotropic, and thus additional transport equations for the separate contributions to the pressure tensor (as opposed to a single transport equation for the granular temperature) are necessary in formulating a predictive multiphase turbulence model.

Sign in / Sign up

Export Citation Format

Share Document