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Lecture 4 : Discrete Phase Model (DPM) Flipbook PDF
Lecture 4 : Discrete Phase Model (DPM)
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Lecture 04: Discrete Phase Model (DPM) ANSYS Fluent Multiphase Flow Modeling
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Outline • Particulate Flow and DPM Applications • Fundamentals of Discrete Phase Modeling (DPM) • DPM Set Up in Fluent • Post Processing • Additional physics modeling features − DDPM, DEM, Erosion-MDM 2
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Dilute Dispersed Flows with Particles and Droplets • Occur in many areas – Automotive – Power – Environmental – Health Care – Fire Protection – Consumer Products – Electronics cooling
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DPM Applications
Erosion in pipe bend
Cyclone separator Particle inhalation Spray impingement 4
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Discrete Phase Model (DPM) • Discrete Phase Model is a multiphase model in which the dispersed phase is tracked in a Lagrangian reference frame • Two different phases are defined in the DPM model: − A continuous phase and a particle phase
𝒅𝒅𝒑𝒑
• The discrete phase is modeled by the Lagrangian method • The continuous phase is modeled by the Eulerian method • The discrete and continuous phases are coupled via sources terms in the governing equations • Limiting assumption: − DPM is valid for volume fraction lower than ~0.1, where the particle phase is sufficiently dilute that particle-particle interactions and the effects of the particle volume fraction on the continuous phase can be neglected 5
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𝑼𝑼𝒒𝒒 𝑳𝑳
Additional Simplifying Assumptions in DPM
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What
Assumption
Particle Volume
Particle does not displace fluid (particle ≡ mass point) Allows to neglect particle volume fraction in continuous phase solver!
Particle Shape
Particle is a sphere Simple (center + diameter) “Shape” needed for anything requiring the particle surface (e.g. drag forces, heat-, mass transfer)
Flow in vicinity of particle
Model flow details around particle Influence of flow details modeled by appropriate (simple) assumptions
Number of particles
Concept of particle parcel Track representative number of physical particles Details later in presentation
Particle Equation of Motion • Particle position
• Particle velocity
• Particle angular velocity
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Drag Force • Particle relaxation time
• Particle relative Reynolds number
• Drag force
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Particle Trajectory • Other forces − Rotational forces − Thermophoretic force − Brownian force − Saffman’s lift force − Virtual mass force − User-defined forces
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Brownian Motion Saffman Lift
Virtual Mass
Rotational Drag and Magnus Lift Rotational drag Force
• Opposes rotational motion of particle • Correlation in Fluent ‒ Dennis et al. 5
ρf dp TRotational Drag = Cω Ω ⋅ Ω 2 2
Magnus lift force
• Particle rotation generates lift force on particle
These forces are analogous to forces arising from translational motion • Translational drag • Saffman lift WWW.GRC.NASA.GOV
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Parcel Concept • It is very expensive to track each individual particle in a particle flow system − For a typical injection, the total particle number could be in millions! • The solution: Parcel concept: Dukowicz (1980) − Each parcel contains particles with same properties: diameter,
velocity, position, and others − The behavior of each parcel is determined by the behavior of the particles inside − The number of particles in each parcel can be a fractional number
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Coupling Between Phases • One-way coupling: − DPM source term is updated − Particle motion is affected by the continuous phase − Continuous phase is not affected by the particle flow
Control volume
Particle Trajectory Mass, Momentum and Heat Exchange
• Two-way coupling: − Particles and continuous flow interact with each other − Particle motion is affected by the continuous phase − Continuous phase is in turn is affected by the particle flow
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Heat and Mass Transfer • Heat transfer
𝒅𝒅𝒅𝒅𝒑𝒑 𝒅𝒅𝒅𝒅𝒑𝒑 𝒎𝒎𝒑𝒑 𝑪𝑪𝒑𝒑 = 𝒉𝒉𝑨𝑨𝒑𝒑 𝑻𝑻∞ − 𝑻𝑻𝒑𝒑 − 𝒉𝒉𝒇𝒇𝒇𝒇 + 𝑺𝑺𝒙𝒙 𝒅𝒅𝒅𝒅 𝒅𝒅𝒅𝒅 𝟏𝟏 𝟏𝟏 𝒉𝒉𝒅𝒅𝒑𝒑 𝑵𝑵𝒖𝒖 = = 𝟐𝟐. 𝟎𝟎 + 𝟎𝟎. 𝟔𝟔𝑹𝑹𝑹𝑹𝒅𝒅 𝟐𝟐 𝑷𝑷𝑷𝑷𝟑𝟑 𝒌𝒌∞
• Mass transfer
– Due to evaporation/boiling/devolatilization/heterogeneous-reactions Particle Type Massless Inert Droplet Multi-component Combusting 13
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Heat and Mass Transfer No drag! Used for Residence Time Distribution Studies Inert Heating and Cooling Heating, Evaporation and Boiling Multi-component evaporation Heating, Devolatilization and heterogeneous reaction
Setting Initial Conditions: Injections • You will define injection(s) which will serve as a way to seed the flow with the discrete phase
Single
• FLUENT provides 11 types of injections: − − − − − − −
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Single Group Cone / Solid Cone (3D) Atomizers Surface File …
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Surface
Group
Hollow Cone
Injection Definition • Every injection definition includes:
− Particle type (inert, droplet, or combusting particle) − Material (from data base) − Initial conditions (except when read from a file)
• Combusting particles and droplets require definition of destination species • Stochastic tracking used to model turbulent dispersion − Details on next slide
• Particle rotation can be modeled
− Additional equation solved to compute torque balance on particles including • Rotational drag forces • Magnus lift force
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Incorporating Turbulence When particles enter a turbulent eddy, they try to follow it for the time they are crossing the eddy, depending on their Stokes number. This effect leads to lateral dispersion which has to be considered in modeling: – Discrete random walk model (Stochastic Tracking) • Accounts for local variations in flow properties • Requires sufficient number of tries for accurate capture of turbulent dispersion – Needed to achieve a statistically meaningful sampling – Insufficient number of tries can lead to convergence problems caused by non-smooth distribution of particle sources
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DPM Boundary Conditions • Escape – Particle leaves the flow domain.
• Trap – Particle is collected on the wall.
• Reflect – Particle bounces off the wall with user-prescribed coefficient of restitution.
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• Wall Jet – Simulates an inviscid jet of particles impacting the wall (no significant liquid film is formed on the wall).
• Wall Film – Similar to wall jet; simulates case where significant film is formed on the wall.
Effect of Particle Rotation in Fluid • Rotating particles in coupled fluid-particle simulations − Effect of Magnus (or rotational) lift force
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Effect of Particle Rotation on Particle-Wall Interaction • Particle rotation can significantly influence particle-wall interaction in confined geometries (pipes, channels, etc.) Particle velocity in flow direction
Without particle rotation Flow direction Particle velocity in flow direction
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With particle rotation
Rough Wall Model for Particles • Virtual wall replaces the real wall during the impact at the point of contact with particle Virtual Wall
γw
Dp
Real Smooth Wall
• The inclination angle γw of the virtual wall is sampled from a Gaussian distribution with 0 mean and standard deviation computed as a function of − Statistical surface roughness parameters − Particle diameter 20
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Effect of Wall Roughness • Gas-Solids Flow in a Horizontal Channel (1) − Gas Velocity 19.7 m/s, developed Flow − 100 micron glass particles − Large wall roughness
Inlet Dispersed flow
1)
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0.035 m
6m
measurement plane at 5.8 m
J. Kussin and M. Sommerfeld. Experimental studies on particle behavior and turbulence modification in horizontal channel flow, Test Case Description
Gas-Solids Flow in a Horizontal Channel
Particle Velocity Magnitude (m/s)
Smooth wall Experiment Sim. Smooth wall Sim. Rough wall
measurement plane at 5.8 m
Rough wall 22
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Particle Tracking Options • Steady particle tracking with steady state solution • Unsteady particle tracking with steady flow • Unsteady particle tracking with unsteady flow − Same particles and continuous phase time step size − Different particles and continuous phase time step size
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Steady Particle Tracking with Steady Flow • DPM calculation at each Nth continuous phase iteration • Particles tracked from injection point till final state/fate • Tracking parameters − Max. number of steps and − Length scale or step length factor
• Integration time step is calculated as − If length scale is specified • ∆𝒕𝒕 =
𝑳𝑳 𝑼𝑼𝒑𝒑 +𝑼𝑼𝒄𝒄
• ∆𝒕𝒕 =
∆𝒕𝒕∗ ∅
− If step length factor is specified
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∆t* Estimated time required for particle to φ
traverse the current cell Step length factor
N
Unsteady Particle Tracking with Steady Flow • Each particle is ADVANCED from its last position in the previous DPM calculation – For specified particle time step size (∆tp) • With the integration time step calculated from tracking parameters – For J number of time steps
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N
∆tp J
Unsteady Particle Tracking with Unsteady Flow Different time step size for particles and continuous phase • Particle injection – Particle Time Step • Injecting particles in each particle time step • Integration time step is the specified particle time step – Fluid Flow Time Step • Injecting particle in each flow time step • Integration time step is the specified particle time step – Particles will always be tracked in such a way that they coincide with the flow time of the continuous flow solver • As long as the maximum number of time steps used to compute a single trajectory is sufficient 26
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Solution Strategies for Steady Flows • Two strategies possible: − Closer coupling between dispersed and continuous flow: • Increase under relaxation factor for Discrete Phase • Decrease number of continuous phase calculations between trajectory calculations ( < 3 ) • Lower under relaxation factors for continuous phase.
− Decoupling of dispersed and continuous flow: • Lower under relaxation factor for Discrete Phase. • Increase number of continuous phase calculations between trajectory calculations ( > 15 )
• Smooth out particle source terms − Increase number of stochastic particle trajectories
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DPM Source Calculations • Effect of Under-Relaxation Factor (URF) – DPM source terms calculated and updated at every particle DPM iteration/time step • # of particle iterations required for achieving full source term increases with decrease in URF • Must use URF of 1 if only one particle iteration is done in a time step – Calculations may not be stable in some cases
• Effect of update DPM Sources Every Flow Iteration – Recommended for unsteady calculations • Particle source terms calculated every DPM iteration and updated every continuous phase iteration
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𝑬𝑬𝒏𝒏𝒏𝒏𝒏𝒏 = 𝑬𝑬𝒐𝒐𝒐𝒐𝒐𝒐 + 𝜶𝜶 𝑬𝑬𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪 − 𝑬𝑬𝒐𝒐𝒐𝒐𝒐𝒐
Postprocessing: Viewing Trajectories
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Particle Track Export • To export particle tracks for viewing in other post-processing tools such as CFDPost or Ensight, use Export > Particle History Data in the File menu − Select File Type, injection, exported particle variables • By default, only particle geometry, ID and residence time are exported − In CFD-Post, use Import from the File menu • The Insert menu can only be used to import particle tracks calculated in CFX
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Time Statistics of Particle Variables • Ability to post process DPM variables − Mean and RMS values for transient simulations
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Time Statistics of Particle Variables • Data sampling for Time Statistics of DPM post processing variables
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Report Definitions for DPM • Report definitions can be used to monitor DPM variables as the solution progresses – – – – –
Injected Mass Mass in Domain Evaporated Mass Penetration Length Escaped Mass
• Can be plotted as the solution progresses and/or saved to a file
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Additional DPM Physics Modeling Features: DDPM and DEM • As the volume fraction of particles increases, particulate flow changes from the dilute disperse flow regime to the dense disperse flow regime, and four-way coupling develops − Particle-particle interaction and particle volume displacement can no longer be neglected
• There are a number of extensions to DPM allowing these effects to be represented − Dense Discrete Phase Model (DDPM) − Discrete Element Model (DEM) − Macroscopic Particle Model (MPM)
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Overview of Modeling Approaches • Dense Discrete Phase Model (DDPM)
DDPM-DEM: Particles colored by residence time
– Treats secondary phase solids as discrete particles dispersed in continuous fluid – Particle-Particle collisions are either modeled (KTGF based approach) or explicitly resolved (DEM based approach) – Applicable from dilute to dense particulate flows with wide particle size distribution – Compatible with species transport, homogeneous and heterogeneous reactions
• Discrete Element Method (DEM)
– Soft-sphere contact model to explicitly resolve particleparticle collisions – Efficiently handles dense and near packing limit particulate flows
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DEM
Additional DPM Physics Modeling Features: Erosion • Erosion is a complex process that is affected by numerous factors and small changes in operational conditions can significantly affect the damage it causes • Erosion leads to a reduction in expected life time of piping systems, and is therefore vital in risk management studies • Fluent's DPM provides validated solid-particle flow modeling capabilities for a wide range of sand particle sizes and loadings – A wide array of industry-accepted erosion models, as well as the ability to include proprietary erosion models if needed – The ability to deform the pipe wall if erosion is affecting the flow pattern
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Sand Erosion in a bend
DPM Erosion Modeling
Define Erosion Models at Walls – can use multiple models at same time • only when erosion modeling performed as a post-processing operation 37
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Post-process particle tracks and erosion contours
Summary • Discrete Phase Model (DPM) allows tracking of dilute, dispersed secondary phases using the Lagrangian method − Secondary phases can be solid particles, liquid droplets, air bubbles, so long as the requirement of volume fraction < 0.10 is satisfied
• Linear motion of particles in the surrounding continuous flow field is computed using Newton's Second Law of Motion − Forces acting on particles include drag and can include various other forces as appropriate for the problem being solved
• DPM particles can exchange momentum, heat and mass (including species) with the continuous phase • Basic set up includes defining one or more injections, defining wall DPM boundary conditions and setting particle tracking options and parameters (such as interaction with continuous phase) • Particle Tracking display used for flow visualization of particles • Additional features extend particle tracking to dense-dispersed flows and erosion 38
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