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NETL 2013 Workshop on Multiphase Flow Science
VALIDATION OF A MULTIPHASE TURBULENCE MODEL USING MESOSCALE DNS OF GRAVITY-DRIVEN GAS-PARTICLE FLOW NETL 2013 MULTIPHASE FLOW WORKSHOP AUGUST 6, 2013
RODNEY O. FOX1,2, JESSE CAPECELATRO3, OLIVIER DESJARDINS3 1DEPARTMENT OF CHEMICAL AND BIOLOGICAL ENGINEERING, IOWA STATE UNIVERSITY 2LABORATOIRE EM2C-UPR, ECOLE CENTRALE PARIS
3SIBLEY SCHOOL OF MECHANICAL AND AEROSPACE ENGINEERING, CORNELL UNIVERSITY
NETL 2013 Workshop on Multiphase Flow Science
Moderately-dilute fluid-particle flows
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
Preferential concentration of cloud droplets by turbulence
Shaw et al. (1998)
Spray flames
Gasification of coal and biomass
C.T. Bowman, Stanford
Atmospheric dispersion
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NETL 2013 Workshop on Multiphase Flow Science
Burlington, Vermont Xu & Zhu, 2011
Mesoscale • Clustering • Bubbling • Particle size segregation • Turbulence modulation
Microscale • Wakes • Particle collisions • Phase change
Macroscale • Large number of
particles • Length scales: m NASA
The multi-scale issue
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
3
NETL 2013 Workshop on Multiphase Flow Science
Microscale • Wakes • Particle collisions • Phase change
Burlington, Vermont Xu & Zhu, 2011
Mesoscale • Clustering • Bubbling • Particle size segregation • Turbulence modulation
Macroscale • Large number of
particles • Length scales: m NASA
The multi-scale issue
Objectives: 1. Formulate from first-principles a macroscopic
turbulence model
2. Investigate the unclosed terms using mesoscale DNS
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
4
NETL 2013 Workshop on Multiphase Flow Science
• Arriving at a macroscopic description of fluid-particle flows
– Mesoscale description
– Reynolds-averaged equations
– Closure models
• Evaluating the unclosed terms using mesoscale DNS
– Simulation configuration
– Extracting the statistics
– Preliminary results
• Conclusions
Outline
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
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NETL 2013 Workshop on Multiphase Flow Science
Multiscale turbulence modeling approach1
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
6 1. Fox, R.O., On multiphase turbulence models for collisional fluid-particle flows, In preparation for JFM, 2013
NETL 2013 Workshop on Multiphase Flow Science
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
Starting from a mesoscale description Kinetic theory model for monodisperse granular flow in the presence of a fluid
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NETL 2013 Workshop on Multiphase Flow Science
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
Starting from a mesoscale description Fluid-phase transport equations
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NETL 2013 Workshop on Multiphase Flow Science
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
Towards a macroscopic model • Reynolds-averaged definitions
• Phase-averaged definitions
• Solve for:
– Particle-phase:
– Fluid-phase:
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NETL 2013 Workshop on Multiphase Flow Science
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
Reynolds-average equations Particle-phase equations
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NETL 2013 Workshop on Multiphase Flow Science
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
Reynolds-average equations Fluid-phase equations
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NETL 2013 Workshop on Multiphase Flow Science
Particle-phase equations
Fluid-phase equations
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
Application to homogeneous gravity-driven flow
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• Single-phase unclosed terms (models exist in literature) • Interphase coupling unclosed terms (new closures needed)
NETL 2013 Workshop on Multiphase Flow Science
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
• Most important term – accounts for flow agitation due to clustering
• Modeling constant can be determined using mesoscale DNS
• In statistically homogeneous flow, this model increases terminal velocity:
A proposed model for drift velocity
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NETL 2013 Workshop on Multiphase Flow Science
Mesoscale DNS framework
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
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2. Desjardins et al., High order conservative finite difference scheme for variable density low Mach turbulent flow, JCP, 2008. 3. Capecelatro, J., Desjardins, O., An Euler-Lagrange strategy for simulating particle-laden flows, JCP, 2012.
• NGA2 – Arbitrarily high-order DNS/LES code – Massively parallel – Conservation of mass, momentum, and kinetic energy – Effective viscosity of Gibilaro et al. (2007):
• Lagrangian particle tracking3
– 2nd-order Runge-Kutta for particle ODEs – Soft-sphere collision model – Linear drag:
• Interphase exchange3
– Filter based on the convolution of mollification and diffusion 1. Mollification: transfer particle data to neighboring cells 2. Diffusion: smooth data with specified width
– Fully conservative, implicit treatment – Transferred data converges under mesh refinement!
NETL 2013 Workshop on Multiphase Flow Science
Simulation configuration
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
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• 3D triply-periodic domain • Mass flow rate forced • Domain: • Mesh: • Case parameters
NETL 2013 Workshop on Multiphase Flow Science
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
Base case simulation
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Degree of segregation
Contribution of the effective viscosity
Iso-surfaces of
Poisson distribution
Simulation
NETL 2013 Workshop on Multiphase Flow Science
Extracting multiphase statistics
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
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• Separation of length scales much be established • Any Lagrangian property is filtered to the mesh by: • Use 2-step filter with characteristic size
• Total fluctuating energy:
• If :
• If :
Particle velocity vectors
NETL 2013 Workshop on Multiphase Flow Science
Choosing the correct filter size
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
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• Use particle field from base case • Assign each particle a random Gaussian velocity with
– Mean set to local filtered velocity – Variance set to a prescribed granular temperature
• Use filter size
NETL 2013 Workshop on Multiphase Flow Science
Instantaneous results (base case)
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
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NETL 2013 Workshop on Multiphase Flow Science
Reynolds number effect
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
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Re=10 Re=20 Re=40
Poisson distribution
Collision frequency Granular temperature
Degree of segregation
NETL 2013 Workshop on Multiphase Flow Science
Conclusions
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In summary
• The exact Reynolds-averaged equations for fluid-particle flows have been derived
• Must distinguish between particle-phase TKE and granular temperature
• 2-step filter can be used to extract meaningful statistics
Looking forward
• Effect of mass loading and concentration on turbulence statistics
• Study wall-bounded risers
• Use RANS ideas in LES framework
Context & Challenges Macroscopic Description Mesoscale DNS Summary & Conclusions
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