Technische Universität München
''Modelling Strategies and Implementation Challenges of Moment Methods for the Simulation ofPolydisperse TwoPhase Flows''
Patrick DemsProf. Wolfgang Polifke, Ph.D.Lehrstuhl für Thermodynamik, TU München
Multiphysical Modelling in OpenFOAM10/21/2011, Riga
Technische Universität München
Multiphysics with OpenFOAM at Lehrstuhl für Thermodynamik
Mixing and autoignitionin turbulent flows
Heat transfer in pulsating flows
Multiphase Flows
Technische Universität München
Projects on Polydisperse MultiPhase Flows
Development of a Moment Method
f
DSpray Combustion with LES
Description of Hydrometeor Populations Process Industry Reacting Bubble Flows
f
D
fDfD
Technische Universität München
Introduction to TwoPhase Flows
TwoPhase FlowsEulerianEulerian Description
twoPhaseEulerFoamwith RANS and Dmean
LESContinuous PhaseDispersed Phase
Polydispersity
Moment Methods:PMOM, QMOM, DQMOM
Reaction
Spray CombustionProcess Industry
Phase ChangeDroplet Evaporation
Condensation, Melting,Freezing of Hydrometeors
Technische Universität München
Modelling of Polydisperse MultiPhase Flows
● Lagrange Particle Tracking (LPT)
● Each particle has its individual diameter and velocity
Technische Universität München
Modelling of Polydisperse MultiPhase Flows
● Eulerian description as continuous fluid
● Different size classes
Technische Universität München
Modelling of Polydisperse MultiPhase Flows
MultiFluid Model
f_D1(x,t)f_D2(x,t) :
Technische Universität München
Modelling of Polydisperse MultiPhase Flows
● MultiFluid Model
f_D1(x,t)f_D2(x,t) :
● Each class has its individual velocity
Technische Universität München
Modelling of Polydisperse MultiPhase Flows
● TwoFluid Model
f_D(x,t)
● Simple model, restricted accuracy
Technische Universität München
● Continuity
Continuous Phase
Dispersed Phase
● Momentum
Classical TwoFluid Model Equations
Technische Universität München
twoPhaseEulerFoam
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From MultiFluid to Moment Methods
f_D1(x,t)f_D2(x,t) f(D;x,t) :
Technische Universität München
Modelling of Polydisperse MultiPhase Flows
● Moments Model f(D;x,t) (Carneiro et al. 20082010)
● Moment transport● Including again size
dependency of particle dynamics
Technische Universität München
Moments Model (PMOM) Basic Equations
● Distribution function
Technische Universität München
Moments Model (PMOM) Basic Equations
● Distribution function
● Moment transport equation
● Relaxation approach
Technische Universität München
Modelling of Polydisperse MultiPhase Flows
● Moments Model f(D;x,t) (Carneiro et al. 20082010)
● Moments transported with their individual moment transport velocities
Technische Universität München
Moments Model (PMOM) Derivation of Transport Equations
Dro
plet
sG
as
Technische Universität München
Moments Model (PMOM) Closure
● Interfacial momentum exchange via drag (Stokes/SchillerNaumann):
● Closure for higher order moments obtained by presuming form of NDF
➢ e.g. Gamma distribution
Technische Universität München
Implementation into OpenFOAM
● alpha.H corresponds to M(3)equation
● M(0) M(2) equations similar
● UEqns.H only slightly modified (UaEqn corresponds to M(3)-equation)
● Drag coefficient replaced by integral value of the Moments Model
● Moment bounding routines (simple algebraic equations)
● LES for gas phase implementation similar to pisoFoam (OF 1.7 and higher)
Technische Universität München
Simple Test Cases (Carneiro et al. 2008)
1.5 cm 5.0 cm 7.0 cm
● RANS● All moments transported
with same velocity
Technische Universität München
Moments and their Physical Meanings ( Results for Borée et al.)
M(0) ~ total number of particlesM(1) ~ diameter sum
M(2) ~ droplet surfaceM(3) ~ volume fraction
Air
Air+Particles
LES, moments transported with individual moment transport velocity
Technische Universität München
Comparison Against Experiment of Sommerfeld & Qiu (1991)
Dems et al. 2011
Technische Universität München
Numerical Settings● Turbulence: WALE (gas phase) / none (dispersed phase)
● temporal backward (2nd order implicit) spatial upwind/central (1st /2nd order)
● CFL for both phases
Technische Universität München
Results for Sommerfeld & Qiu Axial Velocity
Mean RMS
Parti
cles
Gas
Technische Universität München
Results for Sommerfeld & Qiu Axial Velocity
Mean Massflux
Technische Universität München
Results for Sommerfeld & Qiu Radial Velocity
Mean RMS
Parti
cles
Gas
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Results for Sommerfeld & Qiu Azimuthal Velocity
Mean RMS
Parti
cles
Gas
Technische Universität München
Moments Model Evaporation Modelling
(Clausius Clayperon)
(Spalding mass transfer number)
(Frossling correlation)
Technische Universität München
Evaporation 2D, Hexamesh, Qualitative Results
Air cools down...
...droplets cool as well, since droplet thermal conductivity is small...
Volume Fraction
VaporFraction
Technische Universität München
Behind the scenes of PMOM simulations
● Overall stability of the solver mainly depends on valid moments sets.
● Evaporation requires strict bounding of several variables➢ droplet temperature➢ surface vapour fraction➢ surface vapor pressure➢ Nusselt, Sherwood numbers➢ ...
● Numerical stability problems with 3D cases and “nonperfect” meshes
● Tetrahedral meshes are quite challenging...
Technische Universität München
Spray Combustion Ongoing work
● Homogeneous combustion
➢ Fuel vapour and air➢ Standard combustion models (EBC, JPDF, species transport)➢ Implementation of additional equations & chemistry tabulation
● Heterogeneous combustion
➢ single droplet combustion➢ group combustion➢ integral source terms of species mass fractions and heat release
Technische Universität München
Simulation of Hydrometeor Population Dynamics
● Hydrometeors➢ rain drops➢ snowflakes➢ ice particles➢ hail➢ ...
● Sedimentation including➢ breakup➢ coalescence➢ coagulation➢ melting, freezing
Technische Universität München
Modelling Population Balances with QMOM
QMOM (McGraw et al.)
Main advantage: Sum instead of integral, especially in source terms
Technische Universität München
QMOM in OpenFoam
● Several publications and code version● Implementation straight forward● Moment set validity is main stability issue● Ongoing work at our chair...
Technische Universität München
Selected Publications
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