''Modelling Strategies and Implementation Challenges of ...€¦ · Polydisperse TwoPhase Flows''...

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


Multiphysics with OpenFOAM at Lehrstuhl für Thermodynamik

Mixing and autoignitionin turbulent flows

Heat transfer in pulsating flows

Multiphase Flows


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


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


Modelling of Polydisperse MultiPhase Flows

● Lagrange Particle Tracking (LPT)

● Each particle has its individual diameter and velocity



● Eulerian description as continuous fluid

● Different size classes



MultiFluid Model

f_D1(x,t)f_D2(x,t) :



● MultiFluid Model

f_D1(x,t)f_D2(x,t) :

● Each class has its individual velocity



● TwoFluid Model

f_D(x,t)

● Simple model, restricted accuracy


● Continuity

Continuous Phase

Dispersed Phase

● Momentum

Classical TwoFluid Model Equations


twoPhaseEulerFoam


From MultiFluid to Moment Methods

f_D1(x,t)f_D2(x,t) f(D;x,t) :



● Moments Model f(D;x,t) (Carneiro et al. 20082010)

● Moment transport● Including again size

dependency of particle dynamics


Moments Model (PMOM) Basic Equations

● Distribution function


Moments Model (PMOM) Basic Equations

● Distribution function

● Moment transport equation

● Relaxation approach



● Moments Model f(D;x,t) (Carneiro et al. 20082010)

● Moments transported with their individual moment transport velocities


Moments Model (PMOM) Derivation of Transport Equations

Dro

plet

sG

as


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


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)


Simple Test Cases (Carneiro et al. 2008)

1.5 cm 5.0 cm 7.0 cm

● RANS● All moments transported

with same velocity


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


Comparison Against Experiment of Sommerfeld & Qiu (1991)

Dems et al. 2011


Numerical Settings● Turbulence: WALE (gas phase) / none (dispersed phase)

● temporal backward (2nd order implicit) spatial upwind/central (1st /2nd order)

● CFL for both phases


Results for Sommerfeld & Qiu Axial Velocity

Mean RMS

Parti

cles

Gas


Results for Sommerfeld & Qiu Axial Velocity

Mean Massflux


Results for Sommerfeld & Qiu Radial Velocity

Mean RMS

Parti

cles

Gas


Results for Sommerfeld & Qiu Azimuthal Velocity

Mean RMS

Parti

cles

Gas


Moments Model Evaporation Modelling

(Clausius Clayperon)

(Spalding mass transfer number)

(Frossling correlation)


Evaporation 2D, Hexamesh, Qualitative Results

Air cools down...

...droplets cool as well, since droplet thermal conductivity is small...

Volume Fraction

VaporFraction


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...


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


Simulation of Hydrometeor Population Dynamics

● Hydrometeors➢ rain drops➢ snowflakes➢ ice particles➢ hail➢ ...

● Sedimentation including➢ breakup➢ coalescence➢ coagulation➢ melting, freezing


Modelling Population Balances with QMOM

QMOM (McGraw et al.)

Main advantage: Sum instead of integral, especially in source terms


QMOM in OpenFoam

● Several publications and code version● Implementation straight forward● Moment set validity is main stability issue● Ongoing work at our chair...


Selected Publications

''Modelling Strategies and Implementation Challenges of ...€¦ · Polydisperse TwoPhase Flows''...

Documents

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