CFD modelling of multiphase flows

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1 1 Lecture CFD-3 CFD modelling of multiphase flows Simon Lo CD-adapco Trident House, Basil Hill Road Didcot, OX11 7HJ, UK 2 VOF Free surface flows LMP Droplet flows Liquid film DEM Particle flows EMP Particle flows Bubbly flows Population balance Boiling heat and mass transfers Interphase mass transfer Multiphase models and applications 1

2 3 Volume of Fluid (VOF) model Solve equation for volume fraction (based on conservation of mass) to identify location of gas and liquid. αi +. t ( αiu) = m! i Momentum equation for the gas-liquid mixture: t x ( ρ u ) + ( ρ u u τ ) = + ρ g M Properties of mixture: ρ = m p x m i m j i ij m i + j i N ( αiρi ) i= 1 Gas flow µ = m N ( α iµ i ) i= 1 Liquid flow 4 Slug flow in interconnected subchannels Calculation grid 204,512 cells 18.7 mm 20 mm Water Inlet 0.23 m/s 1.7 mm 150 mm Air Inlet 2.0 m/s Air Inlet 0.5 m/s 2

3 5 Slug flow in interconnected subchannels 6 Effects of surface tension S. Tension = S. Tension =

4 7 Free surface flow in drin carton 8 Lagrangian model for particle flows Equation of motion for individual particle: m du dt d d = F dx dt = force acting on particle F u d = d Particle Gas flow 4

5 9 Spray modelling Modified Han et al atomisation model Charalambos (2002)! 10 Droplet collision and coalescence 5

6 11 Spray coating 12 Fluid film boiling Simulation of films and their evaporation on high temperature surfaces Walls above saturation temperature of droplet fluid Required multi-component film 6

7 13 DEM (Discrete Element Method) Linear momentum of particle: dv dt i m i = F Drag + F Contact + Angular momentum: dωi Ii = dt j= 1! M = µ ij!! [ τ ij + M ij] roll! F Contact! ω F M! ij = rolling torque µ = rolling friction coefficient. roll i Other 14 Pneumatic conveying of particles in pipe 7

8 15 Spreading of particles by conveyor belts 16 Eulerian multiphase model Conservation of mass of phase : N ( αρ ) +. ( αρu ) = ( m! j m! j ) t j= 1 Conservation of momentum of phase : t ( α ρ u ) +. ( α ρ u u ) t = α p + α ρ g +. α ( τ + τ ) + M Particle Gas flow 8

9 17 Forces on a particle Forces acting on a particles: Buoyancy, B. Drag, D. Lift, L. Virtual mass, V. Turbulent dispersion, T. Basset force. And others. D B L, T u c g V ud Buoyancy and drag are the dominant ones. Basset force is complicated and almost always ignored. Lift, virtual mass and other forces will be considered later. u d B g D Uniform inlet 18 Slurry flow in horizontal pipe Measurement plane g 1m V D Liquid velocity L=10m Inlet Particle volume fraction Middle Outlet 9

10 Uniform inlet 19 Slurry flow horizontal pipe Measurement plane g 1m V D d=90 µm, vf=0.19, D=103mm, V=3 m/s L=10m d=270 µm, vf=0.2, D=51.5mm V=5.4 m/s d=480 µm, vf=0.203, D=51.5mm V=3.41 m/s d=165 µm, vf=0.189, D=51.5mm, V=4.17 m/s d=165 µm, vf= D=51.5mm V=3.78 m/s d=165 µm, vf=0.273, D=495mm V=3.46 m/s 20 Particle suspension in stirred vessel Liquid Velocities r/r U/Utip Measurement Solids Velocities r/r U/Utip Uz Experimental Uz Star-CCM+ Ur Experimental Ur Star-CCM+ Utheta Experimental Uz Experimental Uz Star-CCM+ Ur Experimental Ur Star-CCM+ Utheta Experimental 10

11 21 Gas dispersion in stirred vessel U= m/s Gas superficial velocity: U= m/s U= m/s U= m/s U=0.201 m/s 22 Comparison of gas holdup Gas holdup [%] Superficial velocity [m/s] Experimental Star- CCM+ STAR-CCM+ 11

12 23 Adaptive MUSIG Model An Eulerian population balance method for poly-disperse multiphase flows. 24 Adaptive MUSIG Model Mass and number density are redistributed between neighbour groups so that each group has the same mass but new diameters d d 12

13 25 Droplet breaup through an orifice Sauter Mean Diameter Breaup Rate (log scale) Turbulent-induced breaup Shear-induced breaup 26 Boiling heat and mass transfers Conservation of energy for phase : t t ( α ρh ) +. ( αρuh ). α λ T + h = Q Wall heat flux is modelled by three mechanisms: q! ʹ ʹ = q! ʹ ʹ + q! ʹ ʹ + q! ʹ ʹ T c q e µ σ h Convective heating Quenching Evaporation qʹ ʹ q! ʹ ʹ! c q q!ʹ ʹ e 13

14 27 D = m L = 2 m P = 147 bar T sat = 613 K Q = MW/m 2 G = g/m 2 s ΔT sub = K Bartolomei (1982) 147 bar experiments g Water + steam Wall heat flux L Sub-cooled water Void fraction Condensation rate 28 Bart : Comparison of axial void profiles 14

15 29 Multi-component multiphase model General species transport equation for phase is: t Y D σ S t ( α ρy ) +. ( αρuy ). α D + Y = S =mass fraction of species or other scalar quantity, =diffusion coefficient, =Schmidt number, =sources. µ σ Y 30 Oxygen transfer in aeration tan Volume fraction of air Oxygen in air Water Air injector Oxygen in water Oxygen level at water surface and exit 15

16 VOF Free surface flows LMP Droplet flows DEM Particle flows EMP Particle flows Bubbly flows Population balance Boiling heat and mass transfers Interphase mass transfer Summary 16

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