Modelling multiphase flows in the Chemical and Process Industry Simon Lo 9/11/09
Contents Breakup and coalescence in bubbly flows Particle flows with the Discrete Element Modelling approach Multiphase flows in pipelines 2
Bubbly flows in pipes and pipe bends 3
Bubble size distribution models Population balance equation: Dn Dt i = B D + B D ibr, ibr, icl, icl, Interfacial area concentration transport (e.g. Ishii s model): Da i Dt = φ + φ br cl 4
Moments of particle size distribution 0 th moment is the particle number density: n = S 0 2 nd moment is related to interfacial area density: A i = 2 nπ d P d ) dd = 0 ( π S 2 3 rd moment is related to dispersed phase volume fraction: 3 πd α = n P( d ) dd = 6 0 π S 6 The Sauter mean diameter is: S 3 6α 1 d 32 = = S π S 2 S 2 3 5
Transport equation The transport equation: S S γ t +.( S u ) = s + s γ Breakup: s br d br cl 3 γ 3 γ d ( N f ( d) 1) = 0 τ br ( d ) Coalescence: np( d) d( d) dd, dd, 2 cl = 0 0 cl Δ γ, cl s K S npd ( ) ddpddd ' ( ) ( ) 6
Hibiki bubble column (2001) Air/Water Cylindrical Test Section 50.8 mm ID, 3.06 m Height Ideal Gas Law for Air (297K) Inlet B.C. at z/d=6 Air/Water Velocities, Void Fraction Atmospheric Exit (pressure boundary) Two-dimensional axisymmetric simulation (20 150 cells) Steady state flow C L = -0.3 03 C VM = 0.5 C D = 1.071 7
Fields distribution bubble size interfacial area density gas phase volume fraction 8
Radial void and velocity distributions 0.4 2.0 20 2.0 0.3 1.5 1.5 -) a G (- 0.2 0.1 voidage radial distribution sim. with star-cd exp. Hibiki et al., 2001 j G =0.321 m/s, j L =0.986 m/s, z/d=53.5 ) v L (m/s) 1.0 0.5 axial velocity profile sim. with star-cd exp. Hibiki et al., 2001 j G =0.321 m/s, j L =0.986 m/s, z/d=53.5 v G (m/s s) 1.0 axial velocity profile sim. with star-cd exp. Hibiki et al., 2001 j G =0.321 m/s, j L =0.986 m/s, z/d=53.5 0.0 0.0 0.2 0.4 0.6 0.8 1.0 r/r (-) 0.0 0.0 0.2 0.4 0.6 0.8 1.0 r/r (-) 0.0 0.2 0.4 0.6 0.8 1.0 r/r (-) Void fraction Liquid velocity Gas velocity 9
Bubble size distributions 5 5 6 4 4 5 d B (mm m) 2 bubble size radial distribution sim. with star-cd exp. Hibiki et al., 2001 j 1 G =0.321 m/s, j L =0.986 m/s, z/d=53.5 d B (mm) 3 2 1 bubble size radial distribution sim. with star-cd exp. Hibiki et al., 2001 j G =0.471 m/s, j L =2.01 m/s, z/d=53.5 )3 d B (mm) 4 3 2 1 bubble size radial distribution sim. with star-cd exp. Hibiki et al., 2001 j G =0.624 m/s, j L =2.01 m/s, z/d=53.5 0 0.0 0.2 0.4 0.6 0.8 1.0 r/r (-) 0 0.0 0.2 0.4 0.6 0.8 1.0 r/r (-) j G and j L. 0 0.0 0.2 0.4 0.6 0.8 1.0 r/r (-) Bubble size distribution in radial direction. Different gas and liquid fluxes are investigated with S γ model. 10
Nottingham Multiphase flow in bend pipes Bubble accumulate at top of the bend Gas vol. fraction Bubble size 2-phase model + S-gamma Uniform bubble distribution in vertical section 11
Nottingham Multiphase flow in bend pipes Large bubblesbbl Medium bubbles Small bubbles Liquid 4-phase model 12
DEM Rotating drum 13
DEM Calculation scheme Solve continuous phase on flow grid. Solve particle tracks accounting for particleparticle and particle-wall interactions. Apply porosity and sources from DEM grid to flow grid. Calculate porosity and sources from particles over a DEM grid. 14
DEM Particle equations Linear momentum of particle: d v dt i m i = F Drag + F Contact + F Other Angular momentum: I i d dt r M ω i = [ τ + M ] k j = 1 r = μ ij ij μ roll r F r ij Contact r ω i M r ij = rolling torque opposes particle rotation μ roll = rolling friction coefficient. 15
DEM Multiple inlets 16
DEM Buoyant particles 17
DEM Particle transport in pipe 18
DEM Non-spherical particles 19
DEM - Break-off of cohesive particle 20
10m riser section of a 100m long pipeline 21
OLGA-STAR coupled model To study 3D effects in in-line equipment: valve, junction, elbow, obstacle, jumper, separator, slug catcher, compressor,... Flow rates from STAR to OLGA Flow rates from OLGA to STAR Inlet Outlet Pressure from STAR to OLGA Pressure from OLGA to STAR 22
Summary Active development of advanced models for multiphase flows found in the chemical and process industry. Breakup and coalescence of bubbles in bubbly flows. Particle-particle, particle-wall collision modelling using the Discrete Element Model (DEM). Modelling of multiphase flows in long pipelines. Coupling 3D CFD to 1D pipeline codes. 23