Multiphase flows in chem. engineering Deciphering ...

Multiphase flows in chem. engineering Deciphering hydrodynamics of packed columns

Martin Isoz UCT Prague, Department of mathematics

Lothar-Collatz seminar April 26, 2016

Intro

Methods Disc. schemes Smooth plate Textured plate Perforated plate Conclusion

Introduction

Martin Isoz, UCT Prague

Multiphase flows in chemical engineering, Deciphering hydrodynamics of packed columns

Why to pay attention to a flow on a plate Numerous applications, our concentration lies in deciphering flow in separation columns

Hydrodynamics • Fuel cells

– water management inside PEMFC fuel cells

• Aerospace engineering

– in flight formation of rivulets on plane wings

Gas-liquid interface • Packed columns

– wetting performance – mass transfer coefficients

• Catalytic reactors

– wetting of the catalyst

[Sulzer ChemTech] Martin Isoz, UCT Prague


Packed column Complex multiphase flow



Structured packing Curled, textured, perforated plate



Structured packing – detail Curled, textured, perforated plate



Separation columns modeling Multiphase hydrodynamics, simultaneous mass and heat transfer, no chemical reaction

Momentum and continuity equations, N phases ρi

∂ (ui ) + ∇ · (ρi ui ⊗ ui + pi E) ∂t ρi = ρ(ci , Ti ),

∇ · (ui )

= ∇ · τ + Fi , = Siρ =

M X

i = 1, . . . , N

c ˆ i,j R

j=1

Mass transfer (no reaction), M species ∂ c ci,j + ∇ · (ui ci,j ) = ∇ · Γci,j ∇ci,j + Si,j , ∂t

j = 1, . . . , M

Heat transfer (no reaction), N phases ∂ Ti + ∇ · (ui Ti ) = ∇ · ΓTi ∇Ti + SiT , ∂t Martin Isoz, UCT Prague

i = 1, . . . , N


Volume-Of-Fluid (VOF) method Interface tracking for isothermal case, incompressible fluids, flow driven by gravity

ut + ∇ · (u ⊗ u) − ∇ · (µ∇u) = ˜ + ∇ · (uh) ˜ = 0, ∂t h

˜ (ρ2 − ρ1 ) , ρ = ρ1 + h Fst Fb Martin Isoz, UCT Prague

1 (−∇p + Fst + Fb ) ρ ∇·u=0

˜ (µ2 − µ1 ) µ = µ1 + h

˜ = γκδ~n = γκ∇h =

T

(ρg sin α, 0, ρg cos α)


Actually solved equations Isothermal case, incompressible fluids, flow driven by gravity, no mass transfer

Momentum and continuity equations ˜ = ut + ∇ · (u ⊗ u) − ∇ · (µ∇u) − (∇u) · ∇h ˜ = −∇pd − g · x ⊗ ∇ρ + γκ∇h ∇·u =

0

Advection equation for gas-liquid interface (GLI) h i ˜ t + ∇ · (uh) ˜ + ∇ · ur h(1 ˜ − h) ˜ =0 h Notations u[m s−1 ] . . . . . . . . . . . . bulk velocity ur [m s−1 ] . . compression velocity µ[Pa s] . . . . . . . . dynamic viscosity ρ[kg m−3 ] . . . . . . . . . . . . . . . . density Martin Isoz, UCT Prague

γ[N m−1 ] . . . . . . . . surface tension g[m s−2 ] gravitational acceleration x[m] . . . . . . . . . . . . . . position vector ˜ h[−] . . . . . . . .GLI tracking function


Important dimensionless number Comparing forces in a falling film

Reynolds number ρU L UL = µ ν U . . . film velocity scale, L . . . film characteristic dimension (thickness) ρ . . . liquid density, µ, ν . . . liquid dynamic/kinematic viscosity Re =

Re =

inertia viscosity

Weber number ρU 2 L γ U . . . film velocity scale, L . . . film characteristic dimension (thickness) ρ . . . liquid density, γ . . . gas-liquid surface tension We =

We = Martin Isoz, UCT Prague

inertia capillarity


Intro


Methodological background



General CFD work process Discretisation of both domain and equations

[F. Moukalled et al., The Finite Volume Method in Computational Fluid Dynamics,Fluid Mechanics and Its Applications 113, Springer 2016] Martin Isoz, UCT Prague


Our tools OpenFOAM and other opensource software

[Andrew King, Fluid dynamics research group, Curtin University of Technology] Martin Isoz, UCT Prague


Quick intro to OpenFOAM Set of C++ libraries for solving problems of Computational Continuum Mechanics

Disclaimer: OpenFOAM is distributed by OpenFOAM Foundation and developed by OpenCFD Ltd. This presentation is not in any way related to or supported by any of those organizations. OpenFOAM in a few points • Free – Open-source – software for numerical simulations, specialized in CFD (CCM) Free – no payments for license and support, even for massively parallel computers (free multi-1000-CPU CFD license) Open-source – suitable for user modifications

• Based on the Finite Volume Method (FVM) • Accessible

Fully supported on linux (pre-compiled packages for Ubuntu) Installed on the UCT cluster (Altix, 192 cores) and on computers of Czech supercomputer center (Salomon, Anselm)

• Actively developed (OpenCFD Ltd. + community) Martin Isoz, UCT Prague


Main software objective Represent differential equation in their natural language

Equation Mimicking • Natural language of continuum mechanics: partial differential equations • Example: Navier-Stokes equation, isothermal case, one phase, incompressible fluid, no body forces ut + ∇ · (u ⊗ u) − ∇ · (ν∇u) = −∇p • Implemantation in OpenFOAM solve ( fvm::ddt(U) + fvm::div(phi,U) - fvm::laplacian(nu,U) == -fvc::grad(p); ); Martin Isoz, UCT Prague


Equations discretization FVM – Transport equation has to be satisfied in the integral form over VP around P

Standard form of transport equation for scalar property φ ∂ρφ + ∇ · (ρuφ) − ∇ · (ρΓφ φ) = Sφ (φ) ∂t Integral form of transport equation for φ t+∆t

Z t

∂ ∂t

Z

Z

VP

∇ · (ρΓφ φ) dV dt

Z

ρφ dV +

∇ · (ρuφ) dV − VP

VP t+∆t

Z

Z

=

Sφ (φ) dV dt t

P . . . . . centroid of the control volume

VP

VP . . . . . . . . . control volume around P

Centroid position: Z

Z

VP xP =

x dV VP


0=

(x − xp ) dV VP


Intro


Discretization schemes



Equation discretization Discretize the terms of the solved transport equation

General transport equation ∂ρφ ∂t

+

∇ · (ρuφ)

Temporal term

+

Convective term

−

∇ · (ρΓφ φ)

=

Sφ (φ)

− Diffusive term = Source

Solved equations ut

+

∇ · (u ⊗ u) −

=

˜t h


−

∇pd +

∇ · (µ∇u) −

˜ ∇ · (uh)

−

g · x ⊗ ∇ρ +

˜ = (∇u) · ∇h +

˜ γκ∇h

∇·u = 0 h i ˜ − h) ˜ = 0 ∇ · ur h(1


Equation discretization Discretize the terms of the solved transport equation

General transport equation ∂ρφ ∂t

+

∇ · (ρuφ)

Temporal term

+

Convective term

−

∇ · (ρΓφ φ)

=

Sφ (φ)

− Diffusive term = Source

Goal: Second order accurate discretization scheme in both space and time Notes: • Usually, Diffusive and Source terms do not pose problems

• The quality of the solution depends heavily on the discretization scheme used for Temporal and Convective terms ˜ (phase volume fraction) is limited, • In our case, the variable h ˜ h ∈ h0, 1i Martin Isoz, UCT Prague


Table of used discretization schemes Second order accurate discretization scheme in both space and time

Term

Used scheme

˜t ut , h

Crank-Nicolson

∇ · (u ⊗ u) ∇ · (µ∇u) ˜ ∇ · (u h h) i ˜ − h) ˜ ∇ · ur h(1 ∇·u

Self-filtered central differencing (SFCD) Central differencing (CD) Interface compression Central differencing (CD) Central differencing (CD)

Table : Schemes used for discretization of temporal and convective terms

Notes: • All the schemes are completed by linear interpolation and Gaussian integration. • SFCD schemes is based on CD with boundedness and oscillations reductions ensured via Total Variation Diminishing (TVD) framework Martin Isoz, UCT Prague


Convective terms discretization Quick intro to bounded high resolution (HR) schemes

[F. Moukalled et al., The Finite Volume Method in Computational Fluid Dynamics,Fluid Mechanics and Its Applications 113, Springer 2016]

Upwind φf = φC 1st order accurate, diffusive 1 Central difference φf = 2 (φC + φD ) 2nd order accurate, dispersive WANTED : Martin Isoz, UCT Prague

Upwind stability

&

CD accuracy



TVD - Total variation diminishing • Steady 2D advection equation, ∇ · (ρuφ) = 0 • Total variation (TV) in discrete case, X TV = |φi+1 − φi | (i)

• TVD requirement

T V (φt+∆t ) ≤ T V (φt )

Statement [Harten, A. High resolution schemes for hyperbolic conservation laws. J Comp. Phys. (1983) 49:357–393]

Monotone scheme is TVD and TVD scheme is monotonicity preserving. A monotonicity preserving scheme does not create any new local extrema within the solution domain, i.e., the value of a local minimum is non-decreasing, and the value of a local maximum is non-increasing. Martin Isoz, UCT Prague



WANTED : Upwind stability

&

CD accuracy

Strategy Start with CD scheme and modify it in such way, that it will become TVD (by blending it with Upwind scheme). Tool Flux limiters: limit the spatial derivatives to physically realisable and meaningfull values Example: 1D semi-discrete scheme dφf dt

1 ∆x

[F (φC ) − F (φD )] = 0 F (φC ) = fCL − ψ(rf ) fCL − fCH L L H F (φD ) = fD − ψ(rn ) fD − fD +

F . . . . . . . . . . . . . . . . . . . edge fluxes ψ(r) . . . . . . . . . flux limiter function f . . . . . . . . . discretization scheme H, L . . . . . . . . . high/low resolution Martin Isoz, UCT Prague



Example: 1D semi-discrete scheme (contd.) dφf dt

1 ∆x

[F (φC ) − F (φD )] = 0 F (φC ) = fCL − ψ(rf ) fCL − fCH L L H F (φD ) = fD − ψ(rn ) fD − fD +

rf =

φf −φn φp −φf ,

ψ(r) ≥ 0

Notes: • ψ(r) = 0 → flux is represented by a low resolution scheme (sharp gradient, opposite slopes,. . . ) – Upwind • ψ(r) = 1 → flux is represented by a high resolution scheme – CD • There is no general (always applicable) limiter → choice of limiters based on trial and error




Example: ψvanLeer (r) =

r + |r| , 1 + |r|

lim ψvanLeer (r) = 2

r→∞

[F. Moukalled et al., The Finite Volume Method in Computational Fluid Dynamics,Fluid Mechanics and Its Applications 113, Springer 2016, Modified] Martin Isoz, UCT Prague


Convective terms discretization SO U

NVD of the used convective terms DD

CD

U D

φf − φU φ˜f = φD − φU

ψ(

rf )

=2

rc

1

intComp, |∇φf | = 0.4 Gamma, βM = 0.2 SCFD

0 0


φC − φU φ˜C = φD − φU

1


Convective terms discretization Importance of convective term in advection equation

Case: Spreading of 2D droplet, R0 = 2 mm, h0 = 0.7 mm, θ∞ = 70◦




Case: Spreading of 2D droplet, R0 = 2 mm, h0 = 0.7 mm, θ∞ = 70◦ ˜ t = 0.01 s Comparison of discretization schemes for ∇ · (uh), ˜ Evolution of h

˜ Evolution of ∂xh

104

1.0

103

0.8

102 ˜ ∂x h

˜ ∈ h0, 1i h

0.6

101

0.4

0.2

0.0 −0.010


intCompression Gamma vanLeer −0.005

0.000 x, [m]

0.005

100

0.010

0 −0.010

−0.005

0.000 x, [m]

0.005

0.010





104

1.0

103

0.8

102 ˜ ∂x h

˜ ∈ h0, 1i h

0.6

101

0.4

0.2

0.0 −0.010



0.000 x, [m]

0.005

100

0.010

0 −0.010

−0.005

0.000 x, [m]

0.005

0.010





104

1.0

103

0.8

102 ˜ ∂x h

˜ ∈ h0, 1i h

0.6

101

0.4

0.2

0.0 −0.010



0.000 x, [m]

0.005

100

0.010

0 −0.010

−0.005

0.000 x, [m]

0.005

0.010





104

1.0

103

0.8

102 ˜ ∂x h

˜ ∈ h0, 1i h

0.6

101

0.4

0.2

0.0 −0.010



0.000 x, [m]

0.005

100

0.010

0 −0.010

−0.005

0.000 x, [m]

0.005

0.010





104

1.0

103

0.8

102 ˜ ∂x h

˜ ∈ h0, 1i h

0.6

101

0.4

0.2

0.0 −0.010



0.000 x, [m]

0.005

100

0.010

0 −0.010

−0.005

0.000 x, [m]

0.005

0.010



Case: Spreading of 2D droplet, R0 = 2 mm, h0 = 0.7 mm, θ∞ = 70◦ ˜ Comparison of discretization schemes for ∇ · (uh)

intCompression

0.6

0.4

0.4

0.2 0.000 x, [m]

0.005

0.2

0.0 −0.010 −0.005

0.010

4

10

0.000 x, [m]

0.005

0.0 −0.010 −0.005

0.010

4

10

103

10

2

10

2

102

10

1

10

1

0.000 x, [m]

0.01 s


0.005

0.010

˜ ∂x h

103

100 0 −0.010 −0.005

0.005

0.010

0.000 x, [m]

0.005

0.010

101

100 0 −0.010 −0.005

0.08 s

0.000 x, [m]

4

103 ˜ ∂x h

˜ ∂x h

0.6

0.4

0.2

vanLeer

0.8

˜ ∈ h0, 1i h

0.6

10

1.0

0.8

˜ ∈ h0, 1i h

0.8

0.0 −0.010 −0.005

Gamma

1.0

˜ ∈ h0, 1i h

1.0

0.000 x, [m]

0.15 s

0.005

0.010

100 0 −0.010 −0.005

0.22 s

0.29 s



Case: Spreading of 2D droplet, R0 = 2 mm, h0 = 0.7 mm, θ∞ = 70◦




Case: Spreading of 2D droplet, R0 = 2 mm, h0 = 0.7 mm, θ∞ = 70◦ ˜ t = 0.01 s - zoomed to the contact line Comparison of discretization schemes for ∇ · (uh), ˜ Evolution of h

0.05


104

intCompression Gamma 103

0.03

102 ˜ ∂x h

˜ ∈ h0, 1i h

0.04

0.02

101

0.01 100 0.00 0.0020


0.0025

0.0030 x, [m]

0.0035

0.0040

0 0.0020

0.0025

0.0030 x, [m]

0.0035

0.0040




0.05


104


0.03

102 ˜ ∂x h

˜ ∈ h0, 1i h

0.04

0.02

101

0.01 100 0.00 0.0020


0.0025

0.0030 x, [m]

0.0035

0.0040

0 0.0020

0.0025

0.0030 x, [m]

0.0035

0.0040




0.05


104


0.03

102 ˜ ∂x h

˜ ∈ h0, 1i h

0.04

0.02

101

0.01 100 0.00 0.0020


0.0025

0.0030 x, [m]

0.0035

0.0040

0 0.0020

0.0025

0.0030 x, [m]

0.0035

0.0040




0.05


104


0.03

102 ˜ ∂x h

˜ ∈ h0, 1i h

0.04

0.02

101

0.01 100 0.00 0.0020


0.0025

0.0030 x, [m]

0.0035

0.0040

0 0.0020

0.0025

0.0030 x, [m]

0.0035

0.0040




0.05


104


0.03

102 ˜ ∂x h

˜ ∈ h0, 1i h

0.04

0.02

101

0.01 100 0.00 0.0020


0.0025

0.0030 x, [m]

0.0035

0.0040

0 0.0020

0.0025

0.0030 x, [m]

0.0035

0.0040


Something is rotten in the state of Denmark Liquid spreading and no slip boundary condition

Huh and Scriven paradox

solid no slip

Even Heracles could not sink a solid. u(0) = 0 ⇐⇒ F → ∞

liquid [Huh, C. Scriven, L. E. Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Col. Int. Sci. 1971, 35 (11), 85–101.]



Solved equations Phase fraction equation and a Poisson equation for dynamic pressure

Original set of equations ˜ = ut + ∇ · (u ⊗ u) − ∇ · (µ∇u) − (∇u) · ∇h ˜ = −∇pd − g · x ⊗ ∇ρ + γκ∇h

. . . momentum

∇ · u = 0 . . . continuity i ˜ t + ∇ · (uh) ˜ + ∇ · ur h(1 ˜ − h) ˜ h = 0 . . . phase fraction h

Strategy 1 2

˜ Solve the phase fraction equation → h

Combine momentum and continuity equations to obtain a Poisson equation for pd



Solved equations Phase fraction equation and a Poisson equation for dynamic pressure

˜ = −∇pd − g · x ⊗ ∇ρ + γκ∇h ˜ ut + ∇ · (u ⊗ u) − ∇ · (µ∇u) − (∇u) · ∇h → rearrange + discretize ← ˜ auC uC = H(u) − ∇pd − g · x ⊗ ∇ρ + γκ∇h nh i o −1 ˜ − ∇pd H(u) − g · x ⊗ ∇ρ + γκ∇h uC = [auC ] → substitute for u in the continuity equation ←

io n o n h −1 −1 ˜ H(u) − g · x ⊗ ∇ρ + γκ∇h ∇ · [auC ] ∇pd = ∇ · [auC ] → solve the resulting system for pd ← Martin Isoz, UCT Prague


Simulation scheme PIMPLE algorithm with adaptive time step

Start

PIMPLE loop

Generate mesh

SIMPLE loop

Input material properties, initial physical field variables and boundary conditions

Calculate phase fraction field

PISO loop

Time loop

Calculate pressure field

Calculate Courant Number to get Δt of this loop

t = t + Δt

PIMPLE loop

no

Flux correction

P = Pnew

P = Pnew

Velocity correction no

Convergence? yes

Reached End Time? yes End


Calculate velocity field

Set cycle control parameters of timestep and storage control parameters of results

Convergence?

no

yes Break the loop


PIMPLE vs. PISO algorithms PIMPLE: improved stability and control BUT at higher computational cost

Mesh: 0.3 millions of ”hex” cells, graded in z-axis direction smooth plate, ReI = 62, We = 0.18



PIMPLE vs. PISO algorithms PIMPLE: improved stability and control BUT at higher computational cost

Mesh: 0.3 millions of ”hex” cells, graded in z-axis direction smooth plate, ReI = 62, We = 0.18



Used methods of numerical linear algebra Solvers for large (sparse) systems of linear algebraic equations (SLAE)

General notes For the solved class of problems, • Meshes usually have 1+ MM cells → systems with millions of unknowns • Phase volume fraction field behaves ”well”

No preconditioning nor advanced solvers are needed for solving the resulting SLAE. Gauss-Seidel method is more than enough (usually converges in 1 or 2 iterations).

• Pressure equation is a bit more complicated

Krylov subspaces based solver, preconditioned conjugate gradient (PCG) has to be employed Rather expensive and powerful preconditioner is necessary (used are fast incomplete Cholesky decomposition (FDIC) and geometric multigrid methods (GAMG).



Intro


Flow on a smooth plate



Flow on a steel plate Smooth plate

Mesh: 6 × 5 × 0.7 cm geometry, 66000 − 1500000 hex cells, ReI = 124, We = 0.71




Mesh size optimization idea 1: Follow the variable of interest, ReI = 124, We = 0.71 H2 O, Re = 60, α = 60◦ 0.6 0.5

aW /aT , [1]

0.4 0.3 0.2 0.1

1536400 1131416 862500 600000 198144 136224 66000

cells cells cells cells cells cells cells

0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 t, [s] Martin Isoz, UCT Prague



Mesh size optimization idea 2: Compare the αL fields, ReI = 62, We = 0.18




Mesh size optimization idea 2: Compare the αL fields, ReI = 62, We = 0.18




Mesh size optimization idea 2: Compare the αL fields, ReI = 62, We = 0.18 Integral difference in αL relative to mesh size

0.7

0.8

High error cells

0.5 0.4

δαL =

0.3 0.2 0.1

85760 cells 123280 cells 276000 cells 365010 cells 493120 cells 706560 cells 1104000 cells 1725000 cells

0.0 0.0

0.50

0.7

0.6

0.5 0.2

0.4

1.0

146

120

0.35

100 80

0.20 0.15 0.10 0


17

26

36

47

57

60 40

Used core hours

140

0.40

0.25

0.4

160

0.45

0.30

δ¯αL =

0.8

Mean integral difference in αL relative to mesh size

X 1 δαi L nTimes i∈(times)

Time, [s]

0.6

nCellserr αL nCellsαL

F α − α C L L nCellsαL

0.6

0.3

0.2

0.1

20

24 0 200000 400000 600000 800000 1000000 1200000 1400000 1600000 1800000 Number of cells in mesh

0.0 0.0

0.2

0.4 0.6 Time, [s]

0.8

1.0



Wetted to total area ratio: Flow regimes in dependence on We




Wetted to total area ratio: Flow regimes in dependence on We

[Yoshiuki I. et al. Numerical and experimental study on liquid film flows on packing elements in absorbers for post-combustion CO2 capture, Energy Procedia, 2013]




Wetted to total area ratio: Flow regimes in dependence on We 1.0 0.9 0.8

aW /aT , [1]

0.7 0.6

Cooke et al. HoffMann et al. (sim) Iso et al. (sim) HoffMann et al. (exp) Iso et al. (exp) drops 3 thin rivulets unstable flows 1 rivulet and progressing film

0.5 0.4 0.3 0.2 0.1 0.0 10−2


10−1 We, [1]

100


Intro


Flow on a textured plate



Flow on a steel textured plate Transversal texture – mesh size opzimization

Case specification: ReI = 62, We = 0.18 Integral difference in αL relative to mesh size

0.7

F α − α C L L nCellsαL

0.6 0.5 0.4

δαL =

0.3 0.2

0.8

276000 cells 493120 cells 706560 cells 1104000 cells 1725000 cells

0.7

0.6

0.1

0.5 0.2

0.4

Time, [s]

0.6

0.8

1.0

Mean integral difference in α relative to mesh size


Used core hours

δ¯αL =

i∈(times)

X 1 δαi L nTimes

L 0.50 149 160 0.45 140 0.40 120 0.35 100 0.30 83 80 73 80 0.25 71 60 0.20 40 0.15 20 0.10 0.05 0 200000 400000 600000 800000 1000000 1200000 1400000 1600000 1800000 Number of cells in mesh

nCellserr αL nCellsαL

0.0 0.0

High error cells

0.4

0.3

0.2

0.1

0.0 0.0

0.2

0.4 0.6 Time, [s]

0.8

1.0


Flow on a steel textured plate Effects of different textures on liquid flow

Qualitative comparison: Effects of textures
























Quantitative comparison: Wetted to total area ratio 1.0 0.9 0.8

aW /aT , [1]

0.7 0.6

no texture transversal texture longitudinal texture drops 3 thin rivulets unstable flow 1 rivulet and progressing film

0.5 0.4 0.3 0.2 0.1 0.0 10−2


10−1 We, [1]

100


Flow on a steel textured plate Pyramidal (complex) texture

Detail: ReI = 124, We = 0.71



Flow on a steel textured plate Pyramidal (complex) texture

Overview: ReI = 62, We = 0.10



Intro


Flow between two perforated plates



Flow between two perforated plates Overall geometry presentation



Flow between two perforated plates Overall geometry presentation



Flow between two perforated plates Uniform plate perforation

Mesh: 6 millions of ”hexahedral” cells, graded in z-axis direction




Overall preview: water on steel, ReL = 240




Focus on droplets formation: water on steel, ReL = 240




Interface area: from the mass and heat transfer point of view, drops, rivulets and film behave differently




Interface area: Relative area available as drop, rivulet and film Gas-liquid interface size, H2 O, α = 60◦ , Re = 240, We = 4.04

0.5 drops

rivulets

film

0.4 0.3 0.2

a ˜i =

P ai

(i)

ai ,

i = drops, rivulets, film

0.6

0.1 0.0 0.0


0.1

0.2

0.3 t, [s]

0.4

0.5

0.6


Flow between two perforated plates Zig-zag perforation

Mesh: 6 millions of ”hexahedral” cells, graded in z-axis direction




Interface area: Uniform (UN) vs. Zig-Zag (ZZ) perforation Gas-liquid interface size, H2 O, α = 60◦ , Re = 240, We = 4.04

0.7 0.6 0.5

UND UNR UNF

0.4

ZZD ZZR ZZF

0.3

a ˜i =

P ai

(i)

ai ,

i = drops, rivulets, film

0.8

0.2 0.1 0.0 0.00


0.05

0.10

0.15

0.20

0.25 t, [s]

0.30

0.35

0.40

0.45

0.50



Stagnant gas?: water on steel, ReL = 240




Detail: Bottom plate, ReI = 240 We = 4.04




Detail: Top plate, ReI = 240 We = 4.04



Intro


Conclusion



Concluding remarks Development of the simulations somehow mimicking the flow in packed columns

Flow on a smooth plate • Already available:

Simulation results in agreement with the published data Identification of flow regimes in dependence on Re, We New

• Outlook:

Study of the influence of boundary conditions on the solution Study of wetting in dependence on plate inclination and liquid type

Flow on a textured plate • Already available:

Automatic geometry creation and meshing (transversal, longitudinal and complex texture New)

• Outlook:

Texture optimization (density, roughness) Hamburg Texture optimization (orientation)



Concluding remarks Development of the simulations somehow mimicking the flow in packed columns

Flow between two perforated plates New • Already available:

Simulations for the case of uniform and zig-zag perforation Automatic geometry creation and meshing (holes location and diameter)

• Outlook:

Study of the flow behavior for different liquid flow rates, plate inclination angles, liquid types, boundary conditions and for different perforations

General topics • Reduction of the modeling computational cost:

Estimates for ICs (extrapolation, POD+DEIM) Hamburg Model reduction (thin film approximation), hybrid models Dynamic meshing

• Development of a more packing-like geometries • Development of surrogate models Martin Isoz, UCT Prague


Thank you for your attention

Simulation control Altix UV 2000, 1.1MM of hex cells, 4 cores



Multigrid methods From coarse to fine mesh and back, great scalability

[Falgout, R. D. An algebraic multigrid tutorial, Lawrence Livermore National Laboratory, Center for Applied Scientific Computing] Martin Isoz, UCT Prague


Multigrid methods From coarse to fine mesh and back, great scalability

[Falgout, R. D. An algebraic multigrid tutorial, Lawrence Livermore National Laboratory, Center for Applied Scientific Computing]



OpenFOAM structure Objects – objects – objects

Software structure • Foundation libraries (discretization, meshing, FVM,. . . ) • Physical modeling libraries (thermo-physical, viscosity, turbulence,. . . models, chemical reactions interface) • Utilities (import/export, parallel processing, postprocessing,. . . ) • Solvers • Linkage for user extensions and on-the-fly data analysis Ideal case (OpenFOAM Executable) • Custom executable for specific physics segment (few 100s of lines of code) • Code is structured, commented and easy to understand and modify • Existing code is used as a basis for custom development • Low-level functions (meshing, parallelization,. . . ) are handled transparently and are available to the user (no need for special coding at top level) Martin Isoz, UCT Prague
