Introduction to DNS! of! Multiphase Flows-II!

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Outline! Motivation and background! Simulations of bubbly channel flows!!laminar Flows; Turbulent Flows; Deformability! Introduction to DNS! of! Multiphase Flows-II!

! Liquid Phase! Methanol! (LPMEOHTM)! Process! From:http://p2pays.org/ref/16/15865.pdf! Synthetic fuel production Mossgas, Mossel Bay, SA From: http://www.fischer-tropsch.

Examples of Applications of Bubble Columns Process Methods and/or Reactants Acetone Acetic acid Oxidation of cumene Oxidation of acetaldehyde Oxidation of sec-butanol Carbonylation of methanol

chlorine Absorption in aqueous solutions of sulfuric acid Absorption in ammoniated brine Carbon disulphide and chlorine Oxidation of cuprous chloride Oxidation of phenol Copper and cupric acid or

cumene Aqueous potassium carbonate Aqueous sodium carbonate Carbon dioxide, aqueous sodium carbonate, and sulfur dioxide Dithiocarbamates, chlorine, and air Oxidation of ethylene in acetic acid

Cumene Cupric chloride Dichlorination Ethyl benzene Hexachlorobenzene Hydrogen peroxide Isobutylene Phtalic acid Phenol Potassium bicarbonate Sodium bicarbonate Sodium metabisulphides Thiuram

Tryggvason, "An Inverse Energy Cascade in Two-Dimensional, Low Reynolds Number Bubbly Flows." J. Fluid Mech. 314 (1996), 315-33. E.A. Ervin and G.

Part I Low Reynolds Number Arrays." J. Fluid Mech. 377 (1998), 313-345. A. Esmaeeli and G. Tryggvason, "Direct Numerical Simulations of Bubbly Flows. Part II Moderate Reynolds Number Arrays" J.

1 Outline! Motivation and background! Simulations of bubbly channel flows!!laminar Flows; Turbulent Flows; Deformability! Introduction to DNS! of! Multiphase Flows-II! Using DNS to help model SIMPLE systems! Flow regime transitions! Mass transfer and chemical reactions! Multiscale Modeling! Grétar Tryggvason! Spring 21! Outlook! Why Bubbly Flows are Important!! Liquid Phase! Methanol! (LPMEOHTM)! Process! From: Synthetic fuel production Mossgas, Mossel Bay, SA From: Applications of DNS to bubbly flows! Examples of Applications of Bubble Columns Process Methods and/or Reactants Acetone Acetic acid Oxidation of cumene Oxidation of acetaldehyde Oxidation of sec-butanol Carbonylation of methanol Oxidation of acetaldehyde Partial oxidation of ethylene Oxidation of ethylbenzene Barium sulfide and chlorine Oxidation of toluene Aqueous calcium oxide and chlorine Aqueous sodium bromide and chlorine Absorption in aqueous solutions of sulfuric acid Absorption in ammoniated brine Carbon disulphide and chlorine Oxidation of cuprous chloride Oxidation of phenol Copper and cupric acid or hydrochloric acid Oxychlorination of ethylene Benzene and ethylene Benzene and chlorine Oxidation of hydroquinone Absorption in aqueous solutions of sulfuric acid Oxidation of xylene Oxidation of cumene Aqueous potassium carbonate Aqueous sodium carbonate Carbon dioxide, aqueous sodium carbonate, and sulfur dioxide Dithiocarbamates, chlorine, and air Oxidation of ethylene in acetic acid solutions Wet oxidation of waste water Acetic anhydride Acetaldehyde Acetophenone Barium chloride Benzoic acid Bleaching powder Bromine Butene Carbon Dioxide Carbone tetrachloride Copper oxychloride Cumene Cupric chloride Dichlorination Ethyl benzene Hexachlorobenzene Hydrogen peroxide Isobutylene Phtalic acid Phenol Potassium bicarbonate Sodium bicarbonate Sodium metabisulphides Thiuram disulphides Vinyl acetate Water After: S. Furusaki, L.-S. Fan, J. Garside. The Expanding World of Chemical Engineering (2nd ed), Taylor & Francis 21! A. Esmaeeli and G. Tryggvason, "An Inverse Energy Cascade in Two-Dimensional, Low Reynolds Number Bubbly Flows." J. Fluid Mech. 314 (1996), E.A. Ervin and G. Tryggvason, "The Rise of Bubbles in a Vertical Shear Flow." ASME J. Fluid Engineering 119 (1997), A. Esmaeeli and G. Tryggvason, "Direct Numerical Simulations of Bubbly Flows. Part I Low Reynolds Number Arrays." J. Fluid Mech. 377 (1998), A. Esmaeeli and G. Tryggvason, "Direct Numerical Simulations of Bubbly Flows. Part II Moderate Reynolds Number Arrays" J. Fluid Mech. 385 (1999), B. Bunner and G. Tryggvason. Direct Numerical Simulations of Three-Dimensional Bubbly Flows. Phys. Fluids, 11 (1999), B. Bunner and G. Tryggvason. Dynamics of Homogeneous Bubbly Flows: Part 1. Rise Velocity and Microstructure of the Bubbles. J. Fluid Mech. 466 (22), B. Bunner and G. Tryggvason. Dynamics of Homogeneous Bubbly Flows. Part 2, Fluctuations of the Bubbles and the Liquid. J. Fluid Mech 466 (22), B. Bunner and G. Tryggvason. G. Bunner and G. Tryggvason. Effect of Bubble Deformation on the Stability and Properties of Bubbly Flows. J. Fluid Mech. 495 (23), High Reynolds Number Bubbles! Bubble Induced Drag Reduction! No Bubbles! Angular pair probability distribution! θ! θ! Slightly deformable bubbles! Nearly! spherical:! N=8, Eo=.5! Deformed:! N=8, Eo=4! Bubble j! Bubble i! R θ G(r ) = V N(N 1) δ (r r ) i j i ij Experiment:! d+=12; We=.686! Simulations:! d+=54; We= ! DNS of bubbles injected near the wall in a a turbulent channel flow show that the deformability of the bubbles plays a major role. Bubbles with a deformability comparable to what is seen experimentally (S. L. Ceccio, taken in the LCC) can lead to drag significant drag reduction, but only for a short time. The simulations clarified the turbulent modification and showed that less deformable bubbles can lead to an increase in the wall drag.! ~2%! 1

DNS of Bubbly Flows Challenges! Real bubbly flows usually involve:!

Large differences in material properties!

Computationally we prefer:! Small number of bubbles!

Moderate differences in material properties! (with J. Lu & S.

Thus, DNS usually require compromises between what is practical

7 wall shear The averaged wall shear stress versus time for the

The dashed lines represent the corresponding the ideal wall shear

1 1 2 3 1 2 3 4 5 6 7 8 4 5 6 7 8 Time wall shear The path of

The cross-channel coordinate versus time for the upflow (left) and

2 DNS of Bubbly Flows Challenges! Real bubbly flows usually involve:! Large number of bubbles! High Reynolds numbers! Large differences in material properties! Bubbly Flows in Vertical Channels! Laminar Flows! Computationally we prefer:! Small number of bubbles! Moderate Reynolds numbers! Moderate differences in material properties! (with J. Lu & S. Biswas)! Thus, DNS usually require compromises between what is practical and what is desirable! π g Flow! Flow! π.9.7 wall shear The averaged wall shear stress versus time for the upflow (top) and the downflow (bottom). The dashed lines represent the corresponding the ideal wall shear stress needed to balance the pressure gradient.! Time wall shear The path of bubbles. The cross-channel coordinate versus time for the upflow (left) and the downflow (right) at approximately steady state.! Time For a nearly spherical bubble! Lift toward wall! Upflow! Lift away from wall! Downflow! The bubble distribution and isocontours of the vertical velocity in the middle plane for upflow on the left and dowflow on the right. The velocity contours are plotted with.5 intervals.! Upflow! Downflow! 2

$ε avg H = ε c ( H 2w) w = H 2 ε c ε avg ( ) w = βh 2Δρg β = dp dy + ρ avg g The average void fraction profile across the channel for the upflow (top) and the downflow (bottom).$

3 Simple two-fluid model for laminar multiphase flow! Lift! Up-flow! Lift! Lift! Down-flow! Lift! d b! H! d b! w! H! w! ε avg ε avg Force balance at steady state:! dτ dx β Δρg ε avg ε(x) ( ) = In the center of the channel there is no shear, therefore! β = Δρg( ε avg ε c ) ε c = ε avg + β Δρg upflow:! β < ε c < ε avg downflow:! β > ε c > ε avg Downflow: The wall layer is void of bubbles. To find its thickness, use the fact that the total bubble volume is conserved:! ε avg H = ε c ( H 2w) w = H 2 ε c ε avg ( ) w = βh 2Δρg β = dp dy + ρ avg g The average void fraction profile across the channel for the upflow (top) and the downflow (bottom). The solid lines denote the results from the simulations and the dashed lines are the analytical results.! Void fraction Void fraction Upflow Downflow simulation model simulation model The average vertical liquid velocity profile across the channel for the upflow (top) and the downflow (bottom). The solid lines are the simulated results, averaged over 8 time units. The dashed line is the analytical results for the downflow. The circles represent the average bubble velocities in 1 equal sized bins across the channel.! Umean Umean Upflow Fluid velocity Average bubbles velocity Downflow Fluid velocity -.2 Analytical fluid velocity averaged bubbles velocity The average Reynolds stress profile versus the cross-channel coordinate for the upflow (top) and the downflow (bottom). The solid lines are the results of averaging over 8 time units. The dashed lines denote the results form the corresponding homogeneous flow.!.5 for the upflow =1.5e-5 for Homogeneous flow for the downflow =-2.11e-5 for Homogeneous flow.5

Experimental results! Effect of Bubble Deformability for! Turbulent Upflow! (with J. Lu)!

1333 Turbulent Upflow: Effect of Deformability!

The bubbles and iso-contours of the instantaneous vertical velocity in a plane through the

bubbles at one time when the flow is approximately at steady state.! M=1.54 1-1! Eo=.45! M=1.54 1-7!

$deformable (right) bubbles at approximately steady state.! Void fraction!$ $The void fraction has major influence of the flow behavior.$ $The wall peak in the void fraction for nearly spherical bubbles results in a reduction in the$ flow rate.! Deformable! Nearly spherical! Average velocity!

flow rate.! Deformable! Nearly spherical! Average velocity!

4 Experimental results! Effect of Bubble Deformability for! Turbulent Upflow! (with J. Lu)! Liu & Bankoff: D p /R=3.6/19=.1895 Serizawa et al: D p /R=4/3=.1333 Turbulent Upflow: Effect of Deformability! Turbulent Upflow: Effect of Deformability! The bubbles and iso-contours of the instantaneous vertical velocity in a plane through the middle of the channel for the upflow of nearly spherical (left) and much more deformable (right) bubbles at one time when the flow is approximately at steady state.! M= ! Eo=.45! M= ! Eo=4.5! The path of the bubbles. The cross-channel coordinate versus time for the upflow of nearly spherical (left) and much more deformable (right) bubbles at approximately steady state.! Void fraction! The void fraction has major influence of the flow behavior. The void fraction is plotted above and the velocity profiles to the right, along with the velocity from flow without bubbles (rescaled to account for the change in average density). The wall peak in the void fraction for nearly spherical bubbles results in a reduction in the flow rate.! Turbulent Upflow: Effect of Deformability! Deformable! Nearly spherical! Average velocity! Turbulent Upflow: Effect of Deformability! The transition from bubbles that keep hugging the wall to bubbles that drift away from the wall appears to be relatively sharp. The figure shows the trajectories of four bubbles for slightly different deformability. The flow is turbulent and the bubbles are released at different initial locations. On the left the bubbles slide along the wall but on the right most of the bubbles drift away. We are currently working on models that capture this behavior.! 2 15 Time 1 5 Case 1 2 tst6a 2 15 Time 1 5 Case 1 2 tst7a 4

consists of a homogeneous core where the

and the total flow rate depends strongly

found for both laminar and turbulent flow.

plays only a minor role, as long as they

of many bubbles to a single large slug in

! A= 1 Vol A= 1 Vol n n S nn da n x n x S

5 Bubbly flows in channels Summary! For nearly spherical bubbles the flow consists of a homogeneous core where the mixture is in hydrostatic equilibrium and a wall-layer.! For upflow the wall-layer is bubble rich and the total flow rate depends strongly on the deformability of the bubbles.! For downflow the wall-layer has no bubbles and the velocity profile is easily found for both laminar and turbulent flow. For downflow the exact size of the bubbles plays only a minor role, as long as they remain nearly spherical.! Coalescence Induced Flow Regime Transitions! (with J. Lu & S. Mortasavi)! For upflow deformable bubbles stay away from walls, completely changing the flow structure! Bubble Coalescence! Coalescence induced flow regime transitions in a laminar bubbly channel flow: The figure shows a preliminary two-dimensional simulation of the transition from a wall peaked distribution of many bubbles to a single large slug in the channels center.! A= 1 Vol A= 1 Vol n n S nn da n x n x S x y nx ny da ny ny F. J. Sowiński, and M. Dziubiński 28 Bubble Coalescence! A simulation of a coalescence induced regime transition in a small threedimensional system! The components of the interface area tensor versus time! 1 Vol S Tim e! Atomization and droplet breakup nn da 5

In general, the interface separating two fluids will undergo topology changes where two regions of one fluid coalesce, or one region breaks in two.

In their simples implementation, explicit tracking method never allow coalescence and method based on a marker function always coalesce two interfaces that are close.

non-continuum attractive forces. In general this draining can not be resolved and must be modeled.

This usually happens when an interface breaks up A thin film ruptures.

6 In general, the interface separating two fluids will undergo topology changes where two regions of one fluid coalesce, or one region breaks in two. Of those, the coalescence problem appears to be the harder one. In their simples implementation, explicit tracking method never allow coalescence and method based on a marker function always coalesce two interfaces that are close. In reality, films between two fluid interfaces take a finite time to drain and rupture only when the thickness is sufficiently small so the film is unstable to non-continuum attractive forces. In general this draining can not be resolved and must be modeled. Governing Equations As the interface evolves, the topology of the interface can change. Topology changes come in two types: A thin thread can pinch. This usually happens when an interface breaks up A thin film ruptures. This usually happens when two fluid masses coalesce Secondary breakup of drops Secondary breakup of drops Primary breakup of jets Primary breakup of jets Three frames from a simulation of the three-dimensional breakup of a jet. The initial twodimensional fold becomes unstable and generates fingers that eventually break into drops. Here, Re=1, We=5, and the density ratio is 1. The simulation is done using 72 by 48 by 38 unevenly spaced grid points in the radial, axial, and azimuthal direction, respectively. 6

Secondary breakup of drops Thermocapilary migration of many drops S. Nas and G. Tryggvason. Thermocapillary interaction of two bubbles or drops.

Computations with GERRIS Thermocapillary migration The temperature is found by solving the energy equation ρc p T + ( ρc p Tu ) = k T t where we

This equation is solved on a fixed grid by an explicit second order method in the same way as the momentum equation.

Here, β >, since surface tension generally is reduced with increasing temperature.

Initially the bubbles are placed near the cold wall. As they rise, the bubbles line up perpendicular to the temperature gradient. S. Nas, M.

Heat and Mass Transfer 49 (26) 2265 2276 Thermocapillary migration Thermocapillary motion of many twodimensional bubbles.

7 Secondary breakup of drops Thermocapilary migration of many drops S. Nas and G. Tryggvason. Thermocapillary interaction of two bubbles or drops. Int l J. Multiphase Flows 29 (23), From S. Zaleski. Computations with GERRIS Thermocapillary migration The temperature is found by solving the energy equation ρc p T + ( ρc p Tu ) = k T t where we have assumed that the fluid is incompressible and that viscous heating can be neglected. This equation is solved on a fixed grid by an explicit second order method in the same way as the momentum equation. The temperature on the surface of the bubble or drop is found by interpolating it from the grid and surface tension is found by σ = σ o β (T To ) Here, β >, since surface tension generally is reduced with increasing temperature. Thermocapillary migration Thermocapillary motion of two three-dimensional bubbles. The top wall is hot and the bottom wall is cold. Initially the bubbles are placed near the cold wall. As they rise, the bubbles line up perpendicular to the temperature gradient. S. Nas, M. Muradoglu and G. Tryggvason. Pattern Formation of Drops in Thermocapillary Migration. Int l J. Heat and Mass Transfer 49 (26) Thermocapillary migration Thermocapillary motion of many twodimensional bubbles. The top wall is hot and the bottom wall is cold. Initially the bubbles are placed near the cold wall. As they rise, they form horizontal layers. These layers, however, block the flow and become unstable to let the fluid flow toward the cold wall as the bubbles move toward the hot one. DNS of shock propagation in bubbly liquids C.F. Delale S. Nas and G. Tryggvason. Direct Numerical Simulations of Shock Propagation in Bubbly Liquids. Physics of Fluids. 17,

Shocks in bubbly liquid Results for 3D simulations of the collapse of a bubble cloud due to an increase in the pressure at the top of the domain! Polytropic gas inside the bubbles!

8 Shocks in bubbly liquid Results for 3D simulations of the collapse of a bubble cloud due to an increase in the pressure at the top of the domain! Polytropic gas inside the bubbles! Shocks in bubbly liquid Electrostatic fields are known to have strong influence on multiphase flows: of Droplet Suspensions Breakup of jets and drops Phase distribution in suspensions Here, we examine the effect of electrostatic fields on a suspension of drops in channel flows by direct numerical simulations. For fluids with small but finite conductivity, Taylor and Melcher (1969) proposed the leaky dielectric model. This model allows both normal and tangential electrostatic forces on a two fluid interface. The fluid flow Momentum (conservative form, variable density and viscosity) ρu + ρu u = p + f t + µ ( u + T u ) + σ κ n δ x x f F ( )da Surface tension Mass conservation (incompressible flows) u = Electric force The electric field is obtained from the equation for the conservation of current: Dq Dt = σe the charge accumulation is found by: q = εe The force on the fluid is then found by: f = qe 1 2 (E E) ε neglecting also convection of charge 8

9 σ i σ o =.5 Re = 2 εi εo =.1 We =.625 α = 2% E * =.182 σ i σ o =.1 Re = 2 εi εo =.1 We =.625 α = 2% The interaction of many drops in channels, with and without flow has been examined. E * =.4 Oblate drops always fibrate as the electrohydrodynamically induced fluid motion works with the electric interactions to line up the drops Fluid shear breaks up the fibers, depositing them on the walls for intermediate flow rate and keeping them in suspension for high enough flow rates Prolate drops exhibit more complex interaction and form additional structures The instability of a thin film: Simulations of The interface and the velocity field at time zero and three subsequent times for S=1 and R=1. The phase change between liquid and solid or between liquid and vapor is the critical step in the processing of most material as well as in energy generation. Computations will make it possible to predict the small scale evolution of systems undergoing phase change from first principles.! To simulate such flows, it is necessary to solve the energy equation for the temperature distribution and to account for the change of phase at the phase boundary.! Governing Equations! ρ u + ρ uu = p + f + µ( u + T u ) + F σκ nδ ( x x f ) da t ct + u ct = k T + t T T q = k1 k 2 n 1 n 2 q δ(x x Tl = Tv = Tsat ( psys ) u = q δ (x x f )da L ρv ρ f 1 q 1 1 Vn = ( ul + uv ) + 2 L ρv ρ f dx f = Vn n + u dt f )da Energy equation! Heat source! Thermodynamic! Mass conservation! Velocity of bdry! 9

10 Computing the volume source! m = ρ l ( u l V n ) = ρ v ( u v V n ) Volume expansion:! u v u l = m 1 1 ρ v ρ l Normal velocity! V n = 1 ( 2 u + u v l ) m ρ v ρ l Source term! u = q 1 1 L ρ v ρ l δ( x x f )ds ul Compute the heat source at the interface! Vn ug q = k T k T n n l T- s (x,y) Ts (x1,y1) T+ Nusselt number versus time! Experimental correlation! Berentson, 1961! Nu B =.425 (Gr Pr/Ja) 1/ 4 The effect of the wall superheat for near critical film boiling! Ja=.35! Ja=.117! Ja=.234! Ja=.468! Ja=1.167! Nucleate Flow Boiling! Assumption : Surface nucleation characteristics determined by size distribution of potentially active sites Random spatial site distribution Random conical cavity size (mouth radius, r) distribution Assume vapor embryo radius = r Assume near wall liquid film is stationary Nucleation site is active if r min > r* 2σTsatυlv r* = Carey (1992) hlv[ Tl Tsat] Simple microlayer model! Nucleation site First grid line R 1 D Q = q dx = δ = D Simple microlayer model! D vapor δ o R o liquid Total heat transfer to the microlayer! Volume expansion! U o q = k T w T f δ δ = δ 2 o 2β t t e = δ 2 o 2β D = U o t e = U oδ o 2 kδt δ 2 o ( 2β U o )x dx = kδt D 1 dx δ o 1 ( 2β δ 2 o U o )x V Q = 1 1 L ρ v ρ f Evaporation of the film! 2β = k ΔT δ Heat transfer! dδ dt = q ρ f L = kδt δρ f L = β Evaporation! δ Integrate to find thickness! Find length of film! Q = δ o U o Lρ f Applied near the apparent contact! 1

Simple microlayer model! Simple microlayer model! vapor Nucleation site First grid line δ = V δ o liquid U o R 1 D R o 1.

When computing the flow, we must add a volume source at the wall to account for vapor generation as the film evaporates! 3.

V Q = 1 1 L ρ v ρ f Q = δ o U o Lρ f Including microlayer! no microlayer! Water at 1atm, Tsat=373.

75 mm; Wall superheat: 18K! 4x4x6 grid resolution! Nucleate Boiling!

development works still needs to be done!! Such simulations should allow us to!

Use the simulations to make predictions about boiling under conditions where experiments are difficult or do not yield the necessary data.

11 Simple microlayer model! Simple microlayer model! vapor Nucleation site First grid line δ = V δ o liquid U o R 1 D R o 1. The motion of the apparent contact point is found by extrapolating its location from the phase boundary close to the wall, giving U o 2. When computing the flow, we must add a volume source at the wall to account for vapor generation as the film evaporates! 3. To find the total heat transfer from the wall, we must correct to take into account the heat transfer needed to evaporate the microlayer! V Q = 1 1 L ρ v ρ f Q = δ o U o Lρ f Including microlayer! no microlayer! Water at 1atm, Tsat=373.15K; liquid/vapor density ratio=165; viscosity ratio=23; thermal conductivity ratio=27; specific heat ratio=1; domain size: 1.5x1.5x15.75 mm; Wall superheat: 18K! 4x4x6 grid resolution! Nucleate Boiling! There appears to be no significant technical obstacles for conducting large scale simulations of nucleate flow boiling however, some development works still needs to be done!! Such simulations should allow us to! Assess the accuracy of the assumptions made in the modeling of the microlayer! Use the simulations to make predictions about boiling under conditions where experiments are difficult or do not yield the necessary data.! Mass Transfer and! Chemical Reactions! Computations of the cleavage of a viscous drop by a soluble surfactant.! Figure from M. Muradoglu, Koc University! Mass transfer and chemical reactions! Computations of mass transfer and chemical reactions in a bubble swarm! A + B R! A + R S! A-liquid reactant,! B-gaseous reactant,! R-desired product,! S-impurity.! A! R! S! Figure from J. G. Khinast, Rutgers and Graz Univ.! 11

DNS with multi-scale models DNS with multi-scale models Multiphase flow DNS with embedded multi-scale models Results from simulations of the of the catalytic hydrogenation of nitroarenes.

In frames a and c the reaction rates are relatively slow, compared with the mass transfer, but in frames b and d the reaction is relatively fast. From Radl et al. Multiscale Issues!

Computational domain Drop Type A Problems: Dealing with Isolated Defects! Gravity Wall Type B Problems: Constitutive Modeling Based on the Microscopic Models! Reference: W. E and B.

12 DNS with multi-scale models DNS with multi-scale models Multiphase flow DNS with embedded multi-scale models Results from simulations of the of the catalytic hydrogenation of nitroarenes. The hydrogen (frames a and b) and hydroxylamine (frames c and d) concentration profiles are shown for one time for two simulations. In frames a and c the reaction rates are relatively slow, compared with the mass transfer, but in frames b and d the reaction is relatively fast. From Radl et al. Multiscale Issues! Some communities have defined two types of multiscale problems.! DNS with multi-scale models Buoyant bubbles in an inclined channel flow! Average Velocity-B! Computational domain Drop Type A Problems: Dealing with Isolated Defects! Gravity Wall Type B Problems: Constitutive Modeling Based on the Microscopic Models! Reference: W. E and B. Enquist, The heterogeneous multiscale methods, Comm. Math. Sci. 1 (23), ! gravity! S. Thomas, A. Esmaeeli and G. Tryggvason. Multiscale computations of thin films in multiphase flows. Int l J. Multiphase Flow 36 (21), Thin film model-a! DNS with multi-scale models Drop motion on a sloping wall. Impact of fully resolving the film between the drop and the wall DNS with multi-scale models Film model linear velocity profile h 1 + ( huf ) = ; t 2 x 2 2h dp ( huf ) + 3 x ( huf2) = ρ dx, t f o 1. Identify whether a grid points at a wall belong to a film or not. 2. For film wall-points, given h and Uf, find the wall-shear and set the ghost velocities. For points outside the film, use the no-slip boundary condition. 3. Solve the Navier-Stokes equations for the velocity and pressure at the next time step, using the ghost velocities set above. Minimum film thickness versus time Wall shear and ghost velocity: τ Δy U ui, = ui,1 f τ f = µo f µd h 4. Integrate the thin film equations, using the pressure at the wall as computed by solving the NavierStokes equations (step 3). 5. Go back to (1) 12

DNS with multi-scale models Mass diffusion in liquids Drop motion on a sloping wall.

the advection diffusion equation and when mass diffusion is low, mass boundary layers can be much thinner than the fluid boundary layers.

And Many More!! Thermocapillary migration Film boiling from a hot cylinder! Summary! Effect of flow on dendritic solidification!

flow problems.! Rayleigh-Taylor! Drop breakup! Splatting drops!

more complexity.! Cavitating bubbles! Fibration due to electric fields! Explosive Boiling!

! Binary drop The presence of separate computational elements to track the front allows for many extensions and improvements! Atomization!

These simulations have been shown to yield insight of the same type obtained from DNS of single phase turbulent flows!

13 DNS with multi-scale models Mass diffusion in liquids Drop motion on a sloping wall. Impact of fully resolving the film between the drop and the wall Coarse grid Coarse with model Fully resolved Scalar diffusion is governed by the advection diffusion equation and when mass diffusion is low, mass boundary layers can be much thinner than the fluid boundary layers. Using a multiscale model for the mass diffusion (and possibly reactions) should extend our ability to simulate chemical reactions in bubble columns. On the left are results from a simple model problem, showing the possibilities Model Under resolved Fully resolved f f 2 f = σn + D 2 t n n And Many More!! Thermocapillary migration Film boiling from a hot cylinder! Summary! Effect of flow on dendritic solidification! The front tracking method described here has the right combination of simplicity and accuracy to allow simulation of fairly complex multiphase flow problems.! Rayleigh-Taylor! Drop breakup! Splatting drops! Generally, explicit tracking provides more accurate results for the same resolution than marker function methods, but at the cost of slightly more complexity.! Cavitating bubbles! Fibration due to electric fields! Explosive Boiling! The control over topology changes provides the user with the ability to either include or exclude such changes.! Binary drop The presence of separate computational elements to track the front allows for many extensions and improvements! Atomization! collision! What Now?! We now have the ability to conduct DNS of disperse multiphase flows for a fairly large range of situations. These simulations have been shown to yield insight of the same type obtained from DNS of single phase turbulent flows! Modeling of multiphase flows is far behind single phase flows and the development of more advanced models that can incorporate the new insight and data is perhaps the most urgent task in computational studies of multiphase flows! Numerical challenges still remain, but those are of critical importance primarily for flows that are more complex than those discussed here (churn-turbulent, phase change, etc.)! One of the biggest obstacle for more rapid increase in the use of DNS is the high entry barrier for new investigators. Many things to learn!! 13

Direct Numerical Simulations of Gas-Liquid Flows

Direct Numerical Simulations of Gas-Liquid Flows 1 Gretar Tryggvason*; 1 Jiacai Lu; 2 Ming Ma 1 Johns Hopkins University, Baltimore, MD, USA; 2 University of Notre Dame, Notre Dame, IN, USA Introduction