Moving Beyond Prediction to ControlFree Surface, Turbulence, and Magnetohydrodynamics:

Interactions and effects on flow control and interfacial transport

Mohamed AbdouProfessor, Mechanical & Aerospace Engineering, UCLA

Seminar on Science in Fusion’s Enabling R&D Program

Gaithersburg, MD, March 13, 2001

Acknowledgment: This presentation was prepared in collaboration with Profs. N. Morley and S. Smolentsev and draws on the work of many scientists in the field.

TURBULENCE

FREE SURFACE PHENOMENA

MHD

SCALAR TRANSPORT

Liquid Wall Researchers are Advancing the Understanding of Interacting Multi-Scale

Phenomena at the Frontiers of Fluid Dynamics

Fluid Out

B

J

V

J

Fluid In

Plasma

Plasma-Liquid Interactions

q

g

Bj

TURBULENCE

FREE SURFACE PHENOMENA

MHD

SCALAR TRANSPORT

Fusion LW Researchers are Contributing to the Resolution

of GRAND CHALLENGES in Fluid Dynamics

0 B Bμ

1j

0

);BV(BΔσμ

1

t

B

0

Tk)T]V(t

T[ρCp

CD)CV(t

C

0V

Bjρ

1

pρ

1-V)V(

t

V

gτ

0)V(t

•Turbulence redistributions at free surface

•Turbulence-MHD interactions

•MHD effects on mean flow and surface stability

•Influence of turbulence and surface waves on interfacial

transport and surface renewal

Teraflop Computer Simulation

Liquid Walls: many interacting

phenomena

Watermark - Shear layer instability at water surface - CalTech Data

• The term free surface is often used for any gas/void to liquid interface, but denotes an interface between a liquid and a second medium that is unable to support an applied pressure gradient or shear stress.

• Formation of surface waves, a distinguishing feature (for LW - Fr > 1, supercritical flow)

• Interfacial flows are difficult to model -computational domain changes in time making application of BCs difficult

• Interfacial tension effects make equations “stiff”- differing time scales for surface wave celerity compared to liquid velocity

“Open Channel Flows are essential to the world as we know it” -Munson, Young, Okiishi (from their Textbook)

Free surface flow forms: films, droplets, jets, bubbles, etc. Fluid regions can coalesce, break up, and exhibit non-linear behavior

CHALLENGE: FREE SURFACE FLOW

Numerically tracking moving interfaces is an ongoing challenge in CFD -

Still NO IDEAL Interface Tracking Method

Volume-of-Fluid (VOF): The method is based on the concept of advection of a fluid volume fraction, . It is then possible to locate surfaces, as well as determine surface slopes and surface curvatures from the VOF data.

Level-Set Method: The method involves advecting a continuous scalar variable. An interface can thus be represented by a level set of the scalar variable. This is a different approach from VOF where the discontinuity represents the interface.

OTHERS:Lagrangian Grid MethodsSurface Height MethodMarker-and-Cell (MAC) Method

10,0 yxt vuVOF

Watermark - milk drop splash simulation using VOF- Kunugi, Kyoto Univ.

Horace Lamb, British physicist:“I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic.”

•In Turbulent Motion the “various flow quantities exhibit random spatial and temporal variations” where “statistically distinct average values can be discerned.” - Hinze

•Turbulence is the rule, not the exception, in most practical flows. Turbulence is not an unfortunate phenomena. Enhancing turbulence is often the goal.

•Vastly different length and time scales make equations stiff - requiring large number of computational cycles. High resolution required to capture all length scales and geometrical complexities.

CHALLENGE: TURBULENCE

Center for Computations Science and Engineering (LBNL). LES simulation of instability in a submerged plane jet.

Teraflop Computers are Making TURBULENCE Accessible

Averaged Models:Some or all fluctuation scales are modeled in an average sense

LES

Super-

Approach Level of description Computational challenge

DNS Gives all informationHigh.

Simple geometry, Low Re

LESResolves large scales.

Small scales are averagedModerate to high

RANS Mean-flow levelLow to moderate.

Complex geometry possible

DNSlength ratio: l/Re

3/4

grid number: N(3Re)9/4

For Re=104 , N1010

Teraflop computingcomputers

RANS

Turbulence Structure Simulated

Turbulence / free surface interaction produces new phenomena - anisotropic near-surface turbulence

Watermark - Vortex structure and free surface deformation (DNS calculation)

•Turbulent production dominated by the generation of wall ejections, formation of spanwise “upsurging vortices”

•Upsurging vortices reach free surface, form surface deformation patches, roll back in form of spanwise “downswinging vortices”, with inflow into the bulk.

•The ejection - inflow events are associated with the deformation of the free surface and a redistribution of near surface vorticity and velocity fields.

Conceptual illustration of experimental observation of burst-interface interactions - From Rashidi, Physics of Fluids, No.9, November 1997.

CHALLENGE: MAGNETOHYDRODYNAMICS

•Complex non-linear interactions between fluid dynamics and electrodynamics

•Powerful mechanism to “influence” fluids

•Strong drag effects, thin active boundary layers, large (possibly reversed) velocity jets are characteristic MHD phenomena

•Large currents with joule dissipation and even self-sustaining dynamo effects add to computational complexity

FLO W

Free surface flow velocity jets produced from MHD interaction - UCLA calculation

Computational Challenge Li flow in a chute in a transverse field with: b=0.1 m (half-

width); B0=12 T (field)

000,100

Ha = B0b mHa

bHa

610

Each cross-section requires MANY uniform grids, or special non-uniform meshes.

102 10)/( Hab

MHD interactions can change the nature of turbulence - providing a lever of CONTROL

From Dresden University of Technology

Experimental control of flow separation by a magnetic field:

fully developed von Kármán vortex street without a magnetic field (upper)

with a magnetic field (right)

•Applied Lorentz forces act mainly in the fluid regions near the walls where they can prevent flow separation or reduce friction drag by changing the flow structure.

•Because heat and mass transfer rely strongly on the flow structure, they can in turn be controlled in such fashion.

Flow direction

Liquid Wall Science is important in many scientific pursuits and applications

• Liquid Jet and Film Stability and Dynamics: fuel injection, combustion processes, water jet cutting, ink jet printers, continuous rod/sheet/ribbon/sphere casting, flood/jet soldering, ocean waves, hull design, ocean/river hydraulic engineering, surfing, liquid walls for fusion reactors

• Liquid MHD / free surface interactions: melt/mold stirring and heating, liquid jet/flow control and shaping, crystal growth, astrophysical phenomena, liquid metal walls for particle accelerators and fusion reactors

• Liquid MHD / turbulence interactions: microstructure control in casting, boundary layer control, astrophysical dynamos and plasmas, liquid walls for particle accelerators and fusion reactors

• Free surface heat and mass transfer: oceanography, meteorology, global climate change, wetted-wall absorbers/chemical reactor, condensers, vertical tube evaporator, film cooling of turbine blades, impurity control in casting, liquid walls for particle accelerators and fusion reactors

Watermark: Turbulent flow effect on dendrite formation in casting - LANL simulation

NSTX Li module HYLIFE-II

Liquid Wall Science is being Advanced in Several MFE & IFE Research Programs

IFMIF

KOH Jacket

KOH

Twisted-Tape

3D LaserBeams

ThinPlastic

JUPITER-IIAPEX CLiFF

MODELING FREE-SURFACE MHD TURBULENCE(from limited DNS/experimental data to real applications)

EXPERIMENTSunderway at UCLA for near

surface turbulence and interfacial transport

measurements

Statistical description of bulk and free surface TURBULENCE

D N Sfor free surface MHD flows

developed as a part of collab-oration between UCLA and

Japanese Profs Kunugi and Satake

RANS TURBULENCE

MODELSK-epsilon

RST model DNS and

Experimental data are used at UCLA for

characterizing turbulence phenomena

and developing closures in RANS

models

Turbulent Prandtl Number

0.75 0.8 0.85 0.9 0.95 1y / h

0

10

20

30

Pr t

From experim ent:R e=13000R e=17900R e=20200R e=32100best fit

Joule Dissipation

0 40 80 120 160y+

-0 .008

-0.004

0

0.004

0.008

0.012

D +

0

1

2

3

4

K +

D I

D II

K

•Strong redistribution of turbulence by a magnetic field is seen.

•Frequency of vortex structures decreases, but vortex size increases.

•Stronger suppresion effect occurs in a spanwise magnetic field

•Free surface approximated as a free slip boundary. Work proceeding on a deformable free surface solution.

A BIG STEP FORWARD - (1st FREE SURFACE, MHD TURBULENT DNS)

“DNS of turbulent free surface flow with MHD at Ret = 150” - Satake, Kunugi, and Smolentsev, Computational Fluid Dynamics Conf., Tokyo, 2000

Ha=20, Streamwise

Ha=0

Ha=10, Spanwise

PUTTING DATA TO WORKRANS EQUATIONS: “K-” model

0 1 2 3 4 5(H a/R e) x 1000

0

4

8

12

Cf x

100

0

Experim ent :R e=29000R e=50000R e=90000calcu la tions

"transition"H a/R e=1/225

"lam inar"C f=2H a/R e

0 .7 5 0 .8 0 0 .8 5 0 .9 0 0 .9 5 1 .0 0

y / h

0

1 0

2 0

3 0

Tur

bule

nt P

rand

tl nu

mbe

r

- R e = 1 3 0 0 0 - 1 7 9 0 0 - 2 0 2 0 0 - 3 2 1 0 0

1

21 - P r_t for a sm ooth surface (from experim enta l data)

2 - P r_t for a w avy surface (expected)

1

2

Comparison of UCLA modelto experimental data

Experimental measurements of Turbulent Prandl number

MHD DEPENDENT TURBULENCE CLOSURES

Magnetic fielddirection

Kem em 3C 4C

Streamwise KBC 203

2

04 BC 0.02 0.015

Wall-normal KBC 203

2

04 BC }0.1exp{9.1 N }0.2exp{9.1 N

Spanwise KBC 203

2

04 BC }0.1exp{9.1 N }0.2exp{9.1 N

K- TURBULENCE MODEL

;])[(

Pr

2

nDissipatio

Kem

Diffusion

jK

t

j

oduction

j

it

jj x

K

xx

v

x

Kv

t

K

.])[( 2

2

1

emj

t

jj

it

jj K

Cxxx

v

KC

xv

t

tttt

tpnpt n

TCvtCq /Pr;

Pr''

Interfacial Transport Experiments in FLIHY

Visualization of sinking and dispersing milk drop in water

2 cm

•Large scale test section with water/electrolyte flow will generate LW relevant flow

•Tracer dye and IR camera techniques will be used to measure interfacial transport at free surface

•PIV and LDA systems for quantitative turbulence comparison to DNS

FLIHY Experiment at UCLA - Test section length = 4 m

Dye Diagnostics for Interfacial Mass Transport Measurements

Profile of dye penetration (red dots)

Local free surface (blue dots)

flow direction ~2 m/s

Water jet

hot droplets

Hot droplet penetrating jet

Dynamic Infrared measurements of jet surface temperature

Impact of hot droplets on cold water jet (~8 m/s) thermally imaged in SNL/UCLA test

NEW PHENOMENA IN LM-MHD FLOW2D Turbulence

LM free surface images with motion from left to right - Riga Data

3D fluctuations on free surfaceN=0

Surface fluctuations become nearly 2D along fieldN=6

Surface fluctuations are nearly suppressed

N=10B

SOME PROPERTIES OF 2-D MHD TURBULENCE:

Inverse energy cascade;Large energy containing vortices;Low Joule and Viscous dissipation;Insignificant effect on the hydraulic drag.

2-D turbulence could be very useful as a mean of intensifying heat transfer.

B

FLO WFLO W

Isolated walls:In the near-surface jet the velocity is about 2 times higher than the mean velocity

Conducting walls:In the near-surface jet the velocity is about 10 times higher than the mean velocity

Electromagnetic Control of Heat Transfer

Velocity profiles with favorable features could be formed by making the side-walls slightly electrically conducting.

Simulations of Flowing Lithium in NSTX

0.0 0.4 0.8 1.2 1.6 2.0D istance, m

0.000

0.004

0.008

0.012

Thi

ckne

ss, m

3 - H in=4 m m2 - H in=3 m m1 - H in=2 m m

123

Upper - “Center Stack +Inboard Divertor”, 2.5-D model;Lower – “Inboard Divertor”, Flow3D-M

MHD and Heat Transfer Conclusions:Stable Li film flow can be established over the Center Stack;The Center Stack projected heat load can be removed by a 4 mm film ejected at 2 m/s.

State-of-the-Art Computational Techniquesare Required for Intensive LW Simulation

Lithium Jet start-up without and with grid adaption - HyperComp Simulation

•Grid adaption or multi-resolution

•Parallel Algorithm Implementation

•Unstructured Meshes

•High-order advection and free surface tracking algorithms

USING MHD FORCES TO CONTROL FLOW

Soaker Hose Concept

•Leak liquid radially inward from supply tubes•Stagnate inward flow and drive liquid radially over short path with applied poloidal current•Complex interaction with other field components seen in simulations

UCLA Simulation

u u u

Ja Poloidal Ja B Radial

B Toroidal

Exploring Free Surface LM-MHD in MTOR Experiment

•Study toroidal field and gradient effects: Free surface flows are very sensitive to drag from toroidal field 1/R gradient, and surface-normal fields

•3-component field effects on drag and stability: Complex stability issues arise with field gradients, 3-component magnetic fields, and applied electric currents

•Effect of applied electric currents: Magnetic Propulsion and other active electromagnetic restraint and pumping ideas

•Geometric Effects: axisymmetry, expanding / contacting flow areas, inverted flows, penetrations

•NSTX Environment simulation: module testing and design

MTOR Magnetic Torus and LM Flowloop:Designed in collaboration between UCLA, PPPL and ORNL

Ultrasonic Transducer Plots

-2.4

1.2

4.8

8.4

12

.0

15

.7

19

.3

22

.9

26

.5

30

.1

33

.7

37

.3

40

.9

44

.5

48

.1

51

.8

55

.4

59

.0

62

.6

66

.2

69

.8

73

.4

77

.0

80

.6

84

.2

87

.9

91

.5

95

.1

Microseconds

Without Liquid Metal With Liquid Metal

Timeof-flight

Liquid Jet Research for IFE ChambersHigh-velocity, oscillating jets for liquid “pocket”•flow trajectory and jet deformation•primary breakup / droplet formation•dissembly processes•liquid debris interaction / clearance•partial head recovery

High-velocity, low surface-ripple jets for liquid “grid”•surface smoothness control•pointing accuracy / vibration•primary breakup / droplet ejection

Graphics from UCB

•Single jet water experiments and numerical simulations demonstrate control of jet trajectory and liquid pocket formation at near prototypic Re

Oscillating IFE jet experiments and simulations

Experimental Data from UCB

FlowDirection

Regions flattened by interaction with neighboring jet

Simulations from UCLA

Flow Direction

Understanding mechanisms of flow instability leads to improved control of

jet surface smoothness for IFE

• Upstream turbulence and nozzle boundary layer thickness heavily influence downstream jet stability

• Turbulence conditioning and boundary layer trimming in nozzle dramatically improves jet quality

UC Berkeley data

Re = 100,000L/D = 44

Re = 75,000L/D = 44

w/ conditioning w/o conditioning

Modeling of Stationary Jet Deformation

•Initially rectangular jets deform due to surface tension and corner pressurization in nozzle

•Capillary waves from corner regions fan across jet face - largest source of surface roughness!

LIF measurement of surface topology at Georgia Tech

Modeling UCLA Experiment

•Numerical simulations and quantitative surface topology measurements are critical tools for understanding jet deformation, and controlling jet behavior with nozzle shaping

Watermark: Turbulent flow effect on dendrite formation in casting - Juric simulation

Liquid Wall Science is important in many scientific pursuits and applications

• Liquid Jet and Film Stability and Dynamics: fuel injection, combustion processes, water jet cutting, ink jet printers, continuous rod/sheet/ribbon/sphere casting, flood/jet soldering, ocean waves, hull design, ocean/river hydraulic engineering, surfing, liquid walls for fusion reactors

• Liquid MHD / free surface interactions: melt/mold stirring and heating, liquid jet/flow control and shaping, crystal growth, astrophysical phenomena, liquid metal walls for particle accelerators and fusion reactors

• Liquid MHD / turbulence interactions: microstructure control in casting, boundary layer control, astrophysical dynamos and plasmas, liquid walls for particle accelerators and fusion reactors

• Free surface heat and mass transfer: oceanography, meteorology, global climate change, wetted-wall absorbers/chemical reactor, condensers, vertical tube evaporator, film cooling of turbine blades, impurity control in casting, liquid walls for particle accelerators and fusion reactors

Increasing Green House Gases: Humidity, CO2, Methane, NOx, Sox etc.

Infra Red Absorption into Green House Gases and on the Earth surface

Preserving Heat in the Air

Temperature Rise in the Air

Earth

I.R.:Infra Red

I.R. Absorption

Sun

Air

I.R.Radiation

Tem

per

atu

re R

ise

(K)

Year

What is Global Warming?

Free surface mass transport is affecting CO2 concentrations

Missing Sink Problem over past 30 years

Measured atmospheric CO2 increase (34 ppm)

- Spent Fossile Fuel emissions (61 ppm)

= Missing Sink(-27 ppm)

Turbulent Heat and Mass transfer across Free Surface ?

CO2 absorption at the turbulent free-surface deformed by the shear wind, by means of direct numerical solution procedure for a coupled gas-liquid flow

Wind flow

Free surface contour - wind-driven calculation

?

Coherent Structures in Wind-driven Turbulent Free Surface Flow

Water

Wind

10-1 10010-7

10-6

10-5

10-4

10-3

Friction Velocity, uτ (m/s)G

ass

Exc

ha

ng

e R

ate

,

k L

(m/s

)

Wind tunnel experiment

X : Measurements at sea: Present study

: Liss & Merlivant (1986)

Atmospheric Pressure Contour Surface (Green)

High Speed Gas Side Regions (Brown)

High Speed Water-Side Regions (Blue)

Streamwise Instantaneous Velocity (Color Section)

DNS

Some Common Aspects between Global Warming and Fusion Science Thermofluid

ResearchSimilar Phenomena•High Pr flow with radiation heating at free surface from plasma•High Sc flow with CO2 absorption at free surface of sea

Similar Flow Characteristics•Re is high, both have the similar turbulence characteristics.•MHD (fusion) and Coriollis (global warming) forces can influence the average velocity

Heat and Mass Transfer Similarity•High Pr, very low thermal diffusivity->very thin thermal boundary layer->large temperature gradient at interface •High Sc, very low molecular diffusivity->very thin concentration boundary layer->large concentration gradient at interface.

Simulation of commercial inkjet by Rider, Kothe, et al. - LANL

Liquid Jet Stability and Breakup

Inkjet Printer quality is hampered by formation of “satellite” droplets

Data from Ho - UCLA

Micro-injector increases relative importance of surface tension by decreasing size - eliminates satellite droplets and improves precision

mic

ro c

omm

erci

al

Vertical B field effects on Liquid Metal Film Flows

Continuous sheet casting can produce smooth free surfaces and film thickness control via MHD forces

Film thickness profiles for various Hartmann NumbersSimulation by Lofgren, et al.

Reflections on 19th & 20th Centuries1850: Navier-Stokes Equation

1873: Maxwell’s Equations

1895: Reynolds Averaging

1900-1960’s: -Averaging techniques, Semi-empirical approach. Heavy reliance on Prototype Testing (e.g. wind tunnels for aerodynamics).

1960’s - 1970’s: -Supercomputers allow direct solution of N-S for simple problems. Advances in Computational Fluid Dynamics (CFD), e.g. utilization of LES technique.

1980’s - 1990’s:-Rapid advances to Teraflop Computers-Rapid advances in CFD and in experimental techniques-Turbulence structure “simulated” and “observed” for key problems-Better understanding of fluid physics and advanced “Prediction” tools-Paradigm Shift:

- From “mostly experimental for empirical global parameters” to “larger share for CFD: simulation first followed by smaller number of carefully planned experiments aimed at understanding specific physics issues and verifying

simulation.”

21st Century Frontiers

Moving Beyond “Prediction” of Fluid PhysicsTo “Control” of Fluid Dynamics

• With the rapid advances in teraflop computers, fluid dynamicists are increasingly able to move beyond predicting the effects of fluid behavior to actually controlling them; with enormous benefits to mankind!

Examples

• Reduction in the Drag of Aircraft

The surface of a wing would be moved slightly in response to fluctuations in the turbulence of the fluid flowing over it. The wings surface would have millions of embedded sensors and actuators that respond to fluctuations in the fluids, P, V as to control eddies and turbulence drag. DNS shows scientific feasibility and MEMS can fabricate integrated circuits with the necessary microsensors, control logic and actuators

• Fusion Liquid Walls

Control of “free surface-turbulence-MHD” interactions to achieve fast interfacial transport and “guided motion” in complex geometries (“smart-liquids”)

• Nano Fluidics: Pathway to Bio-Technologies

Appropriately controlled fluid molecules moving through nano/micro passages can efficiently manipulate the evolution of the embedded macro DNA molecules or affect the physiology of cells through gene expression.