Feedbacks for Fluid Flows and Fusion

Miroslav KrsticDepartment of Mechanical and Aerospace Engineering

Feedbacks for Fluid Flows and Fusion

2

MAE Control Program

Control of Flows and Propulsion Systems:

• Tom Bewley• Bob Bitmead• Miroslav Krstic

Control of Structures:

• Bob Skelton (macro-structures, e.g., satellite

antennas)• Raymond de Callafon (micro-structures, HDD positioning)

Command and Control for Unmanned Aerial Vehicles:

• Bill McEneaney

3

Bluff Body Flow Control

Controlled

Uncontrolled

Ole Morten Aamo

4

Mixing Control in Channels and Pipes

ControlledControlled

UncontrolledUncontrolled

xPxPkxVxV P wallbottom walltop walltop wallbottom )()( Control law:

Pressure distribution

Andras Baloghand

Ole Morten Aamo

5

Jet Flow Control

tpKtUtU ,0)()( 21Controller:

Lawrence Yuan

6

Particle mixing with control

Controlled - heavy particles

Controlled - light particlesUncontrolled

Diffusive mixing

7

Tailored Fuel Injection for Pulsed Detonation Engines

(Aliseda, Ariyur, Lasheras, Krstic, and Williams)

Laser measurement of water droplets sprayed into a glass tube

1 2 3 4 5-0.06

-0.05

-0.04

-0.03

-0.02

1 2 3 4 51

2

3

4

5

6

7

8

time (PDE cycles)

α

u (control)

*α (desired equiv. ratio distribution)

Multivariable PI controller

Actuator valve array

COMBUSTION INSTABILITY CONTROLvia Extremum Seeking

EXTREMUM SEEKER

• Rayleigh criterion-based controllers, which use phase-shifted pressure measurements and fuel modulation, have emerged as prevalent

• The length of the phase needed varies with operating conditions. The tuning method must be non-model based.

phas

e

sin wt

Pressure

s

1 washout

filter

COMBUSTOR

Phase-ShiftingController

Frequency/amplitudeobserver

fuel

Problem Statement

• Tuning allows operation with minimum oscillations at lean conditions

• Reduced engine size, fuel consumption and NOx emissions

Impact

time

ext. seeking suppresses oscillations

Experimental Results (4MW combustor)

with UTRC

AXIAL FLOW COMPRESSOR CONTROLby Extremum Seeking

Problem Statement• Active controls for

rotating stall only reduce the stall oscillations but they do not bring them to zero nor do they maximize pressure rise.

• Extremum seeking to optimize compressor operating point.

CaltechCOMPRESSOR

Air Injection Stall Controller

Pressure rise

s

1 washoutfilter

sin wt

EXTREMUMSEEKER

bleed valve

• Smaller, lighter compressors; higher payload in aircraft

• Patent issued (August 2000)

Impact

H.-H. Wang

timeP

ress

ure

Ris

e

Experimental ResultsExtremum seeking stabilizes the maximum pressure rise.

10

Tokamak: Plasma electro-magnetically confined in a torus, to obtain nuclear fusion energy.

Densities (~1020 particles/m3) and temperatures (~108 K) must be achieved.

100

101

102

103

10-27

10-26

10-25

10-24

10-23

10-22

10-21

Energy (keV)

Rea

ctio

n R

ate

(m3 /s

ec)

D-T

Reactivity rate , vs T, for D-T mixturev Quenching P T

Excursion Thermal P T

Low Temperature – High Density Regime(economically attractive)

Reaction rate increases with temperature

Thermally Unstable

Eugenio Schuster, coadvised w/ George Tynan

Burn Instability Control in Tokamaks

11

Burn Instability

0 20 40 60 80 100 120 140 160 180 2000

5

10

15x 10

19

Time [sec]

Den

siti

es [

1/m

3 ]

n

nDT

nn

ne

0 20 40 60 80 100 120 140 160 180 2000

5

10

15

20

25

30

35

Time [sec]

[%

] -

Tem

pera

ture

[ke

V]

T

Open loop desired equilibrium is unstable MHD stability conditions are violated

Active control is required for stabilization

Our approach: Nonlinear Model-Based Control

12

Model

Total Density

Electron Density enn

Reactivity Rate

Delay Confinement Time

D-T Confinement Time

Alpha Confinement Time

Energy Confinement Time EDTd

vIImpurity Confinement Time

vnn

dt

dn DT

2

2

Alpha Particles Balance Equation

Sn

dt

dn

nv

nn

dt

dn

d

nn

d

nDT

DT

DTDT

2

22

D-T and Neutral Particles Balance Equations

II

II Sn

dt

dn

Impurity Particles Balance Equation

auxradDT

E

PPQvnE

dt

dE

2

2

Energy Balance Equation

eIDTeiIIDTe nnnnnnnnTEnZnnn ,2

3 ,2

Impurity Density In

Fueling Rate

Auxiliary Power

Energy

Neutral Density

Deuterium-Tritium Density

Alpha Density

auxPE

nnDTnn

Impurity Injection ISS

13

Model

EIIEddEDTDTE

auxradDT

iPHITERE

kkkk

PPQvn

P

kPPABRIf

, , ,

2

082.02

47.047.019.05.015.06.102.190ITER Scaling:

Beta Limit

Delay Scaling Constant

Plasma Volume

D-T Scaling Constant

Elongation at

Alpha Scaling Constant

Magnetic Field

Minor Radius

Major Radius

Plasma Current

Impurity Scaling Constant

7k3DTk

1dk

%3.5

5.2lim

aBI

10Ik

MA 22Im 6R

m 15.2aT 85.4B

2.2k3m 1100V

4

63

52

4321exp TaTaTaTaa

T

av rDT Reactivity:

Radiation Losses: Bremsstrahlung (Ab) – Line (Al) – Recombination (Ar)

eIIrIIlIIDTbrad nTnZnATnZnATnZnnAP

23

621

421

2 64164

14

Simulation Results—Region of Stability

0 2 4 6 8 10 12 14 160

0.5

1

1.5

2

2.5

3

3.5

4x 10

20

T [keV]

n e [

m-3

]

Stab ilit y

Linear Pole PlacementLinear Rob ust Nonlinear Eq uilib rium Limit

15

Control of Temperature and Density Profiles

Goal: make the temperature and density converge to desired radial profiles.

• Burn Control• MHD Instability Avoidance• High-beta and High-confinement mode access • Confinement Time Improvement• Transport Reduction

Why control kinetic profiles?

Eugenio Schuster

16

Model

Density Balance Equation

SnVr

nDr

rrt

np

1

Energy Equation

auxbrem PPr

ErD

rrt

E

1

,5.0 ,

sec

0

3

2 2

r

T

T

DV

m

rn

nD p

1 , 22

e

iiieffeeffbbrem nZnZTnZAP

Boundary Conditions and Controls:

),( ,00

),( ,00

tank(a,t)r

n,t)(

r

n

taEk(a,t)r

E,t)(

r

E

n

E

rn

rE

17

Simulation Results

Closed Loop: Energy Profile Evolution Closed Loop: Density Profile Evolution

18

Control of Tokamak Vertical Stability

•Objective: plasma shape control and vertical stability control

•Actuators: poloidal coils

Eugenio Schuster, with Mike Walker and Dave Humphreys (General Atomics)

19

Saturation Anti-Windup Design

Experimental tests at GA

this year

DIII-DTOKAMAK

GA design

Loss of stability due to saturation!

20

Control of Magnetohydrodynamic Flows

•For drag management in hypersonic flight (re-entry vehicles and SCRAMJET propulsion).

•For liquid metal blankets in fusion reactors.

•Control possible using purely electrical actuators and sensors (rather than MicroElectroMechanicalSystems).

Eugenio Schuster

21

MHD Governing Equations

0

0

1

11

2

2

B

v

vBBBvB

BBvvvv

t

Pt

Navier-Stokes Equation

Incompressibility Condition

Magnetic Field Equation

Faraday’s Law

Ampere’s Law

Ohm’s Law

Magnetic Induction Equation

BEj

Bj

EB

v

t

ty conductivi electric:

ty permeabili magnetic:

viscositykinematic:

density mass:

22

Hartmann Flow

Actuators and sensors on the wall.0 0.1 0.2 0.3 0.4 0.5

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

u

y

Velocity Profile - Perfectly Insulating Walls

Ha=0 Ha=2 Ha=5 Ha=10 Ha=100

23

Control Approach

Goal: minimize/maximize the cost functional

t

tdmtE

0 )(lim

Energy functional: dxdybbvuEd vu ,

1

1

0

2222 Bv

dxdy bbbb

R

R

dxdy vvuum

d vy

vx

uy

ux

m

d

yxyx

1

1

0

2222

1

1

0

2222

, BvDissipation functional:

mR

R Reynolds number Magnetic Re number

0

0

2wall ),(

LdxdttxB

Using the minimal amount of control energy

0

0

2wall ),(

Ldxdttxj

0

0

2wall ),(

LdxdttxV

24

Control Results (preliminary)

Pressure or electric potential distribution

Vwall or jwall

wall

zoom out

Velocity or current vectors

Inspired by: