on the dynamics of mercury target delivery and dump by foluso ladeinde stony brook university stony...

On The Dynamics of Mercury Target Delivery and Dump

By

Foluso Ladeinde

Stony Brook University

Stony Brook, New York 11794-2300

Muon Collider Design WorkshopDecember 1-3, 2009; at BNL

Outline• A Mechanical/Aerospace Engineer’s viewpoints on

delivery, jet exhaust, and dump of Hg target– Whither Moody chart (friction factor) or system curve? - A

different kind of pipe analysis– Whither the familiar decay laws for jet flows? – A different

kind of jet analysis– Relevant analytical work on jet exhaust– CFD Analysis

ScopeGoverning Equations The internal flow The jet exhaust The Dump The integrated model pipe-jet flow

– Hybrid CFD-CSM-CFA Analysis

The internal flow problem

Pump/System Curve

Moody Chart

Whither Moody Chart (friction factor) and system curve?

Whither the familiar jet decay laws?

Analysis Options

• Data from physical experiments• Exact, closed-form analysis• Approximate methods

– Computational fluid dynamics (fluid flow problems)– Computational solid mechanics (solid mechanics

problems)– Computational material science (material science

problems)– Computational dynamics analysis (dynamics problems) – Etc…

• Some advantages of numerical methods • Focus on computational fluid dynamics (CFD)e• Procedures for CFD analysis

CFD-Governing Equations

CFD-Governing Equations

CFD-Governing Equations

y

x

Turbulence Modeling Options in CFD

• RANS– Spalart-Allmaras– k- (Launder-

Sharma)– k- (Abid model)– High Re No. k- – k- (Menter’s SST

model)

• LES– Smagorinsky model– Dynamic SGS model– Implicit LES

(Filtering)

• DES– Based on Spalart-

Allmaras

• PRNS– Based on Abid k- – Based on high Re No. k-

• RANS/LES Hybrid

CFD - Numerical ApproachSpatial Discretization MUSCL (2nd-order)

WENO (5th-order)

COMPACT (6th-order)

Time Marching 2nd order Beam-Warming 4th order Runge-Kutta TVD Runge-Kutta

CFD - MUSCL

,2/

,2/

11,21

,21

iiiRi

iiiLi

LR

RiLii J

Q

J

QAFFF

,21,2

12

1ˆˆ

2

1ˆ

1

)2/1(at state averaged-Roe

RoeRoeRoe RRA

i2

1ii

L R

1i

Back to physical space,Numerical flux

Lax-FriedrichsFlux-splitting

CFD - WENO

21

1

21

1 ˆ~~ˆ~~1ˆ

iRoeiRoe

i

FRRFRRF

RoeRoe

FRFRoec

ˆ~ˆ 1 qFF cc ˆ2

1ˆ

1

0

)(

21,2

1,

1

0

)(

21,2

1,

1

0,

)(

21,

~ˆ ,ˆ

ˆ

k

r

r

icric

k

r

r

icric

k

mmricrm

r

ic

FFFF

FcF

1i 1i2

1ii

+ --+

WENOReconstruction

21

21

21

21,2

1

ˆˆˆ

ˆ~ˆ

iii

icRoei

FFF

FRF

Transform to characteristic form: m ax '( )u F u

CFD - WENO…• WENO Evaluation:

Smoothness Indicator

Robustness Factor

• Modifications Made:

~ / /

( )F Fi r ir

r

k

1 2 1 20

1

/ /

( )F Fi r ir

r

k

1 2 1 20

1

rr

ss

k

0

1,

r

r

r

d

2,

r :

:

,/( )F c Fir

rm j r mm

k

1 20

1

r k 0 1, ,

,

• Filter high-frequency noise:

COMPACT

• 6th order theoretical accuracy:

24

1122'1

''1

iiiiiii ab

91,9

14,31,, ba

N

kkiki

kifiif

a

011 2

~~~

The internal flow problem

DELIVERY SYSTEM CFD ANALYSIS – SBU (AEROFLO)

The internal flow problem

DELIVERY SYSTEM CFD ANALYSIS – SBU (AEROFLO)

The internal flow problem

DELIVERY SYSTEM CFD ANALYSIS – SBU (AEROFLO)

The internal flow problem

DELIVERY SYSTEM CFD ANALYSIS – SBU (AEROFLO)

The internal flow problem

DELIVERY SYSTEM CFD ANALYSIS – SBU (AEROFLO)

The internal flow problem

DELIVERY SYSTEM CFD ANALYSIS – SBU (AEROFLO)

The internal flow problem

Coordinate

Y

3

3.2

3.4

3.6

3.8

CoordinateZ

-0.4

-0.2

0

0.2

0.4

U

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

XY

Z

x = 58

DELIVERY SYSTEM CFD ANALYSIS – SBU (AEROFLO)

Jet Flow

– Relevant analytical work on jet exhaust in a magnetic field

• Osima et al. (1987) Field: 1/2 (1-tanh(z-15)/6.2) – inverted “S”Determination of the shape of the free surface Stuart number, Weber number, and εm=a/Lm determine

shape of jetRound, elliptical, lobe-shaped

• Gallardo et al. 2002 Field: Gaussian and other distributions (in z-)Changes in jet cross section and velocity assumed small! If jet enters field close to the axis, induced forces are

compressive and retarding. Hydrostatic pressure and jet diameter increases, then re-accelerates and elongates.

Hydrostatic pressure becomes negative and cavitation occurs as jet leaves field

Instability wave Ansatz

• Circular nozzle– Parallel

– Weakly non-parallel

– Leads to ODE eigenvalue problem (in radial coordinate)– Efficient solution by shooting method

• Chevron nozzle– Parallel

– Weakly non-parallel

Leads to PDE eigenvalue problem in r,

Pipe/Jet, RANS/LESHybrid• Pipe/Jet• RANS/LES,

CFD – Jet Exhaust

JET CFD ANALYSIS – TTC (AEROFLO)

No MHD, energy input

CFD – Jet Exhaust

JET CFD ANALYSIS – TTC (AEROFLO)

No MHD, energy input

CFD – Turbulence ModelingLES / RANSLES / RANS

CFD- Level-Set Equation

i

ti

Ti

i

x

GD

x

GS

x

Gu

t

G

~~

~~~~ (Peters)

Turbulent Flame Speed

G

G~

~~

Flame Curvature

G~

- Distance to the Flame Surface

t

tLt

t

L

t

t

L

LT

Scb

u

S

Scb

b

u

S

Scb

b

S

SS Pr

'

Pr

2'

Pr

223

2

1

23

1

23

(Peters, Pitsch)

Numerical Approach

Spatial Discretization: ENO (up to 6th order)

Time Marching: TVD Runge-Kutta (2nd, 3rd order)

Free Surface Calculation

• - pseudo-time

• is preserved

• numerical approach

Re-initialization Procedure

xGxGGGG 00 ~

0,~

,~

1~

sgn~

G-transport equation:

• Valid only at the flame surface

• Does not preserve the distance

0~G

•Sussman, Smereka, & Osher (1994)

•Russo & Smereka (2000)

•Sussman & Fatemi (1999) (for narrow-band method)

Re-initialization ProcedureCurvilinear Coordinates

GGGwGGwG

/sgn ,sgn 00

G

JG

JG

JJ

x

G xxx

GWGWGWGw

.

,

,

zzyyxx

zzyyxx

zzyyxx

wwwW

wwwW

wwwW

Central Finite Differences Upwinding based on Wi

CFD-Level set/VOF

LEVEL SET METHOD – UCLA (HIMAG)

By Others

CFD-Level Set

LEVEL SET – TTC (AEROFLO)

DUMP: CFD – LEVEL SET

LEVEL SET – RUTHERFORD APPLETON LAB(CFX)

By Others – Tristan Davenne

Dynamic Analysis – Dump material

DYNAMIC ANALYSIS – RUTHERFORD (AUTODYNAMICS)

By Others – Tristan Davenne

Concluding Remarks

• Discussed delivery, jet exhaust, and dump of Hg target, from a mechanical/aerospace engineer viewpoint– No Moody chart, friction factor data, or system curves for

operating point determination– A different kind of jet exhaust!– Couple of relevant analytical work on jet exhaust– CFD holds promise for the hybrid analysis– Level set (VOF) useful in determining free surface; thermal

energy not built into procedures– Hybrid CFD-CSM-CFA Analysis

• More theoretical analysis needed for the internal flow and jet flow; extend with numerical procedures

• Dump analysis will most likely be numerical

The Internal flow problem

Density ( ) 13456

Viscosity ( ) Dynamic Viscosity ( ) Thermal Conductivity ( ) 8.69

Specific Heat ( ) Prandtl Number 0.025

Velocity ( ) 3.4

Static Pressure ( ) Dynamic Pressure ( ) Diameter ( ) 0.884

Mesh File Block # Grid Size Description

pipe_01.grd Block 1 Pipe mesh in concentric cylinder form

pipe_02.grd Block 2 Overset mesh to cover the centerline of pipe

DELIVERY SYSTEM CFD ANALYSIS – SBU (AEROFLO)