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