幻灯片 1 - hep.princeton.edu

幻灯片 1 - hep.princeton.edu

The Effects of Geometrical Configurations on
Department
of
Mechanical
Engineering
Curved Pipe Flow for Muon Collider Project
Annual Stud=1.2)ent Research Poster
Symposium May 4, 2011

,

,

College of Engineering and=1.2) Applied=1.2) Sciences (d=1.2)CEAS)

Yan Zhan (SBU), F. Ladeinde (SBU), H. Kirk (BNL), K. McDonald (Princeton University)

Analytical Analysis for Laminar Curved Pipe Flow

Abstract
Liquid=1.2) mercury has been investigated=1.2) as a potential
high-Z target for the Muon Collid=1.2)er project. The
objective of this part of the project is to d=1.2)evelop a
target d=1.2)elivery system that results in the least turbulent
flow cond=1.2)itions at the exit of the nozzle. In the present
work, several curved pipe configurations have been
stud=1.2)ied=1.2), in which we examined=1.2) the d=1.2)ynamics of flow in
those configurations using theoretical analysis and=1.2)
fluid=1.2) flow mod=1.2)eling. Stead=1.2)y turbulent flows have been
stud=1.2)ied=1.2) for 0/0, 30/30, 60/60, and=1.2) 90/90 elbow
combinations, using several turbulent models, and=1.2)
comparing the results with experimental d=1.2)ata for some
of the cases. The generation of vorticity by pipe
curvature is critically examined=1.2) and=1.2) is reported=1.2) for the
various pipe configurations.

(b)

(a)

Momentum Thickness at the Pipe Exit

Extra Terms for Laminar Curved Pipe Flow
Extra terms in the momentum

*

v
cosw* r * sin *
*
*
*
*
*
*

v

cos

1

cos

v
v
1

w
1

u
d

2
*
z
D* r * sin w* *
w

[
(d=1.2)

)

]
*
*
*
*
*
*
*
*
3
*
z 1 r sin
Re 1 r sin r r 1 r sin z
r
(d=1.2)1 r sin )
dz

Overall Objects and
Procedures

*
2
*
*
*

w
cos

sin

1

w

cos

w

w
1
*
*
*
*
*
*
*
*
Dz r sin w *
vw
u w { 2r sin * 2
(d=1.2) *
sin * )
*
*
*
z 1 r sin
1 r sin
Re
1 r sin r
r
r (d=1.2)1 r * sin ) 2
z
w*
*
*
*
cosv sin u (d=1.2)1 )r sin *
*
*
*

u

v
1
d

*
*
*
2
2
*
z
[(d=1.2)2r sin 1) * r cos * r (d=1.2)sin cos cos * sin sin ) w ]
}
*
3
*
z
z
r
(d=1.2)1 r sin )
dz

Extra terms in the r momentum

Fig. 2 Assessment of extra terms

Numerical Analysis for Turbulent Curved Pipe Flow (Hg)
Turbulence Models Comparison[4]

Turbulence Intensity at the Pipe Exit

(b)

(a)

(a)

u
2k / 3
I
um
um

(b)

n =75 (d=1.2)d=1.2)=1.2))

Fig. 3 (d=1.2)a) Mesh for the 90 test pipe (d=1.2)cross-sectional mesh: nr n =15264) (d=1.2)b) Longitud=1.2)inal d=1.2)istribution of static pressure at the inner, outer and=1.2) bottom of the pipe

Solutions for Mercury Flow in Curved Pipe without Nozzle
(a)

Fig.8 Turbulence intensity d=1.2)istribution comparison at the pipe exit
(d=1.2)a) Along the horizontal plane (d=1.2)b) Along the vertical plane

(b)

Merits and Impacts

Fig. 4 (d=1.2)a) Geometry of pipes without nozzle in varying angles (d=1.2): 0), 30), 60), 90)) (d=1.2)b) Stream-wise velocity and=1.2) velocity vector plots (d=1.2)=60 , inner: left, outer: right)

Solutions for Mercury Flow in Curved Pipe with Nozzle
(a)

Proced=1.2)ures to stud=1.2)y Hg flow in a curved=1.2) pipe:
Analytical analysis for laminar curved=1.2) pipe flow
Numerical solution for turbulent flow in curved=1.2) pipe
without/with nozzle

Assessment of Static Pressure Through the Bernoullis Law

www.Poster Presentations.com

Fig.7 Comparison of momentum
thickness at the pipe exit
(d=1.2)a) 0)/0) (d=1.2)b) 30)/30) (d=1.2)c) 60)/60)
(d=1.2)d=1.2)) 90)/90) (d=1.2)e) Planes d=1.2)efined=1.2) at
the exit
Red=1.2): without nozzle;
Blue: with nozzle.

[2][3]

*

u
w* r * *
*
*2
2 *
*
*
*
*
*
*
u
w sin
1
u
u
2 sin
w
cos
v v
1 u
d

*
* *
*
z sin
Dr w r sin *

[

2
r

sin

(d=1.2)

)

]
2
*
*2
*
*
2
*
*
*
*
*
*
3
*
z 1 r sin Re
z
r
(d=1.2)1 r sin ) z 1 r sin r r r
(d=1.2)1 r sin )
dz

Investigate the fluid=1.2) d=1.2)ynamics of a liquid=1.2) Hg target for
the Muon Collid=1.2)er Accelerator Project:
Dynamics of the Hg flow in a curved=1.2) pipe
Effect of magnetic field=1.2) on Hg pipe flow (d=1.2)MHD)
Hg exhaust jet flow
Effect of magnetic field=1.2) on jet flow
Effect of high energy d=1.2)eposition on jet flow
Combined=1.2) effects of magnetic field=1.2) and=1.2) high energy
d=1.2)eposition on Hg jet flow

POSTER TEMPLATE BY:

u
u
(d=1.2)1 )dr
U
U

(e)

(c)
Fig. 1 (d=1.2)a) Mercury d=1.2)elivery system at CERN (d=1.2)b) Concept of a 4-MW target
station based=1.2) on a free mercury jet insid=1.2)e at 20-T solenoid=1.2) [1] (d=1.2)c) Mercury
supply piping (d=1.2)long curved=1.2) pipe)

R

t 0

Extra terms in the z momentum

Introduction and Motivation
Target d=1.2)elivery system requires a 90/90 elbow
combination for the Hg supply and=1.2) return
Mercury jet exhausts into vacumm/air
High energy beam interacts with Hg jet
The whole system in the high magnetic field=1.2)

Discussions

Turbulent flow cond=1.2)itions are analyzed=1.2) at the exit of
the mercury target supply pipe. The results show :
Realizable k-e turbulence mod=1.2)el is able to simulate
turbulent mercury flow in curved=1.2) pipe.
Bend=1.2) effects: Bigger t near the inner side of the
curved=1.2) pipe, which is even obvious in the 90/90
pipe; the 90/90 pipe has ad=1.2)vantages of symmetry I.
Nozzle effects: Nozzle decreases t, uniforms t and=1.2)
reduces I.

Acknowledgement

(b)

Thanks to the guid=1.2)e from my ad=1.2)visors and=1.2) the help from
the Muon Collid=1.2)er Project group (d=1.2)BNL, CERN, OAK
Rid=1.2)ge National Lab, etc)

References

Fig.5 (d=1.2)a) Geometry of pipes with nozzle in varying angles (d=1.2): 0), 30), 60), 90)) (d=1.2)b) Stream-wise velocity and=1.2) velocity vector plots (d=1.2)=60 , inner: left, outer: right)

2
Ploss Pmain g (d=1.2) 2 helbow hcontr ) g (d=1.2) 2u in2 / 2 g Ku out
/ 2 g ) 198196944 Pa
2
Pin uin2 / 2 gh1 Pout uout
/ 2 gh1 Ploss Pout 208465.3534 Pa

Error Pnum Pana / Pana 100% 189516.3 208465.4 / 208465.4 100% 9.09%

Fig. 6 Static pressure
Contour
for the 90)/90) pipe (d=1.2)assume
smooth pipe, then the
friction loss =zero)

[1]. H.G. Kirk, X. Ding, V.B. Graves,K.T. McDonald=1.2), F. Lad=1.2)eind=1.2)e, Y.
Zhan, J. Back, 2010. A 4-MW Tagert Station for A Muon Collid=1.2)er or
Neutrino Factory, Proceed=1.2)ings of IPAC, Kyoto, Japan
[2] Dean, W. R. 1927. Note on the motion of fluid=1.2) in a curved=1.2) pipe.
Phil. Mag. 4, 208-223
[3] Y. Zhan, F. Lad=1.2)eind=1.2)e, H.G. Kirk, K.T. McDonald=1.2), 2010. The
d=1.2)ynamics of mercury flow in a curved=1.2) pipe, 63rd=1.2) annual meeting of
the APS Division of Fluid=1.2) Dynamics, Vol. 55, No. 16
[4] K. Sud=1.2)o, M. Sumid=1.2)a, H. Hibara, 1998. Experimental investigation
on turbulent flow in a circular-sectioned=1.2) 90-d=1.2)egrees bend=1.2),
Experiments in Fluid=1.2)s. 25, 42-49.

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