zhan_042111x

busyicicleMechanics

Feb 22, 2014 (3 years and 7 months ago)

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Nozzle Study

Yan Zhan,
Foluso

Ladeinde


April , 2011

Outlines


Region of interests


Bend Combinations without nozzle


Bend Combinations Without Nozzle


Turbulence Model Comparisons


Mercury Flow in Curved Pipes


Discussions


Bend Combinations with Nozzle


Bend Combinations With Nozzle


Mercury Flow in Curved Nozzle Pipes


Discussions


Appendix

Region of interests

Hg delivery system at CERN

Simulation
Regime

Interests: Influence of nozzle

& nozzle upstream on the jet exit

Outlines


Region of interests


Bend Combinations without nozzle


Bend Combinations Without Nozzle


Turbulence Model Comparisons


Mercury Flow in Curved Pipes


Discussions


Bend Combinations with Nozzle


Bend Combinations With Nozzle


Mercury Flow in Curved Nozzle Pipes


Discussions


Appendix

Bend Combinations Without Nozzle (1)

Geometry of bends with varying angles

Nondimensionalized

by pipe diameter (
p.d
.);

φ

range: 0⁰, 30⁰, 60⁰, 90⁰.

Mesh at the cross
-
section

n
r

×

n
θ

=152
×
64 (the 1
st

grid center at y
+
≈1)

Geometries without nozzle:

(a) 0⁰/0⁰ ; (b) 30⁰/30⁰; (c) 60⁰/60⁰; (d) 90⁰/90⁰

n
x

=40 +n
φ
+20+ n
φ
+100

where n
φ

depends on the bend angle
φ

Bend Combinations Without Nozzle (2)

(a)

(b)

(c)

(d)

Turbulence Model Comparisons (2)

Sudo’s

Experiment (1998) for 90⁰ bend
*



K.
Sudo
, M. Sumida, H.
Hibara
, 1998. Experimental investigation on turbulent flow in a circular
-
sectioned 90
-
degrees

bend, Experiments in Fluids. 25, 42
-
49.

u
ave

= 8.7 m/s; Re=6
×
10
4
;
ρ
air

= 1.2647;
μ

air

= 1.983
×
10
-
5
; Pr= 0.712

Inlet

Outlet

Turbulence Model Comparisons (3)


Mesh at the cross
-
section

n
r

×

n
θ

=80
×
50 (the 1
st

grid center at y
+
≈1)

Mesh for the test pipe

n
φ

=75 (d
φ
=1.2⁰)

Turbulence Model Comparisons (4)

Longitudinal distribution of wall static pressure

C
p

pressure coefficient

p
ref

reference value of p at z’/d=
-
17.6

RK
ε

is the best of the three in simulating curved pipe flow

Mercury Flow in Curved Pipes (1)


Steady incompressible turbulent flow


Boundary Conditions


Inlet: Fully developed velocity;


Outlet: Outflow;


Wall: non
-
slip


Schemes


3
rd

order MUSCL for momentum and turbulence equations


SIMPLE schemes for pressure linked equations


Convergence Criterion


10
-
5

Mercury Flow in Curved Pipes (2)


Turbulence Characteristics


Turbulence Level (
Flutuating

Velocity
)




Momentum Thickness (
Mean Velocity
)

Measure of the momentum loss within the boundary layer due
to viscosity.


m
m
u
k
u
u
I
3
/
2










R
t
R
t
dr
U
u
U
u
dy
u
U
u
UU
0
0
)
1
(

)
(



Small
I

Big
θ
t

Mercury
Flow in Curved Pipes
(3)


Turbulence Level (1)

Fig. Two shown planes at the pipe outlet

Pipes

I
mean


at outlet

90

/90


5.204039%

60

/60


5.323943%

30

/30



5.368109%

0

/0


4.649036%

Table. Mean turbulence level at pipe outlet
Mean
I
in
=4.600041%

Mercury
Flow in Curved Pipes
(4)


Turbulence Level (2)

Turbulence intensity distribution at the pipe exit

(a)
Horizontal plane (from inner side to outer side )

(b)
Vertical (from bottom to top )

(a)

(b)

Mercury Flow in Curved Pipes (4)


Momentum

Thickness

Momentum thickness distribution

along the wall at the pipe exit

(a) 0⁰/0 ⁰ bend (b)30⁰/30 ⁰ bend

(c) 60⁰/60 ⁰ bend (d) 90⁰/90 ⁰ bend

Discussions


Bend Effects


Bend and turbulence level


Bend enhances the turbulence level but not too much;


The 0⁰/0⁰ bend has the lowest turbulence level;


Symmetry I for the 90⁰/90⁰ bend;


Bend and
θ
t


Bend effects
θ
t not linearly with the increasing bends


The 60⁰/60⁰ bend seems like a turning point


Less uniform
θ
t

distribution in larger bend


θ
t
is bigger near the inner side and smaller near the outer side


Outlines


Region of interests


Bend Combinations without nozzle


Bend Combinations Without Nozzle


Turbulence Model Comparisons


Mercury Flow in Curved Pipes


Discussions


Bend Combinations with Nozzle


Bend Combinations With Nozzle


Mercury Flow in Curved Nozzle Pipes


Discussions


Appendix

Bend Combinations With
Nozzle

Geometry of bends with varying angles

Nondimensionalized

by pipe diameter (
p.d
.);

φ

range: 0⁰, 30⁰, 60⁰, 90⁰.

Mesh at the cross
-
section (half model)

n
r

×

n
θ

=152
×
64 (the 1
st

grid center at y
+
≈1)

Mesh for bends

(a) 0⁰/0⁰ ; (b) 30⁰/30⁰; (c) 60⁰/60⁰; (d) 90⁰/90⁰

n
x

=40 +n
φ
+20+ n
φ
+60+70

where n
φ

depends on the bend angle
φ

(a)

(b)

(c)

(d)

Mercury Flow in Curved Nozzle Pipes (1)

Longitudinal distribution of static pressure for 90⁰/90⁰ Combination

Velocity inlet condition


P
in


30bar;


u
in

fully developed velocity profile;

Outlet flow condition

Mercury Flow in Curved Nozzle Pipes (2)


Main Loss




Assume smooth pipe, thus
P
main
=0


Minor Loss


Elbow Loss



Contraction Loss



Total Loss

2
/
)
/
(
2
/
)
/
(
2
2
in
in
out
out
main
u
D
L
u
d
l
P






m
g
u
h
in
elbow

2618
.
0
2
8
.
9
136
.
4
3
.
0
2
/
2
2







m
g
Ku
h
out
contr

9694
.
0
2
8
.
9
20
0475
.
0
2
/
2
2






Pa

198196944

)
2
(




contr
elbow
main
loss
h
h
g
P
P

Mercury Flow in Curved Nozzle Pipes (3)


Bernoulli’s Law





Comparison




Pa

3534
.
208465
944
.
198196
5
.
0
13546
20
5
.
0
13546
136
.
4
10

3
2
/
5
.
0
2
/
5
.
0
2
2
6
1
2
1
2

















out
out
loss
out
out
in
in
P
P
P
gh
u
P
gh
u
P




%
0898
.
9
%
100
3534
.
208465
3534
.
208465
3
.
189516
%
100







ana
ana
num
P
P
P
Error
Mercury Flow in Curved
Nozzle Pipes (4)


Turbulence Level (1)

Pipes

I
mean

(Nozzle)

I
mean


(No nozzle)

90

/90


㔮ㄴ㌳㐱1

㔮㈰㐰㌹2



/60



㈮㠵㠷㐷8

㔮㌲㌹㐳3



/30


㈮㜰ㄳ㘶7


㔮㌶㠱〹3

0

/0


2.182027%

4.649036%

Fig. Two shown planes at the pipe outlet

Table. Mean turbulence level at pipe outlet
Mean
I
in
=4.599195%

Mercury Flow in Curved Nozzle Pipes
(5)


Turbulence Level (2)

Turbulence intensity distribution at the pipe exit

(a)
Horizontal plane ; (b) Vertical plane

(a)

(b)

Mercury Flow in Curved Pipes (6)


Momentum

Thickness

Momentum thickness distribution

along the wall at the pipe exit

(a) 0⁰/0 ⁰ bend (b)30⁰/30 ⁰ bend

(c) 60⁰/60 ⁰ bend (d) 90⁰/90 ⁰ bend

Discussions (1)

Turbulence intensity distribution at the pipe exit

(a)
Horizontal plane (b)Vertical plane

(a)

(b)

Discussions (2)

The comparison of momentum
thickness distribution at the pipe
exit between pipe with/without
nozzle

(a) 0⁰/0 ⁰ bend (b)30⁰/30 ⁰ bend

(c) 60⁰/60 ⁰ bend (d) 90⁰/90 ⁰ bend

Red: pipe without nozzle;

Blue: pipe with nozzle.

Discussions (3)


Nozzle Effects


Nozzle and turbulence level


Nozzle reduces the turbulence level;


The 90⁰/90⁰ bend doesn’t change too much;


I of the 90⁰/90⁰ bend is far different from other bends


Nozzle and
θ
t


Nozzle decreases
θ
t


Very uniform and similar
θ
t
distribution at the nozzle
exit for all bend pipes


Outlines


Region of interests


Bend Combinations without nozzle


Bend Combinations Without Nozzle


Turbulence Model Comparisons


Mercury Flow in Curved Pipes


Discussions


Bend Combinations with Nozzle


Bend Combinations With Nozzle


Mercury Flow in Curved Nozzle Pipes


Discussions


Appendix

Appendix(1)


Continuity Equation

The two
-
phase model considers mixture comprising of liquid, vapor
and non
-
condensable gas (NCG). Gas is compressible, the liquid and
vapor are impressible. The mixture is modeled as incompressible.




Momentum Equations






0



j
j
x
u
j
j
i
i
j
j
i
x
x
P
x
u
u











)
(

and

}
){
(

where
2
t







k
C
x
u
x
u
i
j
j
i
t
ij








Appendix(2)


Spalart
-
Allmaras

Model














~
2
2
~
]
)
~
(
}
~
)
~
{(
[
1
~
S
Y
x
C
x
x
G
x
u
j
b
j
j
i
i














)
/(
~
~

and

~
~

term
production

The
2
2
2
~
1
d
f
v
S
S
v
S
C
G
v
b






2
1
)
/
~
(

n term
destructio

The
d
v
f
C
Y
w
w



3
.
0
,
1
.
7

2/3,

,
4187
.
0
,
622
.
0
,
1355
.
0
2
1
~
2
1






w
v
b
b
C
C
C
C



2
/
)
(
,
2

and

)
1
/(
1

where
,
,
1
~
2
~
i
j
j
i
ij
ij
ij
v
v
u
u
S
f
f











)
~
/(
~

),
(

,
)]
/(
)
1
[(

where
2
2
6
2
6
/
1
6
3
6
6
3
d
S
v
r
r
r
C
r
g
C
g
C
g
f
w
w
w
w








v
b
b
w
w
C
C
C
C
~
2
2
1
1
3
/
)
1
(
/
2.0,






stresses

Reynolds

the
estimating

ignored

,

term
source

defined
-
User
v
S
Appendix(3)


Turbulent Viscosity (SA)

v
v
C
f
v
v
/
~

and

function

damping

visous
where
3
1
~
3
3
1
~






1
~
~
v
t
f




.
viscosity
kinematic
molecular

the
is

v
Appendix (4)


Standard K
-
ε

model
















S
k
C
G
C
G
k
C
x
x
x
u
t
b
k
j
t
j
j
j















2
2
3
1
)
(
]
)
[(
k
M
b
k
j
k
t
j
j
j
S
Y
G
G
x
k
x
x
k
u
t
k






















]
)
[(
RT
k
M
M
Y
x
T
g
G
x
u
u
u
G
t
t
M
i
t
t
i
b
i
j
j
i
k
















,
2
,
Pr
,
2
3
.
1
,
0
.
1
,
09
.
0
,
92
.
1
,
44
.
1
2
1











k
C
C
C
Appendix (5)


Turbulent Viscosity (SK
ε
)





2
k
C
t

constant.

a

is


C
gradients;
ity
mean veloc

to
due
k

of

generation

:
k
G
buoyance;

to
due
k

of

generation

:
b
G
rate;
n
dissipatio

overall

the
to
turbulence

le
compressib
in

dilatation

g
fluctuatin

the
of
on
contributi

:
M
Y
;

and

for

numbers

Prandtl

turbulent
:
,




k
k
terms;
source

defined
-
user

:
,

S
S
k
Appendix (6)


Realizable K
-
ε

model


k
M
b
k
j
k
t
j
j
j
S
Y
G
G
x
k
x
x
k
u
t
k






















]
)
[(

















S
C
C
k
C
v
k
C
S
C
x
x
x
u
t
b
j
t
j
j
j
















3
1
2
2
1
]
)
[(
ij
ij
S
S
S
k
S
C
2
,
,
]
5
,
43
.
0
max[
1








RT
k
M
M
Y
x
T
g
G
x
u
u
u
G
t
t
M
i
t
t
i
b
i
j
j
i
k
















,
2
,
Pr
,
2
Appendix (7)


Turbulent Viscosity (RK
ε
)





2
k
C
t

k
ijk
ij
ij
k
ijk
ij
ij
ij
ij
ij
ij
s
S
S
U
kU
A
A
C




















,
2
~
,
~
~
,
1
*
*
0
ji
ij
ki
jk
ij
s
S
S
S
S
S
S
S
W
W
A
A






~
,
~
,
3
)
6
(
cos
,
cos
6
,
04
.
4
3
1
0


2
.
1
,
0
.
1
,
9
.
1
,
44
.
1
,
2
2
1










k
ji
ij
ij
C
C
u
u
S
Appendix(8)

Models

Pros

Cons

Spalart
-
Allmaras


(SA)

Low
-
cost;

Aerospace applications involving
wall
-
bounded flows

and with mild
separation;

Can not predict the decay of
homogeneous, isotropic
turbulence;

No claim is made regarding its
applicability to all types of
complex engineering flows;

Standard K
-
ε


(
Sk
ε
)

Robust and reasonably accurate;

Most widely
-
used engineering
model industrial applications;

Contains
submodels

for
buoyancy, compressibility,
combustion, etc;

Must

use wall function for
near wall calculation;

Performs poorly for flows with
strong separation, large
streamline
„curvature, and
large pressure gradient;

Realizable K
-
ε


(
Rk
ε
)

superior performance for flows
involving rotation,
„boundary
layers under strong adverse
pressure gradients, separation,
and recirculation

Appendix (9)


Properties of fluid










Steady incompressible turbulent flow

Variable Values


Pipe

ID

0.884

inch

Nozzle exit ID

0.402

inch

Driving pressure

30 bar

Frequency for Hg supply

12 s

Maximum Cycles

100

Jet Velocity


20 m/s

Jet Diameter

1 cm

Jet Flow rate

1.6 L/sec

Environment

1
atm

air

/vacuum

Mercury Properties (25

䌠)

Density

13.546 kg/L

Sound Speed

1451 m/s

Bulk Modulus

2.67
×
10
10
Pa

Dynamic Viscosity

1.128
×
10
-
7

m
2
/s

Thermal
Conductivity

8.69 W/
m

K

Electrical
Conductivity

10
6

Siemens/m

Specific Heat

0.139 J/
kg

K

Prandtl

Number

0.025

Surface Tension

465 dyne/cm