.,.. ...
_1i_AIa_ -.- --------------, AIAA-91-1678 Inviscid Dynam,ics of TwoDimensiona,1 Shear Layers K.-Y. Chien, R.E. Ferguson, NSWC, Silver Spring, MD; A.L. Kuhl, LLNL, Los Angeles, CA; H.M. Glaz, Univ. of MD, College Park, MD; P. Colella, U.C. Berkeley, CA
AIAA 22nd Fluid Dynamics, Plasma Dynamics & Lqs~C'Pnference June 24-26:, 1991 I Honolulu, Hawaii "
"
,,/
J
=or permis.slon to copy or republish. eontoCtthEr O. The region over which the product (UI - 11)( 11- U2 ) is the largest occurs now where ::::>
(b)
0.8 0.6
(c)
Figure 1. Schematic of the free shear layer calculations: (a) computational grid; (b) Tanh{y) streamwise velocity profile; and (e) density profile.
0.2 O~~~~~~--~----
O.Ot
o
-0.03
- 0.04 ....._0....-_""'-_""--_"'--....... (d)
2.0 1.6 1.2
0.8 0.4 o--~--~~~~~~~
Figure 2. Flow field for Case I: (a) material interrace; (b) shadowgraph from the experiment; (e) density con· tours; (d) vorticity contours (solid lines denote negative values); and (e) overpressure contours (solid lines denote positive values).
o
100
200
x
300
400
SOO
Figure 3. Flow field along the centerline (i.e., y 0.56y) corresponding to Figure 2.
0.5
11
=
=
,,-
Figure 4. Vorticity and density color visualizations for Case I.
Ito Tracer particles J
1(1)
,
.:
!
I
!
0.6r-----r-----.-----~----._----,
'~I,
01- """, '--e~"'~
Y -SO
I
!
.
~v..
18%
J
P2 1Pl
0.5
7
(b)
I
117 0.4
Exp. Calc.
• • •
A 0 Q
0.3
(d)
40
T,lCerr
0.2
cte•
0.1
,
~~! (ei.--=~~~~"'-1 o
100
200
300
400
OE-____~____~__________~~--~
SOO
o
:Jl
Figure 5. Material interface plots comparing the spreading shear layer cases: (a), (b) Case I, (e), (d) Case II, (e) Case III. Figures (b). (d) are photographs of the experimental record (Brown and Roshko 1974).
0.2
0.6
0.8
1.0
Figure 6. Visual spreading rate, 6~i. vs. l, for the spreading shear layer cases.
12
1.0
-
~ I
--S
~
I
t=-
1.0
- fa) 0.8
8;
•
0.6 0.4 0.2 0
200 • 3000 4000 s004 6000 700 v 800 + .900 x
0.6
-S
-
8.
350 SOD
0 0
6SO v 800
0.2
£\
0
1.0
0.8
ICL
..!.=
0.4
.=-
1.0
ct
0.8
..!.= 100 •
(b)
O.B
-
0.6
N
CL
ICL
0.4
0.6 0.4
0.2
0.2
0
0 -0. IS .0.10 -O.OS
0 O.OS 0.10 O.IS 11 Figure 7. Mean velocity and density profiles for
-O.IS ·0.10 .O.OS
0 11
O.OS
0.10 O.IS
Figure 10. Mean velocity and density profiles for Case I; the shaded region~ denote the experimental data band of Drown and Roshko (1974).
Case I.
1.0 0.8
:5
1111
.!.. = 200 8;
0.6
0
400
0
800
£\
0.4 0.2 1.0
Figure 8. Mean velocity profile for Case III. 1.0
-::::. N
I
~
-N
:::::>
-
I
0.8 0.6
Q:
..!. = 100 B;
0.4
I
1111
0.8
0.2
• 200. 3000 4000 s004 6000 700 v
IQ..
~~~~r~
·O.IS -0.10 -O.OS
O.OS
0.10
0
O.OS
0.10 0.15
-11 Figure 11. Mean velocity and density profiJes for Case II; the shaded regions denote- the experimental data band of Drown and Roshko (1974).
_ _ _ _ _ _ _ _ _ _ ~_ _ ~
0
0.4
o
BOO ...
·O.IS -0.10 -O.OS
0.6
0.2
9(0)(
o
(b)
O.IS
11 Figure 9. Mean velocity profile for Case IV.
13
~
1.0
-
~ ~;
0.8
I
-:s
0.6
.;g
0.4
-
0.2
% -= 6SO v
;-
8i
I
~
I
,=-
. i---
0 -0.15 -0.10 -O.OS
700 0 750 0 800 A
8500
o
0.05
-
0.10 0.15
'1
~
I
---. :S'
O.S
-:s
8;
N
~
I
.:a
4000
0.3
200. 3000
500
0.2
6000 700 v 800 + 900 x
0.1
6
\
• • •
0.5 (b)
400 0
-
5006 6000 700 9 800 + 900 x
0.2
0.3
o
~= 100 •
(a)
0.4
(a)
N
Figure 12. :Mean velocity profiles for Case III~ the shaded region denotes the experimental data band of Oster and \Vygnanski (1982).
0.4
~=100 • 8 i 200· 3000
0.5
0.4
N
~
I
-:; :5'
0.5 0.4
o
(b)
0.02
0.3
-
N
(e)
0.01
N
~
"5
~
F: 0.02
-
N
I
-::r -_
I::
0
"
0.05
0.10
O.IS
Figure 14. Time-averaged fluctuating-flow profiles for Case IV: (a) strcamwise velocity; (b) transverse velocity; (c) shear stress.
-0.01 -0.02
-0.03../--_ _ _ _ _ _-.--_ _- - - - . - -0.15 -0.10 -O.OS
-0.02
-O.IS -0.10 -O.OS
1
o
-0.01
-0.03""------------_--_
0.01
N
:::>
(e)
0
0
0.05
0.10 O.lS
'1
Figure 13. Time-averaged fluctuating-flo'A' profiles for Case III: (a) streamwise velocity; (b) transverse velocity; (c) shear stress.
14
.!.=lOO •
6;
O.S
~ I
:S'
-.
~
(a)
200. 3000 4000
0.4
5006
0.3
6000 100 v 800+ 9(0)(
0.2
-=r"
-
0.20
:S'
-.
o
0.1
• •
o ~~~~~~.-------.~~.~~.~~ O.S
0.30
-
~
(b)
I
0.4
0.20
--
0.3
::5"
.b.
_".i 0.10
b.
o
0.2
•
0.1
o
o
~==~~~
__________ ____ ~
~~
0.02
-..;
N
I
0
0.01
-::r
0
:S'
(c)
N
(c)
0.02
I
.•
:S
':::' 0.01
1::- -0.01
\::E,
*0.02
•o
o
-0.03+---_~-____..__-..__-_._-__..-___,
0.40 d)
0.30
0.32 ~
Q..
' Q..
(d)
0.24
6-
~ O.20~
0.16
• E
• •
0.08
o
b. 6-
• -0.15 -0.10 -O.OS
~ 0.10
•
U2 1Ut P11 PI
66-
•
o
O.OS
0.10
0.38
7.0
6-
O.IS
o
"
Figure 15. Time-averaged fluctuating-flow profiles for Case I: (a) streamwise velocity; (b) transverse velocity; (e) shear stress; (d) density.
o
200
400
600
800
1000
Figure 16. Peak r.rn.s. values: (a) streamwise velocitYi (b) transverse velocity; (c) shear stress; (d) density.
15
o.s
--. ~ I
-S
0.4
~= 6SO v B; 700 c
(a)
750 0 ). 800
&SO
0.3
6 0
.
0.2 0.1
0.40
0
-=-= 350 Bi SOO 0 0
0.32
650 v 800 6
O.S
-
0.4
N
(b)
~ -Q,.
N
:':;)
I
---.. :5
0.3 0.2
o -o.tS
(e)
0.01
N
N
I::
0
:a;
S
-0.01 -0.02 ~.03L---~--~~--~--~----r---~
-O.IS
0
-0.10 -0. OS
0.05
0.10
O.lS
Figure 18. Time-averaged fluduating density profiles (or Case I. The shaded region denotes the experimental data band of Konrad (1977).
0.02
I
-0.10 -0.05
"
0
:':;)
0.16
0.08
0.1
-
0.24
0
0.05
0.10 0.15
"
Figure 17. Time-averaged fluet uating-flow profiles (or Case HI: (a) streamwise velocity; (b) transverse velotity; (e) shear stress. Shaded regions denote the data of Oster and Wygnanski (1982). The dashed lines represent the profiles calculated with a 2D vortex dynamics eode (Inoue and Leonard 1987).
16
NOTES
.. NOTES .-
) , 
