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Flow separation and reattachment over the sides of a 90° triangular prism
Journalof Wind Engineemngandlndus~lAerodynam~¢
11(1983) 393--403 Else~er Science PubHshe~ B.V.,Amsterdam--PrintedinThe Netherlands
393
FLOW SEPARATIONAND REATTACHMENTOVER THE SIDES OF A 90o TRIANGULAR PRISM SAAD EL-SHERBINY RESEARCH INSTITUTE UNIVERSITY OF PETROLEUM & MINERALS DHAHRAN, SAUDI ARABIA SUMMARY Mean pressure d i s t r i b u t i o n on the sides of a 90o t r i a n g u l a r prism is i n v e s t i gated experimentally in a uniform smooth flow at the Reynolds number 105. The angle of flow incidence varied from 0° (the apex of the wedge is normal to the flow) to 180o (the base is normal to the flow). The flow is f u l l y attached to two of the three surfaces only when the l i n e bisecting the angle between these surfaces is p a r a l l e l to the incident flow, i.e.
~= 0° and 112.5 o .
For a l l other angles the flow is f u l l y attached to only
one side, and is e i t h e r p a r t l y or f u l l y separated from the second side depending on the angle of incidence. The dependence of vortex shedding from the prism, normalized in the form of the Strouhal number, on the angle of incidence is explained as a function of the flow separation and reattachment to the sides of the prism.
i . INTRODUCTION Flow past sharp edge t r i a n g u l a r prisms has been the subject of active research [1-4] due to t h e i r use as structure members in various a p p lic at ions .
The nature
of the symmetrical flow past a t r i a n g u l a r prism ( 6=0° or 180° , Figure I ) has been studied [2-4] in more d e t a i l than f o r the case o f unsymmetrical flow.
When
the flow approaching the prism is unsymmetrical a trapped surface separation bubble may form on one of the sides of the prism depending on the o r i e n t a t i o n o f the prism.
This bubble is formed due to the separation of the flow from a corner
of the prism followed by i t s reattachment to the side downstream of this corner. Similar separation bubbles are observed f o r the unsymmetrical flow past square [5] or rectangular [6] prisms. Robertson [5] studied the effects of the separation bubble on the aerodynamics of square prisms. He found that the region of flow reattachment to the side is characterised by local increase in both mean and f l u c t u a t i n g pressures.
These
high pressures could be responsible f o r the l o c a l i z e d damage on the skin of a
0304-3908/83/$03.00
© 1983 Else~erSc~nce PubUshe~ B.V.
394
structure subjected to similar flow conditions.
Moreover,the reattachment of
the separated shear layer to the downstream side when the angle of flow increases determines the dynamic s t a b i l i t y of the prism. [7] The location of separated flow reattachment to the downstream surface depends on the angle of incidence of the flow.
In addition, the measurements of both
Robertson [5] and Vickery [8] indicate that increasing the oncoming flow turbulence w i l l increase the tendency of the separated shear layer to reattach. The mean pressure distribution over the region of separation-reattachment was found [5] to behave in a similar manner for various flow angles and could be represented by a universal plot. The present investigation was aimed at studying the effect of angle of incidence on flow separation and reattachment over the sides of a 900 triangular prism. This study is part of a continuing program to investigate the aerodynamics of bluff bodies. 2.
EXPERIMENTALDETAILS The experiment was conducted using a 900 triangular prism made of acrylic sheets.
The model height was 80 cm and the triangular cross section had a base width of 9.9 cm.
Twenty eight pressure taps were distributed along the three sides of the
prism at midspan, Figure 1.
The pressure tap diameter was 0.09 cm and was connected
to the pressure transducer through a 91 cm long, 0.167 cm diameter plastic tubing. The prism was tested in the low speed low turbulence wind tunnel of the Mechnical Engineering Department. Maximumwind speed in the empty tunnel is 35 m/s and turbulence level is less than 0.3%. The tunnel cross section is 0.8 m high, 1.1 m wide and 3.5 m long.
The model was mounted at the center of the test-section
and spanned the tunnel v e r t i c a l l y giving a nominal blockage r a t i o of 9% based on the ratio between prism base area to tunnel cross-sectional area. Surface pressure was measured using a condenser type pressure transducer.
The
unsteady pressure component superposed on the mean value was f i l t e r e d out using the damping c i r c u i t of the D-C voltameter used to read the transducer output. A hot wire probe was positioned 1.5 base length downstream of the model just outside the wake region to measure the unsteady velocity signal.
The frequency
of this signal corresponds to that of vortex shedding from the prism. All tests were conducted at Reynolds number of 10s.
A few runs were carried
out at Reynolds numbers of 0.6 x 10s and 1.2 x 10s and indicated essentially no change in the mean pressure distribution in this ranoe.
395
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..
396
Due t o the small angle a t the c o r n e r , c, where s e p a r a t i o n begins f o r the above two s i d e s , complete s e p a r a t i o n occurs a f t e r a s m a l l e r range of angle (A~ = 12o ) than when s e p a r a t i o n begins a t corner a (As = 35o). The f l o w is always f u l l y corners.
separated from the side between the two downstream
The pressure on t h a t side is n e a r l y uniform when s e p a r a t i o n is t a k i n g
place from the two corners o f t h a t s i d e , e.g. the Base f o r 0 ( ~ and side A f o r 9 5 ~ 1 2 5
o , Figure 4.
l a y e r s is downstream o f the surface.
30o , Figure 2,
In these cases one of the separated shear When the s e p a r a t i o n is o c c u r r i n g at an up-
stream c o r n e r , and t h a t surface i s extended between the two separated shear l a y e r s , the pressure on t h a t surface is not uniform but decreases in the downstream d i r e c t i o r This is c l e a r f o r the Base and side A a t 45 ° ~ 9 0 C at 130° ~ 1 8 0
o , Figure 5.
o , Figure 2 and f o r sides A and
The customary n o t a t i o n of a s i n g l e value of base
pressure is not v a l i d here when the pressure is not uniform. 3.2
Strouhal Number V a r i a t i o n s o f the Strouhal numbers,S, based on prism base w i d t h , and SN, based
on the prism p r o j e c t e d h e i g h t are shown in Figure 7, as f u n c t i o n of angle o f incidence ~.
The continuous change o f S and SN w i t h ~ is dependent on whether the
separated shear l a y e r s forming the wake o r i g i n a t e from a downstream o r an upstream corner. Dependence of the Strouhal number,S, on ~ is reduced when i t p r o j e c t e d h e i g h t in the form o f SN. the s t i l l
is r e f e r r e d t o the
The changes of wake w i d t h w i t h ~ could e x p l a i n
strong v a r i a t i o n of SN w i t h ~.
The sharp drop in SN a t ~ > 30 and a t
> 120 is due to the sharp increase in wake w i d t h as complete s e p a r a t i o n s h i f t from the downstream c o r n e r , b, to the upstream c o r n e r , a, f o r the former and from corner a to corner c f o r the l a t t e r .
On the o t h e r hand sharp increase o f SN a t
> 90 o is due to r e d u c t i o n o f wake w i d t h as a r e s u l t of f l o w attachment to the Base and the delay of s e p a r a t i o n from c o r n e r , c, to c o r n e r , b.
Normalization of
v o r t e x shedding using the d i s t a n c e between separated shear l a y e r s as a l e n g t h parameter, e.g. the Universal Strouhal number would reduce i t s dependence on ~. 4.
CONCLUSIONS The e f f e c t o f varying the angle of f l o w incidence in the range 0 ° ~ 1 8 0
the mean surface pressure and v o r t e x shedding f o r a 90o t r i a n g u l a r
° on
prism could be
summarized as f o l l o w s : ( I ) The f l o w is attached to two sides of the prism only when the l i n e b i s e c t i n g the angle between those sides is p a r a l l e l (2) For a l l
to the i n c i d e n t f l o w .
o t h e r angles the f l o w i s f u l l y
attached to only one side and i s
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402
either partly attached or completely separated from the second side depending on the angle of incidence. (3) The point of flow reattachment depends on the angle of the flow. (4) The flow is f u l l y separated from the side bound by the two downstream corners.
The pressure on that surface is nearly uniform only when separation is
taking place from the corners of that side. (5) The frequency of vortex shedding depends on the wake width which is a function of whether the wake is formed by a shear layer separating from a downstream or an upstream corner. ACKNOWLEDGMENTS This investigation was supported by the University of Petroleum and Minerals, Saudi Arabia.
The author is grateful to the Mechanical Engineering Department
for the use of their aerodynamic laboratory and to the Research I n s t i t u t e for the use of their f a c i l i t y to write the paper. The assistance of both Mr. M. Abdelhalim, who fabricated the triangular prism, and Mr. M.K. Adham, who prepared the experimental set-up, is greatly appreciated.
NOMENCLATURE B
base width, 9.9 cm 2
Cp mean static pressure coefficient, (P-Po)/(O.5 p Uo) S
Strouhal number, [ f B/Uo]
SN Strouhal number based on projected width Uo f l u i d velocity far upstream of prism model X/L relative distance measured along a side of the prism of length L, Figure I f
frequency of vortex shedding
P
surface mean static pressure
Po static pressure far upstream of prism model angle of flow incidence, Figure 1 REFERENCES 1 2 3 4
J . E . Slater, Aeroelastic i n s t a b i l i t y and aerodynamics of structural angle sections, Ph.D Thesis, University of British Columbia, Canada, 1969. A . S . Rammamurthy and P. M. Lee, Wall effects on flow past b l u f f bodies, J. Sound and Vibration, 31 (1973), pp.443-451. C.F.M. Twigge-Molecey and W. D. Baines, Aerodynamic forces on a triangular cylinder, J. Eng. Mech., Proc. ASCE, 99 (1973), pp. 803-818 T. Okamoto, M. Yagita and K. Ohtsuka, Experimental investigation of the wake of a wedge, Bulletin of the JSME, 20 (1977), pp 323-328.
403
5 6 7 8
J.M. Robertson, J. B. Wedding, J. A. Peterka and J. E. Cermak, Wall pressure of separation - reattachment flow on a square prism in uniform flow,J. Ind. Aerody., 2 (1977-78), pp. 345-359. R.G. Sam, R. C. Lessmann and F. L. Test, An experimental study of flow over a rectangular body, J. Fluids Engng., Trans. ASME, 101 (1979), pp. 443-448. G.V. Parkinson and N.P.H. Brooks, On the aeroelastic i n s t a b i l i t y of bluff cylinders, J. Appl. Mech., Trans. ASME, 92 (1971), pp. 252-258. B . J . Vickery, Fluctuating l i f t and drag on a long cylinder of square cross-section in a smooth and in a turbulent stream, J. Fluid Mech., 25 (1966), pp.148-149.
11(1983) 393--403 Else~er Science PubHshe~ B.V.,Amsterdam--PrintedinThe Netherlands
393
FLOW SEPARATIONAND REATTACHMENTOVER THE SIDES OF A 90o TRIANGULAR PRISM SAAD EL-SHERBINY RESEARCH INSTITUTE UNIVERSITY OF PETROLEUM & MINERALS DHAHRAN, SAUDI ARABIA SUMMARY Mean pressure d i s t r i b u t i o n on the sides of a 90o t r i a n g u l a r prism is i n v e s t i gated experimentally in a uniform smooth flow at the Reynolds number 105. The angle of flow incidence varied from 0° (the apex of the wedge is normal to the flow) to 180o (the base is normal to the flow). The flow is f u l l y attached to two of the three surfaces only when the l i n e bisecting the angle between these surfaces is p a r a l l e l to the incident flow, i.e.
~= 0° and 112.5 o .
For a l l other angles the flow is f u l l y attached to only
one side, and is e i t h e r p a r t l y or f u l l y separated from the second side depending on the angle of incidence. The dependence of vortex shedding from the prism, normalized in the form of the Strouhal number, on the angle of incidence is explained as a function of the flow separation and reattachment to the sides of the prism.
i . INTRODUCTION Flow past sharp edge t r i a n g u l a r prisms has been the subject of active research [1-4] due to t h e i r use as structure members in various a p p lic at ions .
The nature
of the symmetrical flow past a t r i a n g u l a r prism ( 6=0° or 180° , Figure I ) has been studied [2-4] in more d e t a i l than f o r the case o f unsymmetrical flow.
When
the flow approaching the prism is unsymmetrical a trapped surface separation bubble may form on one of the sides of the prism depending on the o r i e n t a t i o n o f the prism.
This bubble is formed due to the separation of the flow from a corner
of the prism followed by i t s reattachment to the side downstream of this corner. Similar separation bubbles are observed f o r the unsymmetrical flow past square [5] or rectangular [6] prisms. Robertson [5] studied the effects of the separation bubble on the aerodynamics of square prisms. He found that the region of flow reattachment to the side is characterised by local increase in both mean and f l u c t u a t i n g pressures.
These
high pressures could be responsible f o r the l o c a l i z e d damage on the skin of a
0304-3908/83/$03.00
© 1983 Else~erSc~nce PubUshe~ B.V.
394
structure subjected to similar flow conditions.
Moreover,the reattachment of
the separated shear layer to the downstream side when the angle of flow increases determines the dynamic s t a b i l i t y of the prism. [7] The location of separated flow reattachment to the downstream surface depends on the angle of incidence of the flow.
In addition, the measurements of both
Robertson [5] and Vickery [8] indicate that increasing the oncoming flow turbulence w i l l increase the tendency of the separated shear layer to reattach. The mean pressure distribution over the region of separation-reattachment was found [5] to behave in a similar manner for various flow angles and could be represented by a universal plot. The present investigation was aimed at studying the effect of angle of incidence on flow separation and reattachment over the sides of a 900 triangular prism. This study is part of a continuing program to investigate the aerodynamics of bluff bodies. 2.
EXPERIMENTALDETAILS The experiment was conducted using a 900 triangular prism made of acrylic sheets.
The model height was 80 cm and the triangular cross section had a base width of 9.9 cm.
Twenty eight pressure taps were distributed along the three sides of the
prism at midspan, Figure 1.
The pressure tap diameter was 0.09 cm and was connected
to the pressure transducer through a 91 cm long, 0.167 cm diameter plastic tubing. The prism was tested in the low speed low turbulence wind tunnel of the Mechnical Engineering Department. Maximumwind speed in the empty tunnel is 35 m/s and turbulence level is less than 0.3%. The tunnel cross section is 0.8 m high, 1.1 m wide and 3.5 m long.
The model was mounted at the center of the test-section
and spanned the tunnel v e r t i c a l l y giving a nominal blockage r a t i o of 9% based on the ratio between prism base area to tunnel cross-sectional area. Surface pressure was measured using a condenser type pressure transducer.
The
unsteady pressure component superposed on the mean value was f i l t e r e d out using the damping c i r c u i t of the D-C voltameter used to read the transducer output. A hot wire probe was positioned 1.5 base length downstream of the model just outside the wake region to measure the unsteady velocity signal.
The frequency
of this signal corresponds to that of vortex shedding from the prism. All tests were conducted at Reynolds number of 10s.
A few runs were carried
out at Reynolds numbers of 0.6 x 10s and 1.2 x 10s and indicated essentially no change in the mean pressure distribution in this ranoe.
395
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PRESSURE TAPS
~
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\
SEPERATION BUBBLE
Figure
1 :
s
:
r
:
stognotionpoint point reottochment
Flow p a s t illustration
the
90 ° t r i a n g u l a r of the
separation
prism with bubble
..
396
Due t o the small angle a t the c o r n e r , c, where s e p a r a t i o n begins f o r the above two s i d e s , complete s e p a r a t i o n occurs a f t e r a s m a l l e r range of angle (A~ = 12o ) than when s e p a r a t i o n begins a t corner a (As = 35o). The f l o w is always f u l l y corners.
separated from the side between the two downstream
The pressure on t h a t side is n e a r l y uniform when s e p a r a t i o n is t a k i n g
place from the two corners o f t h a t s i d e , e.g. the Base f o r 0 ( ~ and side A f o r 9 5 ~ 1 2 5
o , Figure 4.
l a y e r s is downstream o f the surface.
30o , Figure 2,
In these cases one of the separated shear When the s e p a r a t i o n is o c c u r r i n g at an up-
stream c o r n e r , and t h a t surface i s extended between the two separated shear l a y e r s , the pressure on t h a t surface is not uniform but decreases in the downstream d i r e c t i o r This is c l e a r f o r the Base and side A a t 45 ° ~ 9 0 C at 130° ~ 1 8 0
o , Figure 5.
o , Figure 2 and f o r sides A and
The customary n o t a t i o n of a s i n g l e value of base
pressure is not v a l i d here when the pressure is not uniform. 3.2
Strouhal Number V a r i a t i o n s o f the Strouhal numbers,S, based on prism base w i d t h , and SN, based
on the prism p r o j e c t e d h e i g h t are shown in Figure 7, as f u n c t i o n of angle o f incidence ~.
The continuous change o f S and SN w i t h ~ is dependent on whether the
separated shear l a y e r s forming the wake o r i g i n a t e from a downstream o r an upstream corner. Dependence of the Strouhal number,S, on ~ is reduced when i t p r o j e c t e d h e i g h t in the form o f SN. the s t i l l
is r e f e r r e d t o the
The changes of wake w i d t h w i t h ~ could e x p l a i n
strong v a r i a t i o n of SN w i t h ~.
The sharp drop in SN a t ~ > 30 and a t
> 120 is due to the sharp increase in wake w i d t h as complete s e p a r a t i o n s h i f t from the downstream c o r n e r , b, to the upstream c o r n e r , a, f o r the former and from corner a to corner c f o r the l a t t e r .
On the o t h e r hand sharp increase o f SN a t
> 90 o is due to r e d u c t i o n o f wake w i d t h as a r e s u l t of f l o w attachment to the Base and the delay of s e p a r a t i o n from c o r n e r , c, to c o r n e r , b.
Normalization of
v o r t e x shedding using the d i s t a n c e between separated shear l a y e r s as a l e n g t h parameter, e.g. the Universal Strouhal number would reduce i t s dependence on ~. 4.
CONCLUSIONS The e f f e c t o f varying the angle of f l o w incidence in the range 0 ° ~ 1 8 0
the mean surface pressure and v o r t e x shedding f o r a 90o t r i a n g u l a r
° on
prism could be
summarized as f o l l o w s : ( I ) The f l o w is attached to two sides of the prism only when the l i n e b i s e c t i n g the angle between those sides is p a r a l l e l (2) For a l l
to the i n c i d e n t f l o w .
o t h e r angles the f l o w i s f u l l y
attached to only one side and i s
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BASE
0.5
1.0
•
0
b
Figure
4 :
SIDE C
X/L
Mean s u r f a c e
pressure
sides
prism,
of
the
0.5
c
distribution
i
LO •
on the
a = gS ° - I Z Z . S °
400
O.5
1.0
~~ '
1,0
I
'
i
'
-
4././~0 ,,x 0.5
/
0.0 -
CF
"
-0,5 "
1
O(• 125" -;It- -j,P . . . . .
127.5
-I.0 -
--
-- - -
/.
-
j /
130..B._.._.~
Aa~¢
_...-- .._._
~
"
"~.
127,5 " ¢ / 7
.-.-_.._d3o
" O(• 125°
'~o -Z.O r
__y~
SIDE A I
0
J
i
I
1.0
•
5 :
Heart s u r f a c e
pressure
sides
prism,
of
the
"
,,o-~ SiDE C
1
i
0 X/L
b
"
,.,,o. BASE
~
0.5
Figure
'
I
0.5
C
distribution ~ = 12S ° - 180 °
•
IJO •
on t h e
401 o
0.5
"~
'
I.O
t-
'
~
--
FULLY
• .o
'
1
O(e
I
-~'~
|
-
'
FULLY
SEp~.,E.o!
~FULLY
- IlO IOO
-
~ULLY
1.0
_FULLY SEPAR&T E~
AT T&CHE D
i |30
- - 90
l
0 SIDE '
. . . .
A
BASE
J
o
•
~
0.5
SIDE
J
,
,,
|
L.O
C [
o
J ....
0.5
1.0
X/L
Figure
-
I-
6 : Position of pressure peaks indicating the variation of point of reattachment with a
'
|
-"'
"
I
I
T
1
L
~
I
0,4-
0.3
S
,
S,S. 02
~ \
O.t
I
,.
0
Figure
.
[ 45
7 :
1
t 90
!
135
I 180
Strouhal number v a r i a t i o n with the angle of incidence
402
either partly attached or completely separated from the second side depending on the angle of incidence. (3) The point of flow reattachment depends on the angle of the flow. (4) The flow is f u l l y separated from the side bound by the two downstream corners.
The pressure on that surface is nearly uniform only when separation is
taking place from the corners of that side. (5) The frequency of vortex shedding depends on the wake width which is a function of whether the wake is formed by a shear layer separating from a downstream or an upstream corner. ACKNOWLEDGMENTS This investigation was supported by the University of Petroleum and Minerals, Saudi Arabia.
The author is grateful to the Mechanical Engineering Department
for the use of their aerodynamic laboratory and to the Research I n s t i t u t e for the use of their f a c i l i t y to write the paper. The assistance of both Mr. M. Abdelhalim, who fabricated the triangular prism, and Mr. M.K. Adham, who prepared the experimental set-up, is greatly appreciated.
NOMENCLATURE B
base width, 9.9 cm 2
Cp mean static pressure coefficient, (P-Po)/(O.5 p Uo) S
Strouhal number, [ f B/Uo]
SN Strouhal number based on projected width Uo f l u i d velocity far upstream of prism model X/L relative distance measured along a side of the prism of length L, Figure I f
frequency of vortex shedding
P
surface mean static pressure
Po static pressure far upstream of prism model angle of flow incidence, Figure 1 REFERENCES 1 2 3 4
J . E . Slater, Aeroelastic i n s t a b i l i t y and aerodynamics of structural angle sections, Ph.D Thesis, University of British Columbia, Canada, 1969. A . S . Rammamurthy and P. M. Lee, Wall effects on flow past b l u f f bodies, J. Sound and Vibration, 31 (1973), pp.443-451. C.F.M. Twigge-Molecey and W. D. Baines, Aerodynamic forces on a triangular cylinder, J. Eng. Mech., Proc. ASCE, 99 (1973), pp. 803-818 T. Okamoto, M. Yagita and K. Ohtsuka, Experimental investigation of the wake of a wedge, Bulletin of the JSME, 20 (1977), pp 323-328.
403
5 6 7 8
J.M. Robertson, J. B. Wedding, J. A. Peterka and J. E. Cermak, Wall pressure of separation - reattachment flow on a square prism in uniform flow,J. Ind. Aerody., 2 (1977-78), pp. 345-359. R.G. Sam, R. C. Lessmann and F. L. Test, An experimental study of flow over a rectangular body, J. Fluids Engng., Trans. ASME, 101 (1979), pp. 443-448. G.V. Parkinson and N.P.H. Brooks, On the aeroelastic i n s t a b i l i t y of bluff cylinders, J. Appl. Mech., Trans. ASME, 92 (1971), pp. 252-258. B . J . Vickery, Fluctuating l i f t and drag on a long cylinder of square cross-section in a smooth and in a turbulent stream, J. Fluid Mech., 25 (1966), pp.148-149.