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Wind effects on structural intersections
Journal of Wind Engineering and Industrial Aerodynamics, 34 (1990) 27-44
27
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
W I N D E F F E C T S ON S T R U C T U R A L I N T E R S E C T I O N S
T.A. FOX* and N. TOY
Department of Civil Engineering, University of Surrey, Guildford, Surrey GU2 5XH (U.K.) (Received October 18, 1988; accepted in revised form June 21, 1989)
Summary The airflow through an unclad lattice structure creates a complex fluid motion which affects the local wind loading of individual members within the framework. Consequently, design loads determined by traditional methods that consider each element as a finite-length member immersed in a uniform flow may be incorrect, particularly at nodal points where the largest disturbance to flow occurs. This paper, therefore, presents details of the wind effects on perpendicular structural intersections composed of either two circular cylinders or two square-section bars. The investigation was performed in a low-speed wind tunnel and models of each configuration were immersed in a steady, low-turbulence, uniform approach flow. Distributions of surface pressure were measured at a Reynolds number of 2 X 104, and these revealed that the wind effects are dependent upon section type, and whether the members intersect in a single plane or are fixed one behind the other with a point of contact.
Notation CD Cp Cpb D PL Po PT
Re Uo X Y Z #
local drag coefficient pressure coefficient pressure coefficient measured on the base centre-line diameter or section depth of model local pressure on model's surface static pressure freestream total pressure Reynolds number, D Uo/v mean freestream velocity in X-direction Cartesian coordinate in longitudinal direction Cartesian coordinate in direction perpendicular to wind tunnel floor Cartesian coordinate in lateral direction dynamic viscosity of fluid
*Present address: Department of Civil Engineering, University of Queensland, St. Lucia 4067, Australia.
0167-6105/90/$03.50
© 1990 Elsevier Science Publishers B.V.
28 t)
P
kinematic viscosity of fluid density of fluid
1. I n t r o d u c t i o n
To ensure the safe and efficient design of unclad lattice structures such as aerial masts, tower cranes, and multiple-layer geodetic frameworks, it is essential to understand the nature of the loading imposed on individual members when the structure is exposed to strong winds. To predict such loads, structural engineers generally consult relevant guides and codes of practice applicable to the particular country in which they work. In the case of the United Kingdom, examples of such documents include Scruton [ 1 ], B.S. 2573 [2 ] and B.S.I. CP3 [3 ]. These provide pressure and force coefficients for a variety of structural shapes, together with criteria for assessing the wind regime to be encountered at the proposed site. For unclad structures and frameworks, these traditional codes enable the engineer to calculate the wind loads acting on individual members of finite length when immersed in a uniform airflow. However, within a complex lattice structure, the proximity of one element to another at an intersection means that parts of each member may be subject to flow conditions considerably different from those associated with a single finite-length member in uniform flow. Consequently, the loading determined by such a method may, at present, be incorrect. It is therefore important to consider the wind effects on groups of members in the region of a nodal point where the largest disturbance to the airflow occurs. A simple structural node is that formed by two perpendicular members which either intersect in the same plane, or are fixed one behind the other with a point of contact at the centre of the geometry. Such configurations produce complex flow fields and associated loading patterns which, as yet, few researchers have studied in detail. A limited number of investigations have been undertaken to examine the interference to flow caused by perpendicular cylinders intersecting in a single plane [4-6] and cylinders placed one behind the other to form a point of contact [ 7 ]. In addition, similar configurations composed of two perpendicular flat plates have also been investigated [8,9]. However, although these studies provided some details of the wind-induced loading in the nodal region, they did not consider adequately the lateral extent of the interference effects. This paper, therefore, presents the results of an experimental investigation to determine the characteristics of the wind effects on perpendicular intersections. For this purpose the model nodes were composed of two circular cylinders, or two square-section bars (both of which represent common structural shapes), either intersecting in the same plane, or fixed one behind the other.
29
2. Experimental details
The experimental investigation was carried out in a low-speed, blow-down, open-circuit wind tunnel facility in the Department of Civil Engineering at the University of Surrey. This has working section dimensions of 1.067 m width X 1.372 m height X 9.0 m length, as shown in Fig. 1, and produces a uniform airflow with a freestream turbulence intensity of ~ 0.17% at the model testing position, where the maximum wall boundary layer thickness is 0.086 m.
The geometry of each model used in the tests is shown in Fig. 2, which also defines the coordinate system. In each case, the model was constructed from smooth aluminium circular cylinders of 30 m m diameter, or 30 m m X 30 m m square-sectional aluminium bars, with the members completely spanning the working section. All four models had equivalent blockage ratios of 5% (calculated in accordance with E.S.D.U. 80024 [10] ). End-plates were not fitted to either member, as they have been shown to produce interference effects when used with a square bar [ 11 ] and would therefore complicate the analysis of the pressure distributions. The experiments were undertaken at a Reynolds number of Re--2 X 104, based on the diameter or section depth of 30 m m and a freestream velocity of 10 m s -1. This value, which is in the upper subcritical range for a circular cylinder, was chosen for its practical significance and is compatible with previous work performed in this field. No attempt was made in the current study to determine the Reynolds number dependence of the results. Mean pressure distributions were measured through the use of pressure-hole tappings of 0.5-mm diameter arranged in fixed configurations on the surface of each model. These were connected to a low-pressure transducer by a Scanivalve switch mechanism. The latter was controlled by a microcomputer, which 5:1 Contraction
t E~ I
-
~
Exit vanes
!
.~ / Model ,n,ersectio/Jil
i
.
1tOt stahc tube . 4,5m
Airflow
-
f
f X
m
i Screens
i
Turnt able/v
Fig. 1. Diagrammatic layout of wind tunnel of 1.067 m width X 1.372 m height X 9.0 m length.
30 Y
f
Sealed Joint
x
x
i
z
I
z
Flow
i ~
F low
II
u Bars
Cylinders
Intersecting
Models
Plane of contact
Point of contact
x
x
~ Flow
z
2"f/
z
/-
lil i'
I
i
I
J
b Bars
Cylinders
Models
with
a Point
of C o n t a c t
Fig. 2. G e o m e t r y of t h e m o d e l s u s e d in t h e e x p e r i m e n t s .
FlOW
31 also performed data acquisition and on-line analysis as described by Savory and Toy [12 ]. The freestream reference pressures were obtained from a pitotstatic tube positioned in the uniform flow. Values of the coefficient of pressure, Cp, were calculated directly for each location by the use of this method and in accordance with the expression P L -- Po
C. - 0.5 pU~) where PL is the local pressure on the model's surface, Po is the freestream static pressure, and 0.5 pU~ is the dynamic head of the freestream. This system produced values of Cp from the mean of 30 000 samples with a repeatable accuracy of 1.5%. Corrections for blockage can be readily applied to surface pressure data in the case of single models of basic cross-sectional geometry through the use of Maskells' theory, E.S.D.U. 80024 [10]. This is based upon a consideration of the area occupied in the freestream by the body and its associated wake. However, it is not, at present, possible to estimate accurately these parameters with regard to the complex bodies and wakes involved in the current study and, therefore, the data are presented without correction. The pressure coefficients recorded along the base centre-line of each model, Cpb, are plotted against the spanwise location, Z/D, or Y/D, and those recorded around the circumference of each section, at various spanwise positions, are plotted against tapping location on a developed section. For the purpose of comparison, in each case, coefficients are plotted to represent the corresponding values measured on a single member in the same test rig. It should, however, be noted that the latter exhibit some degree of spanwise non-uniformity as a result of the decision not to use end-plates. The local pressure drag force is expressed as a non-dimensional coefficient such that CD--
drag force
D × 0.5pU~
where 0.5pU~ is the dynamic head of the freestream and D is the diameter or section depth of the model. This coefficient was determined at various spanwise locations from the circumferential pressure distributions measured on the surface of each member. With regard to the square-sectional bar, the calculation was performed by integration of the pressure distributions on the front and rear surfaces (the contribution to form drag by the side faces being regarded as negligible) through the expression
32
D/2
D/2
1
1
CD= ~ f C~dy-~ f C,dy --D/2 --D/2 (front face) (rear face) For the circular cylinder, the local drag coefficient was obtained by numerical integration of the base pressure distribution in accordance with the relationship
CD fCp =
cos0d0
o
3. Discussion of results
3.1. Intersecting circular members The spanwise distribution of base pressure recorded on the rear surface of a single arm of the intersecting cylinders is shown in Fig. 3. From this it is clear that a gross disturbance to the flow conditions occurs in close proximity to the intersection. In this region, the coefficients of pressure have values considerably higher than those found on the base centre-line of the single cylinder. For example, at the centre of the geometry, a 58% reduction in suction is evident in the value of Cpb= -- 0.52, when compared with Cpb= -- 1.24 measured at the corresponding location on the single cylinder. With increasing spanwise disCpb
-1-2
~J
•
-1.0
Single Cylinder
+ Intersecting Model
-0.8
-0.6
I
Z/D
10
I
I
8
I
|
6
I
l
4
I
I
2
|
I
0
Fig. 3. Spanwise base pressure distribution on a single arm of the intersecting circular cylinders.
33
tance away from the intersection, the base pressure is reduced to a local peak suction, Cpb= -0.9, at two diameters from the centre. This is followed by a slight rise in pressure to Cpb = -- 0.84 at four diameters, and then a continuous decrease to the corresponding single cylinder values, the difference at 10 diameters being only 8% in Cp. This variation in base pressure suggests that a gross interference to flow conditions at the surface of the geometry is largely confined to an inner region within two diameters of the centre, the flow regime in the outer region beyond this being only slightly disturbed. Indeed, this is confirmed by the circumferential pressure distributions recorded around the cylinder at spanwise locations of Z = 10D, Z = 5D, and Z = 2.5D {Fig. 4). In this respect, all three curves are similar in shape to that obtained at the centre-line of the single cylinder and, therefore, exhibit characteristics indicative of a dominant quasi-two-dimensional flow regime. Indeed, the circumferential distribution recorded at 10 diameters from the centre of the configuration is almost identical to the corresponding profile measured at the same location on the single cylinder. However, although the circumferential distributions measured at Z = 5D and Z=2.5D present profiles with shapes similar to the quasi-two-dimensional condition, some interference effects are evident as an increase in the wake pressures. This is reflected in the local drag coefficients presented in Table 1, which show a spanwise variation, with the minimum value recorded being at five diameters from the intersection, CD=0.98, and a local drag at Z = 10D Cp 1.04
Single Cylinder --Centre --
--
Z=
Line IOD
Intersecting Model
0-5
+ Z = IOD xZ=5D o Z=2.5D
e'o '
' do'
'1~,o'
' 1~o'
'18o 0 o
- 0.5
-
1'0
),
:::
Fig. 4. Circumferential pressure distributions at spanwise locations on a single arm of the intersecting circular cylinders.
34 TABLE 1 Local drag coefficients recorded on intersecting models Model
Re
Blockage (%)
Local drag coefficient, ('~ Spanwise location
Cylinders (current study) Cylinders (Osaka et al. [4] ) Bars (current study)
2 X 10 4 0.8 X 10 4 2 X 104
5 2.5 5
2.5D
5i)
IOD
1.01 1.01 1.99
0.98 0.95 1.94
!.08 2. t 2
which is only 4% less than the single cylinder value at the same location. A similar minimum was also found at Z = 5D by Osaka et al. [4 ] in measurements extending to eight diameters; the corresponding values are presented in Table 1 for the purpose of comparison and represent experiments at a lower Reynolds number with a lower blockage ratio. Although the circumferential profiles and drag coefficients for the outer region indicate minimal disturbance to the flow conditions around the cylinder, the base pressure distribution of Fig. 3 suggests that the interference effects that do occur are a result of the presence of secondary flow at the surface of the cylinder at all spanwise locations examined. This is evident in the pressure gradient, which is particularly steep in the highly disturbed inner region where the distribution indicates strong secondary flow away from the centre of the geometry. Beyond the peak in suction at Z= 2D a weaker spanwise movement of fluid occurs which is evidently not sufficient to destroy the dominant quasitwo-dimensional conditions at locations in the outer region. Donoso [8] observed similar changes in the pressure gradient at spanwise locations on the rear surface of intersecting flat plates and deduced that a pair of counter-rotating trailing vortices, one on each side of the base centre-line, are generated within the highly disturbed inner region. Thus, it may be assumed that the peak suction recorded at Z = 2D in Fig. 3 is associated with the formation of similar vortices at the surface of the intersecting cylinders. Indeed, this is compatible with the results of experiments performed by Zdravkovich [6]. From measurements of the mean pressures on the surface of intersecting cylinders with high blockage ratios, Zdravkovich [6] determined a local maximum in the drag coefficient at Z=I.5D, a result also found by Osaka et al. [4]. This feature was coincident with the spanwise location of the minimum value of Cp recorded on the circumference of the cylinder, and was attributed to the presence of trailing vortices with secondary flows outwards from the centre of the intersection. Zdravkovich [6] confirmed the existence of this mechanism by oil film visualization of the corresponding surface flows.
35 Although Fig. 3 indicates that the strong secondary flow associated with the trailing vortices is largely confined to spanwise locations within two diameters of the intersection, it has been shown that these vortices expand considerably in the wake. In this respect, from measurements of vorticity at 12 diameters downstream of a similar configuration, Osaka et al. [4] determined two secondary circulations in each quadrant described by the geometry. These covered a plane five diameters square with an origin at Z = Y = O. Further downstream, at 30 diameters, Osaka et al. found secondary flow vectors which indicated that the trailing vortices occupied a similar plane 10 diameters square. 3.2. Intersecting square members Figure 5 shows the spanwise distribution of base pressure measurec Jn the surface of a single arm of the intersecting square-section bars. This can be divided into similar inner and outer regions dependent upon the degree of interference to the flow conditions around the bar. In the inner region, the gross disturbance to surface flow produces a 56% reduction in suction at the centre of the span compared with the single bar. This corresponds to the 58% reduction found at the same location on the intersecting cylinders. With increasing spanwise distance along the arm of the geometry, the pressure decreases to a peak in suction of Cpb -- -- 1.18 at about two section depths, followed by a slight rise in pressure to Cpb=--1.06 at Z = 4 D . Although this feature is similar to Cpb
•
•
m - - !
m ~
-1.4
~
_ • ~ m
~
m ~
• S i n g l e Bar
-1.2
+ Intersecting Model
- 1,0
-0.8
-0"6
I
ZID
10
i
I
8
i
I
6
i
I
4
I
I
2
I
I
0
Fig. 5. Spanwise base pressure distribution on a single arm of the intersecting square-section bars.
36
that found on the circular cylinders, the peak in this case is more pronounced as a result of the larger spanwise pressure gradients. An increase in the pressure gradient relative to that of the cylinders is also evident in the outer region, where the suction increases spanwise to values of Cpb corresponding to those of the single bar. This might be expected to be the result of a significant disturbance to the flow conditions around the bar. However, the circumferential pressure distribution measured at Z = 10D (Fig. 6) suggests t h a t the interference to quasi-two-dimensional conditions in this region is minimal. Indeed, the distribution is almost identical to t h a t found at the corresponding location on the single square-section bar. However, although the distributions recorded at Z = 5D and Z = 2.5D exhibit similar characteristic shapes, interference effects are evident as an increase in the value of Cp over the side and rear faces. Such an increase in mean pressure has previously been attributed, in the case of a single bar, to a downstream elongation of the vortex formation region [ 13 ]. In the case of intersecting bars, a similar elongation may occur in the outer region as a result of weak secondary flow at the rear surface of the member. These surface pressure changes in the circumferential distributions are reflected in the spanwise variation of the local drag coefficient, shown in Table 1, which is similar in character to the variation of drag associated with the intersecting cylinders. In this respect a spanwise variation is evident, with the m i n i m u m value recorded being CD = 1.94 at Z = 5D. At 10 section depths from the centre, where the flow conditions are relatively undisturbed, the coefficient is 98% of that found at the corresponding position on the single bar (C,~ = 2.16 ). Cp
Single ---
1"01
-
-
Bar
Centre Line Z=IOD
Intersecting
Model
+ Z=IOD x Z = 5D o Z = 2.5D
0"5 Tapping
10-
6
11
10--
x x O 0 0 0 0
15 115
-15
o
~
o
÷-- + + ÷ +
Fig. 6. Circumferential pressure distributions at spanwise locations on a single a r m of the intersecting square-section bars.
37
Although the authors are not, at present, aware of any studies of the flow regimes at the surface of intersecting square bars available to corroborate these results, the discussion above has identified the main wind effects as being similar to those associated with intersecting circular cylinders. Having established this comparison, the remaining section of the paper considers the results obtained with the perpendicular members fixed one behind the other. 3.3. Circular members in contact The spanwise distributions of base pressure measured on the surface of each circular cylinder are shown in Fig. 7 (for the purpose of analysis, it is assumed that the value of Cpb at the precise point of contact between the two cylinders is zero). In the case of the upstream cylinder, at spanwise locations beyond the centre of the geometry the pressure decreases rapidly to a sharp peak in suction of Cpb = -- 1.26 at Y = 1.75D. This is followed by a 35% reduction in suction to Cpb = -0,82 at Y = 5D, which enhances the peak, and then a steady decrease in pressure spanwise towards Cpb values corresponding to those found on the single cylinder. The peak suction at Y = 1.75D is approximately coincident with that found at two diameters from the centre of the intersecting cylinders (Fig. 3), and is indicative of a similar flow regime, characterized by an inner region of highly disturbed conditions. The associated pressure gradient illustrates the presence of strong secondary flow away from the centre of the geometry towards the suction peak. Indeed, such a flow was identified in visualization experiments Cpb
-
1:I " -
• I ~ ' • ~
t
• Single Cylinder • Upstream Member • Downstream Member -0.8
-0.6 ¸
I
I
10
I
8
~
I
6
I
I
4
f
I
2
I
0
Fig. 7. Spanwise base pressure d i s t r i b u t i o n s on the perpendicular circular cylinders f o r m i n g a point of contact.
38 performed by Zdravkovich [7 ], which revealed the existence of two intense trailing vortices, one on either side of the base centre-line, generated from the upstream member near the point of contact of a similar configuration with a higher blockage ratio. The positions of the centres of these vortices were estimated by Zdravkovich [ 7 ], from surface pressure measurements in the region Y< 2D, to be at 0=90 ° at approximately one diameter from the point of contact, Y~ 1D. The circumferential pressure distributions recorded on the upstream cylinder at various spanwise locations are shown in Fig. 8. At the centre of the span the profile is similar to that recorded by Zdravkovich [ 7 ] and is therefore assumed to be associated with the formation of a small recirculation "bubble" adjacent to the rear surface of the cylinder. This feature was examined in detail by Zdravkovich [7 ] by oil film visualization of the surface flow pattern, which revealed a bubble with an arch-like structure in the spanwise direction. In the outer region beyond the highly disturbed conditions, the profiles in Fig. 8 reveal only small changes in the pressure distribution as a result of the weaker secondary fluid motion. The associated effects upon the local drag coefficient can be assessed from the values presented in Table 2, which exhibit a similar spanwise variation to that found on the intersecting cylinders (Table 1 ), i.e. a local minimum value of drag at Y= 5D, and a drag coefficient at 10 diameters from the point of contact, CD= 1.02, which is 9% less than that measured at the corresponding Cp 1"0
Single
Cylinder
Cp
----
Centre
Line
Upstream Member 0.5
+
Y=10D
x
Y=
o
Y = 2.5D
~, Y =
5D OD
-05
- 1.0
Fig. 8. Circumferential pressure distributions at spanwise locations on the upstream member of the perpendicular circular cylinders forming a point of contact.
39 TABLE 2 Local drag coefficients recorded on the circular cylinders fixed one behind the other Spanwise location
2.5D 5D 10D
Local drag coefficient, Co Upstream cylinder
Downstream cylinder
1.16 0.96 1.02
0.93 0.98 1.06
location on the single cylinder ( C D = 1.12). The degree of interference at the latter position is, therefore, greater than that found to be the case with the intersecting cylinders, where the drag at 10 diameters is reduced by only 4% of the corresponding single cylinder value. The spanwise distribution of base pressure recorded on the surface of the downstream cylinder is also shown in Fig. 7. Although initially this appears to have a profile similar to those already described on both the upstream cylinder and the intersecting cylinders, closer inspection reveals two significant differences. These are that the position of peak suction is closer to the centre of the span, at Z = 0.5D, and that the pressure gradient is considerably reduced in the region Z < 0.5D. These differences are associated with the existence of a different flow regime around the cylinder, the nature of which appears to be similar to that found in the work of Zdravkovich [7 ]. From his measurements of the mean pressure distribution on the downstream cylinder in the region Z < 1D, and surface flow visualization experiments, a horseshoe vortex flow pattern was deduced. This involved the generation of two such vortices, one from each side of the point of contact, which remain attached to the surface of the downstream cylinder as they converge in the wake. Consequently, the inner region of the disturbance to flow conditions is restricted to a shorter proportion of the span. At the centre of the span the disturbance has a considerable effect upon the circumferential pressure distribution recorded at the surface of the downstream member (Fig. 9). However, in the outer region the profiles suggest that the quasi-two-dimensional conditions associated with the single cylinder dominate the fluid motion. The spanwise variation of the local drag coefficient recorded on the downstream cylinder is shown in Table 2 and is fundamentally different from that already described in the outer regions of either the upstream cylinder or the intersecting cylinders. In the last two cases a local minimum value was recorded at Z = 5D, whereas in these measurements there is a steady increase in drag with distance from the node. The value recorded at 10 diameters, CD= 1.06, is evidence of the minimum disturbance to the flow around the cylinder at that
40
Cp 1.0~
Single Cylinder ..... Centre Line Downstream Member
0.5
+ Z= 1OD x Z:5D o Z:25D Z:OD . . . .
",~'
',~'
',~o'
',~o'
,%oo °
- 0.5
\
°\°°°°Oooooo
- 1-0
Fig. 9. Circumferentialpressure distributions at spanwlselocationson the downstreammember of the perpendicularcircularcylindersforminga point of contact. location, as it is only 5% lower than the corresponding single cylinder value (CD = 1.12). 3.4. Square members in contact The spanwise distribution of base pressure measured on the upstream member of the same perpendicular configuration composed of two square-section bars is shown in Fig. 10 (the pressure at the surface of contact is assumed to be zero ). In this case, the suction peak of Cpb = -- 1.3 at Y = 2D indicates the presence of secondary flows in the inner region which are similar to those already discussed with regard to the intersecting bars. However, the outer region appears to be considerably more disturbed than has been found in the previous cases, and this is also observed in the circumferential distributions of Fig. 11. These show that quasi-two-dimensional flow conditions are not as clearly discernible in the surface pressures as previously noted in the outer regions of the cylinder configurations and the intersecting square bars. However, despite the increased disturbance to the flow conditions, the local drag coefficients shown in Table 3 exhibit similar trends to those already identified in the results for the intersecting bars and cylinders. In this respect, the coefficients exhibit a spanwise variation, with the minimum value recorded being at Y = 5D. In addition, the drag at 10 section depths from the point of contact has a value of 96% of that found at the corresponding location on a single bar ( CD= 2.16).
41 Cpb
m~1_m 1~'m
-1,4
• Single '
Bar
• Upstream Member
- 1 , 2 -'
• Downstream Member
-1.O
i 10
i 8
I
I
I
I
6
i
T
4
i
2
i 0
Fig. 10. Spanwise base pressure distributions on the perpendicular square-section bars forming a plane of contact.
Cp
Single - --
1'01
Bar
Centre --
Line
Z---10D
Upst ream Member
0.5 Tapping
+
Z=IOD
x o
Z-- 5D Z= 2.5D
-1.0-
oOo
o XXxx~ ÷+÷+ o
11 10
15
oo
o
o
o
-1-5
Fig. 11. Circumferential pressure distributions at spanwise locations on the upstream member of the perpendicular square-section bars forming a plane of contact.
The spanwise distribution of base pressure recorded on the downstream square bar is also shown in Fig. 10. This is in complete contrast to the corresponding distribution obtained on the downstream circular cylinder (Fig. 7), and does not show the distinct peak of suction associated with the presence of the horseshoe vortices adjacent to the centre of the span. Instead, the pressure is constant at Cpb = -- 0.92 in the region Z < 1D, and is seen to decrease contin-
42 TABLE 3
Local drag coefficients recorded on the square-section bars fixed one behind the other Spanwise location
2.5D 5D 10D
Local drag coefficient, CD
Upstream bar
Downstream bar
2.07 1.94 2.07
1.89 2.02 2.20
Cp Single - -
1'01
--
Bar
Centre --
Downstream
0.5 Tapping
-1.011 10
15
o o o
°°°°° x x
Ix
•
÷
+
Z=10D
x o
Z= Z=
Member
5D 2"5D
t
1 5
o
Line
Z=lOD
÷~
~+
-1.5
F Fig. 12. Circumferential pressure distributions at spanwise locations on the downstream member of the perpendicular square-section bars forming a plane of contact.
uously spanwise to Cpb=- 1.43 at Z=8D (a result similar to that found by Donoso [8 ] on the downstream member of a pair of perpendicular flat plates). This difference can be attributed to a fundamental difference in the behaviour of the horseshoe vortices in the near wake of the bar. In this respect, Fox and Toy [14] have shown that the section geometry of the bar delays the convergence process until further downstream, and consequently the vortices are not evident as peak suction values in the base pressure distribution. The spanwise distribution does, however, indicate that a significant disturbance to the flow around the bar occurs over much of the span, and this is indeed the case, as can be deduced from the circumferential pressure distributions of Fig. 12. These show that at 2.5 section depths from the centre-line, the chordwise mean pressures decrease continuously towards the trailing edge, and the distribution on the rear face is almost constant, with no peak suction
43 at the base. At five section depths, the chordwise pressures are still significantly distorted, but the rear face pressures show a profile similar to that of a single bar. However, in the outer region, at 10 section depths from the centre, both the chordwise and rear face pressures have characteristics associated with quasi-two-dimensional conditions. Despite the greater disturbance to the pressure distributions, the local drag coefficients presented in Table 3 have a similar spanwise variation to those obtained on the downstream circular cylinder, with the minimum value recorded being that at Z = 2.5D. However, in this case the coefficient recorded at 10 section depths from the centre-line is 2% greater than the corresponding single bar value, and therefore reflects the increased interference effects associated with this geometry. 4. C o n c l u s i o n s
This paper has presented experimental results which characterize the interference effects in the nodal region of perpendicular intersections. In general, the wind-induced loading experienced by each member of an intersection is reduced, relative to that associated with a single element in uniform flow, within a spanwise region of 10 diameters or section depths from the centre of the geometry. However, the precise nature of the wind effects is dependent upon the section type, and whether the members intersect in a single plane, or are fixed one behind the other with a point of contact. The tests involving circular cylinders which intersect in a single plane have shown that the flow field associated with each arm of the configuration may be divided into two spanwise regions which are defined by the degree of interference caused by the intersection: ( 1 ) an outer region of quasi-two-dimensional conditions, and (2) inner region of highly disturbed flow which extends spanwise approximately two diameters from the centre of the geometry. A similar interference effect was determined on the surface of the intersecting square bars. Indeed, the spanwise locations and characteristics of the main features were found to correspond with those of the intersecting cylinders. However, in this case the pressure gradients in both the inner and outer regions were generally greater. When the cylinders were displaced in the direction of freestream flow, such that they formed a point of contact at the centre, the interference effects altered. In this respect the pressure distribution on the upstream cylinder exhibited similar characteristics to that found on an arm of the intersecting cylinders, whereas the nature of the disturbance in the inner region of the downstream cylinder changed. The pressure gradient from the centre of the geometry was reduced in comparison with the intersecting cylinders, and the
44
division between the inner and outer regions moved closer to the centre of the span. In the case of the square bars arranged in the plane of contact configuration, similar interference effects were determined on the upstream member. However, the nature of the disturbance to the downstream bar was found to be somewhat different, with significant interference effects extending over much of the span. These results can only be regarded as initial work, as there remains considerable scope for further investigation in this field, particularly with regard to the wind effects on other section types commonly used in structural engineering. Acknowledgement
This research was supported through an SERC studentship awarded to T.A. Fox. References 1 2 3 4
5
6 7 8 9 10 11 12 13 14
C. Scruton, An Introduction to Wind effects on Structures, Oxford University Press, Oxford, 1978. B.S. 2573, Rules for the design of cranes, Part 1: Specification for classification, stress calculation and design criteria for structures, British Standards Institution, London, 1983. B.S.I. CP3, Code of basic data for the design of buildings, Chapter V, Loading, Part 2: Wind loads, British Standards Institution, London, 1972. H. Osaka, I. Nakamura, H. Yamada, Y. Kuwata and Y. Kageyama, The structure of a turbulent wake behind a cruciform circular cylinder, 1st Report: the mean velocity field, Bull. Jap. Soc. Mech. Eng., 26 (1983) 356-363. H. Osaka, H. Yamada, I. Nakamura, Y. Kuwata and Y. Kageyama, The structure of a turbulent wake behind a cruciform circular cylinder, 2rid Report: the streamwise development of turbulent flow field, Bull. Jap. Soc. Mech. Eng., 26 ( 1983 ) 521-528. M.M. Zdravkovich, Flow around two intersecting cylinders, Trans. ASME, J. Fluids Eng., 107 (1985) 507-511. M.M. Zdravkovich, Interference between two circular cylinders forming a cross, J. Fluid Mech.. 128 (1983) 231-246. J.A. Donoso, Investigation of wake structure of isolated and intersecting fiat plates, M.Phil. Thesis, University of London, 1980. J.A. Donoso, R. Hillier and C.K. Yeung, The effect of strong three-dimensional disturbance on vortex shedding, J. Wind Eng. Ind. Aerodyn., 11 (1983) 381-392. E.S.D.U., Blockage corrections for bluff bodies in confined flows, Item No. 80024, Eng. Sci. Data Unit, London, 1980. N. Toy and T.A. Fox, The effect of aspect ratio of end plate separation upon base pressures recorded on a square bar, Exp. Fluids, 4 (1986) 266-268. E. Savory and N. Toy, Microcomputer control of wind tunnel instrumentation with on-line data acquisition and analysis, Software Microsyst., 3 (1984) 93-97. P.W. Bearman and D.M. Trueman, An investigationof the flow around rectangular cylinders, Aero. Quart., 23 (1972) 229-237. T.A. Fox and N. Toy, The generation of turbulence from displaced cross-members in uniform flow, Exp. Fluids, 6 (1988) 172-178.
27
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
W I N D E F F E C T S ON S T R U C T U R A L I N T E R S E C T I O N S
T.A. FOX* and N. TOY
Department of Civil Engineering, University of Surrey, Guildford, Surrey GU2 5XH (U.K.) (Received October 18, 1988; accepted in revised form June 21, 1989)
Summary The airflow through an unclad lattice structure creates a complex fluid motion which affects the local wind loading of individual members within the framework. Consequently, design loads determined by traditional methods that consider each element as a finite-length member immersed in a uniform flow may be incorrect, particularly at nodal points where the largest disturbance to flow occurs. This paper, therefore, presents details of the wind effects on perpendicular structural intersections composed of either two circular cylinders or two square-section bars. The investigation was performed in a low-speed wind tunnel and models of each configuration were immersed in a steady, low-turbulence, uniform approach flow. Distributions of surface pressure were measured at a Reynolds number of 2 X 104, and these revealed that the wind effects are dependent upon section type, and whether the members intersect in a single plane or are fixed one behind the other with a point of contact.
Notation CD Cp Cpb D PL Po PT
Re Uo X Y Z #
local drag coefficient pressure coefficient pressure coefficient measured on the base centre-line diameter or section depth of model local pressure on model's surface static pressure freestream total pressure Reynolds number, D Uo/v mean freestream velocity in X-direction Cartesian coordinate in longitudinal direction Cartesian coordinate in direction perpendicular to wind tunnel floor Cartesian coordinate in lateral direction dynamic viscosity of fluid
*Present address: Department of Civil Engineering, University of Queensland, St. Lucia 4067, Australia.
0167-6105/90/$03.50
© 1990 Elsevier Science Publishers B.V.
28 t)
P
kinematic viscosity of fluid density of fluid
1. I n t r o d u c t i o n
To ensure the safe and efficient design of unclad lattice structures such as aerial masts, tower cranes, and multiple-layer geodetic frameworks, it is essential to understand the nature of the loading imposed on individual members when the structure is exposed to strong winds. To predict such loads, structural engineers generally consult relevant guides and codes of practice applicable to the particular country in which they work. In the case of the United Kingdom, examples of such documents include Scruton [ 1 ], B.S. 2573 [2 ] and B.S.I. CP3 [3 ]. These provide pressure and force coefficients for a variety of structural shapes, together with criteria for assessing the wind regime to be encountered at the proposed site. For unclad structures and frameworks, these traditional codes enable the engineer to calculate the wind loads acting on individual members of finite length when immersed in a uniform airflow. However, within a complex lattice structure, the proximity of one element to another at an intersection means that parts of each member may be subject to flow conditions considerably different from those associated with a single finite-length member in uniform flow. Consequently, the loading determined by such a method may, at present, be incorrect. It is therefore important to consider the wind effects on groups of members in the region of a nodal point where the largest disturbance to the airflow occurs. A simple structural node is that formed by two perpendicular members which either intersect in the same plane, or are fixed one behind the other with a point of contact at the centre of the geometry. Such configurations produce complex flow fields and associated loading patterns which, as yet, few researchers have studied in detail. A limited number of investigations have been undertaken to examine the interference to flow caused by perpendicular cylinders intersecting in a single plane [4-6] and cylinders placed one behind the other to form a point of contact [ 7 ]. In addition, similar configurations composed of two perpendicular flat plates have also been investigated [8,9]. However, although these studies provided some details of the wind-induced loading in the nodal region, they did not consider adequately the lateral extent of the interference effects. This paper, therefore, presents the results of an experimental investigation to determine the characteristics of the wind effects on perpendicular intersections. For this purpose the model nodes were composed of two circular cylinders, or two square-section bars (both of which represent common structural shapes), either intersecting in the same plane, or fixed one behind the other.
29
2. Experimental details
The experimental investigation was carried out in a low-speed, blow-down, open-circuit wind tunnel facility in the Department of Civil Engineering at the University of Surrey. This has working section dimensions of 1.067 m width X 1.372 m height X 9.0 m length, as shown in Fig. 1, and produces a uniform airflow with a freestream turbulence intensity of ~ 0.17% at the model testing position, where the maximum wall boundary layer thickness is 0.086 m.
The geometry of each model used in the tests is shown in Fig. 2, which also defines the coordinate system. In each case, the model was constructed from smooth aluminium circular cylinders of 30 m m diameter, or 30 m m X 30 m m square-sectional aluminium bars, with the members completely spanning the working section. All four models had equivalent blockage ratios of 5% (calculated in accordance with E.S.D.U. 80024 [10] ). End-plates were not fitted to either member, as they have been shown to produce interference effects when used with a square bar [ 11 ] and would therefore complicate the analysis of the pressure distributions. The experiments were undertaken at a Reynolds number of Re--2 X 104, based on the diameter or section depth of 30 m m and a freestream velocity of 10 m s -1. This value, which is in the upper subcritical range for a circular cylinder, was chosen for its practical significance and is compatible with previous work performed in this field. No attempt was made in the current study to determine the Reynolds number dependence of the results. Mean pressure distributions were measured through the use of pressure-hole tappings of 0.5-mm diameter arranged in fixed configurations on the surface of each model. These were connected to a low-pressure transducer by a Scanivalve switch mechanism. The latter was controlled by a microcomputer, which 5:1 Contraction
t E~ I
-
~
Exit vanes
!
.~ / Model ,n,ersectio/Jil
i
.
1tOt stahc tube . 4,5m
Airflow
-
f
f X
m
i Screens
i
Turnt able/v
Fig. 1. Diagrammatic layout of wind tunnel of 1.067 m width X 1.372 m height X 9.0 m length.
30 Y
f
Sealed Joint
x
x
i
z
I
z
Flow
i ~
F low
II
u Bars
Cylinders
Intersecting
Models
Plane of contact
Point of contact
x
x
~ Flow
z
2"f/
z
/-
lil i'
I
i
I
J
b Bars
Cylinders
Models
with
a Point
of C o n t a c t
Fig. 2. G e o m e t r y of t h e m o d e l s u s e d in t h e e x p e r i m e n t s .
FlOW
31 also performed data acquisition and on-line analysis as described by Savory and Toy [12 ]. The freestream reference pressures were obtained from a pitotstatic tube positioned in the uniform flow. Values of the coefficient of pressure, Cp, were calculated directly for each location by the use of this method and in accordance with the expression P L -- Po
C. - 0.5 pU~) where PL is the local pressure on the model's surface, Po is the freestream static pressure, and 0.5 pU~ is the dynamic head of the freestream. This system produced values of Cp from the mean of 30 000 samples with a repeatable accuracy of 1.5%. Corrections for blockage can be readily applied to surface pressure data in the case of single models of basic cross-sectional geometry through the use of Maskells' theory, E.S.D.U. 80024 [10]. This is based upon a consideration of the area occupied in the freestream by the body and its associated wake. However, it is not, at present, possible to estimate accurately these parameters with regard to the complex bodies and wakes involved in the current study and, therefore, the data are presented without correction. The pressure coefficients recorded along the base centre-line of each model, Cpb, are plotted against the spanwise location, Z/D, or Y/D, and those recorded around the circumference of each section, at various spanwise positions, are plotted against tapping location on a developed section. For the purpose of comparison, in each case, coefficients are plotted to represent the corresponding values measured on a single member in the same test rig. It should, however, be noted that the latter exhibit some degree of spanwise non-uniformity as a result of the decision not to use end-plates. The local pressure drag force is expressed as a non-dimensional coefficient such that CD--
drag force
D × 0.5pU~
where 0.5pU~ is the dynamic head of the freestream and D is the diameter or section depth of the model. This coefficient was determined at various spanwise locations from the circumferential pressure distributions measured on the surface of each member. With regard to the square-sectional bar, the calculation was performed by integration of the pressure distributions on the front and rear surfaces (the contribution to form drag by the side faces being regarded as negligible) through the expression
32
D/2
D/2
1
1
CD= ~ f C~dy-~ f C,dy --D/2 --D/2 (front face) (rear face) For the circular cylinder, the local drag coefficient was obtained by numerical integration of the base pressure distribution in accordance with the relationship
CD fCp =
cos0d0
o
3. Discussion of results
3.1. Intersecting circular members The spanwise distribution of base pressure recorded on the rear surface of a single arm of the intersecting cylinders is shown in Fig. 3. From this it is clear that a gross disturbance to the flow conditions occurs in close proximity to the intersection. In this region, the coefficients of pressure have values considerably higher than those found on the base centre-line of the single cylinder. For example, at the centre of the geometry, a 58% reduction in suction is evident in the value of Cpb= -- 0.52, when compared with Cpb= -- 1.24 measured at the corresponding location on the single cylinder. With increasing spanwise disCpb
-1-2
~J
•
-1.0
Single Cylinder
+ Intersecting Model
-0.8
-0.6
I
Z/D
10
I
I
8
I
|
6
I
l
4
I
I
2
|
I
0
Fig. 3. Spanwise base pressure distribution on a single arm of the intersecting circular cylinders.
33
tance away from the intersection, the base pressure is reduced to a local peak suction, Cpb= -0.9, at two diameters from the centre. This is followed by a slight rise in pressure to Cpb = -- 0.84 at four diameters, and then a continuous decrease to the corresponding single cylinder values, the difference at 10 diameters being only 8% in Cp. This variation in base pressure suggests that a gross interference to flow conditions at the surface of the geometry is largely confined to an inner region within two diameters of the centre, the flow regime in the outer region beyond this being only slightly disturbed. Indeed, this is confirmed by the circumferential pressure distributions recorded around the cylinder at spanwise locations of Z = 10D, Z = 5D, and Z = 2.5D {Fig. 4). In this respect, all three curves are similar in shape to that obtained at the centre-line of the single cylinder and, therefore, exhibit characteristics indicative of a dominant quasi-two-dimensional flow regime. Indeed, the circumferential distribution recorded at 10 diameters from the centre of the configuration is almost identical to the corresponding profile measured at the same location on the single cylinder. However, although the circumferential distributions measured at Z = 5D and Z=2.5D present profiles with shapes similar to the quasi-two-dimensional condition, some interference effects are evident as an increase in the wake pressures. This is reflected in the local drag coefficients presented in Table 1, which show a spanwise variation, with the minimum value recorded being at five diameters from the intersection, CD=0.98, and a local drag at Z = 10D Cp 1.04
Single Cylinder --Centre --
--
Z=
Line IOD
Intersecting Model
0-5
+ Z = IOD xZ=5D o Z=2.5D
e'o '
' do'
'1~,o'
' 1~o'
'18o 0 o
- 0.5
-
1'0
),
:::
Fig. 4. Circumferential pressure distributions at spanwise locations on a single arm of the intersecting circular cylinders.
34 TABLE 1 Local drag coefficients recorded on intersecting models Model
Re
Blockage (%)
Local drag coefficient, ('~ Spanwise location
Cylinders (current study) Cylinders (Osaka et al. [4] ) Bars (current study)
2 X 10 4 0.8 X 10 4 2 X 104
5 2.5 5
2.5D
5i)
IOD
1.01 1.01 1.99
0.98 0.95 1.94
!.08 2. t 2
which is only 4% less than the single cylinder value at the same location. A similar minimum was also found at Z = 5D by Osaka et al. [4 ] in measurements extending to eight diameters; the corresponding values are presented in Table 1 for the purpose of comparison and represent experiments at a lower Reynolds number with a lower blockage ratio. Although the circumferential profiles and drag coefficients for the outer region indicate minimal disturbance to the flow conditions around the cylinder, the base pressure distribution of Fig. 3 suggests that the interference effects that do occur are a result of the presence of secondary flow at the surface of the cylinder at all spanwise locations examined. This is evident in the pressure gradient, which is particularly steep in the highly disturbed inner region where the distribution indicates strong secondary flow away from the centre of the geometry. Beyond the peak in suction at Z= 2D a weaker spanwise movement of fluid occurs which is evidently not sufficient to destroy the dominant quasitwo-dimensional conditions at locations in the outer region. Donoso [8] observed similar changes in the pressure gradient at spanwise locations on the rear surface of intersecting flat plates and deduced that a pair of counter-rotating trailing vortices, one on each side of the base centre-line, are generated within the highly disturbed inner region. Thus, it may be assumed that the peak suction recorded at Z = 2D in Fig. 3 is associated with the formation of similar vortices at the surface of the intersecting cylinders. Indeed, this is compatible with the results of experiments performed by Zdravkovich [6]. From measurements of the mean pressures on the surface of intersecting cylinders with high blockage ratios, Zdravkovich [6] determined a local maximum in the drag coefficient at Z=I.5D, a result also found by Osaka et al. [4]. This feature was coincident with the spanwise location of the minimum value of Cp recorded on the circumference of the cylinder, and was attributed to the presence of trailing vortices with secondary flows outwards from the centre of the intersection. Zdravkovich [6] confirmed the existence of this mechanism by oil film visualization of the corresponding surface flows.
35 Although Fig. 3 indicates that the strong secondary flow associated with the trailing vortices is largely confined to spanwise locations within two diameters of the intersection, it has been shown that these vortices expand considerably in the wake. In this respect, from measurements of vorticity at 12 diameters downstream of a similar configuration, Osaka et al. [4] determined two secondary circulations in each quadrant described by the geometry. These covered a plane five diameters square with an origin at Z = Y = O. Further downstream, at 30 diameters, Osaka et al. found secondary flow vectors which indicated that the trailing vortices occupied a similar plane 10 diameters square. 3.2. Intersecting square members Figure 5 shows the spanwise distribution of base pressure measurec Jn the surface of a single arm of the intersecting square-section bars. This can be divided into similar inner and outer regions dependent upon the degree of interference to the flow conditions around the bar. In the inner region, the gross disturbance to surface flow produces a 56% reduction in suction at the centre of the span compared with the single bar. This corresponds to the 58% reduction found at the same location on the intersecting cylinders. With increasing spanwise distance along the arm of the geometry, the pressure decreases to a peak in suction of Cpb -- -- 1.18 at about two section depths, followed by a slight rise in pressure to Cpb=--1.06 at Z = 4 D . Although this feature is similar to Cpb
•
•
m - - !
m ~
-1.4
~
_ • ~ m
~
m ~
• S i n g l e Bar
-1.2
+ Intersecting Model
- 1,0
-0.8
-0"6
I
ZID
10
i
I
8
i
I
6
i
I
4
I
I
2
I
I
0
Fig. 5. Spanwise base pressure distribution on a single arm of the intersecting square-section bars.
36
that found on the circular cylinders, the peak in this case is more pronounced as a result of the larger spanwise pressure gradients. An increase in the pressure gradient relative to that of the cylinders is also evident in the outer region, where the suction increases spanwise to values of Cpb corresponding to those of the single bar. This might be expected to be the result of a significant disturbance to the flow conditions around the bar. However, the circumferential pressure distribution measured at Z = 10D (Fig. 6) suggests t h a t the interference to quasi-two-dimensional conditions in this region is minimal. Indeed, the distribution is almost identical to t h a t found at the corresponding location on the single square-section bar. However, although the distributions recorded at Z = 5D and Z = 2.5D exhibit similar characteristic shapes, interference effects are evident as an increase in the value of Cp over the side and rear faces. Such an increase in mean pressure has previously been attributed, in the case of a single bar, to a downstream elongation of the vortex formation region [ 13 ]. In the case of intersecting bars, a similar elongation may occur in the outer region as a result of weak secondary flow at the rear surface of the member. These surface pressure changes in the circumferential distributions are reflected in the spanwise variation of the local drag coefficient, shown in Table 1, which is similar in character to the variation of drag associated with the intersecting cylinders. In this respect a spanwise variation is evident, with the m i n i m u m value recorded being CD = 1.94 at Z = 5D. At 10 section depths from the centre, where the flow conditions are relatively undisturbed, the coefficient is 98% of that found at the corresponding position on the single bar (C,~ = 2.16 ). Cp
Single ---
1"01
-
-
Bar
Centre Line Z=IOD
Intersecting
Model
+ Z=IOD x Z = 5D o Z = 2.5D
0"5 Tapping
10-
6
11
10--
x x O 0 0 0 0
15 115
-15
o
~
o
÷-- + + ÷ +
Fig. 6. Circumferential pressure distributions at spanwise locations on a single a r m of the intersecting square-section bars.
37
Although the authors are not, at present, aware of any studies of the flow regimes at the surface of intersecting square bars available to corroborate these results, the discussion above has identified the main wind effects as being similar to those associated with intersecting circular cylinders. Having established this comparison, the remaining section of the paper considers the results obtained with the perpendicular members fixed one behind the other. 3.3. Circular members in contact The spanwise distributions of base pressure measured on the surface of each circular cylinder are shown in Fig. 7 (for the purpose of analysis, it is assumed that the value of Cpb at the precise point of contact between the two cylinders is zero). In the case of the upstream cylinder, at spanwise locations beyond the centre of the geometry the pressure decreases rapidly to a sharp peak in suction of Cpb = -- 1.26 at Y = 1.75D. This is followed by a 35% reduction in suction to Cpb = -0,82 at Y = 5D, which enhances the peak, and then a steady decrease in pressure spanwise towards Cpb values corresponding to those found on the single cylinder. The peak suction at Y = 1.75D is approximately coincident with that found at two diameters from the centre of the intersecting cylinders (Fig. 3), and is indicative of a similar flow regime, characterized by an inner region of highly disturbed conditions. The associated pressure gradient illustrates the presence of strong secondary flow away from the centre of the geometry towards the suction peak. Indeed, such a flow was identified in visualization experiments Cpb
-
1:I " -
• I ~ ' • ~
t
• Single Cylinder • Upstream Member • Downstream Member -0.8
-0.6 ¸
I
I
10
I
8
~
I
6
I
I
4
f
I
2
I
0
Fig. 7. Spanwise base pressure d i s t r i b u t i o n s on the perpendicular circular cylinders f o r m i n g a point of contact.
38 performed by Zdravkovich [7 ], which revealed the existence of two intense trailing vortices, one on either side of the base centre-line, generated from the upstream member near the point of contact of a similar configuration with a higher blockage ratio. The positions of the centres of these vortices were estimated by Zdravkovich [ 7 ], from surface pressure measurements in the region Y< 2D, to be at 0=90 ° at approximately one diameter from the point of contact, Y~ 1D. The circumferential pressure distributions recorded on the upstream cylinder at various spanwise locations are shown in Fig. 8. At the centre of the span the profile is similar to that recorded by Zdravkovich [ 7 ] and is therefore assumed to be associated with the formation of a small recirculation "bubble" adjacent to the rear surface of the cylinder. This feature was examined in detail by Zdravkovich [7 ] by oil film visualization of the surface flow pattern, which revealed a bubble with an arch-like structure in the spanwise direction. In the outer region beyond the highly disturbed conditions, the profiles in Fig. 8 reveal only small changes in the pressure distribution as a result of the weaker secondary fluid motion. The associated effects upon the local drag coefficient can be assessed from the values presented in Table 2, which exhibit a similar spanwise variation to that found on the intersecting cylinders (Table 1 ), i.e. a local minimum value of drag at Y= 5D, and a drag coefficient at 10 diameters from the point of contact, CD= 1.02, which is 9% less than that measured at the corresponding Cp 1"0
Single
Cylinder
Cp
----
Centre
Line
Upstream Member 0.5
+
Y=10D
x
Y=
o
Y = 2.5D
~, Y =
5D OD
-05
- 1.0
Fig. 8. Circumferential pressure distributions at spanwise locations on the upstream member of the perpendicular circular cylinders forming a point of contact.
39 TABLE 2 Local drag coefficients recorded on the circular cylinders fixed one behind the other Spanwise location
2.5D 5D 10D
Local drag coefficient, Co Upstream cylinder
Downstream cylinder
1.16 0.96 1.02
0.93 0.98 1.06
location on the single cylinder ( C D = 1.12). The degree of interference at the latter position is, therefore, greater than that found to be the case with the intersecting cylinders, where the drag at 10 diameters is reduced by only 4% of the corresponding single cylinder value. The spanwise distribution of base pressure recorded on the surface of the downstream cylinder is also shown in Fig. 7. Although initially this appears to have a profile similar to those already described on both the upstream cylinder and the intersecting cylinders, closer inspection reveals two significant differences. These are that the position of peak suction is closer to the centre of the span, at Z = 0.5D, and that the pressure gradient is considerably reduced in the region Z < 0.5D. These differences are associated with the existence of a different flow regime around the cylinder, the nature of which appears to be similar to that found in the work of Zdravkovich [7 ]. From his measurements of the mean pressure distribution on the downstream cylinder in the region Z < 1D, and surface flow visualization experiments, a horseshoe vortex flow pattern was deduced. This involved the generation of two such vortices, one from each side of the point of contact, which remain attached to the surface of the downstream cylinder as they converge in the wake. Consequently, the inner region of the disturbance to flow conditions is restricted to a shorter proportion of the span. At the centre of the span the disturbance has a considerable effect upon the circumferential pressure distribution recorded at the surface of the downstream member (Fig. 9). However, in the outer region the profiles suggest that the quasi-two-dimensional conditions associated with the single cylinder dominate the fluid motion. The spanwise variation of the local drag coefficient recorded on the downstream cylinder is shown in Table 2 and is fundamentally different from that already described in the outer regions of either the upstream cylinder or the intersecting cylinders. In the last two cases a local minimum value was recorded at Z = 5D, whereas in these measurements there is a steady increase in drag with distance from the node. The value recorded at 10 diameters, CD= 1.06, is evidence of the minimum disturbance to the flow around the cylinder at that
40
Cp 1.0~
Single Cylinder ..... Centre Line Downstream Member
0.5
+ Z= 1OD x Z:5D o Z:25D Z:OD . . . .
",~'
',~'
',~o'
',~o'
,%oo °
- 0.5
\
°\°°°°Oooooo
- 1-0
Fig. 9. Circumferentialpressure distributions at spanwlselocationson the downstreammember of the perpendicularcircularcylindersforminga point of contact. location, as it is only 5% lower than the corresponding single cylinder value (CD = 1.12). 3.4. Square members in contact The spanwise distribution of base pressure measured on the upstream member of the same perpendicular configuration composed of two square-section bars is shown in Fig. 10 (the pressure at the surface of contact is assumed to be zero ). In this case, the suction peak of Cpb = -- 1.3 at Y = 2D indicates the presence of secondary flows in the inner region which are similar to those already discussed with regard to the intersecting bars. However, the outer region appears to be considerably more disturbed than has been found in the previous cases, and this is also observed in the circumferential distributions of Fig. 11. These show that quasi-two-dimensional flow conditions are not as clearly discernible in the surface pressures as previously noted in the outer regions of the cylinder configurations and the intersecting square bars. However, despite the increased disturbance to the flow conditions, the local drag coefficients shown in Table 3 exhibit similar trends to those already identified in the results for the intersecting bars and cylinders. In this respect, the coefficients exhibit a spanwise variation, with the minimum value recorded being at Y = 5D. In addition, the drag at 10 section depths from the point of contact has a value of 96% of that found at the corresponding location on a single bar ( CD= 2.16).
41 Cpb
m~1_m 1~'m
-1,4
• Single '
Bar
• Upstream Member
- 1 , 2 -'
• Downstream Member
-1.O
i 10
i 8
I
I
I
I
6
i
T
4
i
2
i 0
Fig. 10. Spanwise base pressure distributions on the perpendicular square-section bars forming a plane of contact.
Cp
Single - --
1'01
Bar
Centre --
Line
Z---10D
Upst ream Member
0.5 Tapping
+
Z=IOD
x o
Z-- 5D Z= 2.5D
-1.0-
oOo
o XXxx~ ÷+÷+ o
11 10
15
oo
o
o
o
-1-5
Fig. 11. Circumferential pressure distributions at spanwise locations on the upstream member of the perpendicular square-section bars forming a plane of contact.
The spanwise distribution of base pressure recorded on the downstream square bar is also shown in Fig. 10. This is in complete contrast to the corresponding distribution obtained on the downstream circular cylinder (Fig. 7), and does not show the distinct peak of suction associated with the presence of the horseshoe vortices adjacent to the centre of the span. Instead, the pressure is constant at Cpb = -- 0.92 in the region Z < 1D, and is seen to decrease contin-
42 TABLE 3
Local drag coefficients recorded on the square-section bars fixed one behind the other Spanwise location
2.5D 5D 10D
Local drag coefficient, CD
Upstream bar
Downstream bar
2.07 1.94 2.07
1.89 2.02 2.20
Cp Single - -
1'01
--
Bar
Centre --
Downstream
0.5 Tapping
-1.011 10
15
o o o
°°°°° x x
Ix
•
÷
+
Z=10D
x o
Z= Z=
Member
5D 2"5D
t
1 5
o
Line
Z=lOD
÷~
~+
-1.5
F Fig. 12. Circumferential pressure distributions at spanwise locations on the downstream member of the perpendicular square-section bars forming a plane of contact.
uously spanwise to Cpb=- 1.43 at Z=8D (a result similar to that found by Donoso [8 ] on the downstream member of a pair of perpendicular flat plates). This difference can be attributed to a fundamental difference in the behaviour of the horseshoe vortices in the near wake of the bar. In this respect, Fox and Toy [14] have shown that the section geometry of the bar delays the convergence process until further downstream, and consequently the vortices are not evident as peak suction values in the base pressure distribution. The spanwise distribution does, however, indicate that a significant disturbance to the flow around the bar occurs over much of the span, and this is indeed the case, as can be deduced from the circumferential pressure distributions of Fig. 12. These show that at 2.5 section depths from the centre-line, the chordwise mean pressures decrease continuously towards the trailing edge, and the distribution on the rear face is almost constant, with no peak suction
43 at the base. At five section depths, the chordwise pressures are still significantly distorted, but the rear face pressures show a profile similar to that of a single bar. However, in the outer region, at 10 section depths from the centre, both the chordwise and rear face pressures have characteristics associated with quasi-two-dimensional conditions. Despite the greater disturbance to the pressure distributions, the local drag coefficients presented in Table 3 have a similar spanwise variation to those obtained on the downstream circular cylinder, with the minimum value recorded being that at Z = 2.5D. However, in this case the coefficient recorded at 10 section depths from the centre-line is 2% greater than the corresponding single bar value, and therefore reflects the increased interference effects associated with this geometry. 4. C o n c l u s i o n s
This paper has presented experimental results which characterize the interference effects in the nodal region of perpendicular intersections. In general, the wind-induced loading experienced by each member of an intersection is reduced, relative to that associated with a single element in uniform flow, within a spanwise region of 10 diameters or section depths from the centre of the geometry. However, the precise nature of the wind effects is dependent upon the section type, and whether the members intersect in a single plane, or are fixed one behind the other with a point of contact. The tests involving circular cylinders which intersect in a single plane have shown that the flow field associated with each arm of the configuration may be divided into two spanwise regions which are defined by the degree of interference caused by the intersection: ( 1 ) an outer region of quasi-two-dimensional conditions, and (2) inner region of highly disturbed flow which extends spanwise approximately two diameters from the centre of the geometry. A similar interference effect was determined on the surface of the intersecting square bars. Indeed, the spanwise locations and characteristics of the main features were found to correspond with those of the intersecting cylinders. However, in this case the pressure gradients in both the inner and outer regions were generally greater. When the cylinders were displaced in the direction of freestream flow, such that they formed a point of contact at the centre, the interference effects altered. In this respect the pressure distribution on the upstream cylinder exhibited similar characteristics to that found on an arm of the intersecting cylinders, whereas the nature of the disturbance in the inner region of the downstream cylinder changed. The pressure gradient from the centre of the geometry was reduced in comparison with the intersecting cylinders, and the
44
division between the inner and outer regions moved closer to the centre of the span. In the case of the square bars arranged in the plane of contact configuration, similar interference effects were determined on the upstream member. However, the nature of the disturbance to the downstream bar was found to be somewhat different, with significant interference effects extending over much of the span. These results can only be regarded as initial work, as there remains considerable scope for further investigation in this field, particularly with regard to the wind effects on other section types commonly used in structural engineering. Acknowledgement
This research was supported through an SERC studentship awarded to T.A. Fox. References 1 2 3 4
5
6 7 8 9 10 11 12 13 14
C. Scruton, An Introduction to Wind effects on Structures, Oxford University Press, Oxford, 1978. B.S. 2573, Rules for the design of cranes, Part 1: Specification for classification, stress calculation and design criteria for structures, British Standards Institution, London, 1983. B.S.I. CP3, Code of basic data for the design of buildings, Chapter V, Loading, Part 2: Wind loads, British Standards Institution, London, 1972. H. Osaka, I. Nakamura, H. Yamada, Y. Kuwata and Y. Kageyama, The structure of a turbulent wake behind a cruciform circular cylinder, 1st Report: the mean velocity field, Bull. Jap. Soc. Mech. Eng., 26 (1983) 356-363. H. Osaka, H. Yamada, I. Nakamura, Y. Kuwata and Y. Kageyama, The structure of a turbulent wake behind a cruciform circular cylinder, 2rid Report: the streamwise development of turbulent flow field, Bull. Jap. Soc. Mech. Eng., 26 ( 1983 ) 521-528. M.M. Zdravkovich, Flow around two intersecting cylinders, Trans. ASME, J. Fluids Eng., 107 (1985) 507-511. M.M. Zdravkovich, Interference between two circular cylinders forming a cross, J. Fluid Mech.. 128 (1983) 231-246. J.A. Donoso, Investigation of wake structure of isolated and intersecting fiat plates, M.Phil. Thesis, University of London, 1980. J.A. Donoso, R. Hillier and C.K. Yeung, The effect of strong three-dimensional disturbance on vortex shedding, J. Wind Eng. Ind. Aerodyn., 11 (1983) 381-392. E.S.D.U., Blockage corrections for bluff bodies in confined flows, Item No. 80024, Eng. Sci. Data Unit, London, 1980. N. Toy and T.A. Fox, The effect of aspect ratio of end plate separation upon base pressures recorded on a square bar, Exp. Fluids, 4 (1986) 266-268. E. Savory and N. Toy, Microcomputer control of wind tunnel instrumentation with on-line data acquisition and analysis, Software Microsyst., 3 (1984) 93-97. P.W. Bearman and D.M. Trueman, An investigationof the flow around rectangular cylinders, Aero. Quart., 23 (1972) 229-237. T.A. Fox and N. Toy, The generation of turbulence from displaced cross-members in uniform flow, Exp. Fluids, 6 (1988) 172-178.