An Experimental Investigation into Wind Effect on Tall Buildings with Pentagonal Cross Section

The effect of wind load is one of the very significant factors in building and structure design. An investigation has been carried out into the wind effect on a Pentagonal cross-section with an open circuit wind tunnel. The experiment was conducted at a constant flow velocity of 13.2 m/s and a Reynolds number of 4.22 x 104. The test was carried out on a single cylinder positioned facing across the flow direction at various angles of attack from 0° to 72° at a step of 9°. Each face of a pentagonal cylindrical model was divided into five tapping points and connected with inclined multi-manometers using copper capillary and plastic tubes to measure the surface static pressure on the cylinder surface. Pressure coefficients were calculated from the measured surface static pressure, which was then used to estimate the drag and lift coefficients. A significant drop of 0.52 in the drag coefficient values has been observed for the single pentagonal cylinder in comparison to that of the single square cylinder. The overall lift coefficient values of the single pentagonal cylinder are found to be lower than that of a single square cylinder except at 90. The fluctuation of the lift coefficient curve has a 90 phase shift than that of the square cylinder; however, the pattern of their variations has shown a similar trend except for the angle of attack of 00. The stagnation point was identified on the front face of the pentagonal cylinder. These findings will assist engineers and architects in designing much safer buildings.


Introduction
The tall building structures are significantly affected by the wind flow dynamics.Wind loads calculation is essential for designing any structure, structural member, or its component that capable of resisting wind force, and cladding against shear, sliding, overturning, and uplift actions.For very stiff building, the static loads should be taken into consideration, whereas the dynamic response of the structure can be neglected.The effect of static loading is usually taken into account for wind load calculation.However, due to modern tendency to build more slender and lighter structures in recent days, the study of dynamic response of the building has become essential.High wind velocity has unpleasant side effects on buildings, and in extreme cases, it can cause failure to the buildings and structures.The wind speeds in a particular locality are extremely variable; with steady wind at any time, the effects of gusts also present though lasts for a few seconds only.Since the inertia of the building is considerably high, no appreciable increase in the stress development may occur to the main components and building structure by the gusts.Though the response of a building to high wind pressure largely depends on the geographical location and proximity of other obstructions to airflow, the characteristics of the building structure yet has a significant influence on it [1].According to Castro [2], the flow behavior is predominantly defined by vortices developed in front of the building.In addition to this, the opening through buildings, wakes of buildings, spacing of rows, long straight streets, narrowing streets, corners, and courtyards are reported to have some measurable impact on the flow behavior too [3,4].Guo et al. [5] have conducted both the numerical and experimental analysis on a cube-shaped building.Zheng et al [6] have studied the wind effect on different types of square cylinders, which include square shapes with sharp corners, recession and chamfer at the corner, tapered cylinders, and Y-shaped cylinders.Nowadays, both studies with models and full-scale buildings are being performed to compare the results for validation.Due to the high cost of full-scale experiments, modelling simulation, and labscale experiments under various environmental conditions are used to predict the flow around the building.In this study, the variation in the pattern of wind imposed on a building caused by the influence of the nearby buildings has been investigated both experimentally and mathematically.

Materials and Methods
In this investigation, the static pressure distribution around a single pentagonal cylinder at various angles of attack has been measured, and the pressure distributions for different side dimensions of cylinders have been observed.The wind load from the static pressure distributions has been estimated, and a comparison among wind loads for various spacing and side dimensions of the pentagonal cylinders has been carried out.The experimental setup is shown in Figure 1.

Experimental setup
The test was conducted at the exit end of a subsonic open circuit wind tunnel with a maximum capacity of wind velocity of 14 m/s to find the wind load on the pentagonal cylinder.The tunnel was 5.93 meters long with a test section of 460 mm x 460 mm cross-section.A constant height of 990 mm from the floor has been maintained by the central longitudinal axis of the wind tunnel.The pentagonal cylinder model was placed in the wind tunnel such a way that the axis of the cylinder coincides with that of the wind tunnel.In order to ensure smooth entry of air into the tunnel, to maintain uniform flow inside the duct, and to protect the flow from outside disturbances, a converging bell mouth entry was incorporated in the wind tunnel.Two-stage rotating axial flow fans of capacity 18.16 m 3 /s at the head of 152.4 mm of water and 1475 rpm were used to produce induced flow through the wind tunnel.Each motor used in those fans were of 2.25 kW and 2900 rpm.To make the flow uniform a honeycomb was fixed near to the end of the wind tunnel.The flow was controlled with a butterfly valve actuated by a screw thread mechanism positioned behind the fan.For noise reduction, a honeycomb type silencer was fitted at the end of the flow-controlling section.The length of the diverging and converging section of the wind tunnel was 1550 mm, and 16 SWG black sheets was used for making this section.The possibility of flow separation was reduced by minimizing the expansion and contraction losses using the divergenceconvergence section of 7° angle in the wind tunnel arrangement.A 460 mm long pentagonal cylinder made of seasoned teak wood with equal face width of 50 mm was used as the model.Each faces of the cylinder model had five tapping points.The distance between the consecutive tapping points was equal (∆d) as shown in Figure 2. The location of the corner tapping was at a distance of ∆.For identifying each tapping point, a numerical number from 1 to 25 was assigned.
A certain gaps between those numbers were maintained in order to avoid difficulties with the manufacturing.This is considered not to have any effect on the experimental result, because the velocity was a two-dimensional flow.A steel plate was attached to the one end of the model cylinder for mounting with nut and bolt with the extended tunnel wall.The other side of the cylinder was hollow through which the plastic tubes were allowed to pass.One end of the plastic tubes were connected with the copper capillary tubes and the inclined multi-manometer was connected from the other end.The water was used as the manometer liquid.The tapping on the sides of the pentagonal model cylinder was made using the capillary tube.The tapping points were made of copper tubes of 1.71 mm outside diameter.The approximate length of each tapping was of 10mm long.Flexible plastic tube of 1.70 mm inner diameter was press fitted from the end of the copper tube.The pentagonal cylinder model was installed in an integrated section of the wind tunnel in such a way that the axes of the wind tunnel and the model cylinder remained at the same level.The cross sectional area of the exit end of the wind tunnel and that of the extended part was same.The extended section was open from the top and bottom, and was 460 mm x 400 mm in dimension.The cylinder was carefully levelled and set in the test section so that its top and bottom sides were parallel to the flow direction.
The test cylinder was installed in such a way that it can be rotated to various angles to obtain the wind load at different angles of attack.No correction for blockage was done in the analysis as the top and bottom of the extended part of the wind tunnel were open.Since the test cylinders were placed very close to the end of the wind tunnel, the approach velocity on the test cylinder was approximately same to that at the exit end of the wind tunnel.
The room temperature was assumed remaining constant during the measurement of the surface static pressures on the cylinder surface.Therefore, the density of the air was considered unchanged and the minor fluctuations in the temperature were neglected in the calculation.The variation of the manometer reading on the suction side of the cylinder was found to be insignificant.Since the mean value of the manometer reading was taken, the error caused by that trivial fluctuation was neglected.

Test Procedure
The test was carried out on a pentagonal single-cylinder model.The surface static pressures at different locations of the cylinder were measured using an inclined multi-manometer.The inclination of the manometer was adequate to record the pressure with reasonable accuracy.It was ensured carefully that no air bubble deposition occurs anywhere in the limb during taking the manometer reading.static pressure distributions on five faces of the cylinder were measured for each position/ angle of attack starting from 0 0 to 72 0 with an interval of 9 0 .

Pressure Coefficient Estimation:
The pressure coefficients were obtained from the measured surface static pressure on the pentagonal cylinder.From the pressure coefficients, the drag and lift coefficients were estimated using numerical integration method.The pressure coefficient was calculated using the following Equation 1.
Where, ∆P = P -P0, P is the static pressure on the surface of the cylinder, P0 is the ambient pressure,  is the density of the air, U∞ is the free stream velocity, ∆ was obtained from the Equation 2 below: Where, ∆  is the suction head of the anometer limb,   is the specific weight of manometer liquid (water).
Therefore, from Equation 1, the pressure coefficient can be written as Now putting     × , in the above equation Where, density of water   =1000kg/m 3 and density of air  =1.22kg/m 3 , Therefore, it can be written as Where, ∆  is in meter of water height, However, ∆ is usually in mm of water height and  ∞ is in m/s.In this case, one can write the above expression as The velocity of air in the wind tunnel may be written as Where,   is the air head.If   is the specific weight of air, then the relationship would be like this     =     Therefore, the airhead can be written as Now inserting   =  /  and   = ./  , the above equation becomes From equations ( 5) and ( 6), the expression of velocity can be written as Where,   is in meter of water head.
After changing the   in mm of water head, air velocity in the wind tunnel becomes like The free stream velocity in the wind tunnel was obtained using Equation 7, which was then crosschecked with the help of a digital anemometer.For   10.85 mm of water head, the free stream velocity has been calculated from Equation 8, that was  ∞ = ./.
For a suction head of ∆  = . mm of water and  ∞ = . m/s, the pressure coefficient   can be found from the equation ( 4), which is   = 0.75.

Drag and Lift Coefficients Estimation
From Figure 3b, the cylinder has five faces S1, S2, S3, S4, and S5, and the pressure at the various tapping points along the face S1 are P1, P2, P3, P4 and P5 at tapping points of 1, 2, 3, 4, and 5 respectively.F1, F2, F3, F4, F5 correspondingly indicate the forces along the face S1, S2, S3, S4 and S5.These forces can be calculated using the Simpson ' s rule as follows: If the length of the cylinder is chosen as unity, then the above expression becomes, If the component of the force    occurs along the flow direction, then the expression of F can be stated as Similarly, the force component subscriptit    in a direction perpendicular to the flow may be written as, The net force   along the faces S2 can be obtained in the same way as above and that is Therefore, the components of the drag and lift forces along the face S2 are respectively The net force   along the face S3 can be obtained in the same way as above and that is Therefore, the components of the drag and lift forces along the face S3 are respectively The net force F along the face S4 can be obtained in the same way as above and that is Therefore, the components of the drag and lift forces along the face S4 are respectively The net force F along the face S4 can be obtained in the same way as above and that is Therefore, the components of the drag and lift forces along the face S5 are respectively 5 = − 5 (90 0 − ) Drag and lift coefficients are defined as follows and The total drag force along the flow direction is and total lift force in a direction perpendicular to flow is From equations ( 25) and ( 27), the expression of drag coefficient becomes Substituting the values of    ,    ,    ,        obtained from the equations ( 11), ( 14 where, A is the frontal projected area of the cylinder.Now putting the values of F1, F2, F3, F4 and F5 found from the equations ( 10), ( 13), ( 16), ( 19) and ( 22) into the equation ( 30), expressing the equation with pressure coefficients and using 12P0 = 0,   can be obtained as The distribution of pressure coefficient, drag and lift coefficients for different angles of attack have been estimated based on measured surface static pressure values, and using the above calculation method and equations.The obtained data has been plotted into a graph for further analysis.

Experimental Results and Discussions
The distributions of static pressure coefficients, and drag and lift coefficients for various angles of attack have been analysed to extract significant information out of the data.A comparative study has also been carried out among the data recorded for different angles of attack and those from the existing research works under similar environmental conditions.IOP Publishing doi:10.1088/1757-899X/1305/1/0120349

Distribution of Pressure Coefficients
The distributions of static pressure coefficients, CP at different angles of attack have been plotted into a graph to show the relative comparison among them.The CP distribution for various angles of attack from 0 0 to 72 0 is presented in Figure 4. From Figure 4, a common trend has been observed among the CP values at different surfaces under various angles of attack; CP values were considerably high at surfaces S1 and S5 for entire tested angles of attack except for some particular tapping points.However, the CP values remain reasonably low and uniform at surfaces S3 and S4 regardless of the angle of attack.The high CP value at the S1 and S5 surface can be attributed to the fact that the velocity of the air decreases because of the obstacle caused by the cylindrical model when the major portion of the kinetic energy is converted into potential energy; on the other hand, and the low CP value at the surface S3 and S4 was due to the minimally interrupted and comparatively higher air velocity flowing around the cylindrical model.The fluctuation of CP values at various angles of attack on surface S2 was found to be mixed in nature.The distribution of pressure coefficient around the pentagonal cylinder has been seen to remain positive at all five surfaces for the entire angle of attacks from 0 0 to 72 0 except for the angle of attack of 90 and 180 at which some negative pressure coefficient values have been observed at some particular tapping points of the surface S2 and S5.The maximum overall fluctuation of the CP values at all five surfaces of the pentagonal-type cylindrical model is 4.15 for entire tested angles of attack, which is reasonably lower than a typical square-type cylindrical model tested under similar environmental conditions [7].From the figure, it has been further noticed that there is no stagnation point except on tapping point 7 of surface S2 at zero angle of attack.It was because the location at the stagnation point had not been selected for the tapping.Moreover, it has been seen that the pressure coefficient values at surface S1 were comparatively high at a low angle of attack, which gradually decreased with the increase of the angle of attack.An opposite scenario has been observed for the CP values at surface S5.However, the CP values at both the S1 and S5 surfaces were significantly higher than those at any other three surfaces.It was due to vortex formation at the rear surface of the model led to an increase of pressure around the rear surfaces.The pressure developed on the back surface depends on the distance of the vortices.The longer the distance of the vortices from the body, the higher is the back pressure and vice versa.Similar results have been reported  in a study carried out by Guo et al. [5].With the increase of the angle of attack, the path of the shear layers was altered from their point of origin at the front corners of the cylindrical model to the vortex formation region.Lee [8] and Nakamura [9] have made a similar observation based on the results obtained from their investigations.In the absence of turbulence in the incident flow, the shear layers that originate at the front corners of the cylinder curve outward and form the familiar vortex street in the wake close behind the body.Davis [10] and Nakamura [11] have seen a similar behavior in the fluid flow while experimented with a rectangular cylindrical model.An uncertainty analysis has been carried out with the experimental data, where 1.12% uncertainty has been observed in the recorded data.

Variation of Drag Coefficient
Variation of drag coefficient at various angles of attack on the single pentagonal cylinder is shown in Figure 5.The fluctuation of the drag coefficient at the same angles of attack on a single square cylinder under similar flow conditions obtained by Mandal [7] is also presented in this figure for comparison.It can be noticed from this figure that there is a significant drop in the drag coefficient values for the pentagonal cylinder in comparison to that of the square cylinder, and the CD values drop even lower for the hexagonal-shaped cylindrical model.It is seen from this figure at zero angle of attack, the drag coefficient is about 1.48 and at all other angles of attack, the values are close to 1.55 except at angle of attack of 9° and 18 0 , where the value is about 1.30 and 1.22 respectively.The deviation of the average drag coefficient, CD from that of the mathematically calculated value is not more than 4%, which is considerably low.The values of the drag coefficient at various angles of attack for the pentagonal cylinder can be explained from the CP distribution curves.Experimental data shows that the CD values of the pentagonal cylinder model are considerably lower than that of the square cylinder model, which is favourable for designing a tall building/skyscraper.These results can be supported by the findings obtained by Vickery [12] and Zhang et al. [6].

Variation of Lift Coefficient
The fluctuation of lift coefficient at various angles of attack on the single pentagonal cylinder is shown in Figure 6.The lift coefficient for some same angles of attack on a square cylinder at uniform flow obtained by Mandal [7] is also presented in this figure for comparison.From the above figure, it can be observed that the pattern of the lift coefficient fluctuation on the single pentagonal cylinder and single square cylinder are similar except for the angle of attack of 0 0 .The CL curve of the pentagonal cylindrical model has a phase shift to some 9 0 than that of the square cylinder.However, the trend of alteration of the CL values obtained for the pentagonal cylinder has maintained a steadier pattern than that of a square cylinder.Similar to the CD curves analysis, the fluctuation of the lift coefficient values for the single pentagonal cylinder can be described using the CP distribution curves.Observation shows that though the CL value curve of the square cylinder model has got the lowest point between 9 0 and 18 0 on the graph, the overall CL curve obtained for the pentagonal cylinder model remained lower than that of the cylinder for the entire tested angles of attack, which is considered favourable for designing a free-standing tall building/skyscraper.A similar observation has been made by Vickery [12] based on his investigation findings.Therefore, from the perspective of wind loading effect on the building, it can be deduced that the more round the shape of the building is, the less CD and CL values are; and that type of wind loading condition would be more favourable for designing a safer building.

Conclusions
Pentagonal cylinder-shaped building would have lower drag and lift coefficient than square cylindrical building under different wind loading conditions.There was a significant drop in the drag coefficient values for the single pentagonal cylinder in comparison to that of the single square cylinder.The drag coefficient for a single pentagonal cylinder at zero angle of attack was about 1.48 in contrast to that of 2.0 for a single square cylinder at the same angle of attack.The overall CL curve of the pentagonal cylinder model has remained lower than that of the square cylinder for the entire tested angles of attack but for 9 0 .The pattern of CL value fluctuation for the single pentagonal cylinder was quite similar to the variation of lift coefficient for the single square cylinder except at the angle of attack of 0 0 .However, a 9 0 phase shift of the CL graph of the pentagonal cylinder from that of the square cylinder was found.The stagnation point was identified on the front face of the single pentagonal cylinder.These finding would be useful to the structural engineers when designing a free-standing building having a pentagonal crosssection with wind load consideration.

Figure 1 .
Figure 1.Experimental setup a) schematic diagram of the wind tunnel, b) real image of the wind tunnel test section, and c) model position in the wind tunnel.

Figure 2 .
Figure 2 .a) Tapping positions on a cross -section b) Tapping positions on longitudinal section.

Figure 3 .
Figure 3. a) Velocity distribution at the upstream side and b) forces on different faces of the pentagonal cylinder model at an angle of attack.Across the flow direction, the Reynolds number was calculated based on the projected width of 50 mm of the cylinder.The Reynold number value obtained from the calculation was 4.22×104.The surface ), (17), (20) and (23) respectively, the expression of drag coefficient becomes   =  1 ( 18 0 −)− 2  ( 126 0 −)− 3 ( 54 0 −)+ 4 ( 162 0 −)+ 5 ( 90 0 −) and putting the values of surface static pressure coefficient in equation (31), the drag coefficient becomes   = . For similar consideration, putting the values of surface static pressure coefficient in equation (32), the lift coefficient becomes

Figure 4 .
Figure 4. Distribution of pressure coefficient at different angles of attack on the pentagonal cylinder.

Figure 5 .
Figure 5. Variation of Drag Coefficient at different angles of attack on a Single cylindrical model.

11 Figure 6 .
Figure 6.Variation of Lift Coefficient at different angles of attack on a single cylindrical model.