FLUCTUATING WIND VELOCITY CHARACTERISTICS OF THE WAKE OF A CONICAL HILL THAT CAUSE LARGE HORIZONTAL RESPONSE OF A CANTILEVER MODEL

Transcription

1 BBAA VI International Colloqim on: Blff Bodies Aerodynamics & Applications Milano, Italy, Jly, FLUCTUATING WIND VELOCITY CHARACTERISTICS OF THE WAKE OF A CONICAL HILL THAT CAUSE LARGE HORIZONTAL RESPONSE OF A CANTILEVER MODEL Kichiro Kimra, Knihiro Toyoda, Kazya Takakra, Kso Kato and Yoshinob Kbo Department of Ciil Engineering Kysh Institte of Technology, Sensi-cho, Tobata-k, Kitakysh-shi, , Fkoka Japan kimra@ciil.kytech.ac.jp Hitachi Zosen Steel Strctres Corporation (A gradate stdent at Kysh Institte of Technology at the time of this stdy) Keywords: Bffeting, Complex Terrain, Conditional Sampling, Wind Tnnel Test Abstract. As a first step to clarify the bridge response characteristics in complex terrain, the flow strctre in the wake of a conical hill that cases large horizontal response of a horizontally spported cantileer model was stdied. Flctating elocities of -, -, w- components were measred with split film probes, and they were conditionally sampled based on the large horizontal response of the cantileer model. A clear flow strctre with elocity toward downward and inward that acted arond the tip location of the cantileer model was obsered and it was thoght to case the large response. The flow strctre seemed to deelop as a downward flow and change its direction horizontally near the grond, and then intensify its magnitde in horizontal elocity components. The front line of the strctre was skewed abot 4 degrees from normal to the mean flow direction. 1

2 1 INTRODUCTION Effects of complex terrain hae to be careflly considered for the resistant design of long span bridges. In some cases, large along- responses were obsered when the bridge is located in the wake of a hill, which cannot be explained by the conentional bffeting theory [1]. As a step to clarify the case of sch large responses, flctating elocity characteristics acting on a simplified bridge model in the wake of a conical hill were stdied. Similar stdy has been presented by the athors [2] before, bt the data presented in this paper were taken after the stdy for Ref. [2], and somewhat different characteristics were fond and they are mainly discssed here. 2 EXPERIMENTAL SETUP The size of the models was determined so that they corresponds to 1/1333 of the Tatara Bridge case [1]. A simplified conical hill model with height H of 3cm and diameter 2R of 135cm was sed. The bridge model was a rigid sqare cylinder made of wood with width and height of 2.cm and length L of 3cm. It was cantileer-spported horizontally at the height of 3.7cm with a steel plate to be allowed 1DOF along- response. The natral freqency and damping ratio of the model were 7.3Hz and 7.5%. The strctral damping was relatiely large, becase the cantileer model was eqipped with pressre taps and tbes so that the flctating pressre on the model cold be measred simltaneosly with the response and flctating elocity measrements. Althogh the response, flctating elocities, and flctating pressres were measred simltaneosly, only the reslts from the response and flctating elocities are mainly discssed in this paper. An Eiffel type bondary layer tnnel at Kysh Institte of Technology with the test section of width, height and length of 2.4m, 1.8m and 2m was sed. No trblence generating deice was sed bt the bondary layer that can be approximated with power law coefficient of.16 and thickness of 6cm was generated at the hill model location. The bridge model free end was set at the location of x/r=1.48 and y/r=.15, where the origin of the coordinate was taken at the center of the hill model and the height of the bridge model axis with x-coordinate defined toward leeward, z pward and y with the right-handed coordinate system. The yaw angle β of the model was set as 4 from normal to the model axis, so that the bridge model free end pointed toward ward and center of the hill model direction (Fig. (1)). Those conditions were set based on the preios measrements with which large bridge model responses were obsered. The simltaneosly measred bridge model response amplitde and flctating elocities were stored with sampling freqency and time of 1Hz and 5 mintes, respectiely. The measrement was repeated twice, so that the total sampling time was 1 mintes. The approaching gradient speed U was chosen to be 4., 6. and 8. m/s. The flctating elocities were measred by split film probes and hot wire anemometry. By sing different types of split film probes,,, and w-components of the flctating elocity were measred. The measrements were taken at 4cm ward of the model ward srface at the locations as shown in Fig. (2). The axis y was defined at the location of the elocity measrement from the free end location toward the spport direction. The measrement was taken at 6 locations between y /L= and.67. The measrement height was at 11 locations between = and.67 for U=6. m/s. For the cases with U=4. and 8. m/s, measrements were taken at 8 location heights between = and.47. The total nmbers of the measrement locations were 66 for U=6. m/s case and 48 for U=4. and 8. m/s cases. Note that the elocity measrement location is also skewed by 4 as the cantileer model. 2

3 y/r.15 R 1.48 x/r β=4 Figre 1: Model location and definition of axes..67 total nmber of el. measrement location: 66 interal:.67 free end 4(cm) spport end z (w-comp.) y (-comp.) x (-comp.) interal: y /L Figre 2: Wind elocity measrement location (U=6.m/s). With U=4., 6. and 8. m/s, the mean speed at the cantileer model height and spanwise location of y /L=. (and.13) were 1.61 (1.84), 2.4 (2.5), and 3.3 (3.5) m/s, respectiely. Assming that the 1st natral freqency of the along- mode of the prototype bridge nder constrction as.5 Hz, the fll scale mean speeds at the deck height corresponding to U=4., 6. and 8. m/s are 14.7 (16.8), 22 (23), 3 (32) m/s, respectiely. In order to clarify the flctating elocity characteristics that case large horizontal responses, the flctating elocity components were conditionally sampled based on the occrrence of the large response peak. The large response peak was defined in this stdy as that with the leeward amplitde of more than 2.5 times of the standard deiation. The nmbers of the conditionally sampled data were (U=4. m/s), (U=6. m/s), and (U=8. m/s) in total 1 mintes data. The nmber of the sampled data considerably differs among the same speed cases. The nmber is particlarly small with U=8. m/s, bt it was confirmed that the krtosis and non-dimensionalized power spectrm of the response with U=8. m/s were not so mch different from other speed cases. The scatter of the nmbers of the conditionally sampled data was probably de to its sensitieness of slight difference of the response time history characteristics. 3

4 3 EXPERIMENTAL RESULTS The characteristics of flctating elocities after conditional sampling are shown in the following. In all the figres, the origin of the horizontal coordinate corresponds to the instant when the large leeward response peak occrred. 3.1 Time history of the flctating elocities In most of the cases, large elocity flctations were obsered at a short time (.5-.15sec) before the response peak occrrence (t=). These flctations are thoght to case the large response of the bridge model. In the cases with U=6. and 8. m/s, the elocity flctation peaks occrred almost simltaneosly at different y /L locations along the bridge model axis at the bridge model height (z=), as shown in Figs. (3a), (4a) and (5a) as examples. Becase the model was located with yaw angle β=4, this means that the front line of the flow strctre that cased the large response had the same skew angle at the model height. The similar obserations were obtained in preios stdies by the athors [2]. At higher locations (Fig. (3b), (4b) and (5b) as examples), on the other hand, the elocity flctation peaks occrred from the model tip location (y /L=.) to the spport (y /L=.67). y'/l=. y'/l=.13 y'/l=.27 y'/l=.4 y'/l=.53 y'/l=.67 y'/l=. y'/l=.13 y'/l=.27 y'/l=.4 y'/l=.53 y'/l=.67 time(1-3 s) time(1-3 s) (a) =. (b) =.67 Figre 3: Time history of flctating elocity (-component, U=6.m/s). y'/l=. y'/l=.13 y'/l=.27 y'/l=.4 y'/l=.53 y'/l=.67 y'/l=. y'/l=.13 y'/l=.27 y'/l=.4 y'/l=.53 y'/l=.67 time(1-3 s) time(1-3 s) (a) =. (b) =.67 Figre 4: Time history of flctating elocity (-component, U=6.m/s). 4

5 y'/l=. y'/l=.13 y'/l=.27 y'/l=.4 y'/l=.53 y'/l=.67 y'/l=. y'/l=.13 y'/l=.27 y'/l=.4 y'/l=.53 y'/l=.67 time(1-3 s) time(1-3 s) (a) =. (b) =.67 Figre 5: Time history of flctating elocity (w-component, U=6.m/s). This means that the flow strctre was less skewed at higher locations, and it can be nderstood becase the flow is less affected by the hill at higher locations. In Figs. (3)-(5), periodic flctations are obsered in negatie t region, i.e., before large horizontal response of the cantileer model occrred. The period corresponds to the natral period of the cantileer model, and the flctation is thoght to be cased by the conditional sampling based on the large response [4]. 3.2 Possible flow strctre casing large horizontal response A trial was made to isalize the flow strctre that cases the large horizontal responses by drawing the flctating elocity ectors (Figs. (6)-(8)), where the horizontal coordinate is redced x-coordinate. Redced x-coordinate is defined as the length that can be calclated by mltiplying the time, aerage of at the measrement location, and 1. This procedre is similar to the Taylor s frozen trblence approximation. Howeer, becase the flow in the wake of the hill model is not stationary, the approximation cannot be applied. Instead, it has to be nderstood that Figs. (6)-(8) expresses the flow strctre when it passed the elocity measrement location and it is placed side by side so that the oerall characteristics can be caght more clearly. In order to clearly show the flctating elocity strctre, the flctating component was sed to draw the elocity ectors for the stream-wise component of the elocity. At = and y /L= location near the cantileer model free end, a clear flow strctre can be seen with mch larger magnitde that acted on the model jst before the occrrence of large response (Figs. (6a), (7a) and (8a)). The strctre had the downward (mins z-direction) and inward (pls y-direction in Fig. (1)) components. At higher locations, weaker bt similar strctre that acted a little earlier can be obsered, and it probably shows that this flow strctre deeloped from pward to downward. This downward flow strctre probably intensified its elocity in horizontal, - and -components when the flow hit the grond and changed its direction to horizontal. At other y /L locations far from the cantileer model free end, similar strctre was seen, bt its magnitde became smaller. Therefore, this flow strctre which mainly acted arond the free end of the model seems to effectiely generate large response of the cantileer model. In a preios stdy by the athors [2], the flow strctre that cased the large horizontal response of the cantileer model was identified as somewhat pward flow, bt there were 5

6 w 6m/s, 6.m/s, y /L=., -(w +W) -w comp. comp. 1.m/s 1.m/s (a) y /L=. 6m/s, 6.m/s, y /L=.67, -(w +W) -w comp. comp. w 1.m/s 1.m/s (b) y /L=.67 Figre 6: Flctating elocity ectors after conditional sampling, -w-component, U=6.m/s. mistakes in the data processing procedre. The flow strctre discssed in this stdy was also confirmed with other set of experimental data where the elocity was measred with x- probes. In another preios stdy by the athors [3], it was pointed ot that the large horizontal responses of the cantileer model were cased by the flctating pressre pattern of POD 1st mode. Therefore it wold be more reasonable to catch the flow strctre sing a conditional sampling based on the occrrence of large POD 1st modal coordinate. Sch discssion is also gien elsewhere [4]. 4 CONCLUDING REMARKS As a step to nderstand the effects of complex terrain to the -indced response of long-span strctres, tnnel stdies were condcted. Flctating elocities in the wake of a conical hill were measred and conditionally sampled based on the large response of a cantileer model. Conditionally sampled elocity components were analyzed and a possible flow strctre that cased large horizontal response of the cantileer model was discssed. 6

7 6m/s, 6.m/s, =., -( +V) - comp. comp y /L (a) =. 6m/s, 6.m/s, =.2, -( +V) - comp y /L (b) =.2, U=6.m/s 6m/s, 6.m/s, =.6, -( +V) - comp y /L (c) =.67 Figre 7: Flctating elocity ectors after conditional sampling, --component, U=6.m/s. REFERENCES [1] H. Akiyama, R. Torimi and Y. Ohtani. Large scale tnnel test of the Tatara bridge (2nd. report) gst response in complicate topography, Honshi Technical Report 21, pp. 3-36, 1997 (in Japanese). 7

8 6.m/s, 6m/s, y /L=., -w comp. w 1.8m/s 1.8m/s (a) y /L=. 6.m/s, 6m/s, y /L=.67, -w comp. w 1.8m/s 1.8m/s (b) y /L=.67 Figre 8: Flctating elocity ectors after conditional sampling, -w-component, U=6.m/s. [2] K. Kimra, E. Harada, K. Takakra, Y. Kbo and K. Kato. Flctating elocity and pressre characteristics of the flow in the wake of a conical hill casing large horizontal response of a bridge model. Proceedings of the CWE26, Tokyo, pp , 26. [3] K. Kimra, K. Takakra, Y. Kbo and K. Kato. Flctating pressre characteristics on a cantileer model in the wake of a conical hill that case large horizontal response. Proceedings of 12th International Conference on Wind Engineering, Cairns, Astralia, pp , 27. [4] K.Kimra, K. Takakra, K. Toyoda, K. Kato and Y. Kbo. Flctating elocity strctre that case large horizontal response of a cantileer model in the wake of a hill. Proceedings of 2th National Symposim on Wind Engineering, sbmitted, 28 (in Japanese). 8