1 JAXA Special Pblication JAXA-SP-1-E Small-scale trblence affects flow fields arond a blff body and therefore it governs characteristics of cross-sec

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1 First International Symposim on Fltter and its Application, 1 11 IEXPERIMENTAL STUDY ON TURBULENCE PARTIAL SIMULATION FOR BLUFF BODY Hiroshi Katschi +1 and Hitoshi Yamada + +1 Yokohama National University, Yokohama, Japan + Yokohama National University, Yokohama, Japan Wind-indced response/vibration of a bridge deck is governed by the srronding flow field inclding flow separation and reattachment. It was also pointed ot that the flow field is strongly affected by a small-scale trblence component in an approaching flow. In wind-tnnel testing, in order to simlate trblence effects, trblence intensity is sally simlated. However the simlation of the power spectral density (PSD) of a small-scale trblence component (high-freqency sb-inertia range), the so-called trblence partial simlation may be a more rational way. In fact, past stdies sggested that the trblence partial simlation cold give a better explanation for bridge deck vortex-indced vibration response between fll scale and wind-tnnel test. In this stdy, sing redced trblence intensity, the trblence partial simlation was experimentally investigated for blff-body strctres. Reslts showed that redced trblence intensity cold represent trblence effects to the same degree as cold trblence intensity do. In addition, it was observed that a small-scale trblence component governed the flow field arond a blff body. Keyword: trblence partial simlation, blff body, small-scale trblence, wind-tnnel test 1. INTRODUCTION Wind-indced response/vibration of a bridge deck is governed by the srronding flow field inclding flow separation and reattachment. It was also pointed ot that the flow field is strongly affected by a small-scale trblence component in an approaching flow 1). In wind-tnnel testing, in order to simlate trblence effects, simlation of trblence intensity is practically adopted. However the simlation of the power spectral density (PSD) of a small-scale trblence component (high-freqency sb-inertia range), the so-called trblence partial simlation may be a more rational way. In fact, Irwin et al. sggested that the trblence partial simlation cold give a better explanation for bridge deck vortex-indced vibration response between fll scale and wind-tnnel test, 3, ). In this stdy, sing redced trblence intensity, the trblence partial simlation was experimentally investigated for blff-body strctres. For that prpose, more than 1 different trblent flows with different intensity and integral scale were generated by grids. Then wind-tnnel tests were condcted for the following items. Measrement reslts were examined in terms of trblence intensity, integral scale and redced trblence intensity. 1) Base pressre of rectanglar cylinder (B/D =..9) ) Srface pressre and static coefficient of bridge deck (B/D = 5 and 7.5) 3) Srface pressre and PIV test of rectanglar cylinder (B/D = and 3) where B/D is slenderness ratio of blff bodies.. TURBULENCE PARTIAL SIMULATION Trblence flow can be perfectly simlated in a wind tnnel if its PSD is simlated over all freqency range. However, de particlarly to the wind-tnnel size, the trblence scale generated in a wind tnnel is sally mch smaller than that of fll-scale trblence. Therefore, it is very difficlt to simlate the low-freqency part of that (large-scale trblence) in a wind tnnel. +1 katschi@yn.ac.jp, + y-yamada@yn.ac.jp

2 1 JAXA Special Pblication JAXA-SP-1-E Small-scale trblence affects flow fields arond a blff body and therefore it governs characteristics of cross-sectional aerodynamics. On the other hand, large-scale trblence will decrease span-wise correlation and change mean wind speed, which will decrease the amplitde and probability of wind-indced vibration. Disregard of large-scale trblence effects will therefore be practically conservative. Considering these, one can sggest that the simlation of PSD in a high-freqency part might give a good explanation of the fll-scale behavior in a wind-tnnel test. Assming the Karman-type PSD fnction (Eq. 1) and considering the simlation of a high-freqency part of it, Eq. 1 is transformed to Eq.. fs fs U f L 1 7. f L I f U x x / 3 U U x / 3 L where f is freqency, U is wind speed, I is trblence intensity and L x is trblence scale. Qantity f/u has an inverse dimension of length, then replacing f/u by 1/D (D: representative length) transforms Eq. to Eq. 3. Therefore, simlating or eqating a redced PSD yields a similarity law as in Eq.. fs U 1 / 3 x L D I x I / L D m m () x I / p L D p where sbscripts m and p represent model and prototype (fll scale), respectively. From Eq., if a trblence scale ratio to the strctral dimension in a wind tnnel (L x /D) m is by one order smaller than that in the fll scale, the similarity reqirement for the trblence intensity in the wind tnnel will be abot half of that in the fll scale, as shown in Fig. 1. This trblence similarity reqirement (referred to trblence partial simlation) was sggested by Irwin, ) and pointed ot that the fll-scale measrement by Macdonald et al. 3) might prove this. Based on Eq., a new similarity parameter redced trblence intensity calclated by trblence intensity divided by the cbic root of the trblence scale ratio (L x /D) is introdced as shown in Eq. 5. It is nderstood that the similitde of redced trblence intensity represents the trblence partial simlation. x L D / I I r (5) (1) () (3) Figre 1: Trblence partial simlation )

3 First International Symposim on Fltter and its Application, BASE PRESSURE OF RECTANGULAR CYLINDER 5) (1) Base pressre coefficient Wind-indced response of a blff body is governed by the flow field arond the body and it was thoght that base pressre rather than the response wold be sensitive to the change of the flow field and that base pressre coefficient wold be a good indicator to jdge whether the partial simlation is satisfied or not. Base pressre was compared nder varios combinations of trblence properties (intensity and scale). Table 1 shows the trblence properties generated and Fig. shows their PSD. Three different size of a rectanglar cylinder (projection height D = 3, and 9 cm) was sed in order to cover the wide range of the trblence scale ratio to the model size. Of those combinations with the different trblences and model sizes in Table 1, two series of combinations were chosen to investigate the small-scale trblence simlation. First series are different trblence-intensity flows, PSDs of which do not coincide with each other as shown in Fig. (a). Second series are trblence flows with the same PSD in a high-freqency part as shown in Fig. (b). After all, comparisons were made in model cases of D = 9cm as shown in Table 1. The base pressre was measred at a 1Hz sampling freqency for 3 seconds. The Reynolds nmber at the measrement was approximately 3.71 with respect to the model height D. In order to correct the wind-tnnel blockage effect, correction factors were obtained from the base-pressre measrement reslts of the different model size at each B/D ratio based on Ref. ). For the sake of brevity, the base-pressre coefficient represents the corrected one hereinafter. Trblence intensity I (%) Table 1: Properties of trblence generated Trblence scale L x (cm) Ratio of trblence scale and model scale (L x / D) D = 3cm D = cm D = 9cm <1> <> <3> <> <5> <> <7> Smooth * The nmber in < > is referred to in Fig E- 1.E-3 1.E-1 1.E- <3> I =.7%, Lx/D =. <> I = 9.%, Lx/D = 1.7 <5> I = 9.%, Lx/D =.3 <7> I =13.5%, Lx/D = 1.59 <5> fs /U 1.E- 1.E-5 1.E- <1> I = 3.7%, Lx/D = 1.1 <> I =.9%, Lx/D = 1. <3> I =.7%, Lx/D =. <5> I = 9.%, Lx/D =.3 <3> <> <1> fd /U fs /U 1.E-3 1.E- 1.E-5 <7> <> <5> <3> fd /U (a) Different trblence intensity series (b) Small-scale trblence simlation series Figre : Power spectral density of wind-tnnel trblence

4 1 JAXA Special Pblication JAXA-SP-1-E Fig. 3 shows the comparisons of C pb in trblent flows with different trblence intensities bt close trblence scale together with that in a smooth flow. Negative peak of C pb at arond 5.5 of B/D can be seen as pointed ot by past stdies 7, ). It can be seen that C pb for B/D less than the critical vale is not so mch different bt that C pb at and larger than the critical vale becomes large (to positive vale) as the trblence intensity becomes large. This may reslt from the enhancement of interaction of shear layers with small eddies arond the cylinder by the increase of trblence intensity. In addition, the critical slenderness ratio of B/D moves to lower B/D as the trblence intensity increases. Fig. shows the comparisons of C pb for partially simlated trblences. As shown in Fig. (b), trblences <3> and <>, and <5> and <7> are pairs of trblences with PSD simlated in a high-freqency part. These two pairs hold the relationship of Eq.. It can be seen that C pb at and larger than the critical slenderness ration of B/D is almost identical for the partially simlated trblences. This fact proves that flow patterns arond a rectanglar cylinder can be simlated if trblence is simlated in a high-freqency part, in other word, the trblence partial simlation can be achieved. However C pb in Figs. 3 and covers B/D ranging from. to.9 which is mch smaller than a typical vale of a bridge deck (B/D > 3). Base-pressre coefficient <1> I = 3.7%, Lx/D = 1.1 <> I =.9%, Lx/D = 1. <3> I =.7%, Lx/D =. <5> I = 9.%, Lx/D =.3 Smooth flow Base-pressre coefficient <> I = 9.%, Lx/D = 1.7 <7> I =13.5%, Lx/D = 1.59 Smooth flow <3> I =.7%, Lx/D =. <5> I = 9.%, Lx/D = B /D Figre 3: Comparison of C pb in different trblence intensity B /D Figre : Comparison of C pb in partially-simlated trblence () Redced trblence intensity In order to investigate trblence partial simlation qantitatively, base pressre of rectanglar cylinders was measred similarly to the previos section (1) and examined by redced trblence intensity. PSDs of trblences (1, & 3), (, 5 & ) and (7 & ) in a high-freqency part coincide as shown in Fig. 5 and they are partially simlated trblence grops. Table shows the redced trblence intensity for those trblences. It can be recognized that redced trblence intensities for partially simlated trblence grops have close vales and therefore it can be an index of trblence partial simlation. Fig. shows C pb measred vs. slenderness ratios. It can be seen again that C pb for partially simlated trblence pairs fairly agree in a large slenderness ratio range. Fig. 7 shows C pb vs. the redced trblence intensity where broken lines are linear regression lines. Reslts for the slenderness ratio greater than the critical vale are only shown. It can be seen that C pb changes linearly against the redced trblence intensity. It was also checked that C pb has a linear relationship with trblence intensity and trblence scale as shown in Figs. and 9, respectively. However, the degree of linear regression in cases of trblence intensity and trblence scale is less than the case of redced trblence intensity. Based on these observations, the effects of trblence on the base pressre can be represented by redced trblence intensity and in trn the flow field arond a rectanglar cylinder can be simlated by the trblence partial simlation method.

5 First International Symposim on Fltter and its Application, 1 15 fs /U Redced freqency, fd/u Figre 5: PSD of wind-tnnel trblences 1, Ir =.1, Ir =.11 3, Ir =.15, Ir =.9 5, Ir =.9, Ir =.1 7, Ir =.1, Ir =.77 Table : Properties of trblence flows No. I (%) L x (m) I r Base pressre coefficient, Cp Smooth B/D Figre : Base pressre coefficients vs. slederness ratio Base pressre coefficient, C p. B/D =.59 B/D =.11. B/D =.7 B/D =.7 B/D =.77 B/D =.7 B/D = Redced trblence intensity, I r Figre 7: Base pressre coefficients vs. redced trblence intensity Base pressre coefficient, C p... B/D =.59 B/D =.11 B/D =.7 B/D =.7 B/D =.77 B/D =.7 B/D =.97 Base pressre coefficient, C p... B/D =.59 B/D =.11 B/D =.7 B/D =.7 B/D =.77 B/D =.7 B/D = Trblence intensity, I Figre : Base pressre coefficients vs. trblence intensity....1 Trblence scale, L (m) Figre 9: Base pressre coefficients vs. trblence scale. SURFACE PRESSURE AND STATIC COEFFICIENT OF BRIDGE DECK 9) Trblence partial simlation was also checked sing a hexagonal bridge deck model as shown in Fig. 1. Two slenderness ratio models (B/D = 5 and 7.5, B =.3 m) were tested. Srface pressres at 3 points were measred at a wind speed of 1 m/s in partially simlated trblences as shown in Table and Fig. 5. Fig. shows the distribtion of mean srface pressre coefficients for B/D = 7.5 model at degree angle of

6 1 JAXA Special Pblication JAXA-SP-1-E attack. Negative peak pressre was prodced at jst after the leading edge on the pper and lower srfaces. In addition, mean pressre coefficients are not so mch different on leeward srfaces among different trblence flows. The negative peak pressre coefficients are plotted by redced trblence intensity, trblence intensity and trblence scale for B/D = 7.5 and 5 in Figs. 11 and 1, respectively. This is becase the negative peak pressre represents a flow separation intensity, separation flow width and wind excitation force intensity. It can be seen that the negative peak pressre coefficients have the best linear relationship with redced trblence intensity. This implies that the flow field arond the bridge deck can be simlated by the trblence partial simlation, and that redced trblence intensity can be a simlation index. Secondly, lift and pitching moment coefficients were calclated by integrating the srface pressres over the deck cross section in order to estimate the aerodynamic characteristics psedo-dynamically. Figs. 13 and 1 show the slopes of lift and pitching moment coefficients at -degree angle of attack with redced trblence intensity, trblence intensity and trblence scale for B/D = 7.5 and 5, respectively. The slope was calclated as an average slope between - to + degrees. The slope of pitching moment coefficient is insensitive to trblences while that of lift coefficient has a weaker linear relationship with each trblence parameter. However, there is no significant difference among three trblence parameters. This may be de to the fact that srface pressre distribtion is not so different except for neighborhood of the separation point. Contrarily to the negative peak pressre, speriority of redced trblence intensity to trblence intensity or trblence scale was not observed. However it can be nderstood that the redced trblence intensity as well as trblence intensity will be an index of trblence simlation Cp 1L1. 1 1L.5 1L3. 7 L3. L3. 5 L.5 L5. 3 L. smooth Smooth Cp -1.3 Figre 1: Bridge deck model and mean pressre distribtion of B/D = 7.5 Mean Pressre coeff., C p..... R R 乗値平均 = Redced trblence intensity, I r Mean Pressre coeff., C p R = Trblence intensity, I R = Trblence scale, L (a) Redced trblence intensity (b) Trblence intensity (c) Trblence scale Figre 11: Negative peak pressre coefficient at separation point of lower srface for B/D = 7.5 Mean Pressre coeff., C p

7 First International Symposim on Fltter and its Application, 1 17 Mean Pressre coeff., C p. R R 乗値平均 = Redced trblence intensity, I r Mean Pressre coeff., C p R = Trblence intensity, I. R = Trblence scale, L (a) Redced trblence intensity (b) Trblence intensity (c) Trblence scale Figre 1: Negative peak pressre coefficient at separation point of lower srface for B/D = 5 Mean Pressre coeff., C p dc L /d, dc M /d R² =.517 R² =.577 dc L /d, dc M /d R² =.371 R² =.79 dc L /d, dc M /d R² =.55 R² = Redced trblence intensity, I r Trblence intensity, I Trblence scale, L (a) Redced trblence intensity (b) Trblence intensity (c) Trblence scale Figre 13: Slope of lift and pitching moment coefficient for B/D = 7.5 dc L /d, dc M /d R² =.19 R² =. dc L /d, dc M /d R² =.57 R² =.1 dc L /d, dc M /d R² =.151 R² = Redced trblence intensity, I r Trblence intensity, I Trblence scale, L (a) Redced trblence intensity (b) Trblence intensity (c) Trblence scale Figre 1: Slope of lift and pitching moment coefficient for B/D = 5 1, 11) 5. SURFACE PRESSURE AND PIV TEST OF RECTANGULAR CYLINDER (1) Srface pressre In order to nderstand more clearly the effects of the trblence parameters on flow field arond blff bodies, srface pressres of rectanglar cylinders of B/D = and 3 were measred in varios trblent flows. Reslts were examined by focsing on the redced trblence intensity. Measrement was taken at wind speeds of and 9 m/s, which is eqivalent to Reynolds nmber of, and,, respectively. Figs. 15 and 1 show mean srface pressre coefficient arond rectanglar cylinder of B/D = and 3, respectively. Srface pressres at the leading edge generally become smaller as the redced trblence intensity increases. On the other hand, srface pressres at the trailing edge become larger as the redced trblence intensity increases. This sggests that reattachment of the flow to the side srface is enhanced by trblence. In addition, larger redced trblence intensity which is eqivalent to larger small scale trblence

8 1 JAXA Special Pblication JAXA-SP-1-E enhances the reattachment trend. Frthermore, peak location of the mean srface pressre coefficient was identified by fitting a sixth order polynomial eqation. The peak locations on both top and bottom srfaces shift to the leading edge as the redced trblence intensity increases. Therefore, redced trblence intensity might be the better representative index of flow field arond a rectanglar cylinder Redced Trblent Intensity Smooth Flow Ir.9 Ir.5 Ir.9 Ir.73 Ir.113 Ir.1 x/d y/d Figre 15: Mean srface pressre coefficients arond a rectanglar cylinder of B/D = Redced Trblent Intensity Smooth Flow Ir.9 Ir.5 Ir.9 Ir.73 Ir.113 Ir.1 x/d y/d Figre 1: Mean srface pressre coefficients arond a rectanglar cylinder of B/D = 3 () PIV test A PIV test was condcted to illstrate effects of small-scale trblence on flow field arond a rectanglar cylinder. Measrement was done at wind speeds of 5 7 m/s, which is eqivalent to Reynolds nmber of 5,5 73,5, respectively. Fig. 17 shows time-average velocity vector fields for a rectanglar cylinder of B/D = 3. It can be seen that flow separates at the leading edge and does not reattach in a smooth flow case while flow reattaches at the trailing edge in a trblent flow case. Using this PIV test reslts, wind velocity data was taken and PSD was analyzed. Fig. 1 shows the peak freqency in PSD along the shear layer (shown by red circles) for different trblent flows. Generally peak freqency increases near the leading edge while it decreases toward the trailing edge. Clear trend among

9 First International Symposim on Fltter and its Application, 1 19 different trblent flows is not observed, larger redced trblence intensity shows lower peak freqency, however. It can also be nderstood that higher freqency component of trblence (small-scale trblence) enhances flow reattachment near the leading edge. (a) Smooth flow at 5m/s (b) Redced trblence intensity of.1 at m/s Figre 17: Time-average velocity vector field for rectanglar cylinder of B/D = 3 Figre 1: Variation of peak freqency in PSD of shear layer along-wind speed flctation. CONCLUSIONS In this stdy, the trblence partial simlation was experimentally investigated for three different blff-body strctres from the view point of redced trblence intensity. Reslts obtained are as follows:

10 15 JAXA Special Pblication JAXA-SP-1-E Base pressre measrement of rectanglar cylinder (B/D =..9) showed that the base pressre coefficients of a rectanglar cylinder with and larger than the critical slenderness ratio fairly agree in partially-simlated trblences. Measrement of srface pressre and static coefficients of bridge deck (B/D = 5 and 7.5) showed that redced trblence intensity as well as trblence intensity can represent a negative peak pressre of a hexagonal bridge deck. On the other hand, trblence scale cannot represent it as can the redced trblence intensity do. Redced trblence intensity can also represent the slopes of static force coefficients of the bridge deck model as can trblence intensity and trblence scale do. Srface pressre measrement and PIV test of rectanglar cylinder (B/D = and 3) showed that reattachment of the flow to the side srface is enhanced by trblence. In addition, larger redced trblence intensity which is eqivalent to larger small scale trblence enhances the reattachment trend. It can also be nderstood from PIV test that higher freqency component of trblence (small-scale trblence) enhances flow reattachment near the leading edge. Based on these observations, frther stdy on redced trblence intensity shold be condcted. ACKNOWLEDGMENT Wind-tnnel tests were carried ot with great help by gradate stdents of those days. They are Mr. Yashiro Takaoka (Nippon Koei Co., Ltd.), Mr. Keiske Takano (Kajima Corporation), Mr. Yasnori Aoki (Oriental Consltant Co., Ltd.), Dr. Panpipat Sangchwong (Norciv Engineering). They are greatly appreciated. REFERENCES 1) Nakamra, Y., Ohya, Y. and Watanabe, K., The effects of trblence on the aerodynamic characteristics of two-dimensional rectanglar cylinders, Proc. of th National Symposim on Wind Engineering, pp.9-5, 19 (in Japanese). ) Irwin, P. A., The role of wind tnnel modeling in the prediction of wind effects on bridges, Proc. of the Int. Symp.: Advances in Bridge Aerodynamics, Balkema, pp , ) Macdonald, J. H. G., Irwin, P. A. and Fletcher, M. S., Vortex-indced vibrations of the Second Severn Crossing cable-stayed bridge fll scale and wind tnnel measrements, Proc. of the ICE: Strctres and Bildings, SB15(),. ) Irwin, P. A., Blff body aerodynamic in wind engineering, Proc. of BBAA V, Ottawa, Canada, pp.51-57,. 5) Yamada, H. and Katschi, H., Wind-tnnel stdy on effects of small-scale trblence on flow patterns arond rectanglar cylinder, Proc. of VI International Colloqim on Blff Body Aerodynamics & Applications, pp.-7, Milano, Italy,. ) Nakamra, Y. and Ohya, Y., The effects of trblence on the mean flow past two-dimensional rectanglar cylinders, J. Flid Mechanics, 19, pp.55-73, 19. 7) Nakagchi, H., Hashimoto, K. and Mto, S., An experimental stdy on aerodynamic drag of rectanglar cylinders, J. of Japan Society of Aero. Space Science, 1, pp.1-5, 19 (in Japanese). ) Bearman, P. W. and Treman, D. M., An investigation of the flow arond rectanglar cylinders, Aeronatical Qarterly, 3, pp.9-37, ) Katschi, H. and Yamada, H., Stdy on trblence partial simlation for wind-tnnel testing of bridge deck, Proc. of 13th International Conference on Wind Engineering (CD-ROM), Amsterdam, ) Panpipat Sangchwong, Hitoshi Yamada, Hiroshi Katschi, Stdy on trblence effects on flow fields arond sharp-edged blff bodies, J. of Strctral Engineering, Vol.59A, JSCE, pp.7-3, ) Sangchwong, P., Yamada, H. and Katschi, H., Flow visalization stdy on effect of small-scale trblence on flow fields arond sharp-edge blff bodies, Proc. of 1th America Conference on Wind Engineering, No.3., Seattle, USA, 13..