coh R 1/2 K x = S R 1R 2 (K x) S R 1 (K) S R 2 (K) (3) Davenport (1961) proposed one of the first heuristic root-coherence expressions for longitudina

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1 The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7) Shanghai China; September Investigation of spatial coherences of aerodynamic loads on a streamlined bridge deck under active-generated flow conditions K. Xu a L. Zhao b S.Y. Cao c Y. J. Ge d a SLDRCE Tongji University ShanghaiChina firework198864@163.com b SLDRCE Tongji University Shanghai China zhaolin@tongji.edu.cn c SLDRCE Tongji University ShanghaiChina caoshuyang@hotmail.com d SLDRCE Tongji University Shanghai China yaojunge@tongji.edu.cn ABSTRACT A pressure measuring experiment on a streamlined bridge deck section model was conducted under simultaneous two-dimensional incident flows in an active-controlled wind tunnel. A commendable wind velocity modification approach based on the stable flow features of the active-controlled wind tunnel was adopted. The correlations of both incident winds and aerodynamic forces were studied and an obvious impact of integral scales can be seen in this study. The decaying trend of root coherence with large ratios of integral scale to section-interval is a far cry from the conventional exponential expression thus a new empirical expression is proposed to reflect the spatial coherence features in low frequency region. KEYWORDS: active-controlled turbulences; aerodynamic loads; correlation coefficients; spatial coherences; empirical expression 1 INTRODUCTION The existing buffeting theory for bluff body is derived from the airfoil aerodynamics which is assumption. The aerodynamic loads on a deck cross section thus are only due to the incident flows in the same plane with that section which gives the aerodynamic loads a two dimensional feature. When these 2D (two-dimensional) forces are applied to a 3D (three-dimensional) structure the spatial distribution and correlation of these forces along the span-wise have to be sufficiently considered. A criterion for assessing the correlation features of aerodynamic loads or incident flows between two cross-sections is correlation coefficient: Cor x 1 x 2 = v 1(x 1 t) v 2 (x 2 t) 1 v1 v2 where the over bar denotes time-averaging; v(xt) is turbulent wind velocity ; v is standard deviation of the turbulent components. In the frequency domain the joint acceptance function is used to represent the distribution and correlation features of aerodynamic loads or incident winds along the span-wise and between different modes: J(K) 2 = L S R 1R 2 (K x) 0 S R 1 (K) S R 2 (K) i x 1 i x 2 dx 1 dx 2 2 where S R1R2 denotes the cross-spectrum of buffeting forces or oncoming flows on different cross-sections at a distance of ; S Ri (i=12) represents the auto-spectrum of buffeting forces or oncoming flows i (x) is the i th modal shape of the deck; /U is reduced frequency; B is deck width; is oscillation frequency; U is average wind speed; L is deck length. In the above function the normalized cross-spectrum is defined as the root coherence function: 170

2 coh R 1/2 K x = S R 1R 2 (K x) S R 1 (K) S R 2 (K) (3) Davenport (1961) proposed one of the first heuristic root-coherence expressions for longitudinal turbulence which is based on field measurements: coh 1/2 u f X) = exp c f X (4) U where c is decay factor; is reduced frequency also used as a collapsing parameter. In early studies the distribution of buffeting forces along span-wise was considered to be the same as the incident flows however a lot of experiments conducted in wind tunnels revealed a larger spatial coherence of the aerodynamic forces. And spatial coherence is not only related to the flow frequency and section-intervals but also has a relation with the integral scale turbulence intensity section features like the ratio of deck width to deck thickness etc (Matsumoto 1994; Larose ; Nagaoa 2003; el at). Nevertheless all those experiments were carried out in passive atmospheric boundary wind tunnels some of the key fluid features such as integral scale oncoming flow coherence PSD function of fluctuating wind etc cannot be easily reproduced in a passive wind tunnel. Integral scale of stochastic fluctuating wind however has a considerable influence on the spatial coherences of the aerodynamic loads but the integral scale of stochastic fluctuating generated by a passive wind tunnel is always too small comparing with the model scale. Furthermore because the incident flow features on the central point of section model cannot be measured directly the flow features at the up-stream or at the lateral of the section model were just adopted as replacements. As is known the flow energy decays along the longitudinal direction and the wind velocities are not fully correlated along the lateral direction in a passive wind tunnel thus the measured wind features cannot represent the real features on the central points of pressure measuring cross-sections which leaves something to be desired. Moreover the vertical and longitudinal turbulences cannot be well reproduced simultaneously in a passive wind tunnel thus the spatial coherence features under simultaneous 2D turbulences have never been fully studied before. In order to study the spatial correlations of aerodynamic loads under effectively simulated wind features and two-dimensional simultaneous incident flows an experiment involving a stream-lined cross-section model was conducted in the active-controlled atmospheric boundary wind tunnel in Miyazaki University of Japan. closed-box deck designed with emphasis put on aerodynamics but it is a strictly speaking bluff body with separated shear layers. 2 EXPERIMENTAL ARRANGEMENT 2.1 Wind tunnel and experimental facilities Multiple-fans active wind tunnel in Miyazaki University consists of 99 independent blowers. It can effectively simulate the longitudinal average wind speed turbulence profiles and different integral scales. Moreover it can reproduce artificial stochastic wind waves under given controlling parameters (Nishi et al. 1997; Nishi et al.1999; Cao et al. 2002). To generate the vertical turbulent components an active-vibration grids is adopted which can generate the vertical turbulent wind sufficiently. Altogether 390 pressure tapping points were arranged in 5 parallel sections along span-wise each section consists of 78 tapping points arranged along 171

3 The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7) Shanghai China; September chord-wise. Sampling frequency is 200Hz and sampling time is 100s. 3D hot-wire anemometers (KANOMAX model 1008) high precision electronic pressure scanners and simultaneous acquisition facilities (DASBOX model 2800) were adopted. Deviation of the signal caused by the length and diameter of piezometer tubes was modified. The following figure illustrates the multi-fans and active-vibration grids in the active wind tunnel as well as the arrangement of tapping points: section 1 section 2 section 4 section 3 20cm 30cm 30cm 20cm 20cm 20cm section cm tapping point 1 78 wind Figure 1. Active wind tunnel facilities and arrangement of tapping points 2.2 Oncoming flow control and wind velocity modification The multiple-fans active wind tunnel can reproduce the target wind features sufficiently under given parameters. The von karman type wind spectrum was chosen as the target longitudinal wind spectrum which has the following form: S f = 4 I 2 L x /U (5) fl 5/6 x U 2 where S(f) denotes the wind power spectrum; I U Lx and f represent the turbulence intensity average wind speed integral scale along the span wise and wind frequency respectively. As to the vertical turbulent wind spectrum the Panofsky spectrum with the following form is adopted: S f = u 2 /U (6) (1+ f U )2 where and are coefficients relating to height. Figure 2 shows the target and measured spectrums of the u and w components: 172

4 1 target spectrum measured data on section 1 measured data on section 2 Power Spectrum E-3 Power Spectrum 1E-3 1E-4 Panofsky Spectrum measrued data on section 1 measured data on section Frequency (Hz) (Longitudinal Wind) 1E Frequency (Hz) (Vertical Wind) Figure 2. Target and measured power spectrums of longitudinal and vertical components Aerodynamic forces are caused by the incident flows and are functions of the turbulent wind velocities at the reference point. The 1/4 chord point is often taken as the reference point according to the airfoil theory and for bridge deck the central point is always adopted. Because of the existence of section model wind velocity at the central point of the model cannot be measured directly thus the flow features are always measured at the up-stream or at the lateral of the deck. The measured wind features however are often taken as the flow features at the reference point. Because the wind energy decays along the longitudinal direction and the wind velocities are not fully correlated between two points along the lateral direction thus the measured flow features cannot represent the real flow characters of the reference point. To reflect the wind features of the reference point a modification approach was adopted based on the stable flow features in active wind tunnel under given parameters. Firstly a 3D hot-wire anemometer was fixed at the central point of the pressure-measuring section without installing the section model then another one was fixed 45cm above it. Secondly the wind velocities at these two points were measured simultaneously for a while and the correlations of flow features like magnitude and phase between these two points were studied. A modification algorithm was proposed to reproduce the features of the lower point by using the data measured on the upper point. To examine the efficiency of this algorithm ten validation tests under different flow conditions were conducted and it came to a commendable result. Figure 3 illustrates a good modification result. Target wind velocity in this figure denotes the measured data by the 3D hot-wire anemometer fixed at the central point of pressure measuring section without the section model being installed and the measured data denotes the wind velocity measured by the 3D hot-wire anemometer 45cm above the former one. turbulent wind velocity (m/s) target wind velocity measured data before modification time (s) turbulent wind velocity (m/s) target wind velocity measured data after modification time (s) Figure 3. Target wind velocity series and measured data before and after modification 173

5 The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7) Shanghai China; September EXPERIMENT RESULTS AND DISCUSSION Altogether 14 oncoming flow conditions with different flow features like integral scale turbulence intensity and average wind speed were reproduced in the multiple-fans wind tunnel. Only the cross-section pressures of section 1 section 2 and section 4 were measured simultaneously with the incident flow velocities because of the limit on the number of 3D hot-wire anemometers. Thus the test conditions consist of 3 section-intervals (30cm 50cm 80cm) under 14 different flow conditions. The correlation features of aerodynamic forces and incident flows were studies in both time and frequency domains. The schematic diagram of simultaneous measurement of wind velocities and chord-wise pressures is as follows where the red circles in this figure denote 3D hot-wire anemometers. vertical Longitudinal section 4 45cm 45cm section 2 section 1 45cm Figure 4. Schematic diagram of simultaneous measurement of wind velocities and chord-wise pressures 3.1 Correlation coefficients with different section intervals In time domain the correlation coefficients with different section intervals under a given flow condition were calculated and an obvious phenomenon can be found that the correlation coefficients have a tight relationship with integral scales correlation coefficients uu ww DD LL MM correlation coefficients uu ww DD LL MM intervals (m) Condition intervals (m) Condition 8 Figure 5. Correlation coefficients of aerodynamic forces and oncoming flows under condition 1 and 8 Figure 5 illustrates the correlation coefficients under condition 1 ( L u x = 2.033m L w x = 97m U = 4.57m/s ) and condition 8 ( L u x = 3.782m L w x = 0.166m U = 6.54m/s ). By comparing these two pictures we can find that the longitudinal turbulent wind and the aerodynamic drag force obey the same trend and the correlation coefficients primarily dominated by the integral scale of longitudinal turbulent wind. If the integral scale of longitudinal turbulent wind is large enough (much bigger than the section-intervals) the drag forces and longitudinal turbulent winds are almost fully correlated (around 0.95) and do not decay with the increase of section-intervals. Both the aerodynamic lifts and moments show a larger correlation feature than the vertical turbulences. 174

6 correlation coefficients intervals (m) Condition 1 uu ww DD LL MM correlation coefficients intervals (m) Condition 2 Figure 6. Correlation coefficients of aerodynamic forces and oncoming flows under condition 1 and 2 This figure illustrates the correlation coefficients under condition1 (L x u = 2.033m L x w = 97m U = 4.57m/s ) and condition2 ( L x u = 0.562m L x w = 0.2m U = 4.61m/s ). By comparing these two pictures we can find that the longitudinal turbulent wind and the aerodynamic drag still obey the same trend although the integral scale changes a lot. With the integral scale of longitudinal wind changing from 2.033m to 0.562m an obvious decaying trend of the correlation coefficients for both longitudinal wind and aerodynamic drag occurs. With the integral scale of vertical wind changing from 97m to 0.2m an obvious increase of the correlation coefficients of aerodynamic moments can be seen. Both the lifts and moments show a much higher correlation feature than vertical wind. 3.2 Spatial coherences and a new empirical function The root coherences of the three-direction aerodynamic loads have different decaying trends versus frequency. The root coherence of aerodynamic drag is bigger than that of the longitudinal wind at the higher frequency region which has been observed by other researchers too. The aerodynamic lift has an inconsistent decaying trend with the vertical wind and is more correlated in the frequency range of interest. The aerodynamic moment shows a similar decaying trend with the vertical turbulence and has a lower correlation feature than both of the drag and lift forces. uu ww DD LL MM

7 The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7) Shanghai China; September Figure 7. Root coherences of turbulent winds and aerodynamic forces under condition 1 The above figure illustrates the root coherences of the incident flows and aerodynamic forces between two cross sections at an interval of 80cm under condition 1. The blue solid line in this figure denotes the experimental data and the red and black solid lines respectively denote the fitting functions using the exponential expression and a new empirical function which will be discussed later. In order to detect the impacts of integral scales and turbulence intensities on the coherences of aerodynamic loads a series of cases with different ratios of integral scale to section-interval were studied. Figure 8. Root coherences of turbulent winds with different integral scales Figure 8 illustrates that the wind correlation feature improves with the increase of integral scale which is not difficult to understand. It is worth noting that under a large integral-scale condition (e. g L u =2.5) the root coherence shows a different decaying trend versus frequency especially in the low frequency range where the exponential expression is no longer applicable. (a) Drag (b) Lift (c) Moment Figure 9. Root coherences of aerodynamic forces under different flow conditions 176

8 Figure 9(a) shows the coherences of aerodynamic drags under different incident flow conditions. As can been seen from that picture the aerodynamic drag is primarily dominated by the longitudinal wind since the coherence of the aerodynamic drag decays fiercely with the decrease of longitudinal wind integral scale though the integral scale of the vertical wind is increased. As to the aerodynamic moment the coherence is mainly dominated by the vertical wind on account of the similar decaying trends versus frequency at similar vertical wind integral scales although the longitudinal components changes violently which is reflected in Figure 9(c). The aerodynamic lift however seems to have a relation with both of the vertical and longitudinal incident flows as can be seen from Figure 9(b) and its spatial coherence features cannot be simply evaluated by those of the vertical winds. The influence of turbulence intensity was also considered in this approach and an intuitional sense is that with the increase of turbulence intensity the value of root coherence trends to become bigger in the higher frequency region. However because the variation range of turbulence intensities generated in this experiment is small the detail and respective impacts of I u and I w on three aerodynamic forces need further experiments. As mentioned above the form of root coherence differs with the changes of integral scale and turbulence intensity and once the ratio of integral scale to section interval is large enough( >1) the root coherence shows a totally different decaying trend with the exponential expression. Besides the longitudinal and vertical turbulences have different contributions to different direction aerodynamic forces. In order to reflect the influences of these relevant factors and taking into account the different decaying trend with the exponential expression under large integral scale conditions a new empirical expression of root coherence is proposed which is based on the nonlinear least square method and has the following form: Coh 1 2 f x =c c 1 1+exp c 2 f B U c 3 Lx x c 4 c5 I t In this expression f represents the frequency; x denotes the distance between two cross sections; U is average wind speed; B is deck width; c 1 ~c 5 are fitting coefficients. As to L x and I t they denote the integral scale of incident wind along the span-wise and the corresponding turbulence intensity respectively. For the root coherence of longitudinal or vertical turbulent wind L x and I t signify the flow features of its own. And for the aerodynamic forces the static coefficients are adopted to measure the contribution ratios of different turbulent winds to different aerodynamic forces. The static coefficients were measured under uniform flow condition in the TJ-1 wind tunnel of Tongji University Shanghai China. Table 1 shows the values of static coefficients and their slopes under attack angle of zero: Table 1. Static Coefficients Measured in TJ-1 C d 39 C d C L -12 C L C M 04 C M The integral scales and turbulence intensities used in the root coherences of aerodynamic forces can be defined as follows: x L drag x L lift = C d L u +C d L w = C L L u +C L L w x L moment = C M L u +C M L w I w I C drag = C d I u +C d (8) d C d I w I C lift = C L I u +C L (9) L C L I w I C moment = C M I u +C M (10) M C M (7) 177

9 The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7) Shanghai China; September And the fitting coefficients through the nonlinear least square fit are illustrated below: Table 2. Fitting Coefficients C 1 C 2 C 3 C 4 C ~ (The value of C 2 is 20~25 for turbulent winds and 15~20 for aerodynamic forces.) This expression can reflect the impacts of turbulence intensity and ratio of integral scale to section-interval on spatial coherences and can account for the different decaying trends between aerodynamic forces and incident winds through their corresponding integral scales and turbulence intensities. But it is worth noting that this expression is derived from the experimental conditions with different integral scales but limited section-intervals. It can reproduce the decaying trend of root coherences of both aerodynamic forces and incident winds in the low frequency region preferably which is the insufficiency of the exponential expression. However this expression cannot demonstrate the correlations in high frequency region. The combined use of this expression with the exponential expression or a united expression containing both features of these two expressions needs further experiments and study. 4 CONCLUSION The root coherences of both incident winds and aerodynamic forces were studied and an obvious impact of integral scale can be seen. The three-direction aerodynamic loads have different correlation features under same incident flow conditions and the decaying trend of root coherence under large ratios of integral scale to section-interval is a far cry from the exponential expression. A new empirical expression is proposed to reflect the spatial coherence features in low frequency region and taking into account the different contribution ratios of incident winds to different aerodynamic loads. Since it is not applicable for high frequency region the combined use of this expression with the exponential expression or a united expression containing both features of these two expressions needs further experiments and study. 5 ACKNOWLEDGE The authors gratefully acknowledge the supports of the National Science Foundation of China ( and ) and the supports by Kwang-Hua Fund for College of Civil Engineering Tongji University. 6 REFERENCES [1] Matsumoto M Chen X Shiraishi N. Buffeting analysis of long span bridge with aerodynamic coupling (Processing of 13 th National Symp on Wind Engineering) [J]. Japan Association for Wing Engineering [2] Larose G L Mann J. Gust loading on streamlined bridge decks [J]. Journal of Fluids and Structures (5): [3] Larose G L Tanaka H Gimsing N J et al. Direct measurements of buffeting wind forces on bridge decks [J]. Denmark Journal of Wind Engineering and Industrial Aerodynamics 1998 (74-76): [4] Larose G L. The spatial distribution of unsteady loading due to gusts on bridge decks [J]. Journal of Wind Engineering and Industrial Aerodynamics 2003 (91):

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