VORTEX SHEDDING INDUCED VIBRATIONS OF A LIGHT MAST

Transcription

1 BBAA VI International Colloquium on: Bluff Bodies Aerodynamics & Applications Milano, Italy, July, -4 8 VORTEX SHEDDING INDUCED VIBRATIONS OF A LIGHT MAST Bjarni Bessason, and Jónas Thór Snaæbjörnsson Engineering Research Institute University of Iceland, Hjardarhaga -6, 17 Reykjavik, Iceland s: bb@hi.is, jonas@hi.is Keywords: Wind, vortex shedding, vibrations, acceleration, full-scale data, countermeasures. Abstract. The paper reports a case study of wind induced vortex shedding vibrations of a steel light mast. The vibrations are examined, full scale observations reported and the countermeasures devised to reduce the motions are described. The across wind motion of the mast was observed in windy weather shortly after its installation. The amplitude of deflection at the tip of the mast was estimated to be few centimetres and considered unsatisfactory by the owner. A measurement program was initiated to map the vibrations of the mast and to correlate them with wind data. The recorded data showed that the initiation of the intense vibrations as well as the amplitude of the vibrations was in fair agreement with predictions based on theory of bluff body aerodynamics. To reduce the vibrations cylindrical wind flaps were added to the light mast to counteract the formation of vortexes. Comparison of recorded vibration data before and after the installation of the wind flaps show that the flaps significantly reduced the vibrations 1

2 1 INTRODUCTION In the summer of 5 a frame type mast supporting flight control lamps for the approach control of incoming flights to the N-S runway of the airport in Reykjavik, Iceland, was installed. The Reykjavik airport is located in the middle of the city and surrounded by inhabited areas and dens road system. This affected the construction of the light mast in two ways. Firstly, it was considered preferable to design an elegant figuration of the mast that could fit nicely into the surroundings. Secondly, the optimal location of the new light frame interfered with a road intersection and therefore it was necessary to design a cantilever beam stretching out over part of the intersection. The original structure is shown on Fig. (1). Soon after the installation of the light frame, significant across wind motion of the cantilever beam was observed in windy weather by people passing and stopping at the intersection. This was reported to the owner of the mast, the Icelandic Civil Aviation Administration. Field observations confirmed incidental vertical swings of the cantilever beam in modarate winds. The amplitude of deflection at the tip of the beam was estimated to be few centimetres. The Aviation Administration considered these vibrations unacceptable and decided to investigate the problem in order to seek a solution to reduce the swings. The main objective of this paper is to report the investigation of the observed vibrations and the countermeasures carried out in order to reduce the motions. The analysis includes both full scale measurements as well as analytical evaluation of the dynamic behaviour of the light mast. Figure 1: The flight mast with the cantilever beam stretching out over the intersection to the left. The yellow bubbles on the top of the beam are the flight control lamps. WIND INDUCED VIBRATIONS.1 Vortex shedding The flow induced vibrations of the cantilever were traced to the much studied vortex shedding process [1], which can create problems in a variety of contexts in wind engineering. The vortices shed from a bluff body as the flow region is separated induce a fluctuating force on

3 the structure that can lead to vibrations. The intensity of this force acting on the structure controls the amplitude of vibration of the structure that primarily depends on the cross-sectional shape of the structure and the mean wind velocity []. The phenomenon is well described in the literature [3] as well as in design codes (see for instance Ref. [4] EN , Annex E ) and design guidelines, such as Ref. [5] by ESDU. The vortex shedding for rectangular sections is characterized by the Strouhal number, S t, of the flow: S n D V v t = (1) where V is the wind velocity, D is the dimension of the cross-section perpendicular to the wind direction, and n v is the vortex shedding frequency. The Strouhal number depends on the cross section type, the Reynolds number of the flow and the amplitude of the resulting vibration. The customary value for circular cylinders is., but it can be found in the literature, in handbooks and is supplied in design guidelines and codes for various cross section types. If the vortex shedding frequency coincides with a natural frequency of vibration of a member (or an assembly of members), n s, and the damping (structural and fluid) is sufficiently small for the cross flow forces to 'lock on' to the structural natural frequency then large amplitude oscillations result. The wind velocity generating this condition is termed the critical wind velocity, i.e. V ~ V crit, and is evaluated as: V n D s crit = () St The resulting oscillations self limit when the amplitude of the vibration becomes comparable to the size of the vortex. This limit is dependant on the member mode shape, but is often found to be of the order of 1 cross section diameter which is rarely an acceptable limit. The actual vibration amplitude of a structure under the influence of vortex shedding are governed both by the structure s inherent damping characteristics and by the mass ratio between the structure and the fluid it displaces. These two effects are often combined in the Scruton number sometimes referred to as a stability parameter, which is defined as: S c 4π meς T = (3) ρd Here m e is average mass per unit length, ζ T is the total critical damping ratio, ρ is the density of air and D is the across wind dimension of the cross section. Although the damping parameter in Eq.(3) represents the total damping, the damping is almost totally due to structural damping since the aerodynamic fluid damping is usually negligible. As S c increases then the response amplitude proportionally decreases when locking occurs. For a narrow band excitation a sinusoidal excitation model gives, in principle, an adequate representation of the vibration amplitude [], this can be simplified to: y D max kc l = 4π ScSt Here y max is the maximum vibration amplitude, C l is a mode and amplitude dependent lift coefficient. k is a parameter depending on the structural mode shape, given as: (4) 3

4 k = h h φ (z) dz j φ (z) dz j For a cantilever the mode shape φ j (x) can be taken as (x/h) β, where H is the cantilever length. For uniform or near-uniform cantilevers, β can be taken as 1.5 and then k = 1.6. At wind speeds away from V ~ V crit, the locked-in narrow banded behaviour becomes more episodic, and the response decreases. The range of V/V crit for which the oscillations remain significant is considerably wider for lightly damped structures than for heavily damped structures which points to the dominant role of structural damping in determining the amplitude of wind vortex induced oscillations and the range of excitation wind speeds. There are several guidelines available to an engineer which can be used in assessing the susceptibility of structures to wind induced vortex shedding. These include for instance Ref. [5] (ESDU 936) and Ref. [4] (EN Annex E). Both approaches are based on the simple description of the process involved provided her above but with some additions and accompanying datasets. The methodology of Ref. [5] takes into account many parametric effects, such as: Roughness of the vortex generation surface, the effect of atmospheric turbulence, span-wise correlation due to end effects, effects of tapered or stepped diameter members, effect of mode shape on the excitation force, influence of the response amplitude on the excitation force, reduction of response as the wind velocity deviates from the critical wind velocity and includes prediction of low amplitude broad banded responses. The basic technique is to derive the response amplitude at the critical velocity as a function of damping using the standard equations for the member properties. The response is then calculated by interpolating the derived function for the correct value of structural damping. In the case of non-critical wind velocities the response can be corrected based on the damping level and response amplitude at the critical velocity and for low amplitude broad banded responses a modified set of equations are presented and used. The methodology presented in Ref. [4] is similar to the ESDU procedure, but is put forward in somewhat simplified form that does not attempt to account for all the parameters that might influence the response. It is to some extent based on the work of Ruscheweyh et al [6], which developed a mathematical model for predicting the vortex-excited vibration taking into account the increasing correlation length of the exciting force with increasing vibration amplitude, called the correlation length model. (5). Modal analysis and estimation of critical wind velocity for vortex shedding The light mast is a slender steel frame structure. The horizontal beam at the top of the mast is made of welded U-profile (4x4mm) while the columns have a closed rectangular section of same size. All corners are very sharp and therefore susceptible to vortex shedding, but the U-profile section of the cantilever should cause a breakdown of flow regularity to some degree by the irregular nature of the flow trapped within the section. The structure has low internal damping and therefore when excited the duration of vibration is considerable. A 3D beam finite element (FE) model was made of the light mast in SAP [9]. All cross-sections and dimensions were based on the engineering drawings of the light mast. To take into account the weight of the flight lamps and other fittings the dead weight of the steel structure was increased by 1%. The main results of the modal analysis are shown in Table 1. As seen from the table some of the vibration modes were out of plane while the others were in 4

5 the plane of the structure. Field observations showed that it was the vertical motion of the cantilever beam that was most apparent. Therefore modes no., 4 and 6 are of concern, while the out-of-plane modes can be ignored. In Fig. () and Fig. (3) modes and 4 are shown. Mode, which is the most likely candidate for vortex induced vibrations has a natural frequency of.3 Hz. This value corresponds closely to the natural frequency for an equivalent cantilever beam fixed at the column connection (.4 Hz). For this mode the modal analysis showed that the deflection at the middle of the span BC (see Fig. ()) was only 6% of the deflection at point A, thus explaining why the swings were only observed at the tip of the cantilever but not elsewhere along the mast. Mode no. Natural period (s) Natural frequency (Hz) Main description of mode Out-of-plane. Lateral movement of cantilever beam In-plane. Vertical movement of cantilever beam Out-of-plane. Both columns moving in phase In-plane motion. Whole structure is moving Out-of-plane motion. Torsion In-plan motion. Whole beam is moving. A Table 1 - Results of the modal analysis of the flight mast. B C D Figure : Mode, f =.33 Hz. The cantilever beam moving up and down. Figure 3: Mode 4, f 4 =4.6 Hz. The whole structure is moving in plane. Using Eq. (1) the critical velocity for vortex shedding can be deduced from the Strouhal number, based on the natural frequency of the excited mode of the structure and the character- 5

6 istic width of the structure. Based on Ref [4] (EN Annex E) the Strouhal number is ~.1 for a square rectangular section with sharp corners. Ref. [5] (ESDU 936) gives a Strouhal number in the range of.11 to.15. Assuming mode, with a natural frequency of.3 Hz to be the critical mode of vibration with regard to across wind induced vibrations and since the width of the section is.4 m, the critical mean wind velocity was found to lie between 7 and 8 m/s, which is a common wind velocity level in Reykjavik. Higher wind speeds, or 1-15 m/s, are required to excite mode 4, and to excite mode 6 wind speed in the range 4-8 m/s are necessary. Mode 4 and 6 involve movement of the whole frame structure. Those modes are not likely to be involved in vortex or wind induced motion, due to lack of correlation in the wind action over the full frame structure. Open non circular cross sections such as U sections are also prone to galloping oscillations [4], but the onset wind velocity is higher than the wind speed necessary to excite mode by vortex shedding, or about 11 m/s..3 Estimation of vortex shedding Vibration amplitude based on Eurocode The vibration amplitude of a structure under the influence of vortex shedding can be estimated by aerodynamics methods. Both the ESDU method in Ref. [5] as well as the methodology given in Annex E in Eurocode 1 (see Ref. [4]), were applied. In the response estimation the cantilever beam was basically assumed to be fixed at the first column connection (i.e. at point B in Fig. ()) and vibrating in mode. As an example, the following equation from Ref. [4] can then be used to estimate the maximum vertical deflection at the tip of the beam (point A in Fig. ()): δ = 1 1 K K c D (6) A,max W lat St Sc Here S t ~.1 is the Strouhal number, S c is the Scruton number, K W is the effective correlation factor, c lat is a lateral force coefficient and D is the vertical dimension of the cross-section as before. Knowing the critical damping ratio, the mode shape and the equivalent mass per unit length of the beam for the mode of vibration makes it possible to evaluate the Scruton number given by Eq.(3) and estimate the maximum tip displacement of the beam due to vortex induced effects. The two methods tested gave similar results. Assuming a critical damping ratio of 1%, the ESDU [5] estimate was 1 cm but the Eurocode [4] estimate was 6 cm. These results, especially the Eurocode result, corresponded well to the measured value of roughly 6 cm as presented in Section 3.. It should be noted that this type of estimation is quite sensitive to the choice of critical damping ratio. Assuming a lower damping ratio of.5%, which is quite reasonable for this type of structure, would result in a considerably higher estimate for the tip displacement of the cantilever, i.e. 1 cm using Eurocode [4] and 15 cm using ESDU [5]. 3 RECORDINGS OF STRUCTUREAL RESPONSE AND WIND DATA 3.1 Instrumentation To confirm the source of the problem and to map the situation before taking any actions it was decided to carry out a measurement program at the site. The frame was instrumented with a uniaxial vertical accelerometer located at the tip of the beam, and wind velocity and wind direction meters above the other supporting column, see Fig. (4). Monitoring of the vibrations and the 6

7 wind also gave the opportunity to compare the behaviour of the light mast before and after installation of countermeasures and thereby to see the effectiveness of such measures. The accelerometer continuously recorded data with a sampling rate of 3 Hz, i.e..76 million values in one 4-hour day. Referring to the natural frequency of mode from the FE-analysis, this corresponded to approximately 14 samples for one oscillation, which was considered sufficient. The wind velocity meter recorded the average wind speed and wind direction for each minute. The wind direction is given as clockwise angle, θ, from the north, i.e. is north, 9 is east, 18 is south, etc. The plane of the light mast faces north and south, respectively. The data were recorded by a data acquisition station located in a box beneath column BE (see Fig. (4)). The data were transmitted via mobile telephone communication to the laboratory for processing. Wind speed and wind direction meter A B C D Vertical accelerometer E 3.4 m F 7.4 m Figure 4. Location of accelerometer, and wind speed and wind direction meters. 3. Recorded data Data were recorded over a period of six days. When there was little wind the measurements were stopped by a phone call and then started again with another phone call. Otherwise the measurements and the data transfer were completely automatic. During these six days 86 hours of data were collected. Fig. (5) displays an example of the recorded time histories along with wind data for 13 hours of continuous recording. The recorded acceleration and the evaluated displacement at the tip of the beam are displayed in the top two figures, respectively, whereas the wind speed and the wind direction are displayed in the two bottom figures, respectively. The time axis is the same for all four graphs. The wind is blowing from south during these 13 hours, as demonstrated by the bottom graph of Fig. (5). From the graphs displaying the response on one hand and the wind velocity on the other, it is clearly seen how the oscillations of the cantilever beam are strongly correlated to the wind speed. Whenever the wind speed reaches the 6 to 8 m/s range the beam starts vibrating intensively. This wind velocity range is in fair agreement with the critical wind velocity predicted by Eq. (1) in Section (.). The maximum displacement during these 13 hours was 6.43 cm, which corresponds to a peak-to-peak motion of almost 13 cm. This was in fact the maximum recorded deflection in the 86 hours of available data. Another way to present the data is to plot the maximum displacement within every minute versus mean wind speed for the corresponding minute, see Fig. (6). This figure shows, that the peak displacements are within cm, except when the wind speed is above 5.5 m/s. Furthermore, the largest peak displacements (the top 5 values) are observed when the wind speed is in the range 7 to 8.5 m/s which again is in fair agreement with the vortex shedding behaviour discussed in Section (). 7

8 Acceleration - (m/s) Displacement - (cm) Wind speed - (m/s) Time - (h) Wind direction - ( ) North West South East North 4 Time - (h) Figure 5. Example of recorded data for 13 hours ( August 5). 8

9 7 6 Peak displacment - (cm) Wind speed - (m/s) Figure 6: Maximum displacment versus mean wind speed within 1 minute window for 13 hours of recorded data from August 5 (see also fig. (6)). 3.3 Data processing Fig. (7a) shows an example of an acceleration time series recorded during 3 hours of logging and Fig. (7b) shows a 1 second long segment from that same time series. The segment displayed is typical of the behaviour observed within the many bands of increased motion of the cantilever beam during the 3 hour observation period. These bursts of motion are induced by vortex shedding as the wind velocity reaches the critical level. From the time series segment in Fig. (7b) it can be seen that the signal is a narrow-band process and nearly a regular sine wave. Therefore, even without frequency analysis, it can be deduced from the time series alone that the natural frequency of the motion was ~.3 Hz. This result was in good agreement with the results from the modal analysis for mode (Table 1). The nature of these bands of acceleration bursts induced by the vortex shedding process is further displayed in Fig. (8), which shows an example of the shape and duration of a complete band of increased motion. As can be seen from the figure, the duration of the gust induced motion is about minutes, from initiation to termination. Power spectral density of the time series in Fig. (8) is displayed in Fig. (9). As the power spectral density function demonstrates, the response is a narrowbanded process dominated by the second mode, or the first vertical mode of vibration. Further system identification gave a natural frequency of.31. The damping estimation gave values between.5% and 1% of critical. The narrow-band nature of the signal simplifies the data processing, since instead of integrating the acceleration time history numerically, which usually calls for data filtering and corrections for linear trend, etc., the deflection at the tip of the beam can be estimated by assuming that the acceleration is a sine wave, which can be analytical integrated as: 9

10 Acceleration - (m/s ) Acceleration - (m/s ) Time (h) a) b) Time (s) Figure 7: a) Data for 3 hrs. (1:-15:, 17 August 5) from the accelerometer b) 1-second-long segment enlarged from the upper graph ACCELERATION (m/s ) TIME (s) Figure 8: An example of a vortex shedding induced acceleration burst. 1

11 4 Periodogram Power Spectral Density Estimate PSD estimate of the recorded signal PSD of a model output One-sided PSD (db/rad/sample) Normalized frequency ( π rad/sample) Figure 9: Power spectral density estimate of the gust induced acceleration time series displayed in Fig. (8). a( t) = Asin( π n t) 1 d( t) = Asin( π n t) ( π n ) where a stands for acceleration as function of the time, t, A is the maximum amplitude of the acceleration when described as sine-wave, d is the deflection as function of time, and n is the natural frequency of mode. This means that multiplying the recorded acceleration values with the constant 1/(πn ) gives a good estimate of the deflection as a function of time. No other data processing was therefore necessary for the acceleration data in order to estimate the deflections. (7) 4 AERODYNAMIC COUNTERMEASURES As mentioned before, the unpropitious rectangular shape of the cross-section of the beam, sharp corners as well as low internal damping combine to promote vortex shedding excitation. Several measures to reduce the effects of vortex shedding have been suggested in the literature and many have been successfully applied (see for instance Ref. [7] and Ref. [8]). Suppression of vortex induced vibration can be achieved using mechanical means by making changes in member properties and structural detailing. Increase in the natural frequency, stiffness or damping, either singly or in combination, will generally reduce the oscillation amplitude. Another approach is to apply aerodynamic means to reduce the amplitude of response by disrupting the fluid processes involved in the vortex formation. The interaction affects the shedding mechanism primarily by interfering with the wake and reducing spanwise coherence. A mechanical solution would generally be used at the design stage whereas a fluid dynamic solution would be considered if in-situ problems were encountered, such as in the case discussed herein. 11

12 Several possible solutions were considered, such as: To stiffen the beam; To add damping to the system, for instance by using a tuned damping device; To smoothen the corners of the cross-sections; To reduce the dimensions of the cross-section gradually from the column top to the end of the cantilever beam; To make holes in the vertical webs of the cross-section of the cantilever beam; To design wind flaps on the beam. In evaluating the possible solutions, issues like cost and change of appearance of the structure were of concern, in addition to the expected efficiency of the method chosen. Eventually it was decided to install cylindrical wind flaps on the top and bottom of the cantilever beam. This rounds of the cross section and may introduce a positive Reynolds number effect. In addition a 5 mm air gap was intentionally designed between the original beam and the cylinders in order to allow the wind to bleed through the section and thereby counteract the formation of vortices. This implementation does not require redesign of the original crosssection and provided an opportunity to try another solution if the vibration amplitude were insufficiently reduced. The chosen solution is shown by drawing on Fig. (1) and by photos on Fig. (11). New wind-flap Originally cross-section Air gap 1 mm 4 mm 5 mm New wind flap 1 mm 5 mm Figure 1: The original U-profile of the horizontal beam in the light mast, and the new cylindrical wind flaps with air gap for reducing vortex excitation. 5 RECORDINGS AFTER INSTALLATION OF COUNTERMEASURES In order to see the effects of the circular wind flaps data was recorded after their installation. The flaps added some weight to the structure and the response frequency of the recorded data was slightly reduced to. Hz. After the installation of the wind flaps data were recorded for a total of 145 hours during 7 days compared to the 86 hours on 6 days before the installation. In order to see the effects of the countermeasures all the data, before and after installing the flaps, were divided into 1 minute intervals. Within each interval the peak deflection of the beam end and the mean wind speed and the mean wind direction were evaluated. The peak deflection versus the 1 minute mean wind speed for all data recorded before the installation is shown in Fig. (1a) and the same for all data recorded after the installation is shown in Fig. (1b). Comparison of the two 1

13 graphs demonstrates that the flaps are effective and reduce the vortex induced motion by about 7%. The displacements recorded after installation of the flaps are all less than 1.5 cm. Wind direction may of course have played some role in how the beam was excited. Fig. (1) displays data from all recorded wind directions for both cases, i.e. before and after the installation of the flaps. (a) (b) Figure 11: The light mast after installation of wind flaps with air cap on the cantilever beam. (a) The cantilever as seen from Northwest. (b) The intersection and the light mast seen as seen from Northwest. 13

14 Peak displacment - (cm) a) Peak displacment - (cm) Wind speed - (m/s) b) Figure 1: Peak deflection versus mean wind speed for 1 minute intervals, based on recorded data. a) Before installation of flaps (all available data) and (b) After installaion of flaps (all available data). 6 CONCLUSIONS A steel frame structure supporting approach lights for air traffic control was installed at Reykjavik airport. The frames substructure, a cantilever beam, showed significant across wind motion in windy weather. Analysis and measurements revealed that this behaviour was due to vortex shedding effects. The phenomena are well documented and the formulation given in codes and the literature was found to give an accurate prediction of the observed behaviour. However, it should be noted that the response estimates depend strongly on the critical damping ratio which is generally not a well known parameter. Countermeasures in the form of cylindrical wind flaps on the top and bottom of the cantilever beam to reduce the induced vibration amplitude were proposed and implemented. The recorded motions before and after installation of the flaps clearly indicate significant reduction in the vibration amplitude of the cantilever light mast. Recorded peak deflections were roughly 6 cm before the installation of flaps but were reduced to less than cm after the implementation. 14

15 REFERENCES [1] M. Matsumoto. Vortex shedding of bluff bodies: A Review, Journal of Fluids and Structures, 13 (7-8), , [] J. D. Holmes, Wind loading of Structures, Spon Press, 1. [3] R. Höffer. Processes of buffeting and vortex forces in turbulent wind. Journal of Wind Engineering and Industrial Aerodynamics, 64 3-, [4] Eurocode 1: Actions on Structures - Part 1-4. CEN TC 5, pren (E), 4. [5] Engineering Sciences Data Unit (ESDU) Data Item Numbers: Structures of noncircular cross section: dynamic Response to Vortex Shedding, 936. [6] H. Ruscheweyh, M. Hortmanns and C. Schnakenberg Vortex-excited vibrations and galloping of slender elements Journal of Wind Engineering and Industrial Aerodynamics 65 (1996) [7] M. M. Zdravkovich. Review and classification of various aerodynamic and hydrodynamic means for suppressing vortex shedding. Journal of Wind Engineering and Industrial, 7 (), , [8] R. Dutton and N. Isyumov. Reduction of tall building motion by aerodynamic treatments. Journal of Wind Eng. and Industrial Aerodynamics, 36 (1-3) , 199. [9] SAP, Version 1, Integrated Software for Structural and Analysis and Design. Computer & Structures Inc. Berkeley, California, USA. 15