The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7) Shanghai, China; September 2-6, 2012 Wind tunnel measurements of aeroelastic guyed mast models a, Tomasz Lipecki b, -Borowa c a Lublin University of Technology, 40 Nadbystrzycka St, Lublin, Poland b Lublin University of Technology, 40 Nadbystrzycka St, Lublin, Poland c Lublin University of Technology, 40 Nadbystrzycka St, Lublin, Poland ABSTRACT: Dynamic response of guyed masts models to the wind action in the wind tunnel has been analyzed in the paper. Accelerations and forces in guys have been measured. Spectra of the response have been calculated. The influence of the wind structure on the response has been analyzed. The results obtained with experiments have been compared with the ones coming from numerical analysis. KEYWORDS: guyed masts, wind action, wind tunnel, boundary layer, dynamic response. 1 INTRODUCTION Analysis of the dynamic response of guyed masts has been presented in this paper. The problem can be approached in two ways, experimentally or numerically. The measurements can be made in-situ or on models in wind tunnel. Here in this paper, the results from the wind tunnel measurements of two guyed masts models have been presented. Triangular and rectangular shaft masts have been modeled and measured. The research consists of measurements of time series of accelerations in selected points located on the mast models and measurements of force time series in guys. Three cases of approaching flow structure have been used in experiment. Various wind profiles, turbulence intensity profiles and power spectral density functions have been obtained with sets of elements forming boundary layer. Various angles of wind attack have also been considered. The results obtained with experiments have been compared with the results coming from numerical analysis. 2 RESEARCH DESCRIPTION The experiments have been carried out in the boundary layer wind tunnel of the Wind Engineering Laboratory in Cracow, Poland. The scheme of the working section of the wind tunnel has been presented in Figure 1. Figure 1. Working section of the wind tunnel with model location. 1152
The influence of wind characteristics such as vertical mean wind speed profiles, turbulence intensity profiles and wind PSD functions on the response of structure models has been examined. The measurements of masts models have been carried out for three setting of elements forming boundary layer. The settings have been selected with most varying values of obtained wind structure parameters. The following cases, out of 45 all tested ones and 6 previously used in wider analyses, have been selected for this research: bz2kl0 zigzag barrier of 20 cm height, no blocks (profile nr 1); it10bz3kl0 T-shape cross-section spires of 100 cm height, 30 cm zigzag barrier, no blocks (profile nr 3); iv10bz4kl20 triangular cross-section spires of 100 cm height, 40 cm zigzag barrier, blocks set at 20 cm (profile nr 6). Vertical mean wind profiles measured in the wind tunnel have been approximated with the power-law formula [1]: u z k z for z zmin (1) where k and are the values obtained with least square method, z is the height above wind tunnel floor measured in cm. The wind profile coefficients have been reduced to make the wind speed at the height of 70 cm equal in each mean wind speed profile. The wind speed obtained with the formula (1) is expressed in m/s. The calculated values of wind speed profile parameters have been presented in Table 1. Table 1. Parameters for selected vertical mean wind profiles. Profile Symbol k z min 1 bz2kl0 4.26 0.20 1.70 3 it10bz3kl0 2.99 0.28 0.85 6 iv10bz4okl20 0.93 0.55 0.07 Similar procedure has been used in approximation of other wind structure parameters. The more detailed description of the research on wind structure in the wind tunnel of Cracow University of Technology is presented in [2]. Figure 2. Guyed masts model in the wind tunnel. 1153
The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7) Shanghai, China; September 2-6, 2012 Guyed masts have been placed vertically on rotating table in the working section of the wind tunnel. The response of two models have been measured: M1 (m_tr_2x2_circ) of triangular shaft cross-section (three planes of guys); M2 (m_kw_2x2_circ) of rectangular shaft cross-section (four planes of guys). The view of the M1 model in the wind tunnel is presented in Figure 2. Both models are made from steel members of circular cross-section. Shaft legs are made of the 2 mm diameter rods, bracing of rods of the 1 mm diameter. Each model is supported at the base (free rotations) and with use of two levels of guys made of steel wire of the 0.25 mm diameter. The guys are connected to the shafts at the levels of 40 cm and 90 cm with the guy espectively. The side dimension of each shaft cross-section is equal to 2 cm. The overall height of each model is 1 m. The analysis has been made for various rotations of models with angle of wind attack varying the case of the triangular model. The exemplary shaft rotations with mean wind direction and the directions of measured accelerations have been presented in Figure 3. Figure 3. Exemplary rotations of triangular cross-section shaft mast: 0 left, 120 right. The measurements have been made at 16 mean wind speed steps changing from 0 m/s to about 20 m/s. 2.1 Accelerations The measurements of acceleration have been made in two perpendicular directions (along and across wind tunnel in base position) at two levels of each model: at the top (h=100 cm) and in the middle of upper span (h=60 cm). Figure 4. Accelerometers mounted at the mast model structure. 1154
-002 connected to the PULSE measuring system have been used. The instrumentation of the model in wind tunnel is shown in Figure 4. The measurements have been made with the sampling frequency 8192 Hz. The saved time series lasted for about 20 s for each analyzed case. The accelerations have been measured simultaneously with measuring of forces in guys and mean wind speeds. 2.2 Forces in guys Hottinger S2/100 force transducer has been used in these measurements. The range of measured forces is - for this transducer. Time series of forces in guys under wind action have been measured. Forces in both upper (og) and lower (od) guys have been measured. Various characteristic positions (rotations) of the mast have been considered, allowing analysis of the guys at the windward and leeward sides of the mast. The measurements have been made simultaneously with measurements of accelerations with use of accelerometers, wind speed fields with use of hot wire anemometers and mean wind speeds with use of pressure scanner. Simultaneous recording allows further analysis of correlations of wind speeds in turbulent flows and the effects of its action on guyed masts. The mounted force transducer has been shown in Figure 5. Figure 5. Force transducer for measuring forces in guys. 3 RESULTS Time series of the accelerations at selected points of the models have been obtained. Accelerations in two perpendicular directions at the top of the model M1 are presented in Figure 6. Figure 6. Exemplary time series of accelerations: along mean wind (left) and cross-wind (right) components. 1155
The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7) Shanghai, China; September 2-6, 2012 There have been shown exemplary time series of accelerations in Figure 7 for the steps of mean wind speeds selected out of 16 measured ones. There are 6 s views on the left and 0.5 s zooms on the right presented for each time series. Figure 7. Along wind accelerations for triangular shaft model at the top of the structure (od_m_tr_2x2_circ-bz2kl0). Spectral analysis of the measured variation of acceleration has been made as the next step of the research. Power spectral density functions have been calculated with use of the HBM Catman software. PSD functions have been presented in graphs. Exemplary graphs, respective to the time 1156
series presented previously, have been shown below. Whole calculated spectrum is presented on the left, and 100 Hz zoom is shown on the right in Figure 8. Figure 8. PSD functions for along wind accelerations measured at the top of triangular shaft model (od_m_tr_2x2_circ-bz2kl0). Similar graphs, as for the accelerations, have been made for the forces in guys of the mast models. Exemplary graphs of force time series for the lower guy have been presented in Figure 9. There are 20 s long time series presented on the left, and 1 s zooms shown on the right. 1157
The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7) Shanghai, China; September 2-6, 2012 Figure 9. Time series of forces in lower windward guy of triangular shaft model (od_m_tr_2x2_circ-bz2kl0). Spectral analysis of the guy force variations has been made. Exemplary graphs of PSD functions, respective to the time series of force variations in guys, have been presented in Figure 10. The graphs of PSD functions are shown in the same manner as for accelerations. 1158
Figure 10. PSD functions for force variations of lower guy in triangular. The results have been compared with the ones obtained with use of FEM calculations. Own software [3, 4] based on commercial system ALGOR has been used. The wind action has been modeled according to quasi-steady theory [5]. Displacements in selected points of mast structure have been obtained. Exemplary time series of displacements coming from calculations at the top of the mast model have been presented in Figure 11. 1159
The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7) Shanghai, China; September 2-6, 2012 Figure 11. Exemplary time series of displacements of two perpendicular displacements on the top of the mast model. Double differentiation has led to accelerations. Exemplary time series of along wind accelerations have been presented in Figure 12. Figure 12. Exemplary time series of along wind accelerations: 30 s long time series (left), 6 s zoom (right). Amplitudes of accelerations and their standard deviations have been compared with results obtained with measurements at the 8 th wind speed level from wind tunnel tests (Fig. 13). The wind speed in numerical analysis has been set approximately equal to the mean wind speed in measurements at this mean wind speed step (v 10 m/s). Figure 13. Exemplary time series of along wind accelerations from measurements at 8 th mean wind speed step. The obtained time series of accelerations from numerical analysis are in good accordance with the results from measurements in the wind tunnel. Amplitudes of accelerations in numerical analysis reach about 1.6 m/s 2. Similar values have been noticed in the wind tunnel tests. Amplitudes are usually only slightly higher in measurements than the ones obtained in numerical analy- 1160
sis. There may be values of accelerations exceeding 3 m/s 2 coming from the stronger wind gust observed at short period of time. However, this is not changing the overall picture significantly, and the preliminary verification is proved for measurements versus numerical analysis. 4 CONCLUSIONS The following conclusions can be drawn out of the presented results: Amplitudes of accelerations grow rapidly to about 2 m/s 2 in the case a4. Then they are getting smaller to about 1 m/s 2 and in the next steps they constantly grow with the wind speed increase. There is one dominating frequency in the case a4 observed in the graphs of time series of accelerations. This frequency can also be observed in the PSD function graphs. The results of measurements allow us to mark the wind speed in this case as the critical one. The graphs of guy forces show both frequencies that have been observed in acceleration graphs for shafts and new frequencies that can be distinguished, as the ones referring to guys vibrations only, since they have not been observed before. Wind parameters have significant influence on guyed masts response. Accelerations measurements allow recognition of mode shapes of vibrations. Different shapes of shaft cross-section of masts only slightly affect the wind field behind models in comparison to the flow without mast models placed in the wind tunnel. High slenderness of the shafts may be responsible for this result. 5 ACKNOWLEDGEMENTS The work was prepared within Ministry of Science and Higher Education research project No. N506 267337. 6 REFERENCES 1 A. Flaga,, Arkady, Warszawa, 2008. 2 J. T. Lipecki, E. -Borowa, Research on Wind Structure in the Wind Tunnel of Wind Engineering Laboratory of Cracow University of Technology, Journal of Physics: Conference Series 318 (2011) 072003, doi: 10.1088/1742-6596/318/7/072003 3. 4 th Symposium "Environmental Effects on Buildings and People", Cracow, Lublin, Susiec, June 16-18, 2004 4. the 4th European & African Conference on Wind Engineering, July 11-15, 2005, Prague, Czech Republic 5 A. Flaga, Quasisteady theory in aerodynamics of slender structures, Sonderforschungsbereich 151 Tragwerks- any 1161