1. 1. IN-VENTO 2014 XIII Conference of the Italian Association for Wind Engineering 22-25 June 2014, Genova, Italy Performance prediction and validation of a tuned liquid column damper with internal baffles Stefano Cammelli1 , Yin Fai Li2 and Leejay Hsu2 1 BMT Fluid Mechanics, Teddington, UK 2 BMT Fluid Mechanics, Kuala Lumpur, Malaysia Corresponding author: Stefano Cammelli, scammelli@bmtfm.com Abstract During the early design stages of a relatively slender 42-storey high-end residential building located in the Middle East, a series of high-frequency force balance (HFFB) wind tunnel tests highlighted that the highest occupied floors could experience wind-induced motion which depending on the inherent damping of the finished structure had the potential to exceed standard industry occupant comfort criteria. In order to mitigate these excessive vibrations, a Tuned Liquid Column Damper (TLCD) was proposed for this building. The performance prediction and validation of the behaviour of such device involved: an initial campaign of full scale measurements to validate frequencies and inherent damping of the structure near completion; a series of shake table tests employing a 1:20 scale physical model; and a final full scale extrapolation study using Computational Fluid Dynamics (CFD). 1 Introduction The location of the site of the proposed development considered within this technical paper was approximately 1 km from the Mediterranean coastline, with the immediate surrounding area consisting of densely populated low to mid-rise urban sprawl. The 50-yr return period mean-hourly basic wind speed for the region was ~25 m/s (10 m reference height in z0 = 0.03 m) and the characteristic product of the local wind climate was ~4. The height of the building was ~180 m, with a ~22 m ~44 m rectangular floor plan. The lateral stability of the tower was provided by a central reinforced concrete core. The numerically predicted structural frequencies of the three fundamental modes of vibration of the building were: 0.19 Hz, 0.26 Hz and 0.53 Hz, with the first two describing pure sway of the structure along the principal axes of the central core (exponent of these mode shapes were ~1.5) and the third one being torsional. The damper study, which this paper is focused on, was part of a wider range of wind engineering consultancy services which included: wind climate study, pedestrian and terrace / balcony level wind microclimate study, overall wind loading study and cladding pressure study. 2 On-site full scale measurements When the construction of the super-structure of the tower approached its completion and before commencement of the installation of the cladding, a campaign of on-site full scale measurements was conducted to detect some of the key structural parameters of the building; in order to achieve this, the 34th level of the tower was instrumented with a number of low-range high-resolution accelerometers with the aim of acquiring a large number of ambient data records. Before commencement of post- processing, the different time-histories of recorded wind-induced accelerations have been digitally low-pass filtered at a frequency of 1 Hz to remove high-frequency noise content which due to the nature of the site have inevitably been picked up during the measurements.
2. 2. Cammelli et al. Performance prediction and validation of a TLCD with internal baffles The different time-histories have then been analysed making use of the so-called random decrement (RD) technique (Tamura et al., 2000 and Li et al., 1998 & 2003), which enabled the random and chaotic part embedded in the actual measured signals associated with the excitation from the atmospheric turbulence to be fully removed, revealing the far more regular signature left by the structure itself. Subsequently, modal identification techniques (Tamura, 2005) were applied to the RD signatures in order to identify the frequencies and damping of the tower during construction. The first two modes of vibration of the structure (for the specific construction stage the tower was at during monitoring) have been found well aligned with the two principal axes of the structural core of the building and their frequencies in very good agreement with the prediction of the finite element model. The level of inherent structural damping associated with these two modes of vibration of the structure was found to be in the region of ~1.0% of critical. It should be noted that during the period of monitoring the strength of the wind storms that passed through the region was lower than what expected for a typical 1-yr return period event. 3 Concept design of the TLCD A detailed review of the HFFB wind tunnel tests results, performed during the early design stages of the design, revealed that the motion along the weak direction of the building was the key contributor to the peak combined wind-induced acceleration. It was also estimated that, in order to achieve the desired level of occupant comfort at the highest occupied levels of the building for both the more frequent (1-yr return period) and the less frequent (10-yr return period) wind events, a total damping of ~2.0% of critical in the first mode of vibration of the structure was required. Amongst the different types of auxiliary damping devices which could be installed on a tall building, tuned liquid dampers (TLDs) are the most cost-effective. The preliminary design of the damper was conducted following the guidance provided in Vickery (2006). It was estimated that the damping system employed would require a total effective mass of ~80,000 kg, equating to ~0.5% of the modal mass of the first mode of vibration of the tower, and a natural frequency of ~99.5% of the first mode frequency of the building. These estimates were made assuming an efficiency of the damping device of ~75%. Deviation from zero main damping was also duly taken into consideration during concept design. Due to the relatively slender nature of the building here examined (the slenderness ratio of the building in its weak axis was ~1:9), the more compact tuned liquid column damper (TLCD) solution was adopted from the very start of the concept design study. The TLCD damper comprises an auxiliary vibrating system consisting of a column of liquid moving in a tube-like container. The restoring force is provided by gravity, whilst the energy dissipation is achieved at the baffles installed within the horizontal duct. The above estimates and considerations led to the selection of a pair of identical TLCDs in the form of a U-tube water tank to be installed just below the roof level of the building. The internal dimensions (i.e. exclusive of the thickness of the RC wall) of one of the two identical TLCDs are reported in Table 1 below: Table 1. Internal dimensions of one of the two identical TLCDs. Dimensions (mm) Length of the U-tube, Lo 7600 Internal width of each riser, W 1650 Internal breadth of the TLCD, B 4925 Internal height of the horizontal duct, H 1100 Internal free board in each riser, R 900
3. 3. Cammelli et al. Performance prediction and validation of a TLCD with internal baffles The overall arrangement of one of the TLCD is illustrated in Figure 1 below: Figure 1. Internal arrangement of one of the two identical TLCDs. It was estimated that the internal headroom for sloshing dR during a typical 10-yr return period wind event was ~1000mm. It should be noted that the number and location of the required internal baffles was at this stage of the design only indicative. 4 Detail design of the TLCD Physical model testing The concept design of the damper was tested in the 6 degree-of-freedom (6DOF) shake table facility of the Department of Civil Engineering of the University of Bristol. The aim of the model testing was not only to verify the key resulting parameters of the concept design but also to derive the optimal geometry and internal arrangement of the baffles within the TLCD. 4.1 Experimental setup A 1:20 model of the damper was constructed in Plexiglas. The construction of the damper allowed up to five interchangeable porous screens to be inserted within its horizontal duct. The working fluid in the model was water. The model damper was mounted on the shake table via a piezoelectric load cell (see Figure 2). The motion of the shake table was programmed according to the solution of the equation of motion of the first mode of the actual building at various levels of structural damping computed based on wind tunnel measurements. The motion of the shake table was then measured simultaneously with the load cell signal using non-contact displacement transducers. Figure 2. Experimental setup of the 1:20 TLCD model. Model of the TLCD Load cell Shake table
4. 4. Cammelli et al. Performance prediction and validation of a TLCD with internal baffles A video of the model scale experiment is presented in Figure 3. Figure 3. Video of the physical model scale shake table testing (press on the still image to run). 4.2 Results and discussions The energy dissipated within the model can be derived from the simultaneous measurements of the base force reaction and motion of the damper as follows: dtxFFdxW (1) where xxF ,, denotes the measured force, displacement, and time derivative of the displacement (i.e., velocity). The equivalent damping ratio of the TLCD, i.e. the damping ratio of a non-viscous device that would dissipate the same amount of energy per cycle of vibration as a perfectly viscous device at the same amplitude, can be defined as follows: 2 2 22 22 2 1 2 1 2 2 x xF nnn eq neqeq mdtx dtxF mdtxm dtxF dtxmdtxcdtxF (2) where 22 ,,,, xxFneq m are the damping ratio expressed as fraction of critical, mass (in kg), and natural circular frequency (in rad/s) of the system, covariance between measured force and velocity (in Nm/s) and variance of velocity (m/s). It should be noted that the measured ratio of the two covariances is not dimensionless and had therefore to be converted to full scale in order for the equation above to apply. A dimensional analysis revealed that the scaling of the 2 2 x xF term would follow the geometric scale of the model raised to the power of 2.5, i.e.: 2 25.2 2 x xF n L eq m NR (3) where LR and N are the geometric scale and the number of TLCDs installed in the building. Eq. (3) therefore represents a direct relationship between the equivalent damping ratio of the full scale damper system and the model scale 2 2 x xF term, which was measured as a function of standard deviation of excitation displacement.
5. 5. Cammelli et al. Performance prediction and validation of a TLCD with internal baffles In the case of a TLCD installed on a building with fixed structural frequencies and inherent damping, the standard deviation of excitation amplitude during a wind event is controlled by total system damping, which is in turn contributed significantly by the added damping of the TLCD itself. Figure 4 plots the equivalent added damping ratio versus total system damping. It is clear from this graph that for all configurations of porous baffles tested, the equivalent damping generally increased with excitation magnitude, or decreased total damping. Configurations with a larger number of porous baffles generally showed higher energy dissipation at low amplitude, as more energy was dissipated when water moved across the screen. While, on the other hand, configurations with many baffles had the potential to prohibit the build-up of vibration amplitude of the water, hence hindering the damping performance. The actual damping performance, taking into account the inherent damping of the structure, is denoted in Figure 4 by the intersection points between different baffle configurations and different levels of inherent damping. From this plot it is clear that both the 3 baffles and the 5 baffles configurations gave rise to an equivalent damping ratio of ~1.2% of critical which together with a ~1.0% of inherent structural damping corresponded to ~2.0% of critical of total system damping. Figure 4. TLCD performance curves (75% porous baffles). The geometrical arrangement of the best performing baffle arrangement (75% porous) is presented in Figure 5. Figure 5. Arrangement of a 75% porous baffle (dimensions in millimetres).
6. 6. Cammelli et al. Performance prediction and validation of a TLCD with internal baffles 4.3 Comparison with the solution of 2DOF equation of motion In order to further inspect and understand the measured results in terms of total system damping performance, the time domain solution of equation of motion based on Clough and Penzien (1993) for the first mode has been extended to a 2 degree-of-freedom (2DOF) system to incorporate the addition of the TLCD. In order to solve the equation of motion in the time domain the knowledge of the internal damping of the TLCD is required. The internal damping of the damper system with optimal baffle configuration was evaluated via a series of free decay model testing. The free decay of base shear force was measured after the damper was subjected to a step excitation. The internal damping was calculated by applying the logarithmic decay to the measured time histories. It was found that the damping generally reduces with amplitude and, for the operating conditions here examined (10-yr return period wind event), the damping is of the order of ~3.7% 3.9% of critical. A sample of a free decay time history is shown in Figure 5 with damping estimates for different section of the time history. Figure 5. Example of free decay force time history of the physical model of the TLCD. The 2DOF equation of motion was solved for the measured wind excitation, damping ratio and frequency of the TLCD for each time step and the response with and without the TLCD is presented in Figure 6. The peak acceleration response of the primary mass, i.e. the building itself, has reduced from ~21.5 milli-g to ~15.5 milli-g, which is equivalent to an increase in total system damping from ~1.0% of critical to ~1.9% of critical. Figure 6. Solutions of the equation of motion in the time domain, with and without TLCD.
7. 7. Cammelli et al. Performance prediction and validation of a TLCD with internal baffles 5 Detail design of the TLCD CFD study The 1:20 scale physical model testing inevitably left the authors of this technical papers with some uncertainties over the potential for scale effects to affect the performance of the full scale TLCDs. In order to try to quantify these, a number of CFD studies have been undertaken. 5.1 Analysis software The multi-purpose CFD software OpenFOAM (www.openfoam.com) was used for the study. OpenFOAM is an open source CFD package which has gained a large user base in commercial and academic applications which features a wide variety of validated solvers in the area of oscillatory and sloshing flow. 5.2 Geometry and grid The numerical work was focused on a single TLCD, the internal volume of which was discretised with a 3D structured mesh. Areas of particular interest were modelled with a higher level of geometrical detail, such as the regions around each baffle. Figure 7 shows the complete structured mesh of a single TLCD. The green regions are open to atmospheric pressure. The blue regions represent areas of high mesh density near the baffles: properly capturing the flow behaviour in these regions was a high priority. Figure 7. Perspective view of the spatial mesh. 5.3 Porous regions The baffles were modelled as anisotropic porous regions using the Darcy-Forchheimer approach. This model is composed of two parts: a viscous loss term known as the Darcy permeability (first term on the right hand side of Eq. (4)) as well as an inertial loss term known as the Forchheimer term (second term on the right hand side of Eq. (4)): ( ) (4) Where Si is the volumetric source term added to the momentum equations of the baffle zones, Dij and Fij are the prescribed porous media tensors, is fluid dynamic viscosity, is fluid density, Uj is the jth component of the velocity vector, and is the velocity magnitude.
8. 8. Cammelli et al. Performance prediction and validation of a TLCD with internal baffles 5.4 Boundary conditions Rough walls with a no-slip condition (u, v, w = 0) were assumed for all internal surfaces. A turbulent viscous wall function and mean roughness height of 0.025mm (uniform sand grain roughness) were used to simulate the surface roughness of the smooth-finish concrete walls in the full scale simulations of the TLCD. The lateral pressure release openings were modeled as constant atmospheric pressure openings in the CFD grid. 5.5 Turbulence model The standard k- turbulence model was employed in the CFD simulations when assessing the internal flow of the water tank in order to capture recirculation and eddy phenomena (such as the recirculation near the inside corners as illustrated in Figure 8). This turbulence model is one of the most widely used turbulence models for its combination of computational speed and accuracy. Figure 8. Recirculation near the internal corner of the TLCD. 5.6 Solver OpenFOAMs interDyMFoam solver was used for the study. This solver is compatible with 2-phase, isothermal, incompressible, immiscible flows. InterDyMFoam uses a finite volume approach to represent the Navier-Stokes equations, in which each cell in the computational mesh is assigned a single value for each fluid property (i.e. velocity and pressure) that represents the average of these properties over the whole volume of the cell. 5.7 Methodology A 1:20 scale numerical model was initially set-up with the aim of generating results which could have been directly compared with the ones obtained from the physical model testing campaign. A number of mesh independence studies was conducted to determine an optimal computational mesh, as well as to locate potential areas which would benefit from mesh refinement (e.g. regions in which vortices and recirculation were expected, see Figure 9). Once the 1:20 numerical model was finalised, the results were compared to experimental shake table results before performing full scale computational analysis.
9. 9. Cammelli et al. Performance prediction and validation of a TLCD with internal baffles Figure 9. Streamlines under free decay motion. The free-decay logarithmic decrement approach was used to quantify the performance of each simulated TLCD. This method included the excitation of the CFD model with a sinusoidal input wave until the system reached a periodic steady state. The forced movement of the TLCD was then stopped, and the decay of the overall net force was measured over time. The net force measured included the contribution from dynamic pressure acting on the walls and baffles of the TLCD in the direction of the first mode of vibration of the tower. Comparison of damping performance (3 baffles configuration), as simulated in CFD and experimentally gathered in the shake table experiments (~4.2 4.5% and ~3.7 3.9% respectively), was satisfactory given the complex nature of unsteady multi-phase flow (see Figure 10). Figure 10. Example of free decay force time history of the model TLCD, CFD vs. physical testing. Numerically computed studies on a full scale TLCD showed that the damping of the device itself during operating conditions (10-yr return period wind event) decreased by ~10%. This was believed to be due to the different physics controlling the energy dissipation at the two scales: at model scale, in fact, the contribution coming from viscous forces is expecting to be larger than at full scale where, on the other hand, damping at full scale will be more dominated by inertial forces and recirculation within the TLCD. By: Yin Fai Li Date: 18-Jun-13 Status: Final Drawing no.: 431130-FIG-18 431130 Skygate Tower
10. 10. Cammelli et al. Performance prediction and validation of a TLCD with internal baffles 6 Conclusions A pair of identical TLCDs has been designed to mitigate the excessive wind-induced motion of a 42- storey residential tower located in the Middle East. Their concept design, based on an initial desktop study approach, has been subsequently validated via a series of scale model tests performed on a shake table which in turn allowed an optimal configuration of internal porous screens to be obtained. The internal dissipation of each TLCD, in the form of equivalent viscous damping ratio, was extracted from the shake table experiments using energy dissipation considerations as well as directly solving the 2DOF equation of motion: these two analyses led to very consistent results. Finally, the performance of the full scale TLCDs has been evaluated using CFD in an attempt to gain insights on the differences between model scale study and full scale implementation. 7 Acknowledgments The authors of this paper would like to thank Dr John Macdonald from the Department of Civil Engineering of the University of Bristol for his support during the course of the physical model testing campaign and Professor Michael Graham from the Department of Aeronautics of the Imperial College London for his input in the CFD work. References Clough, R.W. and Penzien, J. (1993). Dynamic of Structures. 2nd Ed. McGraw Hill. Li, Q.S., Fang, J.Q, Jeary, A.P., Wong, C.K. (1998). Full Scale Measurements of wind effects on Tall buildings. Journal of Wind Engineering and Industrial Aerodynamics Vol 74-76, pp 741-750. Li, Q.S., Yang, Ke., Wong, C.K., Jeary, A.P. (2003). The effect of amplitude-dependent damping on wind induced vibrations of a super tall building. Journal of Wind Engineering and Industrial Aerodynamics Vol 91, pp 1175-1198. Tamura Y. (2005). Damping in buildings and estimation techniques. Proceedings of APCWE-VI, Seoul, Korea. Tamura, Y., Suda, K., Sasaki, A. (2000). Damping in Buildings for Wind Resistant Design. International Symposium on Wind and Structures for the 21st Century, 26-28 Jan, Cheju, Korea. Vickery, B.J. (2006). On the Preliminary Design of Passive Tuned Mass Dampers to Reduce Wind Induced Accelerations. Australasian Wind Engineering Society Workshop, Queenstown, New Zealand, February.