Simulating the Conductor under Downburst Winds

4 Aerodynamic Damping of Transmission Line Conductors under Downburst Winds

4.3 Evaluation of the Aerodynamic Damping by CFD

4.3.3 Simulating the Conductor under Downburst Winds

As the technique, illustrated in Figure 10, showed reasonable accuracy of estimating the aerodynamic damping and the conductor response under a steady wind, it is used in this section to obtain the conductor response under downburst winds. Velocities associated with a downburst can be decomposed into a non-stationary mean component and a turbulent component. Mean component is extracted from the CFD simulation performed by Hangan and Kim (2007) and scaled by the technique described by Shehata et al. (2005) to represent an event of 500 m diameter with a jet velocity equals to 45m/s. Distance, R, and angle Ɵ, which defines the relative location between the downburst and

the conductor, illustrated by Figure 3.1, are chosen to be 550 m and 0.0ᵒ, respectively. This represents the location that induces maximum conductor loads as indicated by Kim and Hangan (2007). Figure 4.14 shows a time history of the mean downburst velocity component at the conductor midpoint. The figure shows that the mean velocity needs approximately 250 seconds to pass the conductor. Simulating the entire 250 seconds using LES requires large computational demands. Therefore, only 80 seconds near the peak mean velocity, represented by the dotted line in Figure 4.14, are chosen the simulation. Turbulent velocity component is generated using the method indicated by Chen and Letchford (2004a,b) and Chay et al. (2006), where an evolutionary power

0 5 10 15 20 25 30 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time (Sec) x (t )/ xm e a n

Displacement response from the CFD Fitting with the Log. Dec. of Damping

spectral density is used to describe the variation of the turbulent component along the time. Power Spectral Density (PSD) of von Karman spectrum is normalized and used in generating the fluctuating components. Turbulent Intensity is taken equal to 11% which is compatible with those reported by Holmes et al (2008) and Chan et al (2008) for real events. A cut off frequency equals to 0.5 hz is used in generating the turbulent component. Such a frequency is checked to be greater than the frequency of the 1st out of plane conductor mode, f1, which is calculated using Equation 4.19, and illustrated by Figure 4.15. The generated turbulent component is added to the mean component in order to obtain the total velocity at the span midpoint, as shown in Figure 4.16. CFD simulation is performed for the 80 seconds shown in Figure 16. The simulation consumed 312 hours to solve for 640,000 time steps utilizing 24 CPUs. The results are obtained in terms of the displacement response and are plotted using the continuous line shown in Figure 4.17. Such a response represents the total displacement response which can be decomposed into a mean component, a background component, and a resonant component. Resonant component, xr(t), is the only component affected by the aerodynamic damping. Therefore, such a component is extracted and plotted using the dotted line shown in Figure 4.17. The extraction is performed by calculating the summation of the mean and the backgrounds component,xm bg ( )t , as indicated by Equation 4.31, and subtracting it

from the total response. The proposed expression for the aerodynamic damping, given by Equation 4.18, is utilized to obtain the aerodynamic damping. The obtained aerodynamic damping shows variation with the time due to the change of the incoming mean velocity, as shown by Figure 18. The obtained damping is utilized in calculating the conductor response using step by step Newmark’s method. More details about Newmark’s method can be found in Bathe (1996). The total displacement response resulting from Newmark method is plotted by the dashed line in Figure 4.17. The resonant component is also extracted from the total response using the same way that is employed with the CFD results. Resonant displacement component is plotted using the dot-dashed line shown in Figure 4.17. It is clear from Figure 4.17 that both the total and resonant displacement resulting from employing the proposed aerodynamic formula in Newmark method and those resulting from the CFD have an excellent agreement. Such an agreement indicates

the capability of the proposed formula for predicting the aerodynamic damping under downburst winds. 2 x v m bg 1 .V (t).D.L .I 1 x (t) 2 K (t)     Where: 1 2 v v 1 0 2 I_   .(n).dn 



K1(t): modal stiffness for the first mode =(2.π.f1(t))2.M1, M1: modal mass for the first mode =91.3 N/(m/s2)

Equation 4.31

Figure 4.14 Time history of the non-stationary mean velocity component at the conductor midpoint

Figure 4.15 Variation of the 1st natural frequency with time

0 50 100 150 200 250 0 10 20 30 40 50 60 Time (sec) V e lo c it y ( m /s ) Downburst event Studied time interval

0 10 20 30 40 50 60 70 80 90 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 Time (Sec) F re q u e n c y f1 ( h z )

Figure Figure 4.16 Figure 4.17 Figure 4.18 0 -10 0 10 20 30 40 50 60 70 V e lo c it y ( m /s ) 0 -2 0 2 4 6 8 X (t ) (m ) X

tot(t) from the CFD

16 Mean, turbulent and total wind velocity at the conductor midpoint

Total and resonant displacement responses resulted from the CFD and from employing the recent damping formula

18 variation of the aerodynamic

10 20

(t) from the CFD