Vertical Wind Velocity Distribution in Typical Hilly Terrain

Transcription

1 Vertical Wind Velocity Distribution in Typical Hilly Terrain Wen-juan Lou 1), * Hong-chao Liang 2), Zheng-hao Li 3), Li-gang Zhang 4) and Rong Bian 5) 1), 2), 3) Institute of Structural Engineering, Zhejiang University, Hangzhou, Zhejiang, 3158, China 4), 5) State Grid Zhejiang Economic Research Institute, Hangzhou, Zhejiang, 31, China 2) lianghczju@126.com ABSTRACT In this paper, the distribution of vertical wind velocity in typical hilly terrain was studied in consideration of varied influence factors, including the height and the slope of the hill and the length of the corresponding ridge. The vertical wind velocity field of a typical steep hill, measured by a wind tunnel test was established as a benchmark for verifying the CFD simulation method. Then the numerical method was used to study the distribution of vertical wind velocity, considering several topographic features. The numerical results indicated that the vertical wind velocity on the upwind slope, could be up to over 6 percent of the income flow wind speed and the maximum vertical wind velocity was located at about two thirds height of the hill. The profiles of the vertical wind velocity ratio at the top of the hill satisfied the exponential law perfectly and the equations were fitted to profiles with the change of hill height and slope. In the case of 9 wind angle, the maximum updraft velocity on upwind slope and mountaintop both increased with the length of ridge. While at wind angle, the maximum updraft velocity on upwind slope decreased with the length of ridge. 1. INTRODUCTION Vertical wind speed was unfavorable to transmission lines or other structures. Only in the flutter stability analysis of the large span bridge, wind attack angle was taken into consideration. General civil engineering structures tended to neglect the disadvantages of updraft wind in hilly terrain. Researches of hilly terrain wind field had been started since the 8's of last century. Jackson and Hunt (1975) analyzed the wind speed distribution of a two dimensional smooth hill. And developed an analytical method to predict speed-up over it. Since the model s slope was smooth, vertical wind velocity component in the wind field was small, and it s only regarded as disturb to the horizontal wind speed. Taylor (1984) made extensions to above formulas to calculate the velocity of wind speed at different heights. In Weng s work (2), the influence of roughness was introduced to the calculation process, which made the theoretical method became

2 more mature. Up to the 9's, considerable mountain measurements had been accomplished. Taylor et al (1987) analyzed and summarized those researches, and came to a conclusion that the theoretical calculation results of speed-up factor was quite different with the measured results at the near surface. The numerical simulation and wind tunnel tests were compared by Bitsuamlak (24), It came to the conclusion that the numerical simulation results can match well with the experimental results in the upwind slope. Cao Shuyang (212, 214) and Yassin (214) studied the effect of income roughness, hill slope and inflow turbulence to speed-up factor. Yassin concluded that two dimensional CFD simulations were compared well with the experimental results. Furthermore, Takeshi (1999) experimentally studied the typical steep hill though three-dimensional wind velocity measurement devices. The vertical wind speed was observed to be 28.5% of the horizontal wind speed of inflow on the upwind slope. However, the vertical wind speed had not been further studied in details. The above researches improved the understanding of wind field in hilly terrain, and provided more mature wind tunnel test and numerical simulation methods. However, there were two shortcomings in those studies. Firstly most of the current studies focused on the horizontal wind velocity distribution, researches of vertical wind velocity distribution had been almost in blank state, let along studies about how distribution varied with the change of height, slope and length of ridge. Secondly most of current hill models had no ridge, but ridge length could influent the wind speed distribution significantly. For such reasons, this paper referred to the previous studies, carried out a wind tunnel test on a steep hill model with ridge, measured the vertical wind velocity component. Then numerically simulated the hill model, and studied the distribution of vertical wind velocity, and how the distribution varied with hill height, slope and length of ridge. 2. Details of Wind tunnel test The cosine-squared cross section model was the most widely studied hill model previously, so in this paper the cross section of model was also given by as follow 2 x y H cos ( ), x D 2D (1) Where the hill height H was 1 m and the hill bottom radius D was 15 m in the experiment. Besides the length of the hill L was considered to be 3 m. The experiment was carried out at wind tunnel ZD-1 in Zhejiang University. The wind tunnel had an section of 3 m 4 m. The geometrical scale of model was chosen as 1:5, so it could be fitted in the wind tunnel with a block ratio less than 5%. The model was manufactured from polystyrene foam, and the surface of the model was stuck with synthetic fibers, which increased the surface roughness and reduced the Reynolds number effect near the surface of the hill (Lubitz W D, White B R 27). Fig. 1 showed the photo of experiment model. The wind profile was simulated to an exponent law, and the exponent achieved was.15. Cobra Probe was used to measure three components of the velocity vector. Cobra Probe was produced by TFI(Turbulence Flow Instruments)in Australia, was used to measure the three-dimensional turbulent flow

3 signals. The probes were made of 4 pressure sensors and available for three-dimensional turbulent wind velocity and static pressure with the response frequency up to 2 khz and the precision accuracy of velocity within ±.5 m/s. Definition of wind angle and layout of measurement points were as shown in Fig.2. Where measuring points were divided into solid points and hollow points. The three-dimensional wind velocity was measured at the heights 1 m~3 m at solid points, and 1 m only at hollow points. bottom radius Y wind angle D5 D4 D3D2D1 C1 C2 C3 E3 C4 C5 E5 C6 B1 B2 B3 B4 B5 B6 A1 A2 A3 A4 A5 A6 lenth of ridge X 9 wind angle Fig.1 Photo of experiment model Fig.2 Definition of wind angle and layout of measurement points 3. Numerical simulation and its verification CFD analysis method was applied to investigate the distribution of vertical wind velocity. The numerical model chose the same geometrical scale as experiment model. The roughness height of ground and hill surface were set up to.5 m and 1 m. Realizable k-epsilon model was chosen as turbulence model. To provide an self-maintenance of wind profile, the turbulent kinetic energy model was modified to Eq. (2)~(4), where essential height Z and essential velocity U were 1 m and 1m/s, exponent α was.15, turbulence I(z) and turbulence integral scale L u were defined by Japanese Code (24). Parameter Cμ and K in the equations were defined as.9 and.42. Z U( z) U ( ) (2) Z 2 k( z).5[ U( z) I( z )] (3) 4 C k( z) L u (4)

4 5 Experiment result 5 Experiment result 4 4 5m/s Disance (m) Distance (m) (a)profile of speed-up factor (b)profile of vertical velocity Fig.3 Speed-up factor and vertical velocity profiles at middle position of the hill(test point A1~A6) 5 Experiment result 5 Experiment result 4 4 5m/s Distance (m) Distance(m) (a)profile of speed-up factor (b)profile of vertical velocity Fig.4 Speed-up factor and vertical velocity profiles at left side of the hill(test point C1~C6) 5 Experiment result 5 Experiment result 4 4 5m/s Distance (m) Distance (m) (a)profile of speed-up factor (b)profile of vertical velocity Fig.5 Speed-up factor and vertical velocity profiles at cross section of the hill(test point A1,B1,C1,D1~D6)

5 As shown in Fig. 3~5, the speed-up factor, which was defined by Eq. (5), where S(z) was the speed-up factor at a height z above the hill, U(z) was the horizontal wind speed at same height, While U (z) was the upstream speed of the hill. The speed-up was well-fitted with the experiment, especially at the crest and foot of hill. The vertical wind speed profiles fitted with experiment even better. And it can found that vertical wind velocity could up to about 6% of income velocity at point A2 and C2. Which implied that vertical wind speed can t be ignored. U ( z ( ) ) U ( ) z Sz U( z) (5) Further comparison to previous study conducted by Takeshi etc (1999) was made to test the feasibility of numerical simulation method. The model was simulated with the set up mentioned above, and comparison was made in Fig 8. Also the simulation result had a good agreement with Takeshi s work. 4 3 Takeshi' experiment Income flow Test point 4 3 income flow Takeshi' experiment test point 4 3 Income flow Takeshi' experiment Test point Speed-up factor Speed-up factor Speed-up factor Fig.6 Result compared with experiment result down by Takeshi et al 4. Characteristic and fitting of vertical wind velocity 4.1 Selection of fitting formula Plenty of work had conducted to reveal the distribution of speed-up factor profile, but little researches had carried out to study the vertical wind velocity. This section introduced 2 typical methods to calculate speed-up factor in hilly terrain. (1) Original Guidelines Original Guidelines were proposed by Taylor and Lee (1984), it used formulation as below Smax Bh / L1 (6) S S exp( Az / L ) max 1 Where ΔS was speed-up factor, z was the height, A, B were fitting parameters, which determined by the geometric characteristics of the hill. L 1 means the horizontal distance from the peak to the 1/2 height of hill on the slope. (2) New Guidelines Wensong Weng (2) based on the original algorithm, proposed new Guidelines as follow.4

6 Rz Maximum Rz on upwind slop Rz at crest on 1m S H L L = B1 B2ln( ) z max 1 1 S(, z) ln A1 A2 ( z L1 ) A1e S max A3( z/ L1) Where B 1, B 2 were fitting parameters like A, B. A i (i=1, 2, 3)were constant related to the Surface roughness. Other parameters and values were the same as above. As discussed above, speed-up factor profile were commonly described in the exponent form, so this paper tried also using exponent form to describe the distribution of vertical wind velocity ratio, which was defined as (7) R z W U z (8) Where W z was the vertical wind velocity at height z, and U is the wind velocity at the same height of income The effect of hill height Model heights studied in this section varied from 5 m to 4 m, while their bottom radius D remained 1.5H, to provide them with a same slope. The distribution of vertical wind speed along the center line of upwind slope was shown in Fig. 7(a). When -x/d equaled to and 1, respectively, representing the crest and upwind foot of the hill. It s interesting that although hill height H varied, the maximum vertical wind speed appeared at almost the same place, about at two thirds height of upwind slope. And with the increase of hill height H, the position slightly moved upward. The value of maximum vertical wind velocity increased with the hill height, when the height H changed from 5 m to 4 m, the speed-up factor increased 1.88 times H=5m H=1m.8 H=2m H=3m.4 H=4m 2 4 Hill height (m) 4 3 H=5m.12 H=1m H=2m.8 H=3m H=4m 2 4 Hill height (m) x/d (a) along upwind slope (b) at crest Fig.7 Vertical wind velocity ratio distribution under different hill heights Fig. 7(b) showed profiles of vertical wind velocity ratio at the crest of hill under different hill heights. As shown in figure, the maximum vertical wind velocity appeared at Rz

7 z/h the height of.1h, which when the hill height increase, it increased at first and then decreased ln(w/u ) H=5m H=1m H=2m H=3m H=4m Fig.8 Linearity between dimensionless height and logarithmic dimensionless vertical velocity under different hill heights As shown in Fig. 8, linearity, ln(w/u )=az/h+b, was significant between dimensionless height z/h and logarithmic dimensionless vertical velocity above and below z/h=.1. So Eq. (9) was fitted to describe the profile, while z/h=.1 was regard as the demarcation point. In this fitting, more attention was paid to clarify the cases where hill heights were smaller than 3 meters, so that the equation could be simplified. The comparison between fitting and numerical simulation was made, and shown at Fig. 9. The equation result can match the perfectly when hill heights H were below 3 m, and become larger than the when H was larger than 3 m. w U exp( az / H b ) a 1, ( z / H.1 ) or -1.45, ( z / H.1) b -2.45, ( z / H.1 ) or - 1.8, ( z / H.1) (9) 4 35 H=5m 4 35 H=1m 4 35 H=2m 4 35 H=3m 4 35 H=4m Fig.9 Comparison between fitting and numerical simulation under different hill heights

8 z/h Maximum Rz on upwind slop Rz at crest on1 m 4.2 The effect of hill slope Models height H studied in this section were 1 m, and their bottom radius D varied from H to 4H D=1.H D=1.5H D=2.H D=2.5H D=3.H D=4.H.6.4 2H 4H Bottom radius(m) 4 3 D=1.H D=1.5H D=2.H D=2.5H D=3.H D=4.H H 4H Bottom radius(m) x/d (a) along upwind slope (b) at crest Fig.1 Vertical wind velocity ratio distribution under different hill bottom radius As shown in Fig. 1 (a), when the bottom radius increased, the maximum vertical wind speed decreased. It s same that the maximum vertical velocity appeared at the fixed position on the upwind slope, which was about 2/3 H of the upwind slope. The maximum can be over.65 when the hill was steep enough to H/D=1, and it decreased to about.3, when the slope changed to H/D=.25. As shown in Fig. 1(b) the vertical wind speed at crest also decreased with the bottom radius increased. And when the slope H/D was less than.25, the vertical wind velocity almost can be neglected. 4 3 D=1.H D=1.5H D=2.H D=2.5H D=3.H D=4.H Rz ln(w/u ) Fig.11 Linearity between dimensionless height and logarithmic dimensionless vertical velocity under hill bottom radius Still, the linearity between dimensionless height z/h and logarithmic dimensionless vertical velocity ln(w/u ) was significant, as shown in Fig. 11. The exponential law

9 function was still used to fit those profiles. When the hill bottom radius changed. The equation was little more complicated, since the parameter a and b changed significantly with the slope D/H changed. It can be expressed as follow w U exp( az / H b) 2 a.5( D / H).46( D / H) b.27( D / H) 2.9( D / H) 4.2( D / H) 4.2 (1) The fitting result were as follows: 4 3 D=1H 4 3 D=1.5H 4 3 D=2H D=2.5H D=3H D=4H Fig.12 Comparison between fitting and numerical simulation under different hill bottom radius 4.3. The effect of length of ridge This section focused on the influence of the length of ridge on vertical wind velocity distribution. Table 1 showed the cases of numerical simulation. Two wind direction angles were studied respectively. The hill height H was 1 m and the hill bottom radius D was 15 m for those cases. Table 1 Cases of numerical simulation with different hill ridge Wind angle Length of ridge 9.H,.5H, 1.H, 2.H, 3.H, 4.H, 5.H, 8.H.H, 1.H, 3.H, 5.H, 8.H When the wind angle was 9, where the wind direction was normal to the ridgeline, the over-hill effect became more obvious with the increase of the ridge length at the middle of the ridge. As was shown in Table 2, with the increase of ridge length, the

10 Rz maximum vertical wind velocity ratio increased both at the hillside and crest, especially at the middle of ridge, the doubled when the L became 8H. Table 2 Updraft velocity ratio at the height of 1m under 9 wind angle Ridge length L.H.5H 1.H 2.H 3.H 4.H 5.H 8.H Maximum on upwind slope Maximum at middle of ridge L=.5H L=1.H L=2.H L=3.H L=4.H L=5.H L=8.H x/l Fig.13 Updraft velocity ratio changes along the ridge at the height of 1m under 9 wind angle When wind flow over the ridge, the vertical wind velocity presents a certain distribution as shown in Fig. 13. While x, as shown in Fig. 2, meant the distance to the middle of hill. That made x/l present the location along ridge. When x/l was -.5 or.5, it located at left or right crest of the hill. Since the over-hill effect was more obvious at the middle of ridge, velocity ratio was larger at middle of ridge than at crest of the hill. And the velocity ratio changed within 1/1L range around the crest. When the wind direction angle was, where the wind direction was perpendicular to the ridgeline, the maximum vertical wind speed was significantly decreased with the increase of the length of ridge, and the vertical wind speed ratio at crest was almost remain the same, as shown in Table 3 Tab 3 Updraft velocity ratio at the height of 1m under wind angle Length of ridge.h 1.H 3.H 5.H 8.H Maximum on upwind slope Maximum at middle of ridge

11 Rz.15.1 L=1.H L=3.H L=5.H L=8.H Fig.14 Updraft velocity ratio changes along the ridge at the height of 1m under wind angle As shown in Fig. 14, x equated to -.5 and.5, respectively, representing the upwind and leeward crest of the hill. Vertical wind velocity in the top of hill near windward slope was updraft flow, in the middle region of the ridge was almost zero, when at the proximity of the leeward slope, it changed to downdraft flow. Same as 9 wind angle, the velocity ratio changed within 1/1L range around the crest. 5. Conclusions This paper revealed the distribution of vertical wind speed in hill terrain. Studied the influence of topographic features including hill height, hill slope and length of ridge. Fitted the profiles of vertical wind velocity ratio at the crest with varied hill heights and hill slope. And came to conclusions as follows: 1. Vertical wind speed on the upwind side, could up to about 6 percent of the income flow speed and maximum vertical wind velocity located at about two thirds height of the hill on upwind slope. 2. Vertical wind velocity ratio profiles satisfied exponential law at the top of the hill and equations were fitted to profiles with the change of hill height and slope. 3. In the case of 9 wind angle, the maximum updraft velocity on upwind slope and mountaintop both increased with the length of ridge. While at wind angle, the maximum updraft velocity on upwind slope decreased with the length of ridge. REFERENCES Jackson P S, Hunt J. (1975), Turbulent wind flow over a low hill, Quarterly Journal of The Royal Meteorological Society, 11(43), Taylor P, Lee R. (1984), Simple guidelines for estimating wind speed variations due to small scale topographic features, Climatolog. Bull, 18, Wensong W, Peter A. T, John L. W. (2), Guidelines for air flow over complex terrain: model developments, Journal of Wind Engineering and Industrial Aerodynamics, Taylor P A, Mason P J B E. (1987), boundary layer flow over low hills, Boundary-Layer Meteorology, 1-2(39), x/l

12 Bitsuamlak G T, Stathopoulos T, Bedard C. (24), Numerical evaluation of wind flow over complex terrain: Review, Journal of Aerospace Engineering, 17(4), Wang T, Cao S, Ge Y. (214), Effects of inflow turbulence and slope on turbulent boundary layers over two-dimensional hills, Wind And Structures, 19(2), Cao S, Wang T, Ge Y, et al. (212), Numerical study on turbulent boundary layers over two-dimensional hills Effects of surface roughness and slope, Journal of Wind Engineering and Industrial Aerodynamics, 14-16, Yassin M F, Al-Harbi M, Kassem M A. (214), Computational Fluid Dynamics (CFD) Simulations on the Effect of Rough Surface on Atmospheric Turbulence Flow Above Hilly Terrain Shapes, Environmental Forensics, 15(2), Takeshi I., Kazuki H. and Susumu O. (1999), A wind tunnel study of turbulent flow over a three-dimensional steep hill, Journal of Wind Engineering and Industrial Aerodynamics, 83(1 3), Lubitz W D, White B R. (27), Wind-tunnel and field investigation of the effect of local wind direction on speed-up over hills, Journal of Wind Engineering and Industrial Aerodynamics, 95(8), (24) AIJ recommendations for loads on buildings, Japan A I O.