A new method to calculate wind profile parameters of the wind tunnel boundary layer

A new method to calculate wind profile parameters of the wind tunnel boundary layer

ARTICLE IN PRESS Journal of Wind Engineering and Industrial Aerodynamics 91 (2003) 1155–1162 A new method to calculate wind profile parameters of the...

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ARTICLE IN PRESS

Journal of Wind Engineering and Industrial Aerodynamics 91 (2003) 1155–1162

A new method to calculate wind profile parameters of the wind tunnel boundary layer Guoliang Liua,b,*, Jie Xuanc,b, Soon-Ung Parka a

School of Earth and Environmental Sciences, Seoul National University, Seoul 151-742, South Korea b Environment Science Center, Peking University, Beijing 100871, People’s Republic of China c Program in Atmospheric & Oceanic Sciences, University of Colorado at Boulder, Boulder, CO 80309, USA Received 12 November 2002; received in revised form 3 June 2003; accepted 10 June 2003

Abstract This paper introduces a new method to process wind profile data of simulated atmospheric boundary layer flows in the wind tunnel so as to obtain the two important wind profile parameters—the surface roughness length z0 and the friction velocity u : Instead of using the wind speed profile, the turbulent intensity profile of the turbulent surface layer, which is measured with a single probe hot-wire anemometer, is used to calculate the surface roughness length z0 : Then, the calculated surface roughness length z0 is substituted into the mean wind speed profile of the constant flux layer to calculate friction velocity u : From our results this method is better than the simple regression method using the wind speed profile, which has been widely used. r 2003 Elsevier Ltd. All rights reserved. Keywords: Wind tunnel; Turbulent intensity profile; Surface roughness length z0 ; Friction velocity u

1. Introduction In a neutral surface layer, the velocity profile follows the well-known logarithmic law. The mean velocity distribution is given by [1] U 1 ðz  dÞ ; ¼ ln u k z0

ð1Þ

*Corresponding author. School of Earth and Environmental Sciences, Seoul National University, Seoul 151-742, South Korea. E-mail address: guoliang [email protected] (G. Liu). 0167-6105/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0167-6105(03)00057-6

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where U is the mean velocity at the height of z above the surface, u the friction velocity, z0 the surface roughness length, d the zero plane displacement, and k the Von Karman constant (0.4). The universal logarithmic velocity profile in the neutral surface layer now has been widely used in both wind tunnel and in atmospheric field work. It is also applied to estimate the two most important parameters, the surface roughness length z0 and the friction velocity u ; through regression of this equation with observed velocity profile data. However, in practice, this method is hardly allowed to estimate these two parameters accurately and simultaneously because of the zero plane displacement d in Eq. (1). Also, a minute error in estimating the slope of the logarithm-linear segment (the velocity profile of the lower layer) will produce a large error in estimating z0 : The purpose of this paper is to introduce a new method to estimate these parameters simultaneously with more precision using the measured wind profile data in the wind tunnel.

2. Methodology This method utilizes the turbulent intensity profile measured by a single probe of a hot-wire anemometer to calculate the surface roughness length z0 : Then the calculated value of the surface roughness length z0 is substituted into the mean wind speed profile of the constant flux layer to calculate the friction velocity u and zero plane displacement d: The surface roughness length z0 is estimated using the empirical expression given by the Engineering Science Data Unit [2], which had been used as a criterion to test the simulated turbulent boundary layer [3–6]. By correlating strong wind atmospheric data over a large variety of different roughness conditions, ESDU concluded that the variation of the turbulent intensity with height up to 100 m is su ð0:867 þ 0:556 log10 z  0:246 log210 zÞ ¼ B; ln ðz=z0 Þ U

ð2Þ

where B ¼ 1:0 for z0 p0:02 m, B ¼ 0:76z0:07 for 0.02 m
3. Implementation We use our experimental data to show how to determine the wind profile parameters with this method. The data were obtained from a dense gas experiment

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70 Zo=0.01 Zo=0.02 Zo=0.1 Zo=0.2 Zo=0.5

60

50

Z (m)

40

30

20

10

0 0

20

40 60 TURBULENT INTENSITY ( % )

80

100

Fig. 1. Variations of atmospheric turbulent intensity with height for different surface roughness lengths [2].

Table 1 Mean wind speed and turbulent intensity data obtained from the wind tunnel experiment (where Ur is the velocity at the reference height 10 cm) z (cm)

1 2 4 6 8 10 14 20 32 48 64

Ur ¼ 0:59 m s1

Ur ¼ 1:69 m s1

U (m s1)

Turbulent intensity (%)

U (m s1)

Turbulent intensity (%)

0.427 0.466 0.513 0.56 0.575 0.592 0.634 0.712 0.79 0.887 0.961

32.7 31.7 27 26.8 26.7 25.4 25.4 23.1 18.9 15.6 12.2

1.325 1.415 1.554 1.591 1.642 1.69 1.761 1.919 2.155 2.353 2.645

25.1 23.4 23.4 22.3 22.1 22 22 20.4 17.8 16.2 14.1

that was conducted in the Wind Tunnel of the Center of Environment Science, Peking University. The data are listed in Table 1. These two group of data are obtained under the same surface condition so that the surface roughness length z0 of these data is the same.

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1

Z (cm)

10

0

Ur=1.69 m / s Ur=0.59 m / s

10

-1

10

-2

10

0

0.5

1

1.5 U (m/s)

2

2.5

3

Fig. 2. Mean wind profiles.

Fig. 2 shows the variation of mean wind speed with height obtained from the wind tunnel experiment. The layer from 10–70 cm is assumed to be a constant flux layer. Theoretically this layer should satisfy the log-linear relationship in Eq. (1). We can extrapolate the logarithmic wind profile down to a height where the extrapolated wind speed U becomes zero where the height is d þ z0 above the actual ground surface. The results are: d þ z0 E0:55 cm for Ur ¼ 0:59 m s1, and d þ z0 E0:40 cm for Ur ¼ 1:69 m s1. Figs. 3–5 illustrate the method to calculate the surface roughness length z0 : The procedure is, first to change the wind tunnel measured data to the field data with the length-scale factor of 1:100 (This length-scale factor is discretionary); second to draw in one figure the changed experimental data with three profiles of su =U; 1:15su =U and 0:85su =U using Eq. (2) with any reasonably chosen z0 : This is repeated with different values of z0 to determine the most appropriate surface roughness length z0 for the measured data (here we just show three figures for three different values of z0 ). By comparing the figures we can determine the surface roughness length z0 : That best matches the field data is 0.12 m since most of the experimental data lie between 1:15su =U and 0:85su =U: Therefore, the surface roughness length z0 of the wind tunnel data is about 0.12 cm. Then we can calculate the zero plane displacement d by the calculated z0 þ d minus this z0 : Using the calculated z0 and d; Eq. (1) was bestfitted to the mean velocity data in the height range 10 cmpzp64 cm to estimate u ; which resulted in u ¼ 0:057 m s1 for Ur ¼ 0:59 m s1, and u ¼ 0:157 m s1 for Ur ¼ 1:69 m s1. In this example we found that there is no difference in the result of u if we assume d ¼ 0: Fig. 6 shows the result of the log-linear profile from the above-calculated parameters and the measured wind speed data in the wind tunnel.

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70 Ur=0.59 m/s Ur=1.69 m/s -15% +15% ESDU for Zo=0.12 m

60

50

Z (m)

40

30

20

10

0 10

15

20

25 30 35 TURBULENT INTENSITY(%)

40

45

Fig. 3. Comparison of the experiment data with ESDU for z0 ¼ 0:12 m (where ‘ESDU for z0 ¼ 0:12 m’ is the profile of su =U using Eq. (2) with z0 ¼ 0:12 m, ‘15%’ is 0:85su =U; ‘+15%’ is 1:15su =U).

70 Ur=0.59 m/s Ur=1.69 m/s -15% +15% ESDU for Zo=0.05 m

60

50

Z (m)

40

30

20

10

0

0

5

10

15 20 25 30 TURBULENT INTENSITY ( % )

35

40

45

Fig. 4. Same as in Fig. 3 except for z0 ¼ 0:05 m.

Another example to determine z0 and u was carried out for an independent wind tunnel experimental data, as shown in Table 2, obtained under the same surface conditions used to obtain the data in Table 1. The results provide a surface roughness length 0.12 cm and u 0.062 m s1, which agree well with the results from the experimental data in Table 1.

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70 Ur=0.59 m/s Ur=1.69 m/s -15% +15% ESDU for Zo=0.20 m

60

50

Z (m)

40

30

20

10

0

0

5

10

15 20 25 30 TURBULENT INTENSITY (%)

35

40

45

Fig. 5. Same as in Fig. 3 except for z0 ¼ 0:20 m.

600 kU/u*=ln (( Z- d) / Zo) Ur=0.59 m / s Ur=1.69 m / s

500

(Z-d )/ Zo

400

300

200

100

0

2

2.5

3

3.5

4

4.5 kU/u*

5

5.5

6

6.5

7

Fig. 6. Log-linear profile.

4. Conclusion We have shown that the present method is reasonable. Because more information is used in this method, it yielded more consistent and stable estimates of z0 and u

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Table 2 Experimental data measured in the wind tunnel Z (cm)

U (m s1)

Turbulent intensity (%)

1 2 4 6 8 10 14 20 32 48 64 80 96 112 128

0.406 0.509 0.577 0.627 0.612 0.678 0.714 0.79 0.875 0.936 1.019 1.1 1.136 1.16 1.181

33.6 28.5 24.9 23.8 26.3 22.4 22.8 20.4 17.2 14.6 11.7 9.27 7.5 5.6 3.8

compared with the method using the simple regression equation of the wind speed profile. Besides the two methods discussed here (the regression method of the wind speed profile and the present method), another alternative method is to measure friction velocity u first with an X-type hot-wire anemometer, and then to determine z0 by substituting the measured u into the mean wind speed profile of the surface turbulent layer. This method also can yield more consistent and stable estimates of z0 and u compared with the simple regression method of the wind speed profile [7]. The strong point of the present method is to use the turbulent intensity profile which is easily obtained as part of wind speed profile measurements in the wind tunnel experiment.

Acknowledgements The authors are grateful to Professor Jones, the editor of the journal, for additional task on our English.

References [1] O.G. Sutton, Micrometeorology, McGraw-Hill, New York, 1953. [2] ESDU, Characteristics of atmospheric turbulence near the ground, Engineering Science Data Unit Numbers 74030 and 74031, London, 1974. [3] J. Donat, M. Schatzmann, Wind tunnel experiments of single-phase heavy gas jets released under various angles into turbulent cross flows, J. Wind Eng. Ind. Aerodyn. 83 (1999) 361–370.

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[4] J. Shanmugasundaram, P. Harikrishna, S. Gomathinayagam, N. Lakshmanan, Wind terrain and structural damping characteristics under tropical cyclone conditions, Eng. Struct. 21 (1999) 1006–1014. [5] M. Schatzmann, W.H. Snyder, R.E. Lawson, Experiments with heavy gas jets in laminar and turbulent cross-flows, Atmos. Environ. A 27 (1993) 1105–1116. [6] D.E. Neff, Physical modeling of heavy plume dispersion, Dissertation, 1989, pp. 49–50. [7] G. Zhu, S.P. Arya, W.H. Snyder, An experimental study of the flow structure within a dense gas plume, J. Hazard. Mater. 62 (1998) 161–186.