Wind tunnel simulation of the surface layer flow for the prediction of wind loads on low-rise structures

Journal of Wind Engineering and Industrial Aerodynamics, 38 (1991) 151-160

151

Elsevier Science Publishers B.V., AmsterdAm - - Printed in The Netherlands

Wind tunnel simulation of the surface layer flow for the prediction of wind loads on low-rise structures H.W. Tieleman Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0219, USA

Summary The flow in the atmospheric surface layer over non-uniform terrain is analyzed with emphasis on those properties which are essential for the prediction of wind loads from wind tunnel simulation experiments. Near the surface, horizontal turbulence components are not in equilibrium with either the velocity profile or with the local terrain. Use of the "local" roughness length as a representative scaling length for wind tunnel model studies (Jensen's law) may simulate the velocity profile but is inadequate for simulation of the turbulence intensities of the horizontal velocity components. The discrepancies between profile and turbulence become larger as the regional terrain increases in complexity.

1. Introduction

Results from many wind-tunnel model and full-scale comparison experiments for low-rise structures show that fluctuating surface pressures are often difficult to simulate. Accurate flow simulation in the wind tunnel requires modeling of not only the mean velocity profile,but also the turbulence intensity distribution,the corresponding macroscales or integral scales and microscales of all three velocity components. Since these requirements are difficult to satisfy simultaneously, this paper will be devoted to the discussion of possible inadequacies of current modeling techniques for complex terrain. 2. Flat, smooth and uniform terrain

In neutral air over flat, smooth and uniform (FSU) terrain, the friction velocity derived from the turbulent stress, U*= ( - u w ) 1/2, is equivalent to the friction velocity derived from the velocity profile Up. Under these conditions the turbulence ratios Sa/U* are constants Aa. For a = u, v and w, A~ equals 2.5, 2.0 and 1.25 respectively. Eliminating the friction velocity with the use of these turbulence ratios and the logarithmic velocity law leads to: 0167-6105/91/$03.50 © 1991 Elsevier Science Publishers B.V. All rights reserved.

152

Sa/ U= IcAJln ( Z/ Zo)

(1)

or

Zo= exp [ l n z - r.Aa/(SJ U) ]

(2)

Consequently, the roughness length can be a predictor for the turbulence intensity, and vice versa the turbulence intensities can be used to predict the roughness length Zo. Therefore, in the absence of reliable mean wind profile data, the roughness length can still be derived from turbulence measurements at a given observation height. Over FSU terrain the turbulence and the mean flow are both in equilibrium with each other, and also with the terrain; conditions which are rarely satisfied 100%. 3. Perturbed terrain

3.1. Mean wind profile With the presence of only a few isolated obstructions such as trees, dwellings and small hills etc., even as far away as several kilometers, the FSU terrain conditions are not satisfied [ 1,2 ]. Observed wind profiles at Cabauw exhibit "kinks", even in the absence of an obvious and abrupt change in upstream surface roughness. Similarly, mean wind observations at the Boulder Atmospheric Observatory (BAO) show an increase in the profile derived roughness length with height [3,4]. The height of the observed "kink" depends on the upstream distance of these obstructions from the observation site, and generally occurs between 3 m and 20 m. Parameters derived from velocity profiles below the "kink" are considered to be "local" parameters because they are representative of the "local" terrain, within 100 m or so from the observation site. However, parameters derived from velocity profiles above the "kink" are representative of the terrain extending several kilometers upstream of the observation site, and therefore are referred to as "regional" parameters. 3.2. Turbulence The notion that horizontal turbulence components are affected by upstream terrain features was first mentioned by Panofsky et al. [5 ] and later verified experimentally by them and others [6-10 ]. Under neutral stability conditions, the energy-containing eddies of the horizontal components observed on either side of the profile "kink" are quite permanent, adjusting slowly to the "local" terrain conditions, and therefore require scaling with "regional" parameters. Below the profile "kink", the high-frequency fluctuations of the horizontal components as well as the vertical turbulence, the turbulence stress and the mean wind profile all adjust quickly to the "local" terrain and therefore must scale with "local" parameters only. Above the "kink" all observed flow quantities must scale with "regional" parameters.

153

Near the surface the variances of the horizontal velocity components vary littlewith height [10 ].Since these variances are dominated by large-scalefluctuations which are associated with the "regional" terrain, they can only be expected to scale with the "regional" value of the friction velocity. In the absence of reliable observations, the intensities of these components can be derived with the use of eqn. (1), provided "regional" values of the roughness length are used. Here the "regional" roughness length is defined as that of a terrain with uniform roughness over a long fetch for which the turbulence shear and variances are the same as those observed over the actual perturbed (complex) terrain. For slightly perturbed terrain, equilibrium between the turbulence and the velocity profile is also maintained above the "kink". For this situation "regional" values of U* and zo can be based on eddy correlations a n d / o r velocity profiles both derived from observations above the "kink" [1,10]. However, in many practical situations these observations are not available and U* and Zo must then be based either on the streamwise turbulence observations (often below the "kink" and the use of eqn. (2)) or on Wieringa's wind gust method [ 1 ]. For flow over terrain of increased complexity, local wind profiles become so variable and adjust so frequently that equilibrium does not exist at any level. Under these conditions application of the logarithmic velocity law is no longer valid and a "regional" value of zo can only be obtained from the turbulence and not from the wind profile. 4. Discussion of experimental results

As the terrain deviates increasingly from the F S U type and becomes more complex the following observations can be made. (1) The "regional" roughness length is larger than the "local" roughness length. At BAO, for west winds (Zo)local~ 1 c m and (Z0)re~onal~ 4 cm, while for southerly and easterly wind directions the values are I c m and approximately 30 c m respectively [3,4].At Cabauw, The Netherlands, average values for the "local" and "regional" roughness lengths are given in Fig. 1, which also shows the profile "kink". For the complex terrain at Rock Springs, P A [6], the "regional" values of Zo are at least an order of magnitude larger than the "local" values (Fig. 2). (2) The turbulence ratio Su/U* based on observations of both Su and Up at 10 m or lower, are generally larger than the F S U terrain value of 2.5 (Fig. 3 ). The corresponding wind tunnel values are somewhat lower. (3) The turbulence ratios S,/U* and Sv/U* based on the "regional" value of the frictionvelocity approach the F S U terrain values [10 ]. (4) Turbulence ratios SJSw and Sv/Sw exceed the corresponding FSU terrain values of 2.0 and 1.6 respectively (Fig. 4). Average wind tunnel values [11 ] are 1.8 and 1.25 respectively, well below the FSU terrain values.

154 100C z>lOm z
We~ wind zo. c m 46.7 14.9 0.68 0.78

East wind

zo, crn 96.0 19.6 0.35 0,42

z>lOm z<10m

//

d 1130

10

1

I

5

I

15

10

U. rn/s

5

10

U.

15

m/,

Fig. 1. Averaged neutral velocity profilesover slightlyperturbed terrain (west wind) and rougher terrain (east wind) afterBeljaars [2 ]. •11

Mountoln~

Rouoh Rurol Terrain

~

100

II

f Corn l~tubble 0 10

All

•

o

1.0

@

O

0 0

~l

O [] [3

0 o

0,~

200

i"1 220

A

~

i

I

1

i

i

240

260

280

300

320

34,0

360

Wind Direcbon, de9rees

Fig. 2. Comparison of the "local" and "regional" roughness lengths at Rock Springs, PA [6].

(5) Observed turbulence intensitiesof all three components are generally larger than those derived from eqn. (1) when based on the "local" roughness length (Figs. 5-7). For the wind tunnel simulation the predicted values based on the profile-derivedroughness lengths are higher than the actually observed turbulence intensities. (6) For flow over non-FSU terrain,spectraldensitiesof the horizontal components at low wave numbers are larger in comparison with the F S U terrain spectral models developed by Dutton et al. [7 ]. The reason is that over non-

155

"~.2

o

2.4

'

•

~

OO

a

°

E 1.6

0 Aye,bury[12] O C.~th,rsb,rg[1~]

~.~ 0.8

J

F~Uterroin. Su/UN-2.4

0.0

I

I

0.2

0.4

I 0.8 U.. m / L

I

I

0.8

1.0

1.2

Fig. 3. Variation of S. with the "local" U* for perturbed and FSU terrain and for wind tunnel simulations. 6.0

0

$.0 4.0

3.0 ,-

O--

n

O

O O

O

[]

O

O []

[]

[] O

'°; ................. ~

1.0

200

I 220

°_____°_ ...............

F'SUterrain

Mountoin 0.0

O

[3

D

Rough Rural Terrain I 240

I 260

i 280

I 300

W~nd Direction,

degrlos.

I 320

I 340

360

Fig. 4. Variation of the ratio Sv/Swwith wind direction at Rock Springs, PA (complex terrain )

[61.

F S U terrainthe low-frequency fluctuationsassociated with the upstream terrain adjust only slowly to the "local" terrain.Figures 8-10 show the comparison of the u spectra for F S U terrain and complex terrain (Rock Springs) [7], with those from Aylesbury [15 ], Gaithersburg [13 ] and the wind tunnel [11 ] respectively. (7) As well as the inadequacy of the simulation of the spectral densitiesat medium and lower frequencies,the wind tunnel simulations are inadequate in

156 40 0 [] 30

A)~.bu~ [12] Go~ersbur9 [13 l

:

P ~ s Fork [14]

•

W'lndTunnel [11 l

--

F3U tern=in

•

/

• •

J / -

0

20

10 (s~/u)p.x - 9s/In(z/zo) I 20

10

I 30

40

Fig. 5. Comparison of the observed SJU and that derived from the "local" roughness length for FSU and perturbedterrain and for wind tunnel simulations. 6O

50

0 Rock Spr}n9, (mountain) [6] {Z~ Rock Springs (non-mountoin) [6 l

4O

{

30

m

20

~ 0

~

(s~/u)p.x - ~.8/~(=/2o)

, -

I 10

--

r~-~

~C~ -

i 20

0

i O0

I 30

~)

I ~0

0

0

I 50

60

(Sv/U)ob~,n~d. X

Fig. 6. Comparison of the observed S,,/U and that derived from the "local" roughness length for FSU and perturbedterrain and for wind tunnel simulations. the high-frequency range (Fig. 10). In addition to observation (6), one may conclude that simple geometric scaling with height z does not bring the spectra in coincidence, and that the extent of the inertial subrange is much smaller for the wind-tunnel model spectra. Recent work by Tieleman and Akins [16,17] shows clearly the dependence of the mean, root mean square and peak surface pressure coefficients on the spectral content at wavelengths 1/10 of the characteristic length of the modeled obstacle. This requires accurate modeling of the spectral densities in the inertial subrange.

157 24.0

/

20.0

16.0

}

0

Rock S~rin9, (mountoin) [6]

r~ A

Rock Springs (non-mountoin) [6] BA0

*

P~ct, Fork [14]

•

Wind Tunnel [11]

•

~

S2.0

8.0

~

0

~

[30 0 0 0 0

f~ D

0

4.0

(sw/u)p.X - 50/In(z/zo) 0.0

o.o

i

I

4.o

a.0

=

:z.o (s./u~d.

~

l

~s.o

20.0

2,.0

x

Fig. 7. Comparison of the observed Sw/U and that derived from the "local" roughness length for FSU and perturbed terrain and for wind tunnel simulations.

lOZ=

,

i i,itll I

i

I ;illh I

i i I III11~

i i I Illll I

I i , lill~

F'SU terroin [7] ......

/

Rock Springs [7]

-1

Z

-

g to-'y

\

\

U3 Run

-2 j

.......

A32 B=235 degr.

Run A5

B=200

\

U--

J

degr.

=

A>~==buO, [+s]

%_,,

I 'tlllll

10-3

I F TIlIIII

l I llllllI

10-2

IO-L

l I IIlllll

I0o

I r lllill

i0~

f = nz/V

Fig. 8. Comparison of u spectra over complex and F S U terrain with those observed at Aylesbury, z=10m [15].

(8) Flows over complex terrain are associated with high standard deviations of the lateral turbulence component Sv which corresponds to large values of the standard deviation of the wind direction fluctuations SD. At Rock Springs, measurements at z = 3 m show SD to vary between 13 ° and 21 ° [6]. At Prices Fork at z = 10 m, the average value of SD is approximately 20 °. The m a x i m u m SD observed for the wind tunnel simulations is only 10 ° [11 ].

158 i

1111111

i

~ lillll

I

i

i iiiIli

I

I

i

1 I I II;~ i

illlllj

E

ioO~ ~

E_ E

:

lO_;~!

"

j i

i0-~

iIiiIll

i

- ......

F'SU terrain [7] Rock Springa [7]

.....

Goither=burg [13]

i I Illlll

i0-3

I

i

illtlll

I

i0-2

1

I Illlll[

I

lO-I

i

Iiii

i0 o

I0 r

f : nz/V

Fig. 9. Comparison of u spectra over complex and FSU terrain with those observed at Gaithersburg, z = 3 m [13].

IOZE e,l

I

I lllllJ

I

I I Illllj

I

I I lllllJ

I

I I 11111 i

1

I Iii11-1

F

,o °,:_= ~

E

"

C

/ -

10-2=

E 10-3t 10 . 4

IIIH[

!

lO-3

-

F~U

terrain

[7]

\

......

Rock SpringJ [7]

.....

W]nd

I I IHIII

I

I

Tunnel

I IlllJl

I0 -2

\ "\

[11] I

I0 -~

\

I Illlll~

I

I0 O

I

IIIIII I0'

f = nz/V

Fig. 10. Comparison of u spectra over complex and FSU terrain with those observed in the wind tunnel, z = 25 cm [ 11 ].

5. Conclusions The inability to predict mean and root mean square pressure coefficients on low-rise structures from wind tunnel model tests must be attributed to inadequate simulation of the flow characteristics of the atmospheric surface layer. Specifically, if the simulation is based primarily on the "local" roughness length (Jensen's law), discrepancies between model and full-scale surface pressures must be anticipated. Inadequate modeling of the turbulence intensities of the horizontal fluctuations, their integral scales and their small-scale turbulence content, especially for flows over complex terrain, mostly accounts for these discrepancies. As long as one fails to address these points properly, predictions

159

of mean and fluctuating wind loads via either wind-tunnel model tests or numerical methods cannot be expected to be reliable.

Acknowledgments The author is grateful to Dr. J.C. Kaimal for making available the observations from the Boulder Atmospheric Observatory for September 11, 1978 when a strong wind storm passed over the observation site.

References 1 J. Wieringa, Estimation of mesoscale and local-scaleroughness for atmospheric transport modeling. In C. Wispeleare (ed.),Air Pollution Modeling and itsApplication, Plenum, New York, 1981, pp. 279-295. 2 A.C.M. Beljaars,The derivation of fluxes from profilesin perturbed areas, Boundary-Layer Meteorol., 24 (1982) 35-55. 3 S. Schotz and H.A. Panofsky, Wind characteristicsat the Boulder Atmospheric Observatory, Boundary-Layer Meteorol., 19 (1980) 155-164. 4 A. Korrell, H.A. Panofsky and R.J. Rossi, Wind profilesat the Boulder Tower, BoundaryLayer Meteorol., 22 (1982) 295-312. 5 H.A. Panofsky, H. Tennekes, D.H. Lenschow and J.C. Wyngaard, The characteristics of turbulent velocity components in the surface layer under convective conditions, BoundaryLayer Meteorol., 11 (1977) 355-361. 6 H.A. Panofsky, C.A. Egolf and R. Lipschultz, On characteristicsof wind direction fluctuations in the surface layer,Boundary-Layer Meteorol., 15 (1978) 439-446. 7 J.A.Dutton et al.,Statisticsof wind fluctuationsover complex terrain,Final Pep. U.S. Dept. of Energy, DOE/ET/20560-1 UC-60, 1979 (Dept. of Meteorology, Pennsylvania State University,Philadelphia, PA). 8 H.A. Panofsky, M. Vilardo and R. Lipschutz, Terrain effectson wind fluctuations.In J.E. Cermak (ed.),Wind Engineering, Pergamon, Oxford, 1980, Vol. 1, pp. 173-177. 9 H.A. Panofsky, D. Larko, R. Lipschutz, G. Stone, E.F. Bradley, A.J. Bowen and J. Hojstrup, Spectra of velocity components over complex terrain, Q. J. R. Meteorol. Soc., 108 (1982) 215-230. 10 A.C.M. Beljaars,P. Schotanus and F.T.M. Nieuwstadt, Surface layer similarityunder nonuniform fetch conditions,J. Climate Appl. Meteorol., 22 (1983) 1800-1810. 11 R.E. Akins and J.E. Cermak, Wind pressures on buildings, Rep. CER76-77 REA-JEC15, 1976. Fluid Dynamics and Diffusion Laboratory, Colorado State University. 12 K.J. Eaton, J.R. Mayne and N.J. Cook, Wind Loads on Low-Rise Buildings: Effects of Roof Geometry, C P 1/76, 1976 (Building Research Establishment, Garston, Watford). 13 R.D. Marshall, The measurement of wind loads on a full-scalemobile home, NBSIR77-1289, 1977 (Center of Building Technology, National Bureau of Standards, Washington, D C ). 14 H.W. Tieleman, R.E. Akins and P.R. Sparks, A comparison of wind-tunnel and full-scale wind pressure measurements on low risestructures,J. Wind Eng. Ind. Aerodyn., 8 (1981) 319. 15 K.J. Eaton and J.R. Mayne, The measurement of wind pressures on two-storey houses at Aylesbury, J. Ind. Aerodyn., 1 (1975) 67-109.

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H.W. Tieleman and R.E. Akins, Mean and fluctuating pressure distributions on rectangular prisms immersed in a variety of turbulent shear flows, Proc. AIAA/ASME/SIAM/APS, 1st Nat. Fluid Dynamics Congress, Cincinnati, OH, 1988, Vol. 3, AIAA, Washington, DC, 1988, pp. 1749-1756. 17 H.W. Tieleman and R.E. Akins, Effects of incident turbulence on pressure distributions on rectangular prisms, J. Wind Eng. Ind. Aerodyn., 36 (1990) 579-588.