Correction of wind-tunnel pressure coefficients for Reynolds number effect

JOURNAL OF

windml~inemng ELSEVIER

Journal of Wind Engineering and Industrial Aerodynamics 69 71 (1997) 547-555

Correction of wind-tunnel pressure coefficients for Reynolds number effect R.P. Hoxey*, A.P. Robertson, G.M. Richardson, J.L. Short Silsoe Research Institute, Wrest Park, Silsoe, Bedford MK45 4HS, UK

Abstract Detailed measurements on a low-rise building made at full scale and on a wind-tunnel model show a significant Reynolds number effect associated with the separated flow region on the windward roof slope of the building. Other possible causes for the observations are explored but are systematically eliminated. Brief details of the experimental procedure are presented together with significant results which suggest generalised corrections for scale effects. It is also proposed that the sensitivity of the separated flow at the windward eaves to Reynolds number has a secondary effect on the flow pattern downstream. Further detailed measurements are required to enable the correction factors to be generalised for other types of structure. Keywords: Full-scale; Wind-tunnel; Reynolds number; Wind effects

1. Introduction C o m p a r i s o n s of full-scale a n d m o d e l - s c a l e pressure m e a s u r e m e n t s m a d e on a lowrise b u i l d i n g [1 3] have s h o w n significant differences a s s o c i a t e d with regions of s e p a r a t e d flow. A l t h o u g h there is a widely held view that s h a r p changes in g e o m e t r y r e n d e r the flow insensitive to R e y n o l d s n u m b e r , there was no o t h e r a p p a r e n t e x p l a n a tion for the o b s e r v a t i o n s . Hence, a m e t h o d of p r o c e s s i n g the full-scale pressure coefficients was devised to e x a m i n e the p o s s i b i l i t y t h a t these differences were a t t r i b u table to a R e y n o l d s n u m b e r effect. This c o n f i r m e d that, in the vicinity of r e a t t a c h m e n t , pressure coefficients were a function of m e a n w i n d speed and, hence, R e y n o l d s n u m b e r . T h e simple linear r e l a t i o n s h i p devised from full-scale d a t a gave e x t r a p o l a t e d results which were c o n s i s t e n t with the m o d e l - s c a l e d a t a for which the R e y n o l d s n u m b e r was r e d u c e d p r i m a r i l y by the d i m e n s i o n a l scale of 1 : 100. A d d i t i o n a l s u p p o r t i n g evidence for this finding c a m e from full- a n d m o d e l - s c a l e m e a s u r e m e n t s on the s a m e b u i l d i n g when the c o n v e n t i o n a l s h a r p eaves were r e p l a c e d

* Corresponding author. 0167-6105/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PI1 S0 1 67-6 1 0 5 ( 9 7 ) 0 0 1 85-2

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R.P. Hoxey et al./,~ Wind Eng. Ind. Aerodyn. 6~71 (1997) 547-555

by modified curved eaves. The curvature, 635 m m radius, was sufficient to prevent separation, and good agreement was observed between pressure coefficients from full and model scale. Also, detailed analysis of the full-scale mean value coefficients for the curved eaves building showed that they were independent of wind speed. The supporting measurements from the curved eaves building are not presented in this paper but the absence of a dependency of coefficient value upon wind speed for this case, when attached flow occurs, contrasts with the dependency that has been found for the sharp eaves case, when flow separation takes place. These conditional observations provide strong supporting evidence of a Reynolds number effect associated with separated flows around bluff bodies.

2. Experimental description Measurements of surface pressure have been completed at full-scale [4,5] on a low-rise portal framed building 24.1 m long, 12.9 m span, 5.3 m ridge height and 10 ° roof pitch. The building was sited in an open position, on level ground with a surface of cut grass, where the atmospheric boundary layer had a roughness length, derived from the mean velocity profile, of 10 ram. There were two basic configurations of the building, one with traditional sharp eaves, the other with curved eaves of 635 m m radius; in neither case was a gutter present. The eaves detail had a significant effect on the flow pattern. The curved eaves produced attached flow from the side wall to the roof for transverse wind, whilst the sharp eaves produced separated flow. The Reynolds number effect was evident in separated flow and, hence, only the sharp eaves results are presented here. Geometrically similar models of the building were made at 1 : 100 scale with tapping points located at the same positions as those on the full-scale building. The models were tested in two wind tunnels: the University of Western Ontario, Canada, No 1 wind tunnel, and the Building Research Establishment, UK, No 3 wind tunnel. Both tunnels were open return, the U W O was suck-down, and the BRE blow-down. Roughness elements were used to simulate the atmospheric boundary layer with an equivalent full-scale Zo value of 10 ram. An attempt was made to sustain the boundary layer over the smooth turntable by using small roughness elements close to the model, but this was only partially effective since a non-linearity in the 'log-law' profile was evident close to the ground. At both full and model scale, pressure coefficients were non-dimensionalised by the wind dynamic pressure at building ridge height.

3. Results Mean pressure coefficients derived from full-scale measurements are presented in Fig. 1 for the mid-length of the building with sharp eaves; the flow is perpendicular to the side wall. The values were obtained from a 'least-squares' Fourier curve-fit routine through a large number of data points (approx. 1000), each representing a 10 min mean full-scale measured value. The large number of data points, especially with wind

R.P. Hoxey et al./J. Wind Eng. Ind. Aerodyn. 69 71 (1997) 547-555

549

Air F low -1.148

-1.3~227

-0.697 ~

-0.683 ~

28

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. . . .

31

26 0.515-

25

0.435

24

0.363

23

~

-0.245 o~¢

Tap

numbers 23-33

33

-0.180

Fig. 1. Full-scale m e a n pressure coefficients.

directions close to perpendicular to the side wall, gives a small uncertainty in the coefficients (of order 0.01). Mean value coefficients were also obtained from both wind tunnels, and for comparison the average of the two sets of data are given in Fig. 2. The average difference between the two sets of wind-tunnel coefficients was 0.05, with a standard deviation of 0.11. For the tapping points on either side of the ridge there were significant differences and these were the main contributors to the average difference of 0.05 (the BRE values were more negative than the U W O values). The reason for this may be due to flow separation at the ridge: at full-scale there is no evidence of separation but the low coefficients from the BRE wind tunnel suggest separation. The main difference between the two wind tunnels was that the UWO tunnel had solid walls and roof to the working section, whereas the BRE tunnel had permeable sides and roof [6], which may have encouraged flow separation. The difference between the two carefully controlled wind-tunnel experiments suggests an uncertainty of the order of 0.1 in coefficients. Comparing full-scale (Fig. 1) with averaged wind-tunnel coefficients (Fig. 2), shows good agreement on the windward wall (taps 23 25) and reasonable agreement over the ridge, leeward roof and leeward wall (taps 29-33). However, significant differences occur in the vicinity of the flow separation region on the windward roof slope (taps 26-28). Here the difference exceeds experimental error and this provides evidence of Reynolds number effect. To investigate further the existence of a Reynolds number sensitivity, the full-scale measurements of surface pressure were analysed in more detail. Ten-minute mean pressure coefficients were selected which had a 10 rain mean wind direction within one degree of normal to the side wall. Forty-three records satisfied the directional limits and these had a mean velocity span of 7.4-14.4 m/s. The pressure coefficients for tapping point 28, a point on the roof near reattachment, are presented in Fig. 3. The Reynolds number, Re, is based on the building ridge height of 5.3 m. Linear regression analysis and evaluation of Student t-values showed that the slope was highly significant (t = - 4.26) for this tapping point. The slope of the regression lines are summarised in Fig. 4 for all the tapping points; the values represent the change in pressure

550

R.P. Hoxey et al./J. Wind Eng. Ind. Aerodyn. 69 71 (1997) 547-555 Air Flow

-1

.

-0.844

-0.639 -0.471

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T Fig. 2. Average of wind-tunnel pressure coefficients.

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Fig. 3. Mean pressure coefficient (Cp) for tapping point 28 as a function of Reynolds number (Re).

coefficient for an order of magnitude change in wind velocity, i.e. a decade change in Reynolds number. These values have statistical significance only in the region of separated flow, elsewhere, with the exception of the tapping point at the top of the windward wall, they are small and statistically not significant. The scatter of points in Fig. 3 is associated with the sampling of wind velocity upstream of the building, away from the pressure field generated by the building. The sampling point was some 25 m from the windward side wall tapping points. The values presented in Fig. 4 for the Reynolds n u m b e r sensitivity in the separated flow region can be used to linearly extrapolate values from full scale to model scale (1 : 100). These extrapolated pressure coefficients are given in Table 1, where they can be seen to give reasonable agreement with the model-scale coefficients. The use of linear extrapolation from the limited full-scale range of Reynolds n u m b e r to the model-scale Reynolds number, t h o u g h tenuous, is used here to provide an indication. These findings are at variance with the widely held view in bluff-body aerodynamics that the flow over the eaves of a building is Reynolds n u m b e r independent, and, hence, the results have been scrutinised closely for other possible effects as described below.

R.P. Hoxey et al./J. Wind Eng. Ind. Aerodyn. 69-71 (1997) 547-555

551

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-0.041 -0.024 - 0 2 4 - -~ 0 . ~ . 0 1 u ~ - ~

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t

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Fig. 4. Changes in full-scale pressure coefficients for a decade change in Reynolds number.

Table 1 Full-scale and model-scale pressure coefficients over lower part of windward roof slope of building with sharp eaves Tapping point

Distance from leading edge (m)

26 27 28

0.965 1.965 2.965

Full-scaleCp

--1.389 -- 1.148 --0.697

Model-scale Cp --1.104 --0.656 --0.471

Linear-regression estimate of model-scale Cp from full-scale Cp --1.035 --0.650 --0.289

3.1. Variation of turbulence intensity with wind velocity Turbulence intensities were evaluated for the same sets of data with the n a r r o w b a n d of wind direction, and are shown in Fig. 5 where they are plotted against mean wind velocity. Linear regression analysis showed there to be no significant trend between turbulence intensity and mean wind velocity.

3.2. Changes in boundary layer characteristics with mean wind velocity W i n d velocity was measured in the full-scale experiments at the ridge height of the building some distance upstream. The instrument used was a t h r e e - c o m p o n e n t sonic a n e m o m e t e r and the frictional velocity was c o m p u t e d from the 5 H z digital record (u, = x/( - uw). . . . ). The c o m p u t e d frictional velocity, expressed as a p r o p o r t i o n of the m e a n velocity, is shown in Fig. 6, where it is plotted against mean velocity. Again there is no significant trend of u,/u . . . . as a function of the m e a n wind velocity. This is interpreted as an indication that the b o u n d a r y layer is insensitive to Reynolds number.

R.P. ttoxey et al./J. Wind Eng. Ind. Aerodyn. 69 71 (1997) 547-555

552

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variation with mean velocity (u . . . . ).

4. Discussion The comparisons between the full-scale pressure coefficients and the average of those from the two wind-tunnel experiments suggests there is a significant difference in the separated flow region on the windward roof slope. Analysis of the full-scale mean pressure coefficients with respect to mean wind velocity indicates a Reynolds number dependency that is significant in this region. The properties of the atmospheric boundary layer, i.e. turbulence intensity and frictional velocity, show no significant Reynolds number effects in this study, and it is therefore concluded that the separated flow over the windward eaves of the building is Reynolds number dependent. The magnitudes of the estimates of Reynolds number dependency obtained from the full-scale measurements alone are consistent with the differences recorded between the full-scale and the wind-tunnel experiments for the pressures in the separated flow region on the windward roof slope. It is deduced from these observations that the flow pattern at model scale, and hence at low Reynolds number, is different from that observed at full scale at high Reynolds number. This deduced flow pattern is sketched in Fig. 7.

R.P. Hoxey et aL/J. Wind Eng. lnd Aerodyn. 69-71 (1997) 547-555

553

Separation ~e . . . . . . n. . . . .

Stagnation "--full-scale "'-model-scale

"-. t

'

~ . ". _ _ _ _ / _ . ~ n ~

dye1- s c a Ie

~ (high Re ) Reattachment model-scale (low Re)

Fig. 7. D e d u c e d flow pattern at model and full scale.

The Reynolds number dependency derived from full scale and presented in Fig. 4 shows no significant Reynolds number effect on the leeward roof nor on the leeward wall. However, the wind-tunnel results do show some differences compared with the full-scale measurements in the vicinity of the ridge which is consistent with evidence of flow separation at the ridge in the model-scale experiments. It is proposed here that the cause of this separation is, in part, attributable to the change in the shape of the separation at the leading edge of the windward roof slope; the reduced extent of the separated flow region at model scale results in earlier reattachment and a greater extent of attached flow on the windward roof slope which assists the separation at the ridge. The use of smoke at full scale has shown that the flow does not separate at the ridge. This observation implies a secondary influence of the Reynolds number effect on the flow pattern and the pressure field downstream of the reattachment on the windward roof slope. The magnitude of the corrections (to be added to the wind-tunnel coefficients to estimate full-scale values appropriate for building design) and their possible areas of influence are presented in Fig. 8. The values presented indicate the correction required for a decade change in Reynolds number. Thus, for example, in the wind-tunnel measurements quoted here, where the scale factor was 1 : 100, the corrections to be applied for a two decade change are twice the values presented in Fig. 8. The measurements that have been analysed for Reynolds number sensitivity at full scale are restricted in this report to the centre section of the building for a transverse air flow. However, it is expected that the separated flow at the ends of the building will have similar Reynolds number sensitivity and that some sensitivity will remain on the leeward side wall near the ends of the building for transverse air flow. No corrections have been shown in Fig. 8 for the windward wall since Fig. 4 indicates that for the lower part of the windward wall there is little Reynolds number sensitivity. However, for the tapping point near the eaves on the windward wall, there is an indication of Reynolds number sensitivity. Using smoke as an indicator shows that this top tapping point on the windward wall is close to the stagnation point at full scale. The lower pressure coefficient at model scale for this tapping point implies that the stagnation point moves down the wall with lower Reynolds number. The mean stagnation streamlines have been sketched in Fig. 7. The cause may be associated with the separated flow on the roof; at full scale the separated flow is more extensive both

554

R.P. Hoxey et al./J. Wind Eng. Ind. Aerodyn. 69 71 (1997) 547 555

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effects

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along the roof and, significant to the observation here, above the roof, giving a higher separation streamline and hence a higher stagnation streamline.

5. Concluding remarks This work shows that significant corrections are required to predict full-scale coefficients from model-scale studies in regions of flow separation. For the building described here, the corrections required are to enhance the suctions by up to - 0.25 in pressure coefficient per decade of Reynolds number which at 1 : 100 scale requires coefficients to be enhanced by up to - 0.5. The magnitude of the additive correction factors are presented in Fig. 8. This observation is consistent with comments made by other authors [-7-9] where model-scale studies have underestimated full-scale measured suctions. There is also evidence, from the flow over a backward-facing step, of the reattachment length being Reynolds number sensitive [10], particularly at model-scale Reynolds numbers. From the full-scale measurements, it appears that Reynolds number effects are limited to regions of flow separation, but possibly also to the stagnation region on the windward wall. However, it is evident that the change in flow pattern in the separated flow region modifies the flow downstream of the separation (and possibly upstream) and, hence, affects the pressure distribution outside the separated flow region. These observations conflict with the previously held view that bluff-body aerodynamics are Reynolds number insensitive. This requires further urgent investigation. Observations at model scale should be conducted over a range of tunnel speeds, and

R.P. Hoxey et al./J. Wind Eng. Ind. Aerodyn. 69-71 (1997) 547 555

555

a d d i t i o n a l m e a s u r e m e n t s m a d e at a n i n t e r m e d i a t e scale in the a t m o s p h e r i c b o u n d a r y layer, w o r k t h a t is n o w in progress. I n b o t h cases, the b o u n d a r y layer r o u g h n e s s l e n g t h m u s t be scaled to the m o d e l d i m e n s i o n s a n d the b o u n d a r y layer p r o p e r t i e s remain invariant with Reynolds number.

Acknowledgements T h i s p r o g r a m m e of w o r k was f u n d e d by the U K M i n i s t r y of A g r i c u l t u r e , F i s h e r i e s a n d F o o d a n d the B u i l d i n g R e s e a r c h E s t a b l i s h m e n t . F i n a n c i a l a s s i s t a n c e was also received f r o m the N a t u r a l Sciences a n d E n g i n e e r i n g R e s e a r c h C o u n c i l of C a n a d a t h r o u g h o p e r a t i n g g r a n t s m a d e a v a i l a b l e to D. S u r r y a n d A.G. D a v e n p o r t at the U n i v e r s i t y of W e s t e r n O n t a r i o .

References [1] G.M. Richardson, D. Surry, The Silsoe building : a comparison of pressure coefficients and spectra at model and full-scale, J. Wind Eng. Ind. Aerodyn. 41~44 (1992) 1653-1664. I-2] G.M. Richardson, P.A. Blackmore, The Silsoe structures building: comparison of I : 100 model-scale data with full-scale data, J. Wind Eng. Ind. Aerodyn. 57 (1995) 191-201. 1-3] G.M. Richardson, D. Surry, The Silsoe building: comparison between full-scale and wind-tunnel data, J. Wind Eng. Ind. Aerodyn. 51 (1994) 157 176. 1-4] R.P. Hoxey, G.M. Richardson, A.P. Robertson, J.L. Short, The Silsoe structures building: the completed experiment, Part 1, 9th Int. Conf. on Wind Engineering, New Delhi, India, 1995. [5] R.P. Hoxey, P.J. Richards, G.M. Richardson, A.P. Robertson, J.L. Short, The Silsoe structures building: the completed experiment, Part 2, 9th Int. Conf. on Wind Engineering, New Delhi, India, 1995. 1-6] G.V. Parkinson, N.J. Cook, Blockage tolerance of a boundary-layer wind tunnel, J. Wind Eng. Ind. Aerodyn. 41~,4 (1992) 873 884. [7] L.S. Cochran, J.E. Cermak, Full- and model-scale cladding pressures on the Texas Tech University experimental building, J. Wind Eng. Ind. Aerodyn. 41~4 (1992) 1589-1600. 1-8] H. Okada, Y.-C. Ha, Comparison of wind tunnel and full-scale pressure measurements test on the Texas Tech building, J. Wind Eng. Ind. Aerodyn. 41~4 (1992) 1601-1612. 1-9] Y.L. Xu, Model- and full-scale comparison of fatigue-related characteristics of wind pressures on the Texas Tech Building, J. Wind Eng. Ind. Aerodyn. 58 (1992) 147 173. ~10] R~L. Simpson, Turbulent boundary-layer separation, Ann. Rev. Fluid Mech. 21 (1989) 205-234.