Investigation of wind speeds over multiple two-dimensional hills

*Corresponding author.

Journal of Wind Engineeringand Industrial Aerodynamics 83 (1999) 109}120

Investigation of wind speeds over multipletwo-dimensional hills

Paul Carpenter*, Nicholas LockeOpus International Consultants Ltd., Central Laboratories, P.O. Box 30845, Lower Hutt, New Zealand

Abstract

A wind tunnel investigation of the wind #ow over two-dimensional, 1 : 1000 scale hills ina simulated atmospheric boundary layer has been performed. The mean speed and longitudinalturbulence have been measured over a variety of hill geometries which included shallowsinusoidal hills, steep sinusoidal hills, consecutive hills and an irregularly shaped hill. Resultsfrom this investigation are presented and are brie#y compared with wind speeds calculatedusing CFD (computational #uid dynamics). ( 1999 Elsevier Science Ltd. All rights reserved.

Keywords: Computational #uid dynamics; Wind speed; Two-dimensional hill

1. Introduction

Accurate wind speed predictions are required for siting wind turbines and estima-ting their power generation capability. In New Zealand, viable wind farm sites aretypically located at the top of ridges and hills where high wind speeds are induced bythe topography. However, current prediction techniques for the wind characteristicsat such sites are not su$ciently accurate and require improvement.

Much of the past research [1}3] into wind #ow over hills has concentrated on low,gently sloping terrain where there is no signi"cant separation. While the windcharacteristics over such topography are generally well understood, the numericalmodels and prediction tools developed from this research do not extend to steeperterrain where separation has a large e!ect on the #ow, particularly over successivedownwind hills.

0167-6105/99/$ - see front matter ( 1999 Elsevier Science Ltd. All rights reserved.PII: S 0 1 6 7 - 6 1 0 5 ( 9 9 ) 0 0 0 6 5 - 3

The research described in this paper was undertaken to quantify the e!ects of steephills and landform on wind speeds and turbulence, and gauge the ability of engineer-ing computer programs to predict these e!ects. The study has consisted of two mainparts. Firstly, a wind tunnel investigation was performed to measure the wind #owover model hills of di!erent geometry. The con"gurations tested include di!erentshaped hills, multiple hills and irregularities in the windward slope of a hill. This paperpresents results primarily from this wind tunnel study. Previous comparable windtunnel studies include the work of Counihan [4], Bowen and Lindley [5], Pearse et al.[6,7], Gong and Ibbetson [8], Ferreira et al. [9}11], Gong et al. [12], Kin et al. [13],Glanville and Kwok [14] and Ne! and Meroney [15].

The second part of the research involved modelling the wind #ow over hillcon"gurations similar to those tested in the wind tunnel, using a commerciallyavailable computational #uid dynamics (CFD) computer program. The program isa general purpose "nite element #uid analysis package which uses the standard highReynolds number k!e turbulence model, except at the hill surface a one elementthick layer of special elements is employed. The predictions obtained through the useof the CFD program have been compared with the measurements from the windtunnel study. The literature on previous use of CFD for analysis of wind speeds overhills includes studies by Ferreira et al. [11], Selvam and Smith [16], Paterson andHolmes [17] and Finardi et al. [18]. To data, the usefulness of CFD to predict windspeeds in practical applications is limited, but this is likely to continue to improve inthe future.

2. Wind tunnel set up

Wind tunnel measurements were made in the boundary layer wind tunnel ofOpus International Consultants Ltd. at Central Laboratories, at a nominal scaleof 1 : 1000. All the models tested were two-dimensional, extending across thefull-width of the wind tunnel perpendicular to the #ow. The hill geometries testedare shown in Fig. 1. For the three hill con"gurations, an additional fourth hill wasalso modelled downwind of the initial three hills. This was intended to representthe e!ects of a series of hills downwind of those three hills where measurementswere taken.

The wind tunnel test section is 1.22 m high ]2.75 m wide has a 5 m long blockagetolerant ceiling section of the type described by Parkinson and Cook [19]. The modelhills were all 200 mm high (except the half height shallow sinusoidal hill), which gavea blockage ratio of 16%. As models with blockage ratios in excess of 20% have beensuccessfully tested [20] in similar wind tunnels no additional blockage correctionswere applied to the measurements. The longest con"guration was the three shallowhills which were 4800 mm long in total and extended along the full length of the testsection.

The reference wind tunnel speed <3%&

at 200 mm above the #oor was 9.6 m/s givinga Reynolds number based on the hill height of 1.3]105. The relatively large size of themodels was chosen in order to achieve a Reynolds number greater than 105. This was

110 P. Carpenter, N. Locke / J. Wind Eng. Ind. Aerodyn. 83 (1999) 109}120

Fig. 1. Hill geometries tested in the wind tunnel.

important as Ferreira et al. [9,11] has shown that a substantial change in #owconditions occurs for Reynolds numbers less than 105. A standard terrain category2 (Z

0"0.02 m, i.e., open grassland) boundary layer was simulated in the wind tunnel

at a scale of 1 : 1000. Surface roughness consisting of textured wallpaper whichcovered the wind tunnel #oor when the reference velocity and turbulence pro"les weremeasured was also applied over the model hills surface. The average height of thewallpaper texture elements was 1 mm. Wind speeds were measured using a TSItsingle hot-"lm anemometer positioned above the centre-line of the test section. Thesignal was sampled at a rate of 1000 Hz and low-pass "ltered at 500 Hz for a 2 minperiod at each location. Wind speeds were measured at heights between 3 and 900 mmabove the local hill surface, measured from the mid-height of the surface roughnesselements. Following this system, all heights, z, in this paper are quoted as local valueswith a value of zero at the hill surface. The probe wire was orientated horizontallyacross the mean #ow thereby eliminating the cross wind horizontal component ofthe #ow.

The reference mean wind speed at a height of 200 mm (hill height) was set to 1.0,with all other speeds scaled relative to this value. The reference boundary layer pro"lewas measured at X"0, which is at the centre of the wind tunnel test section.Additional pro"les were measured at X"!2500 mm and X"#2500 mm. Thestreamwise changes in these pro"les were used to correct the hill measurements forsmall spatial variations in the wind tunnel #ow. In addition, the reference pro"lemeasured did not exactly match the standard Deaves and Harris Category 2 pro"le

P. Carpenter, N. Locke / J. Wind Eng. Ind. Aerodyn. 83 (1999) 109}120 111

and a further correction was applied for this. The corrections for the mean speed andrms are given below in Eqs. (1) and (2).

<"<.%!4(X,Z)<3%&

*< where *<"<D%!7%4&H!33*4(Z)<8*/$ 56//%-(X,Z)

, (1)

RMS"RMS

.%!4(X,Z)<3%&

#*RMS where

*RMS"*RMS

D%!7%4&H!33*4(Z)<3%&

#

*RMS8*/$ 56//%-(X,Z)<3%&

. (2)

The size of these corrections were, for example, for the 3-hill studies at a height of100 mm above each crest:

Crest 1 (X"!1600) Crest 2 (X"0) Crest 3 (X"1600)*V 0.923 0.970 1.005*RMS !0.021 !0.007 0.003.From these measurements a gust speed was calculated using Eq. (3).

Gust speed"<#3.7RMS. (3)

The mean speed ampli"cation factors (and gust speed ampli"cation factors) pre-sented in the results are simply the ratio of the mean (or gust) speed divided by themean (or gust) speed for the reference pro"le at the same local height above theground.

In the following results and discussion all dimensions are expressed as metres at thenominal full scale, (e.g., the 200 mm model hill height is equivalent to a full-scale hillheight of 200 m.)

3. Wind tunnel results for single and multiple hills

Pro"les of the mean speed and rms at the hill crests and valleys are presented inFig. 2 for the single and multiple sinusoidal hill con"gurations. Note that some careneeds to be taken when comparing the crest pro"les with the reference and valleypro"les, particularly higher up in the boundary layer, as the plotting coordinate z isthe height above the local ground level, (e.g., 700 m above a crest is at the same level as900 m for the reference pro"le).

Fig. 2(a) shows how the mean speeds increase over the crests of the shallow andsteep hills. Between about 10 and 100 m height the mean wind speed above the crestsis essentially constant. Greater separation of the #ow downstream of the steep hillscauses a general decrease in the downstream wind speed, and an increase in therms speeds compared to shallow hills. The wake behind the steep hills is evident in therms pro"les where the largest rms speeds, which correspond to the separated shearlayer, occur at or above 200 m (for X"!800, 800, 2400 m). For the shallow hills therms peaks are around 100 m above the ground and have less severe wind speedgradients through the shear layers. For the multiple hills the separation from the "rsthill is the most severe and results in low wind speeds and high rms values at the second


Fig. 2. (a) Mean speed pro"les measured in the wind tunnel for a single hill and for three consecutive hills.(b) rms speed pro"les measured in the wind tunnel for a single hill and for three consecutive hills.


Fig. 3. (a) Mean speed ampli"cation pro"les measured in the wind tunnel for a single hill and for threeconsecutive hills. (b) Gust speed ampli"cation pro"les measured in the wind tunnel for a single hill and forthree consecutive hills.


hill crest. This increased turbulence at the second hill crest helps reduce the#ow separation from the second hill and so increases the mean speed and reducesthe rms at the third hill crest, relative to that at the second hill crest. This e!ectwas also observed by Counihan [3], who tested up to 12 consecutive hills andreported no changes in the #ow pro"les at corresponding positions downstream ofthe third hill. The di!erence between the shallow and steep hills are most pro-nounced at the second hill crest because of the separation behind the "rst steephill.

Ampli"cation factors for the mean speed and the gust speed at the hill crests areplotted in Fig. 3 (i.e. this is the same information as shown in Fig. 2, but presented inan alternative format). The largest mean speed ampli"cation (Fig. 3(a)) measured atthe hill crests was 2.13 and occurred 5 m above the single shallow hill crest. Thecorresponding value for the steep hill was slightly less at 2.08 at 5 m height. For thegust speeds (Fig. 3(b)), on the shallow sinusoidal hills, the highest gust speed ampli"ca-tion factor was 1.67, again at 5 m height on the single hill. For the steeps hills, the gustspeed ampli"cation factor on the single hill was 1.70 at 5 m height, but increased to1.80 at 3 m height. However, the highest gust speeds occurred on the second steep hill,with the gust speed ampli"cation factor reaching a maximum value of 2.00 at 3 mheight. This is because the turbulence generated by the "rst hill produces increasedgust speed ampli"cation factors over the second hill for the full range of heights up toabout 500 m.

The results shown in Figs. 2 and 3 are for measurements directly above the crest orat the base of the hills. Additional measurements were also obtained at locationsupwind and downwind of the crest. The largest mean speed ampli"cation measured atany position on the hills was 2.43 for the single steep hill, measured 25 m upstream ofthe crest at 3 m height. For the shallow hill the largest mean speed ampli"cation was2.18, measured 100 m upstream of the crest at 3 m height. Consequently, it may beseen that the highest mean speed ampli"cation factors for the steep hills occur near thesurface upwind of the crest.

Wind turbine blades typically operate at heights between 20 and 80 m above thelocal ground level. At a representative height of 50 m, the mean speed ampli"cationfactor was 1.70 for the single shallow hill, and 1.56 for the single steep hill. Thesevalues represent an increase in the available wind energy at that height (proportionalto the wind speed cubed) of 4.9 and 3.8, respectively.

4. Wind tunnel results for a hill with an irregular upwind pro5le

To measure the e!ect of irregularities in the pro"le of a hill, steps were formed onthe upwind slope of the single shallow sinusoidal hill as shown in Fig. 4. Five di!erentstep con"gurations were tested, the e!ects of each step con"guration on the wind #owbeing tested separately. The "ve con"gurations weref a 20 m high step, 400 m upwind of the crest,f a 20 m high step, 200 m upwind of the crest,f a 10 m high step, 200 m upwind of the crest,


Fig. 4. Diagram of step positions in the upwind slope of the shallow sinusoidal hill.

Fig. 5(a) Mean speed pro"les at the hill crest for upwind irregularities in the hill pro"le. (b) rms speedpro"les at the hill crest for upwind irregularities in the hill pro"le.


f a 5 m high step, 200 m upwind of the crest,f a 5 m high step, 100 m upwind of the crest.Pro"les of the mean speed and rms at the crest of the hill are plotted in Figs. 5(a)and (b).

The e!ect each step has on the wind #ow is in#uenced by both the height andposition of the step. The 20 m high step, 200 m upstream of the crest, has the greatestimpact on the wind pro"les at the crest. Below 10 m height the mean speed is halvedand the rms increased by 150%. When the distance to the 20 m step is increased to400 m from the crest, the step has a much smaller e!ect. This change is due to the slopeof the hill, which is greatest 400 m from the crest, that helps the #ow reattach afterpassing over the step. Flow visualisation using wool tufts indicated the #ow reattaches100 m downstream of the 20 m step when it is positioned 400 m upwind of the crest,but takes 170 m to reattach when the 20 m step is only 200 m from the crest. A similartrend was observed for the 5 m high steps when they were placed 100 and 200 mupstream of the crest. The position of the step has a large in#uence on the windpro"les at the crest, with both the hill slope and the distance to the crest beingimportant parameters.

The e!ect of step height was tested using three steps, 5, 10 and 20 m high, positioned200 m upstream of the crest. The mean speed shows a consistent reduction withincreasing step height while the rms similarly increases. The height over whichthe crest pro"les are in#uenced also corresponds to the step height. The maximumrms values for most of the pro"les occur at the same height as that of the stepwhich was tested. It may be seen that a relatively small irregularity can havea signi"cant e!ect on the #ow as shown by the 5 m step, positioned 100 m from the hillcrest.

The in#uence of the half-height (100 m high) upwind hill is also shown in Fig. 5. Thee!ect is similar to some of the steps, but extends over a greater height. The typicalreduction in mean speed caused by the upwind hill is about 14% between 10 and100 m height. This is nearly as great as the e!ect of a full height upwind hill as shownin Fig. 2.

5. Comparison of wind tunnel results and numerical results

A general purpose computational #uid dynamics (CFD) program, as described inthe introduction, was used to model the wind #ow over the single and multiple hillcon"gurations. The same mesh was used for all the hill con"gurations and consisted of41 nodes vertically by 361 nodes in the streamwise direction. The #ow domainextended form X"!4000}#4000 and Z"0}#10 000 m. Inlet conditions werematched to the reference wind tunnel conditions.

In broad terms the mean wind speeds calculated showed reasonable agreement withthe wind tunnel results for geometries which has little #ow separation. The rmscalculated using CFD generally showed poor agreement with wind tunnel results.Fig. 6(a) and (b) show the mean speed ampli"cation factors measured in the windtunnel and calculated using CFD.


Fig. 6. (a) Comparison of wind tunnel and CFD mean speed ampli"cation factors at the crest of a shallowsinusoidal hill and a steep sinusoidal hill. (b) Comparison of wind tunnel and CFD mean speed ampli"ca-tion factors at the crest of multiple shallow sinusoidal hills and multiple steep sinusoidal hills.

Interestingly, for the mean speeds obtained for the single hill crests shown in Fig.6(a), the CFD calculates a lower speed than the wind tunnel for the shallow hill, buttypically calculates a higher speed for the steep hill. It should be noted that, for thesteep hill the wind tunnel measurements at the crest near the ground suggest e!ects of


the onset of separation, whereas the CFD separation commences after the crest. Thehighest mean speed ampli"cation factors measured in the wind tunnel occur prior tothe crest. For the steep hill, the highest values were measured 25 m upwind of the crest.For example at 5 m height, a mean speed ampli"cation factor of 2.26 was measured.This di!erence in position accounts for about half the di!erence between the CFDanalysis and the wind tunnel measurements for the steep hill at this height.

6. Conclusions

An extensive set of wind tunnel measurements of wind speeds over hills has beenperformed. A selection of the results has been presented in this paper. For the heightsof main interest for wind energy applications (i.e., 10}100 m) the measured windspeeds were highest over the single shallow hill. However, for the two sinusoidal hillshapes the largest measured mean speed ampli"cation factor was 2.43, which wasmeasured on the single steep hill, at a height of 3 m, upwind of the crest. For multiplehill con"gurations the mean wind speeds decreased compared to the single hillcon"guration, and also decreased downwind of the "rst hill in the series. The gustspeeds at the crests of the hills showed little variation between di!erent con"gurationsand between adjacent hills, except that the highest gust speeds occurred on the secondhill for the multiple steep hill test.

Steps in the upwind pro"le of a hill produced large changes in the wind character-istics at the crest of the hill. The height of the step, the distance of the step from thecrest and the slope of the hill at the location of the step were all important factors thatin#uenced the resulting #ow at the crest of the hill.

Numerical simulations of the wind #ow over the various hill geometries have beencompared with wind tunnel test results. Only mean speed comparisons have beenincluded in this paper. Rms speeds were also calculated but showed poor agreementbetween the wind tunnel and CFD results.

Acknowledgements

This research has been funded by the New Zealand Government through theFoundation for Research, Science and Technology.

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Investigation of wind speeds over multiple two-dimensional hills