Cao 2006 Journal of Wind Engineering and Industrial Aerodynamics

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Journal of Wind Engineering

and Industrial Aerodynamics 94 (2006) 1–19

0167-6105/$ -

doi:10.1016/j

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Experimental study on roughness effects onturbulent boundary layer flow over a

two-dimensional steep hill

Shuyang Caoa,�, Tetsuro Tamurab

aWind Engineering Research Center, Tokyo Polytechnic University, 1583 Iiyama, Atsugi,

Kanagawa 243-0297, JapanbDepartment of Environmental Science and Technology, Tokyo Institute of Technology, 4259 Nagatsuta,

Yokohama 226-8502, Japan

Received 29 October 2004; received in revised form 5 September 2005; accepted 7 October 2005

Available online 18 November 2005

Abstract

Wind tunnel experiments were carried out to study the effects of surface roughness on the

turbulent boundary layer flow over a two-dimensional steep hill, accompanied by a relatively steady

and large separation, sometimes called a separation bubble. Rough surface conditions were modeled

by placing small cubes on the hill surface with an arrangement whose roughness density equaled

4.1%. Vertical profiles of the turbulence statistics over the hill were investigated, and compared with

those for an oncoming turbulent boundary layer over a flat surface covered by cubes with the same

arrangement. Furthermore, measurements of the turbulent boundary layer flow over a smooth hill of

the same shape were taken in order to identify the surface roughness effects. The speed-up ratio

above the crest and the turbulence statistics in the wake were focused on. Flow structures in the

separation bubble were investigated by measuring the velocity with a split-fiber probe. Measurement

with fine resolution in the streamwise direction for near-ground flows was carried out to detect the

reattachment point. The results show that the roughness blocks both on the hill surface and on the

upstream ground affect the speed-up ratio over the hill. The speed-up ratio above the crest of a rough

hill is larger than that of a smooth hill. The separation bubble of a rough hill extends further

downstream, resulting in a larger reattachment length than a smooth hill. The location with the

maximum turbulence intensity in the downstream profile also moves further downstream for a rough

hill. Profiles of reverse-flow intermittency that give a description of the dynamic behavior of the

see front matter r 2005 Elsevier Ltd. All rights reserved.

.jweia.2005.10.001

nding author. Tel.:+81462429656; fax: +81462429656.

dress: [email protected] (S. Cao).

www.elsevier.com/locate/jweia

ARTICLE IN PRESSS. Cao, T. Tamura / J. Wind Eng. Ind. Aerodyn. 94 (2006) 1–192

separation bubble are presented. In addition, variations of power spectrum of longitudinal velocity

fluctuation downstream of the hill are shown for both surface conditions.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Hill; Roughness; Separation and reattachment; Turbulent boundary layer; Turbulent statistics

1. Introduction

Atmospheric turbulent flow over a steeply curved hill involves complicated flowphenomena such as spatial development, separation, reattachment and downstreamrecovery of the turbulent boundary layer. Increase in velocity, or ‘speed-up’, andseparation and reattachment that cause variations in both mean flow and turbulence, aretwo features particularly important for wind engineering applications. This is because, forinstance, in questions of wind turbine siting, it is crucial to understand the position withaccelerations in the mean wind and its magnitude, whereas changes to both the mean windand turbulence are important when predicting the dispersion of atmospheric pollutants inhilly terrain or estimating wind loading on structures. The majority of past studies onairflow over a steep hill have focused on these two flow features [1–3].Meanwhile, it has been shown that the condition of the hill surface, smooth or rough,

should be considered when studying the effects of topography on the airflow. Neff andMeroney [4] investigated the vegetation influence on wind power availability in terms ofthe amplification of wind speed on a crest with and without vegetation on its surface. Theyshowed that removal of vegetation leads to an increase in the speed-up ratio on the crest.Miller and Davenport [5] examined the current Canadian and UK wind loading codes ofpractice for predicting speed-up on the crests of complex terrain considering the upstreamsurrounding topography and surface roughness. They implied the necessity of consideringsurface roughness and upstream flow conditions when predicting speed-up. Both these twostudies were restricted to the speed-up ratio on the crest of a hill for their practical projects.The fundamental roles played by roughness were not considered.Establishment of a separation bubble in the lee side is another important flow feature in

addition to the speed-up. Thus, the influence of surface roughness on separation alsoattracts a lot of attention. From a review of many field observations and wind tunnelexperiments, Finnigan [1] suggested that the occurrence of separation in the wake regiondepends on the hill shape (2D or 3D), steepness and roughness, and for a 2D hill of givensteepness, separation is more likely to occur with increasing roughness. The local surface-air scalar transfer in a hilly region is considered intuitively to be influenced by the surfaceroughness, especially when a separation bubble is formed in the wake region. Research onmodification made by surface roughness on a turbulent structure over a steep hill is likelyto be important for scalar transfer processes, such as particle deposition and pollutantdispersion, which are dominated by aerodynamics. However, there have been a fewdetailed quantitative studies of the roughness effects on the turbulent boundary layerstructure. The majority past researches on airflow over a fully rough single 2D ridge or 3Dhill or wavy hills have been carried out to study the turbulence over a rough hill, not toclarify roughness effects [6–8]. Meng and Hibi’s [9] work was an exception. They studiedthe profiles of mean velocity, turbulence intensities and turbulence structure over a roughhill in comparison with results obtained over a smooth hill. One result showed the

ARTICLE IN PRESSS. Cao, T. Tamura / J. Wind Eng. Ind. Aerodyn. 94 (2006) 1–19 3

downstream movement of the reattachment points. However, its mechanisms were notgiven. In this study, we carried out an experimental study of the turbulent boundary layerover smooth and rough steep hills, with emphasis on the basic roles of the surfaceroughness played on the behavior of the separation bubble and on the speed-up ratio, anddiscuss the physical mechanism of movement of the reattachment point.

Wind tunnel facilities in the Department of Environment Science and Technology,Tokyo Institute of Technology were employed to study the turbulent boundary layer flowover 2D steep smooth and rough hills. The main objective of this study was to obtainaccurate Reynolds number independent measurement data concerning the mean as well asturbulent flow, including the dynamic behavior of the separation bubble. The profiles ofmean velocity and turbulence intensity, the power spectrum and the turbulent structureover the hill were discussed and compared with those of the oncoming turbulence on a flatplate. Flow over smooth and rough hills were also compared in order to identify the effectsof surface roughness. Roughness effects on the speed-up ratio on the crest and thestructure of the separation bubble were focused on. In this study, the rough surfaceconditions were modeled by placing small cubes on the hill surface, rather than using metalmesh [8] or artificial grass [4,9], which has been widely used by many researchers. Using thecubes, the rough surface itself can be quantified with the aid of roughness parameters, forinstance, roughness density, which will be described later. The hill considered in this studyhad a maximum slope of about 321 in the lee side, which is steep enough to establishrelatively steady separation. Another objective of this study was to provide experimentaldata to validate the numerical model of the CFD analysis of flow over hills, which wasinfluenced by both the curvature and pressure gradient, and thus required particularattention to turbulence modeling.

2. Experimental setup

The experiments were conducted in the 1.0m-wide, 0.8m-high by 7.0m-long test sectionof an open circuit wind tunnel. The free-stream turbulence intensity was about 0.3% at theturntable location. The hill model considered had a hill profile given by

yhðxÞ ¼ H cos2 ðpx=2LÞ; �LoxoL,

yhðxÞ ¼ 0; xo� L;x4L, ð1Þ

where the hill model height H was 40mm and the length L was 100mm. Length L isdefined as half the distance between the upwind hill foot and the downwind hill foot (seeFig. 1). This shape had a maximum slope of about 321 (gradient 0.628) on the lee side,which exceeded the critical value (about 161) suggested by Finnigan for separation to takeplace [1]. End plates were employed at the two sides of the hill model. The length in thespan direction of the hill model was 800mm. This hill model gave a blockage ratio of5.0%.

Neutrally stratified atmospheric boundary layers were simulated by placing two arraysof 50mm-high cubes just downstream of the contraction exit, in other words, at theentrance of the test section, followed by 30- and 10mm-high cubic roughness elements,totally covering a length of 1000mm of the test section floor. The height of these roughnesselements decreased gradually downstream to avoid complicating the flow due to suddenroughness change from rough to smooth [9]. The remaining 6.0m length of the test section

ARTICLE IN PRESS

x

y

1000 4000 2000

H=40

2L=200

800

Test section Traversingmechanism

Contractionchamber

Fig. 1. Sketch of experimental setup (the roughness elements on the front 1000mm were placed for both smooth

and rough surface conditions. The following roughness elements, 5mm cubes, were only placed on the rough

surface condition).

S. Cao, T. Tamura / J. Wind Eng. Ind. Aerodyn. 94 (2006) 1–194

floor was covered by 5mm-high cubic roughness elements when a rough surface conditionwas required, otherwise there were no roughness elements for the relatively smooth surfacecondition. No spires or barriers were used in the experiments. Hence, the generatedturbulent boundary layer was close to a naturally grown neutral one. The reason for alsoplacing roughness blocks at the entrance to the test section for relatively smooth surfaceconditions was that we wished to generate a turbulent boundary layer over a smoothsurface with the same boundary layer depth as that of the rough surface boundary layer. Itwas known that the ratio of the boundary layer depth to the hill height was also a factorinfluencing the characteristics of the boundary layer over a hill. The effect of this ratiocould be excluded when the boundary layer depth was set to be the same for both hillsurface conditions. Fig. 1 illustrates the experimental setup, together with the coordinatesystem utilized in this study, where x, y are the free-stream and wall normal velocitydirections, respectively. The origin of the coordinate system is at the center of the hill 5.0mdownstream from the contraction exit. Meanwhile, a subsidiary vertical coordinate,y0 ¼ y� yhðxÞ, was used to express the height above the hill surface.Measurements of mean flow and turbulence statistics were taken using a cross-wire

probe (55P61) and a split-fiber probe (55R55) in conjunction with a 90N10 DANTECconstant temperature anemometer system. The probes were placed with respect to fixedCartesian coordinates in the tunnel. Measurements with the cross-wire probe wererestricted within the upper part (y=H41:0) of the boundary layer because of the flow withlarge incident angle to the probe in the forebody, and highly turbulent flow and reversedflow in the afterboby of the hill, which lead to unreliable measurement results with thecross-wire probe. The split-fiber probe was applied to locations within y=Ho1:0 in thisstudy. One split-fiber probe contained two nearly identical sensors combined on a commonquartz fiber and permitted highly localized flow field measurements. The working principleof the split-fiber probes was the variation of the local transfer coefficient with flow anglefor a heated cylinder placed in a cross flow. Accordingly, the sum of the heat transfer fromthe two sensors depended only on the velocity, while the difference depended on bothvelocity and flow angle in the plane perpendicular to the two sensors. Split-fiber probeshave been used as an alternative to pulsed wires to measure reversed flow. For instance,Kiya and Sasaki [10] investigated the structure of a turbulent separation bubble formed at


the leading edge of a blunt flat plate with the aid of a split-fiber probe. The calibrationprocedure of the split-fiber probe has been described by Boerner and Leutheusser [11] andmodified by Ishihara et al. [12]. In this study, the split-fiber probe 55R55 was calibratedusing Ishihara et al.’s modified method. The calibration results showed that the deviationof the sum of the output voltages of the two separate sensors with pitch angle was lowerthan 71.5% within the velocity region of 1.0–8.0m/s, while the difference between them,which implies the directional response of the probe, was favorably close to the ideal cosinefunction. The thin nickel films of the split-fiber probe, which are covered with 0.5 mm thickquartz coating to protect against oxidation, were deposited on a 200 mm quartz fiber withan active length of 1.2mm. It was much larger than a standard wire/film probe, so itsfrequency response should be checked before being utilized to measure turbulence. Thepower spectrum of the turbulence in a turbulent boundary layer was measured with astandard 5 mm diameter hot-wire probe (55P61) and a 200 mm diameter split-film probewith the same CTA. The power spectra obtained were practically identical within thefrequency region of less than 1.0KHz (not shown). In all the experiments, the output signalwas digitized and sampled for about 30 s at a frequency of 1KHz for each point in theprofiles.

More than ten thousand small roughness elements (5mm cubes) were placed in astaggered pattern on the wind tunnel floor to generate the rough wall turbulent boundarylayer, as illustrated in Fig. 2. This arrangement gave a roughness density l ¼ 4:1%, wherel is defined as the total roughness front area per unit ground area. This arrangement wasmaintained on the rough hill surface. It has been described by Perry et al. [13] that, for arough wall turbulent boundary layer, two types of roughness can be distinguished, referredto as k- and d-type. k-type roughness follows the well-known Nikuradse–Clausercorrelation scheme of velocity profile. However, for a d-type rough wall, the elementsare more closely spaced. Stable vortices are set up in the grooves so that eddy sheddingfrom the elements into the flow will be negligible. As a result, d-type roughness does notfollow the Nikuradse–Clauser correlation scheme. In this study, the arrangement ofroughness elements (W ¼ 7:0b) corresponded to a k-type rough wall turbulent boundarylayer.

The organized spanwise structures have been observed in several types of separated andreattachment flows, for e.g., in the wake of a bluff body [10] and in the flow around a two-dimensional backward-facing step [14]. However, the variance of mean quantities alongthe spanwise direction reported in these studies was not too significant from the wind

W (35mm)

W (

35m

m)

5mm Cube

b(5mm)

Fig. 2. Arrangement of roughness elements for generating rough wall turbulent boundary layer.


engineering point of view. In a preliminary experiment of this study, we measured themean longitudinal velocity along the spanwise direction on the hill crest and reattachmentlocation. Significant variance was not recognized. Therefore, in this study, the turbulencestatistics were measured in the symmetrical plane of the hill model.

3. Flow characteristics

3.1. Undisturbed turbulence—inflow turbulence

Flat boards covered with, or without, roughness elements were placed first on the windtunnel floor to generate turbulent boundary layers over rough or relatively smoothsurfaces. Measurements at a location of 5.0m downstream of the contraction exit of thewind tunnel (where the hill model would be placed) were taken to obtain the flowcharacteristics of the turbulent boundary layers themselves. The profiles of the mean flowand turbulence determined the ‘reference turbulent boundary layer flow’ to be used forcomparison with the profiles taken over the hills. The flow characteristics of theundisturbed turbulence are shown in Fig. 3(a)–(e). The mean velocity profiles are shown inFig. 3(a), which are normalized by U1, the free stream velocity at the same location. Theturbulent boundary layer depth d was about 250mm, or 6.25 times the hill height for bothsurface conditions. The effects of the ratio of boundary layer depth to hill height couldthus be excluded. Similar measurements (not shown) further upstream and downstream ofthis location showed good agreements. It implied that the boundary layer was fullydeveloped and the free-stream velocity could be considered constant around the hill modellocation. Therefore, the pressure gradient along the flow was considered too small toinfluence the separation and wake characteristics significantly.The roughness length z0 was determined by the best fitting of the log law to the measured

velocity profile, with the friction velocity ut and the zero-plane displacement d determinedbeforehand. ut was derived from the Reynolds stress in the constant shear layer regionobserved adjacent to the wall equilibrium layer. From the profiles of Reynolds stressshown in Fig. 3(b), ut is found to be 0:051U1 and 0:033U1 for the boundary layers ofrough and relatively smooth surfaces, respectively. The zero-plane displacement d wasassumed to be 0.7 h (h: roughness element height), which was suggested by Jackson [15].With the obtained values of ut and d, the roughness length, z0 ¼ 0:2mm, was obtained forthe rough surface (see Fig. 3(e)). This flow had a roughness Reynolds number Res

(¼ ut � z0=n, n is the kinematic viscosity) equal to 3.97, greater than the value of 3 that isoften taken as the lower limit indicative of fully rough flow [16]. Recently, Snyder andCastro [17] showed that this lower limit to maintain the fully rough condition coulddecrease to 1.0 when sharp-edged rectangular cylinders are used to model the roughsurface. Therefore, the generated rough surface boundary layer in this study can beconsidered as fully rough flow. Meanwhile, a roughness length z0 ¼ 0:004mm wasobtained for the relatively smooth surface, which is so small that it can be treated as asmooth surface in practice (called smooth surface hereafter). The root-mean-square (rms)values of the longitudinal and vertical velocity fluctuations, su and sv, are shown inFig. 3(c) and (d), respectively, normalized by ut. Near-surface values of su and sv arecomparable with the measurements of other studies, as summarized in Table 1. These dataare generally consistent with the wall similarity hypothesis. In addition, the turbulent

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0 0.2 0.4 0.6 0.8 10

100

200

300

U/U

y (m

m)

Smooth surfaceRough surface

0 1 2

0.5

1

(y -

d)/�


0 1 2 3

0.5

1

�u/u� �u/u�

(y-d

)/�

Smooth surfaceRough surfaceRough surface (Raupach)

100 101 102 1030

10

20

30


y-d (mm)

U/U

�

z0=0.2mm

z0=0.004mm

0 0.001 0.002 0.003 0.004

0.5

1

-u'v'/U 2 y/

�


(a) (b)

(c) (d)

(e)

Fig. 3. Profiles of turbulent boundary layer over flat surfaces: (a) Longitudinal mean velocity, (b) shear stress, (c)

rms of longitudinal velocity fluctuation, (d) rms of vertical velocity fluctuation and (e) mean velocity profiles

expressed with log law.

S. Cao, T. Tamura / J. Wind Eng. Ind. Aerodyn. 94 (2006) 1–19 7

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Table 1

Measurements of flow characteristics over flat surfaces

Smooth Rough

su=st sv=st su=st sv=st

Present 2.35 1.10 2.15 1.13 (rectangular cylinder)

Andreopoulos and Bradshaw [18] 2.24 1.11 2.09 1.00 (sand)

Perry et al. [19] 2.13 1.13 2.18 1.13 (mesh)

Raupach [20] 2.10 1.01 2.04 1.10 (rectangular cylinder)


intensities at the hill height, normalized by local mean velocity, were 8.93% and 15.1%, forsmooth and rough conditions, respectively.A model/field scale of 1:2000, consistent with an atmospheric boundary layer

approximately 500m high, gives an equivalent full scale of z0 ¼ 0:4m, representative ofa suburban area. It also gives an equivalent height of 80m for a hill, with 10m-highobstacles standing on it. In addition, the values of roughness density (l ¼ 4:1%) androughness length (z0 ¼ 0:2mm) obtained under the rough surface condition follow therelation suggested by Raupach [21], such that z0=h varies linearly with l when theroughness density is low.

3.2. Variations of turbulence structure with surface condition

Reynolds numbers, based on hill height H and velocity UH at the hill height of theundisturbed turbulence over flat plate, were about 12,000 and 10,500 for the smooth andrough surface hills, respectively. The difference between Reynolds numbers of the twosurface conditions was not large, so it was not necessary to consider Reynolds numbereffects. The hill considered in this paper had a large slope, so the application of the well-known analytical method that may help us in interpreting the experimental data, or thecheck of the theoretical scheme using our experimental data in turn, could not be carriedout, because the current analytical method is valid only for low or moderate hills.Fig. 4 compares the profiles of longitudinal mean velocity at several downstream

locations of the smooth and rough surface hills with those of reference boundary layer flowshown in break lines. Longitudinal mean velocity is normalized with U1, the free streamvelocity. Some similar flow characteristics can be found between these two surfaceconditions. Flow decelerates at the upwind hill foot and accelerates at the crest, relative tothe respective profile on flat ground. The profiles of mean velocity on the lee side of the hillare completely different from those on the upstream side because of the reversed flow, orthe separation bubble on the lee side. Furthermore, the mean velocity profile does notrecover to its ‘original’ state as in the upstream flow even at x=H ¼ 7:5, which is thefarthest downstream measurement point during this experiment. This means that theturbulence property is influenced by the hill within a long downstream region. Fig. 5 showsthe profiles of the rms of longitudinal velocity fluctuation su for smooth and rough surfaceconditions, and compares them with the profiles of turbulence of the reference boundarylayers. Although there are no significant variations of su relative to the turbulence ofreference boundary layer on the foreside of the hill, it deviates greatly on the lee side, with

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0

1

2

3

4

y/H

00 0 0 0 0 0 0

0 1

exp., Re=10500

0

Velocity profile of reference boundary layer

0

1

2

3

4x/H=-2.5 2.5 3.75 5.0 6.25

y/H

00 0 0 0 0 0 0

0 1

exp., Re=120007.5

x/H=-2.5 2.5 3.75 5.0 6.25 7.5

0

Velocity profile of reference boundary layer(a)

(b)

U/U

U/U U/U

U/U

Fig. 4. Mean velocity profiles over smooth and rough hills: (a) Smooth surface and (b) rough surface.

0

1

2

3

4

y/H

00 0 0 0 0 0 0

0 0.2

exp., Re=12000

0

Turbulence of reference boundary layer

0

1

2

3

4x/H=-2.5 5.03.75 6.25

y/H

00 0 0 0 0 0 0

0 0.2

exp., Re=105007.5

x/H=-2.5 5.03.75 6.25 7.5

0

Turbulence of reference boundary layer

(a)

(b)

�u /U

�u /U �u /U

�u /U

Fig. 5. Profiles of turbulence intensity over smooth and rough hills: (a) Smooth surface and (b) rough surface.



increased values at approximately the hill height due to the separated shear layer.Although the general structures of the turbulent boundary layers over smooth and roughhills are quite similar, some differences between the statistical and dynamical structures arefound by detailed analysis of the experimental data, among which the roughness effects onthe speed-up ratio, and separation bubble including the reverse-flow intermittency, as wellas the power spectrum are mainly described.

3.2.1. Turbulence statistics on the crest

In assessing the impact of topography on design wind speed, it is convenient to considerthe increase in mean wind velocity over the hill with the aid of a parameter called fractionalspeed-up ratio, which is defined by:

sðx; y0Þ ¼DU

U0ðy0Þ¼

Uðx; y0Þ �U0ðy0Þ

U0ðy0Þ, (2)

where U(x, y0) is the wind speed at height y0 above the local surface of the hill and U0(y0) is

the reference wind speed at the same height above the flat surface. Eq. (2) relates theincrease in wind speed at a given height to the undisturbed wind speed at the same heightabove the surface. Fractional speed-up ratio over a sinusoidal terrain can be satisfactorilypredicted from theoretical frameworks if the slope of the hill is below 0.5. However, for thesteep hill in this study, application of an analytical method will yield unacceptable errors,so a wind tunnel study is often relied on. Several countries have put forward empiricalrelations between fractional speed-up ratio and the scales of the hill shape from extensiveexperimental data as their national wind loading codes. In this study, we reveal the basicrole the roughness blocks play in the velocity change, and shed some light on matters thatneed attention in predicting the speed-up ratio.Profiles of speed-up ratio over smooth and rough hills, obtained at the upwind hill foot,

crest and downwind hill foot, are shown in Fig. 6(a). The rough hill case shows a slightlylarger deceleration at the upwind hill foot than the smooth hill, compared with respectiveupstream profile. Speed-up ratios for both surface conditions are negative at the downwindhill foot where the flow is in the ‘dead water’ region. The most significant location forconsidering the speed-up ratio is on the crest where large acceleration occurs. Themeasurements show that the speed-up ratio at the crest of the rough hill is obviously largerthan that at the crest of the smooth hill below height y0 ¼ 4h (0.5H) (h: height of roughnessblock). The speed-up ratio at y0 ¼ 2h (0.25H) is 0.875 and 0.457 for the rough and smoothhills, respectively. Meanwhile, for the profile of speed-up ratio on the crest, there should bea height y0max where DU is maximum in the profile because of the demand of no-slipcondition on the hill surface. The height y0max and the magnitude are of practicalimportance for wind engineering applications. Unfortunately, we could not detect thembecause the measurements did not reach close enough to the surface. However, we canpredict that y0max on the crest of the rough hill appears at a higher position than on the crestof the smooth hill, because the inner layer where the boundary layer is in local equilibriumbecomes deeper on the crest of the rough hill, which will be described later.The variations of speed-up ratio shown in Fig. 6(a) are obtained for a smooth hill in

smooth flow and a rough hill in rough flow. However, consideration of any realtopography soon shows that these two conditions are highly idealized. It is very commonthat a hill has a roughness cover or roughness grade different with its surroundings. For agiven hill, the change in upstream roughness grade affects the characteristics of upstream

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-1 0 10

2

4

6

8

upwind, smoothupwind, roughcrest, smoothcrest, roughdownwind, smoothdownwind, rough

S

y'/H

0 0.2 0.4 0.6 0.8 10

2

4

6

8

smooth hill in smooth flowrough hill in rough flowsmooth hill in rough flowrough hill in smooth flow

Sy'

/H(a) (b)

Fig. 6. Roughness effects on fractional speed up ratio: (a) At upwind, downwind and crest of hill and (b)

dependence on upstream and surface rough condition.


turbulence, and thus influences the turbulence structure over the hill. Thus, variation ofspeed-up ratio with difference of roughness covered on the hill and on the surroundingsshould also be taken into consideration. An extreme change in roughness grade on thesurface may be a sudden roughness change from smooth to rough or from rough tosmooth. Thus, additional experiments were carried out for a smooth hill in rough flow anda rough hill in smooth flow. The results of speed-up ratio on the crest obtained for thesefour conditions (smooth hill in smooth flow, smooth hill in rough flow, rough hill insmooth flow and rough hill in rough flow) are summarized in Fig. 6(b). With approachingthe hill surface, the speed-up ratios deviate greatly, indicating that they depend strongly onthe surface conditions (smooth or rough) of both the hill and its upstream ground,especially below height y0 ¼ 4h (0.5H). Speed-up ratio at y0 ¼ 2h (0.25H) shows therelation Sroughflow;smoothhillð0:918Þ4Sroughflow;roughhillð0:875Þ4Ssmoothflow;smoothhillð0:457Þ4Ssmoothflow;roughhillð0:245Þ. This can be explained by the following process. Although theturbulence statistics on the upwind hill foot for a given upstream roughness is almostunchanged with the surface condition of the hill (not shown), velocity defection is enlargedcompulsively by the roughness blocks on the hill surface for a rough hill in smooth flow,resulting in a smaller speed-up ratio on the crest than for a smooth hill in smooth flow.However, for a smooth hill in rough flow, the flow accelerates more easily above the hillsurface because of the removal of the roughness blocks, resulting in a larger speed-up ratiothan for a rough hill in rough flow. Thus, it can be concluded that speed-up ratio receivescombined effects of hill surface condition and upstream surface condition. For a steep hillof a given shape, rough upstream surface condition leads to a larger speed-up ratio thanthe smooth upstream surface condition, and hill surface roughness reduces the speed-upratio when the same upstream surface condition is considered.

Turning to turbulence, Fig. 7 shows the profiles of the rms value of longitudinal velocityfluctuation su and Reynolds stress u0v0 on the crest. Each quantity is normalized by its

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0.2 0.4 0.6 0.8 10

0.5

1

�u/�ur

y' /�

y' /�


0 1 20

0.5

1 Smooth surfaceRough surface

u'v'/u'v'r(a) (b)

Fig. 7. Profiles of turbulence statistics on the crest: (a) rms of the velocity fluctuation and (b) Reynolds stress.


value in the upstream flow at the same height, sur and u0v0r. su becomes smaller than in theupstream flow on the crest under both surface conditions. This is evidence of the well-known phenomenon of flow laminarization on the top of a curve. In addition, su=sur forthe rough hill is smaller than that for the smooth hill, especially near the hill surface,indicating that the turbulence is suppressed more for the rough hill. A similar tendency canbe found in the profile of u0v0=u0v0r, shown in Fig. 7(b). The rough hill has a smaller value ofu0v0=u0v0r than the smooth hill, and this becomes more obvious with approach to the hillsurface. In addition, the point with the maximum u0v0=u0v0r is located at a higher position inthe rough surface condition. This suggests that the inner layer expands upwards for therough hill, leading to a higher position of y0max of DUmax.

3.2.2. Turbulence statistics in wake

One significant feature of turbulent flow over a steep hill is the establishment of aseparation bubble on the lee side. Variation of the reattachment point or the length of theflow recirculation zone, with the surface condition is of particular importance inconsidering the scalar transfer on the lee side of the hill. Fig. 8 presents the profiles of timemean longitudinal velocity in and around the separation bubble over smooth and roughhills. The broken line shows the dividing streamline that passes through the points wherethe mean velocity is zero. The dividing streamline lies below the separating and reattachingstreamline, but gives a clear indication of the extent of the separation region. Fig. 8 showsthat, although there is only a slight difference between the heights of the dividing points forthe two surface conditions at x=H ¼ 1:25 above the hill surface, it deviates more noticeablydownstream, and finally reattaches to the ground at the reattachment point at a distancexL=H ¼ 5:4 and 6.5 from the hill center, respectively, for the smooth and rough hills. Thereattachment length of the rough hill is larger. This agrees with our numerical results [22]and Meng et al.’s experimental result [9]. The reattachment point is determined byextrapolating to y ¼ 0 of the dividing points (Fig. 8) in practice. In order to get an accurate

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0

1

2x/H= 0 2.53 3.75 3.0 6.25

y/H

00 0

0

7.5

0

1.25

Smooth surface Rough surface

1

2

0 0 0 0

1U/UU/U

Fig. 8. Dividing streamlines of smooth and rough hills.

4 6 8 10

-1

0

1

2

U (

m/s

)

Int.0.5

1.0

0.0

U

Int.

Smooth hill (y=2mm)

Rough hill(y=7mm)

x/H

Fig. 9. Distribution of mean velocity and reverse flow intermittency.


measurement of the reattachment length, probes are traversed from x ¼ 150 to 320mmwith a downstream interval of 10mm at 2mm above the floor for the smooth hill, and7mm above the floor (2mm above the roughness block) for the rough hill. Fig. 9 shows thedownstream variations of mean velocity of the smooth hill at y ¼ 2mm and for the roughhill at y ¼ 7mm. The point where the mean velocity changes from minus to plus, that is tosay U ¼ 0, is the nearest dividing point to the ground that we could detect in theexperiment. Fig. 9 shows that this dividing point, and thus the reattachment point of therough hill, is further downstream.

Meanwhile, the downstream distributions of reverse-flow intermittency for both surfaceconditions are obtained and shown also in Fig. 9, where reverse-flow intermittency isdefined as the fraction of time during which the flow at a given position is in reversal. Fig. 9shows that at points U ¼ 0 for both surface conditions, the reverse-flow intermittencyequals 0.5, which means that the forward flow and reversed flow share 50% each at thedividing point near the ground. This flow phenomenon was also noticed by Moin et al. intheir numerical research on the backward-facing step flow [23]. Another interestingphenomenon worth noting is that the reverse-flow intermittency never equals unity even atthe middle of the separation bubble. However, the separation point on the hill surface was

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0

0

0 0 0 0 0 0 0 0 0

0.2

1

2

3

4x/H=-2.5 6.253.75 5.0

y/H

Smooth su aceRough surface

7.5Smooth suraceRough surface

�u/�U �u/�U

Fig. 10. Vertical profiles of rms values of longitudinal velocity fluctuation.


not measured during the experiment. We will study it and analyze its variation with surfacecondition in our continuing numerical research.Fig. 10 shows the vertical profiles of rms value of the longitudinal velocity fluctuation su

at several downstream locations. A sharp change in su is noticed in the profile on the leeside. The peak value of su in the profile appears approximately at the hill height. Actuallythe peak position of the rough hill is a little higher than that of the smooth hill, especiallyat x=H ¼ 1:25 and x=H ¼ 2:5, after the separation. The broken line passes the positionwith peak value of su in the profile. This line can be considered as indicative of the centerof the separated shear layer. Fig. 10 shows that the separated shear layer from the roughhill appears at a higher position than that from the smooth hill. Roughness blocks on therough hill surface are considered to contribute to it. Variation of su=U1 with hill surfacecondition is also shown in Fig. 10. It is interesting that, however, su=U1 of the rough hillis larger than that for the smooth hill at the foreside of the hill as well as on the oncomingturbulence, it becomes smaller at the lee side of the hill within the region roughly below thehill height, while it remains in the region above the hill height. This means that theseparated shear layer from the rough hill is not as strong as that from the smooth hill.Based on this and the result that the turbulence on the crest is more suppressed on therough hill (Fig. 7), we predict that the Reynolds stress inside the separation bubble, whichis impossible to measure with the split-fiber probes in this study, is smaller on the roughhill. This prediction is supported by the measurement of Reynolds stress at x=H ¼ 7:5shown in Fig. 11, in which the Reynolds stress is indeed smaller for the rough hillcondition. The momentum from the ground in the near wake region is smaller for therough hill, so the reattachment bubble extends further downstream until the flow returns toa fully turbulent state to reattach on the ground.In addition, Fig. 12 presents the downstream profiles of the rms values of the

longitudinal velocity fluctuation for both rough and smooth hills. The peak positions inthese profiles are generally comparable with respective dividing points in the mean velocityprofile along the near-ground surface shown in Fig. 9. Fig. 12 shows that the downstreamlocation with maximum turbulence intensity in the profile along the near-ground surfacediffers from the surface condition. It shifts further downstream in the rough hill condition.This feature is one important effects of the surface roughness and requires special attentionin wind engineering applications.Fig. 13 presents the distributions of reverse-flow intermittency on the lee side of the hills.

It is found that the reverse-flow intermittency has a value unequal to zero within almost thewhole hill wake region measured in this study for both surface conditions. Reversed flow

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0 0.002 0.004 0.006 0.008 0.010

0.5

1

-u'v'/U 2

y/� 7

.5

Smooth surface

Rough surface

Fig. 11. Vertical profiles of Reynolds stress at x=H ¼ 7:5 (d7:5: depth of the reference boundary layer at

x=H ¼ 7:5).

3 4 5 6 7 8 90.5

0.6

0.7

0.8

0.9

1

x/H

� u (

m/s

)

Rough hill(y=7mm)

Smooth hill(y=2mm)

Fig. 12. Downstream profiles of rms of longitudinal velocity fluctuation.


also exists at points outside of the separation bubble. At a given point, the reverse flowintermittency of the rough hill is larger than that of the smooth hill, and the differencebetween them becomes larger toward the ground. These flow features should be taken intoconsideration when the scalar transfer, e.g., pollutant dispersion, at the lee side, isdiscussed.

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0

0.5

1

1.5

x/H2.5 3.75 5.0 6.25

y/H

0

Int.1.0 Int.

1.25

Smooth Rough

Fig. 13. Profiles of reverse-flow intermittency: (a) Smooth hill and (b) rough hill.


3.2.3. Power spectrum

Spectral analysis was carried on the longitudinal velocity fluctuations in the wake to helpinvestigation of vortex behavior on the lee side of the hill. Fig. 14 shows the power spectraat several downstream locations (x=H ¼ 0:0, x=H ¼ 2:5, x=H ¼ 5:0) with the same height(y0=H ¼ 1:0) above the ground, where f is the frequency. The x and y coordinates in Fig. 14are normalized by the local mean velocity UH and the variance of the velocity fluctuationsu, respectively. The Karman-type power spectra of the inflow turbulence obtained aty=H ¼ 1:0 are also shown as references. The power spectra at three downstream locationsof both hills display �2/3 slope in the inertial subrange, predicted by Kolmogorov’shypothesis. The very dominant spectrum peak usually occurring at the vortex-sheddingfrequency of a bluff body was not found in these power spectra. The measured powerspectrum presents a broad peak at a higher frequency than the oncoming turbulence. Thepower spectrum of the rough hill shows a larger decrease from that of the upstreamturbulence at the low normalized frequency number, than that of the smooth hill.Furthermore, the power spectrum of the smooth hill shows recovery toward the powerspectrum of the inflow turbulence at x=H ¼ 5:0, but it is not clear at the same downstreamlocation for the rough hill. All these factors indicate that a longer downstream distance isnecessary for the turbulent boundary layer over a rough hill to recover its original state asin the upstream turbulence.

4. Summary and conclusions

We have shown wind tunnel measurements of the turbulent boundary layer over a 2Dsteep hill. A split-fiber probe was utilized to measure the high turbulent flow as well asreversed flow. The rough surface condition was modeled by placing small cubes on the hillsurface with an arrangement whose roughness density equaled 4.1%. Vertical profiles ofthe turbulence statistics over the rough hill were compared with the profiles over a flatsurface covered by cubes with the same pattern. Furthermore, for a smooth hill with thesame shape, measurements were taken to identify the surface roughness effects.The measurements show that the fractional speed-up ratio on the crest depends on both

the hill surface condition and the upstream surface condition (smooth or rough). Thedependence becomes stronger with approach to the hill surface, especially below y0o4h.The rough inflow surface condition leads a larger fractional speed-up ratio than thesmooth inflow surface condition, and the hill surface roughness reduces the fractional

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-2/3 slope

100

10-1

10-1 10010-2

10-2

fH /UH

10-1 10010-2

fH /UH

fSu

/ �2

100

10-1

10-2

fSu

/ �2

inflowx/H=0.0x/H=2.5x/H=5.0

inflowx/H=0.0x/H=2.5x/H=5.0

-2/3 slope

(a)

(b)

Fig. 14. Power spectrum.


speed up ratio when the same inflow surface condition is considered. Accordingly,Sroughflow;smoothhill4Sroughflow;roughhill4Ssmoothflow;smoothhill4Ssmoothflow;roughhill.

Variation of flow separation on the hill surface condition was investigated in this study.The separation region, as defined by the U ¼ 0 locus, extends further downstream for therough hill. The separated shear layer of the rough hill is weaker than that of the smoothhill. The momentum from the ground is smaller for the rough hill, so the separation bubbleextends further downstream until the flow returns to the fully turbulent state to reattach tothe ground. In addition, the downstream location with maximum turbulence intensity inthe downstream profile is also dependent on the surface condition. The peak position ofturbulence intensity shifts further downstream in the rough hill condition. Furthermore,the distribution of reverse-flow intermittency on the lee side of the hill is shown. The roughhill has larger reverse-flow intermittency than the smooth hill at a given point, especiallynear the ground. The reverse-flow intermittency has a value not equal to zero withinalmost the whole hill wake region measured in this study. Reversed flow also exists atpoints outside of the separation bubble. However, no separation point was detected in the


experiment. We will study this factor and analyze its variation with surface condition inour continuing numerical research.Power spectra of both surface conditions display �2/3 slope in the inertial subrange, as

predicted by Kolmogorov’s hypothesis. The power spectrum of the rough hill shows alarger decrease from that of the inflow turbulence at the low normalized frequencynumber, than that of the smooth hill. Furthermore, downstream recovery of the powerspectrum is slow for the rough hill.Finally, we point out that the results shown in this paper are the combined effects of the

roughness blocks on the hill surface and on the upstream ground. The variations are notgenerated only by the roughness blocks on the hill surface. The contribution of theroughness blocks on the upstream ground is also important. The rough condition of theupstream ground determines the property of the upstream turbulence, which playsimportant roles in the variation of the turbulent boundary layer over the hill.

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Cao 2006 Journal of Wind Engineering and Industrial Aerodynamics