surface pressure and wind load characteristics on prisms immersed in a simulated transient gust...

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J. Wind Eng. Ind. Aerodyn. 98 (2010) 299–316

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Journal of Wind Engineeringand Industrial Aerodynamics

0167-61

doi:10.1

� Corr

E-m

kareem

miyazak

journal homepage: www.elsevier.com/locate/jweia

Surface pressure and wind load characteristics on prisms immersedin a simulated transient gust front flow field

Kyle Butler a,�, Shuyang Cao b, Ahsan Kareem a, Yukio Tamura c, Shigehira Ozono d

a NatHaz Modeling Laboratory, University of Notre Dame, Notre Dame, IN 46545, USAb State Key Lab for Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, Chinac Wind Engineering Research Center, Tokyo Polytechnic University, Kanagawa 243-02, Japand Department of Applied Physics, Faculty of Engineering, University of Miyazaki, 889-2192, Japan

a r t i c l e i n f o

Article history:

Received 22 March 2009

Received in revised form

23 October 2009

Accepted 18 November 2009Available online 16 December 2009

Keywords:

Thunderstorm

Downburst

Gust fronts

Multiple fan wind tunnel

Transient surface pressures

05/$ - see front matter & 2009 Elsevier Ltd. A

016/j.jweia.2009.11.003

esponding author. Tel.: +1 574 631 8453.

ail addresses: [email protected] (K. Butler), shu

@nd.edu (A. Kareem), [email protected]

i-u.ac.jp (S. Ozono).

a b s t r a c t

Thunderstorm generated gust fronts are responsible for various degrees of structural damage in many

areas of the world. However, the resulting impact of gust front winds is not fully understood to such a

level that their flow kinematics, dynamics and impact on structures can be quantified with some

certainty. Gust front winds are transient in nature and have a flow profile which differs significantly

from a typical boundary layer flow field. This study focuses on investigating the effects of this flow

profile and its transient nature on the aerodynamics of bluff, prismatic bodies. A gust front type flow

field is generated using a multiple fan wind tunnel and the resulting surface pressures are captured on a

suite of prismatic models, which vary in size in relationship to the oncoming wind profile. The temporal

variations in surface pressures are analyzed using traditional time, frequency and time-frequency

domain schemes. Results indicate the changing nature of the surface pressure field in time, highlighting

both qualitative and quantitative differences between local and area-averaged pressures under a host of

flow profiles.

& 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Many severe wind events are not caused by typical boundarylayer type winds and associated fluctuating components, but bylarge scale transient phenomena. Thunderstorm spawned windevents, i.e. gust fronts and downbursts, inflict significant damageand result in loss of lives and property, particularly to low or mid-rise buildings, transmission lines, industrial structures and,potentially, long span bridges (Fujita, 1985, 1990; Holmes,1999; Changnon, 2001; Wakimoto, 2001; Letchford et al., 2002).Studies have shown that thunderstorm generated winds are theprevailing design wind speeds for higher recurrence intervals formany locations within the United States (e.g. Twisdale andVickery, 1992), highlighting the need for more fundamentalstudies of their flow behavior. Thus, new simulation and modelingtechniques are required to effectively reproduce gust frontcharacteristics at the laboratory scale. Characteristics of interestfrom these gust events are, primarily, their horizontal windvelocity profiles near the ground surface and their short life span.Additionally, the impacts of such events are not as easily

ll rights reserved.

[email protected] (S. Cao),

.jp (Y. Tamura), ozono@phys.

quantified as is the impact of typical synoptic boundary layerflows, and little is understood about the true nature of theirinfluence on the aerodynamic behavior of bluff bodies.

The simulation of downbursts and gust fronts has beenattempted through various physical and numerical techniquesincluding impinging jets (e.g. Wood et al., 2001; Chay andLetchford, 2002; Letchford and Chay, 2002), large vortex gen-erators (Sarkar et al., 2006), wall slot jets (Lin and Savory 2006),and a flat plate at high incidence (Butler and Kareem, 2007b),along with various types of numerical schemes and modelsreproducing downbursts (e.g. Nicholls et al., 1993; Chay et al.,2006; Kim and Hangan, 2007). This work presents the use of anew facility to study the impact of gust front type outflows onstructures. As opposed to recreating the entire downburststructure (i.e. a descending core column of air), a more basicapproach was employed to investigate the broader impacts of theground level outflow, identifying features in the resulting surfacepressure field that distinguish the impact of these events fromsynoptic flow systems. In order to accomplish this, a newlydesigned wind tunnel was employed to isolate the impact of twodistinct features of gust front flows: the near ground flow profileshape and the rapid, transient changes. The impact of thesevariations were captured on a series of square cross-section,prismatic models, and the results were analyzed using a variety oftime and time-frequency techniques, comparing them with theexisting body of research regarding flows around prismatic shapes

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K. Butler et al. / J. Wind Eng. Ind. Aerodyn. 98 (2010) 299–316300

(e.g. Kareem and Cermak, 1990; Lin et al., 2005). The resultspresented consider both qualitative and quantitative measures toexpose the underlying aerodynamics involved.

Beyond the basic bluff body aerodynamics viewpoint, theseexperimental results aim to build upon the body of knowledgeregarding bluff body aerodynamics in boundary layer flows thathas, thus far, served as a foundation for the design of windresistant structures. In order to make the proper comparisons,however, the impact from the various features of gust front typeflows should be delineated, making it easier to incorporate intonew design paradigms such as the gust-front factor (Kwon andKareem, 2009). This experimental program attempts to addresstwo of these features: the kinematic effects resulting from thevelocity pressure relationship in the profile shape and thetransient aerodynamic effects resulting from the rapidly varyingflow field.

2. Experimental setup

Experiments were carried out in the 3-D multiple-fan windtunnel constructed at the University of Miyazaki, a description ofwhich is given in Fig. 1a. The tunnel is composed of a series of 99fans arranged in a grid-like pattern, each individually controlledthrough separate AC servo-motors. The development of thisfacility from a 2- to 3-D domain and subsequent experiments

Fans (11 Vertical x 9 Horizontal)

Honeycomb

17.5 mm

52.5 mm

70.0 mm

H

70..0 mm

57.5 mm

12.5 mm

100 D

Fig. 1. (a) Configuration of the 3-D multiple fan wind tunnel, from Cao et al. (2002). (b

utilizing this facility have shown its efficacy in generating andreproducing various statistical characteristics of atmosphericflows (e.g. Nishi and Miyagi, 1995; Cao et al., 2001, 2002; Ozonoet al., 2006). The test section measures 15.5 m long (adjustable),2.6 m wide and 1.8 m high. Based on the dynamic nature of thissystem, and its inherent capability to tailor flow fields, it waspresented as an ideal choice to aid in the modeling of gust fronttype out-flows.

In this study, emphasis was placed on generating a transientvariation of the mean flow profile while also replicating thegeneral shape of a gust front outflow for detailed surface pressuremeasurements. The objective was to capture and identify varioustrends in the resulting surfaces pressures on a prismatic model toboth the inflow profile shape and the concurrent increase in flowspeed. Surface pressures were monitored on three prismaticmodels (a general layout of the measurement locations is shownin Fig. 1b) and each varied in height with respect to the elevationat which the maximum outflow velocity occurred in the gustprofile. The first model (M1, H=0.420 m) was designed such thatthe roof level was above the elevation of maximum velocity in thegust profile, and contained 176 pressure measurement locationsdistributed over the windward, side and leeward surfaces. Thesecond prismatic model (M2, H=0.205 m) was designed such thatits height was closest to the elevation of maximum velocity, andthe third prismatic model (M3, H=0.085 m) was reduced such thatits roof level height was below the elevation of maximum

Turn tableTraverse mechanism

mm

100 mm

) A general schematic of pressure measurement locations on the prismatic model.

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K. Butler et al. / J. Wind Eng. Ind. Aerodyn. 98 (2010) 299–316 301

velocity. On each model, pressure measurements were taken atvarious levels, with 20 pressure measurement locations evenlydistributed on each level. Therefore, the smallest model had 60pressure measurement locations and the mid-height model had120 measurement locations.

In each test case presented, the increase in velocity at theelevation of maximum outflow, between the boundary layercondition and the gust front condition, remained fixed and wasapproximately 7 m/s. Each model was subjected to the same,repeated time history of flow conditions. Additionally, the angle ofattack of each model was varied between 01 and 451. The meanflow profile and the turbulence intensity profiles of boththe boundary layer and gust front flow conditions are presentedin Fig. 2a and b, where z is the height above the surface, zmax isthe elevation at which the maximum velocity occurs and z0.5 is

Fig. 2. (a) Velocity profile of the initial boundary layer and the subsequent gust flow fie

turbulence intensity profile of both the initial boundary layer profile and gust flow fie

the elevation at which the velocity is half of the maximum.The maximum velocity in the gust front profile was locatedat an elevation of approximately 0.246 m above the tunnelfloor.

Statistics for the mean profile and turbulence intensity wereassessed in the time periods before and after the flow accelera-tion/deceleration, thus the transient segments were not included.The mean gust front outflow exhibits the characteristic ‘‘nose’’shape in the near ground region and matches the existing flowregime at the boundary layer height. The higher turbulenceintensity values occur within the region of the increasingvelocities in the near ground region, while only a slight increaseis evident above the maximum outflow elevation. Although thereare measurements of turbulence intensity profiles in relation toimpinging jets and wall jets (i.e. Letchford and Chay, 2002; Lin

ld with a comparison to the full scale data catalogued in Hjelmfelt (1988). (b) The

ld.

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and Savory, 2006), and through some full scale captures of gustfronts and downbursts (e.g. Orwig and Schroeder, 2007), there islittle information regarding the full behavior of the gust frontprofile from which to draw accurate comparisons, particularlyregarding the turbulence profile or the transient development ofsuch a profile. Comparisons with similar test efforts, althoughperformed under different experimental conditions, and availablefull scale measures are shown in Fig. 2a and b.

Fig. 3. (a) Example time history of velocity at the height of maximum outflow velocit

during the flow field change from the initial boundary layer profile to the gust flow fie

3. Results and discussion

Each prismatic model studied was exposed to a gust front likeevent, where the wind speed was accelerated to induce changes inthe flow profile, obtaining the characteristic shape attributed to gustfronts. In this case, the prismatic models were exposed to aboundary layer flow field before a gust front like profile wasinduced for approximately 80 s, ending with the wind speed profile

y. (b) Detail of velocity time history (at the height of maximum outflow velocity)

ld.

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given in the initial flow condition, i.e. the boundary layer flowprofile. Fig. 3a shows an example time history of the velocity at themaximum outflow level. Velocity measurements were acquired, viahot wire probes, at the elevation of maximum velocity established inthe gust profile generated by the tunnel configuration shown inFig. 2a. The gust simulations produced in this experiment occurredwithin a period of 120 s, where velocity and pressures, corrected forany resonant amplification in the tubing, were sampled at 500 Hz.

The scaling of extreme gust events can be based on anynumber of parameters, e.g. downburst outflow radius or max-imum velocity elevation. In this particular case, the gust scale canbe based on the profile shape and the length of the transitionperiod from boundary layer to gust flow. Fujita catalogued variousdifferent downburst cases, which can provide a basis for scalingexperimental conditions. The downburst profiles examined byFujita (1985, 1990) identified maximum outflow velocity atheights between 30 and 100 m and maximum speeds up toapproximately 75 m/s. Based on this particular full scale informa-tion, length scales linked to the elevation of maximum velocityproduced in the wind tunnel approximately range between 1/120and 1/400. Velocity scales based on a maximum outflow speed of11 m/s is approximately 1/7, yielding a range of time scalesbetween 1/17 and 1/57. Assuming that the transition to a gustprofile occurs over an interval of 1–2 s, as presented in this study(a sample time history of which is shown in Fig. 3b, along with asurface pressure time history in Fig. 13a), this represents extremeevents lasting approximately 20–120 s, based on the size of a fullscale event. For comparison, the classic Andrews Air Force Baseevent in 1983 experienced an increase in velocity from theambient condition to a maximum gust speed occurring within awindow of approximately 2 min. However, continued analysis offull scale gust front events will certainly introduce new scalingchallenges.

3.1. Mean and RMS of surface pressures

Comparisons of the mean surface pressures within each of thetwo flow profiles showed variations in both the level of pressureincrease and regions of dominant impact. Mean surface pressures

Fig. 4. (a) Contours of the mean pressure coefficient on model M1 on windward face

pressure coefficient on model M1 on the side face in both boundary layer (left) and gu

were estimated using

Cp ¼pðtÞ�p112rU2

max

ð1Þ

where p(t) was the measured pressure, pN was the atmosphericreference and Umax was the velocity measured at the elevation ofmaximum outflow. The results for the boundary layer casecompares well with other experimental data for tall and low-rise structures (e.g. Surry and Djakovich, 1995; Tamura et al.,1997). The mean pressure coefficient on the windward surface ofM1, shown in Fig. 4a, indicates a shift in both the location of themaximum pressure and an increase in pressures, compared tothe initial boundary layer flow condition, in the lower region ofthe model surface (where z is the vertical direction, x is thehorizontal direction and H and D are the height and width of themodel, respectively). In the boundary layer flow, the meanpressure coefficients on the side faces were more negative thanthat experienced in the gust front flow. Similar trends were alsoobserved on the leeward surface. This may indicate a morecoherent flow field around the prism surface, considering therewas no significant change in the turbulence intensity above themaximum outflow level. Mean pressures on the low and mid-risestructures behaved in much the same fashion as they do aroundthe taller model. Pressure coefficients on the leeward surfacewere more negative in the boundary layer flow when compared tothe gust flow regime over the entirety of the surface, indicatingpossible suppressed vortex development that generally occurswith square cylinders.

However, in similar studies regarding gust front flows andtheir impacts on prismatic models (e.g. Letchford and Chay, 2002),it has been identified that the gust event can induce situationswhere the pressure coefficients achieve an absolute value largerthan that given by a quasi-steady estimate. The increase in thepressure coefficients on the side surfaces in the gust flow field,when compared to boundary layer flows for the examined prisms,as well as the concomitant increase in the windward and leewardsurfaces, indicates that there are similarities in the developmentof the pressure field which occurred independently of theapproach flow profile.

for both boundary layer (left) and gust (right) outflows. (b) Contours of the mean

st (right) outflows.

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Fig. 5. (a) Contours of the RMS of pressure coefficients on model M1 on the windward face in both boundary layer (left) and gust (right) outflows. (b) Contours of the RMS

of pressure coefficients on model M1 on the side face in both boundary layer (left) and gust (right) outflows.

Fig. 6. (a) Contours of the RMS of pressure coefficients on the side face of model M2 in both boundary layer (left) and gust (right) outflows. (b) Contours of the RMS of

pressure coefficients on the side face of model M3 in both boundary layer (left) and gust (right) outflows.


The RMS of the surface pressure fluctuations on M1, shown inFig. 5a and b, indicated decreased variability in the pressurecoefficient on both the windward and side faces, respectively,when the prism was subjected to the gust front flow thancompared to the boundary layer flow. Additionally, the variationin pressure coefficient on the mid- and low-rise prisms, shown inFig. 6a and b, respectively, did show similarity in the distributionof the RMS of pressures corresponding with the height of themodel. The roof level of the mid-rise structure is approximately inline with the height of maximum velocity, and results showedthat the mid-rise model had higher pressure coefficient

fluctuations on the side face than did that of the high and low-rise models. This behavior could result from the opposing velocitygradients in the gust flow field. The high-rise model experiencesboth velocity gradients, the opposition of which could have amoderating effect on fluctuations on the model surface, and couldpotentially be responsible for the higher correlations experiencedon the side faces. The mid-rise model is subject to the near groundsurface velocity gradient, and is indirectly influenced by theopposing velocity gradient not impacted by the model surface. Onthe other hand, the low-rise model is immersed within the lowerhalf of the velocity gradient and is not influenced by the upper

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Fig. 7. (a) Contours of the instantaneous maximum pressure coefficients on the windward surfaces of M1 and M2 during the transition from BL to GF flow fields. (b)

Contours of the instantaneous minimum pressure coefficients on the side surfaces of M1 and M2 during the transition from BL to GF flow fields.


half of the gust front velocity gradient, therefore experiencinglower levels of fluctuations.

Apart from the mean distribution resulting from each profile, thepressure coefficient distribution during the transition period to thegust flow profile reveals more about the impact of the flow structure.Fig. 7 shows the maximum, or minimum, pressure coefficient thatoccurs during the transition period from boundary layer to gustprofile. The maximum pressure coefficient value was determinedfrom the pressure coefficient time history based on

C�pðtÞ ¼pðtÞ�p1

12rðUmaxðtÞÞ

2ð2Þ

where Umax(t) is the time history of the velocity, simultaneouslymeasured with the surface pressures at the maximum outflowelevation. The windward surface (Fig. 7a) of prism M1 shows twodistinct regions of increasing pressure, a pattern which is attributed tothe flow structure in the profile, while a region of decreasing pressureis evident on the trailing edge of the side surface (Fig. 7b) at a heightwhich corresponds to that of the maximum outflow velocity in thegust profile. The distribution of peak pressures is altered by thechanging flow field, modifying the aerodynamics of the flow fielddeveloped from the boundary layer profile.

3.2. Correlation and PSD of pressures

Correlations of pressures along the height and the depth of theprisms reveals distinctions regarding the relation of prism heightto the inflow profile shape. The correlation along the height takenat the leading edge on the side face (Fig. 8a) indicates that the gustfront outflow decreases the level of correlation over the height,though the level of which is dictated by the prism height.Correlation measures taken along the trailing edge on the sideface (Fig. 8b), when compared to those taken on the leading edge,show that the subsistence of correlation measures in the gustfront flow does not occur, as values decrease more rapidly for

prism M1 when compared to that of the smaller prisms. It isinteresting to note, however, when moving from leading edge totrailing edge, that correlations along the model height for the midand low-rise prisms show that the values for the gust front flowbecome larger than those of the boundary layer flow at thetrailing edge. The marked difference in the correlations of M1 overthe height is attributed to the differing velocity gradients in theflow profile, since M1 is exposed to flow above and below theheight of maximum velocity, while M2 and M3 are immersedwithin the flow below maximum velocity elevation.

Similar plots of the correlation along the prism depth taken atmid-level height on the side face, shown in Fig. 9a, on each prismshows varying trends: higher correlations for the gust front profilecompared to the boundary layer profile for M1, while for M2 andM3, the gust profile correlations are lower. This again mayindicate that the large scale flow structure is more coherent whenthe prism is exposed to both velocity gradients in the height of thegust flow field. Additionally, the height-wise correlation ofpressures in both the boundary layer and gust profiles along thecenter line of the windward surface, Fig. 9b, shows that the gustflow profile has a negative correlation in the lower portion of theprofile, indicating an opposing flow structure is derived from thevarying velocity gradients in the flow profile.

Other statistical features, such as the power spectral density(PSD), showed variation in the frequency content at individualpressure measurement locations as a result of the changing flowvelocity. What is of interest is how the height of the building inrelation to the shape of the gust front flow profile modifies thefrequency components of the surface pressures. In similar studies(e.g. Butler and Kareem, 2007a), the effect of turbulence had aspatial evolution with observations from the windward to sideface at the leading corner. As mentioned earlier, the opposingvelocity gradients in the height of the flow field have the potentialof inducing dual natured effects within the surface pressureregime developed by the existing boundary layer flow. The PSD atmid-level height in the high-rise model, making observations

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Fig. 8. (a) Cross-correlation coefficient taken along the prism height at the leading edge. (b) Correlation of pressures taken along the prism height, along the trailing edge.


from the leading edge to the trailing edge, shows a peaked naturethat becomes more defined with the increasing velocity (Fig. 10a).There is no shift in the non-dimensional frequency, possiblyindicating that the gust front flow profile does not directly changethe frequency associated with vortex development around theprism when given time for such a flow field to fully develop.

Comparing the power spectral density of individual pressuremeasurement locations around the high-rise structure with thatof the mid-rise structure (Fig. 10b), it is observed that thefrequency content changes in much the same manner, though

with less relative energy. In addition, the low-rise model hasmarkedly less energy than the taller two models in either flowregime, as development of any stable flow structure is muted withthe truncated prism length (Fig. 10c).

3.3. Drag and lift force coefficients

Examination of global forces, such as lift and drag, offer moreintriguing results. The drag and lift force coefficients, derived

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Fig. 9. (a) Correlation of pressures taken in the alongwind direction on the side surface at mid level height. (b) Correlation of pressures taken along the model height, along

the center line of the windward surface.


through integration of the surface pressures on model M1, a timehistory of which is shown in Figs. 11a and 12a respectively,reveals no clearly delineated impact in either the drag or lift forcecoefficient time histories due to the changing inflow field. Aprobability distribution for each force component, and flowprofile, shows normally distributed lift and a positively skeweddistribution for drag. Table 1 presents the mean values for thedrag and lift force coefficients for the boundary layer and gustflow fields. The time history of the drag force coefficient shows a

slightly higher shift in the mean value for the boundary layer flowcondition, indicating that the gust inflow profile potentiallymoderates the level of suction on the leeward surface, as wellas the level of vortex formation along the prism height.

The corresponding wavelet scalograms for the drag and lift forcecoefficient time histories, shown in Figs. 11b and 12b, respectively,reveal frequency content changes, primarily as a result of thechanging flow speed. What is interesting to note is that the intensityof the wavelet scalogram for the lift force coefficient decreases once

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Fig. 10. (a) PSD of pressure measurements at three locations (indicated on the model figure) at the mid-level elevation for model M1. (b) PSD of pressure measurements at

three locations (indicated on the model figure) at the mid-level elevation for model M2. (c) PSD of pressure measurements at three locations (indicated on the model figure)

at the mid-level elevation for model M3.


exposed to the gust front profile flow, compared to the boundarylayer flow at the beginning and end of each experimental run. Sincethe intensity of fluctuating lift coefficient was not impacted by thechanging flow profile, though the wavelet intensity was compara-tively reduced, it is estimated that a broader range of frequencies wasintroduced with the gust front profile. Additionally, there is noidentifiable frequency content in the scalogram at the instant of flowacceleration or deceleration, possibly due to the inability of thesurrounding flow field to instantaneously adapt to the change invelocity and profile shape.

Comparing wavelet scalograms for the resulting forces onvarious prisms, there is a particular trend that becomes apparentin two instances. In both the case of resulting drag and liftbehaviors, the occurrence of dominant wavelet scalogramenergies occurs before and after the boundary layer flow profileis shifted to the gust flow profile shape. It is worth noting that theturbulence intensity of the gust front inflow profile above themaximum outflow level remains at similar levels, while exhibit-ing an increase below this level for the gust front flow. It is

possible that the turbulence encountered by the model at thelower elevations, below the maximum velocity, may impact thelevel of organized structure development needed for stable vortexshedding over the prism length and the sustenance of frequencycontents during the gust front profile flow.

In order to understand the impact of a non-stationary process,different techniques are required beyond traditional stationaryanalysis schemes. A short-time correlation analysis, using amoving window of 2 s, was performed to uncover the short timebehavior of the system. Fig. 13a and b show the correlationbetween two pressure measurement locations on the side face atmid-level height (Fig. 13a) and the correlation between theoncoming flow and a pressure measurement on the leewardsurface (Fig. 13b). Higher correlation coefficients occurred duringthe instances of accelerated/decelerated flow. By comparingglobal attributes, such as lift, and local features, it is apparentthat the gust front flow field induces higher correlation ofpressures around the model surfaces during significant flowchanges, and that the changed flow field also reduced the global

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Fig. 11. (a) Time history of the drag force coefficient for M1 (right) with corresponding pdf (left). (b) Time history of the lift force coefficient for M1 (right) with

corresponding pdf (left).


pressure impact. Expanding from this, the higher globalcorrelations during the velocity acceleration may attribute tothe fact that there are no major frequency contributions duringthis exchange.

From global trends to temporally localized behavior, waveletscan again prove useful in uncovering instantaneous behavioraltrends in an event. Early research on impulsive flows aroundcircular cylinders (Sarpkaya, 1966) showed evidence of a peak inthe drag force estimate above the steady state level after theinitiation of a transient event, while more recent work hashighlighted changes in the drag force frequency content (Matsu-moto et al., 2007) for rectangular prisms as well. Fig. 14a and bshows zoomed wavelet scalograms of the drag and lift forcecoefficients, respectively, within a 10 s window around the period

of the velocity transition to the gust front flow field impactingprism M1. In the wavelet scalogram of the lift coefficient, Fig. 14b,focusing on the transition from the boundary layer to gust frontflow, it is noted that the frequency change occurs in conjunctionwith the increase in speed, as would be expected since thefrequency of vortex shedding is adjusted with the velocity.However, the corresponding drag force coefficient waveletscalogram, Fig. 14a, shows a brief appearance of two peaks infrequency, similar to that observed by Matsumoto et al. (2007),occurring just after the velocity change has reached its steadystate level.The dual energetic content in the scalogram occur atboth the Strouhal value and half the Strouhal value for the prism.It was concluded that such a shift was the result of a brief changein the vortex development process (Sarpkaya, 1966), though the

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Fig. 12. (a) Wavelet scalogram of the drag force coefficient time history. (b) Wavelet scalogram of the drag force coefficient time history.

Table 1Mean values of the drag and lift force coefficients in boundary layer and gust front

flow fields.

Boundary layer Gust front

Mean lift force coefficient �0.0744 �0.0445

Mean drag force coefficient 0.2186 0.2013


extent of those changes may be muted in this case consideringthat there was a preexisting flow which established a stablevortex development regime and it can be further influenced byother turbulence variations primarily resulting from the dual

gradient profile. The higher intensity content of frequency in theboundary layer flow field compared to the gust front field doessuggest that stable vortex development is dependent upon theapproach flow topology.

3.4. Angle of attack

For angles of attack beyond 151, there is little information that canbe derived from the frequency domain. As in the case of boundarylayer flow, angles of attack beyond approximately 301 have theeffect of diminishing the spectral content of the shedding frequency

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Fig. 13. (a) Running correlation of surface pressures along the side face at mid-level height, between the leading edge and trailing edge pressures. (b) Running correlation

between pressure on the leeward face at mid-level height and the velocity measured at the height of maximum velocity in the gust flow.


(Butler and Kareem, 2007a). As shown in Fig. 15, the frequencycontent for the lift force coefficient is dramatically shifted once theprismatic model is oriented beyond a 01 incidence. There are spectralpeaks that remain for the 151 incidence angle, while no dominantfrequency component occurs at 301 and 451 incidence.

3.5. Additional results

Assessment of the larger scale flow structure was investigatedthrough the use of co-spectral analysis. The co-spectra between

pressure measurement locations on M1 along both the height anddepth of the prism were examined. Fig. 16a shows the normalizedco-spectra between measurement locations along the height ofthe prism on the leading edge of the side face during exposure tothe boundary layer type profile. Fig. 16b shows similarinformation for measurement locations exposed to the gustfront flow field. In both cases, the dominant frequency contentexists nearest the presumed Strouhal value for the prism.Although conventional co-spectral analysis does not portray thetime dependence of embedded correlations in the pressure field, itis interesting to note that the co-spectral content during exposure

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Fig. 14. (a) Temporally localized wavelet scalograms of drag force coefficient (circled: simultaneous frequency event). (b) Temporally localized wavelet scalograms of the

lift force coefficient during the period of accelerated velocity from the boundary layer to gust profile.

Fig. 15. PSD of the lift force coefficient for prism M1 at varying angles of attack, containing both BL and GF flow conditions.


to the gust front flow shows more focused content at the Strouhalvalue when compared to the same content resulting from theboundary layer flow field.

Wavelets, similar to those used to examine drag and liftcoefficients, were also used to investigate local variations in thedominant frequency content of pressures in time. In this analysis,wavelets were used to examine changes in fluctuating surfacepressure frequency. Wavelet co-scalograms were used to identifycommon frequency content between pressure measurementlocations as a function of time, and as a function of the pressuremeasurement location varying in downstream distance along theside face, at various levels. Fig. 17a shows the wavelet co-spectra

for two adjacent pressure locations on the side face (separated by2 cm), in the alongwind direction, at midlevel starting at theleading edge. Higher intensity bursts occur intermittentlythroughout the duration of the gust front profile exposure, andthese bursts occur through a range of frequencies with dominantpeaks centered on the same frequency as that noted in the liftforce, observed in Fig. 12b. Similarly, Fig. 17b shows similarwavelet co-spectra between pressure locations at the leading andtrailing edge (separated by 8 cm) on the side face. In this case, theintermittent bursts of frequency occur at the same dominantfrequency as noted in Fig. 17a, with slightly less intensity in otherfrequency ranges. It is interesting to note that given the level of

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Fig. 16. (a) Co-spectra of pressure measurement locations along the prism height at the leading edge due to exposure to the boundary layer flow field. (b) Co-spectra of

pressure measurement locations along the prism height at the leading edge due to exposure to the gust front flow field.


velocity fluctuations during the gust front event, compared to thatat the beginning and end of the time series, there are prominentsimilarities in the frequency content of surface pressures evenwith an increase in the separation between the points examined.However, there is more intense frequency content whenobserving the resultant forces, lift force in this case, within thelower velocity flow events before and after the gust front. Thisobservation highlights the peculiarities between the integralpressure fluctuations and the global force, which are being

further examined to better understand the interaction of gustfront flow topology with the prismatic shape.

It may be possible to assess the nature of the time-frequencyvariations in surface pressures within a spatial context usingisocontours, generated from scalogram energy, produced from awavelet analysis at critical points (Lee and Sung, 2001), such asleading and trailing edge corners. Surface pressure data, in atime-frequency framework, was organized using a 3-dimensionalrepresentation of a series of wavelet scalograms, where a

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Fig. 17. (a) Wavlet co-scalogram between pressure measurement locations at mid-level height with x/D separation of 0.2 (with central frequency of 3 Hz). (b) Wavlet co-

scalogram between pressure measurement locations at mid-level height with x/D separation of 0.8 (with central frequency of 3 Hz).


scalogram was generated for each surface pressure measurementand assembled along the prism height, offering a spatio-temporalportrait of frequency contours. Fig. 18a illustrates this multi-dimensional wavelet scalogram representation, which gives aspatial overview of the energy distribution in a scalogram,uncovering life-cycles of particular frequency contents and theirspatial extent. This type of representation sheds light on flowstructures, such as the zones of vortical structures wrappedaround the prism, akin to a horseshoe vortex.

Based upon the isocontours generated in Fig. 18a, it can besurmised that during exposure to the gust flow profile, distinct

zones of high and low frequency pressure oscillations, associatedwith vortical flow features at the leading edge, may appear asregions of concentrated energy levels along the prism height.Fig. 18b portrays conceptually how this could manifest itself,based on the typical vortical flow structure which wraps aroundthe base of a prism in a boundary layer flow, referred to as ahorseshoe vortex in the literature. In the case of a gust frontprofile, a typical horseshoe vortex at the base is present whileanother vortex with reverse rotation is plausible at the higherelevations, potentially due to the ‘‘nose’’ shape of the oncomingprofile, as shown around the prism in Fig. 18b. Also shown in

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Fig. 18. (a) 3-Dimensional wavelet scalogram isocontours generated along the model height of M1 at the leading edge. (b) Hypothetical sketch of vortex development

resulting from gust front flow field and corresponding representation of 3-D wavelet scalogram isocontours.


Fig. 18b (right) is an idealized 3-D wavelet scalogram for the twodominant vortical flow structures. However, in a real flow field,this clear delineation is diffused due to interaction with adjacentvortical structures, manifesting as broadbanded isocontours inthis complex flow field. Continued refinement of the waveletscaling and resolution may help to identify changes in the flowfield developed as a result of the profile shape, focusing uponthese zones of concentrated energy at different frequencies.Identification of such changes in the surrounding flow field mayhelp to isolate the nature of increased pressure or integral loads.This visualization of the spatial variation in a series of waveletscalograms may serve as a useful tool for delineating transientspatio-temporal structures in the pressure field on bluff bodies inthese complex flows.

4. Concluding remarks

A fundamental study aimed at delineating the kinematic andtransient effects of variations within the boundary layer flow fieldon the surface pressures of prismatic models is presented. Amultiple fan wind tunnel was employed to simulate a transientgust front flow field with changing flow profile shape. Surfacepressures were examined on a suite of prismatic models,

capturing transient changes within the flow field. The results ofthis experiment were examined through traditional statisticalmethods, and more recent analysis techniques that involve time-frequency domain realizations. It was noted that the correlation ofsurface pressure around the model surfaces was markedly higherin the transition period to the simulated gust flow profile, and thesurface pressures peaks revealed characteristics possibly drivenby the opposing velocity gradients when compared to thesynoptic boundary layer flow. Additionally, wavelet scalogramsof both integral loads and localized pressures showed markeddifferences between the typical boundary layer flow field and thegust front profile. Future work and analysis programs will addressthe more intricate variability in the simulated gust profile and itsimpact on prismatic models, continuing to map the effects of gustfront flows on the surrounding flow field within a spatio-temporalcontext.

Acknowledgements

The authors would like to acknowledge the support providedin part by the Center of Excellence: Wind Effects in Urban Areasand the Global Center of Excellence at Tokyo PolytechnicUniversity: New Frontier of Education and Research in Wind

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Engineering funded by the Ministry of Education, Culture, Sports,Science and Technology (MEXT), Japan. Initial work on thissubject was conducted under NSF Grant CMS 03-24331.

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