Wind Pressures on Irregular Plan Shapes

Journal of Wind Engineering

and Industrial Aerodynamics 93 (2005) 741–756

Experimental and numerical study of wind pressureson irregular-plan shapes

M. Gloria Gomes�, A. Moret Rodrigues, Pedro Mendes

DECivil/ICIST, Instituto Superior Tecnico, Technical University of Lisbon, Av. Rovisco Pais,

1049-001 Lisbon, Portugal

Received 19 July 2004; received in revised form 21 July 2005; accepted 22 August 2005

Abstract

This paper presents the results of a program of wind tunnel model tests on pressure distributions

for irregular-plan shapes (L- and U-shaped models). The experiments were carried out in a closed-

circuit wind tunnel and a multi-channel pressure measurement system was used to measure mean

values of loads on 1:100 scale models. The same tests were carried out on a cube-shaped model as an

experimental validation. The effectiveness of the model shape in changing the surface pressure

distributions is assessed over an extended range of wind directions. The experimental data for the L-

and U-shaped models showed different wall pressure distributions from those expected for single

rectangular blocks. Furthermore, a Computational Fluid Dynamics (CFD) code was used to

illustrate some particular cases and to provide a better understanding of the flow patterns around

these irregular-plan models and of the pressure distributions induced on their faces. Computed

pressure coefficients have also been compared with wind tunnel results for normal and oblique wind

incidence. A general good agreement has been found for normal wind incidence whereas some

differences have occurred for other directions.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Wind engineering; Wind pressure coefficients; Wind tunnel testing; Irregular-plan shapes;

Computational fluid dynamics

ARTICLE IN PRESS

www.elsevier.com/locate/jweia

0167-6105/$ - see front matter r 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jweia.2005.08.008

�Corresponding author. Tel.: +351 218418358; fax: +351 218418359.

E-mail address: [email protected] (M.G. Gomes).

1. Introduction

The innovative designs both in building forms and structural systems with the increaseduse of a boarder range of materials require an accurate description of the wind action andits interaction with the buildings. Therefore, more rational and refined wind designapproaches have been adopted by standards in order to improve both design andanalytical processes. While there is considerable research on cubical and cylindricalstructures—a detailed review of this subject can be found in Meroney’s paper [1]—only afew research studies analyse irregular shapes [2].In the present work, pressure distributions on irregular-plan L- and U-shaped models

were experimentally determined from wind tunnel tests carried out under uniformupstream flow. A cube-shaped model was also tested for comparison and validationpurposes. Although L- and U-shapes are very common building configurations,experimental data for such shapes and different wind directions is very limited.Stathopoulos and Zhou [3] have examined wind loads for L-shaped plan view as well asfor L-shaped cross section (stepped-roof building) through a numerical study. They havefound a good agreement in the latter case between numerically and experimentallyobtained results for normal wind incidence.The aim of the present study is to assess the effects of different model shape on the

surface pressure distributions over an extended range of incident wind directions.

2. Experimental program

The experiments were carried out in a 1.25� 1.00m2 closed-circuit wind tunnel atLaboratorio Nacional de Engenharia Civil (LNEC). More details about this wind tunneland its functional characteristics can be found in [4].A preliminary study was carried out in this wind tunnel for a cube under uniform

upstream flow (uniform mean velocity and low turbulence intensity—less than 0.5%—except in the thin boundary layer near the wind tunnel floor) to validate the experimentalprocess. The velocity in the wind tunnel was approximately 10m/s. Symmetrical L- and U-shaped models were also tested under the same conditions.The models used for the experiments were made of transparent PVC (3mm of

thickness), with a geometric scale of 1:100, and equipped with 35 taps located on each facetested. These pressure taps have been placed as near as possible to the sidewall and roofedges to attempt to capture the high-pressure gradients (suctions) occurring at points offlow separation. The roof is fixed by screws so as to be easily removed and to allow theaccess to the interior of the models. On the cube, although only the roof and one of thewalls were monitored, all the faces were tested by rotation of the model. On thesymmetrical L- and U-shaped models only the inner faces were measured, as the otherswere considered to present surface pressure distributions very similar to those of arectangular block with the same dimensions. This fact is also supported by a study ofStathopoulos and Zhou [3]. The three models are shown in Fig. 1 while their dimensionsalong with the location of the pressure taps are shown in Fig. 2.The cube was tested just for the normal incidence, while the other models were tested for

several flow directions as shown in Figs. 8 and 9. For pressure measurements two differentscanivalve transducer models were used: a multi-point electronic pressure scannerDSA3217 and a mechanical Scanivalve Model J. The latter, which belongs to an older

ARTICLE IN PRESSM.G. Gomes et al. / J. Wind Eng. Ind. Aerodyn. 93 (2005) 741–756742

generation, was intended to save time in increasing the measuring capacity. Even so, thenumber of the Scanivalve’s available channels was insufficient to perform the pressuremeasurements simultaneously on all the model’s faces. Therefore, the experiments had tobe carried out on one face at a time, by sweeping through all incident wind directions.Digitization of pressure signals and analysis of data were performed by a LabVIEWapplication at a sampling frequency of 10Hz for 5min. Only mean pressure coefficients(Cp) are shown in this work (i.e., pressures normalised by the upstream dynamic pressureat roof height). The dynamic pressure of the flow was also measured with Pitot tubes andhot-wire anemometers. Although pressure coefficients are referenced to roof heightdynamic pressure, in this case any height could be chosen, since upstream flow wasuniform. An important problem associated with wind tunnel tests on the flow around bluffbodies is that of blockage. In fact, for some orientations, the L- and U-shaped models’blockage exceeded 10%—note that many authors define blockage ratio limits between 5%and 10% [2,5]—which can have repercussions on the pressure distributions (specially onsuctions) and hence on the drag. However, some tests made in the closed-circuit windtunnel with windows closed and open (taken as limit situations of blockage effects, sincethe closed test section tends to overestimate the drag and the open one has the oppositeeffect [6]) showed maximum differences in pressure measurements within 5–7%, whichsuggested little influence of blockage on results.

3. Numerical study

Numerical simulations were carried out in this study through the Computational FluidDynamic (CFD) package PHOENICS [7], based on the control volume method. The RNG

ARTICLE IN PRESS

Fig. 1. Cube, L- and U-shaped models in the close-circuit wind tunnel.

(cm) (cm)(cm)

Fig. 2. Cube, L- and U-shaped models along with the pressure tap distribution.

M.G. Gomes et al. / J. Wind Eng. Ind. Aerodyn. 93 (2005) 741–756 743

k2e model [8] was used to simulate the turbulence effects. It uses the standard k2e modelequations with the exception of revised model constants and a strain dependent term in theenergy dissipation equation (last term in Eq. (4)). The governing equations are the time-averaged continuity, momentum and transport equations for k and e, as follows:

quiqxi

¼ 0, (1)

qqxj

ðuiujÞ ¼qqxj

ðnþ ntÞquiqxj

� �� 1

rqpqxi

, (2)

qqxj

ðkujÞ ¼qqxj

nþ ntsk

� �qkqxj

� �þ ntSij

quiqxj

� e, (3)

qqxj

ðeujÞ ¼qqxj

nþ ntse

� �qeqxj

� �þ ce1

ekntSij

quiqxj

� ce2e2

k� CmZ3ð1� Z=Z0Þ

1þ bZ3e2

k, (4)

where nt ¼ Cmk2=e (isotropic eddy viscosity), Z ¼ S k=e, S2 ¼ 2SijSij and Sij ¼ ðqui=qxj þ

quj=qxiÞ (mean strain tensor). The turbulence constants are [7]: sk ¼ 0:72; se ¼ 0:72;Cm ¼ 0:085; ce1 ¼ 1:42; ce2 ¼ 1:68; Z0 ¼ 4:38; b ¼ 0:012. These governing equationsassociated with the boundary conditions were transformed into the discrete form, i.e.,an algebric form, using a staggered 3-D Cartesian system and solved numerically by thecontrol volume finite difference method [9]. The adopted solution method for thevelocity–pressure fields was the SIMPLEST algorithm [10], which is a variant of SIMPLE[11]. In order to enhance the stability of the solution process, under-relaxation techniqueswere applied to all the equations. Uniform inlet velocity (U r ¼ 10m=s) and low turbulenceintensity (I ¼ 2

3k

� �1=2=U r ¼ 0:1%) profiles and outlet conditions in terms of zero normal

gradients for all quantities were adopted. Also the no slip condition and turbulence wallfunctions [12] were considered for the ground boundary and for all solid obstacle surfaces.Free slip conditions were assumed for the top and side boundaries.In order to assess the reliability of the code and to conclude on the suitability of the

numerical approach for the type of problems studied, the flow over a cubic obstacle wasinvestigated and compared with other studies. After some trials to test the influence onresults of number of grids and ratio of physical model to domain size, the final simulationused a variable-spaced grid of 48 cells long� 38 high� 43 wide with the domain dimensionabout 15L (length)� 5L (height)� 10L (width), where L is the reference size of the cubicmodel (Fig. 3). A finer mesh is required in the vicinity of walls and ground in order toaccurately resolve the high-gradient regions of the flow field. A similar grid arrangementwas employed for the L- and U-shaped models, with a finer resolution around all solidsurfaces and near the re-entrant corners to improve the accuracy of the simulations.Vertical profiles of longitudinal velocity above and downstream the cube are compared

with wind-tunnel measurements (Castro and Robins [13]) and numerical results (Zhanget al. [14]) in Fig. 4. Lateral profiles downwind of the cube are compared with results fromthe same authors in Fig. 5. Some discrepancies can be noticed between numerical andexperimental results, being more apparent in the near wake region (Fig. 4) essentially dueto the inability of the eddy viscosity concept in dealing with flow separation and localanisotropic turbulence [15]. Nevertheless, the main flow characteristics appear to have been


ARTICLE IN PRESS

L0.5L

Wind

10L

4LL

4.5L

4L

Fig. 3. Computational domain and grid system.

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.0

0.5

1.0

1.5

2.0

2.5

3.0

present study Zhang et al. [14] Castro & Robins [13]

z/L

u/Ur

Wind

z

y x

Fig. 4. Vertical profile of velocity at plane x ¼ L and y ¼ 0.

-3 -2 -1 0 1-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

present studyZhang et al. [14]Castro & Robins [13]

u/U

r

y/L2 3

Fig. 5. Lateral profile of velocity at plane x ¼ 2L and z ¼ 0:5L.


captured by the numerical modelling, which attests the reasonability of the approach andsupports the research of the next section for different model configurations.

4. Results and discussion

4.1. Cube

Pressures on models are presented in terms of mean pressure coefficients. Fig. 6 showsthe results of the surface pressure measurements for the preliminary study carried out on acube under uniform flow and for the incident flow direction normal to the upstream face ofthe cube. As expected, for normal winds, mean pressure coefficients are positive on thewindward wall, with their maximum value at the stagnation point (around mid-heightsince the upstream flow is uniform). Since the flow over the windward face separates fromthe model surface at the corners, near the windward edges pressure decreases, leaving eachside face and roof in a bubble of separated flow and with negative pressures (suctions). Asexpected, negative pressures on the leeward wall are uniformly distributed in the wake

ARTICLE IN PRESS

Fig. 6. Surface pressure coefficient distribution for the cube when normal to the incident flow.

M.G. Gomes et al. / J. Wind Eng. Ind. Aerodyn. 93 (2005) 741–756746

region. Results are compared with the ones published by Castro and Robins [13], as shownin Fig. 7. Except for discrepancies on the roof and side faces, which may be due the highersusceptibility of these faces to the experiment conditions (model edges, turbulenceintensity, blockage effects) [2,13], the results of the experiments are in general agreementwith those of Castro and Robins [13]. This evidence has provided an experimentalvalidation of the remaining model tests.

4.2. L-shaped model

Fig. 8 shows the pressure coefficient contours on the L-shaped model inner faces over anextended range of wind directions.

The general characteristics of the pressure distribution on the inner faces of the L-shapedmodel can be summarised as follows:

� For normal winds (a ¼ 01) the highest positive pressures (stagnation points) on thefront wall are no longer in the middle of the face as in the cube but are moved to

ARTICLE IN PRESS

-1.2-1

-0.8-0.6-0.4-0.2

00.20.40.60.8

11.2

-1.2-1

-0.8-0.6-0.4-0.2

00.20.40.60.8

11.2

0 3

x/L

Cp Closed WT(windows

closed)Closed WT(windowsopen)Castro & Robins [13]

x/L

Cp Closed WT(windows

closed)Closed WT(windowsopen)Castro & Robins [13]

A C DB E

1 2 4 5

0 31 2 4 5

Fig. 7. Comparison of the surface pressure coefficients for the cube when normal to the incident flow, measured in

a closed-circuit wind tunnel (with windows closed and open), with Castro and Robins’ experiments [13].


ARTICLE IN PRESS

Fron

tR

ight

Rig

htR

ight

-1.1

0 -1

.00

-0.9

0 -0

.80

-0.7

0 -0

.60

-0.5

0 -0

.40

-0.3

0 -0

.20

-0.1

0 0

.00

0.1

0 0

.20

0.3

0 0

.40

0.5

0 0

.60

0.7

0 0

.80

0.9

0 1

.00

α=0°

α=60

°

α=30

°α=

90°

α=45

°α=

120°

α=13

5°

α=15

0°

α=18

0°Fr

ont

Fron

t

Fig.8.Surface

pressure

coefficientdistributionontheL-shaped

model

inner

faces.


positions near the re-entrant corner. This is due to the effect of flow separation thatleaves stagnant flow in that re-entrant corner. This phenomenon also affects the rightinner face of the model in the sense that positive pressures arise on almost all its extent.Note that in a single rectangular block, as attested by the cube test, the side faces wouldbe in suction.

� As the angle of the incident flow increases, pressure values become lower on the frontwall and higher on the right one. However, higher positive pressure still exists on the re-entrant corner.

� For orientations between 1201 and 1801, the inner faces of the model are not directlyexposed to the flow, being rather under the wake region influence. As a consequence,the pressure coefficient distribution is negative (suction) and almost uniform. How-ever, for a ¼ 1201 positive pressure increases near the upper right edge of the rightinner face. This can be attributed to the direct incidence of flow on that small area,after skipping over the opposing wing, with a consequent increase of the pressurevalues.

4.3. U-shaped model

Fig. 9 shows the pressure coefficient contours on the U-shaped model inner faces over anextended range of wind directions.

The pressure coefficient distribution on the inner faces of the U-shaped model clearlyshows that:

� Since the flow is symmetrical when the wind blows normally (a ¼ 01), the stagnationpoint is in the middle of the front wall. As on the L-shaped model, these positivepressures on the windward face (front wall) also increase on the downwind end of thelateral wings (right and left walls), whereas suctions only exist near the windward edge.Note that pressure coefficient contourlines have a denser distribution—indicatinghigher pressure gradients—near the windward edges of the roof in the case of the U-shaped model than in the L-shaped one. This may be due to a higher flow rate risingover the U than the L-shaped model.

� As the angle of the incident flow increases, pressure decreases on the front wall.Nevertheless, due to the obstruction of the left wing, the pressure does not increase onthe inner face of the right wing. Positive pressures are still present near the right edge ofthe right wing as long as ao901.

� For a between 901 and 1801 all inner faces have nearly uniform pressure distri-butions, typical in recirculation zones, which denotes a tendency of the flow to skip pastthe U gap, leaving almost stagnant flow in the recess. This effect only occurs when thegap width across the recess is relatively small when compared with the length of themodel, otherwise the flow would tend to enter the recess and act directly on the rightwing [2].

4.4. Numerical versus experimental results

The profile of wind-induced pressure coefficients along the vertical and horizontalcentrelines of the front and sidewalls for a ¼ 01 is compared with the numerical results in

ARTICLE IN PRESSM.G. Gomes et al. / J. Wind Eng. Ind. Aerodyn. 93 (2005) 741–756 749

ARTICLE IN PRESS

Left

Rig

htα=

180°

-1.1

0 -1

.00

-0.9

0 -0

.80

-0.7

0 -0

.60

-0.5

0 -0

.40

-0.3

0 -0

.20

-0.1

0 0

.00

0.1

0 0

.20

0.3

0 0

.40

0.5

0 0

.60

0.7

0 0

.80

0.9

0 1

.00

Fron

tLe

ftR

ight

Fron

t

α=15

0°

α=12

0°

α=90

°α=

0°

α=30

°

α=45

°

α=60

°

Fig.9.Surface

pressure

coefficientdistributionontheU-shaped

model

inner

faces.


Figs. 10–12 for the L- and U-shaped models. The general agreement between experimentaldata and numerical results is quite good. This is particularly noticed in Figs. 11 and 12,where the numerical simulations predict even the thin boundary-layer effect near theground. The largest deviations between numerical and experimental results are restricted tothe upwind ends of lateral wings, with more emphasis for the L-shaped model (Fig. 10),where the numerical simulation underestimates the negative pressures caused there by theaccelerating flow.

ARTICLE IN PRESS

0

0.5

1

-0.6 -0.4 -0.2Cp

z/H

0

0.5

1

z/H

NumExp

H

L Wind

A B

L

A B

0 0.2 0.4 0.6 0.8 1 1.2 -0.6 -0.4 -0.2Cp

0 0.2 0.4 0.6 0.8 1 1.2

Fig. 11. Pressure coefficients along the vertical centrelines (L/2) of the L-shaped model for normal incident flow

(a ¼ 01).

0

0.5

1

-0.6 -0.4 -0.2 1.2Cp

z/H

0

0.5

1

Cp

z/H

NumExp

C D

L WindL

HC

D

0 0.2 0.4 0.6 0.8 1 -0.6 -0.4 -0.2 1.20 0.2 0.4 0.6 0.8 1

Fig. 12. Pressure coefficients along the vertical centrelines (L/2) of the U-shaped model for normal incident flow

(a ¼ 01).

-0.4-0.2

00.20.40.60.8

11.2

x/L

Cp

NumExp

A LL WindB

A B H

-0.4-0.2

00.20.40.60.8

11.2

0.5 1.510 2

x/LCp

NumExp

DCLL Wind

C D H

0 0.5 1 1.5 2

Fig. 10. Pressure coefficients along the horizontal centreline (H/2) of the L- and U-shaped models for normal

incident flow (a ¼ 01).


The numerical results for a ¼ 451 and 1801 have also been compared with theexperimental data, along the vertical and horizontal centrelines of the front and sidewalls,as shown in Figs. 13–18. A reasonable agreement of the numerical results withexperimental data has also been found in these cases, although the global performancehas not been so good as noticed for a ¼ 01. The numerical simulations generally reproducethe experimental profile trends but some large discrepancies of the numerical results occurin particular situations: an overestimation of pressure in the exposed internal corner of theU-shaped model for a ¼ 451 (Fig. 13); a deviation of the vertical profiles on the side wallsof the U-shaped model for a ¼ 451 (Fig. 15); and a staggering of the vertical profiles forboth L- and U-shaped models for a ¼ 1801 (Figs. 17 and 18). The reasons for these

ARTICLE IN PRESS

-0.4-0.2

00.20.40.60.8

11.2

0 0.5 1 1.5 2

x/L

Cp

-0.4-0.2

00.20.40.60.8

11.2

Cp

NumExp

A LLWind

B

A B H

0 0.5 1 1.5 2 2.5 3

x/L

NumExp

C EDLL

Wind

D E HC

Fig. 13. Pressure coefficients along the horizontal centreline (H/2) of the L- and U-shaped models for an incident

angle of a ¼ 451.

0

0.5

1

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2Cp

z/H

0

0.5

1

Cp

z/H

NumExp

A B

H

L

Wind

A B

L

Fig. 14. Pressure coefficients along the vertical centrelines (L/2) of the L-shaped model for an incident angle of

a ¼ 451.

0

0.5

1

-0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3 -0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3Cp

z/H

0

0.5

1

z/H

NumExp

C E

L

WindL

HD

E

C

0

0.5

1

Cp-0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3

Cp

z/H

D

Fig. 15. Pressure coefficients along the vertical centrelines (L/2) of the U-shaped model for an incident angle of

a ¼ 451.


discrepancies might be: (1) insufficient mesh refinement in high velocity gradient zones,either in intensity or direction, leading to a loss of accuracy in the results; (2) numericalfalse diffusion due to the skewness of the flow to the gridlines in the case of a ¼ 451 [9]; (3)inability of the turbulent model used (RNG k2e) to deal with high vorticity flow regions(e.g. wake region and recirculation zones at the re-entrant corners). In fact, although theRNG k2e model prevents the overproduction of turbulent kinetic energy at high vorticityregions, it is still an isotropic eddy viscosity model, and so this can have direct influence onaccuracy of results in regions where the Reynolds stresses are highly anisotropic [16].

ARTICLE IN PRESS

-1.2-1

-0.8-0.6-0.4-0.2

00 0.5 1 1.5 2 0 0.5 1 1.5 2

0.20.4

x/L

Cp

NumExp

A

LL

Wind

B A B H

-1.2-1

-0.8-0.6-0.4-0.2

00.20.4

x/L

Cp

NumExp

C D

LL

Wind

C D H

Fig. 16. Pressure coefficients along the horizontal centreline (H/2) of the L- and U-shaped models for an incident

angle of a ¼ 1801.

00 0.2 0.4 0.6

0.5

1

-1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6-1.2 -1 -0.8 -0.6 -0.4 -0.2Cp

z/H

0

0.5

1

Cp

z/H

NumExp

A B

Wind

H

L

A B

L

Fig. 17. Pressure coefficients along the vertical centrelines (L/2) of the L-shaped model for an incident angle of

a ¼ 1801.

00

0.5

1

-1.2 -1 -0.8 -0.6 -0.4 -0.2 0.2 0.4 0.6 0-1.2 -1 -0.8 -0.6 -0.4 -0.2 0.2 0.4 0.6Cp

z/H

0

0.5

1

Cp

z/H

NumExp

DCL

Wind

L

HC D

Fig. 18. Pressure coefficients along the vertical centrelines (L/2) of the U-shaped model for an incident angle of

a ¼ 1801.


4.5. Numerically predicted flow pattern

In Figs. 19 and 20 the numerically predicted velocity vector field, on the horizontal mid-plane and for wind directions of 01, 451 and 1801, is also shown for the L- and U-shapedmodels, respectively.For all wind directions the wind flows sharply away at high speed from the front wall

near the windward corners (separation and acceleration of flow on the corners) andreverses just behind these corners, giving rise to negative pressures. For normal windincidence (a ¼ 01) two symmetrical vortices appear in the wake region of the U-shapedmodel, very similar to those of rectangular blocks (Fig. 20). However, for the L-geometryonly a large and non-symmetrical vortex forms behind the model (Fig. 19).When the wind blows at a skew angle (a ¼ 451) a larger region of stagnant air forms in

the re-entrant corner of the L-shaped model. The size of this region is highly dependent onthe slenderness of the model: a taller model implies a larger stagnation zone in the re-entrance, as the flow tends to contour the sides rather than flow into the cavity [2].For a ¼ 1801, the wind flow field around the L- and the U-shaped models is very similar

to that of rectangular blocks in the upwind region. However, the flow patterns are totallydifferent behind the models whereas, instead of two symmetrical vortices, there is a largevortex in the L- and U-cavity with smaller vortices appearing behind the downward back

ARTICLE IN PRESS

α=0º α=45º α=180º

Ur=10 m/s

Fig. 19. Velocity vector field around the L-shaped model on the horizontal mid-plane (H/2) for wind directions of

01, 451 and 1801.

Ur=10 m/s

α=0º α=45º α=180º

Fig. 20. Velocity vector field around the U-shaped model on the horizontal mid-plane (H/2) for wind directions

of 01, 451 and 1801.


wall of the wings of the models. All these phenomena are clearly predicted and supportsthe conclusions derived from the experimental data.

5. Conclusions

The present study has shown that incidence of wind on L- and U-shaped models caninduce different pressure distributions on their faces from those of single rectangularblocks. The work was carried out through wind tunnel tests—for a wide range of incidenceangles—on scale models with those two particular shapes and on a cube to represent thesingle block case and to validate the experimental process. A region of stagnant air, inwhich the pressure rises to the stagnant value, has occurred in the re-entrant corner of theL-shaped model for ap901. As the angle of the incident flow increases, the pressure fieldturns out to be negative and almost uniformly distributed, which is characteristic of arecirculation area.

The influence of the additional wing transforming the L into the U-shaped model wasnoticeable on the pressure distribution: suctions on the inner faces occurred earlier for thetested angles and pressure in the recess was almost constant for aX901. This derives fromthe tendency of the flow to skip past the U gap leaving stagnant flow in the recess.

Results of a CFD numerical approach based on the RNG k2e turbulence model showeda general good agreement for normal wind incidence (a ¼ 01) whereas some differenceshave occurred for other directions. Denser mesh arrangements in particular flow regionsand an improved turbulent model that accounts for the Reynolds-stress anisotropy couldcertainly enhance the quality of the numerical results. Nevertheless, the results obtainedare within the expectations and, together with the experimental data, can provide usefulinformation about wind pressures on such irregular-plan shapes.

Acknowledgements

The authors would like to express their appreciation to Professor Jorge Saraiva and Eng.Marques da Silva for their valuable suggestions and to Mila for the precious help she gavewith the wind tunnel experiments performed at LNEC.

References

[1] R.N. Meroney, Wind-tunnel modeling of the flow about bluff bodies, in: F.R.G. Aachen (Ed.), Advances in

Wind Engineering, Proceedings of the Seventh International Congress on Wind Engineering, July 6–10, 1987,

Part 2, Elsevier, Amsterdam, 1988, pp. 203–223.

[2] N.J. Cook, The Designer’s Guide to Wind Loading of Building Structures. Part 2: Static Structures,

Butterworths Press, London, 1985.

[3] T. Stathopoulos, Y. Zhou, Numerical simulation of wind-induced pressures on buildings of various

geometries, J. Wind Eng. Ind. Aerodynam. 46 and 47 (1993) 419–430.

[4] M.G. Gomes, Wind effects on buildings. Experimental evaluation of pressure coefficients for L- and U-

shaped buildings, M.Sc. Thesis, Instituto Superior Tecnico (IST), Technical University of Lisbon, 2003 (in

Portuguese).

[5] E. Houghton, N. Carruthers, Wind Forces on Buildings and Structures. An Introduction, Edward Arnold,

London, 1976.

[6] J.B. Barlow, W.H. Rae Jr., A. Pope, Low-Speed Wind Tunnel Testing, third ed, Wiley, New York, 1999.

[7] D. Spalding, J. Ludwig, PHOENICS 3.4 Documentation, CHAM, 2001.

ARTICLE IN PRESSM.G. Gomes et al. / J. Wind Eng. Ind. Aerodyn. 93 (2005) 741–756 755

[8] V. Yakhot, S.A. Orszag, S. Thangam, T.B. Gatski, C.G. Speziale, Development of turbulence models for

shear flows by a double expansion technique, Phys. Fluids: A: Fluid Dyn. 4 (7) (1992) 1510–1520.

[9] S.V. Patankar, Numer. Heat Transfer Heat Flow, Hemisphere Publishing Corporation, New York, 1980.

[10] D.B. Spalding, Mathematical modelling of fluid-mechanics, Heat-transfer and chemical-reaction processes,

CFDU Report HTS/80/1, Imperial College, London, 1980.

[11] S.V. Patankar, D.B. Spalding, A calculation procedure for heat, mass and momentum transfer in three-

dimensional parabolic flows, Int. J. Heat Mass Transfer 15 (1972) 1787–1806.

[12] B.E. Launder, D.B. Spalding, The numerical computation of turbulent flows, Comput. Methods Appl. Mech.

Eng. 3 (1974) 269–289.

[13] I.P. Castro, A.G. Robins, The flow around a surface-mounted cube in uniform and turbulent streams,

J. Fluid Mech. 79 (2) (1977) 307–335.

[14] Y.Q. Zhang, A.H. Huber, S.P.S. Arya, W.H. Snyder, Numerical simulation to determine the effects of

incident wind shear and turbulence level on the flow around a building, J. Wind Eng. Ind. Aerodyn. 46 and

47 (1993) 129–134.

[15] S. Murakami, A. Mochida, 3-D numerical simulation of airflow around a cubic model by means of the k– emodel, J. Wind Eng. Ind. Aerodyn. 31 (1988) 283–303.

[16] N.G. Wright, G.J. Easom, Comparison of several computational turbulence models with full-scale

measurements of flow around a building, Wind Struct. 2 (4) (1999) 305–323.


Documents

Wind Pressures on Irregular Plan Shapes