Investigation of the Flow and Pressure Characteristics Around
a Pyramidal Shape Building1
M. Ikhwan & B. Ruck
Laboratory of Building- and Environmental Aerodynamics
Institute for Hydromechanics, University of Karlsruhe,
Kaiserstr.12, 76128 Karlsruhe, Germany
Abstract
An experimental investigation of the flow and pressure characteristics around a
pyramidal shape building is presented. The experiments were conducted in an
atmospheric boundary layer wind tunnel. The velocities of the flow around the
pyramid were measured using 2D Laser Doppler Anemometry (LDA). The pressure
distribution on the pyramid surface were measured using standard pressure tapping
technique enabling the generation of pressure coefficient surface map on the pyramid
with different wind direction. This study focuses on shallow pyramid structures
(height to length ratio < 0.5, height to boundary layer ratio < 0.2). The results show
different trends compared to the one from rectangular bluff body buildings and
moderate-high pyramidal shape buildings.
I.
Introduction
Pyramid comes from the Greek word “Pyre” which means fire. It has been the
symbol of the Devine fire, Devine light, the symbol of the main principle of life for all
the living. For millennia the shape of the four-side pyramid has been the subject of
pondering for the curious-minded. Many historical buildings or monuments have
been found in the shape of pyramid. The Cheops pyramid in Egypt which have been
built thousands of years ago is famous as one of the Seven Wonders of the World. In
today’s architectural design, the pyramid shape building is undergoing a renaissance.
Building as a whole for various purposes such as hotels, offices, houses, museums,
halls as well as building component like roof, or entrance hall are constructed in a
pyramidal shape.
From the aerodynamic engineering point of view, the pyramidal shape building
has its own interesting characteristics. The pyramid geometry has a diagnostic value
relative to the rectangular, sharp-edged configurations mainly due to the modifying
effect of the vertical wall taper, which has important implication to environmental and
industrial aerodynamics. Although the surface flow topology for the pyramid and the
cube bear some similarity, the pattern on the leeward face indicates that the mean
structure of the recirculation wakes are very different. Also, the aerodynamic loading
of the structures is distinct for pyramids, since the wall taper results in different
surface pressure distributions than for rectangular buildings [1]. Despite its
distinction to rectangular buildings, the technical layout with respect to the wind load
assumption for the pyramidal shape is usually not listed in standard tables. These
considerations show the importance of this study to investigate the flow and pressure
on the pyramidal shape building.
Full Paper, 10. GALA-Fachtagung “Lasermethoden in der Strömungsmesstechnik“ 10-12 September
2002, Universität Rostock
1
Ruck & Roth [4] carried out an investigation which involved 2 types of
pyramids. They were able to show interesting characteristics of pyramidal shape
buildings, however, more detail information is required to produce a standardization
of flow and pressure characteristic around pyramidal shape building since the shape of
the pyramid itself might have several different configurations (e.g H/L, ). This study
focuses on relatively shallow pyramid in order to observe whether the distinguished
characteristics shown in Ruck and Roth [4] still occur.
II.
Experimental Set-up
The experiments were carried out in a closed-circuit 29 m long atmospheric
boundary layer wind tunnel of the Institute for Hydromechanics, University of
Karlsruhe. The tunnel has a 1.5 m octagonal cross-section, with 50 cm boundary layer
height. The atmospheric boundary layer was developed along 2.6 m roughness
elements combine with two types of vortex generators, 65 cm and 50 cm height. This
combination produce an exponent of  = 0.26 in the exponential velocity law U / U
= (z /). See figure 1 for detail boundary layer set up.
Flow Measurement
Horizontal and vertical velocities were measured with the aid of a twocomponent Laser Doppler Anemometry (LDA) forward light scattering system. The
system consists of an argon-ion laser (1.4 watts) and two bragg cells for frequency
shifting. The LDA signals were detected with photomultipliers and evaluated by
counter-based signal processing (2 x TSI IFA 550). 1,2-propandiol droplets were
generated with a condensation-type particle generator, producing the seeding particles
of 1.5 µm mean diameter [4].
Fig. 1: Experimental set up and pyramid geometry
Pressure Measurement
A total of 46 pressure taps with 1.5 mm diameter were distributed systematically
on the half of the pyramid surface. In order to bring the pressure taps sufficiently near
to the edges, the model is manufactured from a thin (4 mm) but strong Plexiglas. In
this way, a distance of 6.5 mm to the edges was not exceeded. However, the relative
small basis angle,  = 20°, produces a distance of 12 mm between the pressure taps
and the bottom of the pyramid (see figure 2). Dimensionless pressure coefficient
value Cp was calculated by dividing the measured differential pressure with the
dynamic pressure of the flow at the 27.5 cm reference height.
Cp 
p p surface  p stat.

q
 2U ref 2
Fig. 2: Distribution of tapping positions on the pyramid surface
III.
Experimental Results
Flow Measurement
The flow fields were investigated for square-based (L x L =: 20 x 20 cm),
sharp-edge surface-mounted pyramid with basis angle  = 20° and with wind
direction of  = 0° (normal to the front face, see fig.1). The boundary layer was
charaterized by a Reynolds number Re=12.000 based on the pyramid height h=36.4
mm and a free stream velocity, U = 5m/s. The flow field was measured ranging
from 2.5 x L downstream to 1.5 x L upstream of the pyramid, and 5 H (height) over
the pyramid. The flow characteristics are presented in parallel planes at y direction
each spaced by l/8 x L, as can bee seen in figure 3.
z/H
U0
Planes
x/L
z/H
y/L
y/L=0
y/L=0.125
y/L=0.25
y/L=0.375
y/L=0.5
x/L
y/L
Fig. 3: Parallel measuring planes
Planes
Fig. 4: Isolines of mean horizontal velocity around the pyramid in parallel planes.
From the top to bottom: y/L =0 (centre plane), y/L = 0.25, y/L = 0.5
Fig. 5: Isolines of mean vertical velocity around the pyramid in parallel planes.
From the top to bottom: y/L =0 (centre plane), y/L = 0.25, y/L = 0.5
Isolines of horizontal and vertical mean velocities at selected cross-sections, y/L =0
(centre line), y/L = 0.25 and y/L = 0.5, are shown in Figure 4 and 5. From these
figures, no recirculation zone in the lee of the pyramid can be found even though the
pattern shows that the velocity in the lee of the pyramids is decreasing. For steeper
pyramids, the horseshoe vortex, the separation bubble and the reattachment point
should be detectable, see Figure 7 [1], however, in this case of a shallow pyramidal
structure none of them can be identified.
Ruck & Roth [4] and Abuomar & Martinuzzi [1] found that the recirculation
zone in the lee of a pyramid is comparably much shorter in length (streamwise
direction) than that of a rectangular bluff body of the same height (and of almost
every width). The latter seems due to the fact that the recirculating mass and the
recirculation velocity are decreased significantly with structures tapered in height.
The present study shows that if the pyramid is too shallow (base angle is too small),
then, no flow separation will occur. This might be trivial at the first sight, but it is not.
The separation of the flow behind a pyramidal structure cannot be predicted or
inferred from well-known step-type or nozzle- and diffusor-type flow theory since it
has to be assessed in combination with the specific and complex 3-dimensional
pressure field around this pyramidal structure. Thus, there must be a certain H/L and
y/H ratio of the pyramid building which starts generating recirculation zone. Another
variable that should be take into account is the upstream surface roughness which is a
significant factor influencing the separation and reattachment length [3]. These are
important factors to be investigated in near future since the relatively small
dimensions of recirculation zones behind pyramidal structures are interesting not only
in building aerodynamics or architecture. They are as well of interest in technical
processes, where an optimum mixing or heat transfer behind low energy consuming
surface mounted structures is desired.
Fig. 6: Mean velocity vector representation in plan y/H = 0 (centre plane),  = 20°,
 = 0° ; (please note that the horizontal and vertical axis scale with multiples of
pyramid height -> pyramid shape is not realistic)
Fig. 7: Mean vector representation in plan y/H (centre plane),
 = 60°,  = 0° [1]
Pressure Measurement
The pressure measurements were carried out with a flow velocity of 12 m/s in
order to obtain measurable and reliable pressure differences. Two positions of the
pyramid,  = 0° and  = 45° with respect to the flow direction were investigated.
Figure 8 shows the pressure (Cp) distribution on the surface of the investigated
shallow pyramid.
For the 00 flow direction as shown in figure 8–a, the maximum pressure
coefficient was found on the front side at the bottom of the pyramid with a maximum
value of 0.02. On the downstream surface, suction is measured near the top whereas
positive Cp-value are found near the base. As well as on the upstream side, also on the
downstream side pressure coefficients are observed to be more or less evenly
distributed. The maximum suction Cp-value occurs near the upstream edges of the
pyramid on the side surfaces. They are peaked in the upper third of the pyramid.
Symmetrically pressure coefficient distributions were found for the 450 flow direction
as shown in figure 8-b. There are no high levels of suction values anymore as
illustrated in figure 8-b and the maximum positive pressure coefficient are found near
the baseline of the pyramid.
The previous study [4] indicates that the maximum pressure on the upstream
side occur at a height of 53 % of the total pyramid height and maximum suction
values occur at the upstream edges near the baseline (see also [1] ). On the other hand,
this study shows that the maximum pressure occurs at the baseline and the upper
edges are exposed to high suction, which is more similar to rectangular bluff body
flow. This results indicate that the base angle of the pyramid influences significantly
the pressure distribution on the pyramid walls. As a trend, it seems that a steepening
of the pyramid shifts down the point of maximum suction (minimum pressure) on the
side walls towards the baseline and shifts up the point of maximum pressure on the
front side.
Further systematic investigations have to be carried out in order to discretize any flow
and pressure characteristics in the shape range between shallow and steep pyramidal
structures. At the end, the measured results shall be plotted and combined to an
animation from which all relevant load characteristics can be inferred for rectangular
pyramids with increasing steepness in boundary layer flow.
a. Wind Direction: 0°
b. Wind Direction: 45°
Fig. 8: The pressure (Cp) distribution on the surface of the pyramid
Acknowledgement
The financial support of the Deutsche Forschungsgemeinschaft DFG/Bonn within the
project No. Ru 345/25 is gratefully acknowledged by the authors.
References:
1. Abuomar, M.M., Martinuzzi, R.J., 2000. An Experimental Investigation of the
flow around a Surface Mounted Pyramid. 6th Triennal Intermational symposium
on Fluid Control, Measurement and Visualization, August, 13-17, 2000,
Sherbroke, Canada.
2. Heist, D.K., Gouldin, F.C., 1997. Turbulent Flow Normal to Triangular Cylinder.
Journal of Fluid Mechanics, vol.331, pp. 107-125.
3. Peterka, J.A., Meroney, R.N., Kothari, K.M., 1985. Wind Flow Patterns About
Buildings. Journal of Wind Engineering and Industrial Aerodynamics, 21 (1985)
21-38.
4. Ruck, B., Roth, M., 1997. The Flow and Pressure Distribution Around Pyramids.
Laser Anemometry Advances and Applications, Proceedings of the 7th
International Conference, September 8-11, pp.761-769.
5. Tom Lawson, 2001. Building Aerodynamics. Imperial College Press, London
ISBN 1-86094-1 87-7.