6.1 Wind calculation method

Numerical simulations of the wind around the Main Building were performed by the commercially available CFD package Fluent. We used versions 4.4 and 4.5 and the differences between these two versions are not relevant for our purpose. The used turbulence model is a standard - model ([Fluent 1995], or see e.g. [Launder and Spalding 1974] and [Rodi 1980]).

**Model constants**
The applied values for the - model constants are: ,
,
, and
. Except for , the standard
values of the - model have been applied (the model and
the constants are described in [Launder and
Spalding 1974]). The
constant was adapted according to the findings of
[Bottema 1993b], who also compared the results of his simulations
favourably with wind tunnel measurements.

**Grid**
The applied grid is a so-called structured grid. The size of the
three-dimensional computational domain was determined by the
rules of thumb given by [Bottema 1993a] and based on general
estimates of the influence zone in which wind speeds deviate by
more than 10% due to the presence of the building. The reader is also referred to
section 2.1.4. For the
description of this zone the dimension , i.e. the smaller of
and , is used. The upstream influence zone
is about
and its downstream counterpart extends to
. The influence zone in lateral and vertical
directions extends to
. The boundaries of the
computational domain should be outside the influence zone, although for
the downstream influence zone one may make an exception and put the
boundary at only
[Bottema 1993a].

As is 90 m (=) in our case, the computational domain should be about (=1170 m) long along the wind direction. To be able to simulate wind flow around the Main Building at oblique angles, the chosen computational domain is rectangular with the Main Building situated in the south-west corner, at from the south and the west domain boundaries.

The actual three-dimensional computational domain is 1190 m long in east-west direction, 1477 m long in north-south direction and 225 m high. It consists of 95, 96 and 47 cells, respectively. Figure 6.1 shows the computational grid with the three buildings (Auditorium, Main Building and Building T) in it. Two variants of the shown configuration will be applied: with and without Building T. There are two reasons for this. Firstly, the influence of Building T on winds from south-west to south can be presented. Secondly, the grid without Building T is symmetric with respect to the east-west plane. This implies that winds from directions and (where is a value from 0 to 90) can be studied using one simulation.

The grid cells become progressively smaller near building boundaries. The first grid cells on the façade of the Main Building have a thickness of 0.25 m. Care is taken to keep the grid expansion factor of two successive grid lines between 0.7 and 1.3. However, since the grid is structured, undesired large expansion factors and cell aspect ratios are inevitable in some parts of the grid.

**Wind profile**
The profile of the wind entering the domain is described by:

with = longitudinal wind velocity [m s] at height [m] above ground level, = roughness length [m] for 20 m, = roughness length [m] for 20 m, = friction velocity [m s], = friction velocity [m s], resulting from the requirement that is continuous at 20 m, = von Kármán constant (0.4), and = displacement height [m].

The applied values of 1.0 m and 10 m were taken from results of measurements at the site by [Geurts 1997]. The division of the wind profile in two parts is necessary to account for the displacement height of 10 m; otherwise, the wind profile below 10 m height would be undetermined. Moreover, the fetch consists of a park up to a distance of 400 m from the Main Building (therefore an estimated of 0.1 m) and buildings west from the park with a height of 20 m. The choice of and the choice that the boundary between the two parts of the profile is at 20 m height, are relatively arbitrary, but the simulation results are not very sensitive to the precise values of these parameters.

The friction velocity is based on the wind speed at Eindhoven Airport (7.5 km westward from the Main Building, with = 10 m, = 0.03 m and = 0 m). See section 5.2.1 for a discussion on the measurements of .

**Turbulent kinetic energy**
The profiles of the turbulent kinetic energy and its dissipation rate,
for wind coming into the domain are described by:

respectively, with = turbulent kinetic energy per unit of mass [m s], and = energy dissipation rate [m s].

**Terrain roughness**
In Fluent the roughness of surfaces is modelled by the following formula:

The roughness parameter is empirically determined. Its value is
9.8 for a smooth wall. Equation 6.5 corresponds to the
wind profile (eqs. 6.1 and 6.2) if:

**Façade roughness**
Equations 6.5 and 6.6 are also applied to model
the surface roughness of the building façades. As the façade
consists of a smooth glass cladding, a value of 0.0005 m
is assumed for its roughness length ,

**Separation modelling**
Separation of the airflow at corners has been modelled by so-called
``link-cuts'' (i.e. a feature of Fluent by which the wall-function in
a computational cell is disabled).

**Chosen wind speeds and directions**
The following reference wind speeds and directions at the
mast on the Auditorium were chosen for
the wind calculations:

- 3.5, 5.7 and 11.2 m s,
- 210, 240, 270, 300 and 330.

Not every combination was simulated, see table 6.2 for the simulations which were actually performed. Recall that we use two geometrical models, namely with and without the inclusion of Building T, and because of symmetry, the simulations with 240 will be used to represent 300 too. The validity of these `double simulations' will be discussed in section 6.3.

© 2002 Fabien J.R. van Mook

ISBN 90-6814-569-X

Published as issue 69 in the