PRECis – Contract no. JOR3-CT97-0192
Wind Simulations on Acropolis
 
 

REPORT DOCUMENTATION PAGE


Principal:  The Martin Centre for Architectural and Urban Studies Classification:
Address of principal: University of Cambridge

Department of Architecture

6 Chaucer Road

Cambridge CB2 2EB

Storbritania

 		Local co-ordinator: Koen Steemers
Title: PRECis – Wind Simulations on Acropolis Author(s): Ernst A. Meese
Abstract: The wind over Acropolis in Athens is simulated for four directions of wind. The results are presented in the form of streamline plots and velocity vector plots. Approved by: Helge Nørstrud
Keywords: Acropolis, Wind Simulations, Atmospheric Boundary Layer, Incompressible Euler, Viscous Thin Layer

Report number:

223:1999

Preface

The work presented in this report was performed under the EU funded project PRECis – assessing the Potential for Renewable Energy in Cities, Contract No JOR3-CR97-0192.

Contents

Preface *

Contents *

1 Introduction *

2 Generation of the Computer Model and the Grid *

3 Simulations and Results *

4 Conclusions *

Bibliography *

List of Figures *

A Description of the Numerical Method Used *

Bibliography for the appendix *
 
 

  1. Introduction


    2. The objective of the work documented in the current report is to gather information on the influence of Acropolis on the ventilation of Plaka which is located to the north and west of Acropolis. However, this report is limited to the wind simulations and the description of the wind over Acropolis, and do not discuss in any detail the practical implications of the wind patterns discovered.
     

  2. Generation of the Computer Model and the Grid


    3. The computer model of Acropolis was constructed by manually extracting a set of point co-ordinates (x,y,z) from maps found in Ref. [1]. The points were selected as to resolve the characteristic geometrical features of Acropolis. A rectangle surrounding Acropolis at a distance of approximately 300 meters from its geometrical features was used to define the boundary of the model. A set of points was generated on this rectangle at an altitude of 90 meters above sea level.

    The combined set of map extracted points and boundary points was used to construct a triangularisation in the horizontal (x,y)-plane. This triangularisation was then used to linearly interpolate the geometry onto a uniform grid with square cells of 1×1 meter.

    This grid is too fine for practical computations, as it will result in a huge data set. The most characteristic lines of Acropolis were therefore drawn in the in-house grid generator g3dmesh constructing a non-uniform grid with grid refinement at steep gradients (see Figure 4). The fine uniform grid was then loaded into g3dmesh and the non-uniform grid was projected onto this fine grid. The theatre Southwest of Acropolis is the only building modelled. To simplify the grid, it was constructed with a flat roof. This roofing is believed to have insignificant impact on the global flow, as the recirculation flow down in the theatre would act much like a roof on the surrounding flow. Iso-line map for the model is shown in Figure 1, and 3d views are shown in Figure 2.

    The grid was constructed vertically from the surface up to an altitude of 600 meter above sea level to contain the atmospheric boundary layer. Around the grid block holding Acropolis was constructed an O-block for resolution of the far-field (see Figure 3). The Acropolis block consists of 96x71x51 nodes in x, y, and z directions respectively, and the surrounding block consists of 21x331x51 nodes.
     

  3. Simulations and Results


    4. The boundary conditions are an atmospheric boundary layer with uref= 1 m/s, zinf = 400 m and a=0.28 in the formula

    which is considered a characteristic velocity profile with altitude for an atmospheric boundary layer over a city with moderate sized buildings [2].

    Four directions of wind were simulated, namely from West, Southwest, South, and Northwest. The results of the simulations are presented in the plots of Figure 5 through Figure 20. Streamlines for these cases are depicted, but to better illustrate the size and strength of the recirculation zones, velocity vector plots in slice planes in the wind directions are also included.

    It is seen that the character of the flow is very dependent on the direction of wind. With wind from West (Figure 5 through Figure 7), the flow is rather smooth and only a small recirculation zone is found behind Acropolis.

    With wind from Southwest (Figure 8 through Figure 11), Acropolis bends the wind towards West on its north hill-side, and a rather large vortex is generated at the north-western corner. It may also be noted that the theatre to the Southwest of Acropolis generates a small vortex along the southern hill-side of Acropolis.

    Wind from South (Figure 12 through Figure 16) also follow the geometry quite smoothly, but generates re circulation zones both on the plateau of Acropolis and on the northern side of Acropolis. The recirculation zone the north is quite large.

    Finally, for wind from Northwest (Figure 17 through Figure 20), the wind also quite smoothly follows the geometry, but with a moderate vortex to the South of Acropolis.

    The computer program used was j3dieulvl which is an in-house code for doing incompressible Euler/viscous layer simulations. Due to the boundary layer characteristics of the flow, a pure Euler simulation is not recommended. Some details on the method may be found in the appendix.
     

  4. Conclusions


    5. For a given atmospheric boundary layer, Acropolis significantly alters the wind characteristics over Plaka, both by reducing wind speed, altering the direction, and perhaps most important, creating recirculation zones which may result in poor ventilation.

Bibliography
  1. Richard Economakis (ed.), Acropolis Restoration, The CCAM Interventions, Academy editions, 1994.
  2. Helge Nørstrud, Atmosfæren: temahefte i Aerodynamikk, MTF-NTNU.
List of Figures Figure 1 Isolines for the computer model of acropolis with Parthenon inscribed. The figures are in meters above sea-level. *

Figure 2 View of the computer model for Acropolis from a) Southwest, b) Northwest, c) Southeast, and d) Northeast. A line sketch indicates the position of Parthenon. *

Figure 3 The two blocks of the grid. Units of the axis is in meters. *

Figure 4 The grid over Acropolis. *

Figure 5 Overview on streamlines for wind from West (in x-direction). *

Figure 6 Side views on streamlines for wind from west (in x-direction). *

Figure 7 Wind from west. Velocity vectors in the centreplane showing the resirculation zone behind Acropolis. *

Figure 8 Overview on streamlines for wind from Southwest.*

Figure 9 Side views on streamlines for wind from Southwest. *

Figure 10 Position of the Slice for viewing the velocity vectors for wind from Southwest. *

Figure 11 Velocity vectors in the slice for wind from Southwest. *

Figure 12 Overview on streamlines for wind from South. *

Figure 13 Side views on streamlines for wind from South. *

Figure 14 Position of the Slice for viewing the velocity vectors for wind from Southt. *

Figure 15 Velocity vectors in the slice for wind from South. *

Figure 16 Zoom-in on the velocity vectors in the slice for wind from South. *

Figure 17 Overview on streamlines for wind from Northwest. *

Figure 18 Side views on streamlines for wind from Northwest. *

Figure 19 Position of the slice for viewing the velocity vectors for wind from Northwest. *

Figure 20 velocity vectors in the slice for wind from Northwest. *
Figure 1 Isolines for the computer model of acropolis with Parthenon inscribed. The figures are in meters above sea-level.

 
a)
b)
c)
d)
Figure 2 View of the computer model for Acropolis from a) Southwest, b) Northwest, c) Southeast, and d) Northeast. A line sketch indicates the position of Parthenon.

Figure 3 The two blocks of the grid. Units of the axis is in meters.

Figure 4 The grid over Acropolis.

Figure 5 Overview on streamlines for wind from West (in x-direction).

 
 
View from north

View from south
View from west
View from east

Figure 6 Side views on streamlines for wind from west (in x-direction).


 


Figure 7 Wind from west. Velocity vectors in the centreplane showing the recirculation zone behind Acropolis.

Figure 8 Overview on streamlines for wind from Southwest.

 
View from south
View from north
View from west
View from east
Figure 9 Side views on streamlines for wind from Southwest.
 

Figure 10 Position of the Slice for viewing the velocity vectors for wind from Southwest.

Figure 11 Velocity vectors in the slice for wind from Southwest.

Figure 12 Overview on streamlines for wind from South.

 
 
 
View from south
View from north
View from west
View from east
Figure 13 Side views on streamlines for wind from South.

   
 

Figure 14 Position of the Slice for viewing the velocity vectors for wind from South.

Figure 15 Velocity vectors in the slice for wind from South.

Figure 16 Zoom-in on the velocity vectors in the slice for wind from South.

Figure 17 Overview on streamlines for wind from Northwest.

 
 
View from Southeast
View from Northeast
View from Northwest
View from Southwest
Figure 18 Side views on streamlines for wind from Northwest.
 

Figure 19 Position of the slice for viewing the velocity vectors for wind from Northwest.

Figure 20 velocity vectors in the slice for wind from Northwest.

 
  1. Description of the Numerical Method Used
The method used for the solution of the compressible or incompressible Euler equations is a finite volume method based on central differences in space co-ordinates and an explicit Runge-Kutta method for the integration in time [3]. The method starts from an initial field which is marched in time until a stationary condition is reached. At this stationary condition is the conservation equations for mass and momentum satisfied. The time step is calculated locally in each control volume to increase the rate of convergence.

The flow solver facilitates multi-block grids with a general and flexible specification of boundary conditions. The cell centred finite volume discretisation stems from the integral form of the Euler equations which describes conservation of mass and momentum when viscous forces is neglected. On a finite control volume W this reads

where the vector U contains the variables

,

where p is static pressure and c is an artificial speed of sound. The variables u, v, and w are the Cartesian velocity components in x-, y-, and z-direction respectively. The variables are assumed to be averaged over each control volume. In Eq. (2), F refer to the common flux vector for non-viscous transport terms while the vector n is the outward unit normal of the surface with area S.
 

Bibliography for the appendix

  1. Øye, I.J., On the Aerothermodynamic effects on Space Vehicles, dr.ing. thesis, MTF-rapport 1996:140 (D), NTNU, Trondheim 1996.