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06.07.2008

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06.07.2008

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  1. Validation of the CFD program PHOENICS 2008 for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Validation of PHOENICS-2008 for the determination of wind pressures on buildings, by Frank Zimmermann, Heilbronn, D and Dipl.-Ing. Frank Kanters, Heerlen, NL; an English-language version by Brian Spalding. • Contents • 1. Foreword • Introduction • Boundary conditions • 4. Slender tower • 4.1 Wind-tunnel measurements • 4.2 CFD calculations • 4.3 Comparison with DIN 1055-4 • 5. Cube-shaped buildings • 5.1 Wind-tunnel measurements • 5.2 CFD calculations • 5.3 Comparison with DIN 1055-4 • 6. Rectangular buildings H = 0.5 B • 6.1 Wind-tunnel measurements • 6.2 CFD calculations • 6.3 Comparison with DIN 1055-4 • 7. Summary of the results • and conclusions • References 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 1

  2. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL 1.0 Foreword DIN 1055-4 03/2005 permits the determination of wind loads on buildings of rectangular-plan shape with sufficient accuracy. It gives however no guidance regarding buildings of more-complex shape. Since knowledge of the wind loads is necessary for proper design, especially for tall buildings, recourse therefore has in the past had to be made to measurements in wind tunnels, in which the non-uniformity of wind profile and the presence of surrounding buildigs should be represented. These requirements, together with the need for a large large number of measurement locations, make the method costly. For these and other reasons, better accuracy then +/- 15 % is not to be expected. The development of Computational Fluids Dynamics, and of sufficiently powerful computer hardware, now permit wind loads on buildings to be computed without great expense. The use of the large-eddy turbulence model together with parallel processing leads to especially good results. In the present report, the results of calculations made by means of the PHOENICS-2008 CFD-software package are compared with experimental data and with the prescriptions of DIN 1055-4, and are shown thereby to be sufficiently accurate. Such calculations can be made for buildings of any shape. 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 2

  3. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL • Introduction • A validation exercise requires knowledge of varied and reliable experimental data as standards of comparison. • In the present investigation, the following sources were used: • 1. NISTIR 6371, United States Department of Commerce, Technology Administration, • National Institute of Standards and Technology • Building and Fire Research Laboratory, Gaithersburg, [2]. • 2. Numerical Prediction of Wind Loading on Buildings and Structures, • The working group for numerical prediction of wind loading on buildings and structures, • Subcommitee for wind engineering data unit for structural design, • Archtectural Institute of Japan, 1998, [3]. • 3. DIN 1055-4, 03/2005, Einwirkungen auf Tragwerke, Teil 4: Windlasten, [4]. • In [2] the numerical determination of wind loads by means of Large-Eddy Turbulence simulation is • compared with wind-tunnel measurements and with the large-eddy caculations by Shah und Ferziger [5]. • Two building models were used: a tower of 10 x 10 x 80 m and a cube of 30 x 30 x 30 m. • A further comparison was made with the investigation of the AIJ – Report, Architectural Institute of Japan, [3] • for a rectangular-shaped building of 30 x 30 x 15 m which compared CFD calculations with wind-tunnel • measurements. 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 3

  4. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL • Introduction (continued) • The validation was conducted by making calculations with the program Phoenics 2008 from CHAM, London • for the following buildings: • A. Tall Building 10 x 10 x 80 m • 1.1 with vref = constant (uniform Flow) • 1.2 with wind profile (shear Flow), • Exponent n = ¼ , roughness zo = 0,05 m • B. Cubical Building 30 x 30 x 30 m • 1.1 with vref = constant (uniform Flow) • 1.2 with wind profile (shear Flow), • Exponent n = ¼ , roughness zo= 0,05 m • C. Low Flat Building 30 x 30 x 15 m • 1.1 with vref = constant (uniform Flow) • 1.2 with wind profile (shear Flow), • Exponent n = ¼ , roughness zo = 0,05 m 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 4

  5. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL • Boundary conditions • The large-eddy model was chosen because of its advantages [6] . Calculations with the k-epsilon model • lead to more or less the same conclusions provided that one reaches convergence. The LE model is • specially suitable for fine grids. • The LE – Model proved to be more robust, and to converge faster than K-epsilon. • The choice of grid is of great importance in wind simulations. • PHOENICS uses a basically Cartesian grid; and it has two especially valuable features for providing fine • grids where they are needed and for handling surfaces which cut the grid planes obliquely. They are, • respectively: • FINE-GRID EMBEDDING and PARSOL. 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 5

  6. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Pressure contours and vectors between louvres 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 6

  7. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL 3. Boundary conditions (contd) These features are illustrated in the picture on the right. PARSOL smooths the corners. The building shown has the dimensions 30 x 30 x 30 m and is turned through 45 ° . The grid-cell size is 1 m. FGE allowed the grid to be refined still further, without significantly altering the results. The favourable grid generation and the absence of surrounding buildings allowed exemplary convergence to be achieved within 1000 sweeps. For many applications other forms of grid are needed, such as cylindrical-polar for pipe-flow and body-fitted for more complex shapes. For flow around buildings however the combination of FGE and PARSOL is ideal. 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 7

  8. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL 4.0 Tall building 4.1 Wind-tunnel measurements Comparison between the predictions of PHOENICS and the wind-tunnel measurements of NIST3671. Comparisons were made for both uniform-flow and shear-flow wind profiles. 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 8

  9. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings 2 3 1 2 3 4 4 3 1 2 Wind Side Front back Windkanal, uniform Flow nach NIST6371 Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Above: calculations with PHOENICS for uniform flow Left: data from NIST6371 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 9

  10. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings 2 3 1 2 3 4 4 3 1 2 Wind Side Front back Windkanal, shear Flow nach NIST6371 Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Above: calculations with PHOENICS for shear flow Left: data from NIST6371 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 10

  11. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL 4.0 Tall Building 4.2 CFD calculations The results computed by PHOENICS are compared with the CFD calculations of NIST6371. Comparison was made for both uniform and shear–low wind profiles. 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 11

  12. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings 2 3 1 2 3 4 4 3 1 2 Wind Side Front back Berechnung, uniform Flow nach NIST6371 Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Above: calculations with PHOENICS for uniform flow Left: data from NIST6371 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 12

  13. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings 2 3 1 2 3 4 4 3 1 2 Wind Side Front back Berechnung, shear Flow nach NIST6371 Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Above: PHOENICS calculations for shear flow Left: data from NIST6371 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 13

  14. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL 4.0 Tall Building 4.3 Comparison with DIN 1055-4 The results computed by PHOENICS are compared with the values given by DIN 1055-4 . The comparison is made for the uniform-flow wind profile. 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 14

  15. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Plan view Table 3 – External-pressure coefficients for vertical walls of a rectangular building 1 2 2 3 3 4 4 3 1 2 Wind Side Front back Table 4 – External-pressure coefficient for flat roof region Data from DIN 1055-4, März 2005 PHOENICS for uniform Flow 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 15

  16. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL 5.0 Cube-shaped building 5.1 Wind-tunnel measurements Comparison of the predictions of PHOENICS with the wind-tunnel measurements of NIST 6371. Comparisons were made for both shear- and uniform-flow wind profiles. 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 16

  17. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Windkanal, uniform Flow nach NIST6371 Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Left: wind-tunnel data for uniform flow according to NIST6371 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 17

  18. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Windkanal, shear Flow nach NIST6371 Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Left: wind-tunnel data for shear flow according to NIST6371 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 18

  19. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL 5.0 Cube-shaped building 5.2 CFD - calculations Comparison of the predictions of PHOENICS with the CFD – calculations of NIST 6371. Comparisons were made for both shear- and uniform-flow wind profiles. 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 19

  20. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Berechnung, uniform Flow nach NIST6371 Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Left: calculation for uniform flow according to NIST6371 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 20

  21. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Berechnung, shear Flow nach NIST6371 Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Left: calculation for shear flow according to NIST6371 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 21

  22. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL 5.0 Cube-shaped building 5.3 Comparison with DIN 1055-4 Comparison of the calculation results of PHOENICS with the values given in DIN 1055-4 for uniform wind profile. . 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 22

  23. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Table 3 – External-pressure coefficients for the vertical walls of a rectangular building Table 4 – Flat-roof coefficients Values given in DIN 1055-4, March 2005 PHOENICS für uniform Flow  06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 23

  24. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Comparison of Cp;1 and Cp;10 values Cp;1 Cp:10 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 24

  25. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Cp;10 values 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 25

  26. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Wind Wind These images show clearly the dependence of the Cp values on the wind direction! The values in DIN 1055-4 are given only for +/- 45 degrees. 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 26

  27. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL 6.0 Slab-shaped building 6.1 Wind-tunnel measurements Comparison of the results of calculations made by PHOENICS With wind-tunnel measurements according to NIST 6371, for both shear- and uniform-flow wind profiles. 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 27

  28. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Windkanal, uniform Flow nach AIJ Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Wind-tunnel. Uniform flow according to AIJ 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 28

  29. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Windkanal, shear Flow nach AIJ Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Wind-tunnel. Uniform flow according to AIJ 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 29

  30. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL 5.0 Slab-shaped building 5.2 CFD - calculations Comparison of the calculation results of PHOENICS with the CFD calculations according to NIST 6371, for both shear- and uniform-flow wind profiles. 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 30

  31. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Berechnung, uniform Flow nach NIST6371 Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Left: uniform flow according to NIST6371 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 31

  32. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Berechnung, shear Flow nach NIST6371 Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Left: uniform flow according to NIST6371 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 32

  33. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL 6.0 Slab-shaped building 6.3 Comparison with DIN 1055-4 Comparison of the calculation results of PHOENICS with the values given in DIN 1055-4, for uniform-flow wind profile 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 33

  34. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL Values given by DIN 1055-4, März 2005 PHOENICS for uniform Flow 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 34

  35. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL 6.0 Summary of the results; and conclusions There exists a multitude of CFD programs; and within them are to be found many different turbulence models Therefore to prove the general applicability of CFD for the prediction of wind forces on buildings will not be possible until there exists a standardised validation process of the kind which VDI 6020, for example, provides for the simulation of buildings and apparatus. Nevertheless it would be unwise to disregard a calculation method which has delivered excellent and verified results in an enormous number and variety of applications. Indeed, publications from the USA, Japan and Switzerland have shown that CFD calculations of the wind loads on buildings have given acceptable results. In the absence of the above-mentioned standardised validation procedure, there remains the possibility of validating a specific CFD program under precisely-specified boundary conditions. Such a validation must demonstrate conformity with standards and with wind-tunnel measurements. These measurements, of course, stand equally in need of validation. 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 35

  36. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL 6.0 Summary of the results; and conclusions (continued) For buildings of complex form, CFD shows the critical locations instantly and without additional expense. In wind-tunnel investigations one must know, or guess, these locations beforehand so as to set a limit to the number of measurement positions. The picture on pages 18 and 19 show clearly that measuring positions in the guitter region were either omitted, or were in the wrong positions; whereas the CFFD calculations according to [2] bring to light the problems presend by sharp edges. The absence from DIN 1055-4 of the low-pressure zone in the gutter region is probably to be explained by the desire of the investigator to simplify the measuring procedure. 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 36

  37. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL 6.0 Summary of the results; and conclusions (continued) The validation of CHAM‘s PHOENICS program has shown good agreement with the investigations of NISTIR 6371 and AIJfor the buildings which were studied, i.e. those which could evaluated by reference to DIN 1055-4. The agreement with DIN 1055-4, when this is properly interpreted,is of course better, being within than 15 % Validation of the CFD program PHOENICS 2008 for the determination of wind loads on buildings 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 37

  38. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL 6.0 Summary of the results; and conclusions (concluded) This means that the use of PHOENICS for the present application, namely the Hamburg Central Plaz Central Plaza, Hamburg, guarantees conformity with DIN 1055-4 März 2005, if the following conditions are observed: 1. Sufficiently large model with blockage < 5 %. 2. Grid size on the wall surface <= 1m, by using FINE GRID EMBEDDING 3. Representation of slanting surfaces by way of PARSOL 4. Use of the Large-Eddy-Simulation turbulence model 5. Calculation with varying wind direction (in steps of 15 degrees) 6. Calculation of the wind velocity profile of ground-level category IV for plane surfaces and/or 7. In order to determine the influence of surrounding buildings, calculation with a wind-velocity profile of ground-level category II 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 38

  39. Validation of the CFD program PHOENICS 2008for the determination of wind loads on buildings Dipl.-Ing. Frank Zimmermann, Heilbronn, D und Dipl.-Ing. Frank Kanters, Heerlen, NL References: [1] Kiefer, H., Windlasten an quaderförmigen Gebäuden in bebauten Gebieten, Dissertation 2003, Universität Karlsruhe [2] NISTIR 6371, United States Department of Commerce, Technology Administration, National Institute of Standards and Technology Erstellt vom Building and Fire Research Laboratory, Gaithersburg [2] [3] Numerical Prediction of Wind Loading on Buildings and Structures, The working group for numerical prediction of wind loading on buildings and structures, Subcommitee for wind engineering data unit for structural design, Archtectural Institute of Japan, 1998 [3] [4] DIN 1055-4, Einwirkungen auf Tragwerke, Teil 4: Windlasten, März 2005 [5] Shah, Kishan, B. and Joel H. Ferziger, A Fluid Mechanicians View of Wind Engineering: Large Eddy Simulation of Flow Past a Cubic Obstacle, J. Wind Engineering and Industrial Aerodynamics, Vols. 67 & 88, pp 211 – 224,1997 [6] Gary Easom, Improved Turbulence Models for Computitional Wind Engineering, Dissertation 2000, University of Nottingham 06.07.2008 Zimmermann-Becker GmbH Beratende Ingenieure TGA Heilbronn Hamburg Leipzig 39