How To Calculate Wind Loading

Transcription

1 Use of Computational Fluid Dynamics in Civil Engineering Prof. Dr.-Ing. Casimir Katz, SOFiSTiK AG, Oberschleißheim ir. Henk Krüs, Cyclone Fluid Dynamics BV, Waalre Zusammenfassung: Der Einsatz von CFD im Bauwesen stellt nach wie vor eine Nischenanwendung dar. Die Gründe dafür werden beleuchtet und aufgezeigt, warum sich das jetzt ändern wird. Summary: The use of CFD in the civil engineering community is still a rare event. The reasons for that will be discussed and it will be pointed out why that will change now. 1 INTRODUCTION 1.1 Fluid dynamics and their applications CFD is the acronym for Computational Fluid Dynamics. Fluids in civil engineering are mostly air and water and the questions to be answered are the forces induced by fluid motion and the transport of heat or particles within the fluid. Typical questions are Wind loading on bluff bodies Wind loading on moving bodies, especially bridges Wind comfort and nuisance to cyclists and pedestrians Wind energy Heating and Ventilation (HVAC) Fire safety engineering Wave loadings The difference to classical static or dynamic analysis is given by a different mathematical treatment and thus different mathematical tools [1]. While structural mechanics use the Lagrangian approach based on displacements, fluid mechanics prefer the Eulerian approach based on the velocity of the fluid. Structural mechanics use the Finite Element Method, most fluid mechanics use the Finite Volume Method. The basic principles of equilibrium and conservation of mass, energy and momentum are common to both methods. V13-1

2 1.2 Software for CFD Software for CFD has been developed for a long time now, the most well known products today are the big three FLUENT (now Ansys), STAR-CD/STAR-CCM (CD-Adapco) and CFX (now Ansys), but there are many more like the CFDDRC (now ESI-Group), CFDesign (FEM by Blue Ridge Numerics, now Autodesk) and FDS (by NIST). There are also different techniques available like vortex particle and Lattice-Boltzmann methods. The first impression for a structural engineer is, that everything is very complex, that there are hundreds of features and parameters and that it will cost a fortune to start into this field. Over the years the mantra of a technique much too complex for the common engineer and high licence costs has established significant barriers. The same happened to structural FE-Software in the late seventies. SOFiSTiK had success because we anticipated the wide spread of that technique on personal computers in But the CFD-market is changing now, cheaper versions of CFD-software enter the market, and the open source software OpenFOAM has gained wide acceptance especially in the academic world. However the structural beginner is still overwhelmed by a wide range of features. What is needed is a robust, easy to use entry point for this journey. SOFiSTiK has gained some experience with an academic multiphysics software PHYSICA and is now supporting DOLFYN, an open source CFD-Solver used in practice in many engineering fields, which has been fully integrated in the SOFiSTiK environment. 2 BASICS 2.1 Fluid dynamics and their solvers Two important metrics are the Mach number (v/c) defining the ratio of the fluid velocity v to the speed of the sound c and the Reynolds number derived from the fluid velocity u, the kinematic viscosity n, and a characteristic dimension of the structure (like the diameter of a cylinder or the height of a bridge deck): d u kinematic viscosity Re d characteristicdimension m Air ; Water sec m sec V13-2

3 Fluid dynamics cover a broad range of fields, some of them are: Potential Flow (Re = ) Creeping Flow (hardly any flow) Laminar incompressible viscous flow (Navier Stokes) Turbulent Flow (Re large) Compressible Flow (Ma > 0.3) Supersonic Flow (Ma > 1.0) Thermal Effects Combustion & chemical reaction Free Surfaces Non-Newtonian fluids Radiation In civil engineering applications the subsonic incompressible turbulent flow is the most common phenomenon. Compressible flow is needed for shocks and high temperature effects. The major remaining problem is that a direct solution of the Navier-Stokes-equations is only possible for Reynolds-numbers up to approximately , while practical examples are in the range of several millions. Thus turbulence has to be modelled by RANS (Reynolds-Average-Navier-Stokes) models allowing for very large Reynolds numbers but do not model all effects, that s why LES (Large Eddy Simulation) has gained some popularity, but requires still high computational effort. 2.2 Materialparameters The selection of fluid material parameters is straight forward: There is a density [kg/m³], a dynamic viscosity [Pa sec], a compressibility [Pa/m²] and some thermal properties. 2.3 Boundary Conditions Inflow and outflow boundary conditions are in general not complex, but there is a major problem with two aspects. There exists a boundary layer at every wall. At the wall itself there is no flow, then we have a tiny laminar viscous sublayer, followed by the turbulent boundary layer. The treatment of the wall boundary condition is quite difficult. Though there are possibilities for near wall models, the common model is a logarithmic wall law describing the complete wall boundary behaviour for a cell sufficiently far away from the boundary: V13-3

4 However the atmospheric boundary layer has a height larger than one kilometre, thus all civil engineering structures are completely encompassed by it. The design codes for wind loadings describe the layer with a logarithmic or an exponential law. It is not only the velocity but also the turbulence characteristics like the kinetic energy (turbulence intensity) and the dissipation rate (Integral length scale) which need to be described. The correct formulation requires not only to model the roughness of the ground with the correct value of z 0, the driving force at the top of the fluid domain, but also the treatment of the analytic solution of the turbulence equations as initial conditions, which are fully implemented in DOLFYN: * u ABL z z 0 uz ( ) ln z0 u kz ( ) C * 2 ABL * 3 uabl ( z) z z 0 V13-4

5 3 MODELLING 3.1 Windtunnel or CFD? A wind tunnel is just a model of the reality, so is any CFD model. The wind tunnel needs scaling, Reynolds number is not the same and there are cases where this does matter. There is a guideline from the WTG (Windtechnologische Gesellschaft) describing in detail how to perform reliable tests. But for flexible structures, the measurement equipment may change the effects considerably. On the other side there are known deficiencies of numerical analysis, which do not allow taking all results for granted. The purpose of computing is insight, not numbers. said R. Hamming in So the question is not which technique to be used but how to combine both methods to their best use. 3.2 Reality or design case? Is the requested result the mean values of the wind loading for a static analysis or the variation of forces in time either to account for dynamic effects or to get reasonable loads at all. For example a flat horizontal roof on columns will have a zero pressure as mean value, but the wind load is of course not zero! What is appropriate for the design of a building for wind loading, a solitaire in an empty environment: V13-5

6 Or the within the true environment: Most design codes describe wind profiles based on the roughness of the terrain, for urban environment the value of z 0 may be over 2.0 m, which is not suitable as roughness for a CFD wall boundary condition in general, although it is possible for an inlet wind profile. The main purpose is to define loads just based on the velocity distribution, not to perform a fluid analysis. This can be clearly seen by the fact that the velocity does not vanish at the ground. For a wind tunnel test normally the whole environment is modelled. So to compare CFD and wind tunnel, the model size of the wind tunnel (including the true geometry of the equipment) may be analyzed but the analysis of the true scale of the natural model including the environment should be more adequate. And is our interest in a model matching reality as close as possible or can we agree on a model on the safe side? V13-6

7 4 EXAMPLE BUILDING Gerhardt [3] has reported considerable deviations between a CFD-Analysis and measurements for a hull of a building (Re = ), given with a picture as follows: As all other data was missing, personal enquiries yielded a profile exponent of 0.25 (wind tunnel) and 0.27 (analysis), a rather sufficiently large air volume of 2000 x 2000 x 500 m and some inhomogenities along the building and other neighboured buildings in the wind tunnel test. Some tests showed however that the effect of those buildings should be neglectable allowing to concentrate on a 2D section. Thus the section was digitized from the picture, scaled to the real dimensions of 55 m width and 25 m height and an air volume with 500 m distance to the boundaries was used. The mesh density on the hull was selected with 0.25 cm (approx. 30 y+) yielding a total of cells. V13-7

8 The first outcome of the analysis showed, that the selection of the turbulence model had a significant effect on the pressure distribution, the standard k- model created the distribution with the large peaks (left picture) while the RNG-model showed better results (right picture): A deeper look at the inflow parameters however showed some deficiencies. Input velocity and turbulence intensities are well known, but the Eurocode specifies a value for the integral length scale of more than 200 m in a height of 25 m, which is considerably larger than the common CFD value of 0.4*H = 10 m. This contradiction can be overcome if the anisotropic structure of the natural wind is considered. Further the used mesh does not allow for large roughness values. After correcting those parameters, the following pressures have been obtained: However the wind tunnel test was based on a very dense environment consisting not only of other buildings but also of the roughness elements. So any further comparison of the CFD analysis and the wind tunnel becomes useless. V13-8

9 Let s use complex environments for the CFD as well: V13-9

10 V13-10

11 5 EXAMPLE BRIDGE SECTIONS 5.1 Millau Bridge A section of the Millau Bridge has been analyzed with CFD and compared to measurements in a wind tunnel. Despite the good agreement of the measurements with the analysis, some questions remain also in this case. The turbulence parameters in the wind tunnel have not been fully specified. And nobody really knew the wind conditions at the site of the bridge. There is a deep valley and fundamental CFD analysis had been undertaken to get the wind conditions in the nature. But to perform a dynamic analysis of a moving bridge in the wind field, the drag coefficients may be used. V13-11

12 5.2 Bridge in the wind tunnel The second example is the analysis of a bridge section in a wind tunnel [4]. Here the CFD model matches exactly the geometry of the wind tunnel. The inflow parameters are well known (I=3 %, L=0.03 m) The lift and moment coefficients are quite closely matched, but for the horizontal drag, the measurements deviate and the simulation is closer to the pressure measurements. V13-12

13 When analyzing this deck the results deviate to a certain extend. First the flow field is considerably different for the standard k- and the RNG variant: The pressure distribution is very sensitive to the mesh definition, but the principal distribution is: Location / Value Experiment Simulation DOLFYN DOLFYN openfoam k- RNG top spt 01 (tap 31) 0,494 0,650 0,723 0,689 top spt 05 (tap 35) -0,413-1,090-0,676-0,662 top spt 06 (tap 36) -0,902-1,230-1,307-1,181 top spt 18 (tap 8) -0,202-0,270-0,216-0,149 top spt 19 (tap 9) -0,264-0,260-0,199-0,135 top spt 21 (tap 11) -0,270-0,250-0,133-0,096 dwn spt 40 (tap 30) 0,496 0,670 0,779 0,799 dwn spt 34 (tap 24) -0,708-1,110-0,730-0,677 dwn spt 33 (tap 23) -1,083-1,250-1,180-1,065 dwn spt 26 (tap 16) -0,295-0,340-0,335-0,261 dwn spt 25 (tap 15) -0,305-0,300-0,297-0,218 dwn spt 22 (tap 12) -0,303-0,250-0,133-0,109 Drag coefficient (range of values) 0,088 0,075 0,073 0,093 0,081 0,082 0,069 V13-13

14 6 CONCLUSION The critical definitions for a CFD analysis are the selection of the mesh and the inflow conditions. Handled with greater success are bluff bodies with sharp edges, slender structures (e.g. airfoils) need more attention. So there is no free lunch by just buying a CFD software, which is also valid for any other type of complex simulation software (like structural analysis Finite Element). Each journey starts with the first step. It s time to take that first step. 7 DOLFYN DOLFYN [1] is an open source collocated face based Finite Volume software to solve incompressible fluid dynamic problems in 3D. The key features are: Standard k- and RNG turbulence models Stable numerical procedures Temperature / scalars / particles included Postprocessing with ParaView / VisIt (VTK-files) The implementation in the SOFiSTiK environment gives additional Mesh generation with SOFIMSHA / SOFIMSHC Postprocessing with WINGRAF Full CADINP support including formulas for boundary and initial conditions Easy wind definition (atmospheric boundary layer) directly or via SOFiLOAD Direct generation of resulting wind loading in the data base Possible (planned) extensions are: Compressible subsonic flow Free surfaces (VOF) Conjugate heat transfer (heat transfer with different materials) 8 LITERATURE [1] [2] J.H.Ferziger, M.Peric, Numerische Strömungsmechanik, Springer, 2008 [3] H.J. Gerhardt, Experimentelle und numerische Verfahren bei der Bauwerks-Bemessung, Der Prüfingenieur Vol. 24, April 2004 [4] A. Sarkic, C. Neuhaus, R. Höffer, Numerical and experimental determination of aerodynamic forces at a long span bridge girder, Eurodyn 2011, Leuven V13-14