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Large Eddy Simulations with STAR-CCM+
Peter Arnold, Tensys Dynamics, UK

The requirement to successfully simulate mean and fluctuating surface pressure distributions on the surface of buildings in the atmospheric boundary layer is a challenging problem, which has occupied wind engineers for at least two decades.

 
Fig:01 : Shows the centre plane velocity vectors.

  
Figures 2 and 3 show the distribution of the mean and rms pressure coefficients around the mid plane of the cylinder starting at the facing wall. The experimental measurements of this flow by different researchers [1] show more spread in the values than the difference between the three meshes used. Both the mean and rms Cp profiles are known to be sensitive to the inlet turbulence intensity (T.I) with an increase in T.I suppressing the magnitude of both [2]. Consequently a zero T.I inlet condition can be viewed as the worst-case scenario from a wind loading perspective. The experimental data shown has a T.I of 0.04 % [3] and represents the closest case to the numerical simulations where no turbulent fluctuations were imposed on the inlet velocity profile.

To date LES and more recently DES methods are regarded as being the only methods with a practical chance of resolving the large scale instabilities that dominate flows in the built environment. For wind loading purposes, the large Reynolds numbers, geometrical extent and complexity of groups of buildings, imply that the computing power required to calculate these flows to an accuracy comparable with wind tunnel experiments, makes their resolution currently uneconomical by around two orders of magnitude. Several benchmark problems are used to test new developments, of which vortex shedding from a square cylinder is probably the most universal.

It is usually considered that correctly modeling the velocity gradients perpendicular to the wall is a necessary condition for the prediction of flow separation. However sharp edged bluff bodies have well defined flow separation points at their corners, creating shear layers that are highly unstable and drive vortex shedding. The upside to this situation is that resolution of the near wall perpendicular velocity gradients is less important. The downside is the resulting instability requires time dependent simulation to resolve the unstable flow close to the body and vortex shedding in the wake. The surface pressure distribution is dominated by these large scale structures. Tensys Dynamics have been investigating the combined use of embedded polyhedral meshes and time dependent laminar simulations in STAR-CCM+ to resolve these flows. The level of mesh refinement used in this study implies the size of eddies resolvable does not qualify the method to be called Direct Numerical Simulation (DNS) it is rather a LES model with no explicit sub grid scale model, with implicit sub-grid viscosity arising from the advection scheme upwinding.

Simulation Details
The classic case of vortex shedding due to cross flow over an infinite square cylinder was simulated at Re = 22,400. The computational domain was arranged with a cylinder of side D in a rectangular domain such that the front of the cylinder was 4.5D from the constant velocity inlet, while the constant pressure outlet was 20D from the back edge of the cylinder. The domain was 15D in height and 10D in span. The span wise and top and bottom walls were defined as slip walls.

The simulations were run on a series of three progressively refined meshes consisting of 40k, 260k and 620k polyhedral cells, each employing refined embedded regions within them. The height of the first cell from the surface was kept, constant at 0.025D for all cases. The embedded meshes were created in STAR-Design utilizing a recursive method of imprinting nested sub domains which captured the cylinder and its wake. The imprinting method has the flexibility to create sub domains of any shape with arbitrary levels of refinement. This has advantages over traditional hexahedral trimmed cell embedding where only rectangular blocks of meshes refined in multiples of two are possible.

The unusual choice of not using a sub-grid scale model was motivated by a desire to firstly assess the extent to which numerical diffusion contributed to the solution of conventional LES simulations. Secondly to simultaneously assess the inherent numerical diffusion resulting from the use of polyhederal mesh and STAR-CCM+’s 2nd order spatial discretization, as a implicit sub-grid scale model. The time step used for all the simulations was 0.1 units of non-dimensional time (D/V) giving a maximum Courant number on the fine grid of 4. Second order spatial and temporal discretization schemes were used for all calculations. Each simulation was run for at least 50 non-dimensional time units before vortex shedding became sufficiently regular. After this time mean Cp profiles and rms Cp profiles were extracted on the intersection of the centre plane with the cylinder using four line probes at 500 time steps corresponding to about 7 vortex shedding periods. The laminar time dependent method was compared with simulations using unsteady k-w, DES and inviscid models on the coarsest grid only.

Results
Tables 1 and 2 compare the integrated parameters calculated from the laminar simulations with mesh refinement and with turbulence modeling alongside the experimental data of several authors [1]. As expected the drag is the most consistently measured in the experiments and most accurately predicted in the simulations. Different levels of turbulence intensity and length scale at inlet were present in the experimental results.

On the coarse mesh the laminar predictions are closer to the experimental values than the other models. In particular the k-w URANS and DES models add additional unnecessary damping which reduce all parameters. It is quite possible that the seven vortex shedding cycles over which the integrated parameters were extracted over, is an insufficient period. However time constraints on the finest mesh made this necessary.

The effect of grid refinement is seen to steadily increase the magnitude of both the rms and mean Cp values. The increase in the rms values is consistent with the reduction of numerical diffusion originating from the spatial and temporal discretization. The mechanism which correlates an increase in rms Cp values with an increase in mean Cp values in the experimental results is unclear but appears to be mimicked in the numerical results.

The mean and particularly the rms Cp profile from the medium 260K mesh matches the experimental values well, indicating that this amount of numerical dissipation acts as an effective sub grid scale model for this level of inlet turbulence. The coarser mesh solution clearly adds more numerical diffusion and suppresses the rms and mean Cp values further while the finer mesh adds less resulting in increased wind loadings.

The effect of various turbulence models on the 40k coarse mesh is shown in figures 4 and 5. Clearly the addition of more turbulent viscosity worsens the result, which is especially true of the k-w URANS model. This implies there is already too much damping present in the solution from the inherent numerical diffusion.

Conclusions
Simulations of sharp edged bluff bodies such as buildings in the built environment are dominated by large scale unstable structures originating from the flow separations at the buildings corners. The satisfactory resolution of these structures can be achieved using an unsteady laminar simulations in STAR-CCM+ which are equivalent to an LES model with no explicit sub grid scale model, provided the inherent numerical diffusion, arising from the discretization process, is monitored and reduced by a process of mesh refinement. In comparison the type of sub grid model used in conventional LES simulations is far less important.

For this benchmark flow we have found that LES simulations with no explicit sub grid model using embedded polyhedral refinement gives results accurate enough for wind loading purposes with a simulation time equivalent to 50 hrs on a 3.00 MHz PC (260k mesh). Without imposing turbulent fluctuations on the velocity inlet profile equivalent to the experimental values, further mesh refinement may lead to an over estimation of magnitudes of mean and rms pressure coefficients, however in the wind loading context this is no bad thing and can be interpreted as a worst case scenario.

 
 

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