Validation case by @1318980: **Project Link: CAARC Building - Lattice Boltzmann Method, Moment Validation**

# Moment Validation of the CAARC Building.

This validation focuses on validating the moment coefficients using experimental results obtained by RWDI in their wind tunnel tests, published in the paper (Calin Dragoiescu, Jason Garber and Suresh Kumar, 2006) where results were published using two techniques, a high-frequency force balance (HFFB) and high-frequency pressure integration (HFPI) which uses tap points. Both showing mostly good agreement between the two, with HFFB expected to be more accurate.

## Setup

The wind speed was defined using a scalable relationship as defined in the paper (Calin Dragoiescu, Jason Garber and Suresh Kumar, 2006) where U_H/nD_y=4.7 where n was the natural frequency, taken to be 0.2Hz and Dy as the width 45.72m resulting in a velocity at the top of the building to be 42.98. A velocity profile was created, where the roughness height Z_0= 0.1m and the reference velocity was the above at a reference height of 182.88m, the height of the building. The building was rotated around the z-axis at angle beta, where 0 degrees was wind head-on with the largest surface and 90 degrees was head-on with the smallest.

Figure 1: Domain setup, with wind direction, building angle, probe points and local and global axis.

The above figure describes the probe points used in the HFPI experiment, by face and row. The wind direction describes the direction in which the wind blows into the domain and also depicts angle beta, the angle in which the building is rotated. The axis’ show both local and global axis where later the moments in the global axis was transformed into local axis x’ and y’.

The turbulence model used was the K-omega SST IDDES which is an improved detached eddy simulation model, where the near wall regions are treated using the K-omega SST model, and the far-field uses a scale resolving eddy model. This gives the advantage of an accurate wall function as well as the benefits of an accurate transient model, giving a good blend of efficiency and accuracy. This also allows for transient effects to be accurately modelled and analysed, where the possibility of peak results and root mean square results can also be obtained in addition to time-averaged results.

## Mesh

Several mesh refinements were made to ensure good results. The following refinements were made:

- Tight region refinements were made around the building, refined to 0.5m for each cell edge.
- Slightly larger and extending 350m downstream a region refinement of 2m in resolution was made.
- another region refinement was made larger than that 600m downstream at 4m resolution.
- A floor region refinement was made to 1m to ensure a good resolution for the wall model to maintain the atmospheric boundary layer.
- Surface refinement on the building itself was refined to a resolution of 0.125m, producing a mesh of approximately 100 million cells.

Figure 2: Mesh with refinements.

## Results

The moments for each angle were calculated by the result control item in SimScale, where the entire surface pressure distribution is used to calculate moments about a point, being the point centrally located at the top of the building. Moments were taken in reference to the building, so adjustments had to be made to the raw data to return moments about the local axis. The vector manipulation was done on the time-averaged data between 50 and 100s where the flow was considered converged.

Figure 3: Moment Coefficients around the local x-axis.

The results around the x-axis are very close to experimental results. The values at 15 degrees appear to deviate, however, this is not supported as a data point at that location does not exist as experimental results were taken every 10 degrees and simulated results every 15 degrees.

Figure 4: Moment Coefficients around the local y-axis.

Results around the y-axis show good collaboration with experimental results. The only significant deviation exists when experimental points do not.

Figure 5: Moment coefficients about the z-axis.

Moments about the z-axis were significantly smaller than those in the x and y-direction, as a result, were very sensitive to mesh fineness. Figure 5 shows how the z moments deviated from experimental results at different surface refinements. Therefore the points that deviated Figure 6 are expected to improve with better mesh refinement, but they are still good results despite this. 75 degrees deviates also, however, it is hard to tell how much is due to mesh fineness as there is no data point here.

Figure 6: Mesh dependency study, showing different mesh fineness and experimental results.

The mesh independency study above was carried out for moments about the most sensitive axis which is the z-axis as previously mentioned. The HFFB results, which are considered the most accurate, are approached as mesh fitness increases, and with the next iteration, we would expect to converge well if the trend continues.

Figure 7: Vortex structures behind the building, identified by Q-criterion and mapped with velocity.

The above image shows the definition in which the transient turbulence is modelled, the vortices can be seen particularly near the building where the mesh is at its finest, however, the definition is well maintained far downstream.

## Conclusion

The setup, model and LBM have been shown to be highly comparable to experimental results, where apparent inaccuracies are explained, and inaccuracies are shown to be mesh dependent. The methods in the above description can be applied to similar setups, and the project can be used as a basis for other geometries. The processes, such as starting with a coarse mesh and building up, as always, is recommended and its usefulness is shown not only to gauge accuracy but also save core hour use. The time taken to run each direction was between 1700 Core hours and 2000 core hours and took no more than 10 hours real time to solve.

## References

Calin Dragoiescu, Jason Garber and Suresh Kumar (2006) ‘A Comparison of Force Balance and Pressure Integration Techniques for Predicting Wind-Induced Responses of Tall Buildings’.