[mjavrincon]

Dear community,

I have been working in LES on rather complex internal flow cases and found some interesting (and somewhat unsettling results) using OpenFOAM.

METHODOLOGY

Let me first introduce the case and methods to you:

- The case is based on a small-diameter ultrasonic flow meter in which a straight section of pipe is simulated before a constriction where identical stands are located. These stands display a high blockage in the pipe, hence separation, secondary flow, vortices, and generally complex flow conditions are predicted. If you want to know more about the case and its experimental validation, please refer to [1] and [2].

- The case has a friction Reynolds number of around 760 in a wall-modelled LES (WMLES) using the WALE sub-grid scale model. To create inlet turbulent conditions, the recycling method is used, mapping the velocity field at the inlet at 5D in the axial direction. First-order statistics of the velocity are taken until convergence is reached in the axial velocity field.

Now, I have got very different results based on a standard mesh and just changing the divergence schemes applied to the velocity. The different schemes that I have tried are:

- Gauss linear (recommended by OpenFOAM for LES).
- Gauss SFCDV 1.
- Gauss linearUpwind grad(U).
- Gauss filteredLinear2 1 0.05 (based on the results from [3]).

RESULTS

Luckily enough, I have some experimental Laser Doppler Velocimetry (LDV) data and wall-resolved RANS kOmegaSST results that I can compare against LES. In Fig. 1 you can see the qualitative contours for the best LES that I have got.

The case is very interesting since we can evaluate the prediction of the law-of-the-wall (LotW) at the inlet pipe section (where the results are compared to DNS pipe flow data from [4]), the prediction of diverse contours qualitatively, and the prediction of the velocity profiles at different locations of interest.

Here is what I have found:

1. The Gauss linear scheme is too prone to unboundedness when complex cases are evaluated, yielding unphysical results (Fig. 2). It does however perform well in canonical and well-posed cases like a standard pipe/channel flow and accurately predicts the LotW.
2. The Gauss SFCDV 1 scheme adds too much numerical diffusion for LES, not predicting correctly the LotW (Fig. 3) and predicting non-symmetrical results (Fig. 4). This fact propagates to a non-accurate velocity prediction.
3. The Gauss linearUpwind grad(U) scheme displays similar results as
The Gauss SFCDV 1 scheme: wrong axial velocity and LotW prediction.
4. The Gauss filteredLinear2 1 0.05 correctly predicts the LotW and accurately predicts the axial velocity profiles without yielding unbounded or non-physical results (Fig. 5).

CONCLUSIONS

Gauss filteredLinear2 1 0.05 is the only evaluated divergence scheme for the velocity in LES with OpenFOAM that is capable of accurately predicting the LotW and velocity fields in complex internal flow cases. I would strongly suggest to anyone interested in high-fidelity simulations with OpenFOAM to use this scheme and to be critical of their results. The scheme has 2 coefficients that can probably be adjusted and might be case-dependent, although, for unstructured meshes and complex flows, the suggested coefficients by [4] yield accurate results. As a disclaimer, this is just based on a thorough, but not very extended study, so I am sure that there are better approaches to adjust these schemes.

I would like to open this thread, not only to show my findings and recommendations to anyone who can make use of them but to open the discussion of LES accuracy with OpenFOAM to the community. Encouraging that, if we keep collaborating and sharing high-quality results and studies, we could little by little improve the use of open-source CFD for everyone.

Have you found yourself experiencing the same problems? Do you have any (or better) recommendations to obtain high-quality LES results?

REFERENCES

[1] Rincón, M. J., Reclari, M., & Abkar, M. (2022). Turbulent flow in small-diameter ultrasonic flow meters: A numerical and experimental study. Flow Measurement and Instrumentation, 87, 102227.
[2] Rincón, M. J., Reclari, M., Yang, X. I., & Abkar, M. (2023). Validating the design optimisation of ultrasonic flow meters using computational fluid dynamics and surrogate modelling. International Journal of Heat and Fluid Flow, 100, 109112.
[3] Verma, S. (2019). A large eddy simulation study of the effects of wind and slope on the structure of a turbulent line fire (Doctoral dissertation, University of Maryland, College Park).
[4] Wu, X., & Moin, P. (2008). A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow. Journal of Fluid Mechanics, 608, 81-112.