UFR 2-12 Best Practice Advice

Turbulent Flow Past Two-Body Configurations

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Best Practice Advice

NOTE: the BPA formulated below are overall well in line with conclusions based on the outcome of BANC-I [5] and not yet published results of BANC-II.

Key Physics

The key physical features of this UFR are separation of the turbulent shear layer from the upstream cylinder, free shear layer roll-up and chaotization, interaction of the essentially unsteady wake of the upstream cylinder with the downstream one, and massively separated wake of the downstream cylinder. It is found that it is necessary to capture these challenging features in a simulation claiming a reliable prediction of all the UFR characteristics. Whether this is reached or not in a simulation should be checked by:

• Obtaining a visual impression of the unsteadiness of the shear layer separated from the upstream cylinder and of a range of spatial scales present in its wake and in the wake of the downstream cylinder using e.g. a snapshot of isosurface of λ₂ ("swirl") or Q-criterion (see Figure 4 for an example of the former) and vorticity contours (Figure 11).
• Confirming a mixed tonal and broadband nature of the pressure signals on the surface of the cylinders by their spectral analysis (Figure 16).

Numerical Issues

In terms of numerics, based on experience accumulated in the course of the ATAAC and related projects, the following advice can be given:

• In the Focus Region of simulation (see Figure 2), use numerical schemes with as low numerical dissipation as possible, particularly, pure or close to pure CDS for convective fluxes with the order of accuracy not less than 2. Acceptability of the level of numerical dissipation may be assessed by examining snapshots of e.g. vorticity in the focus region: the size of the smallest resolved eddies should not be noticeably larger than the local grid spacing.
• In the Euler and Departure Regions (see Figure 2) use a scheme with sufficient numerical dissipation to prevent grid oscillations or "wiggles" in these regions.
• Use a minimum second order accurate temporal integration scheme.
• Use a time step sufficiently fine to capture the motion of the turbulent eddies resolved by the grid in the Focus Region. This corresponds to the approximate guideline CFL_max ≈ 1.

In terms of grids, although no systematic grid-sensitivity studies for the considered UFR have been carried out, indirect evidence allows the following recommendations:

• In the Focus Region, use nearly isotropic grids with sizes not larger than around 0.02D, although even smaller values are desirable.
• Outside the Focus Region, expand the grid cell size gradually towards the inflow/outflow boundaries, avoiding sudden jumps.

Size of computational domain should not be less than about ±20D in the streamwise and about ±10D in the lateral direction. For the spanwise direction, the domain size should not be less than 3D, but larger domains are strongly recommended provided that available computer resources allow this.

Physical Modelling Issues

Turbulence modelling

• Use hybrid turbulence-resolving approaches, e.g. DDES or similar methods capable of treating the entire turbulent cylinder boundary layer with RANS. Steady and unsteady RANS with the conventional turbulence models (either linear or non-linear eddy viscosity or RSM models) should not be used because of their insufficient accuracy and wall-resolved LES because of its too high computational cost for the considered high Re number flow. IDDES can, in principle, give more accurate predictions than DDES but is shown to be more sensitive to numerics and span-size of the domain and so should be used with special care.
• The choice of background RANS model has not been fully studied, although in the current study SA-based DDES has demonstrated somewhat more "stable" (less code-dependent) behaviour and, in general, a better agreement with experiments than e.g. SST based DDES.

Transition modelling

• For the supercritical flow conditions or if the boundary layers on both cylinders are tripped in the experiment, no specific transition modelling or prescription is required and fully turbulent simulation is quite justified.

Near-wall modelling

All the simulations have been carried out with the use of low-Re versions of background RANS models and so no recommendations on the use of wall-functions are available.

Application Uncertainties

Time sample / statistical processing

1. Ensure that the simulation has bridged the initial transient and entered a statistically steady state before commencing the collection of statistics. This must either be checked by visual inspection of a monitor signal (e.g. drag and lift coefficients) or using a suitablestatistical algorithm (see e.g. [16]). As a guideline, roughly 50–100 convective time units of initial transient can be expected.
2. Compute sufficiently long time samples for reliable statistical quantities. As a general guideline, a minimum time sample of 150 convective units is recommended. An objective evaluation of sufficiency of time sample can be done with the use a suitable statistical algorithm (e.g. [16]2) or by a direct checking the effect of a considerable increase of the time sample.

Recommendations for Future Work

Propose further studies which will improve the quality or scope of the BPA and perhaps bring it up to date. For example, perhaps further calculations of the test-case should be performed employing more recent, highly promising models of turbulence (e.g Spalart and Allmaras, Durbin's v2f, etc.). Or perhaps new experiments should be undertaken for which the values of key parameters (e.g. pressure gradient or streamline curvature) are much closer to those encountered in real application challenges.

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Contributed by: A. Garbaruk, M. Shur and M. Strelets — New Technologies and Services LLC (NTS) and St.-Petersburg State Polytechnic University

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Description

Test Case Studies

Evaluation

Best Practice Advice

References

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