# UFR 2-12 Best Practice Advice

# Turbulent Flow Past Two-Body Configurations

## Flows Around Bodies

### Underlying Flow Regime 2-12

# 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
*λ*_{2}("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 3), 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 3) 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 0.02
*D*, 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 ±20*D* in the streamwise and about ±10*D* in the lateral direction.
For the spanwise direction, the domain size should not be less than 3*D*, 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

- 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 suitable statistical algorithm (see e.g. [16]
^{[1]}). As a guideline, roughly 50–100 convective time units of initial transient can be expected. - 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.

### Comparability of CFD predictions and experiment

- The spanwise domain represents a key source of discrepancy between the CFD and experimental configurations. Ideally, inclusion of the full experimental geometry (i.e. including the "floor" and "ceiling") in the CFD domain would be desirable, however this is currently associated with very high computational cost.
- Use the experimental data with transition trips on both cylinders [4] for best comparability with "fully-turbulent" CFD simulations.

## Recommendations for Future Work

The following recommendations are made to improve further the understanding of this UFR:

- The most unsatisfactory aspect of the simulations is a wide scatter of predictions of the rate of the initial roll-up of the shear layer separated from the upstream cylinder. Efforts to improve the situation by addressing a "grey area" issue in hybrid RANS-LES approaches would be most welcome.

- ↑ A software implementing this algorithm for the estimation of statistical error and the detection of initial transient is commercially available: Contact info@cfd-berlin.com for details
- ↑ Some participants of the BANC Workshops have used pure LES rather than DES-like approaches but these computations had the most difficulty simulating the high Reynolds aspects of the flow [5].

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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