Turbulent flow past a smooth and rigid wall-mounted hemisphere

Semi-confined flows

Underlying Flow Regime 3-33

Best Practice Advice

This section should be structured around the six subsections below.

Wherever possible, the advice should be in the form of an instruction rather than a conclusion. If appropriate, the conclusion can included after the "instruction" in order to provide context. Thus, for example:

"The aerodynamic coefficients can be accurately predicted with algebraic turbulence models. However these fail to predict the detailed dynamics of the wake boundary layer interaction. Such detail can, however, be predicted with reasonable accuracy using Spalart and Allmaras"

is a conclusion. The BPA advice flowing from this conclusion is:

"Use algebraic turbulence models if the requirement is to predict accurately just the aerodynamic coefficents"

"Use the Spalart Allmaras turbulence model if the requirement is to predict the detailed dynamics of the wake-boundary layer interaction as well as the aerodynamic coefficients".

It is generally easier to draw conclusions than to convert these into clear statements of advice. Thus it may be helpful to first set down your conclusions at the end of the Evaluation section and then work on these to develop the BPA.

Be extremely careful to ensure that your BPA is strongly supported by the evidence examined in the Evaluation section. Do not offer advice based upon your own experience or prejudices or upon published/unpublished evidence which is not fully examined in the UFR document (e.g. you may have read a recent paper which concludes Spalart and Allmaras is the best for this test case. You cannot base BPA on this if you have not discussed the calculations here).

Key Physics

Summarise the key flow physics which characterise the UFR and which must be captured for accurate prediction of the assessment parameters.

Numerical Modelling

Discretization accuracy: In order to perform LES predictions it is required that spatial and temporal discretization are both at least of second-order accuracy. It is also important that the numerical schemes applied possesses low numerical diffusion (and dispersion) properties in order to resolve all the scales and not to dampen them out. A predictor-corrector scheme (projection method) of second-order accuracy forms the kernel of the fluid solver. In the predictor step an explicit Runge-Kutta scheme advances the momentum equation in time. This explicit method is chosen because of its accuracy, speed and low memory consumption. The discretization in space is done with second order central discretization scheme without any flux blending.

Grid resolution: The second critical issue to perform LES is the grid resolution. The mesh near the wall, in the free-shear layers and also in the interior flow domain has to be fine enough. For wall-resolved LES the recommendations given by Piomelli and Chasnov (1996) should be followed or outperformed, e.g., y^+ < 2, \; \Delta x^+ < 50, \; \Delta z^+ < 50-150. In the present investigation two different block-structured grids either for the subset and for the full case are used. In the first case the entire grid consists of about 13.5 million control volumes (CVs). For the full geometry the grid possesses about 22.5 million CVs. The first cell center is positioned at a distance of Δz/D=1.7 x 10 − 2. For both setups it was found to be sufficient to resolve the flow accurately at walls as well as in the free shear layers. Similar to the classical flow around a cylinder also in the present configuration it is important to resolve the region close to the separation point and the evolving shear layer region adequately.

Grid quality: The third point is the quality of the grid. Smoothness and orthogonality is a very important issue for LES computations. In order to capture separations and reattachments at the cylinder and on the plate reliably, the orthogonality of the curvilinear grid in the vicinity of the walls has to be high. For deforming grids such as in the present FSI case, it is furthermore crucial to keep a high quality grid after strong grid movements and deformations.

Inlet boundary condition: At the inlet a constant streamwise velocity is set as inflow condition without adding any perturbations. The choice of zero turbulence level is based on the consideration that ,in general, small perturbations imposed at the inlet will anyway not reach the cylinder due to the coarseness of the grid at the outer boundaries. Therefore, all inflow fluctuations will be highly damped. However, since the flow is assumed to be sub-critical and the inflow turbulence level measured in the experimental setup found to be rather small, the neglect of inflow perturbations is of no relevance.

Outlet boundary condition: A convective outflow boundary condition is favored allowing vortices to leave the integration domain without significant disturbances (Breuer, 2002). The convection velocity is set to uinflow.

Physical Modelling

Turbulence modelling
Transition modelling
Near-wall modelling
Other modelling

Application Uncertainties

Summarise any aspects of the UFR model set-up which are subject to uncertainty and to which the assessment parameters are particularly sensitive (e.g location and nature of transition to turbulence; specification of turbulence quantities at inlet; flow leakage through gaps etc.)

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.

Contributed by: Jens Nikolas Wood, Guillaume De Nayer, Stephan Schmidt, Michael Breuer — Helmut-Schmidt Universität Hamburg