The Delft Twist 11 Hydrofoil is a common test case for investigating the interaction between turbulence and cavitation modelling in computational fluid dynamics. Despite repeated investigations, results reported for the lift and drag coefficient are accompanied by significant uncertainties, both in experimental and numerical studies. When using scale-resolving approaches, it is known that turbulent fluctuations must be inserted into the domain in order to prevent the flow from remaining laminar around the body of interest, although this has been overlooked until now for the present test case. This work investigates the errors occurring when a laminar inflow is applied for mildly separated or attached flows, by employing the partially averaged Navier–Stokes equations with varying values for the ratio of modelled-to-total turbulence kinetic energy, and with varying grid densities. It is shown that depending on the grid resolution laminar leading edge separation can occur. When turbulent fluctuations are added to the inflow, the leading edge separation is suppressed completely, and the turbulent separation zone near the trailing edge reduces in size. The inflow turbulence has a large effect on the skin friction, which increases with increasing turbulence intensity to a limit determined by the grid resolution. In cavitating conditions the integral quantities are dominated by the shedding sheet cavity. The turbulence intensity has little effect on the pressure distribution, leading to a largely unaffected sheet cavitation, although the shedding behaviour is affected. It is shown that, especially in wetted flow conditions, with scale-resolving methods inflow turbulence is necessary to match the experimental flow field.

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Different variable resolution turbulence modelling approaches (Hybrid, Bridging models and LES) are evaluated for turbulent channel flow at Re_τ=395, for cases using either streamwise periodic boundary conditions or a synthetic turbulence generator. The effect of iterative, statistical and discretisation errors is investigated. For LES, little difference between the different sub-filter modelling approaches is found on the finer grids, while on coarser grids ILES deviates from explicit LES approaches. The results for Hybrid models are strongly dependent on their formulation, and the corresponding blending between the RANS and LES regions. The application of PANS with different ratios of modelled-to-total kinetic energy, f_k, shows that there is no smooth transition in the results between RANS and DNS. Instead a case-dependent threshold which separates two solution regimes is observed: f_k values below 0.2 yield a proper turbulent solution, similar to LES results; higher f_k values lead to a laminar flow due to filtering of the smallest scales in the inverse energy cascade. The application of a synthetic turbulence generator is observed to yield similar performance for all models. The reduced computational cost and increased flexibility makes it a suitable approach to enable the usage of SRS for industrial flow cases which depend on the development of a turbulent boundary layer. It ensures that sufficient large-scale structures develop over the full boundary layer height, thereby negating the problem of relying on the inverse energy cascade for the development of turbulence. Both LES and PANS with turbulence generator yield a better match with the reference data than Hybrid models; of these methods PANS is preferable due to the separation of modelling and discretisation errors.

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Partially Averaged Navier–Stokes computations can employ three different approaches for specifying the ratio of modelled-to-total turbulence kinetic energy fk. Use can be made of either a constant, a spatially- or a spatially- and temporally-varying value. This work compares different estimates for fk found in literature and evaluates them for two test-cases: a circular cylinder at Re=3900 and a turbulent channel flow at Reτ=395. Additionally, the estimates are compared to the a posteriori computed ratio of modelled-to-total turbulence kinetic energy()hfk˜ obtained from the PANS flow solution. The trends observed for the estimates are similar, although the magnitude varies significantly. All spatially varying fk approaches reduce the PANS model to a DES-like model, thereby entangling modelling and discretisation errors. At the same time, fk˜ shows that the behaviour of these estimates is incorrect: fk becomes too large near the wall of the object and in the far field. It is observed that fk˜ is always lower than the set value, when using fk fixed in space and time. Finally, it is clear that the estimates, applied to internal, boundary layer, flows yield too high values for fk. In order to minimise errors and increase the reliability of industrial CFD results, the approach with a constant fk is still preferable, assuming suitably fine grids are used.@en