A new partially averaged Navier-Stokes (PANS) closure is derived based on the k-kL (KSKL) model. The aim of this new model is to incorporate the desirable features of the KSKL model, compared to the k-ω shear stress transport model, into the PANS framework. These features include reduced eddy-viscosity levels, a lower dependency on the cell height at the wall, well-defined boundary conditions, and improved iterative convergence. As well as the new model derivation, the paper demonstrates that these desirable features are indeed maintained, for a range of modeled-to-total turbulence kinetic energy ratios (fk), and even for multiphase flow.

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Inflow turbulence is relevant for many engineering applications relating to noise generation, including aircraft wings, landing gears, and non-cavitating marine propellers. While modelling of this phenomenon is well-established for higher Mach number aerospace problems, lower Mach number applications, which include marine propellers, still lack validated numerical tools. For this purpose, simplified cases for which extensive measurement data are available can be used. This paper investigates the effect of inflow turbulence on a circular cylinder at a Reynolds number of 14,700, a Mach number of 0.029, and with inflow turbulence intensities ranging between 0% and 22%. In the present work focus is put on the hydrodynamics aspect, with the aim of addressing radiated noise in a later study. The flow is simulated using the partially averaged Navier Stokes equations, with turbulence inserted using a synthetic inflow turbulence generator. Results show that the proposed method can successfully replicate nearfield pressure variations and relevant flow features in the wake of the body. In agreement with the literature, increasing inflow turbulence intensity adds broadband frequency content to all the presented fluctuating flow quantities. In addition, the applied variations in inflow turbulence intensity result in a major shift in flow dynamics around a turbulence intensity of 15%, when the dominant effect of von Kármán vortices on the dominant flow dynamics becomes superseded by freestream turbulence.

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This study evaluates the influence of transition and turbulence modeling on the prediction of wetted and cavitating tip vortices for an elliptical wing, while investigating the numerical errors. Transition modeling increases the quality of numerical predictions since the assumption of a fully turbulent boundary layer, commonly found in literature, contributes to underprediction of the tip vortex cavity size. By applying the local correlation-based transition model (LCTM) and controlling the boundary layer thickness using different turbulent inflow conditions, the pressure in the vortex was found to reduce by 20% for an Angle of Attack (AoA) of 5 deg. The consequent increase in cavity size was found to be of a similar order of magnitude. At 9 deg AoA, transition always occurs just downstream of the leading edge, making this AoA more suitable to investigate the effect of different turbulence modeling approaches. Azimuthal and axial velocity fields are validated against stereographic-particle image velocimetry (S-PIV) measurements. The time-averaged velocity profiles predicted by delayed detached-eddy simulation (DDES) and improved delayed detached-eddy simulation (IDDES) are close to the experiments; however, no velocity fluctuations and vortex dynamics are observed around the vortex. A comparison of wetted and cavitating simulations shows that the cavity leads to a change in the balance between production and destruction of turbulence kinetic energy, which reduces the turbulent diffusion in and around the cavity compared to wetted flow conditions. Consequently, the vapor flow exhibits the characteristics of a potential flow. Whether this is physically plausible remains to be investigated.

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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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A sensitivity analysis of the transitional flow over a NACA66₂ - 415 foil and the elliptical Arndt wing is carried out. The SST turbulence model is complemented with the ? - Re ^~_?t transition model to determine the effect of varying turbulence intensity and eddy-viscosity ratio on the integral quantities and transition locations. Local grid refinement at the transition location is used to improve convergence. The skin friction drag coefficient is found to be more sensitive to the inflow conditions for 5^? angle of attack compared to 9^?. The movement of the transition location on the suction side is found to be responsible for this. The transition model captures a laminar separation bubble at the pressure side for both angles of attack, causing the lift coefficient to drop slightly. 3D calculations for the Arndt wing with the same foil section show that applying a transition model can decrease the boundary layer thickness by a factor of three, which is expected to influence the viscous core radius and consequently the minimum pressure in the tip vortex.

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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

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