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Two-dimensional flow around a semi-circular profile at the zero angle of attack and at Re = 50000 on the self-oscillatory period is extensively studied by the URANS method involving the standard semi-empirical SST turbulence models, the SST turbulence model with the correction for streamline curvature modified within the Rodi-Leschziner-Isaev and Smirnov-Menter approaches, as well as involving Hanjalic's four-parameter eddy viscosity elliptic relaxation model and its analog - eddy viscosity elliptic blending model proposed in the present work. This has been done with the use of different-structure grids (multiblock with structured overlapping and unstructured composite). Different numerical approximation methods realized in six codes (VP2/3, SigmaFlow, Fluent, CFX, OpenFOAM, and StarCCM+) are used. An underestimation (up to 30%) of time-averaged integral aerodynamic loads is revealed by means of the standard near-wall SST model. This is explained by the high vortex viscosity production in the profile wake. Wind tunnel tests show that the location of cutoff washers on the semi-circular profile provides a quasi-two-dimensional flow around it and allows applying measurement data to verify two-dimensional turbulent flow. The best agreement of experimental results and numerical predictions when comparing the Strouhal number and time-averaged surface pressure coefficient distributions is achieved using both the modified SST model with the correction for streamline curvature and the modified eddy viscosity elliptic blending model. When the SST model with the correction for streamline curvature, modified within the Rodi-Leschziner-Isaev, Smirnov-Menter and Durbin approaches, is used, all the above codes yield close predictions of a vertical aerodynamic load on the oscillation period.

The paper presents the results of Newtonian-fluid spiral flow simulation in an annular channel. The simulation parameters were dimeters ratio of 0.5; Re = 100 ÷ 10,000 and dimensionless inner cylinder rotation rate χ = 0.2 ÷ 5. The turbulent flow regimes were simulated using URANS, a non-stationary statistical turbulence model. While simulation, the following flow regimes were detected: homogeneous flow without pronounced structures (Re = 100, χ⩽3 and Re=300, χ⩽0.5); flow with Görtler-type continuous spiral vortices near inner cylinder (Re = 300, χ=1 and Re = 1000 ÷ 10000, χ = 0.5); flow with Taylor-type vortices (Re = 100, χ⩾3 and Re = 300, χ⩾3); flow with small-scale Görtler-type vortices near both channel walls (Re ⩾ 1000 and χ⩾1). The spiral spin of Görtler-type vortices near the outer cylinder was co-directed with the rotation of the inner cylinder, while the vortices near the inner cylinder spin against the rotation. Formation of large Taylor-type vortex structures led to a decrease in the channel skin friction coefficient faRe. Görtler-type vortices interaction near the channel walls triggered the formation of small-scale structures increasing in the channel resistance as the Reynolds number and rotation speed grew.

The paper presents numerical simulation of the flow in hydraulic turbine based on the experimental data of the II Francis-99 workshop. The calculation domain includes the wicket gate, runner and draft tube with rotating reference frame for the runner zone. Different turbulence models such as k-ω SST, ζ-f and RSM were considered. The calculations were performed by means of in-house CFD code SigmaFlow. The numerical simulation for part load, high load and best efficiency operation points were performed.

We performed numerical simulation of flow in a laboratory model of a Francis hydroturbine at three regimes, using two eddy-viscosity- (EVM) and a Reynolds stress (RSM) RANS models (realizable k-, k-ω SST, LRR) and detached-eddy-simulations (DES), as well as large-eddy simulations (LES). Comparison of calculation results with the experimental data was carried out. Unlike the linear EVMs, the RSM, DES, and LES reproduced well the mean velocity components, and pressure pulsations in the diffusor draft tube. Despite relatively coarse meshes and insufficient resolution of the near-wall region, LES, DES also reproduced well the intrinsic flow unsteadiness and the dominant flow structures and the associated pressure pulsations in the draft tube.

Results of unsteady two-dimensional numerical simulations for the turbulent flow over the semi-cylindrical profile at Reynolds number 45000 are presented. Three different turbulence RANS eddy viscosity models are used for the simulation. The calculations show the formation of alternating large-scale vortices shed in the wake of the body. The calculated averaged pressure distribution on the contour demonstrate a good agreement with the experimental data. A series of calculations have been performed for the estimation of influence of mesh resolution in the wake of streamlined body on the unsteady solution accuracy. It was found that a mesh size ~0.04 of chord length is sufficient to resolve the vortex street.