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The paper presents the results of numerical simulation of three-dimensional turbulent flow around a hydraulic turbine guide vane at the angle of attack of 9° with the aspect ratio of the foil equal to 0.8. The influence of turbulence modeling variants on 3D flow effects is analyzed. The 3D boundary layer separation at the vane-sidewall junctions and the flow separation near the trailing edge influence the flow pattern. The study considered various approaches for modeling of a turbulent flow, such as the k-ω SST turbulent viscosity model and several variants of the differential and algebraic Reynolds stress models. At the given angle of attack, the k-ω SST model shows a significant separation zone in the corners between the wall and the vane, while no separation of the flow in the central plane is observed. Both differential and algebraic Reynolds stress models reproduce the secondary vortex flow at the corners and suppress the flow separation near the central cross section.

The results of numerical simulation of cavitating flow around the experimental model of a guide vane of a water turbine are given. The possibilities of the detached eddy simulation (DES) method for calculating the flow dynamics around the hydrofoil in two regimes at 3° and 9° angles of attack are analyzed. The mean flow velocity inside the boundary layer is compared with the experimental data. The dimensions and shape of the three-dimensional vapor cavity are presented in various operating regimes. The cavity dynamics and induced pulsations are analyzed.

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 an investigation into drilling mud flow with cuttings in a vertical well. The drilling mud rheology was described with the Herschel-Bulkley model. The axial Reynolds number was around 1000, the flow regime changing together with drill pipe RPM. The investigation covered the flow’s structures, integral parameters and cuttings transport in relation to drill pipe RPM and rate of penetration (ROP). In the laminar flow, most of the particles were localized in the quasi-solid region to move together with the last; the integral parameters had little dependence on drill pipe RPM increase. Increasing drill pipe RPM resulted in formation of the Görtler vortices near the channel’s external and internal walls, whose interaction led to the formation of smaller eddies converting the flow into a turbulent one. Due to the turbulence dispersion, the region taken by the particles widened. Particles suppress the vortex intensity near the channel’s external wall. Under the conditions described, increasing drill pipe RPM and ROP resulted in higher pressure drops and lower transport efficiency.

Transient three-dimensional flow simulations of power–law fluid in a long axisymmetric annular channel considering 0.5 diameter ratio were performed. An in–house CFD code considering URANS (Unsteady Reynolds Averaged Navier–Stokes), 2D RANS (steady-state axially uniform 2D RANS) and LES (Large Eddy Simulation) approaches were compared to perform the simulations. Flow structure was analyzed. Numerical experiments showed that rotation of the inner cylinder (drill pipe) leads to two effects: decrease of apparent viscosity in the region close to the rotating cylinder, thus decreasing viscous shear stresses; development of secondary vorticity structures increasing energy loss. First mechanism decreases pressure losses and dominates when Re < 300. At Re ∼ 300 the mechanisms compete with each other and pressure losses depends on power–law index n. At Re > 300 mechanism of second vortex structured dominates and increases pressure loss with rotation. Pressure losses for two-dimensional steady-state and three-dimensional transient problems were compared. Pressure losses using a two-dimensional approach can be underestimated by up to 30%.

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.

Fully developed turbulent pipe flows of power-law fluids are studied by means of direct numerical simulation. Two series of calculations at generalised Reynolds numbers of approximately 10000 and 20000 were carried out. Five different power law indexes n from 0.4 to 1 were considered. The distributions of components of Reynolds stress tensor, averaged viscosity, viscosity fluctuations, and measures of turbulent anisotropy are presented. The friction coefficient predicted by the simulations is in a good agreement with the correlation obtained from experiment. Flows of power-law fluids exhibit stronger anisotropy of the Reynolds stress tensor compared with the flow of Newtonian fluid. The turbulence anisotropy becomes more significant with the decreasing flow index n. An increase in apparent viscosity away from the wall leads to the damping of the wall-normal velocity pulsations. The suppression of the turbulent energy redistribution between the Reynolds stress tensor components observed in the simulations leads to a strong domination of the axial velocity pulsations. The damping of wall-normal velocity pulsations leads to a reduction of the fluctuating transport of momentum from the core toward the wall, which explains the effect of drag reduction.

The paper presents a novel Reynolds-averaged turbulence model for flows of power-law fluid. The model uses the elliptic relaxation approach to capture the near-wall turbulence anisotropy. The turbulence model for Newtonians fluids is modified by introducing closed approximations of correlations between velocity and viscosity fluctuations. The approximation for non-Newtonian extra stress is derived with the assumption of smallness of molecular viscosity fluctuations. A closed model for the averaged molecular viscosity is derived which takes into account its nonlinear dependence on the shear rate. Validation of the model against the direct numerical simulation (DNS) data for power-law fluids flows in the pipe demonstrates that new model is able to predict the main features of the non-Newtonian turbulence. Mean velocity, turbulent energy and averaged molecular viscosity distributions agree well with DNS data.

Swirling flows are investigated using an unsteady model based on the Reynolds stress transport equations. Swirling flows with vortex core precession are considered, namely, the swirling flow behind an abrupt expansion and the swirling flow in a burner with an annular fuel inlet. The method under consideration is shown to well reproduce the recirculation flow formed as a result of the vortex core precession, with respect to both mean and fluctuation parameters. At the same time, the calculations in accordance with the unsteady model prolong the central recirculation zone. It is established that the contributions made by the resolvable and modeled components of the Reynolds stress tensor to the turbulent transport are comparable.

Numerical modeling of the unsteady flow in the draft tube of the test bench hydro turbine is conducted. The hybrid RANS-LES methods for modeling turbulent flows are compared. The intensity and frequency of pressure fluctuations, which are induced by the vortex core precession under the runner, and the integral characteristics are considered. An analysis of the synchronous and asynchronous parts of pressure fluctuations is done; the generating and influence of the synchronous component of fluctuations are considered. The vortex core interaction with the draft tube elbow is considered.

Flow regimes and mixing performance in a T-type micromixer at high Reynolds numbers were studied by numerical solution of the Navier–Stokes equations. The Reynolds number was varied from 1 to 1000. The cross section of the mixing channel was 100 μm × 200 μm, and its length was 1400 μm. The transverse inlet channels were symmetric about the mixing channel, and their cross-section was 100 μm × 100 μm, and the total length was 800 μm. Five different flow regimes were identified: (i) stationary vortex-free flow (Re 400). Maximum mixing efficiency is obtained for nonstationary asymmetric vortex flow. In this case, an S-shaped vortex structure is formed in the flow field. The effect of the slip conditions on the flow pattern and mixing efficiency is studied. The slip length varied from 1 to 70 μm in the calculations. It was shown that the mixing can be controlled by hydrophobic coating.

Different turbulence models were studied in application to calculation of swirling flows. The differential models of turbulent viscosity considering streamline curvature and the method of detached eddy simulation were used. Weakly and strongly swirling flows were considered at the example of concentrated vortex in a tube, swirling flow in a diffuser, and vortex breakdown through an abrupt expansion. The RANS models with correction to flow swirling represented well the experimental data for the weakly swirling flows. In case of strongly swirling flows, it was more correct to use the method of detached eddy simulation.

To produce a well safely, the wellbore pressure during drilling must be in a range that prevents collapse yet avoids fracturing. This range is often called “the operating window”. Exceeding the limits of this range can trigger wellbore instability or initiate well control incidents. Pressure prediction requires an understanding of the hydrodynamics processes that occur in a borehole while drilling. Describing these processes is complicated by many factors: the mud rheology is usually non-Newtonian, the flow mode can be laminar or turbulent, and the drillstring can rotate and be positioned eccentrically. Known semi-analytical approaches cannot account for the full range of fluid flows that can arise during drilling. These techniques don’t take into account all factors. Accurate numerical simulation of the flow of drilling fluids is a means to describe the fluid behavior in detail. For numerical solutions of hydrodynamics equations a unique algorithm based on a finite-volume method and a new model of turbulence for non-Newtonian fluids was developed. The model considers string rotation and eccentricity of the drillstring. Newtonian and non-Newtonian fluids as described by the Herschel–Bulkley rheological model have been implemented. Data obtained via systematic parameter studies of the flow in a borehole are available for fast determination of parameters like pressure drop, velocity field, and stresses corresponding to any drilling condition. Applying the new model for the annulus flow and comparing the results to the parallel plate flow approximation enabled us to quantify the error made due to the approximated solution for non-Newtonian fluid rheology. The difference between the solutions grows as the annular gap increases. This situation is a function of the rheological parameters. Secondary flow effects can only be seen when applying the new solution method.

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.