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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.

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.

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%.

Laminar flow of a power-law fluid over a sphere is considered for unbounded shear flow. The Navier–Stokes equations with power-law viscosity are solved numerically using an in-house developed CFD package. Vorticities structures downstream of particle are suppressed for powerlaw fluid. The shear rate influence on drag force is negligible for power index close to unit, and the drag force appreciably decreases with falling power index. For small Reynolds numbers, the lift force coefficient monotonically decreases against the power index and exhibits an opposite behavior for moderate values of Reynolds numbers. The results of the parametric studies are used to derive correlations for the drag force and to detect the hydrodynamic differences from uniform flow. The investigation parameters varied within the following ranges: power-law index 0.3 ≤ n ≤ 1, Reynolds number 0 < Re ≤ 150, and dimensionless shear rate 0.05 ≤ s ≤ 0.4.

The results of direct numerical simulation of turbulent flows of non-Newtonian pseudoplastic fluids in a straight pipe are presented. The data on the distributions of the turbulent stress tensor components and the shear stress and turbulent kinetic energy balances are obtained for steady turbulent flows at the Reynolds numbers of 104 and 2×104. As distinct from Newtonian fluid flows, the viscous shear stresses turn out to be significant even far from the wall. In power-law fluid flows the mechanism of the energy transport from axial to transverse component fluctuations is suppressed. It is shown that with decrease in the fluid index the turbulent transfer of the momentum and the velocity fluctuations between the wall layer and the flow core reduces, while the turbulent energy flux toward the wall increases. The earlier-proposed models for the average viscosity and the non-Newtonian one-point correlations are in good agreement with the data of direct numerical simulation.

Characteristics of the incompressible flow of Herschel–Bulkley fluid over a sphere were studied via systematic numerical modeling. A steady isothermal laminar flow mode was considered within a wide range of flow parameters: the Reynolds number 0 < Re ≤ 200, the Bingham number 0 ≤ Bn ≤ 100, and the power index 0.3 ≤ n ≤ 1. The numerical solution to the hydrodynamic equations was obtained using the finite volume method in the axisymmetric case. The changes in flow structures, pressure and viscous friction distribution, and integral drag as a function of the flow rate and fluid rheology are shown. Depending on whether plastic or inertial effects dominate in the flow, the limiting cases were identified. The power law and Bingham fluid flows were studied in detail as particular cases of the Herschel–Bulkley rheological model. Based on the modeling results, a new correlation was developed that approximates the calculated data with an accuracy of about 5% across the entire range of the input parameters. This correlation is also applicable in the particular cases of the power law and Bingham fluids.

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.

Recognizing the limitations of the conventional linear-eddy-viscosity (LEVM) Reynolds-averaged Navier–Stokes (RANS) models to reproduce complex three-dimensional unsteady flows in hydraulic machinery, we performed a comparative assessment of a second-moment (Re-stress model, RSM) RANS closure and a hybrid RANS/LES method in capturing the flow and vortical structures in the draft tube of a Francis hydroturbine at off-design conditions. Considered is a case of part load (PL) at a flow rate of only 35% of the best efficiency point (BEP) characterised by multiple unsteady vortex systems. Despite some remaining uncertainties in generating the inflow conditions, both approaches reproduced reasonably well the measured mean velocity and the rms of its fluctuations, as well as the pressure spectrum with peaks detecting the precessing vortex core. In contrast to the common LEVMs, the Re-stress closure showed sufficient receptivity to intrinsic unsteadiness and reproduced well the overall flow and vortical patterns as well as the associated pressure pulsations in accord with the experiments. The hybrid RANS/LES method gave similar predictions as the RSM, but resolving a wider range of scales, which however, showed no significant effect on the dynamics of the dominant processing vortex core and the pressure pulsations.

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.

Highly nonlinear spatial-temporal patterns are inevitable features of lasing in the low-Q (bad) cavities where a photon lifetime, T E , is less than a polarization relaxation time (a lifetime of the optical dipole oscillations), T 2 , of the individual active centers excited by pumping [1]. A theoretical analysis of the spatial-temporal dynamics of the field and its spectral and correlation features in such lasers, known as the superradiant lasers, cannot be based on a standard decomposition on neither ‘cold’ no ‘hot’ modes which have fixed spatial profiles and are defined, respectively, by a cavity without or with taking into account the active medium. A progress in modern technologies, especially in the field of semiconductor heterostructures, leaves no doubts about near fabrication of these lasers and their applications in the optical information processing, the wideband dynamical spectroscopy, and diagnostics of many-particle systems in condensed active media.

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.

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.

The current study is devoted to simulating cuttings transport by drilling fluid through a horizontal section of borehole with an annular cross section. Drill pipe rotates in fixed eccentric position. Steady-state flow is considered. Cuttings are rigid spheres with equal diameters. The carrying fluid is drilling mud with Herschel-Bulkley rheology. Suspension rheology depends on local shear rate and particles concentration. Continuous mixture model with algebraic equation for particles slipping velocity is used. Two hydrodynamic regimes are considered: axial flow without drill pipe rotation and with drill pipe rotation. In the case of axial flow was shown that increasing of power index n and consistency factor k increases pressure gradient and decreases cuttings concentration. Increasing of yield stress leads to increasing of pressure gradient and cuttings concentration. Cuttings concentration achieves constant value for high yield stress and not depends on it. Rotation of the drill pipe significantly changes the flow structure: pressure loss occurs and particles concentration decreases in the cross section. Two basic regimes of rotational flow are observed: domination of primary vortex around drill pipe and domination secondary vorticity structures. Transition between regimes leads to significant changes of flow integral parameters.

The article describes the concept of the methodology of intellectual labor automation, a formal description of the conceptual model (CM) at the object level, and also a description of the analytical processing of CM. The conceptual model is the basis for the design of the system. The conceptual model of an applied task reflects the semantics (the system of knowledge) of the subject field in the form of static and dynamic structures and their linkage. The elements of the static structure are subject categories defined by classes: cycle, process, task, component, object, feature, value. The dynamic structure reflects the system of subject dependences which describes the process of performing a subject task. The main stage of conceptual model analytical processing is the restructuring of the dynamic component. The method and technique of descriptions restructuring of subject dependences system at the level of features are developed. The method allows to provide reduction of time and spatial expenses on performance of process of the decision of the applied task in the computing environment at early stages of information-active systems design

The possibility of developing power and transport systems for space applications is examined. It is suggested to use an MHD generator utilizing inhomogeneous gas-plasma flows of inert gas as the source of electric energy in such systems. The plasma of the current layers may be in the state of “frozen ionization,” when the degree of ionization exceeds the equilibrium level thereby providing for an effective MHD interaction with the enthalpy extraction coefficient of 0.4 and adiabatic efficiency of 0.8. Such a plasma is stable with respect to dissipative instabilities (ionization and overheating) and retains its positive properties at a stagnation pressure of the order of 1 MPa. The estimation of the mass-and-size characteristics of a closed-cycle solar MHD facility for space applications reveals that the specific power of the facility may amount to 500 W/kg. It is suggested that the propulsion unit should be provided by an electric rocket engine on the basis of an MHD accelerator, with the working medium provided by a nonuniform gas-plasma flow in which azimuthal plasma rings (T-layers) are inductively connected to the electric energy source. In a flow with T-layers, an efflux velocity of the order of 40 km/s is attained. With a mass flow rate of 50 g/s, the engine may develop a propulsive force of 2000 N.