A. A. Gavrilov

A numerical algorithm for modeling laminar flows in an annular channel with eccentricity

We propose a numerical algorithm for simulating steady laminar flows of an incompressible fluid in annular channels with eccentricity and rotation of the inner cylinder. This algorithm enables us to describe this class of flows for wide ranges of the annular channel and flow parameters. We present the implementation details and the results of testing this numerical method. For a series of flows in an annular clearance, we compare the numerical results to available analytic solutions and experimental data. In all cases under consideration the simulated data agree well with the available experimental, analytical, and numerical solutions.

Application of new numerical algorithm for solving the Navier—Stokes equations for modelling the work of a viscometer of the physical pendulum type

A model is proposed, which describes the work of the viscometer sensor of the physical pendulum type. The model enables the obtaining of data on fluid viscosity directly from the measurement of the settling frequency of sensor oscillations or the amplitude of these oscillations. To describe the sensor operation a numerical computational algorithm is developed. This method enables the solution of a wide class of three-dimensional laminar fluid flow problems involving moving solids of arbitrary geometry. The results of testing the proposed numerical technique are presented.

Modelling of flows in micromixers

A method is proposed for modelling fluid flows in microchannels. The method is tested on the known experimental data on studying the flows in microchannels with the aid of the micro-PIV. The flow regimes in micromixers of the Y- and T-types are studied. The passive and active mixers are considered. The dependence of the mixing efficiency on the Reynolds and Péclet numbers as well as the possibility of using the hydrophobic and ultra-hydrophobic coatings are analysed. A T-mixer is proposed as an active technique of mixing, in which the flow rate in one of the inlet channels varied according to the harmonic law. The dependence of the mixing efficiency on the frequency of the variation of the flow rate and its amplitude is established.

Mixing in a T-shaped micromixer at moderate Reynolds numbers

In the present work, the regimes of the flow and mixing of fluids in a T-shaped micromixer in the range of the Reynolds numbers from 1 to 1000 are investigated systematically with the aid of numerical modeling. The flow and mixing regimes are shown to alter substantially with increasing Reynolds numbers. Five different flow regimes have been identified in the total. The dependencies of the friction coefficient and mixing efficiency on the Reynolds number are obtained. A sharp increase in the mixing efficiency at a flow transition from the symmetric to asymmetric steady regime is shown. On the other hand, the mixing efficiency slightly drops in the laminar-turbulent transition region. A substantial influence of the slip presence on walls on flow structure in the channel and mixing efficiency has been revealed.

Numerical modeling of flow in the Francis-99 turbine with Reynolds stress model and detached eddy simulation method

The paper presents numerical simulation of flow in Francis-99 water turbine under three operation modes: part load, best efficiency point and high load. Calculations were performed by means of Reynolds stress model and detached eddy simulation based on k-omega SST model. The paper focuses on the flows in the draft tube. The calculated mean velocity components in the draft tube are in close agreement with experimental results. Calculated r.m.s velocity components agree with experimental pulsations qualitatively.

Application of Hybrid Methods to Calculations of Vortex Precession in Swirling Flows

Application of DES method for swirling flows was considered. Swirling flow in a diffuser and vortex breakdown past an abrupt expansion were considered to test the application of detached eddy simulation method for swirling flows. Calculations of unsteady flows in draft tube of Kaplan turbine Holleforsen and in draft tube of high head Francis turbine were provided to investigate vortex rope precession in hydro turbine.

Direct numerical simulation of the turbulent flows of power-law fluids in a circular pipe

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.

Investigation of turbulence models for computation of swirling flows

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.

Francis-99 turbine numerical flow simulation of steady state operation using RANS and RANS/LES turbulence model

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.

Development of a High Performance Code for Hydrodynamic Calculations Using Graphics Processor Units

The paper presents the results of the implementation of computational algorithms of hydrodynamics for using graphics processor units. The implementation was carried out on the basis of the in-house CFD code SigmaFlow. Numerical simulations were based on the solution of the Navier-Stokes equations using SIMPLE-like procedure. The discretization of the differential equations was based on the control volume method on unstructured mesh. In the case of multiple CPU/GPU, parallel calculations were performed by means of domain decomposition. In the GPU-version of the code, basic computational functions were implemented as CUDA kernels to perform on GPUs. The code has been verified using several test cases. The computational efficiencies of several GPUs were compared with each other and that of modern CPUs. A modern GPU can increase the calculation performance of CFD problems by more than two times compared to a modern six-core CPU.