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Research subject. Deformations and stress state of rock masses at subsoil use objects.Materials and research methods. Extensive experimental data about the relative deformation of matter and, in particular, about the deformation of rock masses (earth’s crust) allowed the authors to find a solution to this problem using the very behavior of the rock mass during its response to technogenic activity.Results. Novel results were obtained on the relative deformation of matter under the conditions of changing external factors: 1) deformation of rock mass itself; 2) deformation of a surveying tape as a measuring instrument, 3) deformation of a quartz tube in a deformometer as a measuring instrument. Using the results of measurements over the 11-year nanocycle of solar activity available to us, regularities in the emergence of deformations and stresses of rock masses were revealed. A justification was obtained for changing the physical state of measuring instruments based on electromagnetic waves: satellite navigation systems, light and radio range finders. At the same time, it was found that all these parameters change in time continuously and endlessly, thereby requiring constant monitoring for making a reliable forecast of their impact on technogenic activity.Conclusion. The results presented in the article extend previous publications of the authors, the main conclusions of which are as follows. 1. The results about the deformations of rock masses, which are currently being obtained by methods based on various physical principles, are relative; therefore, these results do not allow one to judge about their absolute values. 2. The international community of scientists should develop a mechanism for tracking changes in the deformations and stress state of rock masses.

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.

In the presented studies, the laws of the formation of natural stresses in the rock mass are confirmed, which are the sum of gravitational, static tectonic and variable components that have a variable value as a result of uniform periodic volume expansion and contraction of the Earth. The problem of trunk stability is due to the need to solve problems to determine the level of stress-strain state and strength properties in concrete supports. The stress parameters in the lining of the shafts and the monitoring of their changes are determined using a new method for measuring unloading strains. When comparing the stresses obtained experimentally by analytical methods in the concrete support of mine shafts from 2013 to 2019 at experimental test sites in the support having the lengths of bases of 1600 and 70 mm, provided that the number of geoblock ranks at this base is two, a connection with the results of measurements in an array of rocks based on 50 m with an average size of structural blocks of 0.5 m and an investment coefficient of l = 5, which corresponds to three ranks of geoblocks. In practice, it is proposed to use the main identified provisions, namely: the stress state of the mine shaft lining, which is formed as a function of their structural parameters, the full tensor of gravitational tectonic stresses acting in the rock mass at the time of the start of research and time variables, which are determined by natural and analytical methods.

When summarizing the results obtained on the stability of rock masses a discrepancy was found between the parameters of the strength properties of rock formations, determined according to existing methods and state standards, to their values under natural conditions. As a result of the studies, the degree of geomechanical knowledge of the rock mass of the Gaisky underground mine is significantly increased. Based on the numerical simulation of the stress-strain state of the ore and rock mass, the rationale for the optimal mining of reserves at a depth of -830 / -1390 m was substantiated. The main compressive stresses of the Gaisky deposit act in the sub-latitudinal direction along the axis of the chambers, creating stresses exceeding 100 MPa on their outcrops. If the compressive strength of the massif is up to 100 MPa, found by known methods, ore masses of the third stage (pillars) below the -910 m horizon should be destroyed. In assessing the stability of pillars (chamber walls) in the last 3 years, in some cases, disagreement arose. The calculated stresses exceed the maximum allowable ones, but the pillars (chamber walls) remain stable. It justifies the correction of the obtained values of the ultimate strength of rocks with correction factors and the introduction of the definition of reduced strength (227 MPa), in which the roof, walls of the chambers and pillars are in a stable state. As a result of the study, the obtained values of the stress state of the rock mass and its strength characteristics more realistically reflect the predicted destruction or stability of the rock mass at the mine. The performed studies contribute to a more justified adjustment of mining technology parameters while ensuring the safety of mining operations.

The authors have performed numerical simulation of pressure pulsations in the draft tube of a hydraulic turbine that are excited by large-scale vortex structures. Numerical simulation of unsteady transfer in the draft tube in different operating regimes of the turbine has been carried out. It has been shown that the structure of flow in the outlet diffuser corresponds to vortex-core flow. Calculated data have been compared with experimental results and their agreement has been shown. To suppress pressure pulsations, a study has been made of the influence of various structural inserts into the draft tube, such as fins, a cross piece, and a hollow cylinder in the draft-tube cone. Consideration has been given to the influence of various constructions on the structure of flow behind the wheel and on pressure pulsations on the draft-tube wall. A comparison has been made of the constructions and optimum parameters have been selected to stabilize the flow in the diffuser of the hydraulic-turbine draft tube.

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.

We investigated changes in the temperature regime of post-fire and post-technogenic cryogenic soils of Central Siberia using remote sensing data and results of numerical simulation. We have selected the time series of satellite data for two variants of plots with disturbed vegetation and on-ground cover: natural ecosystems of post-fire plots and post-technogenic plots with reclamation as well as dumps without reclamation. Surface thermal anomalies and temperature in soil horizons were evaluated from remote data and numerical simulation and compared with summarized experimental data. We estimated the influence of soil profile disturbances on the temperature anomalies forming on the surface and in soil horizons based on the results of heat transfer modeling in the soil profile. According to remote sensing data, within 20 years, the thermal insulation properties of the vegetation cover restore in the post-fire areas, and the relative temperature anomaly reaches the level of background values. In post-technogenic plots, conditions are more “contrast” comparing to the background, and the process of the thermal regime restoration takes a longer time (&gt, 60 years). Forming “neo-technogenic ecosystems” are distinct in special thermal regimes of soils that differ from the background ones both in reclamated and in non-reclamated plots. An assumption was made of the changes in the moisture content regime as the main factor causing the long-term existence of thermal anomalies in the upper soil horizons of disturbed plots. In addition, we discussed the formation of transition zones (“ecotones”) along the periphery of the disturbed plots due to horizontal heat transfer.

The article presents results of numerical and experimental investigation of cavitation flow around two subscale models of guide vanes of hydroturbines, one of which has a simplified geometry, while the other has an approximately real geometry. The emphasis was on studying the fluid flow through the gap between the end surface of the hydrofoil and the channel wall, and also on the onset and development of gap cavitation. In the study we used high-speed imaging to analyze the spatial structure and dynamics of cavities. The two-dimensional flow velocity distributions above the hydrofoil surface were measured by the PIV method. In the numerical simulation of cavitation flows around the vanes we used computational fluid dynamics methods based on the solution of Reynolds equations for turbulent flows by means of the finite volume method on a three-dimensional grid of hexahedral cells. The vapor phase was accounted for by solving the equation of transport of vapor fraction. Turbulence was described by the DES method based on a two-parameter model, k-ω SST. As a result, we compared the calculated profiles of flow velocity in the boundary layer on the low-pressure side of the vane with the measurement results; they were in good agreement. In the experiment and in the numerical simulation cavitating vortex structures were observed along with gap cavitation as a vapor film while the fluid was flowing through a narrow gap. At a small angle of attack the vapor film in the gap forms in the vicinity of the trailing edge of the hydrofoil, and immediately behind its leading edge at large angles of attack. In unsteady flow regimes the gap cavitation dynamics substantially depends of the phase of development of the main cavity on the low-pressure side of the vane decompression.

The stress state in the structural elements of development systems is formed as a function of the design parameters of mine workings, the full stress tensor, which includes gravitational-tectonic and time-varying stresses acting in the rock mass at the time of the start of research, taking into account the physical and mechanical properties of the rock massif, modulus of elasticity and additional stresses caused by a subsequent change in the stress field, caused outside the zone of influence of mining by a cyclical change in natural stresses, and in the zone of influence of the mined-out space - by a change in the secondary stress field. An assessment was made of the possibility of self-collapse of overlying rock masses near the workings of block No. 10, No. 20, No. 11, MBTs10-20, No. 21 in the conditions of its undermining by underground mining of horizons 540 m and 480 m of the Sideritovaya mine, and recommendations were developed to ensure production safety works. On the basis of mining and technical documentation of the mine, field and laboratory measurements, an analysis of the mining and geological conditions of development of the investigated deposits, an analysis of the natural stresses of the deposit was carried out, the physical and mechanical properties of rocks were studied, the calculation of the stress-strain state of the rock mass at operation of the Sideritovaya mine near the mine workings of blocks No. 10, No. 20, No. 11, MBTs10-20. An assessment was made of the current state of the stress state at the field, as well as the associated components of the natural environment, and the compliance of this state with the requirements of norms, standards and conditions for the extraction of minerals. The current, operational forecast of changes in the stress-strain state in the field and in the zone of significant influence of its development has been compiled. The presented results of the studies, which significantly increase the degree of geomechanical study of the rock massif of the Bakalskoe deposit. The main purpose of the research was to determine the parameters of the initial stresses acting in the rock mass.

The paper presents a numerical study of the free discharge of water through the turbine with a braked runner. The simulation was carried out for a unit of a full-scale Francis turbine. The finite volume method was employed for unstructured meshes using the DES method. The simulation results show the flow structures, integral characteristics, and pressure pulsations in the flow path. The analysis of the applicability of this approach to real conditions is carried out.

The paper presents a study of the instability of the precessing vortex core in the model of the draft tube of a hydraulic turbine. The study was carried out using numerical modeling using various approaches: URANS, RSM, LES. The best agreement with the experimental data was shown by the RSM and LES methods with the modelling of the runner rotation by the sliding mesh method. In the regime under consideration, the precessing vortex rope is subject to instability, which leads to reconnection of its turns and the formation of an isolated vortex ring. Reconnection of the vortex core leads to aperiodic and intense pressure fluctuations recorded on the diffuser wall.

The stress state of the concrete walling of mine shafts is formed as a function of the structural parameters of the shaft, the total stress tensor, which includes gravitational-tectonic and time-varying stresses acting in the rock mass at the baseline, taking into account the physical and mechanical properties of the rock mass, the elastic modulus of concrete, which depends on the rate of advance and additional stresses caused by a subsequent change in the stress field, determined outside the zone of influence of mining by a cyclic change in natural stresses, and in the zone of influence of the mined-out space - by a change in the secondary stress field. The paper has presented the results of the research, which significantly increase the degree of geomechanical study of the Gaiskoye deposit’s rock mass. The main purpose of the research was to determine the parameters of the initial stresses acting in the concrete walling of the shafts at different depths. The parameters of stresses acting in the shaft walling at deep mine horizons were determined under field conditions, and the stress-deformed state of the shaft walling at various horizons was monitored throughout the depth of the shaft in the period 2013 - 2020.

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.

The results of computational studies of the effect devolatilization models in the processes of ignition and combustion of pulverized coal in the swirling flow at the shooting bench with capacity 2.4 MW. Consider a few devolatilization models in a one and a two-stage approach, as well as models based on the structural features of the structure of the coal substance. For the numerical simulation of turbulent flow of an incompressible fluid used Reynolds equation based on the interfacial interactions. To close the Reynolds equations used a standard two-parameter model of turbulence k–e. To solve the equation of heat radiation used P1 approximation of the method of spherical harmonics. To describe the optical properties of the gas model was used the sum of gray gases. To describe the processes of the movement of coal particles used the method of Lagrange. Burning char based on diffusion – kinetic approach. Comparative analysis of the results of mathematical modeling with experimental data showed that when choosing the correct values of the effective kinetic constants and parameters characterizing the structure of the carbon material, a model release volatiles are consistent with each other and with the experimental data on the distribution of temperature and composition of gases in the combustion chamber.

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.

Anumerical procedure is presented for analysis of pressure pulsations in hydraulic turbines. Results of its use for description of unsteady turbulent flow in the continuous run of a hydraulic turbine are presented. The numerical method is adapted for results of modeling of turbulent unsteady flow in the continuous rune of a high-head HPP. The structure of the flow beyond the impeller and its effect on the intensity of unsteady processes are examined. Results of the analysis are compared with full-scale data. Good agreement is obtained between the computed and experimental results.

The paper presents results of numerical simulation of unsteady three-dimensional flow in the two high-head hydraulic turbines. The numerical technique for calculating of low-frequency pressure pulsations in a hydraulic turbine is based on the DES turbulence model and the approach of rotated reference frame. The paper also presents the analysis of the flow structure behind the runner of the turbines, as well as shows the effect of the flow structure on the frequency and intensity of non-stationary processes in the turbines. Besides, the behavior of the pulsations in the hydraulic turbines was defined. Comparison of the calculation results with the experimental data has shown close agreement between theory and experiment.

Numerical technique for calculating pressure pulsations in the high-head hydro turbines is presented in the paper. The numerical technique is based on the use of DES turbulence model and the approach of “frozen rotor”. This technique is applied for simulating unsteady turbulent flow in a flow path of a high head hydropower plant. The flow structure downstream the runner and its influence on the intensity of non-stationary processes is analyzed. It is shown that the low-frequency pressure pulsations in water turbines are mainly caused by the precessing vortex rope downstream the runner. The vortex dynamics basically determines the pulsational characteristics of turbine operation. It is found that the averaged velocity components of flow downstream the runner can serve as indicators, which characterize the intensity of transient phenomena in the draft tube of water turbine. The comparison of simulation results with the experimental data shows reasonable agreement in the integral characteristics (efficiency, flow rate, power) as well as pulsational characteristics (intensity and frequency) of the flow and turbine operation.

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.

An adaptation of the mathematical model for the investigation of the parameters of orthogonal wind turbine has been performed. The simulation of Darrieus H-type rotor operating modes was performed and compared with experimental data. A kinematic scheme with dynamic blades was used for optimal tip-speed ratio. The results of numerical simulation with different deflection angles at fixed tip-speed ratio 1.6 showed that maximum rotor efficiency is reached for a blade pitch angle equal to 8 degrees. One can see that the use of the kinematic scheme, which allows changing the pitch angle of blades, leads to an increase in the efficiency of the rotor in the range from 12 to 50% (depending on the tip-speed ratio).

The paper deals with the numerical simulation of the flow in the Francis-99 hydraulic turbine at three different problem formulations, namely, the application of the method of rotating coordinate system, sliding mesh model, and consideration of a compressible fluid. The pulsations intensity and pressure pulsation spectra obtained by numerical simulation and experimentally are compared. It is shown that the simulation of a problem considering compressible fluid, and that conducted by the sliding mesh method gives significantly greater pressure amplitudes. It is also shown that the precessing vortex core is a source of pressure waves in the entire turbine flow path.

This paper is devoted to investigation of the swirl flows. Such flows are widely used in various industrial processes. Swirl flows can be accompanied by time-dependent effects, for example, precession of the vortex core. In turn, the large-scale fluctuations due to the precession of the vortex can cause damage of structures and reduce of equipment reliability. Thus, for engineering calculations approaches that sufficiently well described such flows are required. This paper presents the technique of swirl flows calculation, tested for CFD packages Fluent and SigmaFlow. A numerical simulation of several swirl flow test problems was carried out. Obtained results are compared with each other and with the experimental data.

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.

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.

A new hybrid method is proposed for solving the problems of fluid dynamics and heat transfer in complex hydraulic systems. The peculiarity of the method consists in the idea that some elements of the model are represented as network elements, where the solving of the flow distribution problem is carried out on the basis of the hydraulic circuit theory, whereas the flow in the remaining elements is calculated by the spatial methods of computational fluid dynamics (CFD). The results are presented of testing the proposed hybrid method for the problems of fluid dynamics and heat transfer in microchannels. The test calculations demonstrate high efficiency of the 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 startup regimes. Numerical technique for calculating of low frequency pressure pulsations in a water turbine is based on the use of DES (k-ω Shear Stress Transport) turbulence model and the approach of "frozen rotor". The structure of the flow behind the runner of turbine was analysed. Shows the effect of flow structure on the frequency and intensity of non-stationary processes in the flow path. Two version of the inlet boundary conditions were considered. The first one corresponded measured time dependence of the discharge. Comparison of the calculation results with the experimental data shows the considerable delay of the discharge in this calculation. Second version corresponded linear approximation of time dependence of the discharge. This calculation shows good agreement with experimental results.

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.

The paper presents the numerical simulation method of three-dimensional turbulent flows in the hydraulic turbine. This technique was verified by means of experimental data obtained on a water model of the Francis turbines. An aerodynamic stand, which is a miniature copy of the real hydraulic turbine, was designed. A series of experiments have been carried out on this stand and the corresponding calculations were performed. The dependence of the velocity and pressure pulsations profiles for different operation regimes are presented.

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.

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.