Stator Elements Research Articles

Оптимизация ступеней центробежных компрессоров

The article describes а hydraulic efficiency increase in the centrifugal compressor stage using automatic optimization algorithms. The optimization criterion is the polytropic efficiency of the intermediate compressor stage. The sequence of stages of the optimization process in the Fine/Design3D software module of the Numeca software package is presented. The creating process a solid model of the compression stage is shown. The performance curves of the developed stage after optimization of the shape of the rotor and stator elements are also presented.

Substitution of equations for evaluation of energy consumption in rotor-stator mixers

In the presented publication, an attempt to develop the theory of mixing by considering rotor-stator mixers from the standpoint of mechanical mixing devices was made.
 The results of the research on energy consumption are given in the form of analytically substituted expressions for determining power and pressure difference as well as a flow rate in a stage of rotor-stator mixer composed of a pair of the perforated rotor and stator elements with a gap between them, depending on the features of the design, dynamic characteristics of the rotor and flows. The interrelationships between power, pressure difference, and flow rate in the stages of rotor-stator mixers are established. This makes it possible to define the characteristics of mixers, carry out their calculations and reasonably accept the rational design and processing parameters. The peculiarities of the components in obtained equations are indicated. Partial cases of the equations for power consumption in stages of rotor-stator-mixers operated in pulse and impulse modes are considered. The invariant form of obtained equations would help to ease the scaling of rotor-stator mixers.

Rotary Nanomotors in the Rear View Mirror

Rotation is part of our everyday lives. For most of human history, rotation was considered a uniquely human invention, something beyond the anatomical capabilities of organisms. In 1973, Howard Berg made the audacious proposal that the common gut bacterium Escherichia coli swims by rotating helical flagellar filaments. In 1987, Paul Boyer suggested that the FoF1 ATP synthase of E. coli is also a rotary device. Now we know that rotating nanomachines evolved independently at least three times. They power a wide variety of cellular processes. Here, the study of flagellar rotation in E. coli is briefly summarized. In 2020, the Cryo-EM structure of the MotAB stator element of the bacterial flagellum was described. The structure strongly suggests that the MotAB stator rotates to drive flagellar rotation. Similar motors are coupled to other diverse processes. The following articles in this issue review the current knowledge and speculation about rotating biological nanomachines.

Оптимизация обратных направляющих аппаратов высокорасходных центробежных компрессорных ступеней CFD-методами

Calculations performed with modern computer fluid dynamics (CFD) programs aid in optimizing the flow path of a centrifugal compressor. The characteristics of the stator elements of the flow path, calculated by CFD methods, are considered to be quite accurate. Optimization of three-stage reverse-directing devices with a large flow rate (0.15) and different theoretical head coefficients (0.45; 0.60; 0.70) has been carried out. For optimizing return channels a parameterized model was created. Optimization was performed with MOGA (Multi-Objective Genetic Algorithm) optimization method in the Direct Optimization program of the ANSYS software package. The optimization goal was to achieve the minimum loss factor at the design point. In the optimization process, the following parameters were varied: the number of and the inlet angle of the vanes, the height of the vanes at the inlet, external and internal radii of curvature of the U-bend. For the return channel with a minimum loss coefficient, the dependences of this parameter on the flow coefficient were calculated. Comparison with the characteristics of the initial variant showed that the optimized return channels are more efficient over the entire flow range. Optimization allowed reducing the loss factor by 20%.

Features of modeling the system of turbine unit with a variable contact zone of its stator parts

Modeling of stator parts of power units of thermal and nuclear power plants is carried out according to several standard schemes. Common methods of modeling systems with non-uniform and non-stationary contact of stator elements lead to significant errors in calculating the amplitudes of forced vibration displacement at a given external load. The object of this paper is to analyze errors in calculating the displacement amplitudes of forced oscillations in different modeling schemes according to the standard approach and developing a method for constructing a quasi-dynamic model taking into account the time-varying contact of the system’s stator parts as well as other factors. To do this, the author has developed a series of models with different degrees of sampling and considering different system factors. Particular attention is paid to the impact of factors arising from the long operation of the power plant (subsidence of foundation). The modeling was carried out taking into account the calculation method. The finite element method was used to perform calculations. The results of the calculation of forced oscillation displacement amplitudes are available to show the areas of application of different types of three-dimensional models of the steam power unit. The results of research conducted on the developed models show the impossibility of using standard simulation schemes for systems with a variable contact between its stator elements, as shown by the example of a power unit with steam turbine. The efficiency of using the models taking into account the variable contact between the stator parts and other factors to calculate the displacement amplitudes of the forced oscillations with high accuracy is likewise presented. Every specialist should be aware of the factors that influence the research results. This paper is concerned with assessment of the influence of a number of factors on the results of calculating the vibrations of a complex mechanical system.

Numerical simulation and optimization of centrifugal compressor return channels: methods and results

The authors actively use their engineering Universal Modelling Method for gas-dynamic design of centrifugal compressors for industrial partners. Currently, there are two approaches to improving the Method: improving the preliminary design and increasing the accuracy of gas-dynamic characteristics calculation. Computational Fluid Dynamics (CFD) methods give good results for the flow path stator part. Recently, massive CFD calculations of the vaneless diffusers (VLD) characteristics were generalized by a system of algebraic equations, which replaced the previous more complex mathematical model in the Method. Then, based on CFD optimization of a large series of return channels (RCh), corrections were made to the preliminary design of this element of the flow path.This paper presents the results of the joint CFD optimization of a vaneless diffuser and a return channel. Stator elements have many geometric parameters. For a stage with the flow rate coefficient of 0.0597 and the loading factor of 0.60, only the VLD relative radial length D 4/D 2, the number and the inlet angle of the return channel vanes were optimized. Engineering calculations and design experience predicted an optimal value of D 4/D2 within the interval 1.9 - 2.0. CFD optimization demonstrated almost linear reduction of the total head loss towards the end of the investigated range D 4/D2 = 2.3. After careful optimization of the U-bend, the optimization of D 4/D2 was repeated. The influence of on the loss coefficient has decreased, but the value of D 4/D 2 = 2.3 is still far from optimum. It significantly exceeds technically acceptable radial size. The result obtained influenced the design plan of future calculation experiments with a large series of stator elements of the stages in a practically significant range of design parameters.

Optimal Control of the Positional Electric Drive and Its Implementation

The article deals with the optimal control of the positional electric drive of the stator element of a segment-type wind turbine. The calculation options charts current in the assumption of the minimum energy consumption and the implementation of line chart current using the phenomenon of capacitor discharge. The analysis of the implementation is expressed in a jump-like change in current and a triangular graph of the speed change. This article deals with small capacity synchronous wind turbine generators with a segment type stator. These units have the possibility of intentionally changing the air gap between the rotor and stator. This allows: (1) Reduce the starting torque on the rotor shaft, which will allow the rotor to pick up at low wind speeds. (2) Equivalent to change of air gap in this case is change of excitation of synchronous generators. Thus, the purpose of the article is to consider a method of excitation of generators in a segmented design, by controlling the gap with the electric drive, while providing control should be carried out with minimal losses.

Axial forces in multistage back-to-back pumps

Since the pressure of the pumps for the oil and gas industry and feed water pumps for the thermal and nuclear power plants are increasing and at the same time the production costs need to be reduced, the demands for development of the modern multistage centrifugal pumps are increased. An enlargement of stage numbers results in an increase in the distance between the bearings and as a result the shaft deflection increases. Also, a large number of stages leads to occurrence of a significant axial force acting on the pump rotor. These issues are solved by applying a back-to-back design with a throttling bush between the groups of stages. An arrangement with such throttling bush results in an additional axial force due to the different directions of leakage in the channels (side wall gaps) between the main disks of the last impellers of both stage groups and stator elements. Therefore, the design of a throttling bush with special balancing holes was proposed. This paper examines the processes occurring in the throttling bush and compares the operating parameters for two design options-with special balancing holes, and without them.

The Problem of Accounting for Heat Exchange between the Flow and the Flow Part Surfaces When Modeling a Viscous Flow in Low-Flow Stages of a Centrifugal Compressor

In this paper, we review the problem of accounting for heat exchange between the flow and the flow part surfaces when creating a calculation model for modeling the workflow process of low-flow stages of a centrifugal compressor using computational fluid dynamics (CFD). The objective selected for this study was a low-flow intermediate type stage with the conditional flow coefficient Փ = 0.008 and the relative width at the impeller exit b2/D2 = 0.0133. We show that, in the case of modeling with widespread adiabatic wall simplification, the calculated temperature in the gaps between the impeller and the stator elements is significantly overestimated. Modeling of the working process in the flow part was carried out with a coupled heat exchanger, as well as with simplified accounting for heat transfer by setting the temperatures of the walls. The gas-dynamic characteristics of the stage were compared with the experimental data, the heat transfer influence on the disks friction coefficient was estimated, and the temperature distributions in the gaps between disks and in the flow part of the stage were analyzed. It is shown that the main principle when modeling the flow in low-flow stage is to ensure correct temperature distribution in the gaps.

Optimization of Return Channels of High Flow Rate Centrifugal Compressor Stages Using CFD Methods

Calculations performed with modern CFD programs aid in optimizing flow paths of centrifugal compressors. Characteristics of stator elements of flow paths, calculated via CFD methods, are considered quite accurate. We present optimized return channels (RCh) of three model industrial compressor stages with vaneless diffusers. A parameterized model was created for optimization. The MOGA (Multi-Objective Genetic Algorithm) optimization method was applied in the Direct Optimization program of the ANSYS (Analysis System) software package. Optimization objects were return channels of the stages with high flow rate 0.15. The stages have three different loading factors 0.45, 0.60, 0.70. The optimization goal was to achieve the minimum loss coefficient at the design point. During the optimization process, we varied the following: the number of vanes, the inlet angle of the vanes, the height of the vanes at the inlet, the outer and inner radii of curvature of the U-bend. The outlet angle of the vanes was selected to minimize outlet circumferential velocity. In comparison with preliminary design, the optimized RCh are more efficient across the entire range of flow rates. The optimization reduced the loss coefficient by 20% at the design flow rate.

Investigation of a Rotor Speed Controlling of a Promising Wind-Driven Power Plant Using Several Variable Elements of its Geometry

Variants of the rotation frequency stabilization of a promising vertically axial wind-driven power plant consisting of a doubly connected stator and a rotor with blades are considered. The stator as a whole is part of the construction, axisymmetric with the rotor, and the rotor is slightly buried in the upper part of the stator — the bell. This plant can be included as an element in a complex power plant for additional and emergency power supply of both stationary and mobile objects, for example, surface robotic systems. The paper proposes to use an aerodynamic method of the rotor angular speed stabilization by controlling the positions of two variable design elements of the plant with respect to its stator. As such elements, a lower guide structure (one of the stator elements) and an aerodynamic brake flap can be used. The rearrangement of both elements positions relative to the stator changes the effective cross section for the interaction of the wind flow entering the installation with the rotor. The method of controller synthesis by the angular speed of the rotor rotation is considered in detail. A feature of this controller is the presence of two control channels with one state variable. First, it is necessary to determine the dynamic ranges of torque control on the rotor shaft for each of the variable geometry elements. This allows to correctly select the switching condition between the two control channels depending on the degree of deviation of the desired flow rate from the current speed. Based on the second-order control error equation, the desired control law of the angular rotor speed is obtained. Using the example of the problem solving of angular speed stabilization with given quality criteria, we simulated a synthesized control system for various initial data. It is shown that the constructed controller is capable of effectively countering the influence of wind disturbances in a wide range of deviations of the current speed from the frequency desired for a given target value.

Development of a mathematical model of an autonomous power supply source with a free piston motor on the basis of a synchronous electric returning machine with a permanent magnets

One of the current trends at present is the development of small energy, which is a particularly urgent task for the Russian Federation with its vast territories and the specifics of the electric power system. In the Russian Federation, the bulk of the electricity is generated at large power plants and transmitted through power lines. 60–70% of the country's territory lacks a centralized power supply, where more than 20 million people live, and the development of small and micro-energy facilities is necessary. Using a synchronous electric reciprocating machine with permanent magnets in power plants of a modular type makes it possible to rationally design an autonomous power supply source, to obtain the most optimal design. The development of methodological design decisions and the optimization of engine design parameters as part of generating and drive complexes is an important scientific task. A mathematical description of thermodynamic processes in a free-piston internal combustion engine, electromechanical and thermal processes occurring in a synchronous electric reciprocating machine with permanent magnets is developed, which is a necessary condition for designing and optimizing the design of an autonomous electric power complex. According to theoretical calculations, in the Matlab application, on the basis of the additional Simulink module, a simulation model of a free-piston internal combustion engine, linear current load calculation units, stator magnetic induction, magnetic induction created by permanent inductor magnets, electromagnetic force were developed and calculated. The created procedure for calculating the parameters of the electromagnetic component of the force of a synchronous machine with permanent magnets allows you to calculate and optimize the design parameters of the inductor and stator element of the electric motor under consideration. Thus, this will allow us to design electric machines with improved energy characteristics, due to the use of the obtained simulation results, which will allow us to use them more efficiently in the composition of generating and drive complexes.

Turbine Generator Rotor Vibrations with Rubbing in the Span and Supports

The article presents an algorithm for and results from studying the motion of a rotor involving its simultaneous rubbing against the stator elements in the turbine set span and supports. The aim of the study was to develop the mathematical model describing vibration of the rotor resting in a few supports and to select the main assumptions regarding the contact interaction between the rotor and stator that will make it possible to model a real vibrational process that involves rubbing. An abrupt loss of balancing in the rotor’s second span section at the angular rotation speed is taken as the initial disturbance upsetting the turbine set’s normal operation. The case of a constant rotor rotation speed with loss of balancing followed by development of contact interaction between the rotor and stator elements is considered. This scenario seems to be the most plausible because the interaction persists for a short period of time during which the safety system still remains silent in producing the command to disconnect the steam supply to the turbine, and the torque on its shaft remains constant. It is shown that with the adopted clearances in the turbine set span and supports, with the loss of balancing corresponding to detachment of the mass of one turbine blade, and with increased damping in the supports, the rotor motion is accompanied by rubbing in the turbine set supports and span. If the damping coefficient in the supports does not exceed the value of this parameter in the plain bearing oil film, asynchronous reverse whirl of the rotor develops, which is characterized by self-excited vibration caused by the effect of contact interaction forces between the rotor and stator. Owing to consideration of the rotor design features, its frequency characteristics, including the change in the frequency characteristics of the rotor–supports system due to additional reactions arising at the moments in which the rotor comes into contact with the stator, it becomes possible to model the vibration development process not only during strong (when whirl is excited) but also during weak (possible excitation of low-frequency vibration) interactions between the rotor and stator and to analyze the influence of detuning from resonances and other factors on the development of self-excitation processes in systems closer to real ones.

Evolution of the Stator Elements of Rotary Prokaryote Motors.

The bacterial flagellar motor is driven by an ion flux that is converted to torque by motor-attendant complexes known as stators. The dynamics of stator assembly around the motor in response to external stimuli have been the subject of much recent research, but less is known about the evolutionary origins of stator complexes and how they select for specific ions. Here, we review the latest structural and biochemical data for the stator complexes and compare these with other ion transporters and microbial motors to examine possible evolutionary origins of the stator complex.

Stator elements optimization of centrifugal compressor intermediate type stage by CFD methods

Optimal gas-dynamic design is a complex and time-consuming process. Modern CFD methods help in solving optimization problems and reliably calculating characteristics of stator elements of centrifugal compressor stages. To carry out such calculations, it is necessary to create a parametrized model, which facilitates automation of the process of changing the flow path geometry, rebuilding its dimensions and the computational grid. Using the Direct Optimization program of the ANSYS software package, we have optimized the flow path of the stator elements of a centrifugal compressor intermediate type stage consisting of a vaneless diffuser and a return channel. In this paper, the MOGA (Multi-Objective Genetic Algorithm) optimization method was used. The object of the study was stator elements of one of the model stages designed by the Problem Laboratory of Compressor Engineering, SPbPU. The goal was to achieve the minimum value of the loss coefficient of stator elements when changing 5 geometric parameters: the number of vanes, the inlet vane angle, the height of the vane at the inlet to the return channel vane cascade, the radius of curvature of the leading edge and the thickness of the vane profile. For the best variants based on the results of optimization, the characteristics of the loss coefficient depending on the flow rate coefficient were calculated, their characteristics were compared with the initial variant of the stator elements. The best variant in the design mode has a loss coefficient 4.4% lower than the reference model. With a flow rate coefficient of 1.63 times greater than the calculated one, the optimized variant’s loss coefficient is 33% less.

Experience of designing a low-pressing turbocharger compressor using the modern version of a Universal modelling method

The paper presents the joint experience of the NPO “Turbotekhnika” and the R&D Laboratory “Gas Dynamics of Turbomachines” of SPbPU for designing a centrifugal compressor operating at pressure ratio 1.61 and a mass flow rate of 0.62 kg/s. The design was executed using the Universal modelling method and the inviscid quasi-three-dimensional calculation program 3DM.023. At the first step, by the preliminary design program, the stage dimensions were determined. The expected gas-dynamic characteristics are calculated. At the final design step, stator elements were offered by NPO “Turbotekhnika” and the configuration of the impeller blades was optimized based on the non-viscous quasi-three-dimensional calculations. NPO “Turbotekhnika” designed, manufactured and tested the 140E compressor at blade velocities 150, 200, 250 and 300 m/s. A comparison and analysis of experimental and calculated characteristics is presented. The design pressure ratio was calculated almost exactly for the design flow rate at a blade velocity of 300 m/s. The expected efficiency was confirmed. The mathematical model slightly overestimates the efficiency and the pressure ratio for the off-design flow rates.

Vibroacoustic monitoring and troubleshooting of the stators of turbogenerators

The essence of resource-saving technology of turbogenerators operation is to reduce the intensity of vibro-impact processes in defective mounting attachment up to their full blocking by changing the operating parameters of the generator, which do not affect the output of active power. The results on the example of 8 turbogenerators of thermal power plant are shown. It can be seen that the power of vibro-impact processes, and, therefore, the intensity of wear of the stator elements can be significantly reduced in most of the turbogenerators of this station.

A Simple and Efficient Quasi-3D Magnetic Equivalent Circuit for Surface Axial Flux Permanent Magnet Synchronous Machines

This paper presents a simple and efficient magnetic equivalent circuit (MEC) model for surface axial flux permanent magnet synchronous machines. The MEC model is used to solve all the electromagnetic properties of the machine including the no load, full load voltages, cogging torque, torque ripple, and stator iron core losses. Moreover, this approach can be extended for all surface permanent magnet synchronous machines. The main novelty of this approach is the development of a static system, which accounts for the rotation. The model takes into account the rotor rotation via time-dependent permanent magnet magnetization sources. The static system matrix facilitates a very fast solving. In addition, to take into account the three-dimensional (3-D) effect, a multislicing of the machine in the radial direction is done. This boosts the simulation time to only 60 s for six slices and 50 time steps including the nonlinear behavior of the stator elements with a great accuracy. Additionally, the number of elements in the MEC can be adjusted to reduce the computational time. This model is verified by means of 3-D and two-dimensional (2-D) multislice finite-element models. In addition, experimental validations are also provided at the end.

BUS BAR DAMPING IS A WAY OF INCREASING THE VIBRATION RELIABILITY OF TURBOGENERATOR STATORS

Abstract: The work is devoted to the consideration of the bus bar ring damping of turbogenerator stators. The urgency of the problem of ensuring the vibrational reliability of high-power turbogenerator stators is shown. On the model problem, a series of computational studies on the effect of damping properties of materials on the amplitude-frequency characteristics of the stator buses of turbogenerators was carried out. Based on the results of the computational studies, a bus bar design is proposed, comprising a layer of a vibration-absorbing material. The use of a vibration-absorbing polymeric material in bus bar ring can reduce the amplitude of oscillations up to two times and, accordingly, significantly improve the vibration reliability of the stator elements of the turbogenerator. The results of the research are protected by a patent.

About the Inexpediency of Widely Using Honeycomb Seals in Steam Turbine Flow Paths

The article presents the results from an incisive analysis of using end and internal honeycomb seals (HS) in two T-60/73-7.8/0.04 steam turbines produced by the Kaluga Turbine Works (in Russian, KTZ) intended for being used at the Ufa TETs-5 combined heat and power plant. The honeycomb seals were installed in the flow path of these turbines on the customer’s request and have been applied at KTZ for the first time. Expectedly, the use of HSs could decrease parasitic steam leaks, thereby resulting in improvement of the turbine efficiency. According to assessments made by the ARMS research and production enterprise and expectations of KTZ specialists, the replacement of conventionally designed labyrinth seals by seals with honeycomb inserts would make it possible to increase the turbine efficiency by approximately 1% due to essentially narrower radial gaps in the end, diaphragm, and shroud seals. Experimental investigations of HSs during their operation under model test bench conditions have shown that parasitic leaks of working fluid may indeed be reduced using these seals. However, this is only possible for a narrow range of optimal ratios between the physical design parameters of the seal honeycomb structure and the gap between the stator and rotor elements. The ideas of applying HSs in steam turbines were borrowed from the experience gained from operation of gas turbine engines. In steam turbines whose supports are made with plain bearings, the rotor rotates over an intricate trajectory with respect to the steam turbine casing longitudinal axis. With vibration that takes place under steam turbine real operating conditions, the use of HSs is not expedient, at least in turbines with a flexible shaft. It is shown, taking a particular example, that the narrow gaps (0.15–0.30 mm) between the steam turbine stator and rotor elements as recommended by the HS manufacturers, with which the useful effect from application of HSs manifests itself, cannot be implemented under field conditions. Such statement stems from the results of acceptance tests of two T‑60/73-7.8/0.04 steam turbines produced by KTZ that were carried out at the factory’s test bench. It has been found after opening the turbine and examining its parts after the thermal tests on the bench that all HSs made with narrow radial gaps were destructed. The commissioning team involving the customer’s representatives has recognized that further operation of the steam turbines with such seals is impossible. A decision was made at KTZ to fit the steam turbines with new seals with increased radial gaps. Had the turbines not been opened at the factory, the destructions of their HSs would have been revealed in the course of steam turbine overhaul after 6 years of their operation.