Steady-state Mode Research Articles

Low-pressure discharge in a trigger unit of pseudospark switch

The paper deals with the investigations of the discharge in the trigger unit of the pseudospark switch. The main attention is payed to study of the low-current auxiliary glow discharge, which is sustained in the steady-state mode before triggering, and to rearrangement of this discharge when the trigger pulse is applied to the trigger unit. The hydrogen pressure is varied through a range from 0.08 to 0.25 Torr and the auxiliary discharge current in the electrode system with hollow cathode and hollow anode is up to 40 mA. The estimates for the plasma density in the cathode cavity are provided. Under the action of the trigger pulse, the breakdown between the trigger electrodes occurs and the pulsed breakdown current is intercepted to the main cathode cavity of the switch. It is demonstrated that the process of the current interception strongly depends on the regime of sustaining the auxiliary discharge and on the fact, whether the potential electrode of the auxiliary discharge plays a role of the hollow cathode or the hollow anode.

Stressed State of a Viscoelastic Layer on the Rigid Foundation Under the Action of Concentrated Cyclic Loads

By using a generalized two-parameter model, we study main regularities of the deformation of an infinite viscoelastic layer on the rigid foundation under the action of concentrated cyclic loads. The process of transition to the steady-state conditions of deformation under periodic nonharmonic loading is simulated. The possibility of taking into account residual strains (displacements) in a layer made of the Kelvin–Voigt material and their role in the evaluation of the rate of transition into the steady-state mode are analyzed.

MATHEMATICAL MODELING OF INFLUENCE THE OPERATION MODE DIESEL ENGINE ON THE CONTENT OF PARTICULATE MATTER IN EXHAUST GASES

The work is devoted to solving an urgent scientific and practical task – establishing mathematical models that describe the effect of operating modes of diesel engines on the content in the exhaust gases of a dangerous pollutant – particulate matter (PM). The purpose of the work was to create and study the accuracy and practical suitability of the calculation method estimating concentrations and emissions with exhaust gases PM by means of mathematical modeling of the influence on them of parameters that determine steady state and unsteady diesel operation modes. The studies were carried out on the basis of the motor stand of a 4ChN12/14 autotractor diesel equipped with a partial-flow system for diluting EG with air – MKT-2 microtunnels. Measurements mass and vol-ume concentrations – cpt (g/kg) and Cpt (g/mn3), mass – PTmass (g/h) and specific – PTp (g/kWh) PM emissions was carried out by the gravimetric method with errors of ± 3 .. 10% in accordance with the requirements of regulatory documents – ISO8178 standard, UNECE Rules R-49, R-96, etc. As parameters which determine the mode of opera-tion of the diesel engine, were considered: during the study steady-state modes – the number of revolutions of the engine crankshaft (n, min-1) and the load (L,%); in the study of unsteady modes – the parameters n and L and the rate of change over time – Δn/Δt and ΔL/Δt. A dependence has been established for indirectly determining the mass concentration of PM in the exhaust gases at steady and unsteady diesel operating modes, which are charac-terized by a duration of 10 ... 30 s and ranges of vari-ation of the parameters n, L, Δn/Δt and ΔL/Δt, given in di-mensionless form: 0.4 ... 0.8, 0.3 ... 1.0, -0.2 ... 0.2 and -0.35 ... 0.35, respectively. The deviation of the calculated and experimental data when using this dependence is ± 0.005-0.006 g/kg, which is comparable with the sensitivity limit of MKT-2. Keywords: diesel, exhaust gases, particulate matter, concentration, test mode, mathematical model, accuracy.

Estimation of Moisture Content in Dielectrics Using a Four-Element Model of Capacitive Sensors

Disadvantages of existing methods for determining moisture content in insulating liquids used in laboratories of power plants are considered and revealed. A method is proposed for determining moisture content in liquid dielectrics based on the measurement of parameters of multielement two-terminal networks in steady-state and transient modes. The results of the studies as applied to transformer oils are presented.

The results of the experimental nature of the vibrations of the grid cotton cleaner

The article provides a new effective scheme and principle of operation of a multifaceted grid of cotton cleaner from small trash. The results of comparative experimental studies of the grid oscillations and the nature of loading depending on the parameters and modes of cotton cleaning are presented. In the experiments performed, the nature of the vibrations was investigated by studying the component vibrations of two grids simultaneously to compare the results. An analysis of the obtained laws of grid vibrations showed that the amplitude of the recommended multifaceted mesh surface on the elastic supports exceeds the amplitude of vibrations of the existing grid 5–7 times and reaches up to (2 ÷ 2.5) × 10−3 m. In this case, the oscillograms are presented for steady-state modes of the work of the cotton cleaner. The results show that an increase in the coefficient of the number of faces of the grid leads to a decrease in the load of the grid to (0.3 ÷ 0.5) N. The parameters of a multifaceted grid of cotton cleaner from small trash are substantiated. Experimental studies have studied the workload and the law of vibrational motion of the grid surface.

Two-degree-of-freedom vortex-induced vibrations of two square cylinders in tandem arrangement at low Reynolds numbers

Although flow past cylinders has a vast spectrum of applications in various fields of engineering, the existence of flow-induced vibrations (FIVs) add a need for a more precise and thorough approach when studying such flows. In this context, this work investigates the FIVs’ mechanism due to two square cylinders placed in tandem arrangement through a characteristics-based-split (CBS) finite element method. Both cylinders, with a low mass ratio (mr= 2), are free to oscillate in in-line and transverse directions. The center-to-center distance of 5D (D being the cylinder side width) is kept fixed between the cylinders. The Reynolds number (Re) is ranged from 40 to 200 with an increment of 40, and computations are carried out for the reduced velocity (Ur) ranging from 3 to 13 under each Re value. Results show that the effects of Re and Ur on the dynamic responses are qualitatively similar for both cylinders. However, effects on the downstream cylinder are stronger due to the upstream wake. For Re equal to or beyond 120, the in-line low-frequency characteristic becomes obvious at some higher values of Ur for the upstream cylinder, whereas it exists over a wide range of Ur for the downstream cylinder. For lower Re (up to 120), cylinders show steady behavior at Ur= 5. However, for higher Re, they vibrate with the maximum amplitudes (especially the in-line amplitude of the downstream cylinder), and show complex wake flow at the same Ur. Compared to higher Re, the maximum vibration amplitudes in the transverse direction of lower Re are relatively higher, while the opposite trend is observed for in-line vibration amplitudes. Several unstable trajectories are also identified other than the typical figure-eight trajectories. In context of vortex shedding, different permutation of steady state, 2S, P+S, and complex modes are observed for different values of Re. It is also noted that the vortex shedding pattern keeps changing in the far wake for higher Re.

MODELLING OF DYNAMIC MODES OF AN INDUCTION ELECTRIC DRIVE AT PERIODIC LOAD

Goal. Development of methods and mathematical models, based on them, for the calculation of transients and steady-state modes of induction electric drives operating in periodic load mode. Methodology. The developed algorithms are based on a mathematical model of an induction motor, which takes into account the saturation of the magnetic core and the displacement of current in the rotor bars. The processes are described by a system of nonlinear differential equations in the orthogonal axes x, y, which enables the results to be obtained with the smallest amount of calculations. The magnetization characteristics by the main magnetic flux and the leakage fluxes are used to calculate the electromagnetic parameters of the motor. To account for the current displacement in the rotor bars, the short-circuited winding is considered as a multilayer structure formed by dividing the bars in height by several elements. Results. Due to the variable load on the motor shaft, electromagnetic processes in both transient and steady state modes of the electric drive in any coordinate system are described by a system of nonlinear differential equations. The result of the calculation of the transients is obtained as a result of their integration time dependencies of coordinates (currents, electromagnetic torque, etc.) at a given law of change of the moment of loading. The proposed method of calculating steady-state mode is based on algebraization of differential equations on the mesh of nodes of the process cyclicity period and allows to obtain periodic dependencies in the time domain. Originality. The problem of calculating a steady-state periodic mode is solved as a boundary problem for a system of first-order differential equations with periodic boundary conditions, which allows to obtain instantaneous dependences during the period of currents, electromagnetic torque, capacities and other coordinates. Practical significance. Using the developed algorithm, it is possible to calculate the static characteristics of periodic processes as dependencies on different parameters of the cycle of periodic load or other coordinates, which is the basis for the choice of the motor for overload, power, heating, etc., as well as to detect the possibility of resonance.

Modelling of Dynamic Modes of An Induction Electric Drive at Periodic Load

Goal: Development of methods and mathematical models, based on them, for the calculation of transients and steady-state modes of induction electric drives operating in periodic load mode. Methodology: The developed algorithms are based on a mathematical model of an induction motor, which takes into account the saturation of the magnetic core and the displacement of current in the rotor bars. The processes are described by a system of nonlinear differential equations in the orthogonal axes x, y, which enables the results to be obtained with the smallest amount of calculations. The magnetization characteristics by the main magnetic flux and the leakage fluxes are used to calculate the electromagnetic parameters of the motor. To account for the current displacement in the rotor bars, the short-circuited winding is considered as a multilayer structure formed by dividing the bars in height by several elements. Results: Due to the variable load on the motor shaft, electromagnetic processes in both transient and steady state modes of the electric drive in any coordinate system are described by a system of nonlinear differential equations. The result of the calculation of the transients is obtained as a result of their integration time dependencies of coordinates (currents, electromagnetic torque, etc.) at a given law of change of the moment of loading. The proposed method of calculating steady-state mode is based on algebraization of differential equations on the mesh of nodes of the process cyclicity period and allows to obtain periodic dependencies in the time domain. Originality: The problem of calculating a steady-state periodic mode is solved as a boundary problem for a system of first-order differential equations with periodic boundary conditions, which allows to obtain instantaneous dependences during the period of currents, electromagnetic torque, capacities and other coordinates. Practical significance: Using the developed algorithm, it is possible to calculate the static characteristics of periodic processes as dependencies on different parameters of the cycle of periodic load or other coordinates, which is the basis for the choice of the motor for overload, power, heating, etc., as well as to detect the possibility of resonance.

Calculation of degree of coverage in fluidized bed coating

In this study, a new model for the fluidized bed coating process is presented. The model allows to predict the degree of coverage of solid particles. Analytical solutions of model equations for batch apparatus and for continuous apparatus operated in the steady-state mode were obtained. An algorithm for the numerical solution of model equations for multistage apparatus was developed. To identify the parameters of the developed mathematical model and to verify its adequacy, a physical experiment was conducted on a laboratory scale installation. A comparison of calculated and experimental data was performed. Good agreement is observed between the modeling and the measurements.

Development of a novel rotary flow control valve with an electronic actuator and a pressure compensator valve for a gas turbine engine fuel control system

This paper presents a new rotary proportional flow control valve with Cam-Nozzle configuration. The rotating cam against the fixed nozzle changes the flow area and then can meter the fuel flow. This valve equipped with a pressure compensator plunger type valve to retaining constant pressure difference across the flow control or metering valve. The cam shaft directly coupled to an electronic servomotor type rotary actuator and then it is possible to apply digital control techniques such as pulse width modulation (PWM) in this control system. This new valve configuration is developed for an electro hydro mechanical fuel control system in a gas turbine engine. In addition to aero engine application, this type of flow metering valve can widely be used in industrial hydraulic systems. In this unit, the output flow is proportional to the cam's angular position (or throttle command) and it is not sensitive to pressure fluctuations at nozzle inlet and outlet. The aim of this new design is to modify a manual single adjusted hydro-pneumatic fuel control unit to obtain a new electro-hydraulic fuel control system for a gas turbine engine. The main innovations in the presented fuel metering unit include new design of the rotary valve opening shape (Cam-Nozzle) without metal to metal contact, use of a rotary electronic actuating mechanism and also direct coupling between the actuator and the rotating cam. The increased fuel metering precision in the new flow control valve has improved the ultimate control accuracy of system. A computer simulation software based on the proposed model, is performed to predict the steady state and transient performance and to analyze effect of important design parameters on valve outlet fuel flow and obtain the final design parameters. The validity of the proposed valve configuration is assessed experimentally in the steady state and transient modes of operation. The results show good agreement between simulation and experimental in both modes (max. 4% deviation).

Calculation of the Parameters of a Two-Winding Transformer without a Magnetic Circuit

A technique for calculating the parameters of a transformer without a magnetic circuit with two cylindrical coaxial multilayer windings of the same length has been developed. Such parameters as inductance, resistance, capacitance, and temperature of windings are determined, which are used to calculate periodic voltages and currents in the steady-state power supply mode of the active load, when the primary winding of the transformer is connected to the voltage inverter. The formulas for calculating the transformer parameters, voltages, and currents, which are obtained based on the equations of electromagnetic fields and electric circuits, are programmed using the Mathcad software. The method’s reliability is confirmed by a satisfactory agreement between the calculated and the experimental values of the transformer parameters, as well as by similar calculated and experimental values of periodic voltage on the resistive load. The results obtained testify to the possibility of the efficient use of transformers without magnetic circuit with high coupling coefficient at sufficiently high frequencies, when the quality factors of the windings are high, the surface effect in the conductors of the windings is negligible and the undesirable shunting effect of parasitic capacitances in the windings is still insignificant.

Novel dependencies of currents and voltages in power system steady state mode on regulable parameters of three-phase systems symmetrization

The unbalanced mode, negative/zero sequence, variation of real power are caused by the nonlinear or unbalanced loads increase the power transmission losses in distributing power systems and also harmful to the electric devices. Reactive power compensation is considered as the common methods for overcoming asymmetry. The critical issue in reactive power compensation is the optimal calculation of compensation values that is extremely difficult in complex circuits. We proposed a novel approach to overcome these difficulties by providing the creation of new analytical connections of the steady-state mode parameters (voltages, currents) depends on the controlled parameter for the arbitrary circuits. The base of our approach to reactive power compensation is the fractional-polynomial functions. We present a new description of the behavior of voltages and currents depending on the controlled parameters of the reactive power compensation devices, and we prove its effectiveness.

OZONE DECOMPOSITION OVER ACTIVE COAL ANCHORED Cu(II), Co(II), OR Mn(II) CHLORIDES

The known catalyst based on the inorganic support, MnCl2/SiО2, and used in personal respiratory protective devices showed its lack of prospects because of the very heavy load per a protective device and the short time of its protective action. As opposed to it, metal complex compositions based on activated carbons (AC) hold much promise. Since we intended to use activated carbons or compositions based on them in respirators protection against ozone, such an important parameter as the time of protective action was determined for activated carbons of different ranks and for the best one among MCl 2 /AC compositions (M is Cu, Co, or Mn, AC is activated carbon of KAD-iodnii rank) at initial ozone concentrations, СinО 3 , of 1,5 mg/m 3 and 10 mg/m 3 . For selection of the most effective MCl 2 /KAD-iodnii AC composition, the kinetics of ozone decomposition was investigated at СinО 3 = 500 mg/m3. The results of the latter testing showed that activity of the MCl2/KAD-iodnii AC compositions depended not only on the metal and anion nature but also on a degree of the activated carbon surface filling with metal ions. The maximum degree of ozone decomposition in a steady-state mode was demonstrated by MnCl 2 /KAD-iodnii AC. This fact can be explained by MnO 2 formation as a result of MnCl 2 oxidation with ozone. MnO 2 can be a secondary catalyst and stabilize the process of ozone decomposition. The time of protective action for activated carbons significantly depends on their chemical nature and specific micropore and mesopore volumes and increases in the order SKN-K < ART < KAD-iodnii < AG-3 < SKN-2M. MnCl2 anchoring on activated carbon of KAD-iodnii rank resulted in an essential increase in the time of protective action: an ozone outlet concentration was lower than MPCO 3 even in 48 hours. The protective properties of the catalyst for ozone microconcentration decomposition obtained by activated carbon of KADiodnii rank impregnation with MnCl2 are much better than those of the known domestic and foreign analogues and this composition can be used in the devices for protecting environment and human beings against ozone.

Sensitivity of Spin Parameters to Uncertainties of the Aircraft Aerodynamic Model

Reliable prediction of aircraft poststalled dynamics is entirely dependent on the adequacy of the aerodynamic model. A mathematical model of aerodynamic characteristics of a light aircraft is developed for a wide range of angles of attack, sideslip, and angular rates. It is augmented by a model of uncertainties based on a set of repeated measurements of static aerodynamic characteristics. The effect of aerodynamic uncertainties on steady-state and oscillatory spin modes is directly calculated using a continuation on a parameter technique. The influence of aerodynamic uncertainties on spin entry/recovery is also analyzed.

Analysis of performance degradation during steady-state and load-thermal cycles of proton exchange membrane water electrolysis cells

A membrane-electrode assembly based on a 90 μm short-side-chain Aquivion® proton exchange membrane and containing low catalyst loadings, 0.4 mg IrRuOx cm−2 and 0.1 mg Pt cm−2 at anode and cathode, respectively, is investigated for combined thermal and load cycling at high current density (3 A cm−2) in water electrolysis cell. Durability tests under steady-state and load-thermal cycles are compared to evaluate the efficiency losses under specific operating conditions. Ac-impedance spectra and post-operation analyses are carried out to investigate the degradation mechanism. Catalyst degradation occurs more rapidly under cycled operation whereas mass transfer issues are relevant especially under steady-state mode. Membrane thinning appears to be affected by the uptime hours at high current density. The overall cell voltage increase is slightly larger for the cycled operation compared to the steady-state mode. However, this is essentially related to a compensation effect associated to a larger decrease of series resistance during the steady-state durability test. The dynamic electrolysis mode at high current density does not exacerbate significantly the degradation issues of low catalyst loading MEAs compared to a steady-state operation. This confirms the proper dynamic characteristics of the polymer electrolyte membrane electrolyser.

Use of DC voltage fluctuation method to investigate real-time Mode I and Mode II subcritical crack growth behavior in gypsum rock

Subcritical crack growth strongly influences the mechanical behavior of rock and the precursory phase of geohazards and catastrophic failure. In earlier studies, indirect measuring methods were used to investigate the subcritical crack growth behavior of rock materials. However, these methods cannot fully reflect the whole process of subcritical crack growth of geomaterials. Therefore, in this study, a new method (DC voltage fluctuation method) was developed which can monitor the whole process of crack growth and measure the crack growth rate in real time. This method is based on the monitoring principle of change in voltage caused by the change in resistance. Then, the whole processes of Mode I and Mode II subcritical crack growth of gypsum specimen were monitored in real time by the self-designed fracture strain gauge, which consists of 10 breakable resistance wires, and a DC voltage signal monitor. Furthermore, using the measured crack growth rates and the stress intensity factors of varying crack path lengths, the parameters of the modified Charles model were fitted. The results show that: (1) the subcritical crack growth process mainly includes three stages: cracking latent period (primary stage), steady-state crack growth stage (secondary stage), and accelerated crack growth stage (tertiary stage). The cracking latent period lasts for the largest proportion of the entire fracture process duration. The duration of each stage decreases gradually with increasing applied load. (2) In the steady-state crack growth stage, both Mode I and Mode II crack growth rates increase with increasing applied load. However, the crack growth rates in the accelerated stage are basically the same with increasing applied load. When a specimen is subjected to a given constant applied load, the subcritical crack growth rate of Mode II is higher than that of Mode I in the secondary and tertiary stages. (3) The parameters A and n of the subcritical crack growth model (modified Charles model) (secondary stage) increase with increasing external applied load. The parameters are closely associated with the size of fracture process zone at the crack tip. The results of this study can provide a deeper insight into the macroscopic failure of rock, and also provide the parameters for the time-dependent damage evolutional process of underground constructions.

Evaluation of actions efficiency of mobile combat robots by methods of mass-service theory

The article confirms that at the present stage of the development of domestic military science, the simulation of military operations is an important tool for predicting the possible results of a military conflict with the subsequent development of recommendations for its planning and management. It is determined that other mathematical methods provide ample opportunity to solve particular problems in the implementation of the principles of military art. Using various mathematical methods and electronic computer technology, it is possible to develop quantitative recommendations for making decisions in various combat situations.The possibility of using queuing systems techniques for modeling the combat operations of mobile combat robots is shown. The use of such techniques made it possible to obtain an analytical description of the final probabilities for an incompletely accessible queuing system and to expand the possibilities of taking into account the conditions for fulfilling the combat tasks of military units equipped with mobile combat robots. For this purpose, a model is described and considered that describes the battle when the firing is conducted on the observed targets and, in the event of a target hit, the fire is instantly transferred to the unaffected one. This model is illustrated by a functional diagram that clearly shows the work on the targets of five of the same type of mobile combat robots. In this case, the identification of targets is carried out by an exponential law with a function of distributing the service time of the target and the average intensity of their detection and destruction.The characteristics of the efficiency of the queuing system in a stationary (steady state) mode, that is, with an unlimitedly growing time of its operation, are determined. Two coefficients have also been introduced that will characterize the relationship between the duration of the strike phase and the time of the entire process of serving the target. Based on the research, for example, the corresponding calculations were carried out and the boundaries of the possible use of a group of mobile combat robots, consisting of five units, for the military unit were outlined. The workload of each machine and, accordingly, the efficiency of the unit as a whole are determined, recommendations are given on their quantitative composition.

On the adequacy of the frequency-symbolic method for linear parametric circuits analysis

A frequency-symbolic method (FS-method) of the analysis of steady-state mode of linear parametric circuits is intended for forming their transfer functions in the frequency domain. Transfer functions are approximated by Fourier polynomials and contain a complex variable, time variable and parameters of circuit elements in the form of symbols. The coefficients of such Fourier polynomials by the FS-method are unknown in the symbolic systems of linear algebraic equations (SSLAE), and are defined as their solutions in symbolic form. In the paper we present a method of forming an approximation expression which ensures the adequacy of calculations. Examples and results of computer experiments are given. The system of functions MAOPCs based on a frequency-symbolic method is used for the optimal design of electronic devices of noise-immune hidden radio engineering systems using code signals.

A combined mixed-s-skip sampling strategy to reduce the effect of autocorrelation on the X̄ scheme with and without measurement errors

In order to reduce the effect of autocorrelation on the monitoring scheme, a new sampling strategy is proposed to form rational subgroup samples of size n. It requires sampling to be done such that: (i) observations from two consecutive samples are merged, and (ii) some consecutive observations are skipped before sampling. This technique which is a generalized version of the mixed samples strategy is shown to yield a better reduction of the negative effect of autocorrelation when monitoring the mean of processes with and without measurement errors. For processes subjected to a combined effect of autocorrelation and measurement errors, the proposed sampling technique, together with multiple measurement strategy, yields an uniformly better zero-state run-length performance than its two main existing competitors for any autocorrelation level. However, in steady-state mode, it yields the best performance only when the monitoring process is subject to a high level of autocorrelation, for any given level of measurement errors. A real life example is used to illustrate the implementation of the proposed sampling strategy.

Results of mathematical modeling of the mud pump electric drive operation with the compensation unit in the circuit

The mathematical model was developed for the mud pump electric drive with an individual compensation unit in a bypass circuit, which allows simulating the electric drive operation during the start and in steady-state modes with and without regard to the individual compensation unit. The mathematical model of the electric drive of the mud pump was developed with the aim of increasing the reliability and continuity of the drilling rig technological process in case of failure of the frequency-controlled converter of the electric drive. The use of the electric drive parameters given in relative units in a mathematical model allows replicating the obtained simulation results for other modifications of the pump electric drive. It is proved that when an individual compensating unit is included in the electric drive circuit, it reduces the loss of active power in the cable line and overhead line, and helps to increase the efficiency of the mud pump. The simulation results showed the boundary parameters of the dependent and independent variable parameters of the distribution electric network, at which the start-up of the electric drive of the mud pump is completed successfully.