Search results for: Integral differential equations

Authors: Dinara F. Gaynutdinova, Vladimir Ya Modorsky, Nikolay A. Shevelev

Abstract:

The problem under research is that of unpredictable modes occurring in two-stage centrifugal hydraulic pump as a result of hydraulic processes caused by vibrations of structural components. Numerical, analytical and experimental approaches are considered. A hypothesis was developed that the problem of unpredictable pressure decrease at the second stage of centrifugal pumps is caused by cavitation effects occurring upon vibration. The problem has been studied experimentally and theoretically as of today. The theoretical study was conducted numerically and analytically. Hydroelastic processes in dynamic “liquid – deformed structure” system were numerically modelled and analysed. Using ANSYS CFX program engineering analysis complex and computing capacity of a supercomputer the cavitation parameters were established to depend on vibration parameters. An influence domain of amplitudes and vibration frequencies on concentration of cavitation bubbles was formulated. The obtained numerical solution was verified using CFM program package developed in PNRPU. The package is based on a differential equation system in hyperbolic and elliptic partial derivatives. The system is solved by using one of finite-difference method options – the particle-in-cell method. The method defines the problem solution algorithm. The obtained numerical solution was verified analytically by model problem calculations with the use of known analytical solutions of in-pipe piston movement and cantilever rod end face impact. An infrastructure consisting of an experimental fast hydro-dynamic processes research installation and a supercomputer connected by a high-speed network, was created to verify the obtained numerical solutions. Physical experiments included measurement, record, processing and analysis of data for fast processes research by using National Instrument signals measurement system and Lab View software. The model chamber end face oscillated during physical experiments and, thus, loaded the hydraulic volume. The loading frequency varied from 0 to 5 kHz. The length of the operating chamber varied from 0.4 to 1.0 m. Additional loads weighed from 2 to 10 kg. The liquid column varied from 0.4 to 1 m high. Liquid pressure history was registered. The experiment showed dependence of forced system oscillation amplitude on loading frequency at various values: operating chamber geometrical dimensions, liquid column height and structure weight. Maximum pressure oscillation (in the basic variant) amplitudes were discovered at loading frequencies of approximately 1,5 kHz. These results match the analytical and numerical solutions in ANSYS and CFM.

Keywords: Computing experiment, hydroelasticity, physical experiment, vibration.

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Authors: Tuğrul Varol, Halil Barış Özel

Abstract:

In this study which has been conducted in Akçasu Forest Range District of Devrek Forest Directorate; 3 methods (weed control with labourer power, cover removal with Hitachi F20 Excavator, and weed control with agricultural equipment mounted on a Ferguson 240S agriculture tractor) were utilized in weed control efforts in regeneration of degraded oriental beech forests have been compared. In this respect, 3 methods have been compared by determining certain work hours and standard durations of unit areas (1 hectare). For this purpose, evaluating the tasks made with human and machine force from the aspects of duration, productivity and costs, it has been aimed to determine the most productive method in accordance with the actual ecological conditions of research field. Within the scope of the study, the time studies have been conducted for 3 methods used in weed control efforts. While carrying out those studies, the performed implementations have been evaluated by dividing them into business stages. Also, the actual data have been used while calculating the cost accounts. In those calculations, the latest formulas and equations which are also used in developed countries have been utilized. The variance of analysis (ANOVA) was used in order to determine whether there is any statistically significant difference among obtained results, and the Duncan test was used for grouping if there is significant difference. According to the measurements and findings carried out within the scope of this study, it has been found during living cover removal efforts in regeneration efforts in demolished oriental beech forests that the removal of weed layer in 1 hectare of field has taken 920 hours with labourer force, 15.1 hours with excavator and 60 hours with an equipment mounted on a tractor. On the other hand, it has been determined that the cost of removal of living cover in unit area (1 hectare) was 3220.00 TL for labourer power, 1250 TL for excavator and 1825 TL for equipment mounted on a tractor. According to the obtained results, it has been found that the utilization of excavator in weed control effort in regeneration of degraded oriental beech regions under actual ecological conditions of research field has been found to be more productive from both of aspects of duration and costs. These determinations carried out should be repeated in weed control efforts in degraded forest fields with different ecological conditions, it is compulsory for finding the most efficient weed control method. These findings will light the way of technical staff of forestry directorate in determination of the most effective and economic weed control method. Thus, the more actual data will be used while preparing the weed control budgets, and there will be significant contributions to national economy. Also the results of this and similar studies are very important for developing the policies for our forestry in short and long term.

Keywords: Artificial regeneration, weed control, oriental beech, productivity, mechanization, man power, cost analysis.

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Authors: Oksana G. Cherednichenko, Anastasia L. Pilyugina, Sergey N.Lukashenko, Elena G. Gubitskaya

Abstract:

The estimation of accumulated radiation doses in people professionally exposed to ionizing radiation was performed using methods of biological (chromosomal aberrations frequency in lymphocytes) and physical (radionuclides analysis in urine, whole-body radiation meter, individual thermoluminescent dosimeters) dosimetry. A group of 84 "A" category employees after their work in the territory of former Semipalatinsk test site (Kazakhstan) was investigated. The dose rate in some funnels exceeds 40 μSv/h. After radionuclides determination in urine using radiochemical and WBC methods, it was shown that the total effective dose of personnel internal exposure did not exceed 0.2 mSv/year, while an acceptable dose limit for staff is 20 mSv/year. The range of external radiation doses measured with individual thermo-luminescent dosimeters was 0.3-1.406 µSv. The cytogenetic examination showed that chromosomal aberrations frequency in staff was 4.27±0.22%, which is significantly higher than at the people from non-polluting settlement Tausugur (0.87±0.1%) (р ≤ 0.01) and citizens of Almaty (1.6±0.12%) (р≤ 0.01). Chromosomal type aberrations accounted for 2.32±0.16%, 0.27±0.06% of which were dicentrics and centric rings. The cytogenetic analysis of different types group radiosensitivity among «professionals» (age, sex, ethnic group, epidemiological data) revealed no significant differences between the compared values. Using various techniques by frequency of dicentrics and centric rings, the average cumulative radiation dose for group was calculated, and that was 0.084-0.143 Gy. To perform comparative individual dosimetry using physical and biological methods of dose assessment, calibration curves (including own ones) and regression equations based on general frequency of chromosomal aberrations obtained after irradiation of blood samples by gamma-radiation with the dose rate of 0,1 Gy/min were used. Herewith, on the assumption of individual variation of chromosomal aberrations frequency (1–10%), the accumulated dose of radiation varied 0-0.3 Gy. The main problem in the interpretation of individual dosimetry results is reduced to different reaction of the objects to irradiation - radiosensitivity, which dictates the need of quantitative definition of this individual reaction and its consideration in the calculation of the received radiation dose. The entire examined contingent was assigned to a group based on the received dose and detected cytogenetic aberrations. Radiosensitive individuals, at the lowest received dose in a year, showed the highest frequency of chromosomal aberrations (5.72%). In opposite, radioresistant individuals showed the lowest frequency of chromosomal aberrations (2.8%). The cohort correlation according to the criterion of radio-sensitivity in our research was distributed as follows: radio-sensitive (26.2%) — medium radio-sensitivity (57.1%), radioresistant (16.7%). Herewith, the dispersion for radioresistant individuals is 2.3; for the group with medium radio-sensitivity — 3.3; and for radio-sensitive group — 9. These data indicate the highest variation of characteristic (reactions to radiation effect) in the group of radio-sensitive individuals. People with medium radio-sensitivity show significant long-term correlation (0.66; n=48, β ≥ 0.999) between the values of doses defined according to the results of cytogenetic analysis and dose of external radiation obtained with the help of thermoluminescent dosimeters. Mathematical models based on the type of violation of the radiation dose according to the professionals radiosensitivity level were offered.

Keywords: Biodosimetry, chromosomal aberrations, ionizing radiation, radiosensitivity.

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Authors: Riccardo Fratini, Riccardo Santini, Jacopo Serafini, Massimo Gennaretti, Stefano Panzieri

Abstract:

This paper presents a nonlinear differential model, for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi-steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and successively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flows, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal components of relative velocity between flow and airfoil Ut, Up, their derivatives, and section angular velocity ε˙. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R =61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec. The first analysis performed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically periodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller. In particular, when the reference command to be tracked and/or the disturbance to be rejected are periodic signals with a fixed period, the repetitive control strategies can be applied due to their high precision, simple implementation and little performance dependency on system parameters. The functional scheme of a repetitive controller is quite simple and, given a periodic reference command, is composed of a control block Crc(s) usually added to an existing feedback control system. The control block contains and a free time-delay system eτs in a positive feedback loop, and a low-pass filter q(s). It should be noticed that, while the time delay term reduces the stability margin, on the other hand the low pass filter is added to ensure stability. It is worth noting that, in this work, the authors propose a phase shifting for the controller and the delay system has been modified as e^(−(T−γk)), where T is the period of the signal and γk is a phase shifting of k samples of the same periodic signal. It should be noticed that, the phase shifting technique is particularly useful in non-minimum phase systems, such as flexible structures. In fact, using the phase shifting, the iterative algorithm could reach the convergence also at high frequencies. Notice that, in our case study, the shifting of k samples depends both on the rotor angular velocity Ω and on the rotor azimuth angle Ψ: we refer to this controller as a spatial repetitive controller. The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades. The performance of the spatial repetitive controller is compared with an industrial PI controller. In particular, starting from wind speed velocity Vw = 11.4 m/s the controller is asked to maintain the nominal angular velocity Ωn = 1.266rad/s after an instantaneous increase of wind speed (Vw = 15 m/s). Then, a purely periodic external disturbance is introduced in order to stress the capabilities of the repetitive controller. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both external disturbances and periodic trend in the model dynamics. Finally, the nominal value of the angular velocity is reached, in accordance with results obtained with commercial software for a turbine of the same type.

Keywords: Wind turbines, aeroelasticity, repetitive control, periodic systems.

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