Values Of Empirical Coefficients Research Articles

An effective approach for VARANS-VOF modelling interactions of wave and perforated breakwater using gradient boosting decision tree algorithm

In this paper, we propose a systematic and time-efficient approach to calibrate 2D VARANS-VOF models for simulation of wave interaction with porous plate in numerical wave tank. To reach this goal, we develop a data-driven approach in combination with numerical and experimental data to figure out the optimal empirical coefficient associated with linear and non-linear drag force coefficients (α, β). Advanced gradient boosting decision trees algorithms (GBDT) are adopted to capture the accuracy of the prediction model. Although only limited samples, for instance 72 samples are generated and chosen to train and test the prediction model, the GBDT model is able to identify the trend in non-linear influence of model parameters. The advantage of GBDT algorithm can obviously be seen through the regression analysis with very high regression coefficient (R2 > 0.99). The developed model is subsequently employed for a large range of considered parameters as input features of the models to predict the possible hydrodynamics characteristics. The smallest mean squared error between predicted and experimental results, which is 0.00204, is found and used to determine the best performing combination of these model parameters. The numerical model together with selected values of empirical coefficients is then validated using available experimental data in literature. The free surface elevations in front of and behind the structure from the numerical model are nearly identical with the experimental data.

Spatial Distributions of the Dose Created Phantom Pencil Beam of Mono-Energy and Bremsstrahlung Photons in a Water with Energies from 0.25 to 20 MeV

Purpose: Critical analysis of existing and obtaining more accurate data on the spatial dose distributions created in the water phantom by pencil beams (PB) of monoenergetic and bremsstrahlung photons with energies from 0.25 to 20.0 MeV, and approximation of these distributions for the purpose of calculating doses in radiation therapy. Material and Methods: Using the Monte Carlo method, the EGSnrc program and the MATLAB mathematical package, these distributions were calculated for monoenergetic photons in the energy range from 0.25 to 19.75 MeV in increments of 0.5 MeV, for bremsstrahlung photons with a maximum energy of 4.0, 6.0, 10.0, 15.0, 18.0 MeV and for the gamma-radiation spectrum of the therapeutic apparatus ROCUS. The calculation results are converted into the so-called dose kernel of photon pencil beam. The obtained dose kernel values are compared with previously published data and the observed discrepancies are discussed. Depths in water were studied from 1.0 to 40 cm in increments of 0,5 cm and along the radius from 0.02 to 46.0 cm with an uneven grid. For bremsstrahlung and photons with the spectrum of the Rocus apparatus, the possibility of approximating dose kernel values using approximation formulas convenient for calculating doses in radiation therapy has been investigated. Results: On the basis of the results obtained, a new version of the library of dose kernels of a pencil photon beam for water was created, which differs from previous versions by the use for calculating a better description and modeling of the physical processes of the interaction of photons and charged particles with matter, more adequate data on the interaction cross sections and significantly lower values of statistical uncertainties of the results. For bremsstrahlung and photons with the spectrum of the Rocus apparatus, a mathematical model of dose kernels of a pencil beam is proposed, which includes decomposition of the dose kernels into components of the primary and scattered doses, approximation formulas and empirical coefficients convenient for integration. The values of empirical coefficients are determined by fitting to the results of the calculation of dose kernels using a combination of the random search method and the nonlinear regression method. Conclusion: The results obtained in this work will improve the algorithms and increase the accuracy of dose calculation when planning remote therapy with photon beams.

Статистическая математическая модель расчета коэффициента полезного действия компрессоров турбодетандерных агрегатов: усовершенствование и идентификация

Despite their small size turbo expander units used for transportation and processing oil and gas have a capacity of up to 5.5 MW. Designing new turbo-expander units includes several stages, one of which is the variant calculation of the compressor for the given parameters. For calculating the efficiency of the compressor by its main parameters a specialized statistical model is used. The efficiency of stages designed according to a single unambiguous methodology depends on the design parameters and similarity criteria. The generalization of experience in designing turbo-expander units allowed improving the statistical mathematical model used in the Universal Modeling Method, taking into account the specifics of compressors. The new version of the mathematical model correctly takes account of losses in the inlet nozzle, the method of manufacturing the impeller, the diffuser type, etc. The resulting mathematical model includes 22 empirical coefficients. To select the correct values of the coefficients, the results of 26 acceptance tests of turbo-expander compressors were used. The error of the new statistical model with the selected of empirical coefficient values was 1.8%, which is sufficient for its practical application in project activities.

Optimization of deep soil mixing mass for construction of tunnel cross-passage in Bangkok

A cross-passage from a tunnel to an intervention shaft in Bangkok subsoils was modelled using three-dimensional finite element analysis. The optimization was performed for reducing the volume of soil-cement mass while maintaining ground stability. The result showed that the factor of safety increases linearly with the thickness of improved ground. The relationship between the improved groundmass and ground surface settlement curve was made. It was found that the predicted settlement profile can be captured by the formula proposed by Peck and O’Reilly, providing that the empirical coefficient of 0.6 is fit well with the results from the 3D simulation. This value was obtained from the average of empirical coefficient value 0.4 and 0.7, which are the empirical coefficient values of stiff clay and soft clay, respectively based on the overburden thickness.

Ultrafiltration concentration and demineralization of technological solutions using membranes uam-150, upm-100, upm-k

In this work, experimental data on the rejection coefficient and the specific output flux are obtained. Based on the studies, graphical dependencies of the rejection coefficient on the specific output flux were constructed and analyzed. During the analysis, it was noted that with an increase in the output specific flow of the solvent, the rejection coefficient decreases. The reason for this is the boundary layers of fat and protein formed in the near-membrane layers, which prevents the passage of protein molecules through the pores of the membrane. For the theoretical calculation of the rejection coefficient and specific output flux, mathematical expressions are developed and numerical values of the values of empirical coefficients are obtained. The developed mathematical expressions describe the experimental data with good confidence. The obtained experimental and calculated data can be used with great reliability in the calculations of mass-transported flows of substances through semipermeable membranes, as well as in engineering methods for calculating and predicting the effectiveness of the use of membrane processes for the concentration of whey.

Mass Transfer Coefficients in Electrochemical Membrane Process of Iron, Magnesium and Manganese Ions Extraction from Technological Solutions Complicated by Concentration Polarization

The article presents the results of a study of mass transfer in the process of electrochemical extraction of iron, magnesium and manganese ions from technological solutions. Mathematical expressions are obtained, and numerical values of empirical coefficients are determined for theoretical calculation of specific outflow, retention coefficient, and average mass transfer coefficients of the electrochemical membrane process of separation of technological solutions. The dependence of concentration polarization on solution flow rate, pressure gradient, and concentration is analyzed.

Influence of pool width on pioneering flame height of flame spread over jet fuel inside a bench-scale air flow tunnel

The development of liquid fire depends mainly on fuel evaporation and heat feedback of flame configuration which are both influenced by the ambient winds. In current work, the height of pioneering flame in the process of flame spread above the surface of jet fuel is measured inside a bench-scale air flow tunnel. The longitudinal air flow velocities are 0.45, 0.88, 1.3, 1.73, 2.15 and 2.57 m/s for both concurrent and opposed flame spreads. Five oil pans with the same length of 100 cm but different widths of 4, 8, 12, 16 and 20 cm are utilized. The experimental results of flame heights considerably deviate from the calculations of classic Thomas model and Oka et al. model. Then, the new-proposed non-dimensional parameter, characteristic size ratio of pool λ=d/D is introduced into Thomas’ model and Oka et al.’s model respectively. The measured flame heights follow well with the improved models H/d=aṁ*η(u∗)bλc and H/d=αFr2/3Q̇∗βλγ, regardless of direction of air flow. The values of empirical coefficients and exponents of the correlations a, b, c, η in improved Thomas model and α, β and γ in improved Oka et al. model are derived from the experimental results.

Assessment of Conditions for Detecting Corrosion Cracking of Welded Joints by Acoustic Emission Method

The analysis of acoustic emission (AE) signs of the early development of corrosion cracking of a welded joint is carried out on the example of real data of technical diagnostics of a butane heater of a gas fractionation unit obtained using the AE method before and after eliminating the defect. The possibility and conditions of detecting the designated defect were studied using five basic criteria for assessing the degree of hazard of AE sources: amplitude, integral, local dynamic, integral dynamic, and the MONPAC criteria. For all these AE criteria, the values of empirical coefficients that ensure the detection of a defect of this type were determined, and the dynamics of the defect development in the coordinates of the estimated parameters was established. The organizational and technical requirements that increase the likelihood of detecting corrosion damage during AE control are described.

Application of Modeling of Mass Transfer of Substances through Membrane for Designing Industrial Electromembrane Apparatuses

The general stages of application of modeling of mass transfer of substances through a membrane in solution separation process for designing industrial apparatuses are presented. Numerical values of empirical coefficients are obtained to calculate friction coefficients of solvent–membrane, solute–membrane, and solute–solvent systems for anode-adjacent and cathode-adjacent membranes for separation of model aqueous CuSO4, Fe(NO3)3, and Ni(NO3)2 solutions of engineering industries.

Алгоритм определения оптимального числа рабочих колес в проточной части турбомолекулярного вакуумного насоса

The paper considers developing an algorithm for determining the optimum runner number in the blading section of a turbomolecular pump. Such pumps are built into chromatograph mass spectrometers for ensuring vacuum production in the chamber. Turbo-molecular pumps boast a number of advantages over other pumping solutions since it is possible to arrive at the required pumping parameters by means of selecting the optimum blading section configuration. In order to solve this problem, we present an algorithm for calculating the optimum runner number in the blading section of a turbomolecular pump, ensuring the pumping characteristics required: pumping speed and pressure ratio. The algorithm is based on well-known analytical expressions describing processes taking place in pumps of this type, which means it is highly computationally efficient. We determined the respective blading section parameter values, selected the values of empirical coefficients and plotted the pumping performance for the first two runners. The algorithm developed may be used to optimise mass and dimensions of turbomolecular pumps, which could significantly expand their use.

Ultrafiltration concentration of whey in a pilot plant

Experimental data on the retention coefficient and the output specific flow are obtained. The test solutions were goat and cow's milk whey after obtaining cheese. The description, general view and technological scheme of a pilot installation of a tubular type are given. The studies were carried out on semipermeable tubular type ultrafiltration membranes manufactured by AO "ZAVKOM". Based on the studies, graphical dependences of the retention coefficient on the specific output stream were constructed and analyzed. During the analysis, it was noted that with an increase in the output specific flow of the solvent, the retention coefficient decreases. The reason for this is the boundary layers of fat and protein formed in the near-membrane layers, which prevents the passage of protein molecules through the pores of the membrane. Also during the experiment, it was noted that goat milk serum has a more oily structure and requires prior separation. For the theoretical calculation of the retention coefficient and specific output stream, mathematical expressions are developed and numerical values of the values of empirical coefficients are obtained. The developed mathematical expressions describe the experimental data with good confidence. The obtained experimental and calculated data can be used with great reliability in the calculations of mass-transported flows of substances through semipermeable membranes, as well as in engineering methods for calculating and predicting the effectiveness of the use of membrane processes for the concentration of whey.

Моделирование характеристик водокольцевых вакуумных насосов

Physical and mathematical modeling of characteristics of water-ring vacuum pumps has a number of specific features. Isothermal efficiency, i.e. the ratio of the isothermal gas compression power to the pump power consumed is used as an efficiency indicator. The article describes the existing methods of hydraulic calculation of pumping units. An analysis of physical models, numerical values of empirical coefficients is carried out. An improved algorithm for calculating water-ring vacuum pumps of different manufacturers in the framework of previously developed models is presented. The calculations of compressors manufactured by ZAO Beskom (VVN-3, VVN1-6, VVN1-12) and ERSTVAK (ELRS-45, ELRS-57) are considered as examples. The results of tests of vacuum pumps published by the manufacturers in the open press are used as the initial data for the calculations. The experimental dependences of the performance, power expended, isothermal efficiency of water-ring vacuum pumps on the suction pressure are presented. The results obtained make it possible to improve the accuracy and reliability of predicting the amount of displaced liquid or steam during the operation of the pumping unit.

COMBINATORIAL OPTIMIZATION UNDER UNCERTAINTY AND FORMAL MODELS OF EXPERT ESTIMATION

Previously, the author formalized the concepts of uncertainty, compromise solution, compromise criteria and conditions for a quite general class of combinatorial optimization problems. The functional of the class’ problems contains linear convolution of weights and arbitrary numerical characteris­tics of a feasible solution. It was shown that the efficiency of the presented algorithms for the uncertainty resolution is largely determined by the effi­ciency of solving the combinatorial optimization problem in a deterministic formulation. A part of the formulated compromise criteria and conditions uses expert weights. Previously, the author and his disciples also formulated combinatorial optimization models, optimality criteria, criteria for deci­sions’ consistency. The models allow to evaluate and justify the degree of stability and reliability of the estimated values of empirical coefficients using a formally ill-conditioned empirical pairwise comparison matrix of arbitrary dimension. The matrix may contain zero elements. The theoretical research and statistical experiments allowed to choose the most efficient of these optimization models. In this article, on the base of earlier results by the author and his disciples, we formalize and substantiate the efficiency of the proposed sequential procedure for expert estimation of weights that determine compromise criteria and conditions. The procedure is an integral part of the algorithm introduced by the author to solve combinatorial optimization problems under uncertainty of the mentioned class. We give unified algorithm for efficient uncertainty resolution that includes original and efficient formal procedure for expert coefficients’ estimation using empirical matrices of pairwise comparisons.

The application of isodromic equation for calculation of PID-controller integrated component

A functional feature of the application of electronics used for the automatic control of internal combustion engines is necessity in the proportional conversion of ECU electrical signals into the mechanical processes based on corresponding elements motion. For such conversion of information actuating mechanisms are used, referred as actuators. Actuators in the form of electrical machines (stepper or precision electric motors) or electric apparatuses (electromagnets and solenoids) are the mostly widespread in ICE. As a physical object of the research, the unit of Heinzmann, model StG 6-02V that is based on a DC electric drive controlled by a pulse-width modulation signal, was selected in the current work. It has a toothed gearbox and a non-contact reverse positional connection. This actuator pro-vides an output torque of 6 Nm and 36-degree range of output shaft rotational angle. The functional scheme of the electronic system of automatic control of a diesel engine based on mentioned device is developed. The PID regulator with feedback is used to control the actuator. A design formula that can be incorporated in the controller algorithm to calculate the integral component of the PID regulator was also obtained. Values of empirical coefficients were determined in this formula. The results of experimental confirmation of the correctness of the approach taken are presented. Thus, the new formula for determining the integral component of the PID regulator differs positively from the well-known solutions because the new approach is free from storing the whole array of previous data with discrepancy in the controller’s RAM, that simplifies the application of the developed algorithm greatly and speeds up the computational capability of the controller.

Electrobaromembrane apparatuses: Classification and particular application for wastewater treatment

The aims of this work are developing the electrobaromembrane apparatus classification and study of the particular case of electrobaromembrane process application for wastewater treatment in engineering industries. The multilevel classification of electrobaromembrane processes, which takes into account several factors at once, is proposed. A particular case of electrobaromembrane process application for treatment of the galvanic solution produced by JSC "Zavod Tambovpolimermash" is studied in this work. The research was carried out on the experimental electrobaromembrane plant with flat chambers. In addition, some approximation functions and their numerical values of empirical coefficients were obtained for experimental data of the specific flow and the retention factor of membranes OPMN-P and AMN-P. The result comparison of nanofiltration and electronanofiltration processes shows that the permeability of the solution through the membrane pores increases when a constant electric current density is applied to the test system. During nanofiltration, process membranes are compacted due to the overpressure increase. This directly affects the driving force of the membrane separation process for a particular type of solution, thereby the retention factor of porous membranes increases. Retention factor values do not differ a lot for certain types of ions. In contrast, electronanofiltration process is characterized by the selectivity of membranes with respect to a certain type of ions. The near-cathode OPMN-P membrane mainly passes thought itself the Zn2+ cations and holds the Cl- and SO4 2- anions, while the near-anode AMN-P membrane mainly passes thought itself the Cl- and SO4 2- anions and holds the Zn2+ cations.

Сорбционная способность ультрафильтрационных мембран и потенциал поля поверхностных сил в растворах молочных белков

В работе представлен анализ литературных данных по исследованию сорбционной способности мембран и потенциала поля поверхностных сил. Сформулирована цель работы и на основании литературного обзора выполнен выбор исследуемых ультрафильтрационных мембран УАМ­150 и УПМ-100. Методом переменных концентраций проведены экспериментальные исследования по сорбционной активности ультрафильтрационными мембранами белка из подсырной сыворотки. Получены численные значения равновесного коэффициента распределения белка в мембранах УАМ-150 и УПМ-100, и растворах молочной сыворотки в диапазоне изменения концентраций белка от 9 до 32 г/л при температурах от 293 до 308 К. Проанализировано влияние температуры и концентрации раствора молочного белка на сорбционную способность ультрафильтрационных мембран УАМ-150 и УПМ-100. На основании экспериментальных данных найдены численные значения эмпирических коэффициентов для теоретического расчета равновесного коэффициента распределения. Рассчитан потенциал поля поверхностных сил полупроницаемых мембран УАМ-150 и УПМ-100 и интерпретировано его изменение в зависимости от температуры и концентрации молочного белка

Enzyme kinetics of cellulose hydrolysis of Miscanthus and oat hulls.

Experiments were done to model enzymatic hydrolysis of Miscanthus and oat hulls treated with dilute solutions of nitric acid and sodium hydroxide in direct and reverse sequences. The enzymatic hydrolysis kinetics of the substrates was studied at an initial solid loading from 30 to 120g/L. The effects of feedstock type and its pretreatment method on the initial hydrolysis rate and reducing sugar yield were evaluated. The fitting results by the developed models showed good agreement with the experimental data. These models designed for developing the production technology of concentrated glucose solutions can also be applied for glucose fermentation into ethanol. The initial solid loading of 60-90g/L provides the reducing sugar concentration of 40-80g/L necessary for ethanol synthesis. The kinetic model can also be applied to investigate enzymatic hydrolysis of other substrates (feedstock type, pretreatment method) under the similar conditions used herein, with adjusted empirical coefficient values.

Investigation of the Hydrodynamic Flow Pattern in Tubular Membrane Devices

The present work examines the hydrodynamic flow pattern in an industrial tubular baromembrane device on the example of commercially available membrane elements at pressures of 1.0–4.0 MPa. Experimental response curves and dependence curves of the longitudinal mixing coefficient were obtained as a function of the solution flow rate and the pressure in the membrane module. Based on this information, the criterial equation for calculating the longitudinal mixing coefficient was obtained. Numerical values of empirical coefficients are given, which can theoretically be used to calculate the longitudinal mixing coefficients as well as to predict the values for similar constructions of baromembrane systems operating at high transmembrane pressures.

Predictive, adaptive model of PG 9171E gas turbine unit including control algorithms

Contemporary thermal diagnostic systems require computational tools, including mathematical models. Because of required short computation time, these models should have a simple structure. Therefore very often, for these purposes, analytical-empirical models are used. Such models encompass both mass and energy balances and additional empirical functions whose coefficients are estimated by using the measurement results. As a result, changing technical conditions are taken into account. This paper presents a simulation model of PG 9171E gas turbine unit by General Electric which contains partial models of an axial compressor, low-emission combustion chambers, and an axial expander. The unknown values of empirical coefficients were estimated based on the operating data using the least squares method. The simulation model allows the calculation of non-measured operating parameters and energy assessment indicators, e.g. efficiency of electricity production. An important advantage of the developed model is that it has the capability of adapting to the changing technical conditions of the machine. The results of calculations were compared to the results of measurements. Model predictive quality was verified with the use of the determination factor and root mean square error.

Adaptive Simulation Model of a Double-Pressure Heat Recovery Steam Generator for Current Optimization in Control Systems

Control is the conscious impact on a process in order to realize specific goals. When controlling complex industry processes, the most frequent control method is based on a layered structure (hierarchical), which includes a layer of regulation and protection and a layer of optimization. The optimization layer is used to identify the most cost-effective levels for the regulation layer. This includes the use of process static models that must be structurally simple and quick at calculating, while maintaining a high level of accuracy. The most frequent method of model designing involves experimental analysis called process identification. However, we can develop models that result from the laws of physics with additional use of empirical relationships. This article presents a simulation model of a double-pressure heat recovery steam generator (HRSG) in gas turbine combined cycle power plant. The model was developed based on the equations of mass and energy balances and the empirical relationships describing the process of heat transfer and pressure drop of working fluid in the heat exchanger. Unknown values of empirical coefficients were estimated based on the operating data with the least-squares method. The model allows the calculation of nonmeasured operating parameters and energy assessment indicators. An important benefit of the developed model is that it has the capability of adapting to the changing technical conditions of the HRSG. The results of calculations were compared to the results of measurements. Model predictive quality was verified with the use of the determination factor and root mean square error.