The paper presents selected research results concerning the identification and simulation of the TGE S.A. Day-Ahead Market (DAM) system of the day for electricity delivered and sold, listed for the following hours: 5:01-6:00, 11:01-12:00, 17:01-18:00 and 23:01-24:00 in 2019, which were obtained in the MATLAB and Simulink environment using the System Identification Toolbox. As a result of identification, four respective discrete parametric arx models were obtained, which were then subject to quality assessment. Then, a simulation model was built in the Simulink environment, which was used for simulation tests and for assessing the sensitivity of the model created using the data from 2019 as the basis and the data from 2020 for verification. The obtained results confirm the correctness of both the performed discrete parametric identification and the possibility of testing the quality of the model and its sensitivity with the use of the DAM system model in the MATLAB and Simulink environment.
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The paper presents results of numerical analyses of the collision of various bird models(dummies) with a helicopter windshield. Three different numerical bird models were elaborated. According to the subject literature, applying an appropriate equation of state has an influence on impact parameters. The author used the LS_DYNA software package. This is a computational code designed to analyse fast-changing phenomena by means of the finite-element method. SPH method has been used for bird strike simulations. In the research, three different equations of state have been used: Grüneisen's, polynomial and tabulated.
PL
W artykule zaprezentowano wyniki analiz numerycznych zderzenia różnych modeli ptaka z oszkleniem helikoptera. Opracowano trzy różne modele numeryczne ptaka. Jak wynika z analizy literatury przedmiotu badań zastosowanie odpowiedniego równania stanu (EOS, Equation of State) wpływa na parametry zderzenia. W badaniach wykorzystano pakiet oprogramowania LS-DYNA. Jest to kod obliczeniowy do analizy zjawisk szybkozmiennych metodą elementów skończonych. Modele ptaków opracowano z wykorzystaniem metody SPH. W analizach uwzględniono trzy różne równania stanu, takie jak: Grüneisena, wielomianowej oraz w postaci stabelaryzowanej.
The sound speed and parameters of nonlinearity B/A, C/A in a fluid are expressed in terms of coefficients in the Taylor series expansion of an excess internal energy, in powers of excess pressure and density. That allows to conclude about features of the sound propagation in fluids, the internal energy of which is known as a function of pressure and density. The sound speed and parameters of nonlinearity in the mixture consisting of boiling water and its vapor under different temperatures, are evaluated as functions of mass concentration of the vapor. The relations analogous to that in the Riemann wave in an ideal gas are obtained in a fluid obeying an arbitrary equation of state. An example concerns the van der Waals gases. An excess pressure in the reflected wave, which appears when standard or nonlinear absorption in a fluid takes place, is evaluated in an arbitrary fluid.
Determination of gas solubility in polar liquids was analyzed by applying the equations of state and mixing rules. The modified Nakamura-Bredveld-Prausnitz equation with classic mixing rules has been proposed. It was stated that description of gas solubility by MNBP equation needs temperature dependence of the interaction coefficient kij. The parameters of this dependence have been determined for some substances. The comparative calculations showed that the method of equations of state gives good description of CO2 solubility in water.
PL
Zanalizowano zagadnienie opisu rozpuszczalności różnych gazów w rozpuszczalnikach polarnych za pomocą równań stanu i różnych reguł mieszania. Zaproponowano zastosowanie zmodyfikowanego równania Nakamury-Bredvelda-Prausnitza z klasycznymi regułami mieszania. Stwierdzono, że do opisu rozpuszczalności wielu substancji gazowych w wodzie za pomocą równania MNBP konieczne jest uwzględnienie zależności współczynnika interakcji kij od temperatury. Dla szeregu substancji wyznaczono parametry tej zależności. Przeprowadzone obliczenia porównawcze wykazały, że metoda równań stanu daje dobry opis rozpuszczalności CO2 w wodzie.
Comparatible calculations of different equations of state were carried out in order to describe of thermodynamic characteristics of substances in supercritical region. The substances used in supercritical processes and components of gas mixtures are taken into account in the test calculations.
PL
Przeprowadzono obliczenia porównawcze z użyciem różnych równań stanu do opisu charakterystyki termodynamicznej substancji w obszarze nadkrytycznym. W obliczeniach uwzględniono substancje najczęściej stosowane w procesach zachodzących w warunkach nadkrytycznych oraz substancje wchodzące w skład różnych mieszanin gazowych.
The paper deals with the Lennard-Jones fluid and presents the mathematical model of computating thermodynamic functions of state in the liquid and gas domain by means of statistical thermodynamics. To calculate the thermodynamic properties of a real fluid, we used the Johnson-Zollweg-Gubbins model based on the modified Benedict-Webb-Rubin equation of state, the Chunxi-Yigui-Jiufang equation of state based on the simple perturbation theory, and the complex Tang-Tong-Lu model based on the solution of the Ornstein-Zernike equation obtained by means of the perturbation theory. The analytical results are compared with the thermodynamical data, and with the results obtained from classical thermodynamics.
A logarithmic relationship between the phonon thermal conductivity under normal conditions and seismic parameter F (or square of the hydrodynamical velocity of sound) for silicate and oxide minerals related to the Earth's interior is proposed. The considerations are based on Debye's theory of solid phase and on the seismic equations of state for minerals. In numerical calculations the thermodynamical laboratory data of several main silicates were also used.
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