Equation Of State Method Research Articles

Generalized sequential state equation method for moving subsystem-induced structural parametric resonance

Parametric excitation is a unique type of excitation that arises from the time-varying parameters of a dynamical system, typically induced by the periodic movements of the system components. However, the structure-moving subsystems problem creates a new type of parametric excitation where the subsystems do not have exact periodic movements. Under the circumstances, dimension of the mathematical model of such a system exhibits time dependency, which prohibits the employment of conventional analytical methods to predict its stability. In this paper, we propose a novel Generalized Sequential State Equation Method that provides a distinct solution framework for analysis of the subsystem-induced parametric resonance. With the time-domain system partition and state mapping, the proposed method reconfigures the coupled system with a sequence of state space equations and solves them chronologically. The proposed method relaxes the single-subsystem-assumption in its original form and applies to a general scenario where the subsystems travel with arbitrary characteristic period. With the proposed method, occurrences of the subsystem-induced parametric resonance are precisely predicted via a set of analytical stability criteria and the steady state response is determined in an exact analytical form.

Analysis of the general uncertainty propagation and calculation of the systematic uncertainty of the Neumann equation of state for surface free energy determination

The determination of the surface free energy (γSV) of solid materials provides information to explain and understand a wide variety of phenomena in surface science. One of the most widely used methods to determine the value of γSV is the Neumann equation of state (EQS), whose application requires the values of the contact angle (θ) and the surface tension of a probe liquid (γLV). Both parameters are determined experimentally, and their values may be subject to considerable uncertainty. In the present work, the uncertainties of the EQS are analyzed by means of the Taylor series method, using a polynomial adjustment to the EQS previously reported. This analysis allowed us to determine the effects of the θ and γLV uncertainties on γSV values. The γSV of polyoxymethylene (POM) and polytetrafluoroethylene (PTFE) was calculated using the EQS from four probe liquids and taking into account the propagation of the θ and γLV uncertainties. Generally, the comparison of the γSV values calculated from the different probe fluids revealed significant differences. As a solution to this inconsistency in the EQS method, we proposed taking into account a systematic standard uncertainty associated with the method equal to 1.3 mJ/m2. This allowed the differences between the γSV values for the different probe liquids to be non-significant and therefore the method to be consistent.

Techno-economic Analysis of Electric Heating Load Participation in Power System Power Regulation

At the present stage, temperature-controlled loads occupy a considerable proportion, and the adoption of the use of temperature-controlled electric loads is the main issue today. This paper transforms the form of temperature change in the house into an ordinary differential equation, establishes a series of models based on this differential equation, and discusses the ability and characteristics of the electric heating loads' electric behaviour in different situations, using the temperature-controlled intervals as the constraints, and evaluates the economic benefits. In this paper, we first analyse the factors affecting the electric behaviour of electric heating equipment, including the temperature difference between the wall and the room, and analyse the process of temperature change in a typical room by referring to the CTTC model. In this paper, the equation of state method is used to process the ordinary differential equations and convert them into difference equations, which are calculated iteratively using MATLAB. Under the constraints of the given temperature control interval, the steady state solution of the differential equation model is solved, and the characteristics of the heating power, room temperature and wall temperature changes in the steady state are analysed. Secondly, in this paper, the differential equation is used to solve the indoor temperature change equation, taking the last day of the steady state condition, and the indoor temperature at each time point is obtained by iterative computation, one step (1 minute) at a time, and according to the continuity of the indoor temperature when it is adjusted upward or downward, we can get the upward or downward duration by adding up the segment and thus obtaining the duration of upward or downward adjustments.

SAV Finite Element Method for the Peng-Robinson Equation of State with Dynamic Boundary Conditions

SAV Finite Element Method for the Peng-Robinson Equation of State with Dynamic Boundary Conditions

Characterisation and validation of the JWL equation of state parameters for PE4

This investigation focused on determining the Jones-Wilkins-Lee (JWL) equation of state (EoS) parameters for the Australian made explosive PE4-MC. Four cylinder expansion (CYLEX) experiments were conducted using the T-20 methodology with measurements of the time of arrival of the copper cylinder on the perspex plate made using optical fibres connected to an optical pulse timer. Three different model parameter fits were then generated from the CYLEX test data. These were based on; (1) Traditional least-squares fit of CYLEX data to JWL EoS and (2) Inverse modeling method using LS-DYNA and LS-OPT (two different fits). The three parameter sets were then compared in terms of the accuracy of their predictions against two sets of blast loading experiments. The first set of blast loading experiments evaluated the different parameter fits at a scaled distance (Z) of 1.77–2.55 m/kg1/3, representing a mid-field blast loading scenario while the second set of blast loading experiments represented a near-field blast loading scenario (Z = 0.08–0.1 m/kg1/3). The JWL EoS parameters which were derived using the standard fitting method from the CYLEX test data (CYLEX) were shown to provide accurate predictions (within 5% of experiments) in the near-field but under-predicted the peak reflected pressure in the mid-field by more than 20%. The best predictions across both the near and mid-field blast loading scenarios was provided by the two parameters sets (LS-OPT Final and LS-OPT Select), which were derived using an inverse modeling approach, with the LS-OPT Select set of parameters being the preferred option. Additionally, comparisons between the experimental data and predictions using the JWL EoS parameters for the US made C4 explosive indicated that the blast loading in the mid-field was similar between C4 and PE4-MC, which was consistent with the previous literature. However, in the near-field C4 was predicted to provide higher blast loadings. This highlights the importance of validating an explosives EoS across a range of different scaled distances.

Motion Modeling and State Estimation in Range-Squared Coordinate

In some target tracking applications, angle measurements are absent due to sensor characteristics, which makes Cartesian states unobservable for a single stationary sensor. When multi-sensor target tracking techniques with only range or Doppler measurements are applied to produce Cartesian state estimates, their performance and efficiency can be benefited from accurate range and Doppler estimates obtained from single sensors. This paper investigates the range and Doppler estimation problem based on motion modeling in range-squared coordinate considering range-squared as a generic coordinate. A pseudostate vector consisting of range squared and its derivatives is defined to completely summarize the dynamic of the Cartesian nearly constant velocity (NCV) motion and it is found time evolution of the pseudostate is linear based on the methodology of state space representation. To estimate the pseudostate from range-Doppler or range-only measurements, a recursive filter is developed using the decorrelated unbiased converted measurement (DUCM) method. Finally, the pseudostate estimates in the range-squared coordinate are converted into the range coordinate using the scaled unscented transformation (SUT) method to produce range and Doppler estimates. Although the conversion is nonlinear, it is performed outside the filtering recursions without propagating nonlinearity approximation errors in the filtering recursions. Numerical experiments with various conditions of measurements demonstrate the superior performance benefits from the proposed accurate linear state equation and estimation method.

Modeling and Fuzzy Feedforward Control of Fuel Cell Air Supply System

As an important part of the fuel cell subsystem, the air supply system of the proton exchange membrane fuel cell (PEMFC) plays an important role in improving the output performance and durability of fuel cells. It is necessary to control the oxygen excess ratio of fuel cell systems in the process of variable load, preventing the oxygen starvation in the loading process and excessive parasitic power consumption caused by oxygen saturation. At this time, the modeling of fuel cell systems and the development of control strategies are critical. The development of a control strategy depends on the construction of the control model. Aiming at the difficulty of air supply system modeling, this paper uses radial basis function (RBF) neural network and state equation method to establish the dynamic model of air supply systems. At the same time, PID, fuzzy logic plus PID (FL + PID), feedforward plus PID (FF + PID), fuzzy feedforward plus fuzzy PID (FF + FLPID) control strategy are proposed to control the oxygen excess ratio of the system. The simulation results show that fuzzy feedforward plus fuzzy PID (FF + FLPID) has the best effect and the oxygen excess ratio can be followed in 1 s.

Analysis of the Response of Transmission Line Network under Electromagnetic Pulse

Power system transmission line is a very complex network. The response of cable terminal is very different from that of single line. In order to accurately predict the terminal response of the cable under the nuclear electromagnetic pulse, a convenient method is needed to calculate the response of complex network. Based on the state equation method and the extrapolation method, the transmission line is equivalent to the current source or voltage source. Matlab program and Simulink are used to calculate the induced current generated by the cable terminal. The results are compared with those of CST cable studio. The results of CST show that the method is correct.

Reconstructing Magma Storage Depths for the 2018 Kı̄lauean Eruption From Melt Inclusion CO2 Contents: The Importance of Vapor Bubbles

AbstractThe 2018 lower East Rift Zone (LERZ) eruption and the accompanying collapse of the summit caldera marked the most destructive episode of activity at Kı̄lauea Volcano in the last 200 years. The eruption was extremely well‐monitored, with extensive real‐time lava sampling as well as continuous geodetic data capturing the caldera collapse. This multiparameter data set provides an exceptional opportunity to determine the reservoir geometry and magma transport paths supplying Kı̄lauea’s LERZ. The forsterite contents of olivine crystals, together with the degree of major element disequilibrium with carrier melts, indicates that two distinct crystal populations were erupted from Fissure 8 (termed high‐ and low‐Fo). Melt inclusion entrapment pressures reveal that low‐Fo olivines (close to equilibrium with their carrier melts) crystallized within the Halema’uma’u reservoir (∼2‐km depth), while many high‐Fo olivines (>Fo81.5; far from equilibrium with their carrier melts) crystallized within the South Caldera reservoir (∼3–5‐km depth). Melt inclusions in high‐Fo olivines experienced extensive post‐entrapment crystallization following their incorporation into cooler, more evolved melts. This favored the growth of a CO2‐rich vapor bubble, containing up to 99% of the total melt inclusion CO2 budget (median = 93%). If this CO2‐rich bubble is not accounted for, entrapment depths are significantly underestimated. Conversely, reconstructions using equation of state methods rather than direct measurements of vapor bubbles overestimate entrapment depths. Overall, we show that direct measurements of melts and vapor bubbles by secondary‐ion mass spectrometry and Raman spectroscopy, combined with a suitable H2O‐CO2 solubility model, is a powerful tool to identify the magma storage reservoirs supplying volcanic eruptions.

Discussion on evaluation method of water energy in strong water drive gas reservoir

In the process of gas reservoir development, as the pressure of gas reservoir decreases, water will invade into the gas reservoir and form a certain scale of water body, so it is very necessary to know the water body energy correctly. This paper takes strong water drive gas reservoir as an example, and uses equation of state method, pressure drop curve method and material balance method respectively to complete the water body energy evaluation of this block, so as to find the water body energy evaluation method suitable for strong water drive gas reservoir, which plays an important role in implementing water control measures.

Modelling and Thermodynamic Analysis of a Hot-Cold Conversion Pipe Using R134a-DMF-He as the Working Pair

Based on the concept of a diffusion absorption system, a hot-cold conversion pipe utilizing 1,1,1,2-tetrafluoroethane (R134a)-dimethylformamide (DMF)-helium (He) as the working pair is presented with the aim of cooling output by recovering the low-grade waste heat. The model of the hot-cold conversion pipe is established, in which a heat pipe is used to transfer the waste heat as the heat input. The equations of the thermodynamic properties of the working pair are established by equation of state method (EOS). The model of the hot-cold conversion pipe is built based on the mass, species and energy balance equations of each component. The direct conversion of heat to cold is achieved by the desorption, absorption, condensation and diffusion evaporation processes of R134a. The hot-cold conversion pipe is cooled by natural convection, which can be enhanced by chimney effect. The thermodynamic analysis is carried out to analyze the effect of the boundary conditions, i.e. the heat source temperature, the refrigeration temperature, and the environmental temperature, on the system performance. This paper provides a theoretical basis for actual application of the hot-cold conversion pipe in waste heat recovery field.

Elemental mercury partitioning in high pressure fluids part 2: Model validations and measurements in multicomponent systems

A good understanding of the solubility of elemental mercury over wide ranges of temperature, pressure and composition is an important issue to assess the possibility of mercury dropping out in gas processing streams. In this work, new mercury solubility in three multicomponent systems with methane content varying between 89 – 26 mol% have been measured over a wide range of temperature (243.15 to 323.15 K) and pressure and up to 20 MPa. A group contribution method for the Peng-Robinson equation of state has been used to allow calculation of binary interactions between mercury and saturated hydrocarbons, aromatic hydrocarbons, nitrogen and carbon dioxide. The parameters of the group contribution have been adjusted using mercury solubility previously measured in single components. Predictions of the developed model are validated against independent experimental data and the data generated in this work. A good agreement between predictions and experimental data is observed, supporting the reliability of the developed model.

Effects of Leaf Surface Energy on Pesticidal Performance

Surface energy is widely used in the industry to predict behavior of spray droplets on solid surfaces. The targets of pesticide applications which are used extensively in agricultural production are mainly plant leaf surfaces. Digitization of leaf surfaces to estimate the spread and adhesion of a pesticide application is an important approach in providing descriptive information. In this regards, from intensive agricultural products Triticum aestivum L., Citrus sinensis, Fragaria ananassa, Vitis vinifera L., Cucumis sativus, Capsicum annuum L. culture plants, Elymus repens and Sinapis arvensis from weeds were used to determine surface energy. The leaf surface energies were determined by evaluating the contact angles of the drips while obtained from surface tension and its components from known liquids pure water, diiodomethane and formamide liquids on the surface of the leaves according to five different methods. Wu and Equation of State methods have been found to give more accurate results than other methods. Elymus repens and Triticum aestivum L. plants among the statistically three significant grouped leaves were reduce the spreading and sticking of droplets applied on the leaves by providing a more spherical droplet formation. The Fragaria ananassa leaves have encouraged the higher surface energy that they have the spread of the drips on the leaf surface.

Evaluating Cubic Plus Association Equation of State Predictive Capacities: A Study on the Transferability of the Hydroxyl Group Associative Parameters

To create a predictive method for an associative equation of state, the parameters of a specific associative group should be transferrable among molecules. The hydroxyl group, one of the most common associative groups, is a good starting point for this development. On the basis of a previous study where a modified version of the Cubic Plus Association (CPA) EoS was shown to present accurate results for alkanols with almost constant association parameters, this work addresses branched, secondary alcohols, 1,ω-alkanediols, and glycerol to evaluate how CPA can handle steric hindrances and the presence of more than one hydroxyl group. The pure component properties studied here are vapor pressure, saturated liquid density, saturated liquid isobaric heat capacity, and heat of vaporization. Some VLE, LLE, and GLE of binary systems are also analyzed, showing how the modifications affect the description of binary/multicomponent systems. Some systems containing petroleum fluids are also analyzed.

Aligning observed and modelled behaviour based on workflow decomposition

ABSTRACTWhen business processes are mostly supported by information systems, the availability of event logs generated from these systems, as well as the requirement of appropriate process models are increasing. Business processes can be discovered, monitored and enhanced by extracting process-related information. However, some events cannot be correctly identified because of the explosion of the amount of event logs. Therefore, a new process mining technique is proposed based on a workflow decomposition method in this paper. Petri nets (PNs) are used to describe business processes, and then conformance checking of event logs and process models is investigated. A decomposition approach is proposed to divide large process models and event logs into several separate parts that can be analysed independently; while an alignment approach based on a state equation method in PN theory enhances the performance of conformance checking. Both approaches are implemented in programmable read-only memory (ProM). The correctness and effectiveness of the proposed methods are illustrated through experiments.

A first-principles study of the avalanche pressure of alpha zirconium

The critical swelling pressure, the avalanche pressure, is Pa = −15 GPa for alpha zirconium.

Measurement and Prediction Method of Compressibility Factor at High Temperature and High Pressure

In order to get the compressibility factorZof working fluid under different conditions, experimental measurement method ofZunder high pressure and high temperature and data mining method were studied in this paper. Experimental measurement method based on real gas state equation and prediction method based on Least Squares Support Vector Machine were proposed. First, an experimental method for measuringZat high temperature and high pressure was designed; in this method the temperature, pressure, and density (mass and volume) of corresponding state were measured and substituted into the actual gas equation of state, and thenZcan be calculated. Meanwhile, in order to obtain continuous value inT-pplane, Squares Support Vector Machines are introduced to establish the prediction model ofZ. Take Hexamethyldisiloxane, for example; the experimental data ofZwas obtained using the experimental method. Meanwhile the prediction model ofZ, which can be used as calculation function ofZ, was established based on those experimental data, and theZ(T: 500 K~800 K,p: 1.3 MPa~2.25 MPa) was calculated by using this calculation function. By comparison with this published data, it was found that the average relative error was 2.14%.

Method Based on Rough Set and Improved Petri Net for Transformer Faults Diagnosis

Oil chromatographic analysis is widely used in transformer fault diagnosis, but it is difficult to establish accurate maping relationship between the parameter space and the state space, and there is information complexity. This paper adopts the combined diagnostic model of rough sets and petri nets, firstlysimplifies the complex system which contains complicated discrete information by rough set to solve the state space limitations of Petri network; and improves petri network based on mining association rules, adopts the correlation matrix and state equation method to improve the reasoning speed, at the same time turns the diagnosis into matrix operations to change complex calculations to simple math which has certain applicability. Finally the algorithm is applied to gas chromatographic analysis in transformer oil, the calculation results is the same with IEC three ratio method, which proves that this method can quickly and accurately to judge the running state of transformer, so as to improve the safety, stability and economic operation of the flat water transformer.

Inter-atomic potential energy and Grüneisen parameter: A new method for equation of state of solids

This paper presents a rational foundation for the computation of equation of state (EOS) data for solids at high pressure. We demonstrate a new method which makes use of an accurate relation expressing the Grüneisen parameter γ (as a function of the specific volume V of the material) in terms of the specific inter-atomic potential energy ϕ(V). Existing expressions for γ in the literature are usually approximations in terms of total pressure P. There is a variety of such “(γ,P)” formulas and one needs experience in deciding which to use in any particular application. The alternative “(γ,ϕ)” relationship presented here is both unique and exact within the Debye and harmonic approximations and allows the individual terms of the EOS to be determined separately. It is rigorously derived in this paper and solved numerically, using experimental input data for aluminium, copper, lead and gold, to predict ϕ, dϕ/dV, γ, dγ/dV and EOS data for the four metals. Comparison is made with existing computations in the literature showing good agreement. The method can be applied to any metal or non-metal using experimental input data from any suitable volume-dependent locus.

Prediction of Vapor–Liquid Coexistence Data for p-Cymene Using Equation of State Methods and Monte Carlo Simulations

A naturally occurring aromatic organic compound, p-cymene, finds applications as reaction intermediate, solvent in production of pharmaceuticals, fragrances, and fine chemicals. The experimental vapor liquid equilibria (VLE) data of p-cymene is available at pressures up to 537.4 kPa. In this study, the thermodynamic properties of p-cymene are determined using structure property correlations combined with equations of state (EoS) and molecular simulation techniques. Two molecular simulation techniques, Gibbs ensemble Monte Carlo (GEMC) and grand canonical-transition matrix Monte Carlo (GC-TMMC) have been employed for prediction of VLE. The estimates of properties, including vapor pressures, heats of vaporization, coexistence densities, and critical properties have been compared with available experimental data. The thermodynamic properties predicted by molecular simulations and also that obtained from Peng–Robinson (PR) and volume translated Peng–Robinson (VTPR) EoS are generally, in broad agreement with the experimental data. Further, GEMC results for coexistence densities and saturation vapor pressures are compared with that from GC-TMMC technique.