Boundary Diagrams Research Articles

Nonlinear transverse vibrations of angle-ply laminated composite piezoelectric cantilever plate with four-modes subjected to in-plane and out-of-plane excitations

In this paper, the nonlinear vibrations of the laminated composite piezoelectric cantilever plate subjected to the transverse and in-plane excitations are investigated. Based on the Reddy’s third-order plate theory and von Karman nonlinear strain-displacement relation, the nonlinear partial differential governing equations of motion are established for the laminated composite piezoelectric cantilever plate under combined the transverse and in-plane excitations by applying Hamilton’s principle. Employing Galerkin’s approach, we discretize the continuous nonlinear dynamic equations of motion into the ordinary differential equations with four modes. Substituting the actual geometric and physical parameters of the laminated composite piezoelectric cantilever plate into the governing equation of motion, we use numerical method to investigate the effects of the lay-up parameters and the geometric parameters on the dimensionless natural frequencies of the cantilever plate. The amplitude-frequency response curves and the basin boundary diagram of two coexisting steady-state solutions are plotted for the laminated composite piezoelectric cantilever plate. The nonlinear dynamic responses of the laminated composite piezoelectric cantilever plate under combined the transverse and in-plane excitations are investigated by changing the lay-up parameters, the transverse excitation, the voltage excitation and the in-plane excitation. The periodic, the quasi-periodic, the chaotic motions and the nonlinear stiffness characteristics can be found. The nonlinear dynamic behaviors help us to optimize the structural and physical parameters of the laminated composite piezoelectric cantilever plate under combined the transverse and in-plane excitations.

Identification and optimization of thermally safe operating conditions for single kinetically controlled reactions with arbitrary orders in isoperibolic liquid-liquid semibatch reactors

To obtain thermally safe operating conditions for kinetically controlled liquid-liquid reactions occurring in isoperibolic semibatch reactors (SBRs), an extreme scenario in which the product (UA) of the overall heat transfer coefficient (U) and the area (A) is equal to its initial value, (UA)0, was studied and combined with the ideal scenario where the UA is proportional to the liquid volume. Under both scenarios, the jacket temperature evolution of the maximum temperature of synthesis reactions (MSTR) after cooling failure and the corresponding time (θMTSR) for isoperibolic liquid-liquid SBRs was thoroughly investigated, and it was found that four types of thermal behaviors, namely IS (inherently safe), NI (non-ignition), TR (thermal runaway) and QFS (quick onset, fair conversion and smooth temperature condition) can be effectively identified by the variations of θMTSR. Then, a thermal behavior identification criterion was proposed. Subsequently, a series of boundary diagrams based on the proposed criterion were developed along with the corresponding novel adiabatic temperature diagrams to directly provide information about the maximum value of MTSR in the case of cooling failure for any operating points in the boundary diagrams. Further, synthesizing the information from the boundary diagrams and the adiabatic temperature diagrams allows for convenient attainment of generalized thermally safe operating conditions with considerable practicability and sufficient thermal safety even in adiabatic situations.

A robust multiphase isenthalpic flash model for water/solvent/hydrocarbon systems at high pressures and elevated temperatures

Based on the assumption that only the presence of water and solvent is considered in the aqueous phase, a robust and pragmatic water-associated isenthalpic flash (WAIF) model has been developed to perform multiphase isenthalpic flash calculations for water/solvent/hydrocarbon mixtures at high pressures and elevated temperatures. More specifically, the phase boundary diagram in enthalpy-temperature (H-T) space is constructed first for a given water/solvent/hydrocarbon system at a specified pressure. Then, the phase transition enthalpies and temperatures are determined from the H-T diagram, and thus one-, two-, or three-phase isenthalpic flash calculations can be conducted directly without resorting to stability test for a given system at a specified enthalpy and pressure. In addition, a recursive method has been proposed to initialize the temperature so that the energy conservation equation and material balance equation can be solved simultaneously to overcome the convergence difficulties. The newly proposed isenthalpic flash model has been compared with the water-free isenthalpic flash (WFIF) model and conventional three-phase isenthalpic flash (CTIF) model through three case studies. The WAIF model is found to handle the narrow-boiling constraints effectively and accurately. Furthermore, as for Water/C3H8/C16H34 mixture and Water/CO2/C16H34 mixture, a good agreement is achieved between the WFIF model and the WAIF model as the solubility of solvents (i.e., C3H8 and CO2) in the aqueous phase is quite small. With respect to Water/dimethyl ether (DME)/C16H34 mixture, however, the WAIF model is found to more accurately predict the phase behaviour of water/solvent/hydrocarbon mixtures than the WFIF model since the solubility of DME in the aqueous phase cannot be neglected. The case studies demonstrate that the newly developed water-associated isenthalpic flash model for water/solvent/hydrocarbon systems is robust, efficient, and accurate.

Completion of thermal runaway criteria: Two new criteria to define runaway limits

Safe operation of thermally sensitive chemical reactors remains a crucial engineering issue. Thermal runaway occurs mainly due to loss of temperature control, and many chemical accidents initiated by thermal runaway can be foreseen by an appropriate analysis of thermal process data. Thermal runaway criteria can be applied to determine the onset of runaway phenomena and safety boundary diagrams can be constructed. However, several runaway criteria exist, which define the runaway-and safe zones differently. In this work nine commonly applied thermal runaway criteria were analyzed and compared based on their critical curves. As a result of this analysis, two new criteria were developed. Reliability of the derived criteria were investigated, where the occurrence of real runaway was determined based on the number of indications applying different criteria. The two new criteria were tested in three general reaction systems and in case a complex problem, where feeding trajectory of fed-batch reactor was optimized applying new criteria as non-linear constraint. One of the new criteria shows the highest reliability in indication of runaway development from all investigated runaway criteria.

Development of extended boundary diagrams to design thermally safe operating conditions for homogenous semibatch reactors

In our opinion, the thermally safe operating conditions for isoperibolic semibatch reactors (SBRs) should be characteristic of two terms: 1. conforming to QFS operating situation; 2. MTSR < MAT. Regretfully, the traditional boundary diagrams are only helpful for designing QFS operating conditions and can’t predict the value of MTSR. Hence, the extended boundary diagrams have been developed in this work. Using these extended boundary diagrams, not only QFS operating conditions can be identified, but also MTSR can be predicted. In addition, the predicted MTSR is suggested to add up Δτta before checking whether MTSR < MAT, because the value of UA at the end point of dosing period in a realistic case is lower than the ideal value of (UA)0(1 + ε). By this way conservative results will be obtained. Also, a procedure to identify thermally safe operating conditions for SBRs with the extended boundary diagrams is introduced in the last part.

PVTx and thermal-pressure coefficient measurements of the binary CO2 + n-decane mixtures in the critical and retrograde regions

Abstract PVTx and temperature derivative of pressure (thermal-pressure coefficient), γ VX = ( ∂ P / ∂ T ) VX , of binary CO2 + n-decane mixtures have been measured in the critical, supercritical, and retrograde condensation regions (near the critical and cricondenterm points). Most measurements were made in the immediate vicinity of the dew-, bubble, and the critical point curves (in the single – and two-phase regions) to precisely determine the phase boundary properties, T S , P bub , P dew , ρ S ′ , ρ S ″ , ( ∂ P / ∂ T ) VX ′ , and ( ∂ P / ∂ T ) VX ″ .The measurements have been made using a high-temperature, high-pressure, nearly constant-volume adiabatic piezo-calorimeter for three concentrations of 0.095, 0.178, and 0.263 mol fraction of n-decane over the temperature range: (for mixture-1, x = 0.095) from (292 to 567) K along the liquid and vapor densities between (89 and 659) kg·m−3 at pressures up to 28.3 MPa; (for mixture-2, x = 0.178) from (302 to 557) K along the liquid and vapor densities between (85 and 467) kg·m−3 at pressures up to 24.3 MPa; and (for mixture-3, x = 0.263) from (361 to 568) K along the liquid and vapor densities between (298 and 520) kg·m−3 at pressures up to 25.4 MPa. The combined expanded uncertainty of the density, ρ , pressure, P, temperature, T, concentration, x, and the thermal-pressure coefficient, γ VX , measurements at the 68% confidence level with a coverage factor of k = 2 is estimated to be (0.2–0.5)%, (0.5–1.0)%, 15 mK, 0.01 mol%, and (0.2–2.0)% (depending on temperature and pressure), respectively. The critical (the critical temperature, T C , the critical pressure, P C , and the critical density, ρ C ), cricondentherm, and cricondenbar point data of CO2 + n-decane mixture were derived as a function of concentration from phase boundary properties studied. The Krichevskii parameter and isomorphism of the critical behavior of the mixture were studied using the critical curve data for the mixture and vapor pressure data for the pure solvent (CO2). Features of the P S - T S phase boundary diagram and thermodynamic behavior of the mixture near the critical and cricondentherm points and in the retrograde region were observed.

Emergency call system definition via robustness structure in vehicle applications

The European Union Parliament introduced the legislation EU-2015/758 which includes the obligation of emergency call system equipped vehicles in the European countries with the starting date of 31 March 2018. After the regulation is started to be applied, new system updates and modifications in the vehicle systems are released. Emergency call (eCall) system can be applied to the vehicle structures with different types such as manual eCall device, automatic eCall device including control unit and/or measurement unit. When manual eCall device is triggered manually, automatic eCall device is activated automatically when an accident occurs. In this point of view, emergency call structure in the vehicle system is defined with its robust working principles including boundary diagram, P-diagram, and verification methods which enable the system to work properly.

Bifurcation behaviour of PWM controlled DC series motor drive

This study presents a detailed investigation on bifurcation of general period-1 behaviour in a pulse width modulation (PWM) controlled dc series motor drive system. Existence of quasi-periodic behaviour and different bifurcation routes are mainly explored for the drive system under voltage mode control. Occurrences of different types of bifurcations are also validated by computing Floquet multipliers. An algorithm is proposed to introduce a new concept for identification of various system parameters to operate the motor drive in stable period-1 mode. The algorithm is based on Newton-Raphson method and results obtained from the proposed algorithm are presented by stability boundary diagram. MATLAB simulations as well as experimental investigations are performed on a 500 W, 220 V, 1800 rpm dc series motor to study the qualitative behaviour of the motor drive system under variations of different control parameters and also to validate the proposed algorithm.

Looking for a bulk point

We consider Lorentzian correlators of local operators. In perturbation theory, singularities occur when we can draw a position-space Landau diagram with null lines. In theories with gravity duals, we can also draw Landau diagrams in the bulk. We argue that certain singularities can arise only from bulk diagrams, not from boundary diagrams. As has been previously observed, these singularities are a clear diagnostic of bulk locality. We analyze some properties of these perturbative singularities and discuss their relation to the OPE and the dimensions of double-trace operators. In the exact nonperturbative theory, we expect no singularity at these locations. We prove this statement in 1+1 dimensions by CFT methods.

Semi-batch reactors: Thermal runaway risk

The paper deals with the thermal safety and the runaway risk evaluation for semi-batch reactors (SBR). The main contributions consist in:-Construction of a new boundary diagram which describes the reaction temperature vs. target temperature and maximum allowable temperature in order to define the critical conditions for the thermal runaway;-Identification of the most important governing parameters;-Evaluation of the risk of accident by a probabilistic description of the prior cooling problem, the appropriate combination of the critical conditions and the assessment of occurrence probability of the thermal runaway accident.A heterogeneous liquid-liquid reacting system is considered as a case study. A sensitivity analysis is then performed in order to investigate the influence of cooling temperature on the maximum reaction temperature. Monte Carlo simulations are also used in order to calculate the probability of accidents.

Closed-Loop Design for Standalone Photovoltaic-Battery Hybrid Power System

The photovoltaic-battery hybrid power system is constructed with photovoltaic panels and a battery, which are connected to the load via a boost converter and a bidirectional buck/boost converter, respectively. Depending on the amount of available solar power, the photovoltaic panels may operate in a maximum power point tracking (MPPT) mode or off-MPPT mode to regulate the output voltage, and at the same time, the battery may provide power to the load or store energy from the solar power. The whole system is thus designed to operate with multiple operating modes. Compared to the system of single operating mode, the stability analysis and closed-loop design is much more difficult, as the control loops are usually coupled with each other and the design for stable operation of such system requires consideration of the stability conditions for all possible operating modes. To design the closed-loop, the commonly used small-signal analysis method based on averaged state-space is helpless here, and then the nonlinear analysis method with discrete-time mapping model is performed to evaluate the stability boundaries of the system. The parameters of the closed-loop are chosen in the stable region of the stability boundary diagrams. Moreover, a prototype is built and the experimental results are shown to verify the nonlinear analysis method in the design of closed-loop.

Safer operating conditions and optimal scaling-up process for cyclohexanone peroxide reaction

The cyclohexanone peroxide reaction process, one of the eighteen hazardous chemical processes identified in China, is performed in indirectly cooled semibatch reactors. The peroxide reaction is added to a mixture of hydrogen peroxide and nitric acid, which form heterogeneous liquid–liquid systems. A simple and general procedure for building boundary and temperature diagrams of peroxide process is given here to account for the overall kinetic expressions. Such a procedure has been validated by comparison with experimental data. Thermally safer operating parameters were obtained at laboratory scale, and the scaled-up procedure was performed to give the minimum dosing time in an industrial plant, which is in favor of maximizing industrial reactor productivity. The results are of great significance for governing the peroxide reaction process apart from the thermal runaway region. It also greatly aids in determining optimization on operating parameters in industrial plants.

Developing grain boundary diagrams for multicomponent alloys

Impurity-based, premelting-like, intergranular films (IGFs, a common type of grain boundary complexion) can form in various materials and influence sintering, creep, and microstructure development. A thermodynamic framework is presented to forecast the formation and stability of these premelting-like grain boundary complexions (a.k.a. interfacial “phases” that are thermodynamically two dimensional) in multicomponent alloys to consider the interactions of multiple alloying elements. Key thermodynamic parameters that control the interfacial segregation and disordering behaviors have been identified and systematically examined. Subsequently, ternary and quaternary grain boundary diagrams have been computed and used to forecast the sintering behaviors of W–Ni–M (M=Fe, Co, Cr, Zr, Nb and Ti) and Mo–Si–B–M (M=Ni, Co and Fe) systems. This work supports a long-range scientific goal of extending bulk computational thermodynamics and CALPHAD methods to interfaces and developing grain boundary complexion (interfacial “phase”) diagrams as extensions to bulk phase diagrams, which can be a generally useful materials science tool.

Boundary Diagrams Safety Criterion for Liquid Phase Homogeneous Semibatch Reactors

In this work a summary of safety assessments based on a concept of boundary diagrams safety criterion (BDSC) is given and adapted for liquid phase homogeneous reactions carried out in batch and semibatch reactors. First, on the basis of theoretical considerations, the operating diagrams have been elaborated, which make possible a selection of safe or inherently safe operating conditions for any liquid homogeneous reaction, even with limited information on the reaction kinetics. To use the proposed method, a detailed reaction mechanism is not required; only fundamental kinetic information is necessary. Usually, the reaction kinetic constants at two chosen temperatures should be determined. Next the reaction enthalpy and a few well-known parameters used for characterization of the reacting system are utilized. The proposed approach is crucial for practical applications of this method, because in industrial practice—e.g., in the fine chemicals industry—usually there is no time and there are no funds for detailed investigations of the reaction kinetics. The proposed BDSC method has been verified with our own experimental data. Despite the fact that this method has been developed for a single second order reaction, it can be conservatively applied also for reactions of an order different from two as well as for parallel reactions.

Selectivity problem for fine chemical reactions leading to non volatile products: Process configuration and boundary diagrams

In the fine chemical and pharma industry a number of reaction processes undergo selectivity losses since the target product (typically a low volatility compound) can further react with one of the reactants leading to by-products that must be separated from the target product itself and finally disposed as wastes. In such a situation, even performing the reaction in a standard semi-batch reactor requires a large excess of one reactant to limit the selectivity drop. However, operating the reactor with a large excess of one reactant lowers the reactor productivity. In this work, a process configuration is discussed that, limiting the target product accumulation in the reactor, allows achieving both high process selectivity and high reactor productivity. Moreover, general and easy to use boundary diagrams have been developed, through which the optimal process operating parameters can be easily estimated without solving the mathematical model of the system. Several boundary diagrams are provided for different systems together with a general procedure for their use.

Developing grain boundary diagrams as a materials science tool: A case study of nickel-doped molybdenum

Impurity-based, premelting-like, grain boundary (GB) ``phases'' (complexions) can form in alloys and influence sintering, creep, and microstructural development. Calculation of Phase Diagrams (CalPhaD) methods and Miedema-type statistical interfacial thermodynamic models are combined to forecast the formation and stability of subsolidus quasiliquid GB phases in binary alloys. This work supports a long-range scientific goal of developing ``GB (phase) diagrams'' as a new materials science tool to help controlling the materials fabrication processing and resultant materials properties. Using nickel-doped molybdenum as a model system, a type of GB diagram (called ``\ensuremath{\lambda} diagram'') is computed to represent the temperature- and composition-dependent thermodynamic tendency for general GBs to disorder. Subsequently, controlled sintering experiments are conducted to estimate the GB diffusivity as a function of temperature and overall composition, and the experimental results correlate well with the computed GB diagram. Although they are not yet rigorous GB-phase diagrams with well-defined transition lines, the predictability and usefulness of such \ensuremath{\lambda} diagrams are demonstrated. Related interfacial thermodynamic models and computational approaches are discussed.

Complete closed-form solutions of the Stark problem

Perturbed two-body problems play a special role in Celestial Mechanics as they capture the dominant dynamics for a broad range of natural and artificial satellites. In this paper, we investigate the classic Stark problem, corresponding to motion in a Newtonian gravitational field subjected to an additional uniform force of constant magnitude and direction. For both the two-dimensional and three-dimensional cases, the integrals of motion are determined, and the resulting quadratures are analytically integrated. A complete list of exact, closed-form solutions is deduced in terms of elliptic functions. It is found that all expressions rely on only seven fundamental solution forms. Particular attention is given to ensure that the expressions are well-behaved for very small perturbations. A comprehensive study of the phase space is also made using a boundary diagram to describe the domains of the general types of possible motion. Numerical examples are presented to validate the solutions.

Safe operating conditions for semibatch processes involving consecutive reactions with autocatalytic behavior

When strongly exothermic chemical processes are dealt with, safe and productive operating conditions may be difficult to identify; particularly if the reaction scheme is complex and the desired product is an intermediate. In this work, a new procedure for building boundary and temperature diagrams is developed to account for arbitrary kinetic expressions and multiple reactions. Such a procedure has been validated by comparison with literature experimental data involving autocatalytic consecutive reactions.

Simple Procedure for Optimally Scaling-up Fine Chemical Processes. I. Practical Tools

A simple and general scale-up procedure, based on boundary and temperature diagram safety criteria for exothermic semibatch reactors (SBRs), has been developed. Such a procedure is based on a few graphical correlations that allow end users, dealing with homogeneous as well as heterogeneous SBRs (with or without autocatalytic behavior), an easy selection of safe operating conditions at the laboratory scale and for their scale-up to the industrial one, maximizing at the same time the industrial reactor productivity.

Safe and Productive Operation of Homogeneous Semibatch Reactors Involving Autocatalytic Reactions with Arbitrary Reaction Order

In this work a procedure for easily selecting safe and productive operating conditions of homogeneous semibatch reactors in which exothermic autocatalytic reactions are performed is developed and presented. Such a procedure is based on the boundary and temperature diagram method previously proposed in the literature for nonautocatalytic reactions. In the autocatalytic case an additional parameter appears in the mathematical model of the reactor as well as in the safety criterion, that is, the initial catalyst amount which is directly related to the coreactant accumulation in the system. A number of diagrams for identifying inherently safe operating conditions is provided, together with some rules of thumb for their use, allowing for easily selecting safe and productive operating conditions of homogeneous semibatch reactors in which exothermic reactions with autocatalytic behavior occur.