Safe Operating Region Research Articles

Numerical analysis of unsteady flow under high‐head operating conditions in Francis turbine

PurposeThe purpose of this paper is to describe how the hydraulic performance and pressure fluctuations in the entire flow passage of a Francis turbine were predicted numerically for the highest head. The calculations are used to partition the turbine operating regions and to clarify the unsteady flow behavior in the entire flow passage including the blade channel vortex in the runner and vortex rope in the draft tube.Design/methodology/approachThree‐dimensional unsteady numerical simulations were performed for a number of operating conditions at the highest head. The unsteady Reynolds‐averaged Navier‐Stokes equations with the k‐ω based SST turbulence model were solved to model the unsteady flow within the entire flow passage of a Francis turbine.FindingsThe predicted pressure fluctuations in the draft tube agree well with the experimental results at low heads. However the peak‐to‐peak amplitudes in the spiral case are not as well predicted so the calculation domain and the inlet boundary conditions need to be improved. The unsteady simulation results are better than the steady‐state results. At the most unstable operating condition of case a0.5h1.26, the pulse in the flow passage is due to the rotor‐stator interference between the runner and the guide vanes, the blade channel vortex in the runner blade passage and the vortex rope in the draft tube.Originality/valueThis study investigates the characteristics of the dominant unsteady flow frequencies in different parts of the turbine for various guide vane openings at the highest head. The unsteady flow patterns in the turbine, including the blade channel vortex in the runner and the helical vortex rope in the draft tube, are classified numerically, and the turbine operating regions are partitioned to identify safe operating regions.

Operating Regions in Cooling Cocrystallization of Caffeine and Glutaric Acid in Acetonitrile

A complete temperature-dependent solute−solute−solvent phase diagram is an essential starting point for cooling cocrystallization process development. In this study, the phase diagram of caffeine−glutaric acid−acetonitrile in the temperature range of 10−35 °C was charted using attenuated total reflectance−Fourier transform infrared (ATR-FTIR) spectroscopy to measure concentrations in situ. Solution-mediated phase transformation was exploited to locate the eutectic points. The operating region was then prescribed according to the stoichiometry of the cocrystal, and the boundary of stability zones at the initial and final temperatures of cooling crystallization. It was demonstrated that cocrystal purity could be compromised when crystallization occurs outside the safe operating region. The complete phase diagram has laid the foundation for further cocrystallization process development of the model system.

Influence of the operation pressure on slug length in near horizontal gas–liquid pipe flow

Slug flow is commonly observed in gas production offshore fields. At high operation pressure only short hydrodynamic slugs are observed. However, as the offshore fields become older, the operation pressure becomes lower and long slugs may form. At near atmospheric pressures the long slugs may reach a size of 500 pipe diameters or more. Such slugs can cause serious operational failures due to the strong fluctuating pressure. Identifying the operation pressure conditions at which the long slugs appear, may reduce or prevent these negative effects. In this paper we process and analyse gas–liquid flow measurements in order to investigate the different slug types and their sensitivity to the operation pressure. The measurements were performed in a 103 m long pipe with an internal diameter of 0.069 m and an inclination of −0.1° from the horizontal. Three types of slugs were categorized according to the difference in liquid levels (liquid excess) between the slug front and tail. The long slugs were found to have the largest liquid excess after formation, whereas the hydrodynamic slugs had no liquid excess. The analysis of the measurements provides a detailed overview on the effect of pressure on the long slug length, and a safe operation region where long slugs will not appear.

Detection of Safe Operating Regions: A Novel Dynamic Process Simulator Based Predictive Alarm Management Approach

The operation of complex production processes is one of the most important research and development problems in process engineering. A safety instrumented system (SIS) performs specified functions to achieve or maintain a safe state of the process when unacceptable or dangerous process conditions are detected. A logic solver is required to receive the sensor input signal(s), to make appropriate decisions based on the nature of the signal(s), and to change its outputs according to user-defined logic. The change of the logic solver output(s) results in the final element(s) taking action on the process (e.g., closing a valve) to bring it back to a safe state. Alarm management is a powerful tool to support the operators’ work to control the process in safe operating regions and to detect process malfunctions. Predictive alarm management (PAM) systems should be able not only to detect a dangerous situation early enough, but also to give advice to process operators which safety action (or safety element(s)) must be applied. The aim of this paper is to develop a novel methodology to support the operators how to make necessary adjustments in operating variables at the proper time. The essential of the proposed methodology is the simulation of the effect of safety elements over a prediction horizon. Since different manipulations have different time demand to avoid the evolution of the unsafe situation (safety time), the process operators should know which safety action(s) should be taken at a given time. For this purpose a method for model based predictive stability analysis has been worked out based on Lyapunov’s stability analysis of simulated state trajectories. The proposed algorithm can be applied to explore the stable and unstable operating regimes of a process (set of safe states), information that can be used for PAM. The developed methodology has been applied to two industrial benchmark problems related to the thermal runaway.

Variability of operating safety limits with catalyst within a fixed-bed catalytic reactor for vapour-phase nitrobenzene hydrogenation

The safety in operation of a fixed-bed catalytic reactor remains a sensitive issue when a highly exothermic reaction is conducted and various process development elements such as controllability, stability, risk, and economic aspects are considered. Several model-based methods are used to estimate the safe operating region limits. Nominal conditions are set to limit the hot spot in the tubular reactor and avoid excessive thermal sensitivity to variations in the process parameters. When the catalyst or its characteristics are changed, the operating conditions have to be adjusted accordingly. The safety problem becomes more important when the production optimization requires setting the nominal operating point in the vicinity of the safety limits. This paper investigates the advantages as well as the precautions that need to be taken when using a more sophisticated model-based global sensitivity criterion (MV of Morbidelli & Varma) to routinely update the runaway critical conditions when changes in the investigated system frequently occur. A concrete example is provided for the case of an industrial fixed-bed catalytic reactor for nitrobenzene hydrogenation in vapour-phase. The analysis points out the discrepancies in predicting the runaway boundaries for complex processes between precise sensitivity-based MV-method and shortcut methods, and the importance of accounting for parameter uncertainty for both evaluation of the confidence region around the runaway boundaries and for the optimal set-point location. The close connection between the operating risk limits and the process kinetics is also highlighted even if the reactor geometry and the main flow conditions are kept unchanged.

Decision tree and first-principles model-based approach for reactor runaway analysis and forecasting

Decision trees (DTs) are effective in extracting linguistically interpretable models from data. This paper shows that DTs can also be used to extract information from process models, e.g. they can be used to represent homogenous operating regions of complex process. To illustrate the usefulness of this novel approach a detailed case study is shown where DTs are used for forecasting the development of runaway in an industrial, fixed bed, tube reactor. Based on first-principles knowledge and historical process data the steady-state simulator of the tube reactor has been identified and validated. The runaway criterion based on Ljapunov's indirect stability analysis has been applied to generate a data base used for DT induction. Finally, the logical rules extracted from the DTs are used in an operator support system (OSS), since they are proven to be useful to describe the safe operating regions. A simulation study based on the dynamical model of the process is also presented. The results confirm that by the synergistic combination of a DT based on expert system and the dynamic simulator a powerful tool for runaway forecasting and analysis is achieved and it can be used to work safe operating strategies out.

Transient Capability of Superconducting Devices on Electric Power Systems

Superconducting devices operating within a power system are expected to go through transient overload conditions during which the superconducting coil has to carry currents above the rated values. Designing the coil to remain superconducting through any possible fault scenario can be cost prohibitive, necessitating operation beyond the critical current for short periods. In order to set operating limits and design adequate protection systems for superconducting devices connected to a power system, the region of safe operation of these devices has to be described with general capability curves. Existing standards that define limits for these over-current situations are based on copper winding experience that do not apply to devices with superconducting components because of the highly nonlinear interaction between magnetic fields, operating temperature, and current density in the superconductor, and the rapidly varying material properties at cryogenic temperatures. In this paper, the behavior of superconducting coils during over-currents is discussed and a simplified capability curve is described to help standardize device capabilities. These curves are necessary to aid power system designers in appropriately designing the system and associated protection systems.

Thermal and Metallurgical Modelling of Laser Transformation Hardened Steel Parts

When applying laser transformation hardening (LTH) on a steel part the aim is to harden a localized area, which results in high hardness value for a defined width and depth of the material. To assure the hardened zone and keep the maximum temperature of the surface below the melting point we have used a finite element model (FEM) to compute the solution for heat distributions and the phase transformation of the material during LTH. Modelling results were used to introduce safe operating regions for LTH with different processing conditions. A problem associated with some LTH applications is the necessity to overlap the hardening passes. The temperature distribution of this phenomenon was also modelled using FEM which truly assist in finding optimum overlapping and technological parameters.

Topology Optimization for an Evolutionary Design of a Thermal Protection System

An optimal thermal protection system design for a spacecraft operating in extreme environments of thermal and acoustic loading is of significant importance for today's military space missions. These military space missions tend to push the envelope of the spacecraft's capabilities to the extreme, requiring robust performance of all key systems to assure a successful mission. Because thermal protection system protects the entire spacecraft, its survival from these extreme conditions is critical to the safety of the mission. The design criteria for the thermal and acoustic loading conditions tend to be conflicting. To reduce thermal stress, free boundaries that allow for expansion of the thermal protection system are desirable. However, the random sound pressure level fluctuations associated with, for example, engine noise during ascent, subject the thermal protection system to a wide-band random excitation. Therefore, if the thermal protection system possesses low frequency modes, damaging strains could result. To limit the magnitude of the strains, higher frequency (stiffer) designs with fixity at the boundary are desirable. Therefore, when designing the thermal protection system within these two simultaneous operating environments, the safe operating region is often severely restricted. This research aims at evolving a design that satisfies these two design requirements.

Nonlinear dynamics of a sliding beam on two supports under sinusoidal excitation

This study deals with the nonlinear dynamics associated with large deformation of abeam sliding on two-knife edge supports under external excitation. The beam is referred to as a Gospodnetic-Frisch-Fay beam, after the researchers who reported its static deformation in closed form. The freedom of the beam to slide on its supports imparts a nonlinear characteristic to the force-deflection response. The restoring elastic force of the beam possesses characteristics similar to those of the roll-restoring moment of ships. The Gospodnetic-Frisch-Fay exact solution is given in terms of elliptic functions. A curve fit of the exact solution up to eleventhorder is constructed to establish the governing equation of motion under external excitation. The dynamic stability of the unperturbed beam is examined for the damped and undamped cases. The undamped case reveals periodic orbits and one homoclinic orbit depending on the value of the initial conditions. The response to a sinusoidal excitation at a frequency below the linear natural frequency is numerically estimated for different excitation amplitude and different values of initial conditions covered by the area of the homoclinic orbit. The safe basins of attraction are plotted for different values of excitation amplitude. It is found that the safe region of operation is reduced as the excitation amplitude increases

Nonlinear Dynamics of a Sliding Beam on Two Supports and its Efficacy as a Non-Traditional Isolator

This study deals with the nonlinear dynamics associated with large deformations of a beam sliding on two knife-edge supports under external excitation. The beam will be referred to as Gospodnetic-Frisch-Fay beam, after the researchers who reported its static deformation in a closed form. The freedom of the beam to slide on its supports imparts a nonlinear characteristic to the force-deflection response. The restoring elastic force of the beam possesses characteristics similar to those of the roll restoring moment of ships. The Gospodnetic-Frisch-Fay exact solution is given in terms of elliptic functions, and a curve fit of the exact solution up to eleventh-order is constructed to establish the governing equation of motion under external excitation. The dynamic stability of the unperturbed beam is examined for the damped and undamped cases. The undamped case reveals periodic orbits and one homoclinic orbit depending on the initial conditions. The steady state response and transmissibility of the beam are predicted using multiple-scales method and numerical simulation. The transmissibility of the nonlinear beam outperforms linear isolators only at the linear resonance frequency. The response to a sinusoidal excitation at a frequency below the linear natural frequency is numerically estimated for different excitation amplitudes and different values of initial conditions covered by the area of the homoclinic orbit. The safe basins of attraction are plotted for different values of excitation amplitude. It is found that the safe region of operation is reduced as the excitation amplitude increases. Under random excitation, the response probability density function is obtained in a closed form and the response mean energy is found to depend nonlinearly on the excitation spectral density.

Theory of electrothermal behavior of bipolar transistors: part III-impact ionization

A detailed theoretical and numerical analysis of single-finger and two-finger bipolar transistors is proposed, which includes both self-heating and impact-ionization effects. Although related to completely different physical phenomena, self-heating and impact ionization share a common feature in that they introduce a positive feedback mechanism that causes the same singularities in the current-voltage characteristics, namely, a snapback (or flyback) behavior and current bifurcation. These singularities are triggered if either one or both effects are activated. Based on a rigorous mathematical referred to as the Jacobian method, generalized conditions are derived for determining the onset of flyback and bifurcation, which ultimately limit the safe operating region, as a result of the combined action of impact ionization and self-heating. The proposed formulation also includes several important effects not considered in previous contributions. Finally, a detailed analysis of the limiting boundaries for safe device operation is presented, and simple criteria for the optimal choice of the ballasting network are suggested

Reactivity investigation of mixtures of propane and nitrous oxide

AbstractSupercritical and vapor‐phase reactions of oxidizers and fuels under pressure are of commercial interest. Because mixtures of propane and nitrous oxide have the potential to be explosive, a model mixture was studied with the intent of defining safe operating boundaries. This work investigated the nitrous oxide/propane oxidant/fuel system, diluted with the inert solvent carbon dioxide, and a catalyst as an accelerant, to determine the safe operating regions for the oxidation reaction. Using an ARC® calorimeter for the evaluations, variables included initial system density, catalyst, and mixture compositions. Density of the system ranged from 0.05 to 0.62 g/cm3. A number of catalysts were investigated with 10% Pd on carbon being the most active. Strongest reactivity was observed when the mixture was stoichiometric to the complete combustion products of nitrogen, carbon dioxide, and water. Three distinct regions of reactivity were observed: mild reactivity (starting at the sensitivity of the ARC of dT/dt = 0.02 to about 0.1° C/min); strong exothermic reaction (dT/dt ≅ 1° C/min); and flammable and/or explosive (a distinct and substantial jump in dP/dt in <1 s). As a result, a boundary has been proposed for safe mixtures of nitrous oxide, propane, and carbon dioxide, and a basis for determining safe operating compositions for other systems. The computed adiabatic reaction temperature was used to correlate the experimental results to establish the boundary for safe operation. © 2005 American Institute of Chemical Engineers Process Saf Prog, 2005

Theory of Electrothermal Behavior of Bipolar Transistors: Part I—Single-Finger Devices

A detailed theoretical and numerical analysis of the electrothermal behavior of single-finger bipolar transistors is proposed. Two models of different complexities are introduced to investigate self-heating effects in bipolar junction transistors (BJTs) and heterojunction bipolar transistors (HBTs) biased with a constant base-emitter voltage source or with a constant base current source. In the constant base-emitter voltage case, simple relations are derived for determining the onset of the flyback behavior in the output characteristics which defines the boundary of the safe operating region. The model indicates that the flyback behavior disappears at high V/sub BE/ values, and predicts a thermal hysteresis phenomenon at high currents. It is also shown that at high current levels the electrothermal behavior is dominated by ohmic base pushout. If a constant base current is applied, the model shows that both BJTs and HBTs are unconditionally thermally stable. The transient behavior is also considered, and the temperature evolution is investigated for different bias conditions. The model shows that, if the device is biased in the thermally unstable region, thermal breakdown occurs within a finite time instant in the limit case of a zero ballast resistance. Finally, the reduction in the safe operating area due to avalanche effects and to the temperature dependence of thermal conductivity is discussed, and a simplified model is proposed.

Bounds on Operating Conditions Leading to Melting during Olefin Polymerization

We present a novel, simple method for predicting the operating conditions under which overheating by gas-phase exothermic olefin polymerization may lead to melting. The boundaries of the operating regions which can lead to melting are constructed using a simple, pseudo-steady, lumped thermal model which ignores temperature gradients within the particle and assumes that the active-sites distribution is uniform within growing polymer particles. It is shown that intraparticle temperature rise has a negligible impact on the boundaries of the safe region. The boundary of the unsafe operating region of the simple model is adequate also for predicting melting by dynamic models, such as the multilayer and polymeric-flow models. The region of safe operation can be increased by decreasing the initial particle diameter or the loading of the catalyst. The predicted boundaries of safe operating conditions are somewhat conservative as the simple model does not account for the time during which the particle heats to att...

Impact ionization measurements and modeling for power PHEMT

A systematic study of impact ionization in pseudomorphic high electron mobility transistors (PHEMTs) has been carried out using temperature-dependent electrical measurements as well as modeling for optimizing the power performance of the devices through the best layout parameters. A measurement procedure makes it possible to define a safe transistor operation region is proposed. Impact ionization in the channel is parameterized by specific gate current and voltage values. Temperature-dependent measurements are shown to provide distinction between the impact ionization current and the thermionic field emission current. A methodology for defining an optimum vertical structure and a lateral layout for a given application and operational conditions is developed. Empirical models for optimum lateral layout for a power application were developed based on a statistical Device Zoo approach. The results point to an optimal gate-to-drain distance for minimum impact ionization current.

The effect of vertical emitter ballasting resistors on the emitter current crowding effect in heterojunction bipolar transistors

In order to improve thermal stability and extend their safe operation region, epitaxial emitter ballasting resistors have been incorporated into power heterojunction bipolar transistors (HBTs). In this report, we show that this lightly doped layer not only can function as ballasting resistors used in multi-finger power HBT cells, but also can reduce the emitter current crowding effect which is an important limitation in bipolar transistors operating at high emitter current densities.

Steady-state operability characteristics of idealized reactors

Operability analysis is one of the bridges that links process design and control. In this paper, we analyze the steady-state operability characteristics of classical reactors (CSTR and PFR) in the framework of Vinson and Georgakis (DYCOPS-5, Fifth IFAC Symposium on Dynamics and Control of Process Systems, 1998, pp. 700–709; J. Proc. Control 10 (2000) 185). Reaction schemes vary from simple first-order A→B to industrially relevant competing reactions. The nonlinear nature of reactors requires the use of special computational techniques for the determination of the operability index (OI). This study clearly brings out the potential of the OI framework. In addition to measuring the servo, regulatory, and overall operability of the systems studied, we were able to identify safe operating regions and tolerable disturbances with the available inputs. This analysis also points to optimized process conditions.

MBE grown vertical emitter ballasting resistors to reduce the emitter current crowding effect in heterojunction bipolar transistors

In order to improve thermal stability and extend their safe operation region, epitaxial emitter ballasting resistors have been incorporated into power heterojunction bipolar transistors (HBTs). In this report, we show that this lightly doped layer not only can function as ballasting resistors used in multi-finger power HBT cells, but also can reduce the emitter current crowding effect which is an important limitation in bipolar transistors operating at high emitter current densities.

Continuously stirred decanting reactor: Operability and stability considerations

AbstractA continuously stirred decanting reactor (CSDR) is a well‐mixed vessel fed with two immiscible liquid phases, while its effluent consists of a single phase containing the reaction products. We consider a CSDR in which a desired highly exothermic reaction occurs in one phase, while an undesirable exothermic side reaction occurs in the second extracting phase. The holdup of the two phases in the CSDR is sensitive to its temperature. Thus, the reactor has to be kept in a narrow temperature range to avoid break‐through, that is, with effluent containing both phases, and to maintain a high selectivity of the desired product. Pilot‐plant data for a proprietary selective‐oxidation process verified the predictions of the steady‐state model.A high rate of heat generation may lead to various exotic and undesired periodic and aperiodic oscillations, which may shift the reactor out of the region of safe operation and have deleterious impact on the decantation efficiency. In some cases, the oscillations lead to a breakthrough during part of the period. To avoid these oscillatory states, one may have to maintain a sufficiently small difference between the reactor and coolant temperatures. We show how loci of local and global singular points of codimension 1 and 2 can be used to construct maps of parameter regions with qualitatively different steady‐state and dynamic bifurcation diagrams. These maps clearly describe the desirable regions of operation and point out all the potential stability and operability issues in other regions.