Stability Map Research Articles

An improved reduced order model for nonlinear stability analysis of spatial xenon oscillations

In this paper, an improved reduced order model for studying spatial xenon oscillations has been developed which can be utilized for stability analysis (linear as well as nonlinear). The model presented in this paper has been developed to overcome situations of unphysical results which were obtained by earlier models which used quasi static assumption when the system moves away from the equilibrium point. The earlier model consisted of multipoint neutron kinetics equations including xenon and iodine feedback. In order to eliminate unphysical behaviour in the earlier model, the quasi-static approach is discarded and the total power control is represented by an ordinary differential equation. It represents the action of a reactivity device governed by the deviation of the total power from the steady state power level. In the current approach, a PHWR is modelled by dividing it into two regions. The linear and nonlinear stability analysis was carried out using the new model and compared with the older results. Linear stability maps were constructed in different parameter planes and were found to be identical. However, there was a change in the nonlinear characteristics of the system and the results are presented in this paper. Moreover, the effect of control device on the system behaviour especially on total power variation is studied through numerical simulations.

Mechanical characterization and deformation behavior of β-stabilized Ti-Nb-Sn-Cr alloys

A serial of Ti-25 wt% Nb-(1, 3, 5) wt% Sn-(2, 4) wt% Cr alloys were designed with aim to obtain a single β phase matrix in the microstructure for high performance. The newly designed alloys were produced through cold crucible levitation melting to characterize the effect of Cr and Sn on the microstructure, phase constitution and mechanical properties of the titanium alloys. All the investigated alloys display a monolithic β phase microstructure and exhibit high maximum strength (∼5 GPa) as well as superior plasticity (∼80%, without failure even though the maximum load limit is reached at the load capacity of 100 kN). Deformation mechanism is anticipated on the basis of twins and slip band patterns obtained in the vicinity of micro-hardness indentation, Bo¯-Md¯ phase stability map and e/a¯-Δr¯ diagram. Moreover, shear band analyses on deformed samples are also conducted. Additionally, the evaluation of wear resistance indices (H/E and H3/Eeff2) are employed in the present work. Amongst all the investigated alloys, Ti-25Nb-1Sn-2Cr shows the lowest Young’s modulus (66 GPa) with the highest values of yield strength, hardness and wear resistance indices.

Aeroelastic behaviour of a parameterised circulation-controlled wing

The aeroelastic behaviour of the wing of a short take-off and landing aircraft using the Coandă effect depends on its properties and shape. An existing reduced-order model is parameterised for detailed investigations. On the one hand, varying mass due to tank level and varying overall stiffness is implemented in the reduced-order model. The influence of the mass change on the aeroelastic behaviour is reflected in the stability maps. On the other hand, two-dimensional steady and unsteady aerodynamics of different nose shapes are investigated with detailed computational fluid simulations and included in the reduced-order model. The dependence on the profile shape and the frequency is described. Their influence on the aeroelastic behaviour is reflected by the stability maps as well.

Landscape Conservation Planning to Sustain Ecosystem Services under Climate Change

Sustainable conservation aims to ensure the sustained conservation of landscape multi-functionality which in turn requires ensuring ecosystem service (ES) and habitat quality (HQ) sustainability with inclusive landscape-scale conservation planning. This study proposes a landscape conservation planning (LCP) framework for landscape-scale ES-HQ conservation and sustainability. Spatially explicit hotspots for five ESs and HQs are identified via InVEST and LISA software. Spatiotemporal changes in ES-HQ hotspots, in terms of stability and resilience, are delineated. The Zonation technique is applied to prioritize areas for conservation based on ES-HQ hotspot stability and resilience maps. High priority conservation areas are identified and are used as reserve area inputs for land use modeling with CLUE-S software to simulate future land use change under climate change scenarios. This study reports that varied rainfall and climate are major driving factors of ES-HQ sustainability disturbance in the study area. Furthermore, our proposed conservation Strategy 2 demonstrates that a larger extent of landscape multi-functionality can be sustained when the existing conservation area includes the total area of identified ES-HQ resilient hotspots. This study effectively identifies the stability and resiliency of ES-HQ hotspot areas affected by disturbances for high priority landscape conservation requirements to ensure ES-HQ sustainability and landscape multi-functionality in the study area.

Heat transfer and instability characteristics of a loop thermosyphon with wide range of filling ratios

A series of experiment using flow visualization technique and simultaneous measurement of pressure and temperature signals, are conducted to thoroughly investigate the heat transfer and instability characteristics in a loop thermosyphon with filling ratios ranging widely from 38% to 87% over a broad range of input heat flux from 35 to 395 W cm−2. The filling ratios are classified into three groups based on their distinctive heat transfer and instability behavior. The effects of filling ratio, input heat flux and inclination angle on the temperature nonuniformity, thermal resistance and instability features are examined in detail. The results show that, under the high filling ratios, the heat transfer capacity is seriously limited by the phase-change suppression and the consequent pressure soaring, while is advantageous in avoiding the evaporator dryout. Under the moderate filling ratios, the heat transfer capacity could be significantly higher, but the geyser boiling instability is obvious for a relatively large range of input heat flux, inducing the fluctuation of pressure and temperature. Under the low filling ratios, the heat transfer capacity is the highest; however, the transient local “Near-dryout” is easier to occur, causing large temperature overshoot and oscillation. The different variation trends of thermal resistance and temperature nonuniformity with filling ratios and input heat flux can generally be explained by the variation of the portions of latent and sensible heat transfer. Under the moderate and high filling ratios, the loop thermal resistance decreases somewhat with the decrease of inclination angle due to the elongation of the phase-change surfaces. A thermodynamic state diagram is drawn, indicating the measured average pressure - temperature of the working fluid at the evaporator for the three groups of filling ratios, with distinctly different instability issues, along with the saturation line to aid in the mechanism analysis and trouble diagnosis. A stability map in terms of the phase change number, Npch, and the filling ratio is presented, in which the boundaries dividing the different types of instability and the stable conditions are marked as a guidance for practical design and operation.

Development of planar meso­scale combustor with double narrow slit flame holder and various aspect ratios for micropower generator

We have investigated the effects of the aspect ratio of the rectangular mesoscale combustor with a narrow slit flame holder on the flame stability limit, flame behavior and uniformity of combustor wall temperature. The combustor was made of copper with a cross-section area of 6 mm2. The combustor aspect ratio (AR) was varied as 1, 1.5, 2.67, and 6. LPG and pure oxygen were premixed and the experiment was conducted at a limited flow rate. Pure oxygen is selected as an oxidizing agent with the intention of revealing in detail the range of flame stability within a very narrow quenching distance. All observed flames were inside the combustion chamber, not outside the channel. This research used a new type of flame holder namely double narrow slit flame holder as a flame stabilizer. The flame holder with double slit and a kind of bluff body in the center helps recirculate the flow and prolong the residence time to make the flame more stable. The use of double narrow slit flame holder successfully extended the stability map to a very lean equivalence ratio (f). However, there was a dead zone near stoichiometry condition due to very high flame propagation speed. Aspect ratio had an important role for the non-circular combustor. The aspect ratio gave a great effect to determine the limit of the stability map that can be achieved at the rich mixture. The combustor with AR=1.5 had the widest range of flammability limit, while AR=6 hadthe narrowestflame stability limits. However, the latter reached the most uniform wall temperature, which is important to obtain high efficiency thermal to electric energy conversion. The results of this study can be used to determine the right fuel mixture on the mesoscale combustor as a heat source on the micro power generator/thermal electric system

Periodic Motion and Stability of Gravitational Planar Triple Systems

The stability of gravitational triple systems is a well known problem in celestial mechanics. The basic model used is the general three body problem. Many criteria estimated from the integrals of motion and zero velocity curves or from purely numerical simulations have been given in literature. In this paper we propose a different approach for the study of stability of triple systems based on the numerical computation of manifolds of periodic orbits and their linear stability. Such an approach has been used for the study of two-planet exosolar systems but here, applying the method of continuation with respect to the masses, we refer to systems where all bodies can have similar mass values. In the present work we apply the proposed approach by starting from the circular family of periodic orbits, which is known to exist for the planetary type problem, and we restrict our computations to the case of two equal masses. By considering that the system has a hierarchical structure, the constructed manifold of periodic solutions can be projected on a plane defined by the relative distance and the relative mass of the system. On such a plane a stability map can be constructed showing the stability limits on the manifold of periodic orbits.

Developing Swirl Boundary Layer and Flow Separation at the Inlet of a Coaxial Rotating Diffuser or Nozzle

When an axial flow enters a rotating diffuser or nozzle, a swirl boundary layer appears at the wall and interacts with the axial boundary layer. Below a critical flow number φc, there is a flow separation, known in the turbomachinery context as part load recirculation. This paper extends the previous work for a cylindrical coaxial rotating pipe still considering the influence of the centrifugal force by varying the pipe's radius, yielding a coaxial rotating circular diffuser or nozzle. The integral method of boundary layer theory is used to describe the flow at the inlet of a rotating circular diffuser or nozzle, obtaining a generalized von Kármán momentum equation. This work conducts experiments to validate the analytical results and shows the influence of Reynolds number, flow number, apex angle, and surface roughness on the boundary layers evolution. By doing so, a critical flow number for incipient flow separation is analytically derived, resulting in a stability map for part load recirculation depending on Reynolds number and apex angle. Hereby, positive apex angles (diffuser) and negative apex angles (nozzle) are considered.

Vibration Control and Manufacturing of Intelligibly Designed Axially Functionally Graded Cantilevered Macro/Micro-tubes

Abstract In the last decade, extensive attention is devoted to intelligibly designed materials of macro/micro-structures containing the fluid flow. In this study, intelligent control and vibrational stability of cantilevered fluid conveying macro/micro-tubes utilizing axially functionally graded (AFG) materials are considered. The governing equation of motion of the system is derived based on modified couple stress theory and then is discretized using Galerkin method. A detailed investigation is carried out to elaborate the influence of various parameters such as material properties, axial compressive load, and Pasternak foundation on the dynamical behavior of the system, all of which are influential in stability control of the structure. It is observed that by the intelligible selection of material gradation, the desired functionality of the fluid-conveying structure could be achieved. Furthermore, scrutinizing the stability map, it is elucidated that compared with uniform structures, the decrease of material gradient parameter leads to a more stable system for a wider range of mass ratios and as a result, the system’s instability could be properly controlled. The results of this study will hold a great promise for engineers and designers who try to intelligibly optimize and manufacture novel macro/micro-structure systems carrying fluid flow as core elements in various macro, micro, and nanosystems.

Advanced chemical stability diagrams to predict the formation of complex zinc compounds in a chloride environment.

A chemical stability map is advanced by incorporating ion complexation, solubility, and chemical trajectories to predict ZnO, Zn(OH)2, ZnCO3, ZnCl2, Zn5(CO3)2(OH)6, and Zn5(OH)8Cl2·H2O precipitation as a function of the total Zn content and pH of an NaCl solution. These calculations demonstrate equilibrium stability of solid Zn products often not considered while tracking the consumed and produced aqueous Zn ion species concentrations through chemical trajectories. The effect of Cl-based ligand formation is incorporated into these stability predictions, enabling enhanced appreciation for the local corrosion conditions experienced at the Zn surface in chloride-containing environments. Additionally, the complexation of Cl− with Zn2+ is demonstrated to compete with the formation of solid phases, making precipitation more difficult. The present work also extends the chemical stability diagram derivations by incorporating a Gibbs–Thompson curvature relation to predict the effect of nanoscale precipitate phase formation on species solubility. These thermodynamic predictions correlate well with experimental results for Zn corrosion in full and alternate NaCl immersion, and have far-reaching utility in a variety of fields requiring nanoscale, semiconductor, and/or structural materials.

Limit map of pulsating instability in hydrogen/air partially premixed counterflow flames

Pulsating instabilities in hydrogen/air double-flame partially premixed counterflow flames are numerically investigated with detailed chemistry and transport. The whole stability map on the equivalence ratio-strain rate plane is obtained. With the increase of the equivalence ratio or strain rate, there are two transitions for combustion patterns from stable to unstable, and to stable again. For the one transition presented at the smaller equivalence ratio and strain rate, it is similar to that in the pure premixed flame. After this transition, the flames do not extinguish with the increase of equivalence ratio or strain rate, but transit from unstable to stable. For the second transition appeared at the larger equivalence ratio and strain rate, the effects of equivalence ratio and strain rate on the pulsating instability are completely contrary to those in pure premixed flames. The effective activation energy of the premixed flame of partially premixed flame predicted by a new method is applied to calculate the Zeldovich number. Then the first transition is proved to satisfy Sivashinsky-like criterion, but the critical value is larger than that for pure premixed flame due to the heat transfer between premixed and non-premixed flames. It means that the pulsating instability is more difficult to happen in partially premixed flames. From the first transition to the second transition along the equivalence ratio or strain rate, though the premixed flame becomes weaker, the increase degree of heat transfer from non-premixed flame to premixed flame is much larger than the decrease degree of max heat release of the premixed flame due to decrease of distance and increase of temperature difference of two flames, which induces the premixed flame stable again. The second transition is therefore controlled by the heat transfer between two flames.

Axial and torsional self-excited vibrations of a distributed drill-string

We consider a distributed axial-torsional drill-string model with a rate-independent bit-rock interaction law to study the occurrence and non-local characteristics of axial and torsional self-excited vibrations as caused by the regenerative effect. A first contribution of the paper is the derivation of a non-dimensional version of the full non-linear distributed drill-string–bit-rock interaction model and showing how it relates to the minimal set of characteristic quantities. Using this model the study shows how multiple axial modes of the drill-string are excited, or attenuated, depending on the bit rotation rate. This indicates that a lumped drill-string model approximation is insufficient for the general case. Then, a comprehensive simulation study is performed to create a stability map for the occurrence of stick-slip oscillations. In particular, the significance of the axial topside boundary condition, i.e., constant velocity vs. constant hook-load, is evaluated. A central finding is that increasing the axial loop gain (determined by the bit-rock parameters) tends to both increase the area of stable torsional dynamics and increase the rate of penetration for a constant imposed weight on bit. This also corresponds to a more severe axial instability.

Ductility and Stability in Metallic Materials

Ductility is the property of a given material to deform without fracture. In other words, is the capacity to maintain a structural stability under stresses. It is an important property that is difficult to predict since many microstructural and experimental factors play a role. A review of the most important approaches on ductility is given in this work with special emphasis in the high temperature deformation and the deformation mechanisms. The stability of materials is also analyzed and new concepts on the conditions for hot working are included. Stability maps are analyzed and conclusions on the various stability criteria are given on the base of magnesium alloys.

Instability of common beans during storage causes hardening: The role of glass transition phenomena

Long-term storage of common beans leads to loss of cooking quality and an ill-defined solution, appropriate storage, is recommended. Therefore, the polymer science theory of glasses that hypothesizes stability of a system below its glass transition temperature (Tg) was applied to determine bean stability during storage in relation to cooking behavior. Since composition influences Tg, powders of cotyledons and seed coats in addition to whole beans were equilibrated above different saturated salt solutions in order to generate materials with different moisture contents. A thermal mechanical compression test which measures compressibility changes in a system upon reaching its glass-rubber transition temperature region was conducted to obtain the Tg. A Tg-moisture relation was established, whose relevance was confirmed by storage and cooking experiments which showed development of hard-to-cook in beans stored above Tg but not below it. Therefore, this relation constitutes a stability map for storage of common beans.

Ab Initio Thermodynamics of Iridium Surface Oxidation and Oxygen Evolution Reaction

Iridium-based materials are considered as state-of-the-art electrocatalysts for oxygen evolution reaction (OER), however, their stability and catalytic activity greatly depend on surface-state changes induced by electrochemical cycling. To better understand the behavior of the low-index Ir surfaces in an electrochemical environment, we perform a systematic thermodynamic analysis by means of the density functional theory (DFT) calculations. On the basis of computed surface energies of the Ir (111), (110) and (100) facets as a function of applied electrode potential and coverage of adsorbed water species we determine stability maps and predict equilibrium shapes of Ir nanoparticles. Our calculations also show that metastable oxide precursors formed at the initial stages of Ir surface oxidation are responsible for enhanced catalytic activity toward OER as compared to metal surfaces covered by oxygen adsorbates and thick-oxide films. Such enhancement occurs not only due to the modified thermodynamic stability...

Numerical and experimental analysis of a rectangular single-phase natural circulation loop with asymmetric heater position

A simple rectangular natural circulation loop (NCL) consists of a heater, a cooler, cold leg and hot leg. The main aim of an NCL is to reject heat from heat sources to heat sinks with the use of a mechanical pump. NCL is used in various energy systems, such as solar heaters, nuclear reactors, geothermal power production and engine and computer cooling. In this study, a simple rectangular single-phase NCL with an asymmetric heater is numerically analyzed with respect to tested experimental data. First governing equations, i.e., mass, momentum, and energy balance equations are derived. Then, these equations are written in dimensionless form with proper definitions of the dimensionless parameters. The boundary conditions of NCL are heater power and cooler temperature that are modeled by modified Grashof number and modified Stanton number, respectively. A continuous friction law is used for numerical solution of governing equations that are applicable for the laminar, transition and turbulent flow regimes. The governing equations are solved for both the steady state and transient. The equations of the transient state are solved with both linear and nonlinear methods. In most of the earlier literature, a stability map has been reported that is only applicable for laminar or turbulent flows. But in the present work, a stability map is obtained, which is valid for all the three regions (laminar, transition, and turbulent). Finally, the experimental data are compared with the numerical results.

Stability of coupled human and stand-up paddle board

This study investigates the rider stability on a stand-up paddle board (SUP) based on board dimensions, rider body parameters, and skill level using a buoyant body dynamics approach. For this study, the system of a rider standing on an SUP is modeled as a planar motion of a rectangular cross-sectional buoyant body with an added mass attached at a fixed height. A stability map is developed to visualize stability regions for various system parameters. The result shows that eigenvalue contours are in good agreement with qualitative terms, such as beginner and professional. A new approach of describing rider skill level is proposed. Wave tank experiments are conducted to verify the analytic equations. Analytical results of the rectangular board show the same trend as the experimental results from a real SUP product.

The dynamic analysis of a uniformly heated channel at a supercritical pressure using a simple nonlinear model

This study develops a simple nonlinear dynamic model of a supercritical uniformly heated channel by dividing the channel into three regions coupled with linear profile approximations between flow enthalpy and flow density. Stability map, nonlinear characteristics and parametric effects of a uniformly heated channel with supercritical water are investigated. The results indicate that the nonlinear oscillations between inlet flow velocity and outlet flow velocity tend to present out-of-phase in the supercritical heated system. The parametric studies on system stability suggest that increasing inlet flow resistance or enlarging the channel diameter would stabilize the system, while increasing outlet flow resistance or lengthening the channel length would destabilize the system. In addition, complex nonlinear phenomena, i.e. supercritical Hopf bifurcations and period-doubled bifurcations, could exist in this supercritical uniformly heated channel system. In the deep unstable region of high pseudo-subcooling number, various periodic oscillations through a series of period-doubled bifurcations would eventually lead to chaotic oscillations. The appearance of period three (P-3) oscillation deduces that unimaginable periodic types of nonlinear oscillations could occur in the limited unstable space of this system.

An improved zero-dimensional model for simulation of TRIGA Mark II dynamic response

The primary aim of this work is to improve the analysis of the dynamic behaviour of the TRIGA Mark II reactor at the University of Pavia through a zero-dimensional approach. Besides the coupling between neutronics (point-reactor kinetics with six delayed neutron precursors group) and thermal-hydraulics (two-region model, with fuel and coolant) implemented in earlier works, the new model considers also the time behaviour of the mass flow rate due to natural circulation, of the neutron poisons and of the primary and secondary pool temperature. The system of coupled first-order differential equations is non-linear, as some state variables, such as the mass flow rate and the coolant temperature, multiply each other. The Simulink™ programming environment for dynamic analysis and control purposes is used to solve the system. A comparison with experimental data collected on-site for different reactor power transients and with measurements of the poison anti-reactivity during reactor shut-down and of the pool temperature allows the validation of the model. The model results and the experimental data reach a remarkable agreement. In addition, a linear stability analysis of the reactor is performed through the root locus and the stability map in terms of the thermal feedback coefficients. This analysis shows how the power level influences the dynamic of the system, and that, for certain values (always negative) of the fuel thermal feedback coefficient, positive values of the one for the moderator still ensures the system stability.

Detecting stability of conical spouted beds based on information entropy theory

Effects of particle size, particle density, gas inlet diameter and static bed height on the stability of operation in conical spouted beds were investigated through analyses of information entropy of pressure fluctuations. In this respect, the maximum information entropy of pressure fluctuations was used as a stability criterion. The results showed that stability of the bed increases with an increase in the maximum entropy. The maximum information entropy of pressure fluctuations increases with increasing particle size and bed height while decreases with increasing gas inlet diameter and particle density. A stability map was also prepared to present the effect of operating parameters on the maximum entropy. Moreover, a correlation for prediction of maximum information entropy was developed to determine the stable operation conditions of conical spouted beds operating with low as well as high density particles.