Stability Map Research Articles

Probabilistic assessment of induced seismicity at the Alberta No. 1 geothermal project site

Alberta No. 1 (ABNo1) is a geothermal project targeting deep carbonate, conglomerates, and sandstone formations in a potential production and injection zone for geothermal energy exploitation within the Municipal District of Greenview south of Grande Prairie, Alberta, Canada. In geothermal systems without a steam fraction (typically systems under 170 °C), rapid widespread pore pressure changes and slow temperature changes have led to increased deviatoric stresses, resulting in induced seismicity. A concern for the ABNo1 Geothermal Project is that anthropogenic seismicity from oil, gas, and well field fluid injection has created felt events in Alberta. Thus, at the beginning of this type of project, it is prudent to review the potential for induced seismicity. In this study, a geomechanical study of the Leduc and Granite Wash Formations, two potential geothermal fluid exploitation zones, has been undertaken based on borehole geophysics and regional injection-induced earthquake data. Determining subsurface properties such as state of stress, pore pressure, and fault properties, however, poses uncertainties in the absence of actual data from the target formations. Geomechanical analysis results (with associated uncertainties) are used to assess the potential for injection-induced earthquakes. A Monte Carlo probability analysis is employed to estimate the likelihood of slippage of the known faults close to the ABNo1 Geothermal Project. A cumulative distribution function of the critical pore pressure on each fault is derived from the local tectonic stress state and Mohr–Coulomb shear parameter analyses. The resultant probabilistic fault stability maps can serve as a baseline for future fluid injection projects in the region including wastewater disposal, hydraulic fracture stimulation, CO2 sequestration, as well as geothermal energy extraction.

Stability maps for the 5/3 mean motion resonance between Ariel and Umbriel with inclination

AbstractThe evolution of the five largest satellites of Uranus during the crossing of the 5/3 mean motion resonance between Ariel and Umbriel is strongly affected by chaotic motion. Studies with numerical integrations of the equations of motion and analysis of Poincaré surface sections provided helpful insights to the role of chaos on the system. However, they lack of a quantification of this chaos in the phase-space. Here, we construct stability maps using the frequency analysis method. We determine that for low energies (small eccentricity and/or inclinations), the phase-space is mainly stable. As the energy increases, the chaotic regions replace the stable motion, until only small, localized libration regions remain stable.

Nonlinear stability analysis for severe slugging in an air–water two-phase flow

This works presents a numerical study of the types of severe slugging through nonlinear stability analysis. The Landau equation, considered as an asymptotic solution of a two-phase flow model in a pipeline–riser system, is derived. From the Landau equation, the Landau coefficient μ is calculated and, consequently, the saturation amplitudes of the state variables at the limit cycle are determined. Based on the amplitude of the gas superficial velocity at the bottom of the riser, the condition where severe slugging type 3 (SS3) occurs can be determined. Also, based on the amplitude of the liquid superficial velocity at the top of the riser, the condition of severe slugging with liquid fallback can be determined. The results are presented in stability maps and are compared with experimental data reported in the literature, with a good agreement.

A systematic approach for selecting suitable morphologies for supercapacitor applications through morphological stability map – A case of Ni-MOF

Nickel metal organic frameworks (Ni MOFs) were synthesized employing microwave technique for supercapacitor applications using Ni(NO3)2·6H2O (=M) and p-benzenedicarboxylic acid (=L) in M:L ratios of 1:1–4:1, 150–200 °C. Flakes, plates, nanoflowers, and globules are obtained and arranged in M:L-Temperature space to yield morphological stability map. Flakes appear at all M:L, 150 °C; plates form at M:L = 1:1, ≥ 165 °C; nanoflowers are seen at M:L ≥ 2:1, 165 °C; globules form at M:L ≥ 2:1, ≥ 180 °C. Cyclic voltammograms from these morphologies within 0 and + 0.6 V vs SCE at 10–100 mV s−1 show redox peaks corresponding to partial diffusion control, substantiated by galvanostatic charge-discharge (GCD) curves. From GCD, globules at M:L = 3:1 exhibit the highest specific capacitance (Csp) of 1361–600 F g−1 at 0.5–5.0 A g−1. This is attributed to their smallest size, presence of monoclinic and γ-NiOOH phases. Further, globules exhibit the lowest charge transfer resistance as estimated from the Nyquist plots showing two incomplete depressed semicircles. This work presents a systematic approach to select suitable Ni MOF morphologies for supercapacitor applications using morphological stability map. Also, it answers the question: “why does a particular morphology exhibit superior charge storage performance?”

Complete Stability Analysis and Optimization of the Extended Delayed Resonator With Virtual Natural Frequency Adjustment

AbstractThe delayed resonator (DR) is known for its ideal vibration suppression and simple control logic, but its operable frequency range is also known limited due to stability issues and practical hardware constraints. To extend the limited operable frequency range, we inject an additional nondelayed control term into the feedback loop of the classic DR such that the equivalent natural frequency of the DR can be real-time tuned, so the creation of DR with virtual natural frequency adjustment (DRV). Besides, we take the difference between the adjustable natural frequency of the DRV and the excitation frequency as a control parameter to further enhance the vibration suppression leading to optionally tuned parameters for a given excitation. For this, we start with the complete stability analyses of the DRV and the associated coupled system following independent and purely analytical approaches, and the obtained nonconservative stability maps reveal DRV's greatly extended operable frequency range. Given the optional tuned parameters, an optimization procedure aiming for a faster transient process and stronger robustness is proposed to determine the optimal parameter composition. Finally, three numerical case studies are prepared to demonstrate the benefits of the DRV compared with the classic DR. In addition to extending the operable frequency range of the classic DR, this work simplifies the stability analysis of the existing DR investigations and provides a guideline for the tuned control parameter design if they are optional.

An unconstrained approach to systematic structural and energetic screening of materials interfaces

From grain boundaries and heterojunctions to manipulating 2D materials, solid-solid interfaces play a key role in many technological applications. Understanding and predicting properties of these complex systems present an ongoing and increasingly important challenge. Over the last few decades computer simulation of interfaces has become vastly more powerful and sophisticated. However, theoretical interface screening remains based on largely heuristic methods and is strongly biased to systems that are amenable to modelling within constrained periodic cell approaches. Here we present an unconstrained and generally applicable non-periodic screening approach for systematic exploration of material’s interfaces based on extracting and aligning disks from periodic reference slabs. Our disk interface method directly and accurately describes how interface structure and energetic stability depends on arbitrary relative displacements and twist angles of two interacting surfaces. The resultant detailed and comprehensive energetic stability maps provide a global perspective for understanding and designing interfaces. We confirm the power and utility of our method with respect to the catalytically important TiO2 anatase (101)/(001) and TiO2 anatase (101)/rutile (110) interfaces.

Numerical evaluation of static and dynamic stability characteristics of a supercritical CO[formula omitted]-driven natural circulation loop

The stability characteristics of closed supercritical natural circulation loop has hardly been explored owing to the mathematical complexity and absence of explicit boundary condition. Present numerical study investigates the nature of both static and dynamic instability in a rectangular loop with carbon dioxide as the working medium. Sharp deterioration in the steady-state circulation rate can be observed, consistent to existing multidimensional analyses. Loop exhibits Ledinegg instability for an intermediate range of heater power, characterized by multiple steady-state solutions. Appearance of static instability has been substantiated following the pressure drop versus mass flow rate profiles, leading to the development of the stability maps. Dynamic instability has also been identified by introducing perturbation during transient simulations, and the range of both static and dynamic instabilities conforms well with each other. A novel approach of approximating the location of the stability threshold using time-series data has also been proposed.

Effect of fuel reactivity on flame properties of a low-swirl burner

The present paper examines the capability of low swirl flows in stabilizing low calorific value fuels. To such an aim, CO2 gas is used to adjust the reactivity of CH4/air mixtures. The results show that increases in CO2 percentage in the fresh mixture result in shrinking the burner stability map by moving the lean and rich blowout limits toward the stoichiometric condition. The effects of CO2 addition on rich blowout limits are more intense than the lean blowout limits. For instance, the equivalence ratio associated with the lean blowout increases by 0.23, when the discharge flow velocity from the burner rises from 1.5 to 5 m/s in the 40 % CO2 diluted case. Under a similar augmentation in the burner discharge velocity, the rich blowout limit reduces by more than 0.5 in the 40 % CO2 diluted case. Unlike the lean blowout, the rich blowout limit responds non-monotonically to the discharge flow velocity from the burner for both undiluted and diluted mixtures. For the 50 % CO2 diluted case, the low swirl burner operates efficiently at low discharge velocities (1.5 to 3.5 m/s), but it blows out at high discharge velocities (3.5 to 9 m/s). Furthermore, unsteady features of low swirl flame near blowout limits are studied in detail. Moreover, strong curvy structures appear at the flame boundary prior to the flame flashback. However, such structures diminish occasionally and specifically as the flame approaches the flashback. Some deterministic features are more obvious before the flame blowout than those before the flame flashback.

Stability and Hopf bifurcation of a love model with two delays

We analyze the stability and Hopf bifurcation of a proposed nonlinear love model with two delays. The nonlinearity stems from a logistic term injected to meticulously depict a couple’s cautious love affairs. The analysis is based on the linearization theory and starts with a single-delay case assuming that one of the two characters is always impulsive. The critical delay values and existence conditions for the Hopf bifurcation are obtained. Subsequently, we extend to the more practical but also more involved dual-delay case where the delays affect the emotions of both individuals. Accordingly, a non-trivial resultant-based analysis framework is proposed, and the corresponding Hopf bifurcation is detected intuitively and exhaustively by an obtained stability map in the delay domain. The results explain an interesting and well-known feature in our daily life, i.e., proper time delays stabilize the love dynamics. Furthermore, the spectral analysis based on a numerical case reveals another common emotional experience, that proper delays not only lead to a smoother transition process but also yield a shorter settling time for the love convergence. The numerical bifurcation diagram and computational cost are also considered to demonstrate the effectiveness and efficiency of the presented analysis framework. Finally, some additional suggestions are provided for the studied couple to earn a sweet love relationship.

A new Galerkin Reduction approach for the analysis of a fully coupled foil air bearing rotor system with bilinear foil model

The foil air bearing (FAB) is a key enabler of the rapidly expanding technology of oil-free turbomachinery. However, it presents a formidable computational challenge due to the intricacy of the mathematical modelling of the nonlinear interaction between the foil structure, air film, and rotor. Galerkin Reduction (GR) allows the integration of the compressible Reynolds Equation within a FAB-rotor model without the need for spatial discretisation, resulting in a considerable gain in computational efficiency relative to grid/mesh-based methods like Finite Difference (FD) and Finite Element (FE). GR has so far been limited to a simple model that ignores the detachment of the top foil from the underlying foil. A new GR approach is developed to overcome this limitation. Following transient and static equilibrium analyses of the nonlinear system, Jacobian-based linearization is used to extract the full mode set, Campbell diagram and linear stability map. The use of GR instead of FD reduced the computational time by over 50% and required 20-60 times less memory for saving the results, without compromising accuracy and reliability. In particular, Jacobian-based linearization using GR retains the ability to detect instabilities (like top foil flutter) that are beyond the capability of the traditional linear force coefficients method.

Trojan asteroids and the co-orbital dust ring of Venus

Context. Co-orbital asteroids have been thought to be the possible source of the zodiacal dust ring around the orbit of Venus, but the conclusions about the orbital stability and thus about the existence of Venus Trojans are inconsistent in the literature. Aims. We present a systematic survey of the orbital stability of Venus Trojans that takes the dynamical influences from General Relativity and the Yarkovsky effect into account. Methods. The orbits of thousands of fictitious Venus Trojans were simulated numerically. Using a frequency analysis, we describe their orbital stabilities and the dynamical mechanisms behind them. The influences of General Relativity and of the Yarkovsky effect, which were previously either neglected or oversimplified, were investigated in long-term numerical simulations. Results. The stability maps on the (a0, i0) plane and (a0, e0) plane are depicted, and the most stable Venus Trojans are found to occupy low-inclination horseshoe orbits with low eccentricities. The resonances that carve the fine structures in the stability map are determined. General Relativity decreases the stability of orbits only little, but the Yarkovsky effect may drive nearly all Venus Trojans out of the Trojan region in a relatively short time. Conclusions. The Venus Trojans have a poor orbital stability and cannot survive to the age of the Solar System. The zodiacal dust ring found around the orbit of Venus is more likely a sporadic phenomenon, as the result of a temporary capture into the 1:1 mean motion resonance of dust particles that were probably produced by passing comets or asteroids, but not by Venus Trojans.

Complete stability assessment of LTI systems with multiple constant-coefficient distributed delays using the improved frequency sweeping framework

The stability problem of linear time-invariant systems with multiple constant-coefficient distributed delays is investigated from a new perspective. We present an equivalent system with multiple lumped delays and then apply the Dixon resultant to determine the exact upper bound of the projected imaginary spectra of the system. We then adopt the improved frequency sweeping framework over the obtained range to get the kernel and offspring hypersurfaces (KOH). Furthermore, the singularity at the zero characteristic root is scrutinised, leading to what we call the stationary root boundary (SRB) in the domain of the delays. With these, we resort to the Cluster Treatment of Characteristic Roots (CTCR) paradigm to determine the complete stability map of the system with the complete knowledge of the KOH and SRB. Finally, the effectiveness of our proposed procedure is shown by two case studies.

Global dynamics visualisation from Lagrangian Descriptors. Applications to discrete and continuous systems

This paper introduces a new global dynamics and chaos indicator based on the method of Lagrangian Descriptor apt for discriminating ordered and deterministic chaotic motions in multidimensional systems. The selected implementation of this method requires only the knowledge of orbits on finite time windows and is free of the computation of the tangent vector dynamics (i.e.,variational equations are not needed). To demonstrate its ability in visualising different dynamical behaviours, in particular for highlighting chaotic regions, several stability maps of classical systems, obtained with different phase space methods, are reproduced. The benchmark examples are rooted in discrete and continuous nearly-integrable dynamical systems, with prominent features played by resonances. These include the Chirikov standard map, higher dimensional symplectic and volume preserving maps, fundamental models of resonances, and a 3 degrees-of-freedom nearly-integrable Hamiltonian system with a dense web of resonances. The indicator thus appears to be relevant for understanding phase space transport mediated by resonances in nearly-integrable system, as ubiquitous in celestial mechanics or astrodynamics.

Attraction, Lyapunov stability and orbital maps for semigroup actions on topological spaces and fiber bundles

Attraction, Lyapunov stability and orbital maps for semigroup actions on topological spaces and fiber bundles

Phase plane analysis applied to non-explicit multibody vehicle models

A new methodology for constructing stability maps (phase-plane analysis) is presented and validated for application to complex multibody vehicle models implemented in Multibody Dynamics simulation software (Adams®). Traditional methodologies are developed to be applied to explicit mathematical models. Given the complexity of some special multibody systems, particularly in vehicle dynamics, simplifications are needed to apply this stability analysis technique. The main limitation when using simplified models is the need to neglect components which could have a significant influence on the dynamic behavior of the system and therefore on its stability. In the proposed methodology it is not necessary to have access to explicit mathematical models of multibody systems. Thus, the stability map of a vehicle model can be constructed by considering highly nonlinear dynamic elements, such as tires and silent-blocks components, modeled using the nonlinear finite element technique.

Suppression of thermoacoustic instabilities by flame-structure interaction

We present here an experimental study of the influence of the aeroelastic coupling between the combustion chamber walls and the acoustic fluid field on the onset and development of thermoacoustic instabilities in stoichiometric propane-air premixed flames. A horizontal quasi-two-dimensional Hele–Shaw chamber formed by two parallel plates separated a small distance h is used. The flames are ignited at the open end, in contact with the atmosphere, and propagate towards the opposite closed end. The experiments reveal three distinct propagation regimes determined by the stiffness of the plates and the evolution of the pressure perturbation generated during ignition: (i) for sufficiently rigid plates, we observed secondary acoustic instabilities with large amplitude oscillations in the direction of propagation of the flame; for flexible enough walls to be compliant with ignition-related pressure changes, (ii) the propagation of the flame undergoes small-amplitude oscillations (primary acoustic instabilities) along the channel or (iii) it is smooth with no oscillations whatsoever. The flexural rigidity of the plate is modified experimentally by changing both the width W and thickness hw of the top plate of the Hele–Shaw cell. The data recorded by the pressure transducer and the accelerometer is used to plot a stability map in the W−hw parametric space to define the combination of structural parameters that triggers the onset of thermoacoustic instabilities. Our experimental measurements, supplemented with results from a theoretical analysis of the walls vibration modes, indicated that deformation-induced volume changes of around 0.1% of the volume of the Hele–Shaw cell are sufficient to suppress thermoacoustic instabilities.

A simulation and experimental study of the parasitic reaction and flow field in the growth of metal–oxide films

Metal–organic chemical vapor deposition (MOCVD) is an important method for growing metal–oxide semiconductor films. However, owing to problems associated with gas-phase parasitic reactions and wall deposition, this method achieves low growth efficiency and affects the film quality. Computational fluid dynamics (CFD) has been widely used in MOCVD research and can be employed to investigate the flow field and the chemical vapor deposition (CVD) process in the reactor. In this study, considering the growth of zinc oxide and indium oxide as examples, a four-step reaction mechanism is proposed based on a combination of the multi-step reaction mechanism and experimental results. The effect of chemical reactions on the film growth rate is studied based on the Arrhenius plot and experimental results. A new flow stability map is proposed, and the flow field stability under different pressures is investigated to explore the influence of the flow field on the film growth rate. Results show that the deposition rate is influenced by both the gas-phase parasitic reactions and the effect of the flow field on the source component distribution. Furthermore, the causes and factors influencing sidewall deposition are revealed.

Challenges to incorporate high contents of bio-based isobornyl methacrylate (IBOMA) into waterborne coatings

Emulsion polymerization of (meth)acrylic bio-based monomers is a promising method to obtain waterborne coatings with reduced carbon footprint. However, the high hydrophobicity of some bio-based monomers can hinder the straightforward incorporation of such monomers in waterborne dispersions. In this work, we explore the copolymerization of bio-based isobornyl methacrylate (IBOMA) with 2-octyl acrylate (2-OA) to produce latexes with >70 % bio-content suitable for coating applications. First, the homopolymerization of IBOMA is studied to gather more information on the emulsion polymerization of the monomer producing high Tg polymer with different surfactants. It is found that the batch emulsion homopolymerization of IBOMA is challenging due to coagulation during the polymerization, likely as a result of mass transport limitations due to the high hydrophobicity of IBOMA. Interestingly, stable dispersions are achieved when 5 % of the IBOMA is substituted by methyl methacrylate. The stability of the IBOMA/2-OA copolymer system is found to be dependent on both the IBOMA concentration in the copolymer and the solids content of the latex. Thus, we provide a stability map for IBOMA/2-OA copolymers with different compositions and solids contents showing the areas where stable and not-stable dispersions are obtained.

Computation-accelerated discovery of the K2NiF4-type oxyhydrides combing density functional theory and machine learning approach.

The emerging K2NiF4-type oxyhydrides with unique hydride ions (H−) and O2- coexisting in the anion sublattice offer superior functionalities for numerous applications. However, the exploration and innovations of the oxyhydrides are challenged by their rarity as a limited number of compounds reported in experiments, owing to the stringent laboratory conditions. Herein, we employed a suite of computations involving ab initio methods, informatics and machine learning to investigate the stability relationship of the K2NiF4-type oxyhydrides. The comprehensive stability map of the oxyhydrides chemical space was constructed to identify 76 new compounds with good thermodynamic stabilities using the high-throughput computations. Based on the established database, we reveal geometric constraints and electronegativities of cationic elements as significant factors governing the oxyhydrides stabilities via informatics tools. Besides fixed stoichiometry compounds, mixed-cation oxyhydrides can provide promising properties due to the enhancement of compositional tunability. However, the exploration of the mixed compounds is hindered by their huge quantity and the rarity of stable oxyhydrides. Therefore, we propose a two-step machine learning workflow consisting of a simple transfer learning to discover 114 formable oxyhydrides from thousands of unknown mixed compositions. The predicted high H− conductivities of the representative oxyhydrides indicate their suitability as energy conversion materials. Our study provides an insight into the oxyhydrides chemistry which is applicable to other mixed-anion systems, and demonstrates an efficient computational paradigm for other materials design applications, which are challenged by the unavailable and highly unbalanced materials database.

Effect of the recess length on the dynamic characteristics of liquid-centered swirl coaxial injectors

In general, a recess in shear coaxial/swirl coaxial injectors positively affects the stable combustion and combustion efficiency. However, a recess in a liquid-centered gas-liquid swirl coaxial injector may cause spray oscillations, known as self-pulsation. In this study, the effects of the recess length on the spray dynamic characteristics and their mechanisms were investigated. Four liquid-centered liquid-gas swirl coaxial injectors with different recess lengths were manufactured by metal additive manufacturing. Cold-flow tests were performed in a broad range of liquid and gas Reynolds numbers through the injectors. Pressure fluctuations in the gas and liquid injector manifolds were measured using dynamic pressure sensors, and high-speed instantaneous spray images were captured using a high-speed camera. The data obtained from the two measurement methods were analyzed using the fast Fourier transform technique. The recess length affects the frequency and intensity of the self-pulsation and stability map. In all injectors, the self-pulsation frequency increases with the liquid Reynolds number, but the effect of the gas Reynolds number differs with the recess number. Thus, the characteristics of self-pulsation change depending on whether the recess number <1 or ≥1. The present experimental results were utilized in proposing self-pulsation mechanisms based on the recess number.