Stability Map Research Articles

Mutually interacting SNG-air premixed flames

Experimental and numerical studies were conducted to grasp the flame characteristics for mutually interacting SNG-air premixed flames with a counterflow configuration. Five different reaction mechanisms (GRI 3.0, USC 2.0, Aramco 2.0, UCSD, and CRECK) were tested to give the priority in tracing measured lean extinction boundaries. UCSD mechanism best traced the measured data. The flame stability map was presented with a functional dependency on methane mole fractions in the reactant streams issuing from the lower and upper nozzles, by varying the global strain rate.With increasing global strain rate, lean and rich extinction boundaries were gradually slanted, forming an island of flammable region and finally only one flammable condition at 740 s−1 via a continuous shrinkage of flammable region. For asymmetric lean-lean and rich-rich flames, the weaker flame was survived via thermally and chemically symbiotic relation of it to the stronger flame. For lean-rich flames, triple flame is changed into bi-brachial flames via a merging of diffusion flame lean flame at high strain rates. This behavior could be explained well by introducing a specific heat release rate. Extinction mechanism could be reasonably explained by the relation of specific heat release rate (as a reactivity of flame) to conductive heat loss from the strong flame to unburned mixture.

Comparative analysis of the stability and structure of premixed C3H8/O2/CO2 and C3H8/O2/N2 flames for clean flexible energy production

The study compares the macrostructure and stabilization parameters of premixed oxy-propane (C3H8/O2/CO2) and oxygen-enriched air-propane (C3H8/O2/N2) flames at fixed inlet velocity of 5.2 m/s and under similar conditions of oxygen fraction (OF= 21%–70%) and equivalence ratio (ϕ=0.1−1.0) in a model dry-low-emissions (DLE) gas turbine combustor. The combustor stability maps were plotted within the ϕ-OF domain against background contours of constant adiabatic flame temperature (AFT), to quantify the blowout and flashback limits. It was found for both CO2- and N2-diluted flames that the blowout and flashback limits followed constant AFT contours on the stability maps. The blowout limit of both types of flames roughly followed the same AFT contour of about ∼1580 K, while the flashback limits followed the constant AFT contour of 2350 K. This implies that C3H8/O2/N2 flames blow out at leaner conditions compared to C3H8/O2/CO2 flames. The effect of diluent type on blowout limit diminishes at higher OF; above 55% both flames blow out at ϕ∼0.2. All flames of the same AFT exhibited considerably identical shapes despite having different OF and ϕ. Based on that, the design and operation of future oxy-fuel turbines is recommended to be AFT-based rather than OF or ϕ.

Vibration of viscoelastic axially graded beams with simultaneous axial and spinning motions under an axial load

For the first time, the structural dynamics and vibrational stability of a viscoelastic axially functionally graded (AFG) beam with both spinning and axial motions subjected to an axial load are analyzed, with the aim to enhance the performance of bi-gyroscopic systems. A detailed parametric study is also performed to emphasize the influence of various key factors such as material distribution type, viscosity coefficient, and coupled rotation and axial translation on the dynamical characteristics of the system. The material properties of the system are assumed to vary linearly or exponentially in the longitudinal direction with viscoelastic effects. Adopting the Laplace transform and a Galerkin discretization scheme, the critical axial and spin velocities of the system are obtained. An analytical approach is applied to identify the instability thresholds. Stability maps are examined, and for the first time in this paper, it is demonstrated that the stability evolution of the system can be altered by fine-tuning of axial grading or viscosity of the material. The variation of density and elastic modulus gradient parameters are found to have opposite effects on the divergence and flutter boundaries of the system. Furthermore, the results indicate that the destabilizing effect of the axial compressive load can be significantly alleviated by the simultaneous determination of density and elastic modulus gradation in the axial direction of the system.

A novel harmonic solution for chatter stability of time periodic systems

Chatter vibrations strongly limit productivity in milling. Due to the presence of rotating parts with asymmetric stiffness and stability enhancement strategies which act through a periodic variation of stiffness, there is growing interest in estimating the stability maps of systems with Linear Time Periodic dynamics together with periodic cutting excitation. Applying Exponentially Periodic Modulated test signals to the dynamic cutting force equation and representing the dynamics of the system through the Harmonic Transfer Function, the innovative Harmonic Solution (HS) and its zero-order approximation were derived in this research. HS is a frequency domain representation of a system described by the combination of two independent periodicities. It is possible to take into account these periodicities together in HS or singularly, resulting in the Zero Order HS or in the well-known Multi-Frequency Solution. This novel formulation can deal efficiently with spindle dependent and independent dynamics and is prone to industrial applications due to its flexibility and efficiency. More specifically, in this work the developed methodologies were used to assess the cutting stability of systems with a periodically modulated stiffness. The accuracy and efficiency of HS were validated by comparison with the results achieved by the use of the semi-discretization method. Results are in agreement with those obtained using semi-discretization. Moreover, admitting a slight precision loss, HS and its zero-order approximation are orders of magnitude faster than semi-discretization, giving reliable stability maps from seconds to a few minutes.

The Influence of Maltodextrin on the Thermal Transitions and State Diagrams of Fruit Juice Model Systems.

The state diagram, which is defined as a stability map of different states and phases of a food as a function of the solid content and temperature, is regarded as fundamental approach in the design and optimization of processes or storage procedures of food in the low-, intermediate-, and high-moisture domains. Therefore, in this study, the effects of maltodextrin addition on the freezing points (, ) and glass transition temperatures (, ) required for the construction of state diagrams of fruit juice model systems by using differential scanning calorimetry methods was investigated. A D-optimal experimental design was used to prepare a total of 25 anhydrous model food systems at various dry mass fractions of fructose, glucose, sucrose, pectin, citric acid, and maltodextrin, in which this last component varied between 0 and 0.8. It was found that maltodextrin mass fractions higher than 0.4 are required to induce significant increases of , , , and curves. From this perspective, maltodextrin is a good alternative as a cryoprotectant and as a carrier agent in the food industry. Furthermore, solute-composition-based mathematical models were developed to evaluate the influence of the chemical composition on the thermal transitions and to predict the state diagrams of fruit juices at different maltodextrin mass fractions.

Dynamic characteristics and stability of pipe-in-pipe system conveying two-phase flow in thermal environment

Pipe-in-pipe (PIP) systems are utilized widely in modern petroleum industry owing to their good insulation effect. In present work, a novel mathematical model for the free vibration of the fluid-conveying cantilevered PIP system considering thermal effect and two-phase flow is proposed. The insulation layer connecting two concentric pipes is simplified as the distributed springs and dampers here. The governing equation of the pipe system is then derived using Hamilton's principle based on Euler-Bernoulli beam theory. Then the Galerkin method is applied to the free vibration analysis. In the numerical section, parametric analysis is performed to elucidate the effects of different physical factors, such as environment temperature, equivalent stiffness and damper of the insulation layer, structural damping, two-phase flow, and axial load on the dynamic characteristic and stability of the PIP system through the forms of Argand diagram, stability map, and time history diagram. The results show that the PIP system has an advantage over a single fluid-conveying pipe in terms of stability considering thermal effect, axial load, and structural damping. Besides, different from single pipe, two different frequencies are found for each vibration mode, and two-pipe coupled flutter instability occurs to the PIP system as the fluid velocity exceeds the critical fluid velocity. The theoretical work is helpful to improve the analysis and design of the PIP system with consideration of internal two-phase flow and environmental temperature.

Uncertainty evaluation for twist drilling stability model

This paper describes the first uncertainty analysis for drilling stability using a frequency-domain drilling stability model. The stability model inputs include: the modal parameters for the torsional-axial vibration mode from the twist drill-holder-spindle axial frequency response function; and the mechanistic coefficients that relate the torque and thrust force to chip area for the selected drill-workpiece material combination. Monte Carlo simulation is applied to propagate the input uncertainties to output uncertainty in the predicted stability map, which separates stable from unstable (chatter) zones in the spindle speed-chip width parameter space. The mean stability boundary and its 95% confidence intervals are determined for five cases: varying all four inputs simultaneously and varying them individually. This enables the individual sensitivities to be compared. Experimental results from drilling tests are included for comparison to the prediction. Additionally, Matlab code is provided to implement the stability model and Monte Carlo uncertainty analysis.

Experimental investigation of combustion instabilities of a mesoscale multinozzle array in a lean-premixed combustor

Self-excited combustion instabilities in a mesoscale multinozzle array, also referred to as a micromixer-type injector, have been experimentally investigated in a lean-premixed tunable combustor operating with preheated methane and air. The injector assembly consists of sixty identical swirl injectors of 6.5 mm inner diameter, which are evenly distributed across the combustor dump plane. Their flow paths are divided into two groups – inner and outer stages – to form radially stratified reactant stoichiometry for the control of self-excited instabilities. OH PLIF measurements of stable flames reveal that the presence of radial staging has a remarkable influence on stabilization mechanisms, reactant jet penetration/merging, and interactions between adjacent flame fronts. In an inner enrichment case, two outer (leaner) streams merge into a single jet structure, whereas the inner (richer) reactant jets penetrate far downstream without noticeable interactions between neighboring flames. The constructed stability map in the 〈ϕi, ϕo〉 domain indicates that strong self-excited instabilities occur under even split and outer enrichment conditions at relatively high global equivalence ratios. This is attributed to large-scale flame surface deformation in the streamwise direction, as manifested by vigorous detachment/attachment movements. The use of the inner fuel staging method was found, however, to limit the growth of large-amplitude heat release rate fluctuations, because the center flames are securely anchored during the whole period of oscillation, giving rise to a moderate lateral motion. We demonstrate that the collective motion of sixty flames – rather than the individual local flame dynamics – play a central role in the development of limit cycle oscillations. This suggests that the distribution pattern of the injector array, in combination with the radial fuel staging scheme, is the key to the control of the instabilities.

Vibration of spinning functionally graded nanotubes conveying fluid

As a first attempt, the vibration and stability analysis of magnetically embedded spinning axially functionally graded (AFG) nanotubes conveying fluid under axial loads is performed based on the nonlocal strain gradient theory (NSGT). A detailed parametric investigation is conducted to elucidate the influence of key factors such as material distribution type and size-dependent parameters on the divergence and flutter instability borders. Also, a comparative study is conducted to evaluate the available theories in the modeling of nanofluidic systems. The material characteristics of the system are graded along the longitudinal direction based on the power-law and exponential distribution functions. To accurate model and formulate the system, the no-slip boundary condition is considered. Adopting the Laplace transform and Galerkin discretization technique, the governing size-dependent dynamical equations of the system are solved. The backward and forward natural frequencies, as well as critical fluid and spin velocities of the system, are extracted. Besides, an analytical approach is applied to identify the instability thresholds of the system. Dynamical configurations, Campbell diagrams, and stability maps are analyzed. Meanwhile, it is concluded that, in contrast to the influence of nonlocal and density gradient parameters, the increment of strain gradient and elastic modulus gradient parameters expands the stability regions and alleviate the destabilizing effect of the axial compressive load.

Analytic Stability Maps of Unknown Exoplanet Companions for Imaging Prioritization

Abstract Identifying which systems are more likely to host an imageable planet can play an important role in the construction of an optimized target list for future direct imaging missions, such as the planned Coronagraph Instrument (CGI) technology demonstration for the Nancy Grace Roman Space Telescope. For single-planet systems, the presence of an already detected exoplanet can severely restrict the target’s stable region and should therefore be considered when searching for unknown companions. To do so, we first analyze the performance and robustness of several two-planet stability criteria by comparing them with long-term numerical simulations. We then derive the necessary formulation for the computation of (a, R) analytic stability maps, which can be used in conjunction with depth-of-search grids in order to define the stable-imageable region of a system. The dynamically stable completeness (i.e., the expected number of imageable and stable planets) can then be calculated via convolution with the selected occurrence grid, obtaining a metric that can be directly compared for imaging prioritization. Applying this procedure to all the currently known single-planet systems within a distance of 50 pc, we construct a ranked target list based on the CGI’s predicted performance and SAG13 occurrence rates. Finally, we evaluate the importance of considering the radial velocity data from past Doppler surveys in order to rule out entire regions of our parameter space where, if a planet existed, it would have certainly been detected by previous RV observations.

Linear stability investigations on the inward flow between closely spaced co-rotating disks

In order to identify transitional flow, the linear stability of inward flow in a narrow gap between co-rotating disks is studied. Two methods are developed. The local approach assumes periodic nature of the flow in radial and circumferential direction, whereas the computationally more expensive biglobal variant only requires periodicity in circumferential direction. Stability maps are provided for a single set of operating conditions spanning a range of Reynolds numbers at fixed rotor geometry and rotational speed. The theoretical findings are compared to a set of experimental velocity profiles that includes the transitional region according to profile shapes. Apart from some explainable inconsistencies, the determined stability limits agree with each other and with results from previous studies.

Spectrum-domain stability assessment and intrinsic oscillation for aggregated mobile energy storage in grid frequency regulation

This paper assesses the aggregation stability of mobile energy storage for the grid frequency regulation, which employs distributed electric-vehicle capacities. To reveal the aggregation dynamics, a multiple-aggregator model is established in the state space, which introduces aggregation factors coupled with the time for distributed vehicles. Interlinking the aggregated model of mobile energy storage system with the electrical grid model, an integration model is developed for the stability assessment. According to the transcendental model feature, an efficient stability region extraction method is then proposed to disclose the unstable risk, which consists of four sequential stages: quasi-polynomial formulation, Dixon-resultant based spectrum estimation, oscillation spectrum extraction, and stability map determination. In the first stage, Rekasius substitution is deployed converting the notoriously complicated model to a quasi-polynomial form. Since the real and imaginary parts of the quasi-polynomial have to vanish simultaneously, an elimination method called Dixon resultant is utilized, which constructs the necessary and sufficient assessment condition. After that, the discriminant is carried out to generate the imaginary spectra bound, which is scanned to finally determine the oscillation spectrum. It is revealed that the aggregation of mobile energy storage system might induce an oscillation spectrum due to asynchronous processes. Besides, the bound of the oscillation caused by the aggregation process is disclosed. Moreover, the established mapping relationship between the kernel curve and their offspring curves visualizes the complete stability map. The whole model and stability analysis are theoretically derived and verified through a typical grid frequency regulation system with mobile energy storage.

A numerical investigation of conjugate thermal boundary layers in a differentially heated partitioned cavity filled with different fluids

In this study, the instability mechanisms in the conjugate thermal boundary layers (TBLs) adjacent to a partition in a differentially heated dual-chamber cavity are investigated numerically. The two chambers of the cavity are filled with air (Pr = 0.71) and water (Pr = 8.58), and the partition is assumed to have a zero thickness. The effects of the aspect ratios of both chambers (Aair and Awater) and the overall temperature difference (ΔT) on the interactions between the conjugate air- and water-side TBLs are extensively investigated. It is found that Aair has a more significant impact on the instabilities of the TBLs than Awater. For a relatively small Aair (e.g., 10/3) and a relatively large Aair (e.g., 10), the water-side TBL resonates with the air-side TBL at the frequencies of the corner flow instabilities in the air chamber. For medium Aair (e.g., 4, 5, and 20/3), the air-side TBL becomes weakly turbulent, causing the water-side TBL to become chaotic. Furthermore, if ΔT is reduced, the air-side TBL becomes quasi-periodic, limiting the turbulence growth on the water side. A stability map illustrating the major instability mechanisms controlling the interactions between the conjugate TBLs is presented on the (Aair, Ra) domain for Awater = 5.

Coherent and incoherent space-charge effects in high-intensity hadron rings

A brief overview is given of the recent work done by the beam-physics group of Hiroshima University on resonant beam instabilities in high-intensity hadron rings. Emphasis is placed upon two essentially different instability mechanisms, namely, coherent and incoherent resonances that occur respectively in the beam core and in the beam tail. On the basis of a semi-empirical coherent resonance condition, a simple rule is introduced to construct a new type of stability map. The proposed diagram enables one to find the optimum operating region of any circular machine in the betatron tune space very easily and quickly.

Effect of rotor misalignment on stability of journal bearings with finite width

The present work studies the dynamic response of fluid film bearing of finite length which is subjected to rotor misalignment. Vibration analysis of the rotor is used to obtain the limits of stability at different operating conditions. The lubricant flow in the bearing is considered laminar, incompressible and isoviscous. For a given small excitation of the bearing shaft, a time dependent Reynolds equation is introduced to investigate the dynamic response of the fluid film bearing. At a misalignment direction angle and misalignment degree, nonlinear perturbation dynamic equations are introduced and solved to determine the critical stability limit of motion for different values of eccentricity ratio. Vibration data is collected to obtain the transition from stable to unstable operating conditions (stability map). It is concluded here that increasing the value of misalignment degree yields to an increase in the value of critical bearing stability limit for a given value of misalignment direction angle. The critical stability number increases as the misalignment direction angle decreases and/or the steady state eccentricity ratio increases.

Effects of pressure oscillation on aerodynamic characteristics in an aero-engine combustor

The effects of pressure oscillation on aerodynamic characteristics in an aero-engine combustor are investigated. A combustor test rig is designed to simulate the pressure drop characteristics of a practical annular combustor. The pressure drop characteristics are firstly measured under atmosphere condition with non-reacting flow (or cold flow), and the air mass flow proportion of each component (dome/liner) are obtained; these properties are base lines for comparison with combustion state. The combustion tests are then carried out under conditions of inlet temperature 340–450 K, fuel air ratio 0.010–0.028. The stability map and the oscillation frequencies are obtained in the tests, the results show that pressure oscillation amplitude increases with the increase of fuel air ratio. Phase trajectory reconstruction is applied to classify the pressure oscillation motion; there are three motions captured in the tests including: “disk”, “ring” and “cluster”. The pressure drops across the dome under strong pressure oscillation are distinctly divergent from the cold flow, and the changes of pressure drops are mainly affected by pressure oscillation amplitude, but is less influenced by pressure oscillation motion nor oscillation frequencies. Based on the mass flow conservation, the reduction of effective flow area of combustor under strong pressure oscillation is demonstrated. Liner wall temperatures are analyzed through Multiple Linear Regression (MLR) method to estimate the reduction of the air mass flow proportion of the liner cooling under strong pressure oscillation. Finally, the air mass flow proportions of each component under strong pressure oscillation are estimated, the results show that the pressure oscillation motion also has influence on air mass flow proportion.

Effect of Flow Parameters and Injection Flow Area on Non-Premixed Methane/Oxygen Diffusion Flame Stability

ABSTRACT The focus of this research was the design, fabrication, and testing of an experimental non-premixed flame burner to determine the effect of gaseous flow parameters and flow geometry on the stability of methane/oxygen combustion. The non-premixed burner consisted of a horizontally mounted, rectangular combustion chamber with a single coaxial injector, capable of introducing reactants at a specified impingement angle of 30° at the exit plane. Gaseous oxygen was the primary flow and gaseous methane was the secondary flow. The non-premixed burner was equipped with optical windows on both sides of the chamber parallel to the axis of the flame, which allowed for clear viewing of the product flame. Ignition of the reactants was achieved by a retractable spark plug. Stability maps of the resultant diffusion flame were created for three different injection flow areas based upon reactant equivalence ratio and primary reactant Reynolds numbers. The results showed that decreasing the primary flow area resulted in a more stable flame condition over a broader range of Reynolds numbers (laminar flow to over 40000) and equivalence ratios (fuel-lean 0.27 to fuel-rich 4.94). Increasing Reynolds number also resulted in a transition from a stable, anchored flame to a detached, unstable flame.

The Climatic Response of Tree Ring Width Components of Ash (Fraxinus excelsior L.) and Common Oak (Quercus robur L.) from Eastern Europe

This paper aims to develop the first differentiated (earlywood—EW, latewood—LW, and total ring width—RW) dendrochronological series for ash (Fraxinus excelsior L.) and oak (Quercus robur L.) trees from the Republic of Moldova, and to analyze their climatic response and their spatio-temporal stability. For this, 18 ash and 26 oak trees were cored from the Dobrușa protected area, Republic of Moldova, Eastern Europe, and new EW, LW, and RW chronologies were developed for ash and oak covering the last century. The obtained results showed that the RW and LW have a similar climatic response for both species, while EW is capturing interannual climate variations and has a different reaction. The analyses performed with monthly climatic data revealed a significant and negative correlation with the mean air temperature and a significant and positive correlation with precipitation and the Standardized Precipitation-Evapotranspiration Index (SPEI) for both ash and oak. The temperature during the vegetation period has a strong influence on all tree-ring components of ash, while for oak the strong correlation was found only for LW. The positive and significant correlation between LW and RW with precipitation for both species, suggests that ash and oak are sensitive to the hydrological component and the precipitation is the main tree growth-limiting factor. Despite the significant correlation with precipitation and temperature for the whole analyzed period, the 25-year moving correlation analyses show that they are not stable in time and can switch from positive to negative or vice versa, while the correlation with SPEI3 drought index, which is a integration of both climatic parameters, is stable in time. By employing the stability map analysis, we show that oak and ash tree ring components, from the eastern part of the Republic of Moldova, have a stable and significant correlation with SPEI3 and scPDSI drought indices from February (January) until September, over the eastern part of Europe.

Quasi-Binary Transition Metal Dichalcogenide Alloys: Thermodynamic Stability Prediction, Scalable Synthesis, and Application.

Transition metal dichalcogenide (TMDCs) alloys could have a wide range of physical and chemical properties, ranging from charge density waves to superconductivity and electrochemical activities. While many exciting behaviors of unary TMDCs have been demonstrated, the vast compositional space of TMDC alloys has remained largely unexplored due to the lack of understanding regarding their stability when accommodating different cations or chalcogens in a single-phase. Here, a theory-guided synthesis approach is reported to achieve unexplored quasi-binary TMDC alloys through computationally predicted stability maps. Equilibrium temperature-composition phase diagrams using first-principles calculations are generated to identify the stability of 25 quasi-binary TMDC alloys, including some involving non-isovalent cations and are verified experimentally through the synthesis of a subset of 12 predicted alloys using a scalable chemical vapor transport method. It is demonstrated that the synthesized alloys can be exfoliated into 2D structures, and some of them exhibit: i) outstanding thermal stability tested up to 1230 K, ii) exceptionally high electrochemical activity for the CO2 reduction reaction in a kinetically limited regime with near zero overpotential for CO formation, iii) excellent energy efficiency in a high rate Li-air battery, and iv) high break-down current density for interconnect applications. This framework can be extended to accelerate the discovery of other TMDC alloys for various applications.

Experimental and numerical studies on two-phase flow instability behavior of a parallel helically coiled system

This paper reports on the experimental and numerical studies on two-phase flow instability behavior of a parallel helically coiled system. The experiment employs two vertically parallel helical tubes both with 9 mm hydraulic diameter (350 mm coil diameter, 4790 mm length, 10° helix angle) connected by a lower and an upper header. The experiment is carried out in a matrix of conditions: pressures (2 MPa, 4 MPa, 6 MPa), mass fluxes (120–500 kg/m2s), inlet subcooling (from 20% up to 0) and inlet throttling (35–245 entrance resistance coefficient). Within the experiment range, parametric effects of thermal power, mass flow rate and inlet throttling are consistent with classical two-phase flow instability theory in straight tubes, however some characteristics on pressure and inlet subcooling are highlighted for helical tubes. The period of oscillations and stability maps of the experimental facility are also discussed in this paper. In the end, the experimental data are compared with the numerical simulation results of a modified RELAP5 code.