Shape Bifurcation Research Articles

Intermittency of Flame Structure and Thermo-Acoustic Behavior in a Staged Multipoint Injector Using Liquid Fuel

Abstract This study investigates the impact of the staging factor, the ratio between the fuel injected through the pilot stage and the multipoint injection, on the flame dynamic. The BIMER combustor is an atmospheric pressure rig equipped with two corotating swirling air injections (a fixed amount of around 87% of the air goes inside the multipoint stage) and two fuel injection paths for staged combustion. Liquid dodecane is injected with air preheated at 437 K with a global equivalence ratio of 0.6 and a thermal power of around 72 kW. The change of the staging factor from 100% (pilot-only injection) toward 0% (multipoint-only injection) generates changes in the flame-shape which bifurcates from an anchored V-flame into a lifted flame. This flame shape bifurcation appears at a staging of factor around 25%. Around this staging factor, one can witness multistable flames where the flame structure transits randomly between five different states. Processing microphone signals recorded in the chamber provides an understanding of the flame dynamics. The attached flame presents limited pressure fluctuations level at 270 Hz, while the lifted flame features high-pressure fluctuations at 323 Hz. The intermittency between the five states (including the two stable states) is investigated.

Snap-induced morphing: From a single bistable shell to the origin of shape bifurcation in interacting shells

The bistability of embedded elements provides a natural route through which to introduce reprogrammability to elastic meta-materials. One example of this is the soft morphable sheet, in which bistable elements that can be snapped up or down, are embedded within a soft sheet. The state of the sheet can then be programmed by snapping particular elements up or down, resulting in different global shapes. However, attempts to leverage this programmability have been limited by the tendency for the deformations induced by multiple elastic elements to cause large global shape bifurcations. We study the root cause of this bifurcation in the soft morphable sheet by developing a detailed understanding of the behaviour of a single bistable element attached to a flat ‘skirt’ region. We study the geometrical limitations on the bistability of this single element, and show that the structure of its deformation can be understood using a boundary layer analysis. Moreover, by studying the compressive strains that a single bistable element induces in the surrounding skirt we show that the shape bifurcation in the soft morphable sheet can be delayed by an appropriate design of the lattice on which bistable elements are placed.

Relationship between fractal dimensions of stream and morphometric characteristics of basin for the soil conservation from water erosion

The network of streams continuously changes its location based on time, environmental factors and human interventions. It is very important to study the stream changes in order to provide the management solutions for the soil conservation. One of the new methods in this regard is to use the fractal geometry. The purpose of this study was to investigate the relationship between fractal and morphometric characteristics of the basin and the possibility of fast, low cost and accurate management of the stream network based on this relationship. For this purpose, using data basic maps, drainage networks map and Digital Elevation Model (10 meter) of the ground by ArcGIS 10.7 was prepared. Then applying the rules Horton-Strahler river network, fractal dimensions were calculated to examine the relationship between fractal dimension and some rivers geomorphic features were investigated. Finally, by entering the data obtained from the calculations in SPSS 22 and Curve Expert software, the morphometric characteristics of the basin associated with the fractal dimensions were investigated. In the Curve Expert software, the exponential, logarithmic, linear and power models of dependent variable (fractal dimension) and independent variable (morphometric characteristics) were investigated and the model that had the higher determination coefficient and was significant in SPSS 22 software for the nonlinear univariate regression was selected and introduced as the appropriate model for the relationship between the two studied variables. Results showed, the fractal dimension of stream branch, fractal dimension of drainage density and fractal dimension of total basin area were 1.84, 0.71 and 1.46, respectively. The results also showed, fractal dimension of watersheds have meaningful relations with factors such as shape form, area, bifurcation ratio and length ratio in the watersheds. Due to the importance of stream characteristics in the management of watersheds in terms of flood, erosion and soil conservation, the fractal models can be used to make quick and accurate decisions about the stream management.

Numerical analysis of flame shape bifurcation in a two-stage swirled liquid burner using Large Eddy Simulation

A flame shape bifurcation in the liquid-fueled two-stage swirled BIMER combustor is studied using Large Eddy Simulations. This combustor, developed at the EM2C Laboratory to study Lean Premixed Prevaporized (LPP) burners, is composed of a two-stage injection system: a central swirled pilot stage fueled with a pressure-swirl atomizer, to sustain a piloting flame, and an outer swirled stage fed with a multi-point injection, to generate the LPP regime. After ignition in the pilot-only operating condition, a V flame is stabilized near the Inner Shear Layer (ISL). When switching to multipoint-only injection, a flame shape transition is observed and the flame bifurcates into a M-shape. In this work, we identify the mechanisms that lead to this bifurcation, and we show that the transition is driven by a complex coupling between the flame, the chamber acoustics and the ISL vortices. By switching to a multipoint-only injection, the fuel is essentially given to the ISL flame, which is mainly premixed. Because of the increased heat release rate and thanks to positive Rayleigh criterion, the quarter wave mode of the chamber is promoted. The ISL vortices, locked to this mode, increase in size until they are large enough to merge the flame in the CRZ, the radial momentum budget forcing the flow topology to switch to a bubble-like structure. Therefore, these results show that it is the existence of two possible flow topologies that renders this flame shape transition possible, the instability being responsible for transferring sufficient energy to the flow to enable the transitioning and the flame then changing its shape simply to adapt to the new topology.

High-speed simultaneous PLIF/PIV imaging of a lift-off swirling flame under acoustic forcing

The detailed understanding of the flow-flame interaction in a swirling flame is crucial for the study of turbine engine combustion. The phase and amplitude of the heat release rate as a function of the frequency and amplitude of the flow-field oscillations determine the thermo-acoustic instability of the combustion system. The responses of a lift-off swirling flame under acoustic forcing, which operates near its blow-off limit and often shows flame shape bifurcation between attached and lift-off configurations, have not been experimentally investigated. Here, we present simultaneous 20 kHz particle image velocimetry (PIV), fuel tracer and CH2O planar laser-induced fluorescence (PLIF) measurement of a lean-premixed swirling flame enclosed in a model gas turbine burner in order to study the effect of equivalence ratio and forcing on the flame structure and dynamics. We studied the bistable states that have intermittent transitions between the anchored V-shape flame and the detached lift-off flame in which the precessing vortex core is formed. The time-resolved lift-off and re-attachment transitions between the V-flame and lifted flame configuration of the bistable flames are captured by the high repetition rate burst mode imaging. The high-repetition PLIF/PIV results demonstrate that the lifted flame can be re-attached on increasing the equivalence ratio or the forcing frequencies and amplitudes.

Mode‐matching analysis for characterization of the sectoral waveguide mode converters

AbstractAn S‐band sectoral waveguide (SWG) mode converter was presented for simulation and electromagnetic analysis. A mode‐matching technique (MMT) for the electromagnetic analysis of an SWG mode converter has been proposed. The problem of trifurcation of the coaxial waveguide to shape SWGs and bifurcation of SWGs is discussed. In this framework, the selections of appropriate testing modes at each junction are justified. The simulation time has improved and the complexity of the proposed problem has reduced by the proposed approach. The numerical results of the MMT are compared against simulation results and are found to be in good agreement. The efficiency of both the simulated and analyzed results shows a mode conversion efficiency higher than 98.0%. An experimental evaluation shows the mode conversion of TM01 to TE11 mode using far‐field radiation patterns and has been compared with simulation results. Also, the MMT and simulation validate the mode conversion of TM01 to TE11 mode.

Solidification process of hybrid nano-enhanced phase change material in a LHTESS with tree-like branching fin in the presence of thermal radiation

Large amount of energy can be stored using the Latent Heat Thermal Energy Storage Systems (LHTESS). Present study deals with solidification process of Hybrid nano-enhanced Phase Change Material (HNEPCM) in a thermal storage system enhanced in the presence of tree-like branching fins and thermal radiation effect. In order to enhance the thermal conductivity of system, TiO2-Cu nanoparticles are added to water which is considered as phase change material. In order to simulate the unsteady heat and mass transfer during the solidification process, the Finite Element Method (FEM) along with adaptive mesh are employed. The effects of nanoparticles shape factor, radiation parameter and bifurcation angle of fin on solidification process are investigated. Applying Response Surface Methodology (RSM), a correlation for full solidification time as a function of nanoparticles shape factor, radiation parameter and bifurcation angle of fins is extracted. Results indicated that by enhancing the thermal radiation parameter and fin bifurcation angle, the average temperature and total energy of the system experience lower values, while the solid fraction increases.

Rigidisation of deployable space polymer membranes by heat-activated self-folding

Current gossamer space structures such as solar sails usually rely on bracing structures, inflation gas, or centrifugal force to deploy and maintain a structural shape, which leads to a system that is sometimes complicated, while a concise system can be achieved if the gossamer structure could self-rigidise and support load. The present study proposes a self-folding polymer membrane based on space-qualified materials and is potentially mass-producible by industrial roll-to-roll processes. It can permanently transform a flat gossamer membrane into a load-bearing 3D configuration when heated by sunlight in space, while the folding-induced shape bifurcation and buckling are prevented using a kirigami hinge design. The shape transformation is demonstrated in lab by a tubular and an origami structure that are formed from a flat membrane when heated to 82 °C in oven. Thermal radiation analyses have also verified the feasibility of sunlight-activated folding in space when vapour-deposited metallic coatings are applied onto the hinges. The proposed material offers a new generation of gossamer space membrane that can automatically morph from a stowed configuration to a load-bearing structure, and potentially provide built-in functionalities.

Successive torus doubling and birth of strange non‐chaotic attractors in non‐linear electronic circuit

The authors experimentally demonstrate successive torus doubling and the birth of strange non-chaotic attractors (SNAs) in a quasi-periodically forced Chua's oscillator. So far it has been believed that the torus doubling occurs only a finite number of times. In this Letter, the authors report experimental observation of a certain kind of torus doubling called swollen shape bifurcation occurs an infinite number of times and leads to the birth of SNA. In the Poincare of the section, the torus undergoes a series of period doubling and after a particular value of control parameter, the infinitely period doubled torus in the localised regime termed as a chaotic band. While the Lyapunov exponent of the attractor has a negative value and confirms the attractor becomes strange and non-chaotic. Experimentally observed results are confirmed by a Poincare map, singular-continuous spectrum analysis and the finite-time Lyapunov exponent.

Shape bifurcation of a pressurized ellipsoidal balloon

It is well-known that for most spherical and cylindrical rubber balloons the pressure versus volume curve associated with uniform inflation both has an N-shape, but their shape bifurcation has different characters: whereas a spherical balloon tends to bifurcate into a pear shape through localized thinning near one of the poles, a cylindrical balloon would always bulge out locally in a symmetric manner. To understand the connection between these two different bifurcation behaviors, we study in this paper the shape bifurcation of an ellipsoidal balloon which becomes a spherical balloon when the three axes are identical, and approximates a cylindrical balloon when one axis is much larger than the other two axes. The ellipsoidal shape is obtained by rotating an ellipse about one of its axes, that gives rise to two possibilities: a rugby shape or a pumpkin shape. It is shown that for a rugby-shaped balloon, there exists a threshold axes ratio below which the slender ellipsoidal balloon behaves more like a tube and bifurcation into a pear shape becomes impossible, whereas for a pumpkin-shaped balloon bifurcation into a pear shape is always possible.

Shape Bifurcation of a Spherical Dielectric Elastomer Balloon Under the Actions of Internal Pressure and Electric Voltage

Under the actions of internal pressure and electric voltage, a spherical dielectric elastomer balloon usually keeps a sphere during its deformation, which has also been assumed in many previous studies. In this article, using linear perturbation analysis, we demonstrate that a spherical dielectric elastomer balloon may bifurcate to a nonspherical shape under certain electromechanical loading conditions. We also show that with a nonspherical shape, the dielectric elastomer balloon may have highly inhomogeneous electric field and stress/stretch distributions, which can lead to the failure of the system. In addition, we conduct stability analysis of the dielectric elastomer balloon in different equilibrium configurations by evaluating its second variation of free energy under arbitrary perturbations. Our analyses indicate that under pressure-control and voltage-control modes, nonspherical deformation of the dielectric elastomer balloon is energetically unstable. However, under charge-control or ideal gas mass-control mode, nonspherical deformation of the balloon is energetically stable.

Shapes of sedimenting soft elastic capsules in a viscous fluid.

Soft elastic capsules which are driven through a viscous fluid undergo shape deformation coupled to their motion. We introduce an iterative solution scheme which couples hydrodynamic boundary integral methods and elastic shape equations to find the stationary axisymmetric shape and the velocity of an elastic capsule moving in a viscous fluid at low Reynolds numbers. We use this approach to systematically study dynamical shape transitions of capsules with Hookean stretching and bending energies and spherical rest shape sedimenting under the influence of gravity or centrifugal forces. We find three types of possible axisymmetric stationary shapes for sedimenting capsules with fixed volume: a pseudospherical state, a pear-shaped state, and buckled shapes. Capsule shapes are controlled by two dimensionless parameters, the Föppl-von-Kármán number characterizing the elastic properties and a Bond number characterizing the driving force. For increasing gravitational force the spherical shape transforms into a pear shape. For very large bending rigidity (very small Föppl-von-Kármán number) this transition is discontinuous with shape hysteresis. The corresponding transition line terminates, however, in a critical point, such that the discontinuous transition is not present at typical Föppl-von-Kármán numbers of synthetic capsules. In an additional bifurcation, buckled shapes occur upon increasing the gravitational force. This type of instability should be observable for generic synthetic capsules. All shape bifurcations can be resolved in the force-velocity relation of sedimenting capsules, where up to three capsule shapes with different velocities can occur for the same driving force. All three types of possible axisymmetric stationary shapes are stable with respect to rotation during sedimentation. Additionally, we study capsules pushed or pulled by a point force, where we always find capsule shapes to transform smoothly without bifurcations.

Volume regulation and shape bifurcation in the cell nucleus.

Alterations in nuclear morphology are closely associated with essential cell functions, such as cell motility and polarization, and correlate with a wide range of human diseases, including cancer, muscular dystrophy, dilated cardiomyopathy and progeria. However, the mechanics and forces that shape the nucleus are not well understood. Here, we demonstrate that when an adherent cell is detached from its substratum, the nucleus undergoes a large volumetric reduction accompanied by a morphological transition from an almost smooth to a heavily folded surface. We develop a mathematical model that systematically analyzes the evolution of nuclear shape and volume. The analysis suggests that the pressure difference across the nuclear envelope, which is influenced by changes in cell volume and regulated by microtubules and actin filaments, is a major factor determining nuclear morphology. Our results show that physical and chemical properties of the extracellular microenvironment directly influence nuclear morphology and suggest that there is a direct link between the environment and gene regulation.

Modelling fibers in growing disks of soft tissues

Despite its simple geometry and pertinence to biological systems, the growth of soft tissue disks has not been studied systematically in finite elasticity. Here with this simple geometry, we perform theoretical studies of constitutive laws concerning fibrous samples in growth or atrophy. Considering the radial growth of an incompressible neo-Hookean disk of matter, reinforced by fibers, we focus on the possible shape bifurcation from the circular to the wavy geometry. By analytical means based on a variational formulation of the theory of elasticity with growth we show that the radial geometry is lost for a critical growth anisotropy coefficient which plays the role of a control bifurcation parameter. Above a threshold which depends on the fiber invariants, the border of the disk becomes undulated with selection of a low wavenumber for low anisotropic coefficient. Radially or circumferentially oriented fibers favor undulations, but not intermediate cross-linked fibers, which inhibit undulations. Our systematic analysis shows the key role of the anisotropic growth coefficient as well as the fiber orientation for the observation of undulated patterns. Such models can explain experimental observations for skin tumors, biofilms and yeast colonies.

Studying Relationships between the Fractal Dimension of the Drainage Basins and Some of Their Geomorphological Characteristics

Complex nonlinear dynamic systems are ubiquitous in the landscapes and phenomena studied by earth sciences in general and by geomorphology in particular. Many natural landscape features have an aspect such as fractals. In the many geomorphologic phenomena such as river networks and coast lines this is visible. In recent years fractal geometry offers as an option for modeling river geometry and physical processes of rivers. The fractal dimension is a statistical quantity that indicates how a fractal scales with the shrink, the space occupied. This theory has the mathematical basis but also applied in geomorphology and also shown great success. Physical behavior of many natural processes as well as using fractal geometry is predictable relations. Behavior of complex natural phenomena as rivers has always been of interest to researchers. In this study using data basic maps, drainage networks map and Digital Elevation Model of the ground was prepared. Then applying the rules Horton-Strahler river network, fractal dimensions were calculated to examine the relationship between fractal dimension and some rivers geomorphic features were investigated. Results showed fractal dimension of watersheds have meaningful relations with factors such as shape form, area, bifurcation ratio and length ratio in the watersheds.

Zêta Hydride Precipitation in Zirconium Alloys: an Example of Elastically Driven Morphology of Coherent Trigonal Precipitates inside a Сlose-Packed Hexagonal Matrix

The influence of a crystallographic symmetry break on the morphology of precipitates during the coherent precipitation of a trigonal phase in a close packed hexagonal matrix is analyzed. It is pointed out that in spite of the isotropy of the stress free strain of the precipitate in the basal plane, the existence of an extra elastic constant in the precipitate (associated to the loss of symmetry) induces a morphological evolution from a shape having a symmetry of revolution around the threefold axis to a needle-like one oriented along the compact directions in the basal plane. These general considerations are applied to the case of zêta zirconium hydrides the crystallography of which has been recently identified to be coherent with that of the alpha Zr matrix. The influence of symmetry break and elastic heterogeneity on precipitation morphology has been numerically addressed by using different approaches. An analytical approximation to the elastic energy based on Eshelby equivalent inclusion method allows obtaining a qualitative criterion to determine the occurrence of a shape bifurcation of zêta hydrides.

Multiple-lobed bifurcation of rotating liquid drops levitated by ultrasound

It is previously predicted that the equilibrium shape of a rotating liquid drop evolves from the axisymmetric to the two-, three-, and four-lobed morphologies as the angular velocity increases. Although the two- and three-lobed shape bifurcations have been observed in experiments, the four-lobed equilibrium shape is scarcely reported. Here, we investigate the multiple-lobed shape bifurcations of rotating drops by using acoustic levitation, and in particular, follow the evolution of the four-lobed equilibrium shape. A new shape family of rotating drops characterized by five-lobed bifurcation is also observed, which is unexpected in the theoretical predictions. A numerical method is employed to simulate the shape evolution of acoustically levitated and rotating drops. And the results validate the existence of bifurcation point shifts among all the lobed-shape families due to the initial drop flattening induced by the acoustic radiation pressure, which plays a decisive role in the emergence of the five-lobed shape.

Propulsion with a Rotating Elastic Nanorod

The dynamics of a rotating elastic filament is investigated using Stokesian simulations. The filament, straight and tilted with respect to its rotation axis for small driving torques, undergoes at a critical torque a strongly discontinuous shape bifurcation to a helical state. It induces a substantial forward propulsion whatever the sense of rotation: a nanomechanical force-rectification device is established.

Droplets, bubbles, and vesicles at chemically structured surfaces

Liquid droplets, gas bubbles, and membrane vesicles which are in contact with chemicallystructured substrate surfaces can undergo morphological transitions or shape transformations.The structured surfaces considered here consist of two types of surface domains,γ and δ, which attract and repel the droplets, bubbles, and vesicles, respectively. For droplets on a stripedγ domain, one has to distinguish droplets with fixed end caps from those with freely movingend caps. Both types of channels undergo morphological wetting transitions. For vesicles,one has a strong adhesion regime in which the vesicle shapes have constant mean curvatureand exhibit effective contact angles. One can then map the shape bifurcation diagram forvesicles onto the one for droplets if one includes the constraint of fixed membrane area. Wealso report preliminary experimental observations of the adhesion of vesicles to chemicallystructured surfaces.

Two- and three-dimensional equilibrium morphology of a misfitting particle and the Gibbs–Thomson effect

The equilibrium shapes of misfitting precipitates in elastically anisotropic systems are obtained in both two and three dimensions, and the corresponding Gibbs–Thomson equation is derived as a function of the characteristic ratio between elastic and interfacial energies, L′. The effect of elastic inhomogeneity is investigated systematically. For soft or moderately hard particles, the stable equilibrium shape bifurcates from a fourfold symmetric shape to a twofold symmetric one in 2D and from a cubic symmetric shape to a plate-like one in 3D. For a very hard particle, the shape bifurcation is not observed in 2D for the range of L′ investigated, but both plate-like and rod-like shapes are found in 3D. The computed Gibbs–Thomson equation is well approximated by a piecewise linear function of L′. Predictions are made for coarsening of many-particle systems based on an established mean-field theory. The results predict that the elastic stress has no effect on coarsening kinetics where most particles are highly symmetric (fourfold in 2D and cubic in 3D), and the exponent remains 1/3 but the rate constant increases if stress is sufficient to induce symmetry-breaking bifurcation on most particles.