Bénard-Marangoni Instability of a Two-Layer System with Allowance for Variations in the Interfacial Internal Energy

The effect of variations of the internal surface energy due to local increments in the interfacial area on the conditions of onset of thermocapillary Marangoni instability in a two-layer system of reduced-viscosity fluids is studied. It is shown that in the linear approximation the effect considered leads to stabilization of the development of the monotonic instability mode.     

Combined PDA and LIF applied to size–temperature correlations measurements in a heated spray

This paper aims to demonstrate the possibility to achieve droplet temperature measurements per droplet size class by combining two-color laser-induced fluorescence (LIF) and phase Doppler analyzer (PDA). For that purpose, PDA and LIF signal acquisitions are synchronized on the same time base. LIF signal is processed on each of the defined size classes in order to derive the droplet temperature. Since PDA is roughly sensitive to D ² and LIF roughly to D ³, the detection range of the combination of the two techniques in term of droplet size is carefully analyzed. Finally, the technique is demonstrated on a spray of n-decane injected in a turbulent over-heated air flow. The influence of the droplet size and Stokes number on the heating process of the droplets is clearly highlighted.     

Finite-time synchronization control for a class of perturbed nonlinear systems with fixed convergence time and hysteresis quantizer: applied to Genesio–Tesi chaotic system

In the present article, a terminal sliding mode control strategy has been proposed in order to address the synchronization problem for a class of perturbed nonlinear systems with fixed convergence time and input quantization. The proposed protocol guarantees the fixed-time convergence of the sliding manifold to the origin, which means that the convergence time of the proposed sliding manifold does not change on the variations of initial values, different from typical control methods. Here, the hysteresis quantizer, as a specific type of quantizer with nonlinear sector-bounded, is applied in order to quantize the input signal. The proposed quantized control scheme vigorously prevents the potential adverse chattering phenomenon which is experienced in the common quantization methods. The proposed controller does not need the limiting criteria related to considered parameters of quantization compared to recent control approaches. Finally, the designed controller is implemented on the perturbed Genesio–Tesi (G–T) chaotic systems to verify effectiveness and strength of the proposed method.

     

Multiple scales and normal forms in a ring of delay coupled oscillators with application to chaotic Hindmarsh–Rose neurons

We study the appearance and stability of spatiotemporal periodic patterns like phase-locked oscillations, mirror-reflecting waves, standing waves, in-phase or antiphase oscillations, and coexistence of multiple patterns, in a ring of bidirectionally delay coupled oscillators. Hopf bifurcation, Hopf–Hopf bifurcation, and the equivariant Hopf bifurcation are studied in the viewpoint of normal forms obtained by using the method of multiple scales which is a kind of perturbation technique, thus a clear bifurcation scenario is depicted. We find time delay significantly affects the dynamics and induces rich spatiotemporal patterns. With the help of the unfolding system near Hopf–Hopf bifurcation, it is confirmed in some regions two kinds of stable oscillations may coexist. These phenomena are shown for the delay coupled limit cycle oscillators as well as for the delay coupled chaotic Hindmarsh–Rose neurons.     

N-Fold generalized Darboux transformation and semirational solutions for the Gerdjikov-Ivanov equation for the Alfvén waves in a plasma

Nonlinear Dynamics - Alfvén waves propagating parallel to the ambient magnetic field are modeled via the Gerdjikov-Ivanov equation. With respect to the transverse magnetic field perturbation...     

Instability conditions for a class of switched linear systems with switching delays based on sampled-data analysis: applications to DC–DC converters

General instability (critical) conditions for a class of switched linear systems (such as DC–DC converters) with switching delays are derived. Many instability conditions for the systems with fixed/variable-switching frequency under various control schemes are also derived. The conditions also show the required ramp slopes to stabilize the converters. Some previously known instability conditions become special cases in this generalized framework. Given an arbitrary control scheme, a systematic procedure is proposed to derive the instability condition for that control scheme. Different control schemes (such as \(V^{2}\) control and voltage/current mode control, for example) are shown to have similar forms of instability conditions.     

One-way coupled fluid–structure interaction of gas–liquid slug flow in a horizontal pipe: Experiments and simulations

Pipelines conveying a multiphase mixture must withstand the cyclic induced stresses that occur due to the alternating motion of gas pockets and liquid slugs. Few previous studies have considered gas–liquid slug flow and the associated fluid–structure interaction problems. In this study, experimental and numerical techniques were adopted to simulate and analyze the two-phase slug flow and the associated stresses in the pipe structure. In the numerical simulation, a one-way coupled fluid–structure framework was developed to explore the slug flow interaction with a horizontal pipe assembly under various superficial gas and liquid velocities. A modified Volume of Fluid and finite element methods were utilized to model the fluid and structure domains. The file-based coupling technique was adopted to execute the coupling mechanism. By contrast, slug characteristics were measured experimentally, while Bi-axial strain gauges were used to capture time-varying strain signals. Excellent agreements between the predicted and measured stress results were achieved with a maximum error of 10.2 %. It was found that at constant superficial liquid velocity, the maximum induced stresses on the pipe wall increased with increasing the slug length and slug velocity. While for the slug frequency, the maximum principal stresses decreased with increasing the slug frequency.     

Investigation of bubble breakup and coalescence in a packed-bed reactor – Part 1: A comparative study of bubble breakup and coalescence models

In a packed-bed reactor a comparative study of bubble breakup and coalescence models has been investigated to study bubble size distributions as a function of the axial location. The bubble size distributions are obtained by solving population balance equations that describe gas–liquid interactions. Each combination of bubble breakup and coalescence models is examined under two inlet flow conditions: (1) predominant bubble breakup flow and (2) predominant bubble coalescence flow. The resulting bubble size distributions, breakup and coalescence rates estimated by individual models, are qualitatively compared to each other. The change of bubble size distributions along the axial direction is also described with medians. The medians resulting from CFD analyses are compared against the experimental data. Since the predictions estimated by CFD analyses with the existing bubble breakup and coalescence models do not agree with the experimental data, a new bubble breakup and coalescence model that takes account of the geometry effects is required to describe gas–liquid interactions in a packed-bed reactor.     

Analysis of vertical cracking phenomena in tensile-strained epitaxial film on a substrate: Part II. Application to InxGa1−xAs/InP system

Cracking phenomena in tensile-strained In_xGa_1?xAs epitaxial film on an InP substrate are analyzed via the formulation given in Part I [Lee, S., Choi, S.T., Earmme, Y.Y., 2006. Analysis of vertical cracking phenomena in tensile-strained epitaxial film on a substrate: Part I. Mathematical formulation. International Journal of Solids and Structures 43, 3401–3413], where the solution for a dislocation in an anisotropic trimaterial is used as a fundamental solution and the crack is modeled by the continuous distribution of dislocations. Misfit strains and stresses are evaluated as a function of indium content x in an In_xGa_1?xAs/InP system. A single crack and periodic cracks, respectively, induced by the misfit stresses are considered. The crack opening profile, the crack mouth displacement, and the energy release rate as a function of the crack length are obtained. The critical conditions for a single crack and periodic cracks, respectively, are thus obtained, and are found to depend on the film thickness, the crack length, and the period of the cracks. The results of these analyses are also compared with published data obtained from experiments.     

Dynamics and bifurcations in the weak electrolyte model for electroconvection of nematic liquid crystals: a Ginzburg–Landau approach

In this paper we present the results of a bifurcation study of the weak electrolyte model for nematic electroconvection, for values of the parameters including experimentally measured values of the nematic I52. The linear stability analysis shows the existence of primary bifurcations of Hopf type, involving normal as well as oblique rolls. The weakly nonlinear analysis is performed using four globally coupled complex Ginzburg–Landau equations for the waves' envelopes. If spatial variations are ignored, these equations reduce to the normal form for a Hopf bifurcation with $O(2)\times O(2)$ symmetry. A rich variety of stable waves, as well as more complex spatiotemporal dynamics is predicted at onset. A temporal period doubling route to spatiotemporal chaos, corresponding to a period doubling cascade towards a chaotic attractor in the normal form, is identified. Eckhaus stability boundaries for travelling waves are also determined. The methods developed in this paper provide a systematic investigation of nonlinear physical mechanisms generating the patterns observed experimentally, and can be generalized to any two-dimensional anisotropic systems with translational and reflectional symmetry.     

Importance of unsteady contributions to force and heating for particles in compressible flows : Part 1: Modeling and analysis for shock–particle interaction

Shock–particle interaction is an important phenomenon. The interaction can be accurately resolved by direct numerical simulations. However, as the length scales of interest are much larger than the particle size in many applications, fully resolving the flow around the particle is impractical. Therefore, rigorous model for momentum and energy exchange in the interaction is very important. Shock–particle interaction is strongly time-dependent, so unsteady mechanisms play important roles in momentum and energy transfer. A model that includes unsteady contributions to force and heating is proposed. The model is used to investigate particle interactions with a planar shock wave and a spherical shock wave. The peak values and the net effects of unsteady contributions are used to measure their importance. The results show the peak values of unsteady contributions are much larger than the quasi-steady ones for a wide range of particle parameters. The net effects of unsteady contributions are important when the particle-to-gas density ratio is small. For the flow behind the spherical shock is unsteady and non-uniform, unsteady contributions have long-time influence on the particle evolution.     

Chapman–Enskog solutions to arbitrary order in Sonine polynomials IV: Summational expressions for the diffusion- and thermal conductivity-related bracket integrals

The Chapman–Enskog solutions of the Boltzmann equations provide a basis for the computation of important transport coefficients for both simple gases and gas mixtures. These coefficients include the viscosity, the thermal conductivity, and the diffusion coefficient. In a preceding paper on simple gases, we have shown that the use of higher-order Sonine polynomial expansions enables one to obtain results of arbitrary precision that are free of numerical error. In two subsequent papers, we have extended our original simple gas work to encompass binary gas mixture computations of the viscosity, thermal conductivity, diffusion, and thermal diffusion coefficients to high-order. In all of this previous work we retained the full dependence of our solutions on the molecular masses, the molecular sizes, the mole fractions, and the intermolecular potential model via the omega integrals up to the final point of solution via matrix inversion. The elements of the matrices to be inverted are, in each case, determined by appropriate combinations of bracket integrals which contain, in general form, all of the various dependencies. Since accurate, explicit, general expressions for bracket integrals are not available in the literature beyond order 3, and since such general expressions are necessary for any extensive program of computations of the transport coefficients involving Sonine polynomial expansions to higher orders, we have investigated alternative methods of constructing appropriately general bracket integral expressions that do not rely on the term-by-term, expansion and pattern matching techniques that we developed for our previous work. It is our purpose in this paper to report the results of our efforts to obtain useful, alternative, general expressions for the bracket integrals associated with the diffusion- and thermal conductivity-related Chapman–Enskog solutions for gas mixtures. Specifically, we have obtained such expressions in summational form that are conducive to use in high-order transport coefficient computations for arbitrary gas mixtures and have computed and reported explicit expressions for all of the orders up to 5.     

Correction to: Effect of trigonometric sine,square and triangular wavetype time-periodic gravity-aligned oscillations on Rayleigh–Bénard convection in Newtonian liquids and Newtonian Nanoliquids

Meccanica - The original article has been updated due to typesetting mistakes made in Section 2.2 Mathematical formulation, Table 1 and in Equation (51).     

Chapman–Enskog solutions to arbitrary order in Sonine polynomials III: Diffusion,thermal diffusion,and thermal conductivity in a binary,rigid-sphere,gas mixture

The Chapman–Enskog solutions of the Boltzmann equation provide a basis for the computation of important transport coefficients for both simple gases and gas mixtures. These coefficients include the viscosity, the thermal conductivity, and the diffusion coefficient. In a preceding paper (I), for simple, rigid-sphere gases (i.e. single-component, monatomic gases) we have shown that the use of higher-order Sonine polynomial expansions enables one to obtain results of arbitrary precision that are free of numerical error and, in a second paper (II), we have extended our initial simple gas work to modeling the viscosity in a binary, rigid-sphere, gas mixture. In this latter paper we reported an extensive set of order 60 results which are believed to constitute the best currently available benchmark viscosity values for binary, rigid-sphere, gas mixtures. It is our purpose in this paper to similarly report the results of our investigation of relatively high-order (order 70), standard, Sonine polynomial expansions for the diffusion- and thermal conductivity-related Chapman–Enskog solutions for binary gas mixtures of rigid-sphere molecules. We note that in this work, as in our previous work, we have retained the full dependence of the solution on the molecular masses, the molecular sizes, the mole fractions, and the intermolecular potential model via the omega integrals. For rigid-sphere gases, all of the relevant omega integrals needed for these solutions are analytically evaluated and, thus, results to any desired precision can be obtained. The values of the transport coefficients obtained using Sonine polynomial expansions for the Chapman–Enskog solutions converge and, therefore, the exact diffusion and thermal conductivity solutions to a given degree of convergence can be determined with certainty by expanding to sufficiently high an order. We have used Mathematica® for its versatility in permitting both symbolic and high-precision computations. Our results also establish confidence in the results reported recently by other authors who used direct numerical techniques to solve the relevant Chapman–Enskog equations. While in all of the direct numerical methods more-or-less full calculations need to be carried out with each variation in molecular parameters, our work has utilized explicit, general expressions for the necessary matrix elements that retain the complete parametric dependence of the problem and, thus, only a matrix inversion at the final step is needed as a parameter is varied. This work also indicates how similar results may be obtained for more realistic intermolecular potential models and how other gas-mixture problems may also be addressed with some additional effort.     

Influence of friction and asymmetric freeplay on the limit cycle oscillation in aeroelastic system: An extended Hénon’s technique to temporal integration

Nonlinear effects such as friction and freeplay on the control surfaces can affect aeroelastic dynamics during flight. In particular, these nonlinearities can induce limit cycle oscillations (LCO), changing the system stability, and because of this it is essential to employ computational methods to predict this type of motion during the aircraft development cycle. In this context, the present article presents a matrix notation for describing the Hénon’s method used to reduce errors when considering piecewise linear nonlinearities in the numerical integration process. In addition, a new coordinate system is used to write the aeroelastic system of equations. The proposal defines a displacement vector with generalized and physical variables to simplify the computational implementation of the Hénon’s technique. Additionally, the article discusses the influence of asymmetric freeplay and friction on the LCO of an airfoil with control surface. The results show that the extended Hénon’s technique provides more accurate LCO predictions, that friction can change the frequency and amplitude of these motions, and the asymmetry of freeplay is important to determine the LCO behavior.