Curvature and Velocity of Methane-Air Bunsen Flame Tips

PIV and photographic recording are used to measure the velocity of the fresh gas and the shape of the reaction layer in a region around the tip of a methane-air Bunsen flame attached to a cylindrical burner. The results compare well with numerical simulations carried out with an infinite activation energy reaction model. The experimental and numerical results confirm that the well-known linear relation between flame velocity and flame stretch derived from asymptotic theory for weakly curved and strained flames is valid for small and moderate values of the flame stretch if the modified definition of stretch introduced by Echekki and Mungal (Proc Combust Inst 23:455?C461, 1990) and Poinsot et al. (Combust Sci Technol 81:45?C73, 1992) is used. However, the relation between flame velocity and modified stretch ceases to be linear and approaches a square root law for large values of the stretch, when the curvature of the flame tip becomes large compared to the inverse of the thickness of a planar flame.     

Local Controllability to Trajectories of the Magnetohydrodynamic Equations

In this paper we prove the local controllability to trajectories of the three dimensional magnetohydrodynamic equations by means of two internal controls, one in the velocity equations and the other in the magnetic field equations and both localized in an arbitrary small subset with not empty interior of the domain. This paper improves the previous results (Barbu et al. in Comm Pure Appl Math 56:732–783, 2003; Barbu et al. in Adv Differ Equ 10:481–504, 2005; Havârneanu et al. in Adv Differ Equ 11:893–929, 2006; Havârneanu, in SIAM J Control Optim 46:1802–1830, 2007) where the second control is not localized and it allows to deduce the local controllability to trajectories with boundary controls. The proof relies on the Carleman inequality for the Stokes system of Imanuvilov et al. (Carleman estimates for second order nonhomogeneous parabolic equations, preprint) to deal with the velocity equations and on a new Carleman inequality for a Dynamo-type equation to deal with the magnetic field equations.     

Effects of Turbulence, Evaporation and Heat Release on the Dispersion of Droplets in Dilute Spray Jets and Flames

The dispersion characteristics of a selection of non-evaporating non-reacting, evaporating non-reacting, and reacting dilute spray jets issuing in ambient air (Gounder et al, Combust Sci Technol 182:702–715, 2010; Masri and Gounder, Combust Flame 159:3372–3397, 2010) and in a hot coflow (Oloughlin and Masri, Flow Turbul Combust 89:13–35, 2012) are analysed. Other than the cases found in those contributions, two additional sprays of kerosene have been investigated in order to systematically study the effects of evaporation. The burners are well designed such that boundary conditions may be accurately measured for use in numerical simulations. The dynamics and dispersion characteristics are analysed by conditioning results on the droplet Stokes numbers and by systematically investigating changes in dispersion and dynamics as a function of carrier air velocity, liquid loading, ignition method, and location within the flame or spray jet. The tendency for droplet dispersion defined by the ratio of radial rms velocity to axial mean velocity varies significantly between reacting and non-reacting flows. However, dispersion is found to be largely unaffected by evaporation. The total particle concentration, or number density of droplets within the spray has also been used as a direct measure of spray dispersion with the effect of evaporation on a turbulent polydisperse spray being isolated by investigating acetone and kerosene sprays with similar boundary conditions. The rate of change of droplet size with radial position is almost identical for the kerosene and acetone cases. The dispersion characteristics, closely related to the ‘fan spreading’ phenomenon are dependant on the carrier air velocity and axial location within the spray.     

Flow temporal reconstruction from non-time-resolved data part I: mathematic fundamentals

At least two circumstances point to the need of postprocessing techniques to recover lost time information from non-time-resolved data: the increasing interest in identifying and tracking coherent structures in flows of industrial interest and the high data throughput of global measuring techniques, such as PIV, for the validation of computational fluid dynamics (CFD) codes. This paper offers the mathematic fundamentals of a space--time reconstruction technique from non-time-resolved, statistically independent data. An algorithm has been developed to identify and track traveling coherent structures in periodic flows. Phase-averaged flow fields are reconstructed with a correlation-based method, which uses information from the Proper Orthogonal Decomposition (POD). The theoretical background shows that the snapshot POD coefficients can be used to recover flow phase information. Once this information is recovered, the real snapshots are used to reconstruct the flow history and characteristics, avoiding neither the use of POD modes nor any associated artifact. The proposed time reconstruction algorithm is in agreement with the experimental evidence given by the practical implementation proposed in the second part of this work (Legrand et al. in Exp Fluids, 2011), using the coefficients corresponding to the first three POD modes. It also agrees with the results on similar issues by other authors (Ben Chiekh et al. in 9 Congrès Francophone de Vélocimétrie Laser, Bruxelles, Belgium, 2004; Van Oudheusden et al. in Exp Fluids 39-1:86?C98, 2005; Meyer et al. in 7th International Symposium on Particle Image Velocimetry, Rome, Italy, 2007a; in J Fluid Mech 583:199?C227, 2007b; Perrin et al. in Exp Fluids 43-2:341?C355, 2007). Computer time to perform the reconstruction is relatively short, of the order of minutes with current PC technology.     

Analytical Validation of a Continuum Model for Epitaxial Growth with Elasticity on Vicinal Surfaces

Within the context of heteroepitaxial growth of a film onto a substrate, terraces and steps self-organize according to misfit elasticity forces. Discrete models of this behavior were developed by Duport et al. (J Phys I 5:1317–1350, 1995) and Tersoff et al. (Phys Rev Lett 75:2730–2733, 1995). A continuum limit of these was in turn derived by Xiang (SIAM J Appl Math 63:241–258, 2002) (see also the work of Xiang and Weinan Phys Rev B 69:035409-1–035409-16, 2004; Xu and Xiang SIAM J Appl Math 69:1393–1414, 2009). In this paper we formulate a notion of weak solution to Xiang’s continuum model in terms of a variational inequality that is satisfied by strong solutions. Then we prove the existence of a weak solution.     

Simultaneous particle image velocimetry and chemiluminescence visualization of millisecond-pulsed current�Cvoltage-induced perturbations of a premixed propane/air flame

The effects of millisecond-wide, pulsed current?Cvoltage-induced behavior in premixed laminar flames have been investigated through the simultaneous collection of particle image velocimetry (PIV) and chemiluminescence data with particular attention paid to the onset mechanisms. Disturbances caused by applied voltages of 2?kV over a 30-mm gap to a downward propagating, atmospheric pressure, premixed propane/air flame with a flow speed near 2?m/s and an equivalence ratio of 1.06 are investigated. The combined PIV and chemiluminescence-based experimental data show the observed disturbance originates only in or near the cathode fall region very close to the burner base. The data also suggest that the coupling mechanism responsible for the flame disturbance behavior is fluidic in nature, developing from the radial positive chemi-ion distribution and an ion-drift current-induced net body force that acts along the annular space discharge distribution in the reaction zone in or near the cathode fall. This net body force causes a reduction in flow speed above these near cathodic regions causing the base of the flame to laterally spread. Also, this effect seems to produce a velocity gradient leading to the transition of a laminar flame to turbulent combustion for higher applied current?Cvoltage conditions as shown in previous work (Marcum and Ganguly in Combust Flame 143:27?C36, 2005; Schmidt and Ganguly in 48th AIAA aerospace sciences meeting. Orlando, 2010).     

Experimental and Numerical Study of the Scalar Turbulent/Non-Turbulent Interface Layer in a Jet Flow

Based on two large-eddy simulations (LES) of a non-reacting turbulent round jet with a nozzle based Reynolds number of 8,610 with the same configuration as the one that has recently been investigated experimentally (Gampert et al., 2012; J Fluid Mech, 2012; J Fluid Mech 724:337, 2013), we examine the scalar turbulent/non-turbulent (T/NT) interface layer in the mixture fraction field of the jet flow between ten and thirty nozzle diameters downstream. To this end, the LES—one with a coarse grid and one with a fine grid—are in a first step validated against the experimental data using the axial decay of the mean velocity and the mean mixture fraction as well as based on radial self-similar profiles of mean and root mean square values of these two quantities. Then, probability density functions (pdf) of the mixture fraction at various axial and radial positions are compared and the quality of the LES is discussed. In general, the LES results are consistent with the experimental data. However, in the flow region where the imprint of the T/NT interface layer is dominant in the mixture fraction pdf, discrepancies are observed. In a next step, statistics of the T/NT interface layer are studied, where a satisfactory agreement for the pdf of the location of the interface layer from the higher resolved LES with the experimental data is observed, while the one with the coarse grid exhibits considerable deviations. Finally, the mixture fraction profile across the interface is investigated where the same trend as for the pdf of the location is present. In particular, it is found that the sharp interface that is present in experimental studies (Gampert et al., J Fluid Mech, 2013; Westerweel et al., J Fluid Mech 631:199, 2009) is less distinct in the LES results and rather diffused in radial direction outside of the T/NT interface layer.     

Simultaneous measurement of velocity and pressure in a plane jet

A new technique was developed for the simultaneous measurement of velocity and pressure in turbulent flows. To accomplish this objective, a new probe (hereafter called the combined probe) that consists of an X-type hot-wire probe and a newly devised pressure probe was developed. The pressure probe was miniaturized by the MEMS fabrication process and by using a 0.1-in. microphone as a pressure sensor for improving the spatial resolution. This pressure probe was placed between two hot-wire sensors of which the X-type hot-wire probe was composed. The pressure probe was given a hemispherical tip, like that of a pitot tube, because an earlier pressure probe with a conical tip suffered from a reduction in spatial resolution. The spatial arrangement of the pressure probe and the hot-wire probe for the combined probe was carefully determined, because there was a risk that the measurement accuracy of one probe will be influenced by disturbances caused by the other probe when the two probes were placed very close to each other. Therefore, the combined probe was arranged to engender no noticeable interference between the velocity data and the pressure data measured by their respective probes. As one application of this combined probe, simultaneous measurements of pressure and two components of instantaneous velocity were performed in a plane jet. The turbulent energy budget and the cross-correlation coefficient of velocity and pressure in the intermittent region of the plane jet were estimated. The results show that the mean streamwise velocity, velocity fluctuation, and pressure fluctuation profiles were consistent with those measured individually using the X-type hot-wire probe or pressure probe. Moreover, it was shown that the integral value of the diffusion term (which should theoretically be equal to zero) in the turbulent energy transport equation was closer to zero than previous reports (Bradbury in J Fluid Mech 23(Part 1):31–64, 1965). In addition, the time variation of the cross-correlation coefficient in the intermittent region supports the vortex structure model predicted in previous studies (Browne et?al. in J Fluid Mech 149:355–373, 1984; Tanaka et?al. JSME Int J Ser B 49(4):899–905, 2006; Sakai et?al. J Fluid Sci Technol 2(3):611–622, 2007).     

Well-Posedness for the Motion of Physical Vacuum of the Three-dimensional Compressible Euler Equations with or without Self-Gravitation

This paper concerns the well-posedness theory of the motion of a physical vacuum for the compressible Euler equations with or without self-gravitation. First, a general uniqueness theorem of classical solutions is proved for the three dimensional general motion. Second, for the spherically symmetric motions, without imposing the compatibility condition of the first derivative being zero at the center of symmetry, a new local-in-time existence theory is established in a functional space involving less derivatives than those constructed for three-dimensional motions in (Coutand et al., Commun Math Phys 296:559–587, 2010; Coutand and Shkoller, Arch Ration Mech Anal 206:515–616, 2012; Jang and Masmoudi, Well-posedness of compressible Euler equations in a physical vacuum, 2008) by constructing suitable weights and cutoff functions featuring the behavior of solutions near both the center of the symmetry and the moving vacuum boundary.     

On the Formulation of Continuum Thermodynamic Models for Solids as General Equations for Non-equilibrium Reversible-Irreversible Coupling

The purpose of this work is the comparison of some aspects of the formulation of material models in the context of continuum thermodynamics (e.g., ?ilhavý in The mechanics and thermodynamics of continuous media, Springer, Berlin, 1997) with their formulation in the form of a General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC: e.g., Grmela and Öttinger in Phys. Rev. E 56: 6620–6632, 1997; Öttinger and Grmela in Phys. Rev. E 56: 6633–6655, 1997; Öttinger in Beyond equilibrium thermodynamics, Wiley, New York, 2005; Grmela in J. Non-Newton. Fluid Mech. 165: 980–998, 2010). A GENERIC represents a generalization of the Ginzburg-Landau model for the approach of non-equilibrium systems to thermodynamic equilibrium. Originally developed to formulate non-equilibrium thermodynamic models for complex fluids, it has recently been applied to anisotropic inelastic solids in a Eulerian setting (Hütter and Tervoort in J. Non-Newton. Fluid Mech. 152: 45–52, 2008; 53–65, 2008; Adv. Appl. Mech. 42: 254–317, 2009) as well as to damage mechanics (Hütter and Tervoort in Acta Mech. 201: 297–312, 2008). In the current work, attention is focused for simplicity on the case of thermoelastic solids with heat conduction and viscosity in a Lagrangian setting (e.g., ?ilhavý in The mechanics and thermodynamics of continuous media, Springer, Berlin, 1997, Chaps. 9–12). In the process, the relation of the two formulations to each other is investigated in detail. A particular point in this regard is the concept of dissipation and its model representation in both contexts.     

The Two-Dimensional Euler Equations on Singular Domains

We establish the existence of global weak solutions of the two-dimensional incompressible Euler equations for a large class of non-smooth open sets. Loosely, these open sets are the complements (in a simply connected domain) of a finite number of obstacles with positive Sobolev capacity. Existence of weak solutions with L ^p vorticity is deduced from a property of domain continuity for the Euler equations that relates to the so-called γ-convergence of open sets. Our results complete those obtained for convex domains in Taylor (Progress in Nonlinear Differential Equations and their Applications, Vol. 42, 2000), or for domains with asymptotically small holes (Iftimie et al. in Commun Partial Differ Equ 28(1–2), 349–379, 2003; Lopes Filho in SIAM J Math Anal 39(2), 422–436, 2007).     

Traveling Wave Solutions for a Predator?CPrey System With Sigmoidal Response Function

We study the existence of traveling wave solutions for a diffusive predator?Cprey system. The system considered in this paper is governed by a Sigmoidal response function which in some applications is more realistic than the Holling type I, II responses, and more general than a simplified form of the Holling type III response considered before. Our method is an improvement to the original method introduced in the work of Dunbar (J Math Biol 17:11?C32, 1983; SIAM J Appl Math 46:1057?C1078, 1986). A bounded Wazewski set is used in this work while unbounded Wazewski sets were used in Dunbar (1983, 1986). The existence of traveling wave solutions connecting two equilibria is established by using the original Wazewski??s theorem which is much simpler than the extended version in Dunbar??s work.     

Dynamics and Control at Feedback Vertex Sets. I: Informative and Determining Nodes in Regulatory Networks

We consider systems of differential equations which model complex regulatory networks by a graph structure of dependencies. We show that the concepts of informative nodes (Mochizuki and Saito, J Theor Biol 266:323–335, 2010) and determining nodes (Foias and Temam, Math Comput 43:117–133, 1984) coincide with the notion of feedback vertex sets from graph theory. As a result we can determine the long-time dynamics of the entire network from observations on only a feedback vertex set. We also indicate how open loop control at a feedback vertex set, only, forces the remaining network to stably follow prescribed stable or unstable trajectories. We present three examples of biological networks which motivated this work: a specific gene regulatory network of ascidian cell differentiation (Imai et al., Science 312:1183–1187, 2006), a signal transduction network involving the epidermal growth factor in mammalian cells (Oda et al., Mol Syst Biol 1:1–17, 2005), and a mammalian gene regulatory network of circadian rhythms (Mirsky et al., Proc Natl Acad Sci USA 106:11107–11112, 2009). In each example the required observation set is much smaller than the entire network. For further details on biological aspects see the companion paper (Mochizuki et al., J Theor Biol, 2013, in press). The mathematical scope of our approach is not limited to biology. Therefore we also include many further examples to illustrate and discuss the broader mathematical aspects.     

Stability of quadruped robots’ trajectories subjected to discrete perturbations

In this paper, we study the stability of a mathematical model for trajectory generation of a qua-druped robot. We consider that each movement is composed of two types of primitives: rhythmic and discrete. The discrete primitive is inserted as a perturbation of the purely rhythmic movement. The two primitives are modeled by nonlinear dynamical systems. We adapt the theory developed by Golubitsky et?al. in (Physica D 115: 56?C72, 1998; Buono and Golubitsky in J. Math. Biol. 42:291?C326, 2001) for quadrupeds gaits. We conclude that if the discrete part is inserted in all limbs, with equal values, and as an offset of the rhythmic part, the obtained gait is stable and has the same spatial and spatiotemporal symmetry groups as the purely rhythmic gait, differing only on the value of the offset.     

Study of the inertial effect and the nonlinearities of?the?CRONE suspension based on the hydropneumatic technology

In this paper, we emphasize two main effects involved in the CRONE car suspension technology (CRONE: French acronym for Commande Robuste d??Ordre Non Entier). In a first time, we present the influence of the inductive or inertial effect of the pipes that links the different cells of the hydropneumatic car suspension. These components are mainly resistive and capacitive devices. Then, we analyze the nonlinear relations that link the hydraulic power variables (the flow and the pressure) of the hydraulic resistors and the hydropneumatic accumulators and we study the effect of the nonlinear terms on the car suspension response. Our study is based on the gamma RC arrangement developed in Altet et al. (In: Analysis and design of hybrid systems??proceedings of ADHS03, pp. 63?C68. Elsevier, Amsterdam, 2003) and Serrier et al. (In: Proceedings of IDETC/CIE 2005: ASME 2005 international design engineering technical conferences and computers and information in engineering conference, Long Beach, CA, USA, 24?C28 September 2005). In a second time, we focus only on the gamma RLC arrangement, introduced in Abi Zeid Daou et al. (Int. J. Electron. 96(12):1207?C1223, 2009). We show whether the parasite effect due to the pipes or the nonlinear RC components affect the system??s response. The simulation results show that neither the inertial effect caused by these parasite pipes of one meter length nor the use of the nonlinear resistors or the accumulators modifies the response of the gamma RC arrangement.     

Towards the Development of an Evolution Equation for Flame Turbulence Interaction in Premixed Turbulent Combustion

Flame turbulence interaction is one of the leading order terms in the scalar dissipation \(\left (\widetilde {\varepsilon }_{c}\right )\) transport equation [35] and is thus an important phenomenon in premixed turbulent combustion. Swaminathan and Grout [36] and Chakraborty and Swaminathan [15, 16] have shown that the effect of strain rate on the transport of \(\widetilde {\varepsilon }_{c}\) is dominated by the interaction between the fluctuating scalar gradients and the fluctuating strain rate, denoted here by \(\overline {\rho }\widetilde {\Delta }_{c}= \overline {\rho {\alpha }\nabla c^{\prime \prime }S_{ij}^{\prime \prime }\nabla c^{\prime \prime }}\) ; this represents the flame turbulence interaction. In order to obtain an accurate representation of this phenomenon, a new evolution equation for \(\widetilde {\Delta }_{c}\) has been proposed. This equation gives a detailed insight into flame turbulence interaction and provides an alternative approach to model the important physics represented by \(\widetilde {\Delta }_{c}\) . The \(\widetilde {\Delta }_{c}\) evolution equation is derived in detail and an order of magnitude analysis is carried out to determine the leading order terms in the \(\widetilde {\Delta }_{c}\) evolution equation. The leading order terms are then studied using a Direct Numerical Simulation (DNS) of premixed turbulent flames in the corrugated flamelet regime. It is found that the behaviour of \(\widetilde {\Delta }_{c}\) is determined by the competition between the source terms (pressure gradient and the reaction rate), diffusion/dissipation processes, turbulent strain rate and the dilatation rate. Closures for the leading order terms in \(\widetilde {\Delta }_{c}\) evolution equation have been proposed and compared with the DNS data.     

A phenomenological model for microstructure-dependent inelasticity in shape-memory alloys

Degradation in shape-memory alloy response is a crucial concern for a variety of innovative applications. Under cyclic loadings, these materials generally experience permanent inelastic deformations. The onset of plasticization is known to be very sensitive to the microstructure of the polycrystalline specimen. Moving from recent experimental findings (Malard et al. in Funct Mater Lett 2:45–54, 2009; Acta Mater 59:1542–1556, 2011), we present a phenomenological model for permanent inelastic effects in shape-memory alloys taking into account the polycrystalline microstructure. In particular, the mechanical response under cyclic loadings is investigated in connection with the mean crystal grain size. Formulated within the variational frame of generalized standard materials, the model consists in an extension of the model in Auricchio et al. (Int J Plast 23:207–226, 2007) to the case of microstructure-dependent parameters. The mathematical setting is discussed and numerical simulations showing the capability of the model to reproduce experiments are presented.     

Analysis of Algebraic Closures of the Mean Scalar Dissipation Rate of the Progress Variable Applied to Stagnating Turbulent Flames

In the turbulent premixed reactive flows considered in this study, i.e. large Damköhler and Reynolds numbers, the flamelet regime of turbulent combustion applies and the scalar dissipation rate and mean reaction rate are inter related. In this situation various algebraic models for the mean chemical rate that are obtained from an equilibrium of the dominant terms of the transport equation for the scalar dissipation rate, are evaluated through their application to flames stabilized in a turbulent stagnating flow. An asymptotic analysis is first performed and results obtained through the resulting one-dimensional calculation are compared with the experimental data of Li et al. (Proc Combust Inst 25:1207–1214, 1994). Eventually, three-dimensional CFD calculations including suited algebraic closures to represent the turbulent transport terms are carried out. Results are satisfactorily compared to the experimental data of Cho et al. (Proc Combust Inst 22:739–745, 1988). As a first outcome, the analysis confirms the interest and the relevance of the corresponding algebraic closures to deal with turbulent premixed combustion in such conditions. In the search of a satisfactory representation of such premixed impinging flames, the computational results also clearly emphasize the strong intertwinment that exits between the mean reaction rate, i.e. scalar dissipation rate or micro-mixing taking place at the smallest scale of the reactive flowfield, and the Reynolds fluxes modelling, i.e. turbulent macro-mixing.     

Estimation of the largest Lyapunov exponent-like (LLEL) stability measure parameter from the perturbation vector and its derivative dot product (part 2) experiment simulation

Controlling system dynamics with use of the Largest Lyapunov Exponent (LLE) is employed in many different areas of the scientific research. Thus, there is still need to elaborate fast and simple methods of LLE calculation. This article is the second part of the one presented in Dabrowski (Nonlinear Dyn 67:283–291, 2012). It develops method LLEDP of the LLE estimation and shows that from the time series of two identical systems, one can simply extract value of the stability parameter which value can be treated as largest LLE. Unlike the method presented in part, one developed method (LLEDPT) can be applied to the dynamical systems of any type, continuous, with discontinuities, with time delay and others. The theoretical improvement shows simplicity of the method and its obvious physical background. The proofs for the method effectiveness are based on results of the simulations of the experiments for Duffing and Van der Pole oscillators. These results were compared with ones obtained with use of the Stefanski method (Stefanski in Chaos Soliton Fract 11(15):2443–2451, 2000; Chaos Soliton Fract 15:233–244, 2003; Chaos Soliton Fract 23:1651–1659, 2005; J Theor Appl Mech 46(3):665–678, 2008) and LLEDP method. LLEDPT can be used also as the criterion of stability of the control system, where desired behavior of controlled system is explicitly known (Balcerzak et al. in Mech Mech Eng 17(4):325–339, 2013). The next step of development of the method can be considered in direction that allows estimation of LLE from the real time series, systems with discontinuities, with time delay and others.