Measurement and chemical kinetic model predictions of detonation cell size in methanol–oxygen mixtures

In this study, detonation cell sizes of methanol–oxygen mixtures are experimentally measured at different initial pressures and compositions. Good agreement is found between the experiment data and predictions based on the chemical length scales obtained from a detailed chemical kinetic model. To assess the detonation sensitivity in methanol–oxygen mixtures, the results are compared with those of hydrogen–oxygen and methane–oxygen mixtures. Based on the cell size comparison, it is shown that methanol–oxygen is more detonation sensitive than methane–oxygen but less sensitive than hydrogen–oxygen.     

The propagation mechanism of high speed turbulent deflagrations

The propagation regimes of combustion waves in a 30 cm by 30 cm square cross–sectioned tube with an obstacle array of staggered vertical cylindrical rods (with BR=0.41 and BR=0.19) are investigated. Mixtures of hydrogen, ethylene, propane, and methane with air at ambient conditions over a range of equivalence ratios are used. In contrast to the previous results obtained in circular cross–sectioned tubes, it is found that only the quasi–detonation regime and the slow turbulent deflagration regimes are observed for ethylene–air and for propane–air. The transition from the quasi–detonation regime to the slow turbulent deflagration regime occurs at (where D is the tube “diameter” and is the detonation cell size). When , the quasi–detonation velocities that are observed are similar to those in unobstructed smooth tubes. For hydrogen–air mixtures, it is found that there is a gradual transition from the quasi–detonation regime to the high speed turbulent deflagration regime. The high speed turbulent deflagration regime is also observed for methane–air mixtures near stoichiometric composition. This regime was previously interpreted as the “choking” regime in circular tubes with orifice plate obstacles. Presently, it is proposed that the propagation mechanism of these high speed turbulent deflagrations is similar to that of Chapman–Jouguet detonations and quasi-detonations. As well, it is observed that there exists unstable flame propagation at the lean limit where . The local velocity fluctuates significantly about an averaged velocity for hydrogen–air, ethylene–air, and propane–air mixtures. Unstable flame propagation is also observed for the entire range of high speed turbulent deflagrations in methane–air mixtures. It is proposed that these fluctuations are due to quenching of the combustion front due to turbulent mixing. Quenched pockets of unburned reactants are swept downstream, and the subsequent explosion serves to overdrive the combustion front. The present study indicates that the dependence on the propagation mechanisms on obstacle geometry can be exploited to elucidate the different complex mechanisms of supersonic combustion waves. Received 5 November 2001 / Accepted 12 June 2002 / Published online 4 November 2002 Correspondence to: J. Chao (e-mail: jenny.chao@mail.mcgill.ca) An abridged version of this paper was presented at the 18th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Seattle, USA, from July 29 to August 3, 2001.     

Characteristics of liquid sheets formed by splash plate nozzles

An experimental study was conducted to identify the effect of viscosity on the characteristics of liquid sheets formed by a splash plate nozzle. Various mixtures of corn syrup and water are used to obtain viscosities in the range 1–170 mPa.s. Four different splash plates with nozzle diameters of 0.5, 0.75, 1, and 2 mm, with a constant plate angle of 55° were tested. Liquid sheets formed under various operating conditions were directly visualized. The sheet atomization process for the range of parameters studied here is governed by two different mechanisms: Rayleigh–Plateau (R–P) and Rayleigh–Taylor (R–T) instabilities. R–P occurs at the rim and R–T occurs on the thin sheet. The rim instability can be laminar or turbulent, depending on the jet Reynolds number. The R–T instability of the sheet is observed at the outer edges of the radially spreading sheet, where the sheet is the thinnest. It can also occur inside the sheet, due to formation of holes and ruptures.     

Aspect-ratio dependence of transient Taylor vortices close to threshold

We perform a detailed numerical study of transient Taylor vortices arising from the instability of cylindrical Couette flow with the exterior cylinder at rest for radius ratio η = 0.5 and variable aspect ratio Γ. The result of Abshagen et al. (J Fluid Mech 476:335–343, 2003) that onset transients apparently evolve on a much smaller time–scale than decay transients is recovered. It is shown to be an artefact of time scale estimations based on the Stuart–Landau amplitude equation which assumes frozen space dependence while full space–time dependence embedded in the Ginzburg–Landau formalism needs to be taken into account to understand transients already at moderate aspect ratio. Sub-critical pattern induction is shown to explain the apparently anomalous behaviour of the system at onset while decay follows the Stuart–Landau prediction more closely. The dependence of time scales on boundary effects is studied for a wide range of aspect ratios, including non-integer ones, showing general agreement with the Ginzburg–Landau picture able to account for solutions modulated by Ekman pumping at the disks bounding the cylinders.      

Estimation of Chaotic and Regular (Stick–Slip and Slip–Slip) Oscillations Exhibited by Coupled Oscillators with Dry Friction

In this paper, we present a novel approach to quantify regular or chaotic dynamics of either smooth or non-smooth dynamical systems. The introduced method is applied to trace regular and chaotic stick–slip and slip–slip dynamics. Stick–slip and slip–slip periodic and chaotic trajectories are analyzed (for the investigated parameters, a stick–slip dynamics dominates). Advantages of the proposed numerical technique are given.     

Solving initial–boundary-value creep problems

The Galerkin–Bubnov method with global approximations is used to find approximate solutions to initial–boundary-value creep problems. It is shown that this approach allows obtaining solutions available in the literature. The features of how the solutions of initial–boundary-value problems for oneand three-dimensional models are found are analyzed. The approximate solutions found by the Galerkin–Bubnov method with global approximations is shown to be invariant to the form of the equations of the initial–boundary-value problem. It is established that solutions of initial–boundary-value creep problems can be classified according to the form of operators in the mathematical problem formulation     

Non-Ergodicity of the Nosé–Hoover Thermostatted Harmonic Oscillator

The Nosé–Hoover thermostat is a deterministic dynamical system designed for computing phase space integrals for the canonical Gibbs distribution. Newton’s equations are modified by coupling an additional reservoir variable to the physical variables. The correct sampling of the phase space according to the Gibbs measure is dependent on the Nosé–Hoover dynamics being ergodic. Hoover presented numerical experiments to show that the Nosé–Hoover dynamics are non-ergodic when applied to the harmonic oscillator. In this article, we prove that the Nosé–Hoover thermostat does not give an ergodynamical system for the one- dimensional harmonic oscillator when the “mass” of the reservoir is large. Our proof of non-ergodicity uses KAM theory to demonstrate the existence of invariant tori for the Nosé–Hoover dynamical system that separate phase space into invariant regions. We present numerical experiments motivated by our analysis that seem to show that the dynamical system is not ergodic even for a moderate thermostat mass.     

Prediction of separation flows around a 6：1 prolate spheroid using RANS/LES hybrid approaches

This paper presents hybrid Reynolds-averaged Navier–Stokes (RANS) and large-eddy-simulation (LES) methods for the separated flows at high angles of attack around a 6:1 prolate spheroid. The RANS/LES hybrid methods studied in this work include the detached eddy simulation (DES) based on Spalart–Allmaras (S–A), Menter’s k–ω shear-stress-transport (SST) and k–ω with weakly nonlinear eddy viscosity formulation (Wilcox–Durbin+, WD+) models and the zonal-RANS/LES methods based on the SST and WD+ models. The switch from RANS near the wall to LES in the core flow region is smooth through the implementation of a flow-dependent blending function for the zonal hybrid method. All the hybrid methods are designed to have a RANS mode for the attached flows and have a LES behavior for the separated flows. The main objective of this paper is to apply the hybrid methods for the high Reynolds number separated flows around prolate spheroid at high-incidences. A fourth-order central scheme with fourth-order artificial viscosity is applied for spatial differencing. The fully implicit lower–upper symmetric-Gauss–Seidel with pseudo time sub-iteration is taken as the temporal differentiation. Comparisons with available measurements are carried out for pressure distribution, skin friction, and profiles of velocity, etc. Reasonable agreement with the experiments, accounting for the effect on grids and fundamental turbulence models, is obtained for the separation flows. The project supported by the National Natural Science Foundation of China (10502030 and 90505005).     

Deformation and short-term damage of physically nonlinear stochastic composites

The studies on the deformation and short-term damage of physically nonlinear homogeneous and composite materials are systemized. A single microdamage is modeled by an empty quasispherical pore in place of a microvolume damaged in accordance with the Huber–von Mises failure criterion. The ultimate microstrength is assumed to be a random function of coordinates. The porosity balance equation is derived. Together with the macrostress–macrostrain relationship, it constitutes a closed-form system of equations. The damage–macrostrain relationship and macrostress–macrostrain curves for homogeneous and composite materials are analyzed     

A comparison of three adsorption equations and sensitivity study of parameter uncertainty effects on adsorption refrigeration thermal performance estimation

This paper presents isosteric-based adsorption equilibrium tests of three activated carbon samples with methanol as an adsorbate. Experimental data was fitted into Langmuir equation, Freundlich equation and Dubinin-Astakov (D–A) equation, respectively. The fitted adsorption equations were compared in terms of agreement with experimental data. Moreover, equation format’s impacts on calculation of the coefficient of performance (COP) and refrigeration capacity of an adsorption refrigeration system was analyzed. In addition, the sensitivity of each parameter in each adsorption equation format to the estimation of cycle’s COP and refrigeration capacity was investigated. It was found that the D–A equation is the best form for presenting the adsorptive property of a carbon-methanol working pair. The D–A equation is recommended for estimating thermal performance of an adsorption refrigeration system because simulation results obtained using the D–A equation are less sensitive to errors of experimentally determined D–A equation’s parameters.     

Possibilities and Limitations of Computer Simulations of Industrial Turbulent Dispersed Multiphase Flows

We give an overview on the usage of computer simulations in industrial turbulent dispersed multiphase flows. We present a few examples of industrial flows: bubble columns and bubbly pipe flows, stirred tanks, cyclones, and a fluid catalytic cracking unit. The fluid catalytic cracking unit is used to illustrate the complexity of the physical phenomena involved, and the possibilities and limitations of the different approaches used: Eulerian–Lagrangian (particle-tracking) and Eulerian–Eulerian (two-fluid). In the first approach, the continuous phase is solved using either RANS simulations (Reynolds-Averaged Navier–Stokes simulations) or DNS/LES (Direct Numerical Simulations/Large-Eddy Simulations), and the individual particles are tracked. In the second approach, the dispersed phase is averaged, leading to two sets equations, which are quite similar to the RANS equations of single-phase flows. The Eulerian–Eulerian approach is the most commonly used in industrial applications, however, it requires a significant amount of modelling. Eulerian–Lagrangian RANS can be simpler to use; in particular in situations involving complex boundary conditions, polydisperse flows and agglomeration/breakup. The key issue for the success of the simulations is to have good models for the complex physics involved. A major weakness is the lack of good models for: the turbulence modification promoted by the particles, the inter-particle interactions, and the near-wall effects. Eulerian–Lagrangian DNS/LES can play an important role as a research tool, in order to get a better physical understanding, and to improve the models used in the RANS simulations (either Eulerian–Eulerian or Eulerian–Lagrangian).     

Combined effect of thermal modulation and rotation on the onset of stationary convection in a porous layer

The stability of a fluid-saturated horizontal rotating porous layer subjected to time-periodic temperature modulation is investigated when the condition for the principle of exchange of stabilities is valid. The linear stability analysis is used to study the effect of infinitesimal disturbances. A regular perturbation method based on small amplitude of applied temperature field is used to compute the critical values of Darcy–Rayleigh number and wavenumber. The shift in critical Darcy–Rayleigh number is calculated as a function of frequency of modulation, Taylor number, and Darcy–Prandtl number. It is established that the convection can be advanced by the low frequency in-phase and lower-wall temperature modulation, where as delayed by the out-of-phase modulation. The effect of Taylor number and Darcy–Prandtl number on the stability of the system is also discussed. We found that by proper tuning of modulation frequency, Taylor number, and Darcy–Prandtl number it is possible to advance or delay the onset of convection.     

On the Range of Applicability of the Reissner–Mindlin and Kirchhoff–Love Plate Bending Models

We show that the Reissner–Mindlin plate bending model has a wider range of applicability than the Kirchhoff–Love model for the approximation of clamped linearly elastic plates. Under the assumption that the body force density is constant in the transverse direction, the Reissner–Mindlin model solution converges to the three-dimensional linear elasticity solution in the relative energy norm for the full range of surface loads. However, for loads with a significant transverse shear effect, the Kirchhoff–Love model fails. This revised version was published online in June 2006 with corrections to the Cover Date.     

Effect of yaw on the starting point of curvature for reflected diffracted shock wave (subsonic and sonic cases)

Lighthill (Proc. R. Soc. A 198, 454–470, 1949) considered the diffraction of a normal shock wave passing over a small bend. The bend being small Lighthill was able to linearize the flow equations and solved the problem through several mathematical techniques. Following Lighthill (Proc. R. Soc. A 198, 454–470, 1949), Srivastava and Chopra (J. Fluid Mech. 40, 821–831, 1970) extended the work to the diffraction of oblique shock waves. Srivastava (AIAAJ 33, 2230–2231, 1995) considered the problem of starting point of curvature and extended the work to yawed wedges (Srivastava in Proceedings of the 14th International Mach reflection symposium Sun Marina Hotel, Yonezawa, Japan, 1–5 October 2000, pp. 225–249, 2002). Srivastava (Shock waves 13, 323–326, 2003) considered the problem for starting point of curvature when the relative outflow behind reflected shock before diffraction has been subsonic and sonic. The present work is an extension of the work published in Srivastava (Shock waves 13, 323–326, 2003) when the wedge has been yawed through an angle. The results have been obtained for two angles χ = 60° and χ = 40° (χ is the angle of yaw).      

Vlasov–Maxwell–Boltzmann Diffusive Limit

Inspired by the work (Bastea et al. in J Stat Phys 1011087–1136, 2000) for binary fluids, we study the diffusive expansion for solutions around Maxwellian equilibrium and in a periodic box to the Vlasov–Maxwell–Boltzmann system, the most fundamental model for an ensemble of charged particles. Such an expansion yields a set of dissipative new macroscopic PDEs, the incompressible Vlasov–Navier–Stokes–Fourier system and its higher order corrections for describing a charged fluid, where the self-consistent electromagnetic field is present. The uniform estimate on the remainders is established via a unified nonlinear energy method and it guarantees the global in time validity of such an expansion up to any order.     

<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript> Formulation of Multidimensional Scalar Conservation Laws

We show that Kruzhkov’s theory of entropy solutions to multidimensional scalar conservation laws (Kruzhkov in Mat Sb (N.S.), 81(123), 228–255, 1970) can be entirely recast in L ² and fits into the general theory of maximal monotone operators in Hilbert spaces. Our approach is based on a combination of level-set, kinetic and transport-collapse approximations, in the spirit of previous works by Brenier (in C R Acad Sci Paris Ser I Math, 292, 563–566, 1981; in J Diff Equ, 50, 375–390, 1983; in SIAM J Numer Anal, 21, 1013–1037; in Methods Appl Anal, 11, 515–532, 2004), Giga and Miyakawa (in Duke Math J, 50, 505–515, 1983), and Tsai et al. (in Math Comp, 72, 159–181, 2003).     

On a Generalized Nonlinear K–ε Model and the Use of Extended Thermodynamics in Turbulence

A resent extension of the nonlinear K–ε model is critically discussed from a basic theoretical standpoint. While it was said in the paper that this model was formulated to incorporate relaxation effects, it will be shown that the model is incapable of describing one of the most basic such turbulent flows as is obvious but is described for clarity. It will be shown in detail that this generalized nonlinear K–ε model yields erroneous results for the Reynolds stress tensor when the mean strains are set to zero in a turbulent flow – the return-to-isotropy problem which is one of the most elementary relaxational turbulent flows. It is clear that K–ε type models cannot describe relaxation effects. While their general formalism can describe relaxation effects, the nonlinear K–ε model – which the paper is centered on – cannot. The deviatoric part of the Reynolds stress tensor is predicted to be zero when it actually only gradually relaxes to zero. Since this model was formulated by using the extended thermodynamics, it too will be critically assessed. It will be argued that there is an unsubstantial physical basis for the use of extended thermodynamics in turbulence. The role of Material Frame-Indifference and the implications for future research in turbulence modeling are also discussed. Received 19 February 1998 and accepted 23 October 1998     

Solution of initial–boundary-value problems of electroelasticity revisited

The Hamilton–Ostrogradsky principle is used to substantiate the statement of initial–boundary-value problems of electroelasticity. The free vibrations of a piezoceramic layer are used as an example to illustrate some features of solving nonstationary problems of electroelasticity Translated from Prikladnaya Mekhanika, Vol. 44, No. 12, pp. 62–69, December 2008.     

Development and validation of a thermo-mechanical finite element model of the steel quenching process including solid–solid phase changes

A computational thermo-metallographic and thermoelastoplastic model for the analysis of the quenching process is developed and validated. The diffusive transfor-mations are modeled according to the Johnson–Mehl–Avrami–Kolmogorov model and the Scheil’s additivity rule. Two different models are investigated for the non-diffusive transformation—the Koistinen–Marburger model and the Yu model. A large displacement formulation is assumed for the deformation analysis, modeling the plastic behavior of the material according to the Prandtl–Reuss model. Two different bilinear hardening models—the isotropic and the kinematic hardening model—are used and compared. The model allows to evaluate the transient stress and strain distributions during the quenching process, the final phases and hardness distributions, and to predict the residual stress and the final deformation of the processed part. A good agreement between computational results and reference data is found