Group Properties of 2–Submodels for the Evolutionary Class of Gas–Dynamic Equations

Invariant 2–submodels (submodels with two independent variables) of the evolutionary class are considered for the equations of gas dynamics with an equation of state of general form. Group analysis of these submodels is performed. Allowable operators and transformations of equivalence are indicated, and group classification is performed.     

Preparation of nano-sized Al2O3–2SiO2 powder by sol–gel plus azeotropic distillation method

Nano-sized amorphous Al₂O₃–2SiO₂ powder was prepared by a sol–gel method coupled with azeotropic distillation. The structure of the powder was investigated by DTS, BET, TEM, FT-IR, TG-DTA and XRD, showing that n-butanol azeotropic distillation could effectively remove water from the aluminosilicate gels and prevent the formation of hard agglomerates in the drying process. The average particle diameter of the powder was about 70 nm. The largest BET specific surface area of the powder was 669 m²/g. To examine the alkali-activation reactivity of the powder, alkali-activation tests were performed with the powder reacting with sodium silicate solution. The synthetic powder was found to be highly reactive.     

Validation of a 2-D semi-coupled numerical model for fluid–structure–seabed interaction

A 2-D semi-coupled model PORO-WSSI 2D (also be referred as FSSI-CAS 2D) for the Fluid-Structure-Seabed Interaction (FSSI) has been developed by employing RANS equations for wave motion in fluid domain, VARANS equations for porous flow in porous structures; and taking the dynamic Biot's equations (known as "u − p" approximation) for soil as the governing equations. The finite difference two-step projection method and the forward time difference method are adopted to solve the RANS, VARANS equations; and the finite element method is adopted to solve the "u − p" approximation. A data exchange port is developed to couple the RANS, VARANS equations and the dynamic Biot's equations together. The analytical solution proposed by Hsu and Jeng (1994) and some experiments conducted in wave flume or geotechnical centrifuge in which various waves involved are used to validate the developed semi-coupled numerical model. The sandy bed involved in these experiments is poro-elastic or poro-elastoplastic. The inclusion of the interaction between fluid, marine structures and poro-elastoplastic seabed foundation is a special point and highlight in this paper, which is essentially different with other previous coupled models The excellent agreement between the numerical results and the experiment data indicates that the developed coupled model is highly reliablefor the FSSI problem.     

Measure Valued Solutions of the 2D Keller–Segel System

We develop a theory of global measure-valued solutions for the classical Keller–Segel model. These solutions are obtained considering the limit of solutions of a regularized problem. We also prove that different regularizations yield different limit measures in the case in which classical solutions of the Keller–Segel system are not globally defined in time.     

Determination of the effective elastic–plastic response of metal–ceramic composites

The mechanical response of metal–ceramic composites is analysed through a homogenization model accounting for the mechanical behaviour of the constituent materials. In order to achieve this purpose a nonlinear homogenization method based on the phase field approach has been suitably implemented into a numerical code. A prescribed homogenized strain state is applied to a unit volume element of a metal–ceramic composite with proportional loading in which all components of the strain tensor are proportional to one scalar parameter. The mechanical response of the material has been modeled by considering a von Mises plasticity model for the metal phase and a Drucker–Prager associative elastic–plastic material model for the ceramic phase. A two stages plasticity has been obtained in which inelastic strain develops in the metal phase followed by a fully plastic response. A comparison with a finite element model of the stress–strain response of an axisymmetric unit cell has been carried out with the purpose to validate the homogenization based modeling presented in the paper. Plastic parameters of a Drucker–Prager yield surface for the homogenized composite have been calculated at different materials compositions. Associative Drucker–Prager plasticity has been found to be accurate for high ceramic content.     

2D FE–DEM analysis of tractive performance of an elastic wheel for planetary rovers

We have been developing a simulation program for use with soil–wheel interaction problems by coupling Finite Element Method (FEM) and Discrete Element Method (DEM) for which a wheel is modeled by FEM and soil is expressed by DEM. Previous two-dimensional FE–DEM was updated to analyze the tractive performance of a flexible elastic wheel by introducing a new algorithm learned from the PID-controller model. In an elastic wheel model, four structural parts were defined using FEM: the wheel rim, intermediate part, surface layer, and wheel lugs. The wheel rigidity was controlled by varying the Young’s Modulus of the intermediate part. The tractive performance of two elastic wheels with lugs for planetary rovers of the European Space Agency was analyzed. Numerical results were compared with experimentally obtained results collected at DLR Bremen, Germany. The FE–DEM result was confirmed to depict similar behaviors of tractive performance such as gross tractive effort, net traction, running resistance, and wheel sinkage, as in the results of experiments. Moreover, the tractive performance of elastic wheels on Mars was predicted using FE–DEM. Results clarified that no significant difference of net traction exists between the two wheels.     

Effect of glycine–starch mixing ratio on the structural characteristics of MgAl2O4 nano-particles synthesized by sol–gel combustion

Sol–gel auto-ignition was used to prepare nano-scale magnesium aluminate spinel, using nitrate salts as an oxidizer and glycine–starch mixtures as the fuel. The glycine–starch mixture was varied to understand the effect of fuel mixing ratio on the structural characteristics of the resulting magnesium aluminate. The products were characterized by thermogravimetric-differential thermal analyses, Fourier-transform infrared spectroscopy, X-ray diffraction, Brunauer–Emmett–Teller surface area measurements, and transmission electron microscopy. The phase purity and crystallite size of the powder products depended on the fuel mixing ratio. The presence of starch in the fuel facilitated the preparation of pure nano-particles. To prepare nano-particles of uniform spherical morphology and diameter of <13 nm, the starch content should be optimized to avoid agglomeration.     

Experimental and numerical analysis of nonlinear dynamics of rotor–bearing–seal system

Nonlinear dynamics and stability of the rotor–bearing–seal system are investigated both theoretically and experimentally. An experimental rotor–bearing–seal device is designed and corresponding tests are carried out. The experimental rotor system is simplified as the Jeffcott rotor. The nonlinear oil–film forces are obtained under the short bearing theory and Muszynska nonlinear seal force model is used. Numerical method is utilized to solve the nonlinear governing equations. Bifurcation diagrams, waterfall plots, Poincaré maps, spectrum plots and rotor orbits are drawn to analyze various nonlinear phenomena and system unstable processes. Theoretical results from numerical analysis are in good agreement with results from experiments. Conclusions are drawn and prove that this study will contribute to the further understanding of nonlinear dynamics and stability of the rotor system with the fluid-induced forces from oil–film bearings and the seals.     

An example of stick–slip and stick–slip–separation waves

The dynamical problem of a brake-like mechanical system composed of an elastic cylindrical tube with Coulomb's friction in contact with a rigid and rotating cylinder is considered. This model problem enables us to give an example of non-trivial periodic solutions in the form of stick–slip or stick–slip–separation waves propagating on the contact surface. A semi-analytical analysis of stick–slip waves is obtained when the system of governing equations is reduced by condensation to a simpler system involving only the contact displacements. This reduced system, of only one space variable in addition to time, can be solved almost analytically and gives some interesting informations on the existence and the characteristics of stick–slip waves such as the wave numbers on the circumference, stick and slip proportions, wave celerities, tangential and normal forces. It is shown in particular that the stick–slip–separation solutions would occur for small normal pressures or high rotational speeds. Since the analytical discussion becomes cumbersome in this case, a second approach based on numerical analysis by the finite element method is performed. The existence and the characteristics of stick–slip and stick–slip–separation waves are discussed numerically.     

A Feature-Based Stochastic Permeability of Shale: Part 2–Predicting Field-Scale Permeability

Transport in Porous Media - In a recent numerical study, it was demonstrated that characterizing reservoir permeability in terms of rock’s quality, as observed in lab and field, is the most...     

Preparation of calcium sulfate whiskers from FGD gypsum via hydrothermal crystallization in the H2SO4–NaCl–H2O system

Little attention has thus far been paid to the potential effect of solution composition on the hydrothermal crystallization of calcium sulfate whiskers prepared from flue-gas desulfurization (FGD) gypsum. When purified FGD gypsum was used as raw material, the morphology and phase structure of the hydrothermal products grown in pure water, H₂SO₄–H₂O, NaCl–H₂O, and H₂SO₄–NaCl–H₂O solutions as well as the solubility of purified FGD gypsum in these solutions were investigated. The results indicate that calcium sulfate whiskers grow favorably in the H₂SO₄–NaCl–H₂O system. When prepared using 10–70 g NaCl/kg gypsum −0.01 M H₂SO₄–H₂O at 130 °C for 60 min, the obtained calcium sulfate whiskers had diameters ranging from 3 to 5 μm and lengths from 200 to 600 μm, and their phase structure was calcium sulfate hemihydrate (HH). Opposing effects of sulfuric acid and sodium chloride on the solubility of the purified FGD gypsum were observed. With the co-presence of sulfuric acid and sodium chloride in the reaction solution, the concentrations of Ca²⁺ and SO₄²⁻ can be kept relatively stable, which implies that the crystallization of the hydrothermal products can be controlled by changing the concentrations of sulfuric acid and sodium chloride.     

Dynamics of cavitation–structure interaction

Cavitation–structure interaction has become one of the major issues for most engineering applications. The present work reviews recent progress made toward developing experimental and numerical investigation for unsteady turbulent cavitating flow and cavitation–structure interaction. The goal of our overall efforts is to(1) summarize the progress made in the experimental and numerical modeling and approaches for unsteady cavitating flow and cavitation–structure interaction,(2) discuss the global multiphase structures for different cavitation regimes, with special emphasis on the unsteady development of cloud cavitation and corresponding cavitating flow-induced vibrations,with a high-speed visualization system and a structural vibration measurement system, as well as a simultaneous sampling system,(3) improve the understanding of the hydroelastic response in cavitating flows via combined physical and numerical analysis, with particular emphasis on the interaction between unsteady cavitation development and structural deformations. Issues including unsteady cavitating flow structures and cavitation–structure interaction mechanism are discussed.     

Weierstrass elliptic function solutions and their degenerate solutions of (2+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation

Nonlinear Dynamics - Weierstrass elliptic function solutions are investigated by applying the traveling wave transformation and auxiliary equations to a (2+1)-dimensional potential...     

Detonability of THDCPD-exo–air mixtures

In the frame of industrial risk and propulsive application, the detonability study of JP10–air mixtures was performed. The simulation and measurements of detonation parameters were performed for THDCPD-exo/air mixtures at various initial pressure (1 bar < P ₀ < 3 bar) and equivalence ratio (0.8 < Φ < 1.6) in a heated tube (T ₀ ~ 375 K). Numerical simulations of the detonation were performed with the STANJAN code and a detailed kinetic scheme of the combustion of THDCPD. The experimental study deals with the measurements of detonation velocity and cell size λ. The measured velocity is in a good agreement with the calculated theoretical values. The cell size measurements show a minimum value for Φ ~ 1.2 at every level of initial pressure studied and the calculated induction length L _i corresponds to cell size value with a coefficient k = λ/L _i = 24 at P ₀ = 1 bar. Based on the comparison between the results obtained during this study and those available in the literature on the critical initiation energy E _c, critical tube diameter d _c and deflagration to detonation transition length L _DDT, we can conclude that the detonability of THDCPD–air mixtures corresponds to that of hydrocarbon–air mixtures.

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This paper is based on the work presented at the 33rd International Pyrotechnics Seminar, IPS 2006, Fort Collins, July 16–21, 2006.     

A combined experimental–numerical investigation of ductile fracture in bending of a class of ferritic–martensitic steel

We present a combined experimental–numerical study on fracture initiation at the convex surface and its propagation during bending of a class of ferritic–martensitic steel. On the experimental side, so-called free bending experiments are conducted on DP1000 steel sheets until fracture, realizing optical and scanning electron microscopy analyses on the post mortem specimens for fracture characterization. A blended Mode I – Mode II fracture pattern, which is driven by cavitation at non-metallic inclusions as well as martensitic islands and resultant softening-based intense strain localization, is observed. Phenomena like crack zig-zagging and crack alternation at the bend apex along the bending axis are introduced and discussed. On the numerical side, based on this physical motivation, the process is simulated in 2D plane strain and 3D, using Gurson’s dilatant plasticity model with a recent shear modification, strain-based void nucleation, and coalescence effects. The effect of certain material parameters (initial porosity, damage at coalescence and failure, shear modification term, etc.), plane strain constraint and mesh size on the localization and the fracture behavior are investigated in detail.     

Yielding and intrinsic plasticity of Ti–Zr–Ni–Cu–Be bulk metallic glass

Bulk metallic glass with composition Ti₄₀Zr₂₅Ni₈Cu₉Be₁₈ exhibits considerably high compressive yield stress, significant plasticity (with a concomitant vein-like fracture morphology) and relatively low density. Yielding and intrinsic plasticity of this alloy are discussed in terms of its thermal and elastic properties. An influence of normal stresses acting on the shear plane is evidenced by: (i) the fracture angle (<45°) and (ii) finite-element simulations of nanoindentation curves, which require the use of a specific yield criterion, sensitive to local normal stresses acting on the shear plane, to properly match the experimental data. The ratio between hardness and compressive yield strength (constraint factor) is analyzed in terms of several models and is best adjusted using a modified expanding cavity model incorporating a pressure-sensitivity index defined by the Drucker–Prager yield criterion. Furthermore, comparative results from compression tests and nanoindentation reveal that deformation also causes strain softening, a phenomenon which is accompanied with the occurrence of serrated plastic flow and results in a so-called indentation size effect (ISE). A new approach to model the ISE of this metallic glass using the free volume concept is presented.     

A nonlocal phase-field model of Ginzburg–Landau–Korteweg fluids

A thermodynamic model of Korteweg fluids undergoing phase transition and/or phase separation is developed within the framework of weakly nonlocal thermodynamics. Compatibility with second law of thermodynamics is investigated by applying a generalized Liu procedure recently introduced in the literature. Possible forms of the free energy and of the stress tensor, which generalize some earlier ones proposed by several authors in the last decades, are carried out. Owing to the new procedure applied for exploiting the entropy principle, the thermodynamic potentials are allowed to depend on the whole set of variables spanning the state space, including the gradients of the unknown fields, without postulating neither the presence of an energy or entropy extra-flux, nor an additional balance law for microforce.     

Existence of Quasipattern Solutions of the Swift–Hohenberg Equation

We consider the steady Swift–Hohenberg partial differential equation, a one-parameter family of PDEs on the plane that models, for example, Rayleigh–Bénard convection. For values of the parameter near its critical value, we look for small solutions, quasiperiodic in all directions of the plane, and which are invariant under rotations of angle ${\pi/q, q \geqq 4}$ . We solve an unusual small divisor problem and prove the existence of solutions for small parameter values, then address their stability with respect to quasi-periodic perturbations.     

2D FE–DEM analysis of contact stress and tractive performance of a tire driven on dry sand

Normal and tangential stresses acting over a contact interface of a tire driven on dry sand were investigated to expand the applicability of our model incorporating 2D FE–DEM with proportional–integral–derivative (PID) control. A simple averaging method for contact reaction was introduced: computational segments were defined over the lower half part of the tire circumference that translates without rotation with the tire; then the contact stresses were calculated segment by segment. For the analysis, it was assumed that the tire was in rigid contact mode and that it would travel on the model sand terrain in stationary condition. The integration of normal and tangential contact stresses with respect to the angle of rotation was then applied to calculate the vertical contact load, gross tractive effort, net traction, and running resistance of the tire by parametric (or semi-empirical) analysis. The result of tractive performance obtained through the parametric analysis was found to be similar to the result of tractive performance obtained directly using FE–DEM analysis. A forward shift of the consistent angle of rotation for maximum normal contact stress and that for maximum tangential contact stress with the increase of slip from 22% was also observed in the FE–DEM result.