Large Eddy Simulation of a Methane–Air Diffusion Flame

Large Eddy Simulation has been applied to a piloted methane/air diffusion flame—the Sandia D flame—for which detailed experimental data are available. To evaluate the reacting density, temperature and species mass fractions a conserved scalar laminar flamelet formulation is employed, utilising a single virtually unstrained flamelet. The results of two simulations are discussed, comparing the use of the standard Smagorinsky model and a dynamic variant for closure of the unknown sub-grid stress. The chosen sub-grid scale model is shown to be extremely influential on the final solution. Whilst the use of the standard model results in a relatively poor simulation the dynamic closure offers an excellent velocity field prediction throughout the flame. Although the flame does show some strain rate influence on burning, particularly close to the inlet nozzle, the relatively simple ‘unstrained’ flamelet model applied is shown to provide an accurate representation of temperature and major species distribution.     

Existence and Characterization of Attractors for a Nonlocal Reaction–Diffusion Equation with an Energy Functional

In this paper we study a nonlocal reaction–diffusion equation in which the diffusion depends on the gradient of the solution. Firstly, we prove the existence and uniqueness of regular and strong solutions. Secondly, we obtain the existence of global attractors in both situations under rather weak assumptions by defining a multivalued semiflow (which is a semigroup in the particular situation when uniqueness of the Cauchy problem is satisfied). Thirdly, we characterize the attractor either as the unstable manifold of the set of stationary points or as the stable one when we consider solutions only in the set of bounded complete trajectories.

     

Stability and Spectral Comparison of a Reaction–Diffusion System with Mass Conservation

We study the global-in-time behavior of solutions to a reaction–diffusion system with mass conservation, as proposed in the study of cell polarity, particularly, the second model of the work by Otsuji et al. (PLoS Comput Biol 3:e108, 2007). First, we show the existence of a Lyapunov function and confirm the global-in-time existence of the solution with compact orbit. Then we study the stability and instability of stationary solutions by using the semi-unfolding-minimality property and the spectral comparison. As a result the dynamics near the stationary solutions is qualitatively characterized by a variational function.     

Dirichlet Problem of a Delayed Reaction–Diffusion Equation on a Semi-infinite Interval

We consider a nonlocal delayed reaction–diffusion equation in a semi-infinite interval that describes mature population of a single species with two age stages (immature and mature) and a fixed maturation period living in a spatially semi-infinite environment. Homogeneous Dirichlet condition is imposed at the finite end, accounting for a scenario that boundary is hostile to the species. Due to the lack of compactness and symmetry of the spatial domain, the global dynamics of the equation turns out to be a very challenging problem. We first establish a priori estimate for nontrivial solutions after exploring the delicate asymptotic properties of the nonlocal delayed effect and the diffusion operator. Using the estimate, we are able to show the repellency of the trivial equilibrium and the existence of a positive heterogeneous steady state under the Dirichlet boundary condition. We then employ the dynamical system arguments to establish the global attractivity of the heterogeneous steady state. As a byproduct, we also obtain the existence and global attractivity of the heterogeneous steady state for the bistable evolution equation in the whole space.     

Stability Analysis of a Reaction–Diffusion Equation with Spatiotemporal Delay and Dirichlet Boundary Condition

In this paper, we concentrate on the study of a reaction–diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition. It is shown that a positive spatially nonhomogeneous equilibrium can bifurcate from the trivial equilibrium. Moreover, the stability of the bifurcated positive equilibrium is investigated. And we prove that, for the given spatiotemporal delay, the bifurcated equilibrium is stable under some conditions, and Hopf bifurcation cannot occur.     

The influence of the axial force on the vibration of the Euler–Bernoulli beam with an arbitrary number of cracks

The exact closed-form solution for the vibration modes and the eigen-value equation of the Euler–Bernoulli beam-column in the presence of an arbitrary number of concentrated open cracks is proposed. The solution is provided explicitly as functions of four integration constants only, to be determined by the standard boundary conditions. The enforcement of the boundary conditions leads the exact evaluation of the vibration frequencies as well as the buckling load of the beam-column and the corresponding eigen-modes. Furthermore, the presented solution allows a comprehensive evaluation of the influence of the axial load on the modal parameters of the beam. The cracks, which are not subjected to the closing phenomenon, are modelled as a sequence of Dirac’s delta generalised functions in the flexural stiffness. The eigen-mode governing equation is formulated over the entire domain of the beam without enforcement of any further continuity condition. The influence of the axial load on the vibration modes of beam-columns with different number and position of cracks, under different boundary conditions, has been analysed by means of the proposed closed-form expressions. The presented parametric analysis highlights some abrupt changes of the eigen-modes and the corresponding frequencies.     

Numerical Simulation of the Physical–Chemical–Thermal Processes During Hydration Reaction of the Calcium Oxide/Calcium Hydroxide System in an Indirect Reactor

Transport in Porous Media - Solutal convection in a horizontal layer filled with porous media with horizontal seepage of a mixture is investigated considering the solute immobilization and...     

Surface/interface effects on elastic behavior of a screw dislocation in an eccentric core–shell nanowire

The elastic behavior of a screw dislocation which is positioned inside the shell domain of an eccentric core–shell nanowire is addressed with taking into account the surface/interface stress effect. The complex potential function method in combination with the conformal mapping function is applied to solve the governing non-classical equations. The dislocation stress field and the image force acting on the dislocation are studied in detail and compared with those obtained within the classical theory of elasticity. It is shown that near the free outer surface and the inner core–shell interface, the non-classical solution for the stress field considerably differs from the classical one, while this difference practically vanishes in the bulk regions of the nanowire. It is also demonstrated that the surface with positive (negative) shear modulus applies an extra non-classical repelling (attracting) image force to the dislocation, which can change the nature of the equilibrium positions depending on the system parameters. At the same time, the non-classical solution fails when the dislocation approaches very close to the surface/interface with negative shear modulus. The effects of the core–shell eccentricity and nanowire diameter on dislocation behavior are discussed. It is shown that the non-classical surface/interface effect has a short-range character and becomes more pronounced when the nanowire diameter is smaller than 20 nm.     

Study of the effects of inner pressure and surface tension on the fibre drawing process with the aid of an analytical asymptotic fibre drawing model and the numerical solution of the full N.–St. equations

Micro-structured optical fibres (i.e. fibres that contain holes) have assumed a high profile in recent years and given rise to many novel optical devices. The problem of manufacturing such fibres by heating and then drawing a preform is considered for the case of annular capillaries. A fluid mechanics model suggested in the literature that uses asymptotic analysis based on the small aspect ratio of capillaries has been compared with the full 3D set of the N.–St. equations, for modelling the fabrication of capillaries. The final asymptotic equations, analysed in some asymptotic limits, are solved numerically and then compared with the N.–St. solutions, obtained with a commercial finite elements solver. These asymptotic limits give valuable practical information about the control parameters that influence the drawing process, taking into account the effects of surface tension and inner pressure, since those are of essential importance during drawing. It is shown that the asymptotic method delivers reliable results as long as the inner pressure does not exceed too high values.