Volume 18, Issue 7-8 -

This paper examines the influence of mixing a fuel with an oxidizer-rich reactant on the existence and propagation of partially premixed flames formed in a porous-wall channel. The amount of the injected fuel has been taken as a parameter to generate different states of the combustion mixtures. The problem has been mathematically formulated in the framework of the thermodiffusive model under a single-step chemical reaction. Numerical simulations based on finite elements were then employed to solve the governing partial differential equations. The study has shown that the degree of fuel premixing in the combustion mixtures as well as the value of the Lewis number of fuel and oxidizer plays a great role on the existence and structure of triple flames. It is found also that flame extinguishes for larger values of the premixing parameter. Flame structures were also found to exhibit several changes such as the shift of the leading edge toward the fuel supply side and the formation of twin flames. It has been predicted that the premixing can substantially enhance the reactivity of the combustion mixture, but on the other hand it tends to shift the flame to the boundary which may destroy the underlying combustion chamber. For nonunit Lewis numbers, fuel premixing is found to shift triple flames from the stoichiometric surface and attach the flame to the channel walls. It is predicted also that the maximum reaction rate reduces with increasing the Lewis numbers.

The accurate prediction of self-aerated flow is not always easy to obtain, particularly if the computational performance is the main concern. Two-fluid formulation is suitable to simulate the dispersed air in a continuous water phase (e.g. bubbly flows) in a fine mesh, whereas the interface tracking methods are used for sharp interfaces with two continuous and contiguous phases (e.g. free-surface flows). Several approaches have emerged to combine both methods; however all found a gap in the transition between resolved and unresolved scales of air at the interface. Including a source term that predicts the self-aeration process is viewed as a promising step to overcome such difficulty. In this work, we added to the volume-of-fluid formulation an extra advection-diffusion equation connected to a source of air at the free surface to simulate the dispersed bubble phase. One-way coupling and two-way coupling versions of this model are tested along with sensitivity tests to show the accuracy of the new source term that does not require calibration. The location of the aeration is analysed and investigated. Results are obtained in terms of free-surface flow depths, air–concentration profiles and velocity fields and compared to experimental data acquired in a scaled stepped spillway model with good agreement. The free-surface given by the air-entrainment model is in good agreement in both non-aerated and aerated zone of the spillway.

In this article, we mainly prove the existence of extremal solutions for a fractional q$q$-difference equation involving Riemann–Lioville type fractional derivative with integral boundary conditions. A comparison theorem under weak conditions is also build, and then we apply the comparison theorem, monotone iterative technique and lower–upper solution method to prove the existence of extremal solutions. Moreover, we can construct two iterative schemes approximating the extremal solutions of the fractional q$q$-difference equation with integral boundary conditions. In the last section, a simple example is presented to illustrate the main result.

This paper discusses the existence of mild solutions for a class of fractional impulsive evolution equation with periodic boundary condition and noncompact semigroup. By using some fixed-point theorems, the existence theorems of mild solutions are obtained, our results are also more general than known results. Furthermore, as an application that illustrates the abstract results, two examples are given.

This study aims to solve the transmission failure caused by warping and crackling on frictional and steel disks of a wet multi-disk clutch. Thus, a dynamic model is proposed to describe the transient contact process of the disks, as well as the heat transfer laws, during the engagement of the clutch using the commercial software MSC/NASTRAN. Moreover, the heat transfer laws, which varies with engagement time within a contact area, is investigated. On the basis of these results, some rules for heat conduction in a wet multi-disk clutch are developed. By measuring the pressure and temperature of the inlet and outlet of the clutch, the correctness of the theoretical analysis method is indirectly verified.

Adaptive control is capable of handling systems with uncertain parameters in terms of asymptotic performance; however, it is not so well in the transient performance. Even though adaptation gain is part of adaptive controller having much effects on the transient response, it has been considered as a constant gain most of the times. In this paper, a new Laypunov-based mechanism is proposed to find optimal values of adaptation gains in nonlinear adaptive control design. The algorithm inspired of the halving method for finding polynomial roots tries to find optimum values of the adaptation gains in a direction of minimizing a cost function. The simulation results show satisfactory performance of the proposed controller especially in terms transient performance.

In order to analyze the influence of the random parameters of the system on the nonlinear dynamic characteristics of the gear transmission system, considering the random perturbation of damping ratio, gear backlash, meshing frequency, meshing stiffness and the low frequency excitation caused by torque fluctuation, the random vibration equations of three-degree-of-freedom gear transmission system are established according to the Newton’s law. The motion differential equations are solved by the Runge–Kutta method. The effects of different random parameters such as load ratio, tooth frequency ratio, damping ratio, gear backlash and meshing stiffness on the dynamic response of the gear transmission system are analyzed in light and heavy loads and low and high speeds.