Wave drift force in a two-layer fluid of finite depth

Based on the momentum and energy conservation principles, a compact calculation formula is analytically derived for the wave-drift force on a 2-D body floating in a two-layer fluid of finite depth. In a two-layer fluid, two different wave modes (the surface-wave mode with longer wavelength and the internal-wave mode with shorter wavelength) exist not only in the incident wave but also in the body-scattered wave, and these wave characteristics are properly incorporated in the obtained formula. It is noted that, unlike the single-layer case, the wave-drift force can be negative in the incident wave of surface-wave mode, if the transmitted wave with internal-wave mode is large. Numerical computations are implemented for a Lewis-form body by means of the boundary-integral-equation method with Green’s function for the two-layer fluid problem. The effects of density ratio, interface position, and body motions on the wave-drift force are studied, and some important features are found for two-layer fluids.     

Second-order Wagner theory of wave impact

The paper deals with the two-dimensional unsteady problem of the impact of a liquid parabola onto a rigid flat plate at a constant velocity. The liquid is assumed ideal and incompressible and its flow potential. The initial stage of the impact is the main concern in this study. The non-dimensional half-width of the contact region between the impacting liquid and the plate plays the role of a small parameter in this problem. The flow region is subdivided into four parts: (i) the main flow region, the dimension of which is of the order of the contact-region width, (ii) the jet-root region, where the curvature of the free surface is very high and the flow is strongly nonlinear, (iii) the jet region, where the flow is approximately one-dimensional, (iv) the far-field region, where the flow is approximately uniform at the initial stage of impact. A second-order solution in the main flow region has been derived and matched to the first-order inner solution in the jet-root region. The matching conditions provide an estimate of the dimension of the contact region for small time. Pressure distributions in both the main flow region and the inner region are derived. The accuracy of the obtained asymptotic formulae is estimated. The second-order hydrodynamic force acting on the plate is obtained and compared with available experimental data. A fairly good agreement is reported.     

A FETI-like domain decomposition method for coupling finite elements and boundary elements in large-size problems of acoustic scattering

Numerical simulations of acoustic scattering in the frequency domain based on hybrid methods coupling finite elements and boundary elements are the most suited for dealing with problems involving wave propagation in inhomogeneous media. Furthermore, it is necessary to resort to high performance computing to effectively solve the large size problems. However, the direct coupling yields a linear system with a matrix which is partly dense and partly sparse and thus not adapted to high performance computing. To avoid this difficulty, we present a new iterative method constructed from a non overlapping domain decomposition technique.     

Experimental and computational analysis on guide vane losses of impulse turbine for wave energy conversion

This paper deals with the detailed flow analysis of impulse turbine with experimental and computed results for wave energy power conversion. Initially, several turbulence models have been used in two-dimensional (2-D) computational fluid dynamic (CFD) analysis to find a suitable model for this kind of slow speed unconventional turbine. Experiments have been conducted to validate the CFD results and also to analyze the aerodynamics at various stations of the turbine. The three-dimensional (3-D) CFD model with tip clearance has been generated to predict the internal flow and to understand the effect of tip clearance leakage flow on behavior of the turbine in design and off-design conditions. As a result, it is found from the 2-D results that the comparison between computed and experimental data is good, qualitatively and the turbulence model, standard k–ε can predict the experimental values reasonably well, especially the efficiency of the turbine. Experimental results reveal that the downstream guide vanes are more responsible for low efficiency of the turbine and it is measured that 21% average pressure is lost due to downstream guide vanes. It is proved from the 3-D CFD model with tip clearance that it can predict the experimental values quantitatively and qualitatively. Furthermore, it is estimated from the computed results that the efficiency of the turbine has been reduced about 4%, due to tip clearance leakage flow at higher flow coefficients.     

PROPAGATION OF GASLESS COMBUSTION FRONTS: NONZERO REACTION RATE IN THE WHOLE DOMAIN

This paper deals with the gasless combustion problem in an infinite one-dimensional medium. The possibility of the existence of steadily propagating reaction waves is stated for system models with nonzero reaction rates everywhere but at the boundaries. Two forms for the chemical reaction rate dependence on the temperature are considered: the classical Arrhenius, and a modified Arrhenius incorporating and ignition temperature. The equations for the steadily propagating waves are studied in the phase-plane of the temperature and its derivative. The analysis first addresses the question of whether steadily propagating waves are admissible. Then bounds for the propagation velocity are sought and found. The results of the closed-form analysis are successfully tested against numerical experiments. Non-steady propagation regimes are also found, and regions in the parameter space associated with different asymptotic dynamical behaviour are identified.     

Deterministic learning of completely resonant nonlinear wave systems with Dirichlet boundary conditions

In this paper, we investigate the approximation of completely resonant nonlinear wave systems via deterministic learning. The plants are distributed parameter systems (DPS) describing homogeneous and isotropic elastic vibrating strings with fixed endpoints. The purpose of the paper is to approximate the infinite-dimensional dynamics, rather than the parameters of the wave systems. To solve the problem, the wave systems are first transformed into finite-dimensional dynamical systems described by ordinary differential equation (ODE). The properties of the finite-dimensional systems, including the convergence of the solution, as well as the dominance of partial system dynamics according to point-wise measurements, are analyzed. Based on the properties, second, by using the deterministic learning algorithm, an approximately accurate neural network (NN) approximation of the the finite-dimensional system dynamics is achieved in a local region along the recurrent trajectories. Simulation studies are included to demonstrate the effectiveness of the proposed approach.     

Enhanced extraction of isoflavones from Korean soybean by ultrasonic wave

The amounts of isoflavones extracted from Korean soybean by various ultrasonic waves were compared using 60% aqueous ethanol solution. The effect on extraction yield of variations in solvent composition, temperature, and extraction time was investigated. The experimental results confirmed that ultrasonic waves are a desirable method to extract isoflavones from Korean soybean. The highest yield of aglycone isoflavones was obtained by ultrasonic waves with a frequency of 20 KHz and an extraction time of 10 min, which produced yields of glycoside and aglycone isoflavones three-fold greater than those by dipping method.     

Analytical ray tracing system: Introducing art, a C-library designed for seismic applications

Ray tracing technique is an important tool not only to forward but also for inverse problems in Geophysics, which most of the seismic processing steps depend on. However, implementing ray tracing codes can be very time consuming. This article presents a computer library to trace rays in 2.5D media composed by a stack of layers. The velocity profile inside each layer is such that the eikonal equation can be analytically solved. Therefore, the ray tracing within such profile is made fast and accurate. The great advantage of an analytical ray tracing library is the numerical precision of the quantities computed and the fast execution of the implemented codes. Even though ray tracing programs exist for a long time, for example the seis88 package by ?ervený, most of those programs use a numerical approach to compute the ray. Regardless of the fact that numerical methods can solve more general problems, the analytical ones could be part of a more sophisticated simulation process, where the ray tracing time is completely relevant. We demonstrate the feasibility of our codes using several examples (Miqueles et al., 2013)  [1]. The library can also be used for other applications besides seismic, e.g., optics and tomography.     

Modeling of photocatalytic oxidation of VOCs in a packed bed reactor under continuous and discontinuous illuminations

In this paper, a mathematical model is presented to describe the photocatalytic degradation of VOCs in a packed bed reactor. Here, the adsorption of VOCs on the wall of the reactor is taken into account and the diffusion of VOCs in the axial direction is neglected. First-order kinetics is used to describe the photocatalytic oxidation of VOCs. The analytical solution of the present model is obtained by traveling wave method. The solution shows that the reactor performance is totally dependent on the inlet concentration of VOCs when the time is large enough. The present model is validated through the experimental result of the photocatalytic oxidation of trichloroethylene in a packed bed and the predicted results accord well with the experimental data. The influence of flow rate and inlet concentration on the performance of the reactor is discussed in detail. High flow rate offers high reaction rate and low conversion efficiency. The different inlet conditions and different reaction patterns are also investigated. The model would be useful to estimate the rate constant and help to the design of the reactor.