A coupled blade element momentum – Computational fluid dynamics model for evaluating tidal stream turbine performance

A modelling approach based on blade element momentum theory is developed for the prediction of tidal stream turbine performance in the ocean environment. Through the coupling of the blade element momentum method with computational fluid dynamics, the influence of upstream hydrodynamics on rotor performance is accounted for. Incoming flow onto the rotor can vary in speed and direction compared to free-stream conditions due to the presence of obstructions to the flow in the upstream, due to other devices for example, or due to the complexity of natural bathymetries. The relative simplicity of the model leads to short run times and a lower demand on computational resources making it a useful tool for considering more complex engineering problems consisting of multiple tidal stream turbines. Results from the model compare well against both measured data from flume experiments and results obtained using the classical blade element momentum model. A discussion considering the advantages and disadvantages of these different approaches is included.     

A discrete prey–predator model preserving the dynamics of a structurally unstable Lotka–Volterra model

Leslie's method to construct a discrete two dimensional dynamical system dynamically consistent with the Lotka–Volterra type of competing two species ordinary differential equations is applied in a newly extended manner for the Lotka–Volterra prey–predator system which is structurally unstable. We show that, independently of the time step size, the derived discrete prey–predator system is dynamically consistent with the continuous counterpart, keeping the nature of neutrally stable periodic orbit. Further, we show that the extended method to construct the discrete prey–predator system can provide a dynamically consistent model also for the logistic Lotka–Volterra one.     

Analysis on dynamics of a population model with predator–prey-dependent functional response

We consider a reaction–diffusion population model with predator–prey-dependent functional response. Firstly, we discuss the conditions which ensure the model has a unique positive constant solution. Secondly, we investigate the dynamical properties of the model, including the large time behaviors of the nonconstant solutions and the local and the global asymptotic stability of the positive constant solution.     

The impact of Wolbachia on dengue transmission dynamics in an SEI–SIS model

Dengue has grown dramatically in recent decades globally. In order to investigate the spread of dengue with vector control, especially, the impact of Wolbachia on dengue transmission, a mathematical model is established and analyzed to study dengue transmission between humans and mosquitoes. Firstly, model qualitative analysis including the existence and local asymptotic stability of dengue-free equilibria and endemic equilibria is done. It is found that dengue will disappear when the basic reproduction number is less than one, and dengue will prevail when the basic reproduction number is larger than one. More important finding is that the persistence of Wolbachia is determined by its fitness effect on mosquitoes, and Wolbachia can drastically reduce dengue fever transmission. All the results are verified by numerical simulation. Secondly, sensitivity analysis is done to explore the relative importance of different parameters on the system. It is obtained that parameters with strong sensitivity and controllability are the biting rate, the probability of dengue infection between mosquitoes and humans and the recovery rate of infectious humans. Finally, the control methods are discussed.     

The Mackey–Glass model of respiratory dynamics: Review and new results

Since the celebrated Mackey–Glass model of respiratory dynamics was introduced in 1977, many results on its qualitative behavior have been obtained, including oscillation, stability and chaos. The paper reviews some known properties and presents new results for more general models: equations with time-dependent parameters, several delays, a positive periodic equilibrium and distributed delays. The problems considered in the paper involve existence, positivity and permanence of solutions, oscillation and global asymptotic stability. In addition, some general approaches to the study of nonlinear nonautonomous scalar delay equations are outlined. The paper generalizes and unifies existing results and provides an outlook on further studies.     

Comment on “A note on a study on an integrable system of coupled KdV equations”

We analyze the note by Muraved [A note on A study on an integrable system of coupled KdV equations [1], Commun Nonlinear Sci Numer Simulat. doi:10.1016/j.cnsns.2010.06.018]. Author tried to show that our approach is curious. We demonstrate that, author has not shown any error and presented a curious note.     

Stability of Taylor–Couette and Dean flow: A semi-analytical study

An alternative method is presented for solving the eigenvalue problem that governs the stability of Taylor–Couette and Dean flow. The eigenvalue problems defined by the two-point boundary value problems are converted into initial value problems by applying unit disturbance method developed by Harris and Reid [27] in 1964. Thereafter, the initial value problems are solved by differential transform method in series and the eigenvalues are computed by shooting technique. Critical wave number and Taylor number for Taylor–Couette flow are computed for a wide range of rotation ratio (μ), −4 ? μ ? 1 (first mode) and −2 ? μ ? 1 (second mode). The radial eigenfunction and cell patterns are presented for μ = −1, 0, 1. Also, we have computed critical wave number and Dean number successfully.     

Direct numerical simulation of the laminar–turbulent transition at hypersonic flow speeds on a supercomputer

A method for direct numerical simulation of three-dimensional unsteady disturbances leading to a laminar–turbulent transition at hypersonic flow speeds is proposed. The simulation relies on solving the full three-dimensional unsteady Navier–Stokes equations. The computational technique is intended for multiprocessor supercomputers and is based on a fully implicit monotone approximation scheme and the Newton–Raphson method for solving systems of nonlinear difference equations. This approach is used to study the development of three-dimensional unstable disturbances in a flat-plate and compression-corner boundary layers in early laminar–turbulent transition stages at the free-stream Mach number M = 5.37. The three-dimensional disturbance field is visualized in order to reveal and discuss features of the instability development at the linear and nonlinear stages. The distribution of the skin friction coefficient is used to detect laminar and transient flow regimes and determine the onset of the laminar–turbulent transition.     

Competing through altering the environment: A cross-diffusion population model coupled to transport–Darcy flow equations

We consider an evolution model describing the spatial population distribution of two salt tolerant plant species, such as mangroves, which are affected by inter- and intra-specific competition (Lotka–Volterra), population pressure (cross-diffusion) and environmental heterogeneity (environmental potential). The environmental potential and the Lotka–Volterra terms are assumed to depend on the salt concentration in the root region, which may change as a result of mangroves’ ability to uptake fresh water and leave the salt of the solution behind, in the saturated porous medium. Consequently, partial differential equations modelling the population dynamics on the surface are coupled with Darcy–transport equations modelling the salt and pressure-velocity distribution in the subsurface. We prove the existence of weak solutions of the coupled problem and provide a numerical discretization based on a stabilized mixed finite element method, which we use to numerically demonstrate the behaviour of the system.     

A numerical study of air–vapor–heat transport through textile materials with a moving interface

This paper focuses on the numerical study of heat and moisture transfer in clothing assemblies, which is described by a multi-component and multiphase air–vapor–heat flow with a moving interface. A splitting semi-implicit finite volume method is applied for the system of nonlinear parabolic equations and an implicit Euler scheme is used for the interface equation. In terms of classical Dirichlet to Neumann map, the implicit system can be solved directly and no iteration is needed. Two types of clothing assemblies are investigated and the comparison with experimental measurements is also presented.     

CFD simulation of gas–solid flow with a cluster structure-dependent drag coefficient model in circulating fluidized beds

To model the effect of clusters on hydrodynamics of gas and particles phases in risers, the interfacial drag coefficient is taken into account in computational fluid dynamic simulations by means of a two-fluid model. The momentum and energy balances that characterize the clusters in the dense phase and dispersed particles in the dilute phase are described by the multi-scale resolution approach. The model of cluster structure-dependent (CSD) drag coefficient is proposed on the basis of the minimization of energy dissipation by heterogeneous drag (MEDHD) in the full range of Reynolds number. The model of CSD drag coefficient is then incorporated into the two-fluid model to simulate flow behavior of gas and particles in a riser. The distributions of volume fraction and velocity of particles are predicted. Simulated results are in agreement with experimental data published in the literature.     

Analysis of a FEM–BEM model posed on the conducting domain for the time-dependent eddy current problem

The three-dimensional eddy current time-dependent problem is considered. We formulate it in terms of two variables, one lying only on the conducting domain and the other on its boundary. We combine finite elements (FEM) and boundary elements (BEM) to obtain a FEM–BEM coupled variational formulation. We establish the existence and uniqueness of the solution in the continuous and the fully discrete case. Finally, we investigate the convergence order of the fully discrete scheme.     

The influence of a DC electric field on the von Kármán vortex street in the wake of a confined cylinder

We investigate the influence of a DC electric field on the flow around and in the wake of a confined cylinder by means of numerical simulations. Our results indicate that even very small electrical perturbations have significant impact on the settling time of the lift coefficient. Moreover, the oscillations of the lift coefficient of pure pressure-driven and pressure-driven flow with induced electrical field are in anti-phase. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Concept and prototype of a web tool for public–private project contracting based on a system dynamics model

Central European Journal of Operations Research - Contracting has a significant impact on the efficiency of acquisition processes, especially in the context of so-called public–private...     

A study of the influence of center conditions on the domain of parameters of Newton’s method by using recurrence relations

This paper focuses on the importance of center conditions on the first derivative of the operator involved in the solution of nonlinear equations by Newton’s method when the semilocal convergence of the method is established from the technique of recurrence relations.     

Efficient simulation of gas–liquid pipe flows using a generalized population balance equation coupled with the algebraic slip model

The inhomogeneous generalized population balance equation, which is discretized with the direct quadrature method of moment (DQMOM), is solved to predict the bubble size distribution (BSD) in a vertical pipe flow. The proposed model is compared with a more classical approach where bubbles are characterized with a constant mean size. The turbulent two-phase flow field, which is modeled using a Reynolds-Averaged Navier–Stokes equation approach, is assumed to be in local equilibrium, thus the relative gas and liquid (slip) velocities can be calculated with the algebraic slip model, thereby accounting for the drag, lift, and lubrication forces. The complex relationship between the bubble size distribution and the resulting forces is described accurately by the DQMOM. Each quadrature node and weight represents a class of bubbles with characteristic size and number density, which change dynamically in time and space to preserve the first moments of the BSD. The predictions obtained are validated against previously published experimental data, thereby demonstrating the advantages of this approach for large-scale systems as well as suggesting future extensions to long piping systems and more complex geometries.     

Cattaneo–Christov heat flux model for three-dimensional flow of a viscoelastic fluid on an exponentially stretching surface

ABSTRACT

In this article, we explore the three-dimensional boundary-layer flow over an exponentially stretching surface in two parallel ways. Constitutive equations of a second-grade fluid are used. Instead of classical Fourier’s law, Cattaneo–Christov heat flux model is employed for the formulation of the energy equation. This model can predict the effects of thermal relaxation time on the boundary layer. The resulting partial differential equations are reduced into ordinary differential equations by similarity transformations. Homotopy Analysis Method (HAM) is employed to solve the non-linear problem. Physical impact of emerging parameters on the momentum and thermal boundary-layer thickness are studied.     

Simulation of a reacting gas–liquid bubbly flow with CFD and PBM: Validation with experiments

In this work we use computational fluid dynamics (CFD) to simulate a reactive gas–liquid bubbly system in a rectangular bubble column, operating at low superficial velocities (i.e. homogeneous regime). The gas bubbles, injected in the column through a sparger, contain one of the reactants, namely CO₂, that via mass transfer moves to the continuous liquid phase, where it reacts with NaOH. A key role is played by the bubble size distribution (BSD) and the specific surface area that define the overall mass transfer rate in the CFD model. In order to correctly predict the BSD and the polydispersity of the bubbly system the population balance equation is solved by the quadrature method of moments (QMOM), within the OpenFOAM (v. 2.2.x) two-fluid solver compressibleTwoPhaseEulerFoam. To reduce the computational time and increase stability, a second-order operator-splitting technique for the solution of the chemically reactive species is also implemented, allowing to solve the different processes involved with their own time-scale. To our knowledge this is the first time that QMOM is employed for the simulation of a real reactive bubbly system and predictions are validated against experiments.     

A study on the local convergence and the dynamics of Chebyshev–Halley–type methods free from second derivative

The error behavior of exponential operator splitting methods for nonlinear Schrödinger equations in the semiclassical regime is studied. For the Lie and Strang splitting methods, the exact form of the local error is determined and the dependence on the semiclassical parameter is identified. This is enabled within a defect-based framework which also suggests asymptotically correct a posteriori local error estimators as the basis for adaptive time stepsize selection. Numerical examples substantiate and complement the theoretical investigations.     

The effect of predator competition on positive solutions for a predator–prey model with diffusion

A diffusive predator–prey model with predator competition is considered under Dirichlet boundary conditions. Some existence and non-existence results are firstly obtained. Then by investigating the bifurcation of positive solutions, the multiplicity of positive solutions is established for suitably large m$m$. Furthermore, by meticulously analyzing the asymptotic behaviors of positive solutions when k$k$ goes to ∞$\infty$, we find that there is at most a positive solution for any c∈R$c\in R$ when k$k$ is sufficiently large. At last, some numerical simulations are presented to supplement the analytic results in one dimension.