On the development of a triple‐preserving Maxwell's equations solver in non‐staggered grids

We present in this paper a finite difference solver for Maxwell's equations in non‐staggered grids. The scheme formulated in time domain theoretically preserves the properties of zero‐divergence, symplecticity, and dispersion relation. The mathematically inherent Hamiltonian can be also retained all the time. Moreover, both spatial and temporal terms are approximated to yield the equal fourth‐order spatial and temporal accuracies. Through the computational exercises, modified equation analysis and Fourier analysis, it can be clearly demonstrated that the proposed triple‐preserving solver is computationally accurate and efficient for use to predict the Maxwell's solutions. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical study of vortex shedding from a rotating cylinder immersed in a uniform flow field

A numerical study is made of the unsteady two‐dimensional, incompressible flow past an impulsively started translating and rotating circular cylinder. The Reynolds number (Re) and the rotating‐to‐translating speed ratio (α) are two controlled parameters, and the influence of their different combinations on vortex shedding from the cylinder is investigated by the numerical scheme sketched below. Associated with the streamfunction (ψ)–vorticity (ω) formulation of the Navier–Stokes equations, the Poisson equation for ψ is solved by a Fourier/finite‐analytic, separation of variable approach. This approach allows one to attenuate the artificial far‐field boundary, and also yields a global conditioning on the wall vorticity in response to the no‐slip condition. As for the vorticity transport equation, spatial discretization is done by means of finite difference in which the convection terms are handled with the aid of an ENO (essentially non‐oscillatory)‐like data reconstruction process. Finally, the interior vorticity is updated by an explicit, second‐order Runge–Kutta method. Present computations fall into two categories. One with Re=10³ and α≤3; the other with Re=10⁴ and α≤2. Comparisons with other numerical or physical experiments are included. Copyright © 2000 John Wiley & Sons, Ltd.     

Simulations of the unsteady separated flow past a normal flat plate

Well-resolved two-dimensional numerical simulations of the unsteady separated flow past a normal flat plate at low Reynolds numbers have been performed using a fractional step procedure with high-order spatial discretization. A fifth-order upwind-biased scheme is used for the convective terms and the diffusive terms are represented by a fourth-order central difference scheme. The pressure Poisson equation is solved using a direct method based on eigenvalue decomposition of the coefficient matrix. A systematic study of the flow has been conducted with high temporal and spatial resolutions for a series of Reynolds numbers. The interactions of the vortices shed form the shear layers in the near-and far-wake regions are studied. For Reynolds numbers less than 250 the vortices are observed to convect parallel to the freestream. However, at higher Reynolds numbers (500 and 1000), complex interactions including vortex pairing, tearing and deformations are seen to occur in the far-wake region. Values of the drag coefficient and the wake closure length are presented and compared with previous experimental and numerical studies.     

Unsteady compressible boundary layer flow in the stagnation region of a sphere with a magnetic field

Summary An analysis is performed to study the unsteady compressible laminar boundary layer flow in the forward stagnation-point region of a sphere with a magnetic field applied normal to the surface. We have considered the case where there is an initial steady state that is perturbed by the step change in the total enthalpy at the wall. The nonlinear coupled parabolic partial differential equations governing the flow and heat transfer have been solved numerically using a finite-difference scheme. The numerical results are presented, which show the temporal development of the boundary layer. The magnetic field in the presence of variable electrical conductivity causes an overshoot in the velocity profile. Also, when the total enthalpy at the wall is suddenly increased, there is a change in the direction of transfer of heat in a small interval of time. Received 15 January 1996; accepted for publication 21 November 1996     

Modelling of the free surface with heat and mass transfer considerations on a liquid filling a porous slab heated from its sides

The position of the free surface is calculated numerically for a porous slab which is partly filled with a liquid and differentially heated from its sides. A coordinate transformation is used to transform the original problem from a physical coordinate system to a non‐orthogonal system where the free surface becomes a fixed straightline. The transformed problem is then solved using a finite difference method. Results are obtained for Rayleigh numbers up to 1000. The Nusselt numbers increase slightly with medium Rayleigh numbers (convection‐dominated region) as expected. Since at low Ra the conduction is dominant and at high Ra radiation is dominant. Hadizadeh and Tien (Int. J. Heat Mass Transfer 2004; 17 (6):799–804) studied the forced convection on the surface of porous layer. In that paper they dealt with in detail the boundary regime of liquid in the channel and modelled the flow and heat transfer. Copyright © 2007 John Wiley & Sons, Ltd.     

Analysis of the anisotropy of group velocity error due to spatial finite difference schemes from the solution of the 2D linear Euler equations

Numerical differencing schemes are subject to dispersive and dissipative errors, which in one dimension, are functions of a wavenumber. When these schemes are applied in two or three dimensions, the errors become functions of both wavenumber and the direction of the wave. For the Euler equations, the direction of flow and flow velocity are also important. Spectral analysis was used to predict the error in magnitude and direction of the group velocity of vorticity–entropy and acoustic waves in the solution of the linearised Euler equations in a two‐dimensional Cartesian space. The anisotropy in these errors, for three schemes, were studied as a function of the wavenumber, wave direction, mean flow direction and mean flow Mach number. Numerical experiments were run to provide confirmation of the developed theory. Copyright © 2012 John Wiley & Sons, Ltd.     

Normalization of the stress concentrations at the rounded edges of an interference fit between a solid shaft subjected to bending and a hub

The elastic stress concentrations are addressed that are developed from the keyless frictionless press fit of a shaft subjected to bending into a hub with rounded bore edges. Derived from a formal modeling of the title problem in terms of an integral equation, a set of normalized parameters is proposed that accounts for the combined effects on the hub stress concentration of the fillet radius, the shaft radius, the hub outer radius, the hub axial length, the interference, the Young's modulus, and the bending couple. A numerical validation of the normalized parameters is presented. With the aid of Finite Elements, various design charts are compiled that (a) forecast the bending couple initiating the detachment between the shaft and the hub, and (b) report the elastic stress concentrations within the hub versus the proposed normalized parameters in the absence of shaft–hub detachment. Such charts assist the designer in dimensioning an interference fit in the presence of a bending couple.     

Use of a sliding plate rheometer to measure the first normal stress difference at high shear rates

The use of a sliding plate rheometer (SPR) to determine the first normal stress difference of molten polymers and elastomers at high shear rates is demonstrated. The simple shear flow in this instrument is not subject to the flow instabilities that limit the use of rotational rheometers to shear rates often below 1 s⁻¹. However, issues of secondary flow and wall slip must be addressed to obtain reliable data using an SPR. A highly entangled, monodisperse polybutadiene and a commercial polystyrene were the polymers studied. The inclusion of the polystyrene made it possible to compare data with those obtained by Lodge using a stressmeter, which is an instrument based on the measurement of the hole pressure. The data from the two instruments are in good agreement and are also close to the predictions of an empirical equation of Laun based on the storage and loss moduli.     

Symmetrical Representation of Stresses in the Stroh Formalism and its Application to a Dislocation and a Dislocation Dipole in an Anissotropic Elastic Medium

Symmetrical stress representation in the Stroh formalism for anisotropic elastic bodies is introduced and the range of its applicability is analysed. By making use of this stress representation new formulae for influence functions giving stresses in an infinite anisotropic medium subjected to a straight dislocation and a straight dislocation dipole are derived. The advantage of the new formulae is that they explicitly show the symmetrical structure of these influence functions not referred to previously. Relations of these influence functions to influence functions giving stresses and Airy stress function due to a straight wedge disclination, whose explicit expressions are also introduced, are derived. Application of these results in computation of stresses by the hypersingular and regularized Somigliana stress identities is discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

High-fidelity numerical simulation of the flow field around a NACA-0012 aerofoil from the laminar separation bubble to a full stall

In the present work, large eddy simulations of the flow field around a NACA-0012 aerofoil near stall conditions are performed at a Reynolds number of 5 × 10⁴, Mach number of 0.4, and at various angles of attack. The results show the following: at relatively low angles of attack, the bubble is present and intact; at moderate angles of attack, the laminar separation bubble bursts and generates a global low-frequency flow oscillation; and at relatively high angles of attack, the laminar separation bubble becomes an open bubble that leads the aerofoil into a full stall. Time histories of the aerodynamic coefficients showed that the low-frequency oscillation phenomenon and its associated physics are indeed captured in the simulations. The aerodynamic coefficients compared to previous and recent experimental data with acceptable accuracy. Spectral analysis identified a dominant low-frequency mode featuring the periodic separation and reattachment of the flow field. At angles of attack α ≤ 9.3°, the low-frequency mode featured bubble shedding rather than bubble bursting and reformation. The underlying mechanism behind the quasi-periodic self-sustained low-frequency flow oscillation is discussed in detail.     

A simple sliding‐mesh interface procedure and its application to the CFD simulation of a tidal‐stream turbine

An effective way of using computational fluid dynamics (CFD) to simulate flow about a rotating device—for example, a wind or marine turbine—is to embed a rotating region of cells inside a larger, stationary domain, with a sliding interface between. This paper describes a simple but effective method for implementing this as an internal Dirichlet boundary condition, with interfacial values obtained by interpolation from halo nodes. The method is tested in two finite‐volume codes: one using block‐structured meshes and the other unstructured meshes. Validation is performed for flow around simple, isolated, rotating shapes (cylinder, sphere and cube), comparing, where possible, with experiment and the alternative CFD approach of fixed grid with moving walls. Flow variables are shown to vary smoothly across the sliding interface. Simulations of a tidal‐stream turbine, including both rotor and support, are then performed and compared with towing‐tank experiments. Comparison between CFD and experiment is made for thrust and power coefficients as a function of tip‐speed ratio (TSR) using Reynolds‐averaged Navier–Stokes turbulence models and large‐eddy simulation (LES). Performance of most models is good near the optimal TSR, but simulations underestimate mean thrust and power coefficients in off‐design conditions, with the standard k– ? turbulence model performing noticeably worse than shear stress transport k– ω and Reynolds‐stress‐transport closures. LES gave good predictions of mean load coefficients and vital information about wake structures but at substantial computational cost. Grid‐sensitivity studies suggest that Reynolds‐averaged Navier–Stokes models give acceptable predictions of mean power and thrust coefficients on a single device using a mesh of about 4 million cells. Copyright © 2013 John Wiley & Sons, Ltd.