International Journal for Numerical Methods in Fluids

Carvalho, M. S.

doi: 10.1002/fld.452pmid: N/A

Coating process is an important step in the manufacturing of different products, such as paper, adhesive and magnetic tapes, photographic films, and many other. The tensioned web roll coating is one the several methods used by different industries. It relies on the elastohydrodynamic action between the fluid and the tensioned substrate for transferring and applying the liquid. The main advantage of this method is its ability to apply very thin liquid layers with less sensitivity to mechanical tolerance at relative small cost. Despite its industrial application, theoretical analysis and fundamental understanding of the process are limited. This work analyses this elastohydrodynamic action by solving the differential equations that govern the liquid flow, described by the Navier–Stokes equation, and the web deformation, modelled by the cylindrical shell approximation. The goal is to determine the operating conditions at which the process is two dimensional and defect free. The equations are discretized by the Galerkin/finite‐element method. The resulting non‐linear system of equations is solved by Newton's method coupled with pseudo‐arc‐length continuation in order to obtain solutions around turning points. The theoretical results are used to construct an operating window of the process that is in agreement with limited experimental data. Copyright © 2003 John Wiley & Sons, Ltd.

Stockie, John M.; Promislow, Keith; Wetton, Brian R.

doi: 10.1002/fld.453pmid: N/A

We present a mathematical model for multicomponent gas transport in an anisotropic fuel cell electrode.The model couples the Maxwell–Stefan equations for multicomponent diffusion along with Darcy's law for flow in a porous medium. The equations are discretized using a finite volume approach with the method of lines, and the resulting non‐linear system of differential equations is integrated in time using a stiff ODE solver. Numerical simulations are performed to validate the model and to investigate the effect of various parameters on fuel cell performance. Copyright © 2003 John Wiley & Sons, Ltd.

Adachi1, T.; Uehara, H.

doi: 10.1002/fld.456pmid: N/A

We have conducted the linear stability analysis of flow in a channel with periodically grooved parts by using the spectral element method. The channel is composed of parallel plates with rectangular grooves on one side in a streamwise direction. The flow field is assumed to be two‐dimensional and fully developed. At a relatively small Reynolds number, the flow is in a steady‐state, whereas a self‐sustained oscillatory flow occurs at a critical Reynolds number as a result of Hopf bifurcation due to an oscillatory instability mode. In order to evaluate the critical Reynolds number, the linear stability theory is applied to the complex laminar flow in the periodically grooved channel by constituting the generalized eigenvalue problem of matrix form using a penalty‐function method. The critical Reynolds number can be determined by the sign of a linear growth rate of the eigenvalues. It is found that the bifurcation occurs due to the oscillatory instability mode which has a period two times as long as the channel period. Copyright © 2003 John Wiley & Sons, Ltd.

Grigoriadis, D. G. E.; Bartzis, J. G.; Goulas, A.

doi: 10.1002/fld.458pmid: N/A

Incompressible turbulent flow past a long square cylinder is investigated using large eddy simulations (LES). Results are presented and compared with available experimental databases for a Reynolds number Red=22000. The problem served as one of the validation cases for the development of a numerical code designed for efficient, parallel, three‐dimensional N‐S computations in complex geometrical configurations. In contrast with previous studies, the geometrical definition of the problem is established by the immersed boundary concept (IMB) while pressure solution is performed by a fast, fully parallel direct pressure solver. Calculations were performed with the widely applied Smagorinsky turbulence model and the filtered structure function model (FSF) which has not been previously applied to the flow case under consideration. In order to assess the potential of LES at its lowest (RANS), and highest (DNS) limit, different numerical resolutions were examined. Depending on the available resolution, either no‐slip conditions or a modified Werner and Wengle approximate wall boundary condition was used. The predicted mean velocity and fluctuation profiles, force statistics and Strouhal numbers were found to be in very good agreement with the experimental data sets. Analysis of the results indicates that for time varying bluff‐bodies flows that involve complex flow phenomena, successful large eddy simulations are not just possible, but can also achieve an excellent quality of results at a relatively low cost. Copyright © 2003 John Wiley & Sons, Ltd.

Mazaheri, Karim; Roe, Philip L.

doi: 10.1002/fld.460pmid: N/A

In solution of the Euler equations in the steady state external flows, error or residual waves are blamed for decelerating the convergence. These waves may be damped by adding a bulk viscosity term to the momentum equations. We analyse effects of this term on the linearized differential equations, and study its explicit and implicit implementation in one and two space dimensions. Optimum values of the bulk viscosity damping (BVD) are discussed. After generalization to two space dimensions, its performance both alone and in combination with a soft wall boundary condition and residual smoothing in central differencing codes is reviewed. It is shown that BVD is complementary to them, and acts independently of them. Finally, application of BVD in solution of low Mach number flows is considered, to show how it can strongly stabilize and accelerate these low Mach number computations. Copyright © 2003 John Wiley & Sons, Ltd.

Nilsson, P.; Bai, X. S.

doi: 10.1002/fld.465pmid: N/A

The difference between a presumed distribution of flamelet position and a numerically simulated distribution of distance function (a signed distance to flamelet) is investigated. It is shown that even if the distribution of flamelet position is symmetrical and close to Gaussian, the distribution of distance function away from the mean flame position is skewed towards the mean position and the mean of the distance function is also different from the distance to the mean position. The difference depends on the distance to the mean flame and the flame wrinkling amplitude. An extension method for the variance of the distance function and an upwind scheme for solving the re‐initialization equation are presented. A numerical simulation of a premixed turbulent flame is compared to experimental data. Copyright © 2003 John Wiley & Sons, Ltd.