A new study of laminar natural convection in two concentric vertical cylinders

5 and cylinder aspect ratios of 0.5 to 10. The effects of the changes in these parameters on the variation of the temperature and flow patterns within the cylinder have been studied. The local and average Nusselt numbers correlations of interest in determining the insulating value of an annular cavity formed by two concentric vertical cylinders have been obtained. Received on 24 July 1998     

Solutions to a nonlinear Poisson–Nernst–Planck system in an ionic channel

A limiting one‐dimensional Poisson–Nernst–Planck (PNP) equations is considered, when the three‐dimensional domain shrinks to a line segment, to describe the flows of positively and negatively charged ions through open ion channel. The new model comprises the usual drift diffusion terms and takes into account for each phase, the bulk velocity defined by (4) including the water bath for ions. The existence of global weak solution to this problem is shown. The proof relies on the use of certain embedding theorem of weighted sobolev spaces together with Hardy inequality. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical investigation of transient nozzle flow

Abstract. The starting process of two-dimensional and axisymmetric nozzle flows has been investigated numerically. Special attention has been paid to the early phase of the starting process and to the appearance of a strong secondary shock wave. For both cases, shock intensities and velocities are obtained and discussed. The flow evolution in the axisymmetric case is proved to be more complex and the transient starting process is slower than in the plane case. Finally, the effects of changing the nozzle angle and the incident shock wave Mach number on the transient flow are addressed. It is shown that a faster start-up can be induced either by decreasing the nozzle angle or increasing the Mach number of the incident shock wave. Received 16 November 2001 / Accepted 24 September 2002 / Published online 4 December 2002 Correspondence to:A.-S. Mouronval (e-mail: mouronv@coria.fr)     

Numerical study of shock-wave mitigation through matrices of solid obstacles

Shock-wave propagation through different arrays of solid obstacles and its attenuation are analyzed by means of numerical simulations. The two-dimensional compressible Navier–Stokes equations are solved using a fifth-order weighted essentially non-oscillatory scheme, in conjunction with an immersed-boundary method to treat the embedded solids within a cartesian grid. The present study focuses on the geometrical aspects of the solid obstacles, particularly at lower effective flow area, where the frictional forces are expected to be important. The main objective is to analyze the controlling mechanism for shock propagation and attenuation in complex inhomogeneous and porous medium. Different parameters are investigated such as the geometry of the obstacles, their orientation in space as well as the relaxation lengths between two consecutive columns. The study highlights a number of interesting phenomena such as compressible vortices and shock–vortex interactions that are produced in the post-shock region. This also includes shock interactions, hydrodynamic instabilities and non-linear growth of the mixing. Ultimately, the Kelvin–Helmholtz instability invokes transition to a turbulent mixing region across the matrix columns and eddies of different length scales are generated in the wake region downstream of the solid blocks. The power spectrum of instantaneous dynamic pressure shows the existence of a wide range of frequencies which scales nearly with f ^?5/3. In terms of shock attenuation, the results indicate that the staggered matrix of reversed triangular prism (where the base of the triangular prism is facing the incoming shock) is the most efficient arrangement. In this case, both static and dynamic pressure impulses show significant reduction compared to the other studied configurations, which confirms the effectiveness of this type of barrier configuration. Furthermore, the use of combination of reverse–reverse arrangement of triangular prism obstacle maze is found more effective compared to the forward–reverse or forward–forward arrangements.