A numerical study of flow through wavy-walled channels

A numerical procedure is developed for the analysis of flow in a channel whose walls describe a travelling wave motion. Following a perturbation method, the primitive variables are expanded in a series with the wall amplitude as the perturbation parameter. The boundary conditions are applied at the mean surface of the channel and the first-order perturbation quantities are calculated using the pseudospectral collocation method. Although limited by the linear analysis, the present approach is not restricted by the Reynolds number of the flow and the wave number and frequency of the wavy-walled channel. Using the computed wall shear stresses, the positions of flow separation and reattachment are determined. The variations in velocity and pressure with frequency of excitation are also presented

Stability characteristics of wavy walled channel flows13;

The linear temporal stability characteristics of converging-diverging, symmetric wavy walled channel flows are numerically investigated in this paper. The basic flow in the problem is a superposition of plane channel flow and periodic flow components arising due to the small amplitude sinusoidal waviness of the channel walls. The disturbance equations are derived within the frame work of Floquet theory and solved using the spectral collocation method. Two-dimensional stability calculations indicate the presence of fast growing unstable modes that arise due to the waviness of the walls. Neutral stability calculations are performed in the disturbance wavenumber-Reynolds number (as-R) plane, for the wavy channel with wavenumber k 1 =0.2 and the wall amplitude to semi-channel height ratio, E,,., up to 0.1. It is also shown that the two-dimensional wavy channel flows can be modulated by a suitable frequency of wall excitation cog , thereby stabilizing the flow

Dynamical characteristics of wave-excited channel flow

This paper is part of a study on the receptivity characteristics of the shear flow in a channel whose walls are subjected to a wave-like excitation. The small amplitude forced wavy wall motion is characterised by a wave number vector 21, 22 and a frequency owg. The basic flow in the problem is a superposition of the Poiseuille flow and a periodic component that corresponds to the wave excitation of the wall. The aim of the study is to examine the susceptibility of this flow to transition. The problem is approached through studying the stability characteristics of the basic flow with respect to small disturbances. The theoretical framework for this purpose is Floquet theory. The solution procedure for solving the eigenvalue problem is the spectral collocation method. Preliminary results showing the influence of the amplitude and the wave number of the wall excitation on the stability boundary of the flow are presented

A beginner's guide to the use of the spectral collocation method for solving some eigenvalue problems in fluid mechanics

The present quot;Guidequot; aims to introduce- through selected examples the use of the spectral collocation method for solving eigenvalue problems. The focus of attention in the quot;Guidequot; is the recasting of the differential eigenvalue problem into its algebraic counterpart (matrix eigenvalue problem). Starting from an outline of the method, the steps of discretisation and transformation according to the spectral collocation method are illustrated in detail for the selected examples ordered according to increasing complexity. The two simple examples are differential equations of second and fourth order with constant coefficients. The chosen example from fluid mechanics is the propagation of small amplitude disturbances in the fully developed channel flow 13; (Orr-Sommerfeld equation). The quot;Guidequot; includes FORTRAN source programs for the examples.13; 13; 13

Hitzdrahtmesstechnik Grundlagen und Anwendungen

TIB: RO 2014 (101) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman