Catálogo de publicaciones - libros

Transition to turbulence in pipe flow has posed a riddle in fluid dynamics since the pioneering experiments of Reynolds[1]. Although the laminar flow is linearly stable for all flow rates, practical pipe flows become turbulent at large enough flow speeds. Turbulence arises suddenly and fully without distinct steps and without a clear critical point. The complexity of this problem has puzzled mathematicians, physicists and engineers for more than a century and no satisfactory explanation of this problem has been given. In a very recent theoretical approach it has been suggested that unstable solutions of the Navier Stokes equations may hold the key to understanding this problem. In numerical studies such unstable states have been identified as exact solutions for the idealized case of a pipe with periodic boundary conditions[2, 3]. These solutions have the form of waves extending through the entire pipe and travelling in the streamwise direction at a phase speed close to the bulk velocity of the fluid. With the aid of a recently developed high-speed stereoscopic Particle Image Velocimetry (PIV) system, we were able to observe transients of such unstable solutions in turbulent pipe flow[4].

We present recent results concerning the linearized inviscid stability and propagation characteristics of disturbances to the boundary-layer flow due to an in- finite rotating disk in otherwise still fluid. Such disturbances are expected to decay exponentially outside the boundary layer, but we have found a situation where exponential growth can occur in the wall-normal direction. It is shown, by considering the solution to the initial-value problem, that this behaviour can be predicted by using modes with exponentially divergent eigenfunctions.

Numerical results on the stability of boundary layers in the presence of streaks, assumed steady and spanwise periodic, are presented. The instability features are retrieved both from stability analysis and from the numerical simulation of the flow impulse response. It is found that the presence of streaks of moderate amplitudes is able to quench the viscous Tollmien-Schlichting waves. However, a threshold exists beyond which secondary inflectional instabilities occur. Streaky basic flows unstable to both sinuous and varicose perturbations are considered. To gain physical understanding of the instability mechanisms the equation for the perturbation kinetic energy is analysed. To investigate the sinuous instability modes an analytical model streak is also proposed.

The laminar flow through a pipe of constant average radius is shown to display linear instability at low Reynolds number. This is offered as a possible mechanism that could be operating in small-scale flows. The effect of changing geometry, which could be a significant factor, is studied. A multigrid algorithm is used for computing the meanflow and a full non-parallel stability analysis is conducted.

At a previous meeting results based on wavelet analysis demonstrated similarities between triggered turbulent spots and the turbulent patches caused by wake interactions on compressor and turbine blading[1]. Hughes and Walker[2] went further and used wavelet conditioning to identify the prevalence of Tollmien-Schlichting instability phenomena in the flow over axial flow compressor blades. In the current investigation transition phenomena occurring in axial flow compressors are simulated on a larger scale to provide further evidence on the similarities between turbomachinery and wind tunnel flows. The applicability of the intermittency-based approaches to the closure of laminar separation bubbles is demonstrated. The spacing between impinging wakes is systematically varied and it is found that the calmed region acts to suppress turbulence, even for closely spaced wakes.

We investigate the influence of free-stream turbulent vortical disturbances on a compressible laminar boundary layer by solving the unsteady linear boundary equations for the velocity and temperature fluctuations. These equations describe the evolution of the perturbations when the boundary layer thickness becomes of the order of the transverse free-stream integral length scale of turbulence. Similar to the incompressible case, low-frequency disturbances penetrate into the boundary layer to form streamwise-elongated streaks, often referred to as “Klebanoff” modes. High-frequency fluctuations are instead absorbed in the outer edge layer. We find that increasing the Mach number and the free-stream turbulent length scale both have a stabilizing effect on the growth of r.m.s. of mass flux fluctuations in the core of the boundary layer.

The effect of viscosity stratification on the different mechanism of transition to turbulence is not well understood. In this paper, a viscosity variation normal to the flow in a channel is investigated. The primary and secondary instability are computed, and the transient growth is analysed. It is found that viscosity stratification can have different effects in each case.

The scope of the present study is to demonstrate the use of spectral/-element methods in understanding the global instability mechanisms of vortex dominated flows. Using a BiGlobal stability analysis, analytically constructed and numerically evaluated base flows have been investigated, with the leading eigenvalues obtained by the Arnoldi algorithm. Subsequently, Direct Numerical Simulation (DNS) was used to investigate the non-linear development of an unstable Batchelor vortex. It was found that a spiral-type instability, if allowed to develop in an axially unconstrained manner, leads to an axial loss of energy and the formation of a stagnation point.

The present paper is devoted to the detailed experimental study of weakly nonlinear resonant interactions of Tollmien-Schlichting waves in a specially designed 2D non self-similar boundary layer on an airfoil. The influence of the fundamental frequency on the eficiency of the tuned subharmonic resonance is investigated as well as the influence of frequency and spanwise wavenumber detunings. The results are compared with Direct Numerical Simulations based on a vorticity-velocity formulation of the complete Navier-Stokes equations. Good overall agreement is achieved.

A simplified DNS study is presented of the evolution of Klebanoff-type modes in swept 3D boundary layers (Falkner-Skan-Cooke flows) with adverse and favourable streamwise pressure gradients.