Search results for "Transition to turbulence"
showing 7 items of 7 documents
Transition to turbulence in toroidal pipes
2011
AbstractIncompressible flow in toroidal pipes of circular cross-section was investigated by three-dimensional, time-dependent numerical simulations using a finite volume method. The computational domain included a whole torus and was discretized by up to ${\ensuremath{\sim} }11. 4\ensuremath{\times} 1{0}^{6} $ nodes. Two curvatures $\delta $ (radius of the cross-section/radius of the torus), namely 0.3 and 0.1, were examined; a streamwise forcing term was imposed, and its magnitude was made to vary so that the bulk Reynolds number ranged between ${\ensuremath{\sim} }3500$ and ${\ensuremath{\sim} }14\hspace{0.167em} 700$. The results were processed by different techniques in order to confirm…
Analysis of complex singularities in high-Reynolds-number Navier-Stokes solutions
2013
AbstractNumerical solutions of the laminar Prandtl boundary-layer and Navier–Stokes equations are considered for the case of the two-dimensional uniform flow past an impulsively-started circular cylinder. The various viscous–inviscid interactions that occur during the unsteady separation process are investigated by applying complex singularity analysis to the wall shear and streamwise velocity component of the two solutions. This is carried out using two different methodologies, namely a singularity-tracking method and the Padé approximation. It is shown how the van Dommelen and Shen singularity that occurs in solutions of the Prandtl boundary-layer equations evolves in the complex plane be…
Route to chaos in the weakly stratified Kolmogorov flow
2019
We consider a two-dimensional fluid exposed to Kolmogorov’s forcing cos(ny) and heated from above. The stabilizing effects of temperature are taken into account using the Boussinesq approximation. The fluid with no temperature stratification has been widely studied and, although relying on strong simplifications, it is considered an important tool for the theoretical and experimental study of transition to turbulence. In this paper, we are interested in the set of transitions leading the temperature stratified fluid from the laminar solution [U∝cos(ny),0, T ∝ y] to more complex states until the onset of chaotic states. We will consider Reynolds numbers 0 < Re ≤ 30, while the Richardson numb…
Direct numerical simulations of creeping to early turbulent flow in unbaffled and baffled stirred tanks
2018
Abstract It has been known for a long time that the fluid flow and several global quantities, such as the power and pumping numbers, are about the same in baffled and unbaffled mechanically stirred vessels at low Reynolds numbers, but bifurcate at some intermediate Re and take drastically different values in fully turbulent flow. However, several details are not yet completely understood, notably concerning the relation of this bifurcation with the flow features and the transition to turbulence. In order to shed light on these issues, computational fluid dynamics was employed to predict the flow field in two vessels stirred by a six-bladed Rushton turbine at Reynolds numbers from 0.2 to 600…
Transition to turbulence in serpentine pipes
2017
Abstract The geometry considered in the present work (serpentine pipe) is a sequence of U-bends of alternate curvature. It is characterized by pipe diameter, d = 2a and bend diameter, D = 2c. The repeated curvature inversion forces the secondary flow pattern, typical of all flows in curved ducts, to switch between two mirror-like configurations. This causes (i) pressure drop and heat or mass transfer characteristics much different from those occurring either in a straight pipe or in a constant-curvature pipe, and (ii) an early loss of stability of the base steady-state flow. In the present work, four values of the curvature δ = a/c (0.2, 0.3, 0.4 and 0.5) were considered. For each value of …
Numerical simulation of reciprocating turbulent flow in a plane channel
2009
Direct numerical simulation results were obtained for oscillatory flow with zero time mean (reciprocating flow) in a plane channel using a finite volume method, Crank-Nicolson time stepping and central approximation of the advection terms. A pressure gradient varying co-sinusoidally in time was imposed as the forcing term, and its frequency and amplitude were made to vary so as to span a range of regimes from purely laminar to fully turbulent. For the limiting cases of reciprocating laminar flow and steady-state turbulent flow, numerical results were validated against analytical solutions and classic experimental literature data, respectively. For general reciprocating flows, predictions we…
Steady, periodic, quasi-periodic and chaotic flow regimes in toroidal pipes
2012
Incompressible flow in a toroidal pipe was investigated by direct numerical simulation. The curvature a/c (radius of the cross section / radius of the torus) was 0.3 or 0.1 and the bulk Reynolds number ranged between 3500 and 14 700. The study revealed a rich scenario of transition to turbulence. For the higher curvature a/c = 0.3, a supercritical transition from stationary to periodic flow (Hopf bifurcation) was observed at Re=4600. The periodic flow was characterized by a travelling wave which, in the whole periodic Re range, took the form of a varicose modulation of the twin Dean vortex rings, included 8 wavelengths along the axis of the torus, and exhibited instantaneous anti-symmetry a…