A mechanism for bypass transition from localized disturbances in wall-bounded shear flows

1993 ◽  
Vol 250 ◽  
pp. 169-207 ◽  
Author(s):  
Dan S. Henningson ◽  
Anders Lundbladh ◽  
Arne V. Johansson
Keyword(s):  
Shear Flows ◽  
Stokes Equations ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Normal Velocity ◽  
Bypass Transition ◽  
Nonlinear Interactions ◽  
Streamwise Vorticity ◽  
Low Velocity ◽  
Transfer Energy

The linear, nonlinear and breakdown stages in the transition of localized disturbances in plane Poiseuille flow is studied by direct numerical simulations and analysis of the linearized Navier–Stokes equations. Three-dimensionality plays a key role and allows for algebraic growth of the normal vorticity through the linear lift-up mechanism. This growth primarily generates elongated structures in the streamwise direction since it is largest at low streamwise wavenumbers. For finite-amplitude disturbances such structures will be generated essentially independent of the details of the initial disturbance, since the preferred nonlinear interactions transfer energy to low streamwise wavenumbers. The nonlinear interactions also give a decrease in the spanwise scales. For the stronger initial disturbances the streamwise vorticity associated with the slightly inclined streaks was found to roll up into distinct streamwise vortices in the vicinity of which breakdown occurred. The breakdown starts with a local rapid growth of the normal velocity bringing low-speed fluid out from the wall. This phenomenon is similar to the low-velocity spikes previously observed in transition experiments. Soon thereafter a small turbulent spot is formed. This scenario represents a bypass of the regular Tollmien–Schlichting, secondary instability process. The simulations have been carried out with a sufficient spatial resolution to ensure an accurate description of all stages of the breakdown and spot formation processes. The generality of the observed processes is substantiated by use of different types of initial disturbances and by Blasius boundary-layer simulations. The present results point in the direction of universality of the observed transition mechanisms for localized disturbances in wall-bounded shear flows.

Numerical Prediction of Impact-Related Wave Loads on Ships

2006 ◽  
Author(s):  
Thomas E. Schellin ◽  
Ould El Moctar
Keyword(s):  
Stokes Equations ◽  
Numerical Procedure ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Ship Motions ◽  
Normal Velocity ◽  
Wave Loads ◽  
Critical Areas ◽  
Strip Theory ◽  
A Chain

We present a numerical procedure to predict impact-related wave-induced (slamming) loads on ships. The procedure was applied to predict slamming loads on two ships that feature a flared bow with a pronounced bulb, hull shapes typical of modern offshore supply vessels. The procedure used a chain of seakeeping codes. First, a linear Green function panel code computed ship responses in unit amplitude regular waves. Wave frequency and wave heading were systematically varied to cover all possible combinations likely to cause slamming. Regular design waves were selected on the basis of maximum magnitudes of relative normal velocity between ship critical areas and wave, averaged over the critical areas. Second, a nonlinear strip theory seakeeping code determined ship motions under design wave conditions, thereby accounting for the ship’s forward speed, the swell-up of water in finite amplitude waves, as well as the ship’s wake that influences the wave elevation around the ship. Third, these nonlinearly computed ship motions constituted part of the input for a Reynolds-averaged Navier-Stokes equations (RANSE) code that was used to obtain slamming loads. Favourable comparison with available model test data validated the procedure and demonstrated its capability to predict slamming loads suitable for design of ship structures.

scholarly journals Nonlinear control of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow

2013 ◽  
Vol 737 ◽  
pp. 440-465 ◽  
Author(s):  
S. Cherubini ◽  
J.-C. Robinet ◽  
P. De Palma
Keyword(s):  
Stokes Equations ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Control Procedure ◽  
Normal Velocity ◽  
Optimal Control Strategy ◽  
Navier Stokes Equations ◽  
Target Time ◽  
Layer Flow ◽  
Laminar State

AbstractThe present work provides an optimal control strategy, based on the nonlinear Navier–Stokes equations, aimed at hampering the rapid growth of unsteady finite-amplitude perturbations in a Blasius boundary-layer flow. A variational procedure is used to find the blowing and suction control law at the wall providing the maximum damping of the energy of a given perturbation at a given target time, with the final aim of leading the flow back to the laminar state. Two optimally growing finite-amplitude initial perturbations capable of leading very rapidly to transition have been used to initialize the flow. The nonlinear control procedure has been found able to drive such perturbations back to the laminar state, provided that the target time of the minimization and the region in which the blowing and suction is applied have been suitably chosen. On the other hand, an equivalent control procedure based on the linearized Navier–Stokes equations has been found much less effective, being not able to lead the flow to the laminar state when finite-amplitude disturbances are considered. Regions of strong sensitivity to blowing and suction have been also identified for the given initial perturbations: when the control is actuated in such regions, laminarization is also observed for a shorter extent of the actuation region. The nonlinear optimal blowing and suction law consists of alternating wall-normal velocity perturbations, which appear to modify the core flow structures by means of two distinct mechanisms: (i) a wall-normal velocity compensation at small times; (ii) a rotation-counterbalancing effect al larger times. Similar control laws have been observed for different target times, values of the cost parameter, and streamwise extents of the blowing and suction zone, meaning that these two mechanisms are robust features of the optimal control strategy, provided that the nonlinear effects are taken into account.

scholarly journals Finite-amplitude steady waves in plane viscous shear flows

1985 ◽  
Vol 160 ◽  
pp. 281-295 ◽  
Author(s):  
F. A. Milinazzo ◽  
P. G. Saffman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Navier Stokes ◽  
Unidirectional Flow ◽  
Viscous Shear ◽  
Finite Amplitude Waves

Computations of two-dimensional solutions of the Navier–Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.

scholarly journals Numerical simulation of Faraday waves

2009 ◽  
Vol 635 ◽  
pp. 1-26 ◽  
Author(s):  
NICOLAS PÉRINET ◽  
DAMIR JURIC ◽  
LAURETTE S. TUCKERMAN
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Oscillation Period ◽  
Finite Amplitude ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Faraday Waves ◽  
Temporal Behaviour ◽  
Two Fluids ◽  
Front Tracking Method

We simulate numerically the full dynamics of Faraday waves in three dimensions for two incompressible and immiscible viscous fluids. The Navier–Stokes equations are solved using a finite-difference projection method coupled with a front-tracking method for the interface between the two fluids. The critical accelerations and wavenumbers, as well as the temporal behaviour at onset are compared with the results of the linear Floquet analysis of Kumar & Tuckerman (J. Fluid Mech., vol. 279, 1994, p. 49). The finite-amplitude results are compared with the experiments of Kityk et al (Phys. Rev. E, vol. 72, 2005, p. 036209). In particular, we reproduce the detailed spatio-temporal spectrum of both square and hexagonal patterns within experimental uncertainty. We present the first calculations of a three-dimensional velocity field arising from the Faraday instability for a hexagonal pattern as it varies over its oscillation period.

Numerical Prediction of Impact-Related Wave Loads on Ships

2006 ◽  
Vol 129 (1) ◽  
pp. 39-47 ◽  
Author(s):  
Thomas E. Schellin ◽  
Ould el Moctar
Keyword(s):  
Stokes Equations ◽  
Numerical Procedure ◽  
Navier Stokes ◽  
Ship Motions ◽  
Normal Velocity ◽  
Wave Loads ◽  
Navier Stokes Equations ◽  
Critical Areas ◽  
Strip Theory ◽  
A Chain

We present a numerical procedure to predict impact-related wave-induced (slamming) loads on ships. The procedure was applied to predict slamming loads on two ships that feature a flared bow with a pronounced bulb, hull shapes typical of modern offshore supply vessels. The procedure used a chain of seakeeping codes. First, a linear Green function panel code computed ship responses in unit amplitude regular waves. Ship speed, wave frequency, and wave heading were systematically varied to cover all possible combinations likely to cause slamming. Regular design waves were selected on the basis of maximum magnitudes of relative normal velocity between ship critical areas and wave, averaged over the critical areas. Second, a nonlinear strip theory seakeeping code determined ship motions under design wave conditions, thereby accounting for the nonlinear pressure distribution up to the wave contour and the frequency dependence of the radiation forces (memory effect). Third, these nonlinearly computed ship motions constituted part of the input for a Reynolds-averaged Navier–Stokes equations code that was used to obtain slamming loads. Favorable comparison with available model test data validated the procedure and demonstrated its capability to predict slamming loads suitable for design of ship structures.

Modelling of By-Pass Transition With Conditioned Navier-Stokes Equations and a K-E Model Adapted for Intermittency

1994 ◽  
Author(s):  
J. Steelant ◽  
E. Dick
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Suction Side ◽  
Navier Stokes ◽  
Intermittent Flow ◽  
Time Averaging ◽  
Bypass Transition ◽  
Navier Stokes Equations ◽  
Direct Excitation ◽  
Energy Equations

Turbomachinery flows are characterized by a very high intensity turbulent mean part. As a consequence, laminar flow in boundary layer regions undergoes transition through direct excitation of turbulence. This is the so-called bypass transition. Regions form that are intermittently laminar and turbulent. In particular in accelerating flows, as on the suction side of a turbine blade, this intermittent flow can extend over a very large part of the boundary layer. Classical turbulence modelling based on global time averaging is not valid in intermittent flows. To take correctly account of the intermittency, conditioned averages are necessary. These are averages taken during the fraction of time the flow is turbulent or laminar respectively. Starting from the Navier-Stokes equations, conditioned continuity, momentum and energy equations are derived for the laminar and turbulent parts of an intermittent flow. The turbulence is described by the classical k-ε model. The supplementary parameter introduced by the conditioned averaging is the intermittency factor. In the calculations, this factor is prescribed in an algebraic way.

Studying turbulence using direct numerical simulation: 1987 Center for Turbulence Research NASA Ames/Stanford Summer Programme

1988 ◽  
Vol 190 ◽  
pp. 375-392 ◽  
Author(s):  
J. C. R. Hunt
Keyword(s):  
Boundary Layers ◽  
Turbulent Flows ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Turbulent Boundary Layers ◽  
Finite Amplitude ◽  
Wall Layer ◽  
Navier Stokes ◽  
Scale Motion

This paper is an account of a summer programme for the study of the ideas and models of turbulent flows, using the results of direct numerical stimulations of the Navier-Stokes equations. These results had been obtained on the computers and stored as accessible databases at the Center for Turbulence Research (CTR) of NASA Ames Research Center and Stanford University. At this first summer programme, some 32 visiting researchers joined those at the CTR to test hypotheses and models in five aspects of turbulence research: turbulence decomposition, bifurcation and chaos; two-point closure (or k-space) modelling; structure of turbulent boundary layers; Reynolds-stress modelling; scalar transport and reacting flows.A number of new results emerged including: computation of space and space-time correlations in isotropic turbulence can be related to each other and modelled in terms of the advection of small scales by large-scale motion; the wall layer in turbulent boundary layers is dominated by shear layers which protrude into the outer layers, and have long lifetimes; some aspects of the ejection mechanism for these layers can be described in terms of the two-dimensional finite-amplitude Navier-Stokes solutions; a self-similar form of the two-point, cross-correlation data of the turbulence in boundary layers (when normalized by the r.m.s. value at the furthest point from the wall) shows how both the blocking of eddies by the wall and straining by the mean shear control the lengthscales; the intercomponent transfer (pressure-strain) is highly localized in space, usually in regions of concentrated vorticity; conditioned pressure gradients are linear in the conditioning of velocity and independent of vorticity in homogeneous shear flow; some features of coherent structures in the boundary layer are similar to experimental measurements of structures in mixing-layers, jets and wakes.The availability of comprehensive velocity and pressure data certainly helps the investigation of concepts and models. But a striking feature of the summer programme was the diversity of interpretation of the same computed velocity fields. There are few signs of any convergence in turbulence research! But with new computational facilities the divergent approaches can at least be related to each other.

3D Viscous Inverse Design of Vaned Diffuser to Suppress Flow Unsteadiness in a Centrifugal Compressor

2005 ◽  
Author(s):  
Victor I. Mileshin ◽  
Igor A. Brailko ◽  
Andrew N. Startsev ◽  
Igor K. Orekhov
Keyword(s):  
Centrifugal Compressor ◽  
Stokes Equations ◽  
Reverse Flow ◽  
Pressure Ratio ◽  
Design Procedure ◽  
Inverse Design ◽  
Navier Stokes ◽  
Low Velocity ◽  
Vaned Diffuser ◽  
Pressure Surface

Present paper is devoted to numerical investigation of unsteadiness caused by impeller-diffuser interaction in a 8:1 total pressure ratio centrifugal compressor. The compressor designed by CIAM [7], and manufactured and tested by Customer gave satisfactory performances even under the first test. Further development requires new insights and advanced numerical tools. In this context, this paper presents Navier-Stokes computations of 3D viscous unsteady flow field within the impeller-diffuser configuration. Steady and unsteady computations indicated spacious zone of low velocity / reverse flow on pressure surface of the diffuser vane. To suppress this reverse flow, new vaned diffuser has been tailored through application of 3D inverse design procedure for Navier-Stokes equations [8]. Subsequent steady and unsteady N-S calculations performed for compressor with the new diffuser demonstrated depression of reverse flow within diffuser and different unsteady loading of the diffuser vane.

Streamwise vortices in shear flows: harbingers of transition and the skeleton of coherent structures

2010 ◽  
Vol 661 ◽  
pp. 178-205 ◽  
Author(s):  
PHILIP HALL ◽  
SPENCER SHERWIN
Keyword(s):  
Coherent Structures ◽  
Shear Flows ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Streamwise Vortex ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Turbulent Shear Flows ◽  
External Flows

The relationship between asymptotic descriptions of vortex–wave interactions and more recent work on ‘exact coherent structures’ is investigated. In recent years immense interest has been focused on so-called self-sustained processes in turbulent shear flows where the importance of waves interacting with streamwise vortex flows has been elucidated in a number of papers. In this paper, it is shown that the so-called ‘lower branch’ state which has been shown to play a crucial role in these self-sustained processes is a finite Reynolds number analogue of a Rayleigh vortex–wave interaction with scales appropriately modified from those for external flows to Couette flow, the flow of interest here. Remarkable agreement between the asymptotic theory and numerical solutions of the Navier–Stokes equations is found even down to relatively small Reynolds numbers, thereby suggesting the possible importance of vortex–wave interaction theory in turbulent shear flows. The relevance of the work to more general shear flows is also discussed.

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