scholarly journals Restricted nonlinear model for high- and low-drag events in plane channel flow

2019 ◽  
Vol 864 ◽  
pp. 221-243 ◽  
Author(s):  
Frédéric Alizard ◽  
Damien Biau
Keyword(s):  
Channel Flow ◽  
Plane Channel ◽  
Wall Turbulence ◽  
Asymptotic State ◽  
State Variables ◽  
Mean Flow ◽  
Quadratic Interaction ◽  
Maximum Drag Reduction ◽  
The Mean ◽  
Plane Channel Flow

A restricted nonlinear (RNL) model, obtained by partitioning the state variables into streamwise-averaged quantities and superimposed perturbations, is used in order to track the exact coherent state in plane channel flow investigated by Toh & Itano (J. Fluid Mech., vol. 481, 2003, pp. 67–76). When restricting nonlinearities to quadratic interaction of the fluctuating part into the streamwise-averaged component, it is shown that the coherent structure and its dynamics closely match results from direct numerical simulation (DNS), even if only a single streamwise Fourier mode is retained. In particular, both solutions exhibit long quiescent phases, spanwise shifts and bursting events. It is also shown that the dynamical trajectory passes close to equilibria that exhibit either low- or high-drag states. When statistics are collected at times where the friction velocity peaks, the mean flow and root-mean-square profiles show the essential features of wall turbulence obtained by DNS for the same friction Reynolds number. For low-drag events, the mean flow profiles are related to a universal asymptotic state called maximum drag reduction (Xi & Graham, Phys. Rev. Lett., vol. 108, 2012, 028301). Hence, the intermittent nature of self-sustaining processes in the buffer layer is contained in the dynamics of the RNL model, organized in two exact coherent states plus an asymptotic turbulent-like attractor. We also address how closely turbulent dynamics approaches these equilibria by exploiting a DNS database associated with a larger domain.

scholarly journals Pressure, density, temperature and entropy fluctuations in compressible turbulent plane channel flow

2014 ◽  
Vol 757 ◽  
pp. 701-746 ◽  
Author(s):  
G. A. Gerolymos ◽  
I. Vallet
Keyword(s):  
Channel Flow ◽  
Plane Channel ◽  
Correlation Coefficients ◽  
Statistical Modelling ◽  
Transport Equations ◽  
Wall Turbulence ◽  
State Variables ◽  
Turbulent Plane ◽  
Thermodynamic Variables ◽  
Plane Channel Flow

AbstractWe investigate the fluctuations of thermodynamic state variables in compressible aerodynamic wall turbulence, using results of direct numerical simulation (DNS) of compressible turbulent plane channel flow. The basic transport equations governing the behaviour of thermodynamic variables (density, pressure, temperature and entropy) are reviewed and used to derive the exact transport equations for the variances and fluxes (transport by the fluctuating velocity field) of the thermodynamic fluctuations. The scaling with Reynolds and Mach number of compressible turbulent plane channel flow is discussed. Statistics and correlation coefficients of the thermodynamic fluctuations are examined. Finally, detailed budgets of the transport equations for the variances and fluxes of the thermodynamic variables are analysed. The implications of these results, leading both to the understanding of the thermodynamic interactions in compressible wall turbulence and to possible improvements in statistical modelling, are assessed. Finally, the required extension of existing DNS data to fully characterise this canonical flow is discussed.

Numerical simulations of transition in oscillatory plane channel flow

1989 ◽  
Vol 208 ◽  
pp. 45-66 ◽  
Author(s):  
Bart A. Singer ◽  
Joel H. Ferziger ◽  
Helen L. Reed
Keyword(s):  
Channel Flow ◽  
Positive Curvature ◽  
Plane Channel ◽  
Maximum Growth ◽  
Mean Flow ◽  
Low Frequencies ◽  
Frequency Maximum ◽  
The Mean ◽  
The Stability ◽  
Plane Channel Flow

The effect of flow oscillation on the stability of plane channel flow is studied via numerical simulation. For weak oscillation, the ratio of the Stokes layer thickness to the distance from the wall to the critical layer in steady flow provides the best normalization for the mean-flow frequency. Maximum growth rates occur when the instantaneous velocity profile has large regions of positive curvature. The effect of oscillation is generally stabilizing. However, at low frequencies, TS wave energies may vary by 106 in a cycle and irreversible secondary instability may be produced at the peak.

The Destruction-of-Dissipation Tensor εεij in Wall Turbulence

2017 ◽  
Author(s):  
G. A. Gerolymos ◽  
I. Vallet
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Plane Channel ◽  
Wall Turbulence ◽  
Scaling Relations ◽  
Pressure Term ◽  
Turbulent Plane ◽  
Plane Channel Flow ◽  
Production Mechanisms ◽  
Molecular Viscosity

The paper investigates the destruction-of-dissipation tensor εεij in low-Reynolds number turbulent plane channel flow. This tensor, which represents the destruction of the dissipation tensor εij (appearing in the budgets of the covariances of fluctuating velocities rij) by molecular viscosity, exhibits specific near-wall anisotropy and is not 2-C at the wall. The budgets of εεij (turbulent and viscous diffusion, pressure-term, various production mechanisms, and destruction by molecular viscosity εεεij) are studied and various scaling relations are examined.

Instabilities in a plane channel flow between compliant walls

1997 ◽  
Vol 352 ◽  
pp. 205-243 ◽  
Author(s):  
CHRISTOPHER DAVIES ◽  
PETER W. CARPENTER
Keyword(s):  
Dispersion Relation ◽  
Shear Layer ◽  
Channel Flow ◽  
Plane Channel ◽  
Mean Flow ◽  
Blasius Flow ◽  
Divergence Instability ◽  
Compliant Walls ◽  
Tollmien Schlichting ◽  
Plane Channel Flow

The stability of plane channel flow between compliant walls is investigated for disturbances which have the same symmetry, with respect to the channel centreline, as the Tollmien–Schlichting mode of instability. The interconnected behaviour of flow-induced surface waves and Tollmien–Schlichting waves is examined both by direct numerical solution of the Orr–Sommerfeld equation and by means of an analytic shear layer theory. We show that when the compliant wall properties are selected so as to give a significant stability effect on Tollmien–Schlichting waves, the onset of divergence instability can be severely disrupted. In addition, travelling wave flutter can interact with the Tollmien–Schlichting mode to generate a powerful instability which replaces the flutter instability identified in studies based on a potential mean-flow model. The behaviour found when the mean-flow shear layer is fully accounted for may be traced to singularities in the wave dispersion relation. These singularities can be attributed to solutions which represent Tollmien–Schlichting waves in rigid-walled channels. Such singularities will also be found in the dispersion relation for the case of Blasius flow. Thus, similar behaviour can be anticipated for Blasius flow, including the disruption of the onset of divergence instability. As a consequence, it seems likely that previous investigations for Blasius flow will have yielded very conservative estimates for the optimal stabilization that can be achieved for Tollmien–Schlichting waves for the purposes of laminar-flow control.

scholarly journals Numerical Simulations of Heat Transfer in Plane Channel Flow

2011 ◽  
Vol 312-315 ◽  
pp. 671-675 ◽  
Author(s):  
Najla El Gharbi ◽  
Rafik Absi ◽  
Ahmed Benzaoui
Keyword(s):  
Channel Flow ◽  
Plane Channel ◽  
Turbulence Models ◽  
Streamwise Velocity ◽  
Navier Stokes ◽  
Mean Flow ◽  
Rans Turbulence Models ◽  
Simulation Results ◽  
Plane Channel Flow

Reynolds-averaged Navier–Stokes “RANS” turbulence models (such as k-ε models) are still widely used for engineering applications because of their relatively simplicity and robustness. In fully developed plane channel flow (i.e. the flow between two infinitely large plates), even if available models and near-wall treatments provide adequate mean flow velocities, they fail to predict suitable turbulent kinetic energy “TKE” profiles near walls. TKE is involved in determination of eddy viscosity/diffusivity and could therefore provide inaccurate concentrations and temperatures. In order to improve TKE a User Defined Function “UDF” based on an analytical profile for TKE was developed and implemented in FLUENT. Mean streamwise velocity and TKE profiles were compared to DNS data for friction Reynolds number Reτ = 150. Simulation results for TKE show accurate profiles. Simulation results for horizontal heated channel flows obtained with FLUENT are presented. Numerical results are validated by direct numerical simulation “DNS” data for Reτ = 150.

Reduced-basis modeling of turbulent plane channel flow

2006 ◽  
Vol 35 (2) ◽  
pp. 189-207 ◽  
Author(s):  
P.S. Johansson ◽  
H.I. Andersson ◽  
E.M. Rønquist
Keyword(s):  
Channel Flow ◽  
Plane Channel ◽  
Reduced Basis ◽  
Turbulent Plane ◽  
Plane Channel Flow
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