DNS of the Turbulent Flow Evolving in a Plane Channel from the Entry to the Fully Developed State

2016 ◽  
pp. 127-131
Author(s):  
M. Capuano ◽  
A. Cadiou ◽  
M. Buffat ◽  
L. Le Penven
Keyword(s):  
Turbulent Flow ◽  
Plane Channel

Numerical simulation of reciprocating turbulent flow in a plane channel

2009 ◽  
Vol 21 (9) ◽  
pp. 095106 ◽  
Author(s):  
Massimiliano Di Liberto ◽  
Michele Ciofalo
Keyword(s):  
Numerical Simulation ◽  
Turbulent Flow ◽  
Plane Channel

Characteristics of the leading Lyapunov vector in a turbulent channel flow

2018 ◽  
Vol 849 ◽  
pp. 942-967 ◽  
Author(s):  
Nikolay Nikitin
Keyword(s):  
Turbulent Flow ◽  
Buffer Layer ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Spatial Scales ◽  
Plane Channel ◽  
Base Flow ◽  
Lyapunov Vector ◽  
Perturbation Growth ◽  
Near Wall

The values of the highest Lyapunov exponent (HLE)$\unicode[STIX]{x1D706}_{1}$for turbulent flow in a plane channel at Reynolds numbers up to$Re_{\unicode[STIX]{x1D70F}}=586$are determined. The instantaneous and statistical properties of the corresponding leading Lyapunov vector (LLV) are investigated. The LLV is calculated by numerical solution of the Navier–Stokes equations linearized about the non-stationary base solution corresponding to the developed turbulent flow. The base turbulent flow is calculated in parallel with the calculation of the evolution of the perturbations. For arbitrary initial conditions, the regime of exponential growth${\sim}\exp (\unicode[STIX]{x1D706}_{1}t)$which corresponds to the approaching of the perturbation to the LLV is achieved already at$t^{+}<50$. It is found that the HLE increases with increasing Reynolds number from$\unicode[STIX]{x1D706}_{1}^{+}\approx 0.021$at$Re_{\unicode[STIX]{x1D70F}}=180$to$\unicode[STIX]{x1D706}_{1}^{+}\approx 0.026$at$Re_{\unicode[STIX]{x1D70F}}=586$. The LLV structures are concentrated mainly in a region of the buffer layer and are manifested in the form of spots of increased fluctuation intensity localized both in time and space. The root-mean-square (r.m.s.) profiles of the velocity and vorticity intensities in the LLV are qualitatively close to the corresponding profiles in the base flow with artificially removed near-wall streaks. The difference is the larger concentration of LLV perturbations in the vicinity of the buffer layer and a relatively larger (by approximately 80 %) amplitude of the vorticity pulsations. Based on the energy spectra of velocity and vorticity pulsations, the integral spatial scales of the LLV structures are determined. It is found that LLV structures are on average twice narrower and twice shorter than the corresponding structures of the base flow. The contribution of each of the terms entering into the expression for the production of the perturbation kinetic energy is determined. It is shown that the process of perturbation development is essentially dictated by the inhomogeneity of the base flow, as well as by the presence of transversal motion in it. Neglecting of these factors leads to a significant underestimation of the perturbation growth rate. The presence of near-wall streaks in the base flow, on the contrary, does not play a significant role in the development of the LLV perturbations. Artificial removal of streaks from the base flow does not change the character of the perturbation growth.

scholarly journals Spectral-element simulations of variable-density turbulent flow in a plane channel

2017 ◽  
Vol 159 ◽  
pp. 00041 ◽  
Author(s):  
Vladimir Ryzhenkov ◽  
Vladislav Ivashchenko ◽  
Ricardo Vinuesa ◽  
Rustam Mullyadzhanov
Keyword(s):  
Turbulent Flow ◽  
Plane Channel ◽  
Spectral Element ◽  
Variable Density

II. Determination of constitutive coefficients and illustrative examples

1989 ◽  
Vol 327 (1595) ◽  
pp. 449-475 ◽  
Keyword(s):  
Turbulent Flow ◽  
Constitutive Equations ◽  
Theoretical Calculations ◽  
Equations Of Motion ◽  
Plane Channel ◽  
General System ◽  
Turbulent Fluctuation ◽  
System Of Equations ◽  
Constitutive Response

This paper is a continuation of Part I under the same title and is concerned mainly with the determination of the constitutive response coefficients, as well as some simple illustrative examples. First, a system of simplified constitutive equations for incompressible viscous turbulent flow is obtained from the more general system of equations in Part I through a judicial choice of retaining only those terms which appear to represent major features of the turbulent flow. Even for this simplified system of equations, the identification of some of the constitutive coefficients presents a formidable task; and this is especially true in the case of those coefficients that are associated with the presence of the additional independent variables of the theory due to the manifestation of the alignment of eddies (on the microscopic scale), turbulent fluctuation and eddy density. Because of this difficulty, the present effort for identification of the various constitutive coefficients must be regarded partly as tentative, pending future availability of suitable relevant experimental data and/or pertinent numerical simulation results. Keeping this background in mind, most of the relevant coefficients in the constitutive equations are determined, or the nature of their functional forms are estimated, through consideration of‘cartoon-like’ models on the microscopic level and these results are then used in conjunction with the macroscopic equations of motion to examine a number of simple solutions. These include the possibility of a flow possessing a constant uniform velocity gradient and solutions pertaining to decay of flow anisotropy and plane turbulent channel flows. The predicted theoretical calculations are in general accord with experimental observations. In addition, for plane channel flow, plots of variation along the width of the channel for the turbulent temperature and the macroscopic velocity compare favourably with corresponding known experimental results.

LES and DNS of Turbulent Flows in Weakly Compressible Condition

2007 ◽  
Author(s):  
Takeo Kajishima ◽  
Takashi Ohta
Keyword(s):  
Mach Number ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Plane Channel ◽  
Scale Model ◽  
Turbulent Shear ◽  
Quadrant Analysis ◽  
Number Range ◽  
Low Mach Number ◽  
Flow Scheme

Flow field of low Mach number (e.g. M &lt;0.3) is usually simulated by the incompressible flow scheme due to the severe limitation of time-increment in the compressible flow scheme. In this work, we propose a modification to the usual incompressible scheme, based on the elliptic equation for pressure, to improve the accuracy for turbulent flows considering weak compressibility. Two examples will be shown to validate our method. (1) LES (Large-Eddy Simulation) was conducted for turbulent flow around NACA0012 airfoil. Particular attention was focused on the influence of compressibility, despite the low Mach number range. In addition, new subgrid scale model of one-equation type using dynamic procedure was compared with traditional Smagorinsky model. Our method successfully reproduced the separation bubble near the leading edge, resulted in the improvement in the intensity of pressure fluctuation. (2) DNS (Direct Numerical Simulation) of turbulent flow in a plane channel is carried out, taking wall temperature difference into account. As a result of the density fluctuation in near-wall eddies, asymmetric profiles are observed in turbulence statistics. By the 4-quadrant analysis of turbulent shear stress, it is found that the ejection events in the vicinity of the walls are particularly affected by the density variation.

scholarly journals The laminar generalized Stokes layer and turbulent drag reduction

2010 ◽  
Vol 667 ◽  
pp. 135-157 ◽  
Author(s):  
MAURIZIO QUADRIO ◽  
PIERRE RICCO
Keyword(s):  
Turbulent Flow ◽  
Drag Reduction ◽  
Plane Channel ◽  
Phase Speed ◽  
Life Time ◽  
Turbulent Structures ◽  
Stokes Layer ◽  
Plane Channel Flow ◽  
The Waves ◽  
Spanwise Flow

This paper considers plane channel flow modified by waves of spanwise velocity applied at the wall and travelling along the streamwise direction. Both laminar and turbulent regimes for the streamwise flow are studied. When the streamwise flow is laminar, it is unaffected by the spanwise flow induced by the waves. This flow is a thin, unsteady and streamwise-modulated boundary layer that can be expressed in terms of the Airy function of the first kind. We name it the generalized Stokes layer because it reduces to the classical oscillating Stokes layer in the limit of infinite wave speed. When the streamwise flow is turbulent, the laminar generalized Stokes layer solution describes well the space-averaged turbulent spanwise flow, provided that the phase speed of the waves is sufficiently different from the turbulent convection velocity, and that the time scale of the forcing is smaller than the life time of the near-wall turbulent structures. Under these conditions, the drag reduction is found to scale with the Stokes layer thickness, which renders the laminar solution instrumental for the analysis of the turbulent flow. A classification of the turbulent flow regimes induced by the waves is presented by comparing parameters related to the forcing conditions with the space and time scales of the turbulent flow.

The structure of turbulent boundary layers in the wall region of plane channel flow

2006 ◽  
Vol 463 (2078) ◽  
pp. 593-612 ◽  
Author(s):  
Giancarlo Alfonsi ◽  
Leonardo Primavera
Keyword(s):  
Velocity Field ◽  
Turbulent Flow ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Plane Channel ◽  
Navier Stokes ◽  
Wall Region ◽  
Navier Stokes Equations ◽  
Plane Channel Flow ◽  
Proper Orthogonal

The flow of a viscous incompressible fluid in a plane channel is simulated numerically with the use of a computational code for the numerical integration of the Navier–Stokes equations, based on a mixed spectral-finite difference technique. A turbulent-flow database representing the turbulent statistically steady state of the velocity field through 10 viscous time units is assembled at friction Reynolds number Re τ =180 and the coherent structures of turbulence are extracted from the fluctuating portion of the velocity field using the proper orthogonal decomposition (POD) technique. The temporal evolution of a number of the most energetic POD modes is represented, showing the existence of dominant flow structures elongated in the streamwise direction whose shape is altered owing to the interaction with quasi-streamwise, bean-shaped turbulent-flow modes. This process of interaction is responsible for the gradual disruption of the streamwise modes of the flow.

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