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.

Numerical simulation of turbulent flow in a pipe oscillating around its axis

2000 ◽  
Vol 424 ◽  
pp. 217-241 ◽  
Author(s):  
MAURIZIO QUADRIO ◽  
STEFANO SIBILLA
Keyword(s):  
Turbulent Flow ◽  
Stokes Equations ◽  
Streamwise Vortex ◽  
Longitudinal Axis ◽  
Navier Stokes ◽  
Planar Geometry ◽  
Wall Region ◽  
Navier Stokes Equations ◽  
Moving Wall ◽  
Direct Numerical Solution

The turbulent flow in a cylindrical pipe oscillating around its longitudinal axis is studied via direct numerical solution of the Navier–Stokes equations, and compared to the reference turbulent flow in a fixed pipe and in a pipe with steady rotation. The maximum amount of drag reduction achievable with appropriate oscillations of the pipe wall is found to be of the order of 40%, hence comparable to that of similar flows in planar geometry. The transverse shear layer due to the oscillations induces substantial modifications to the turbulence statistics in the near-wall region, indicating a strong effect on the vortical structures. These modifications are illustrated, together with the implications for the drag-reducing mechanism. A conceptual model of the interaction between the moving wall and a streamwise vortex is discussed.

scholarly journals Application of Slender Body Theory to Describe Wall Turbulence

1990 ◽  
Vol 43 (5S) ◽  
pp. S245-S245
Author(s):  
Thomas J. Hanratty ◽  
K. Kontamaris
Keyword(s):  
Turbulent Flow ◽  
Stokes Equations ◽  
Flow Direction ◽  
Three Dimensional ◽  
Slender Body ◽  
Wall Turbulence ◽  
Navier Stokes ◽  
Wall Region ◽  
Slender Body Theory ◽  
Navier Stokes Equations

Observations of turbulent flow close to a wall reveal turbulent eddies which are elongated in the flow direction. This has motivated the use of a slender body assumption to simplify the Navier Stokes equations. Derivatives in the flow-direction are neglected so that three velocity components are calculated in a plane. The application of this 2 1/2D model to the viscous wall region (y+ < 40) shows that the turbulent velocity field can be represented by interaction of two eddies with spanwise wavelengths of 100 and 400 wall units. This model has been used to investigate the effect of favorable pressure gradients on a turbulent boundary-layer and to explore what determines the size of the stress producing eddies close to the wall. The accuracy of the basic physical assumptions are explored by examining resulte from a computer simulation of the three-dimensional time dependent turbulent flow in a channel. Some possible improvements are discussed, which make use of the observation that spatial derivatives in the flow direction can be related to time derivatives by using a convection velocity.

Numerical Prediction of Turbulent Wakes Behind a Square Cylinder

1998 ◽  
Vol 14 (1) ◽  
pp. 23-29
Author(s):  
Robert R. Hwang ◽  
Sheng-Yuh Jaw
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Wall Region ◽  
Square Cylinder ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Turbulent Vortex Shedding ◽  
Model Equations ◽  
Good Agreement

ABSTRACTThis paper presents a numerical study on turbulent vortex shedding flows past a square cylinder. The 2D unsteady periodic shedding motion was resolved in the calculation and the superimposed turbulent fluctuations were simulated with a second-order Reynolds-stress closure model. The calculations were carried out by solving numerically the fully elliptic ensemble-averaged Navier-Stokes equations coupled with the turbulence model equations together with the two-layer approach in the treatment of the near-wall region. The performance of the computations was evaluated by comparing the numerical results with data from available experiments. Results indicate that the present study gives good agreement in the shedding frequency and mean drag as well as in some phase profiles of the mean velocity.

Computational analysis of turbulent flow through an eccentric annulus under different temperature conditions

2018 ◽  
Vol 28 (9) ◽  
pp. 2189-2207 ◽  
Author(s):  
Erman Ulker ◽  
Sıla Ovgu Korkut ◽  
Mehmet Sorgun
Keyword(s):  
Turbulent Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Content Type ◽  
Non Linear ◽  
Fully Developed Turbulent Flow ◽  
Effects Of Temperature ◽  
Eccentric Annuli ◽  
Pipe Rotation

Purpose The purpose of this paper is to solve Navier–Stokes equations including the effects of temperature and inner pipe rotation for fully developed turbulent flow in eccentric annuli by using finite difference scheme with fixing non-linear terms. Design/methodology/approach A mathematical model is proposed for fully developed turbulent flow including the effects of temperature and inner pipe rotation in eccentric annuli. Obtained equation is solved numerically via central difference approximation. In this process, the non-linear term is frozen. In so doing, the non-linear equation can be considered as a linear one. Findings The convergence analysis is studied before using the method to the proposed momentum equation. It reflects that the method approaches to the exact solution of the equation. The numerical solution of the mathematical model shows that pressure gradient can be predicted with a good accuracy when it is compared with experimental data collected from experiments conducted at Izmir Katip Celebi University Flow Loop. Originality/value The originality of this work is that Navier–Stokes equations including temperature and inner pipe rotation effects for fully developed turbulent flow in eccentric annuli are solved numerically by a finite difference method with frozen non-linear terms.

scholarly journals Local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition

2009 ◽  
Vol 629 ◽  
pp. 41-72 ◽  
Author(s):  
ALEXANDER HAY ◽  
JEFFREY T. BORGGAARD ◽  
DOMINIQUE PELLETIER
Keyword(s):  
Sensitivity Analysis ◽  
Proper Orthogonal Decomposition ◽  
Stokes Equations ◽  
Orthogonal Decomposition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Reduced Order ◽  
Selection Step ◽  
Low Dimensional ◽  
Proper Orthogonal

The proper orthogonal decomposition (POD) is the prevailing method for basis generation in the model reduction of fluids. A serious limitation of this method, however, is that it is empirical. In other words, this basis accurately represents the flow data used to generate it, but may not be accurate when applied ‘off-design’. Thus, the reduced-order model may lose accuracy for flow parameters (e.g. Reynolds number, initial or boundary conditions and forcing parameters) different from those used to generate the POD basis and generally does. This paper investigates the use of sensitivity analysis in the basis selection step to partially address this limitation. We examine two strategies that use the sensitivity of the POD modes with respect to the problem parameters. Numerical experiments performed on the flow past a square cylinder over a range of Reynolds numbers demonstrate the effectiveness of these strategies. The newly derived bases allow for a more accurate representation of the flows when exploring the parameter space. Expanding the POD basis built at one state with its sensitivity leads to low-dimensional dynamical systems having attractors that approximate fairly well the attractor of the full-order Navier–Stokes equations for large parameter changes.

Steady Flow in the Transition Length of a Straight Tube

1942 ◽  
Vol 9 (2) ◽  
pp. A55-A58 ◽  
Author(s):  
Henry L. Langhaar
Keyword(s):  
Velocity Field ◽  
Steady Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Straight Tube ◽  
Pressure Function ◽  
Navier Stokes Equations ◽  
Dimensionless Constant ◽  
The Family ◽  
Transition Length

Abstract By means of a linearizing approximation, the Navier-Stokes equations are solved for the case of steady flow in the transition length of a straight tube. The family of velocity profiles is defined by Bessel functions, and the parameter of this family is tabulated against the axial co-ordinate in a dimensionless form. Hence, the length of transition is obtained. The curves give a comparison of the author’s calculations of the velocity field with those of other investigators, and with the experimental data of Nikuradse. The pressure function is derived from the computed velocity field by means of the energy equation, and the pressure drop in the transition length is defined by a dimensionless constant m, which is computed to be 2.28. A discussion of this constant is given in the conclusions.

On the limitation of imposed velocity field strategy for Coulomb-driven electroconvection flow simulations

2013 ◽  
Vol 727 ◽  
Author(s):  
Philippe Traoré ◽  
Jian Wu
Keyword(s):  
Velocity Field ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Simulations ◽  
Mobility Parameter ◽  
The Rich ◽  
Strong Injection ◽  
Unipolar Injection

AbstractThis study refers to the article of Chicón, Castellanos & Martion (J. Fluid Mech., vol. 344, 1997, pp. 43–66), who presented a numerical study of electroconvection in a layer of dielectric liquid induced by unipolar injection. An important characteristic of the numerical strategy proposed by Chicón et al. lies in the fact that the Navier–Stokes equations are never solved to obtain the velocity field, which is subsequently needed in the charge density transport equation. Instead, the velocity field is explicitly provided by an expression obtained with some assumptions about the flow structure and related to the electric field (the imposed velocity field approach; IVF). The validity of the above simplification is examined through a direct comparison of the solutions obtained by solving the Navier–Stokes equations (the Navier–Stokes computation approach; NSC). It is clearly demonstrated that, even in the strong injection regime ($C= 10$), the results look very similar for a given range of the mobility parameter $M$; however, in the weak injection regime ($C= 0. 1$), significant discrepancies are observed. The rich flow structures obtained with the NSC approach invalidate the use of the IVF approach in the weak injection regime.

Turbulent Flow Velocity Between Rotating Co-Axial Disks of Finite Radius

1989 ◽  
Vol 111 (3) ◽  
pp. 333-340 ◽  
Author(s):  
J. F. Louis ◽  
A. Salhi
Keyword(s):  
Turbulent Flow ◽  
Turbulence Model ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Finite Radius ◽  
Navier Stokes Equations ◽  
Rotating Cavity ◽  
Tangential Wall ◽  
Frictional Forces

The turbulent flow between two rotating co-axial disks is driven by frictional forces. The prediction of the velocity field can be expected to be very sensitive to the turbulence model used to describe the viscosity close to the walls. Numerical solutions of the Navier–Stokes equations, using a k–ε turbulence model derived from Lam and Bremhorst, are presented and compared with experimental results obtained in two different configurations: a rotating cavity and the outflow between a rotating and stationary disk. The comparison shows good overall agreement with the experimental data and substantial improvements over the results of other analyses using the k–ε models. Based on this validation, the model is applied to the flow between counterrotating disks and it gives the dependence of the radial variation of the tangential wall shear stress on Rossby number.

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