Control of Bursting in Boundary Layer Models

1994 ◽  
Vol 47 (6S) ◽  
pp. S139-S143 ◽  
Author(s):  
B. D. Coller ◽  
Philip Holmes ◽  
John L. Lumley
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Control Strategy ◽  
Coordinate Transformation ◽  
Point Of View ◽  
Time Dependent ◽  
Dimensional Model ◽  
Similar Strategy ◽  
Dimensional Models ◽  
Low Dimensional

We continue our investigation of using feedback to control low dimensional models of bursting in a turbulent boundary layer. We begin by describing, from the viewpoint of a time-dependent coordinate transformation, our previous control strategy developed for a four dimensional model. Using this new point of view, we develop a similar strategy for the ten-dimensional model of Aubry et al. [1988].

The dynamics of coherent structures in the wall region of a turbulent boundary layer

1988 ◽  
Vol 192 ◽  
pp. 115-173 ◽  
Author(s):  
Nadine Aubry ◽  
Philip Holmes ◽  
John L. Lumley ◽  
Emily Stone
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Stokes Equations ◽  
Outer Part ◽  
Streamwise Vortex ◽  
Decomposition Theorem ◽  
Chaotic Regime ◽  
Galerkin Projection ◽  
Wall Region ◽  
Low Dimensional

We have modelled the wall region of a turbulent boundary layer by expanding the instantaneous field in so-called empirical eigenfunctions, as permitted by the proper orthogonal decomposition theorem (Lumley 1967, 1981). We truncate the representation to obtain low-dimensional sets of ordinary differential equations, from the Navier–Stokes equations, via Galerkin projection. The experimentally determined eigenfunctions of Herzog (1986) are used; these are in the form of streamwise rolls. Our model equations represent the dynamical behaviour of these rolls. We show that these equations exhibit intermittency, which we analyse using the methods of dynamical systems theory, as well as a chaotic regime. We argue that this behaviour captures major aspects of the ejection and bursting events associated with streamwise vortex pairs which have been observed in experimental work (Kline et al. 1967). We show that although this bursting behaviour is produced autonomously in the wall region, and the structure and duration of the bursts is determined there, the pressure signal from the outer part of the boundary layer triggers the bursts, and determines their average frequency. The analysis and conclusions drawn in this paper appear to be among the first to provide a reasonably coherent link between low-dimensional chaotic dynamics and a realistic turbulent open flow system.

scholarly journals The beginning of the movement of bottom sediments in an unsteady flow

2021 ◽  
Vol 263 ◽  
pp. 02042
Author(s):  
Sobir Eshev ◽  
Isroil Gaimnazarov ◽  
Shakhboz Latipov ◽  
Nurbek Mamatov ◽  
Feruz Sobirov ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Bottom Sediments ◽  
Point Of View ◽  
Wave Flow ◽  
Flow Conditions ◽  
Second Stage ◽  
Tangential Stresses ◽  
Friction Parameter ◽  
Critical Dynamic

This article discusses the problems of determining the friction parameter and non-eroding conditions in a wave flow are considered from the standpoint of an approach using a critical dynamic speed. In the first stage of research, the question of the formation of an unsteady turbulent boundary layer is substantiated. Because of the research, dependences were obtained for the most important value from the point of view of sediment transport - the friction parameter. Based on the data of these measurements, a plot of dependence was built, which differs from the previously obtained analytical relationships. For the convenience of practical use of the obtained empirical connection approximated. The second stage of research is the development of a method for calculating the critical tangential stresses corresponding to the beginning of the movement of bottom sediments. Based on the Shilds method, a curve similar to the Shilds curve for wave flow conditions was constructed, which was approximated for the convenience of practical use.

Reduced Order Modelling in Nonlinear Mechanical Oscillators With Energy Pumping

2005 ◽  
Author(s):  
Xianghong Ma ◽  
Alexander F. Vakakis ◽  
Lawrence A. Bergman
Keyword(s):  
Dimensional Model ◽  
Reduced Order ◽  
Energy Pumping ◽  
Weakly Coupled ◽  
Nonlinear Mechanical ◽  
Dimensional Models ◽  
Mechanical Oscillators ◽  
Low Dimensional ◽  
Nonlinear Components ◽  
And Control

Energy pumping in nonlinear mechanical oscillators has been discovered and studied in mechanical systems consisting of weakly coupled, linear and nonlinear components [1–3]. In this paper this phenomenon is further studied and numerically verified on an 11 degree of freedom system. It also presents a technique to create low dimensional models for energy pumping systems using the Karhunen-Loeve (K-L) decomposition method. It is shown that energy pumping can be identified from the dominant K-L modes. The low dimensional models are used to reconstruct the system responses. From the comparisons between the reconstructed and simulated response, we can see that the K-L mode-based low-dimensional model can represent the system responses; it can be used for monitoring, diagnosis and control purposes.

FLUCTUATION OF SURFACE IN POLISHING PROCESS

Fractals ◽  
1996 ◽  
Vol 04 (02) ◽  
pp. 213-218 ◽  
Author(s):  
Y. HASEGAWA ◽  
S. MIYAZIMA ◽  
Y. NAMBA
Keyword(s):  
Point Of View ◽  
Time Dependent ◽  
Surface Pattern ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Polishing Process ◽  
Two Dimensional Model

A change of surface pattern of materials during polishing is simulated and analyzed from the fractal point of view. We have proposed a simple two-dimensional model for microscopic processes of polishing. We have obtained a result that the time dependent fluctuation of surface scales with the momentum of the polishing particle.

Simultaneous flow visualization and Reynolds-stress measurement in a turbulent boundary layer

1986 ◽  
Vol 163 ◽  
pp. 459-478 ◽  
Author(s):  
A. M. Talmon ◽  
J. M. G. Kunen ◽  
G. Ooms
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Flow Visualization ◽  
Reynolds Stress ◽  
Stress Measurement ◽  
Three Dimensional ◽  
Time Dependent ◽  
Flow Structures ◽  
Wall Region ◽  
Measured Velocity

Flow visualization and Reynolds-stress measurement were combined in an investigation of a turbulent boundary layer in a water channel. Hydrogen bubbles were used to visualize the flow; a laser-Doppler anemometer capable of measuring two velocity components was applied to measure the instantaneous value of the Reynolds stress. Owing to the three-dimensional, time-dependent character of the flow it was rather difficult to identify flow structures from measured velocity signals, especially at larger distances from the wall. Despite this difficulty a method based on the instantaneous value of the Reynolds stress could be developed for detecting bursts in the wall region of the boundary layer. By this method the three-dimensional, time-dependent character of the flow is taken into account by attributing to the same burst ejections occurring successively with very short time intervals. This identification procedure is based on a comparison on a one-to-one basis between visualized flow structures and measured values of the Reynolds stress. The detected bursts were found to make a considerable contribution to the momentum transport in the boundary layer.

Direct simulation of a turbulent boundary layer up to Rθ = 1410

1988 ◽  
Vol 187 ◽  
pp. 61-98 ◽  
Author(s):  
Philippe R. Spalart
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Multiple Scale ◽  
Theoretical Models ◽  
Point Of View ◽  
Navier Stokes ◽  
Statistical Point

The turbulent boundary layer on a flat plate, with zero pressure gradient, is simulated numerically at four stations between Rθ = 225 and Rθ = 1410. The three-dimensional time-dependent Navier-Stokes equations are solved using a spectral method with up to about 107 grid points. Periodic spanwise and streamwise conditions are applied, and a multiple-scale procedure is applied to approximate the slow streamwise growth of the boundary layer. The flow is studied, primarily, from a statistical point of view. The solutions are compared with experimental results. The scaling of the mean and turbulent quantities with Reynolds number is compared with accepted laws, and the significant deviations are documented. The turbulence at the highest Reynolds number is studied in detail. The spectra are compared with various theoretical models. Reynolds-stress budget data are provided for turbulence-model testing.

An Integral Method for the Oscillating Turbulent Boundary Layer

1981 ◽  
Vol 32 (4) ◽  
pp. 271-298 ◽  
Author(s):  
M.H. Patel
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Streamwise Velocity ◽  
Travelling Wave ◽  
Time Dependent ◽  
Very High Frequency ◽  
Streamwise Pressure Gradient ◽  
The Mean ◽  
Momentum Integral

SummaryThe linearised time dependent momentum integral equation is used in conjunction with assumed velocity profiles and a quasi-static skin friction approximation to predict the turbulent boundary layer response to sinusoidal streamwise velocity fluctuations in the freestream. The mean zero pressure gradient case, corresponding to flat plate flow, is presented in detail and verified by comparison with experimental data and alternative calculations. The asymptotic turbulent boundary layer response to very high frequency perturbations is also derived. It is shown that a travelling wave component in the freestream, with its associated time dependent streamwise pressure gradient, has a dominant effect on the turbulent boundary layer response.

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