Bounds for turbulent shear flow

1970 ◽  
Vol 41 (1) ◽  
pp. 219-240 ◽  
Author(s):  
F. H. Busse
Keyword(s):  
Shear Flow ◽  
Turbulent Flow ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Variational Problems ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Navier Stokes Equations ◽  
Experimental Values

Bounds on the transport of momentum in turbulent shear flow are derived by variational methods. In particular, variational problems for the turbulent regimes of plane Couette flow, channel flow, and pipe flow are considered. The Euler equations resemble the basic Navier–Stokes equations of motion in many respects and may serve as model equations for turbulence. Moreover, the comparison of the upper bound with the experimental values of turbulent momentum transport shows a rather close similarity. The same fact holds with respect to other properties when the observed turbulent flow is compared with the structure of the extremalizing solution of the variational problem. It is suggested that the instability of the sublayer adjacent to the walls is responsible for the tendency of the physically realized turbulent flow to approach the properties of the extremalizing vector field.

Computations of Ship Stern and Wake Flow and Comparisons with Experiment

1990 ◽  
Vol 34 (03) ◽  
pp. 179-193
Author(s):  
V. C. Patel ◽  
H. C. Chen ◽  
S. Ju
Keyword(s):  
Experimental Data ◽  
Shear Flow ◽  
Numerical Method ◽  
Stokes Equations ◽  
Ship Hull ◽  
Wake Flow ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Navier Stokes Equations

A numerical method for the solution of the Reynolds-averaged Navier-Stokes equations has been employed to study the turbulent shear flow over the stern and in the wake of a ship hull. Detailed comparisons are made between the numerical results and available experimental data to show that most of the important overall features of such flows can now be predicted with considerable accuracy.

Large-scale instabilities of turbulent wakes

1972 ◽  
Vol 54 (3) ◽  
pp. 481-488 ◽  
Author(s):  
W. C. Reynolds
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Small Scale ◽  
General Interest ◽  
Turbulent Shear Flow ◽  
Navier Stokes Equations ◽  
Eddy Structures ◽  
The Stability

The equations describing the statistical features of small amplitude waves in a turbulent shear flow are derived from the Navier-Stokes equations. Closure is achieved through a postulated constitutive equation for the alteration of the statistical properties of the turbulence by the organized wave. The theory is applied in an examination of the stability of a hypothetical wake consisting of small-scale turbulence enclosed within a steady uncontorted superlayer. A set of superlayer jump conditions is derived from fundamental considerations, and these are of more general interest. For this hypothetical flow the analysis predicts largescale instabilities and superlayer contortions reminiscent of large-eddy structures observed in real flows. These instabilities therefore offer an explanation of the presence of large-scale organized motions in turbulent free shear flows.

Numerical Investigation of the Coulter Principle in a Microfluidic Device

2013 ◽  
Author(s):  
Muheng Zhang ◽  
Yongsheng Lian
Keyword(s):  
Electric Field ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Navier Stokes ◽  
Working Mechanism ◽  
Navier Stokes Equations ◽  
Sheath Flow ◽  
Coulter Counters ◽  
Pass Through ◽  
Cell Motion

Coulter counters are analytical microfluidic instrument used to measure the size and concentration of biological cells or colloid particles suspended in electrolyte. The underlying working mechanism of Coulter counters is the Coulter principle which relies on the fact that when low-conductive cells pass through an electric field these cells cause disturbances in the measurement (current or voltage). Useful information about these cells can be obtained by analyzing these disturbances if an accurate correlation between the measured disturbances and cell characteristics. In this paper we use computational fluid dynamics method to investigate this correlation. The flow field is described by solving the Navier-Stokes equations, the electric field is represented by a Laplace’s equation in which the conductivity is calculated from the Navier-Stokes equations, and the cell motion is calculated by solving the equations of motion. The accuracy of the code is validated by comparing with analytical solutions. The study is based on a coplanar Coulter counter with three inlets that consist of two sheath flow inlet and one conductive flow inlet. The effects of diffusivity, cell size, sheath flow rate, and cell geometry are discussed in details. The impacts of electrode size, gap between electrodes and electrode location on the measured distribution are also studied.

On Direct Numerical Simulation of Turbulent Flows

2011 ◽  
Vol 64 (2) ◽  
Author(s):  
Giancarlo Alfonsi
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
High Performance Computing ◽  
Turbulent Flows ◽  
High Performance ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Navier Stokes Equations ◽  
Performance Computing

The direct numerical simulation of turbulence (DNS) has become a method of outmost importance for the investigation of turbulence physics, and its relevance is constantly growing due to the increasing popularity of high-performance-computing techniques. In the present work, the DNS approach is discussed mainly with regard to turbulent shear flows of incompressible fluids with constant properties. A body of literature is reviewed, dealing with the numerical integration of the Navier-Stokes equations, results obtained from the simulations, and appropriate use of the numerical databases for a better understanding of turbulence physics. Overall, it appears that high-performance computing is the only way to advance in turbulence research through the front of the direct numerical simulation.

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.

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.

scholarly journals Vortex motion of a continuous medium depending on the pressure change

2020 ◽  
Vol 2020 (6) ◽  
Author(s):  
Alexander Braginsky
Keyword(s):  
Angular Velocity ◽  
Continuous Medium ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Vortex Motion ◽  
Pressure Change ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Least Action ◽  
Force Components

Abstract In this paper, we study the vortex motion of a continuous medium, which is described by forces obtained from the principle of least action. It is shown that in a continuous medium the vortex force components are proportional to the velocity and pressure gradient components. This article gives a description of the 2D vortex motion of air in zones of high and low pressure. If the pressure decreases, the angular velocity of rotation of the continuous medium increases, whereas if the pressure increases, the angular velocity fades. The lifting force is obtained due to the vortex movement of air in the form of a funnel. It is shown that the vortex force contains a vortex term of the Euler hydrodynamic equations with a relative factor equal to the velocity of the continuous medium squared divided by the sound velocity squared. To describe the motion of a continuous medium correctly it is necessary to replace the forces obtained by Euler with the forces obtained from the minimum of action in the equations of motion. It is concluded that vortex motions and turbulence are described by the obtained equations of motion, and not by the Navier–Stokes equations. Most likely, this is related to the Problem of the Millennium description of turbulence announced at the International Congress of Mathematics in 2000.

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