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 simulations of three-dimensional plunging breaking waves: generation and evolution of aerated vortex filaments

2015 ◽  
Vol 767 ◽  
pp. 364-393 ◽  
Author(s):  
P. Lubin ◽  
S. Glockner
Keyword(s):  
Stokes Equations ◽  
Early Stage ◽  
Flow Direction ◽  
Three Dimensional ◽  
Air Entrainment ◽  
Breaking Waves ◽  
Navier Stokes ◽  
Vortex Filaments ◽  
Navier Stokes Equations ◽  
Main Flow Direction

AbstractThe scope of this work is to present and discuss the results obtained from simulating three-dimensional plunging breaking waves by solving the Navier–Stokes equations, in air and water. Recent progress in computational capabilities has allowed us to run fine three-dimensional simulations, giving us the opportunity to study for the first time fine vortex filaments generated during the early stage of the wave breaking phenomenon. To date, no experimental observations have been made in laboratories, and these structures have only been visualised in rare documentary footage (e.g. BBC 2009 South Pacific. Available on YouTube, 7BOhDaJH0m4). These fine coherent structures are three-dimensional streamwise vortical tubes, like vortex filaments, connecting the splash-up and the main tube of air, elongated in the main flow direction. The first part of the paper is devoted to the presentation of the model and numerical methods. The air entrainment occurring when waves break is then carefully described. Thanks to the high resolution of the grid, these fine elongated structures are simulated and explained.

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.

Vortex-Induced Vibration of Two Side-by-Side Cylinders With a Small Gap in Uniform Flow

2017 ◽  
Author(s):  
Adnan Munir ◽  
Ming Zhao ◽  
Helen Wu
Keyword(s):  
Stokes Equations ◽  
Flow Direction ◽  
Three Dimensional ◽  
Cross Flow ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Gap Ratio ◽  
Vortex Induced Vibrations ◽  
Lock In

Vortex-induced vibrations of two elastically mounted and rigidly coupled circular cylinders in side-by-side arrangement in steady flow are investigated numerically. The vibration of the cylinders is limited to the cross-flow direction only. The three-dimensional Navier-Stokes equations are solved using the Petrov-Galerkin Finite element method and the equation of motion is solved using the fourth order Runge Kutta method. It is well known that when the gap between two stationary side-by-side cylinders is very small, the flow between the two cylinders is biased towards one cylinder and the lift force on each cylinder is significantly smaller than that of an isolated single cylinder. The aim of this study is to investigate the effect of a small gap ratio of 0.5 between the two cylinders on the lock-in regime and the amplitude of the vibration of two side-by-side cylinders in a fluid flow. Simulations are carried out for a constant mass ratio of 2, a constant Reynolds number of 1000 and a range of reduced velocities. It is found that in the lock-in range of the reduced velocity, the two cylinders vibrate about their balance position with high amplitudes. Outside the lock-in regime the flow from the gap becomes biased towards one cylinder, which is similar to that from the gap between stationary cylinders.

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.

Experimental Research and Turbulent Flow Simulation of the Updraft Free-Exit-Flow Hydropower Turbine System

2002 ◽  
Author(s):  
Haifeng Li ◽  
Yulin Wu ◽  
David T. Kao
Keyword(s):  
Turbulent Flow ◽  
Experimental Research ◽  
Production Efficiency ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Flow Simulation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Predicting Performance ◽  
Optimizing Design

During development of the updraft free-exit-flow hydropower turbine system, serious attention was paid to impact of the traditional turbine system to environment. The paper presents results of experimental research and three-dimensional turbulent flow simulation of the runner. The experiment demonstrated that, on one hand, the system can enhance exit flow aeration and downstream water quality; on the other hand, it gives good results in terms of its power production efficiency, about 85%. Based on the time-averaged Navier-Stokes equations and standard k-ε model, the SIMPLEC algorithm was applied for the numerical analysis. To guarantee credibility of the calculation, FLUENT5.5 code was used, which can provide distribution of pressure and velocity respectively. With comparison between the experimental data and calculating results, it can be concluded that flow simulation can be an effective tool for predicting performance and optimizing design of new turbine runner.

scholarly journals Theoretical and Experimental Investigations About Vaneless Return Channels of Multi-Stage Radial Flow Turbomachines

1982 ◽  
Author(s):  
W. Fister ◽  
G. Zahn ◽  
J. Tasche
Keyword(s):  
Radial Flow ◽  
Stokes Equations ◽  
Flow Direction ◽  
Three Dimensional ◽  
Computer Time ◽  
Navier Stokes ◽  
Experimental Investigations ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Multi Stage

Based on the Navier-Stokes-Equations, a numerical method which is a variation of the “partially-parabolic” approach used by Moore et al., was applied to calculate the three-dimensional, turbulent, viscous flow in vaneless return channels of multistage radial flow turbomachines. To avoid the high demand for computer time and storage capacity generally needed for the numerical treatment of the Navier-Stokes-Equations, the method is restricted to the calculation of flows with a predominant flow direction without separation. The procedure carries out an iteration between a marching integration of the conservation equations through the three-dimensional flow field along the mean flow direction and the solution of an elliptic pressure correction equation. So it is guaranteed that downstream influences can be considered upstream.

Resistance Reduction in Pulsating Turbulent Pipe Flows

2003 ◽  
Author(s):  
Marcello Manna ◽  
Andrea Vacca
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Pipe Flow ◽  
Navier Stokes ◽  
Recent Experimental Data ◽  
Wall Region ◽  
Navier Stokes Equations ◽  
Oscillating Motion ◽  
Near Wall

The paper describes the effects of a forced harmonic oscillations of fixed frequency and amplitudes in the range Λ = Um/Ub = 1 ÷ 11 on the characteristics of a turbulent pipe flow with a bulk Reynolds number of 5900. The resulting Stokes layer δ is a fraction of the pipe radius (χ = R/δ = 53) so that the vorticity associated to the oscillating motion is generated in a small near wall region. The analysis is carried out processing a set of statistically independent samples obtained from wall resolved Large Eddy Simulations; time and space averaged global quantities, extracted for the sake of comparison with recent experimental data, confirm the presence of a non negligible drag reduction phenomenon. Phase averaged profiles of the Reynolds stress tensor components provide valuable material for the comprehension of the effects of the time varying mean shear upon the near wall turbulent flow structures. The large scale of motion are directly computed through numerical integration of the space filtered three dimensional Navier-Stokes equations with a spectrally accurate code; the subgrid scale terms are parametrized with a dynamic procedure.

Resistance Reduction in Pulsating Turbulent Pipe Flows

2005 ◽  
Vol 127 (2) ◽  
pp. 410-417 ◽  
Author(s):  
Marcello Manna ◽  
Andrea Vacca
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Pipe Flow ◽  
Navier Stokes ◽  
Recent Experimental Data ◽  
Wall Region ◽  
Navier Stokes Equations ◽  
Resistance Reduction ◽  
Oscillating Motion ◽  
Near Wall

The paper describes the effects of forced harmonic oscillations of fixed frequency and amplitudes in the range Λ=Um/Ub=1-11 on the characteristics of a turbulent pipe flow with a bulk Reynolds number of 5900. The resulting Stokes layer δ is a fraction of the pipe radius χ=R/δ=53 so that the vorticity associated to the oscillating motion is generated in a small near wall region. The analysis is carried out processing a set of statistically independent samples obtained from wall-resolved large eddy simulations (LES); time and space averaged global quantities, extracted for the sake of comparison with recent experimental data, confirm the presence of a non-negligible drag reduction phenomenon. Phase averaged profiles of the Reynolds stress tensor components provide valuable material for the comprehension of the effects of the time varying mean shear upon the near wall turbulent flow structures. The large scales of motion are directly computed through numerical integration of the space filtered three-dimensional Navier-Stokes equations with a spectrally accurate code; the subgrid scale terms are parametrized with a dynamic procedure.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

Sign in / Sign up

Export Citation Format

Share Document