scholarly journals WATERWAVES CALCULATION BY NAVIER-STOKES EQUATIONS

1982 ◽  
Vol 1 (18) ◽  
pp. 53
Author(s):  
O. Daubert ◽  
A. Hauguel ◽  
J. Cahouet
Keyword(s):  
Stokes Equations ◽  
Vertical Plane ◽  
Viscosity Coefficient ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Simple Simulation ◽  
The Mean ◽  
Basic Equations ◽  
Eddy Viscosity Coefficient

N.S.L. program is a finite-difference code for two dimensionnal flows with a free surface in a vertical plane. Basic equations are Navier-Stokes Equations with a simple simulation of turbulent effects by an eddy viscosity coefficient related to the mixing length and the mean velocity gradient. Theses equations are solved in a variable domain in time. The main features of the numerical method are presented. Some comparisons with theoretical solutions give a good validation of the code both in linear and non linear cases. Other examples of application are given.

scholarly journals Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels

2013 ◽  
Vol 734 ◽  
pp. 275-316 ◽  
Author(s):  
Rashad Moarref ◽  
Ati S. Sharma ◽  
Joel A. Tropp ◽  
Beverley J. McKeon
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Low Rank ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Self Similar ◽  
The Mean ◽  
High Reynolds

AbstractWe study the Reynolds-number scaling and the geometric self-similarity of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), in order to obtain a description of the streamwise turbulence intensity from direct consideration of the Navier–Stokes equations. Under this formulation, the velocity field is decomposed into propagating waves (with single streamwise and spanwise wavelengths and wave speed) whose wall-normal shapes are determined from the principal singular function of the corresponding resolvent operator. Using the accepted scalings of the mean velocity in wall-bounded turbulent flows, we establish that the resolvent operator admits three classes of wave parameters that induce universal behaviour with Reynolds number in the low-rank model, and which are consistent with scalings proposed throughout the wall turbulence literature. In addition, it is shown that a necessary condition for geometrically self-similar resolvent modes is the presence of a logarithmic turbulent mean velocity. Under the practical assumption that the mean velocity consists of a logarithmic region, we identify the scalings that constitute hierarchies of self-similar modes that are parameterized by the critical wall-normal location where the speed of the mode equals the local turbulent mean velocity. For the rank-1 model subject to broadband forcing, the integrated streamwise energy density takes a universal form which is consistent with the dominant near-wall turbulent motions. When the shape of the forcing is optimized to enforce matching with results from direct numerical simulations at low turbulent Reynolds numbers, further similarity appears. Representation of these weight functions using similarity laws enables prediction of the Reynolds number and wall-normal variations of the streamwise energy intensity at high Reynolds numbers (${Re}_{\tau } \approx 1{0}^{3} {\unicode{x2013}} 1{0}^{10} $). Results from this low-rank model of the Navier–Stokes equations compare favourably with experimental results in the literature.

Experimental and Numerical Investigation of Two-Dimensional Parallel Jets

2001 ◽  
Vol 123 (2) ◽  
pp. 401-406 ◽  
Author(s):  
Elgin A. Anderson ◽  
Robert E. Spall
Keyword(s):  
Good Accuracy ◽  
Stokes Equations ◽  
Numerical Models ◽  
Symmetry Plane ◽  
Turbulence Models ◽  
Turbulent Jets ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
The Mean

The flowfield of dual, parallel planar turbulent jets is investigated experimentally using an x-type hot-wire probe and numerically by solving the Reynolds-averaged Navier-Stokes equations. The performance of both differential Reynolds stress (RSM) and standard k-ε turbulence models is evaluated. Results show that the numerical models predict the merge and combined point characteristics to good accuracy. However, both turbulence models show a narrower width of the jet envelope than measured by experiment. The predicted profiles of the mean velocity along the symmetry plane agree well with the experimental results.

Similarity in non-rotating and rotating turbulent pipe flows

1999 ◽  
Vol 379 ◽  
pp. 1-22 ◽  
Author(s):  
MARTIN OBERLACK
Keyword(s):  
Reynolds Number ◽  
Scaling Laws ◽  
Stokes Equations ◽  
Scaling Law ◽  
Navier Stokes ◽  
Invariant Solutions ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Pipe Flows ◽  
The Mean

The Lie group approach developed by Oberlack (1997) is used to derive new scaling laws for high-Reynolds-number turbulent pipe flows. The scaling laws, or, in the methodology of Lie groups, the invariant solutions, are based on the mean and fluctuation momentum equations. For their derivation no assumptions other than similarity of the Navier–Stokes equations have been introduced where the Reynolds decomposition into the mean and fluctuation quantities has been implemented. The set of solutions for the axial mean velocity includes a logarithmic scaling law, which is distinct from the usual law of the wall, and an algebraic scaling law. Furthermore, an algebraic scaling law for the azimuthal mean velocity is obtained. In all scaling laws the origin of the independent coordinate is located on the pipe axis, which is in contrast to the usual wall-based scaling laws. The present scaling laws show good agreement with both experimental and DNS data. As observed in experiments, it is shown that the axial mean velocity normalized with the mean bulk velocity um has a fixed point where the mean velocity equals the bulk velocity independent of the Reynolds number. An approximate location for the fixed point on the pipe radius is also given. All invariant solutions are consistent with all higher-order correlation equations. A large-Reynolds-number asymptotic expansion of the Navier–Stokes equations on the curved wall has been utilized to show that the near-wall scaling laws for at surfaces also apply to the near-wall regions of the turbulent pipe flow.

A Study of Unsteady Rotor–Stator Interactions

1989 ◽  
Vol 111 (4) ◽  
pp. 394-400 ◽  
Author(s):  
Reda R. Mankbadi
Keyword(s):  
Pressure Field ◽  
Stokes Equations ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Turbulence Energy ◽  
Mean Flow ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
The Mean ◽  
Field Decay

This work is concerned with simulations of rotor-generated unsteady response of the turbulent flow in a stator. The rotor’s effect is represented by moving cylinders of equivalent drag coefficient that produce passing wakes at the entrance of the stator. The unsteady incompressible Navier–Stokes equations are solved on a staggered grid and eddy viscosities are obtained using a k–ε model. The rotor-generated wakes were found to produce a pressure field at the stator’s entrance that increases in the direction of the wake traverse. At a streamwise distance equal to the distance between the stator blades, the pressure becomes uniform across the channel and the oscillations in the pressure field decay. Because of the initial asymmetry of the pressure field, the time-averaged mean velocity is no longer symmetric. This asymmetry of the mean flow continues along the passage even after the pressure has regained its symmetry. As a result of the passing of the rotor-generated wakes, large periodic oscillations are introduced into the mean velocity and turbulence energy. The time-averaged turbulence energy and the wall shear stress increases in the direction of the rotor traverse.

RANS Predictions in an Idealized Lower-Plenum Model

2006 ◽  
Author(s):  
Joshua D. Hodson ◽  
Robert E. Spall ◽  
Barton L. Smith
Keyword(s):  
Stokes Equations ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Pressure Losses ◽  
Pressure Loss Coefficient ◽  
The Mean ◽  
Recirculation Length

The two-dimensional, unsteady, Reynolds-averaged Navier-Stokes equations have been solved for the flow across a row of confined cylinders with a pitch-to-diameter ratio of 1.7, a configuration which was designed to model a next generation nuclear plant lower-plenum. Four different turbulence models were used: k–ε, k–ω, v2–f, and differential Reynolds-stress transport. Comparisons with available experimental data were made for pressure losses, recirculation lengths, and mean velocity profiles. The results indicate that all models did a reasonable job of predicting the pressure loss coefficient. However, in terms of the mean velocities and recirculation length, the determination of which model performed best is not clear.

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.

scholarly journals Aerodynamic Dissipation

1958 ◽  
Vol 8 ◽  
pp. 966-974
Author(s):  
H. E. Petschek
Keyword(s):  
Stokes Equations ◽  
Viscosity Coefficient ◽  
Mean Free Path ◽  
Navier Stokes ◽  
Small Scale ◽  
Minimum Length ◽  
Ionized Gas ◽  
Navier Stokes Equations ◽  
Flow Equations ◽  
Rate Of Dissipation

Analyses of aerodynamic dissipation in ordinary un-ionized gases are all based upon the Navier-Stokes equations. These equations relate the rate of dissipation to the local gradients in velocity and temperature through the viscosity and heat conduction coefficients. Although it is true that in many flow situations the magnitude of the total dissipation in the gas does not depend on the magnitude of the viscosity coefficient, this coefficient does determine the minimum scale of variations observed in the gas and the form of the Navier-Stokes equations determines the type of phenomena which are observed on a small scale. In order to discuss dissipation in an ionized gas in the presence of a magnetic field, it is therefore necessary to re-examine the derivation of the basic flow equations. This paper attempts to do this for a case of a completely ionized gas and demonstrates that the basic microscopic dissipation mechanism is appreciably different. For example, it is shown that the minimum length in which the properties of the flow field can change noticeably is appreciably less than one mean free path.

Probability Density Functions of Vorticities in Turbulent Channels with Effects of Blowing and Suction

2016 ◽  
Vol 17 (2) ◽  
pp. 127-135
Author(s):  
Can Liu ◽  
Xi Chen
Keyword(s):  
New York ◽  
Probability Density ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Generalized Hyperbolic Distribution ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Turbulent Channel Flows ◽  
Probability Density Function Pdf

AbstractThis paper presents direct numerical simulation (DNS) result of the Navier–Stokes equations for turbulent channel flows with blowing and suction effects. The friction Reynolds number is ${\rm{R}}{{\rm{e}}_\tau} = 394$ and a range of blowing and suction conditions is covered with different perturbation strengths, i. e. $A = 0.05, $ 0.1, 0.2. While the mean velocity profile has been severely altered, the probability density function (PDF) for (spanwise) vorticity – depending on wall distance $({y^ +})$ and blowing/suction strength (A) – satisfies the generalized hyperbolic distribution (GHD) of Birnir [The Kolmogorov-Obukhov statistical theory of turbulence, J. Nonlinear Sci. (2013a), doi: 10.1007/s00332-012-9164–z; The Kolmogorov-Obukhov theory of turbulence, Springer, New York, 2013b] in the bulk of the flow. The latter leads to accurate descriptions of all PDFs (at ${y^ +} = 40, $ 200, 390 and $A = 0.05, $ 0.2, for instance) with only four parameters. The result indicates that GHD is a general tool to quantify PDF for turbulent flows under various wall surface conditions.

Improved κ-ɛ Modelling of Impeller Flow Performance of a Mixed-Flow Pump under off-Design Operating States

1993 ◽  
Vol 207 (4) ◽  
pp. 219-229 ◽  
Author(s):  
S M Fraser ◽  
Y Zhang
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Careful Analysis ◽  
Navier Stokes ◽  
Mean Flow ◽  
Mixed Flow ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
The Mean ◽  
Flow Pump

Three-dimensional turbulent flow through the impeller passage of a model mixed-flow pump has been simulated by solving the Navier-Stokes equations with an improved κ-ɛ model. The standard κ-ɛ model was found to be unsatisfactory for solving the off-design impeller flow and a converged solution could not be obtained at 49 per cent design flowrate. After careful analysis, it was decided to modify the standard κ-ɛ model by including the extra rates of strain due to the acceleration of impeller rotation and geometrical curvature and removing the mathematical ill-posedness between the mean flow turbulence modelling and the logarithmic wall function.

Energy stability of the Ekman boundary layer

1971 ◽  
Vol 47 (2) ◽  
pp. 405-413 ◽  
Author(s):  
Joseph J. Dudis ◽  
Stephen H. Davis
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Critical Value ◽  
Ekman Layer ◽  
Navier Stokes ◽  
Asymptotically Stable ◽  
Lagrange Equations ◽  
Navier Stokes Equations ◽  
The Mean ◽  
Energy Theory

The critical value RE of the Reynolds number R is predicted by the application of the energy theory. When R < RE, the Ekman layer is the unique steady solution of the Navier-Stokes equations and the same boundary conditions, and is, further, stable in a slightly weaker sense than asymptotically stable in the mean. The critical value RE is determined by numerically integrating the relevant Euler-Lagrange equations. An analytic lower bound to RE is obtained. Comparisons are made between RE and RL, the critical value of R according to linear theory, in order to demark the region of parameter space, RE < R < RL, in which subcritical instabilities are allowable.

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