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.

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.

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.

Oscillatory forcing of flow through porous media. Part 1. Steady flow

2002 ◽  
Vol 465 ◽  
pp. 213-235 ◽  
Author(s):  
D. R. GRAHAM ◽  
J. J. L. HIGDON
Keyword(s):  
Porous Media ◽  
Flow Rate ◽  
Stokes Equations ◽  
Nonlinear Flow ◽  
Navier Stokes ◽  
Full Time ◽  
Inertial Effects ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
The Mean

Oscillatory forcing of a porous medium may have a dramatic effect on the mean flow rate produced by a steady applied pressure gradient. The oscillatory forcing may excite nonlinear inertial effects leading to either enhancement or retardation of the mean flow. Here, in Part 1, we consider the effects of non-zero inertial forces on steady flows in porous media, and investigate the changes in the flow character arising from changes in both the strength of the inertial terms and the geometry of the medium. The steady-state Navier–Stokes equations are solved via a Galerkin finite element method to determine the velocity fields for simple two-dimensional models of porous media. Two geometric models are considered based on constricted channels and periodic arrays of circular cylinders. For both geometries, we observe solution multiplicity yielding both symmetric and asymmetric flow patterns. For the cylinder arrays, we demonstrate that inertial effects lead to anisotropy in the effective permeability, with the direction of minimum resistance dependent on the solid volume fraction. We identify nonlinear flow phenomena which might be exploited by oscillatory forcing to yield a net increase in the mean flow rate. In Part 2, we take up the subject of unsteady flows governed by the full time-dependent Navier–Stokes equations.

A Numerical Study of Vortex Breakdown in Turbulent Swirling Flows

1999 ◽  
Vol 122 (1) ◽  
pp. 179-183 ◽  
Author(s):  
Robert E. Spall ◽  
Blake M. Ashby
Keyword(s):  
Reynolds Stress ◽  
Stokes Equations ◽  
Vortex Breakdown ◽  
Numerical Study ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Stress Model ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
The Mean

Solutions to the incompressible Reynolds-averaged Navier–Stokes equations have been obtained for turbulent vortex breakdown within a slightly diverging tube. Inlet boundary conditions were derived from available experimental data for the mean flow and turbulence kinetic energy. The performance of both two-equation and full differential Reynolds stress models was evaluated. Axisymmetric results revealed that the initiation of vortex breakdown was reasonably well predicted by the differential Reynolds stress model. However, the standard K-ε model failed to predict the occurrence of breakdown. The differential Reynolds stress model also predicted satisfactorily the mean azimuthal and axial velocity profiles downstream of the breakdown, whereas results using the K-ε model were unsatisfactory. [S0098-2202(00)01601-1]

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.

Twin Inclined Circular Jets Evolution Through a Cool Crossflow

2007 ◽  
Author(s):  
Amina Radhouane ◽  
Nejla Mahjoub Sai¨d ◽  
Hatem Mhiri ◽  
George Lepalec ◽  
Philippe Bournot
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Vortical Structures ◽  
Circular Jets ◽  
Turbulent Closure ◽  
The Mean ◽  
Good Agreement

The aim of this paper is to examine experimentally as well as numerically the flowfield resulting from the interaction between a twin circular inclined hot jets emerging into a cooling crossflow. The resulting flowfield is quite complex due to the presence of different vortical structures including the kidney vortex, the horse-shoe vortex, etc... The evolution of the twin inclined jets through the crossflow could be depicted by tracking the mean-flow velocity field and its associated turbulence statistics by means of the PIV technique. This evolution can be influenced by many factors. Herein, we will deal with that resulted by the injection nozzles’ inclination and the jets’ spacing. Then, we performed a three dimensional sample of the studied configuration in order to simulate the evolution of the resulting flowfield. For that, the Navier Stokes equations were simulated with an RSM second order turbulent closure model. Then a non uniform meshing was applied. A good agreement was obtained between the experimental data and the numerical modeling. After validation we could represent in addition to the available results, the temperature distribution and the effects the variation of the injection inclination and that of the jets’ spacing bring on it (on its spatial evolution).

Numerical Flow Prediction in Inlet Pipe of Vertical Inline Pump

2017 ◽  
Vol 140 (5) ◽  
Author(s):  
Christopher Stephen ◽  
Shouqi Yuan ◽  
Ji Pei ◽  
Xing Cheng G
Keyword(s):  
Stokes Equations ◽  
Reverse Flow ◽  
Pressure Coefficient ◽  
Navier Stokes ◽  
Mean Flow ◽  
Inlet Pipe ◽  
Navier Stokes Equations ◽  
Computational Fluid Dynamics Cfd ◽  
The Mean ◽  
Good Agreement

For a pump, the inlet condition of flow determines the outlet conditions of fluid (i.e., energy). As a rule to minimize the losses at the entry of pump, the bends should be avoided as one of the methods. But for the case of vertical inline pump, it is unavoidable in order to save the space for installation. For the purpose of investigation in inlet pipe of vertical inline pump, the unsteady Reynolds-averaged Navier–Stokes equations are solved using the computational fluid dynamics (CFD) code. The results have been shown that there is a good agreement between the performance characteristics obtained from the simulation and experiments. The velocity coefficient from the simulation along the inlet pipe sections is well matched with the theoretical values and found to have variation near the exit of inlet pipe. The pressure and velocity coefficients studies depict the flow physics at each section along with the study of helicity at the exit of inlet pipe to determine the recirculation effects. It is observed that the vortices associated with the motion of the particles are moved toward the surfaces and are more intense than the mean flow. The trends of pressure coefficient at the exit of inlet pipe were addressed with reference to the various flow rates for eight set of radial lines. Hence, this work concludes that for inlet pipe, the generation of circulation was due to the stream path and the reverse flow from the impeller and was reconfirmed with the literature.

A resonant wave theory

1999 ◽  
Vol 395 ◽  
pp. 237-251 ◽  
Author(s):  
LUN-SHIN YAO
Keyword(s):  
Stokes Equations ◽  
Flow Instability ◽  
Initial Conditions ◽  
Laminar Flows ◽  
Navier Stokes ◽  
Real Interval ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
The Mean ◽  
The Waves

Analysis is used to show that a solution of the Navier–Stokes equations can be computed in terms of wave-like series, which are referred to as waves below. The mean flow is a wave of infinitely long wavelength and period; laminar flows contain only one wave, i.e. the mean flow. With a supercritical instability, there are a mean flow, a dominant wave and its harmonics. Under this scenario, the amplitude of the waves is determined by linear and nonlinear terms. The linear case is the target of flow-instability studies. The nonlinear case involves energy transfer among the waves satisfying resonance conditions so that the wavenumbers are discrete, form a denumerable set, and are homeomorphic to Cantor's set of rational numbers. Since an infinite number of these sets can exist over a finite real interval, nonlinear Navier–Stokes equations have multiple solutions and the initial conditions determine which particular set will be excited. Consequently, the influence of initial conditions can persist forever. This phenomenon has been observed for Couette–Taylor instability, turbulent mixing layers, wakes, jets, pipe flows, etc. This is a commonly known property of chaos.

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