Calculation of turbulence-driven secondary motion in non-circular ducts

1984 ◽  
Vol 140 ◽  
pp. 189-222 ◽  
Author(s):  
A. O. Demuren ◽  
W. Rodi
Keyword(s):  
Eddy Viscosity ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Momentum Equation ◽  
Shear Stresses ◽  
Reynolds Stresses ◽  
Calculation Methods ◽  
Mean Flow ◽  
Square Duct ◽  
Secondary Motion

Experiments on and calculation methods for flow in straight non-circular ducts involving turbulence-driven secondary motion are reviewed. The origin of the secondary motion and the shortcomings of existing calculation methods are discussed. A more refined model is introduced, in which algebraic expressions are derived for the Reynolds stresses in the momentum equations for the secondary motion by simplifying the modelled Reynolds-stress equations of Launder, Reece & Rodi (1975), while a simple eddy-viscosity model is used for the shear stresses in the axial momentum equation. The kinetic energy k and the dissipation rate ε of the turbulent motion which appear in the algebraic and the eddy-viscosity expressions are determined from transport equations. The resulting set of equations is solved with a forward-marching numerical procedure for three-dimensional shear layers. The model, as well as a version proposed by Naot & Rodi (1982), is tested by application to developing flow in a square duct and to developed flow in a partially roughened rectangular duct investigated experimentally by Hinze (1973). In both cases, the main features of the mean-flow and the turbulence quantities are simulated realistically by both models, but the present model underpredicts the secondary velocity while the Naot-Rodi model tends to overpredict it.

Tilting at wave beams: a new perspective on the St. Andrew’s Cross

2017 ◽  
Vol 830 ◽  
pp. 660-680 ◽  
Author(s):  
T. Kataoka ◽  
S. J. Ghaemsaidi ◽  
N. Holzenberger ◽  
T. Peacock ◽  
T. R. Akylas
Keyword(s):  
Wave Field ◽  
Finite Length ◽  
Line Source ◽  
Cutoff Frequency ◽  
Three Dimensional ◽  
Resonance Phenomenon ◽  
Buoyancy Frequency ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Viscous Effects

The generation of internal gravity waves by a vertically oscillating cylinder that is tilted to the horizontal in a stratified Boussinesq fluid of constant buoyancy frequency, $N$, is investigated. This variant of the widely studied horizontal configuration – where a cylinder aligned with a plane of constant gravitational potential induces four wave beams that emanate from the cylinder, forming a cross pattern known as the ‘St. Andrew’s Cross’ – brings out certain unique features of radiated internal waves from a line source tilted to the horizontal. Specifically, simple kinematic considerations reveal that for a cylinder inclined by a given angle $\unicode[STIX]{x1D719}$ to the horizontal, there is a cutoff frequency, $N\sin \unicode[STIX]{x1D719}$, below which there is no longer a radiated wave field. Furthermore, three-dimensional effects due to the finite length of the cylinder, which are minor in the horizontal configuration, become a significant factor and eventually dominate the wave field as the cutoff frequency is approached; these results are confirmed by supporting laboratory experiments. The kinematic analysis, moreover, suggests a resonance phenomenon near the cutoff frequency as the group-velocity component perpendicular to the cylinder direction vanishes at cutoff; as a result, energy cannot be easily radiated away from the source, and nonlinear and viscous effects are likely to come into play. This scenario is examined by adapting the model for three-dimensional wave beams developed in Kataoka & Akylas (J. Fluid Mech., vol. 769, 2015, pp. 621–634) to the near-resonant wave field due to a tilted line source of large but finite length. According to this model, the combination of three-dimensional, nonlinear and viscous effects near cutoff triggers transfer of energy, through the action of Reynolds stresses, to a circulating horizontal mean flow. Experimental evidence of such an induced mean flow near cutoff is also presented.

scholarly journals Three-Dimensional Turbulent Vortex Shedding From a Surface-Mounted Square Cylinder: Predictions With Large-Eddy Simulations and URANS

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
B. A. Younis ◽  
A. Abrishamchi
Keyword(s):  
Experimental Data ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Large Eddy Simulations ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Large Eddy

The paper reports on the prediction of the turbulent flow field around a three-dimensional, surface mounted, square-sectioned cylinder at Reynolds numbers in the range 104–105. The effects of turbulence are accounted for in two different ways: by performing large-eddy simulations (LES) with a Smagorinsky model for the subgrid-scale motions and by solving the unsteady form of the Reynolds-averaged Navier–Stokes equations (URANS) together with a turbulence model to determine the resulting Reynolds stresses. The turbulence model used is a two-equation, eddy-viscosity closure that incorporates a term designed to account for the interactions between the organized mean-flow periodicity and the random turbulent motions. Comparisons with experimental data show that the two approaches yield results that are generally comparable and in good accord with the experimental data. The main conclusion of this work is that the URANS approach, which is considerably less demanding in terms of computer resources than LES, can reliably be used for the prediction of unsteady separated flows provided that the effects of organized mean-flow unsteadiness on the turbulence are properly accounted for in the turbulence model.

3D Reynolds Stress Modelling of Turbulent Flow in Linear Turbine Cascade

1997 ◽  
Author(s):  
M. Kanniche ◽  
R. Boudjemadi ◽  
F. Déjean ◽  
F. Archambeau
Keyword(s):  
Reynolds Stress ◽  
Eddy Viscosity ◽  
Strain Tensor ◽  
Secondary Flows ◽  
Turbulence Closure ◽  
Turbine Cascade ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Principal Axes ◽  
The Mean

The flow in a linear turbine cascade (Gregory-Smith et al. (1990)) is numerically investigated using a Reynolds Stress Turbulence closure. A particular attention is given to secondary flows where the normal Reynolds stresses are expected to play an important role. The most classical turbulence closure, the k-epsilon model uses the Boussinesq Eddy Viscosity concept which assumes an isotropic turbulent viscosity. The Reynolds stresses are then related to local velocity gradients by this isotropic eddy viscosity. Corollary, the principal axes of the Reynolds stress tensor are colinear with those of the mean strain tensor. The advantage of Reynolds Stress Turbulence closure is the calculation of Reynolds stresses by their own individual transport equations. This leads to a more realistic description of the turbulence and of its dependance on the mean flow. The most classical Second Order turbulence model (Launder et al. (1975)) is applied to a linear turbine cascade, and the results are compared to secondary velocity and turbulence measurements at cross-passage planes.

Numerical Simulation of a Three-Dimensional Axisymmetric Hill: Performance Evaluation of Hybrid RANS-LES Models

2021 ◽  
Author(s):  
Tausif Jamal ◽  
Varun Chitta ◽  
Dibbon K. Walters
Keyword(s):  
Eddy Viscosity ◽  
Turbulence Modeling ◽  
Three Dimensional ◽  
Boundary Layer Separation ◽  
Wake Flow ◽  
Dynamics Simulation ◽  
Recirculation Region ◽  
Mean Flow ◽  
Large Eddy ◽  
Rans Models

Abstract Computational fluid dynamics simulation of flow over a three-dimensional axisymmetric hill presents a unique set of challenges for turbulence modeling. The flow past the crest of the hill is characterized by boundary layer separation, complex vortical structures, and unsteady wake flow. As a result, traditional eddy-viscosity Reynolds-averaged Navier-Stokes (RANS) models have been found to perform poorly for this benchmark test case. Recent studies have focused on the use of large-eddy simulation (LES) and hybrid RANS-LES (HRL) methods to improve accuracy. In this study, several different HRL models are investigated and results from the different models are evaluated relative to each other, to an eddy-viscosity RANS model, and to previously documented high-fidelity large-eddy simulations and experimental data. Results obtained from the simulations in terms of mean flow statistics, surface pressure distribution, and turbulence characteristics are presented and discussed in detail. Results indicate that HRL models can significantly improve predictions over RANS models, but only when the development of turbulent velocity fluctuations in the separated shear layer and recirculation region are well resolved.

Large-scale vortex structures in turbulent wakes behind bluff bodies. Part 1. Vortex formation processes

1987 ◽  
Vol 174 ◽  
pp. 233-270 ◽  
Author(s):  
A. E. Perry ◽  
T. R. Steiner
Keyword(s):  
Large Scale ◽  
Vector Fields ◽  
Vortex Formation ◽  
Three Dimensional ◽  
Point Theory ◽  
Shear Stresses ◽  
Bluff Bodies ◽  
Two Dimensional ◽  
Mean Flow ◽  
Turbulent Wakes

An investigation of turbulent wakes was conducted and phase-averaged velocity vector fields are presented, as well as phase-averaged and global Reynolds normal and shear stresses. The topology of the phase-averaged velocity fields is discussed in terms of critical point theory. Here in Part 1, the vortex formation process in the cavity region of several nominally two-dimensional bluff bodies is investigated and described using phase-averaged streamlines where the measurements were made in a nominal plane of symmetry. It was found that the flows encountered were always three-dimensional and that the mean-flow patterns in the cavity region were quite different from those expected using classical two-dimensional assumptions.

Measurement of the Reynolds stresses and the mean-flow field in a three-dimensional pressure-driven boundary layer

1982 ◽  
Vol 119 ◽  
pp. 121-153 ◽  
Author(s):  
Udo R. Müller
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Flow Field ◽  
Three Dimensional ◽  
Turbulent Shear ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Flow Acceleration ◽  
The Mean

An experimental study of a steady, incompressible, three-dimensional turbulent boundary layer approaching separation is reported. The flow field external to the boundary layer was deflected laterally by turning vanes so that streamwise flow deceleration occurred simultaneous with cross-flow acceleration. At 21 stations profiles of the mean-velocity components and of the six Reynolds stresses were measured with single- and X-hot-wire probes, which were rotatable around their longitudinal axes. The calibration of the hot wires with respect to magnitude and direction of the velocity vector as well as the method of evaluating the Reynolds stresses from the measured data are described in a separate paper (Müller 1982, hereinafter referred to as II). At each measuring station the wall shear stress was inferred from a Preston-tube measurement as well as from a Clauser chart. With the measured profiles of the mean velocities and of the Reynolds stresses several assumptions used for turbulence modelling were checked for their validity in this flow. For example, eddy viscosities for both tangential directions and the corresponding mixing lengths as well as the ratio of resultant turbulent shear stress to turbulent kinetic energy were derived from the data.

The Numerical Prediction of Developing Turbulent Flow and Heat Transfer in a Square Duct

1980 ◽  
Vol 102 (1) ◽  
pp. 51-57 ◽  
Author(s):  
A. F. Emery ◽  
P. K. Neighbors ◽  
F. B. Gessner
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Algebraic Closure ◽  
Three Dimensional ◽  
Shear Stresses ◽  
Closure Model ◽  
Constant Wall Temperature ◽  
Square Duct ◽  
Constant Wall Heat Flux ◽  
Temperature Constant

Velocity and temperature profiles were computed for developing turbulent flow in a square duct with constant wall temperature, constant wall heat flux or asymmetric heating. The computations utilized an explicit numerical differencing scheme and an algebraic closure model based upon a three-dimensional mixing length. The computed local and fully-developed shear stresses and heat transfer are shown to be in good agreement with measured data and with predictions using the k–ε closure model.

Turbulent flow field in a scour hole at a semicircular abutment

2005 ◽  
Vol 32 (1) ◽  
pp. 213-232 ◽  
Author(s):  
Subhasish Dey ◽  
Abdul Karim Barbhuiya
Keyword(s):  
Flow Field ◽  
Turbulent Flow ◽  
Three Dimensional ◽  
Shear Stresses ◽  
Reynolds Stresses ◽  
Primary Vortex ◽  
Scour Hole ◽  
Turbulent Flow Field ◽  
Development And Validation ◽  
Bed Shear Stresses

The three-dimensional turbulent flow field in a scour hole at a semicircular abutment under a clear water regime was experimentally measured in a laboratory flume using an acoustic Doppler velocimeter. The distributions of time-averaged velocity components, turbulent intensity components, turbulent kinetic energy, and Reynolds stresses at different azimuthal planes are presented. Upstream, presentation of flow field through vector plots at azimuthal and horizontal planes shows the existence of a large primary vortex associated with the downflow inside the scour hole. On the other hand, downstream, the flow field is irregular. The bed shear stresses are determined from the Reynolds stresses and velocity gradients. The data presented in this paper would be useful for the development and validation of flow field models, which can be used to determine the strength of the primary vortex that is used to estimate scour depth at bridge abutments.Key words: bridge abutments, fluid flow, three-dimensional flow, turbulent flow, open channel flow, scour, sediment transport, hydraulic engineering.

Multiple Jets in a Crossflow: Detailed Measurements and Numerical Simulations

1997 ◽  
Vol 119 (2) ◽  
pp. 330-342 ◽  
Author(s):  
P. Ajersch ◽  
J.-M. Zhou ◽  
S. Ketler ◽  
M. Salcudean ◽  
I. S. Gartshore
Keyword(s):  
Numerical Simulations ◽  
Film Cooling ◽  
Three Dimensional ◽  
Light Sheet ◽  
Algebraic Model ◽  
Laser Doppler Velocimeter ◽  
Width Ratio ◽  
Video Tape ◽  
Reynolds Stresses ◽  
Mean Flow

The fluid mechanics and heat transfer characteristics of film cooling are three-dimensional and highly complex. To understand this problem better, an experimental study was conducted in a low-speed wind tunnel on a row of six rectangular jets injected at 90 deg to the crossflow (mainstream flow). The jet-to-crossflow velocity ratios (blowing ratios) examined were 0.5, 1.0, and 1.5, and the jet spacing-to-jet width ratio was 3.0. No significant temperature difference between jet and crossflow air was introduced. Mean velocities and six flow stresses were measured using a three-component laser-Doppler velocimeter operating in coincidence mode. Seeding of both jet and cross-stream air was achieved with a commercially available smoke generator. Flow statistics are reported in the form of vector plots, contours, and x-y graphs, showing velocity, turbulence intensity, and Reynolds stresses. To complement the detailed measurements, flow visualization was accomplished by transmitting the laser beam through a cylindrical lens, thereby generating a narrow, intense sheet of light. Jet air only was seeded with smoke, which was illuminated in the plane of the light sheet. Therefore, it was possible to record on video tape the trajectory and penetration of the jets in the crossflow. Selected still images from the recordings are presented. Numerical simulations of the observed flow field were made by using a multigrid, segmented, k–ε CFD code. Special near-wall treatment included a nonisotropic formulation for the effective viscosity, a low-Re model for k, and an algebraic model for the length scale. Comparisons between the measured and computed velocities show good agreement for the nonuniform mean flow at the jet exit plane. Velocities and stresses on the jet centerline downstream of the orifice are less well predicted, probably because of inadequate turbulence modeling, while values off the centerline match those of the experiments much more closely.

Explicit Algebraic Reynolds-stress Modeling of Pressure-induced Separating Flows in the Presence of Sidewalls

2021 ◽  
Author(s):  
Abdelouahab Mohammed Taifour ◽  
Julien Weiss ◽  
Louis Dufresne
Keyword(s):  
Reynolds Stress ◽  
Test Section ◽  
Three Dimensional ◽  
Wind Tunnel Test ◽  
Shear Stresses ◽  
Mean Flow ◽  
Flow Topology ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Good Agreement

Abstract RANS approach is used to simulate the steady state of a family of pressure-induced turbulent separation bubbles in the presence of sidewalls. Different turbulence models are employed with a specific emphasis on the BaSeLine Explicit Algebraic Reynolds Stress Model (BSL-EARSM) and the simulations are compared with experimental data. The separation and reattachment of a flat-plate turbulent boundary layer is generated through a combination of adverse and favorable pressure gradients (APG-FPG) by numerically reproducing the geometry of the wind-tunnel test section used for the experiments. Three cases are considered, a large (LB) and a medium (MB) bubble presenting mean backflow, and a small bubble (SB) without mean-flow reversal. This is achieved by varying the streamwise position of the APG/FPG transition. Good agreement between the BSL-EARSM-computed solutions and the experimental results are obtained for wall-pressure and skin-friction distributions on the centerline plane of the test section as well as for the overall three-dimensional flow topology. However, both detachment and reattachment are predicted too early and the bubble length is slightly overestimated for Cases LB and MB. For Case LB, the streamwise Reynolds stress is estimated fairly well but its production is somewhat delayed. Normal and shear stresses are in good agreement with the experiments in the upstream part of the bubble but are significantly over-estimated in the reattachment region. The k ?? ! Shear-Stress Transport (SST) model with the so-called reattachment modification performs better than the other tested linear-eddy-viscosity models but it is still unable to reproduce accurately the three-dimensional flow topology even for the 'simplest' case SB. Overall, the results suggest that BSL-EARSM is the most suitable turbulence model for this flow configuration.

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