The Calculation of Properties of the Flow over a Backward Facing Step With the k-ε Model of Turbulence

1984 ◽  
Vol 8 (3) ◽  
pp. 165-170
Author(s):  
L.P. Hackman ◽  
A.B. Strong ◽  
G.D. Raithby
Keyword(s):  
Experimental Data ◽  
Kinetic Energy ◽  
Turbulent Flow ◽  
Skin Friction ◽  
Turbulent Kinetic Energy ◽  
Reasonable Agreement ◽  
Shear Stresses ◽  
Backward Facing Step ◽  
Mean Velocity ◽  
The Mean

This paper reports predictions of the mean velocity, the turbulent kinetic energy and the pressure and skin friction coefficients for turbulent flow over a backward facing step based on the standard k – ε closure for the turbulence shear stresses. In previous publications, errors due to the numerical algorithm as distinct from the turbulence model have been carefully assessed using different numerical schemes and finite volume geometries and it is argued that the current results are numerically accurate. Thus one can now assess the accuracy of the k – ε model of turbulence independently of numerical error. The results predicted herein were found to be in reasonable agreement with relevant experimental data.

Measurements of Losses and Reynolds Stresses in the Secondary Flow Downstream of a Low-Speed Linear Turbine Cascade

2010 ◽  
Author(s):  
G. D. MacIsaac ◽  
S. A. Sjolander ◽  
T. J. Praisner
Keyword(s):  
Kinetic Energy ◽  
Turbulent Flow ◽  
Secondary Flow ◽  
Turbulent Kinetic Energy ◽  
Pressure Probe ◽  
Turbine Cascade ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Hole Pressure ◽  
The Mean

Experimental measurements of the mean and turbulent flow field were preformed downstream of a low-speed linear turbine cascade. The influence of turbulence on the production of secondary losses is examined. Steady pressure measurements were collected using a seven-hole pressure probe and the turbulent flow quantities were measured using a rotatable x-type hotwire probe. Each probe was traversed downstream of the cascade along planes positioned at three axial locations: 100%, 120% and 140% of the axial chord (Cx) downstream of the leading edge. The seven-hole pressure probe was used to determine the local total and static pressure as well as the three mean velocity components. The rotatable x-type hotwire probe, in addition to the mean velocity components, provided the local Reynolds stresses and the turbulent kinetic energy. The axial development of the secondary losses is examined in relation to the rate at which mean kinetic energy is transferred to turbulent kinetic energy. In general, losses are generated as a result of the mean flow dissipating kinetic energy through the action of viscosity. The production of turbulence can be considered a preliminary step in this process. The measured total pressure contours from the three axial locations (1.00, 1.20 and 1.40Cx) demonstrate the development of the secondary losses. The peak loss core in each plane consists mainly of low momentum fluid that originates from the inlet endwall boundary layer. There are, however, additional losses generated as the flow mixes with downstream distance. These losses have been found to relate to the turbulent Reynolds stresses. An examination of the turbulent deformation work term demonstrates a mechanism of loss generation in the secondary flow region. The importance of the Reynolds shear stress to this process is explored in detail.

Measurements of Losses and Reynolds Stresses in the Secondary Flow Downstream of a Low-Speed Linear Turbine Cascade

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
G. D. MacIsaac ◽  
S. A. Sjolander ◽  
T. J. Praisner
Keyword(s):  
Kinetic Energy ◽  
Turbulent Flow ◽  
Secondary Flow ◽  
Turbulent Kinetic Energy ◽  
Pressure Probe ◽  
Turbine Cascade ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Hole Pressure ◽  
The Mean

Experimental measurements of the mean and turbulent flow field were preformed downstream of a low-speed linear turbine cascade. The influence of turbulence on the production of secondary losses is examined. Steady pressure measurements were collected using a seven-hole pressure probe and the turbulent flow quantities were measured using a rotatable x-type hotwire probe. Each probe was traversed downstream of the cascade along planes positioned at three axial locations: 100%, 120%, and 140% of the axial chord (Cx) downstream of the leading edge. The seven-hole pressure probe was used to determine the local total and static pressure as well as the three mean velocity components. The rotatable x-type hotwire probe, in addition to the mean velocity components, provided the local Reynolds stresses and the turbulent kinetic energy. The axial development of the secondary losses is examined in relation to the rate at which mean kinetic energy is transferred to turbulent kinetic energy. In general, losses are generated as a result of the mean flow dissipating kinetic energy through the action of viscosity. The production of turbulence can be considered a preliminary step in this process. The measured total pressure contours from the three axial locations (1.00, 1.20, and 1.40Cx) demonstrate the development of the secondary losses. The peak loss core in each plane consists mainly of low momentum fluid that originates from the inlet endwall boundary layer. There are, however, additional losses generated as the flow mixes with downstream distance. These losses have been found to relate to the turbulent Reynolds stresses. An examination of the turbulent deformation work term demonstrates a mechanism of loss generation in the secondary flow region. The importance of the Reynolds shear stresses to this process is explored in detail.

Interaction between a spatially growing turbulent boundary layer and embedded streamwise vortices

1996 ◽  
Vol 326 ◽  
pp. 151-179 ◽  
Author(s):  
Junhui Liu ◽  
Ugo Piomelli ◽  
Philippe R. Spalart
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Turbulent Kinetic Energy ◽  
Vortex Core ◽  
Eddy Viscosity ◽  
Shear Stresses ◽  
Streamwise Vortices ◽  
Mean Velocity ◽  
Production Term

The interaction between a zero-pressure-gradient turbulent boundary layer and a pair of strong, common-flow-down, streamwise vortices with a sizeable velocity deficit is studied by large-eddy simulation. The subgrid-scale stresses are modelled by a localized dynamic eddy-viscosity model. The results agree well with experimental data. The vortices drastically distort the boundary layer, and produce large spanwise variations of the skin friction. The Reynolds stresses are highly three-dimensional. High levels of kinetic energy are found both in the upwash region and in the vortex core. The two secondary shear stresses are significant in the vortex region, with magnitudes comparable to the primary one. Turbulent transport from the immediate upwash region is partly responsible for the high levels of turbulent kinetic energy in the vortex core; its effect on the primary stress 〈u′v′〉 is less significant. The mean velocity gradients play an important role in the generation of 〈u′v′〉 in all regions, while they are negligible in the generation of turbulent kinetic energy in the vortex core. The pressure-strain correlations are generally of opposite sign to the production terms except in the vortex core, where they have the same sign as the production term in the budget of 〈u′v′〉. The results highlight the limitations of the eddy-viscosity assumption (in a Reynolds-averaged context) for flows of this type, as well as the excessive diffusion predicted by typical turbulence models.

Simulation of a propelled wake with moderate excess momentum in a stratified fluid

2011 ◽  
Vol 692 ◽  
pp. 28-52 ◽  
Author(s):  
Matthew B. de Stadler ◽  
Sutanu Sarkar
Keyword(s):  
Kinetic Energy ◽  
Velocity Profile ◽  
Turbulent Kinetic Energy ◽  
Vertical Direction ◽  
Qualitative Change ◽  
Stratified Fluid ◽  
Mean Velocity ◽  
Moderate Amount ◽  
Excess Momentum ◽  
The Mean

AbstractDirect numerical simulation is used to simulate the turbulent wake behind an accelerating axisymmetric self-propelled body in a stratified fluid. Acceleration is modelled by adding a velocity profile corresponding to net thrust to a self-propelled velocity profile resulting in a wake with excess momentum. The effect of a small to moderate amount of excess momentum on the initially momentumless self-propelled wake is investigated to evaluate if the addition of excess momentum leads to a large qualitative change in wake dynamics. Both the amount and shape of excess momentum are varied. Increasing the amount of excess momentum and/or decreasing the radial extent of excess momentum was found to increase the defect velocity, mean kinetic energy, shear in the velocity gradient and the wake width. The increased shear in the mean profile resulted in increased production of turbulent kinetic energy leading to an increase in turbulent kinetic energy and its dissipation. Slightly larger vorticity structures were observed in the late wake with excess momentum although the differences between vorticity structures in the self-propelled and 40 % excess momentum cases was significantly smaller than suggested by previous experiments. Buoyancy was found to preserve the doubly inflected velocity profile in the vertical direction, and similarity for the mean velocity and turbulent kinetic energy was found to occur in both horizontal and vertical directions. While quantitative differences were observed between cases with and without excess momentum, qualitatively similar evolution was found to occur.

Wall Pressure Fluctuations in the Reattachment Region of a Backward Facing Step

2007 ◽  
Author(s):  
Yu-Tai Lee ◽  
Theodore M. Farabee ◽  
William K. Blake
Keyword(s):  
Kinetic Energy ◽  
Turbulent Flow ◽  
Turbulent Kinetic Energy ◽  
Source Term ◽  
Pressure Fluctuations ◽  
Wall Pressure ◽  
Mean Flow ◽  
Backward Facing Step ◽  
Fluctuating Pressure ◽  
Wall Pressure Fluctuations

Steady mean flow fields and turbulent flow characteristics obtained from solving the Reynolds Averaged Navier Stokes (RANS) equations with a k-ε isotropic turbulence model are used to predict the frequency spectrum of wall-pressure fluctuations for flow past a backward facing step. The linear source term (LST) of the governing fluctuating-pressure equation is used in deriving the final double integration formula for the fluctuating wall pressure. The integrand of the solution formula includes the mean-flow velocity gradient, modeled turbulence normal fluctuation, Green’s function and the spectral model for the interplane correlation. An anisotropic distribution of the turbulent kinetic energy is implemented using a function named anisotropic factor. This function represents a ratio of the turbulent normal Reynolds stress to the turbulent kinetic energy and is developed based on an equilibrium turbulent flow or flows with zero streamwise pressure gradient. The spectral correlation model for predicting the wall-pressure fluctuations is obtained through modeling of the streamwise and spanwise wavenumber spectra. The nonlinear source term (NST) in the original fluctuating-pressure equation is considered following the conclusion of Kim’s direct numerical simulation (DNS) study of channel flow. Predictions of frequency spectra for the reattachment flow past a backward facing step (BFS) are investigated to verify the validity of the current modeling. Detailed turbulence features and wall-pressure spectra for the flow in the reattachment region of the BFS are predicted and discussed. DNS and experimental data for BFSs are used to develop and validate these calculations. The prediction results based on different modeling characteristics and flow physics agree with the observed turbulence field.

The Present State of the Turbulence Problem

1933 ◽  
Vol 1 (1) ◽  
pp. 19-28
Author(s):  
Walter Tollmien
Keyword(s):  
Turbulent Flow ◽  
Flat Plate ◽  
Skin Friction ◽  
Turbulence Theory ◽  
Shearing Stress ◽  
Mean Velocity ◽  
Fully Developed Turbulence ◽  
Developed Turbulence ◽  
The Mean ◽  
Real Goal

Abstract In this survey the author first describes certain types of turbulent flow, following which he deals successively with the production of turbulent motion; the instability of the laminar motion; fully developed turbulence; momentum interchange and mixing lengths; and relations between the shearing stress at the wall and the mean velocity distributions. Finally he takes up the calculation of skin friction for simple cases of fully developed turbulence, especially for that of the flat plate. Although the methods outlined have often led to practically useful results, it is the author’s belief that they should be considered only as advances toward the real goal of the turbulence theory. The derivation of turbulence phenomena from the hydrodynamical equations will, in his opinion, be possible only by the application of statistical methods.

Experimental Study of Reynolds Number Effects on Three-Dimensional Offset Jets

2014 ◽  
Author(s):  
Zacharie M. J. Durand ◽  
Shawn P. Clark ◽  
Mark F. Tachie ◽  
Jarrod Malenchak ◽  
Getnet Muluye
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Reynolds Shear Stress ◽  
Three Dimensional ◽  
Shear Stresses ◽  
Mean Velocity ◽  
Flow Measurements ◽  
Reynolds Number Effects

The effect of Reynolds number on three-dimensional offset jets was investigated in this study. An acoustic Doppler velocimeter simultaneously measured all three components of velocity, U, V and W, and turbulence intensity, urms, vrms, and wrms, and all three Reynolds shear stresses, uv, uw, and vw. Turbulent kinetic energy, k, was calculated with all three values of turbulence intensities. Flow measurements were performed at Reynolds numbers of 34,000, 53,000 and 86,000. Results of this experimental study indicate the wall-normal location of maximum mean velocity and jet spread to be independent of Reynolds number. The effects on maximum mean velocity decay are reduced with increasing Reynolds number. Profiles of mean velocities, U, V and W, turbulence intensities, urms, vrms, and wrms, and turbulent kinetic energy, k, show independence of Reynolds number. Reynolds shear stress uv was independent of Reynolds number while the magnitude of uw was reduced at higher Reynolds number.

PIV Investigation of Separated and Reattached Turbulent Flows Over Ribs of Various Aspect Ratio

2014 ◽  
Author(s):  
Kathryn M. Atamanchuk ◽  
Mark F. Tachie
Keyword(s):  
Kinetic Energy ◽  
Aspect Ratio ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Reynolds Shear Stress ◽  
Separated Flow ◽  
Particle Image Velocimetry System ◽  
Shear Stresses ◽  
Mean Velocity ◽  
Freestream Velocity

An experimental study is undertaken to investigate the features of separated and reattached flow over surface mounted traverse ribs of varying aspect ratio (1:1, 1:2, and 1:4) in a recirculating open channel turbulent flow. A particle image velocimetry system was used to conduct the velocity measurements. Upstream conditions were kept consistent among all three test cases. The reattachment length of the separated flow was found to decrease as rib aspect ratio increased, primarily as a result of a secondary separation reattachment formation on the ribs of increased aspect ratio. Contour plots of mean velocities, turbulence intensities, turbulent kinetic energy and Reynolds shear stresses, as well as one-dimensional profiles of streamwise mean velocity, turbulent kinetic energy and Reynolds shear stress in the recirculation and reattachment region are presented and discussed. The results show that maximum wall-normal mean velocities are approximately 40% of the approach freestream velocity. The results also indicate that the turbulence levels downstream of the block tend to decrease as the rib aspect ratio increases.

Experimental investigation of jets in a crossflow

1984 ◽  
Vol 138 ◽  
pp. 93-127 ◽  
Author(s):  
J. Andreopoulos ◽  
W. Rodi
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Velocity Ratio ◽  
Three Dimensional ◽  
Turbulent Shear ◽  
Shear Stresses ◽  
Hot Wire ◽  
Mean Flow ◽  
Mean Velocity ◽  
Turbulent Kinetic Energy Equation

The paper reports on measurements in the flow generated by a jet issuing from a circular outlet in a wall into a cross-stream along this wall. For the jet-to-crossflow velocity ratios R of 0.5, 1 and 2, the mean and fluctuating velocity components were measured with a three-sensor hot-wire probe. The hot-wire signals were evaluated to yield the three mean-velocity components, the turbulent kinetic energy, the three turbulent shear stresses and, in the case of R = 0.5, the terms in the turbulent-kinetic-energy equation. The results give a quantitative picture of the complex three-dimensional mean flow and turbulence field, and the various phenomena as well as their dependence on the velocity ratio R are discussed in detail.

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