Erratum: “Reynolds-Stress Modeling of Three-Dimensional Secondary Flows With Emphasis on Turbulent Diffusion Closure” [Journal of Applied Mechanics, 2007, 74(6), pp. 1142–1156]

2008 ◽  
Vol 75 (4) ◽  
Author(s):  
I. Vallet
Keyword(s):  
Reynolds Stress ◽  
Turbulent Diffusion ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Applied Mechanics ◽  
Stress Modeling

Reynolds-Stress Modeling of Three-Dimensional Secondary Flows With Emphasis on Turbulent Diffusion Closure

2007 ◽  
Vol 74 (6) ◽  
pp. 1142-1156 ◽  
Author(s):  
I. Vallet
Keyword(s):  
Reynolds Stress ◽  
Turbulent Diffusion ◽  
Three Dimensional ◽  
Theoretical Work ◽  
Reynolds Stress Model ◽  
Secondary Flows ◽  
Velocity Correlation ◽  
Mean Velocity ◽  
Diffusion Term ◽  
Spatial Gradients

The purpose of this paper is to assess the importance of the explicit dependence of turbulent diffusion on the gradients of mean-velocity modeling in second moment closures on three-dimensional (3D) detached and secondary flows prediction. Following recent theoretical work of Younis, Gatski, and Speziale, 2000, [Proc. Royal Society Lon. A, 456, pp. 909–920], we propose a triple-velocity correlation model, including the effects of the spatial gradients of mean velocity. A model for both the slow and rapid parts of the pressure-diffusion term was also developed and added to a wall-normal-free Reynolds-stress model. The present model is validated against 3D detached and secondary flows. Further developments, especially on the echo terms (which should appear in the formulation of pressure-velocity correlation), are discussed.

Near-Wall Turbulent Pressure Diffusion Modeling and Influence in Three-Dimensional Secondary Flows

2006 ◽  
Vol 129 (5) ◽  
pp. 634-642 ◽  
Author(s):  
E. Sauret ◽  
I. Vallet
Keyword(s):  
Diffusion Model ◽  
Turbulent Diffusion ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Moment Closure ◽  
Complex Flows ◽  
Diffusion Term ◽  
Pressure Diffusion ◽  
Turbulent Pressure ◽  
Near Wall

The purpose of this paper is to develop a second-moment closure with a near-wall turbulent pressure diffusion model for three-dimensional complex flows, and to evaluate the influence of the turbulent diffusion term on the prediction of detached and secondary flows. A complete turbulent diffusion model including a near-wall turbulent pressure diffusion closure for the slow part was developed based on the tensorial form of Lumley and included in a re-calibrated wall-normal-free Reynolds-stress model developed by Gerolymos and Vallet. The proposed model was validated against several one-, two, and three-dimensional complex flows.

Reynolds stress distribution and turbulence generated secondary flow in the turbulent three-dimensional wall jet

2016 ◽  
Vol 800 ◽  
pp. 613-644 ◽  
Author(s):  
L. Namgyal ◽  
J. W. Hall
Keyword(s):  
Secondary Flow ◽  
Reynolds Stress ◽  
Reynolds Shear Stress ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Half Width ◽  
Stereoscopic Particle Image Velocimetry ◽  
Wall Jet ◽  
Normal Stresses ◽  
Reynolds Stresses

The lateral half-width of the turbulent three-dimensional wall jet is typically five to eight times larger than the vertical half-width normal to the wall. Although the reason for this behaviour is not fully understood, it is caused by mean secondary flows that develop in the jet due to the presence of the wall. The origin of the secondary flow has been associated previously with both vorticity reorientation and also gradients in the Reynolds stresses, although this has not been directly quantified as yet. The present investigation focuses on a wall jet formed using a circular contoured nozzle with exit Reynolds number of 250 000. Stereoscopic particle image velocimetry measurements are used herein to measure the three-component velocity, thereby allowing access to the full Reynolds stress tensor that contributes to the secondary flow in a turbulent three-dimensional wall jet. Throughout the jet, the Reynolds normal stress ($\overline{u^{2}}$) makes the largest contribution to the Reynolds stress field whereas Reynolds shear stress ($\overline{vw}$) is found to be negligible when compared with other stresses. In particular, the differences in the Reynolds normal stresses ($\overline{v^{2}}-\overline{w^{2}}$) are found to be significantly larger than $\overline{vw}$; these terms are important for the generation of turbulence secondary flow in the wall jet. Above all, the differences in the Reynolds normal stresses are oriented to reinforce the near-wall streamwise vorticity, and thus contribute to the large lateral growth of this flow. The contours of the turbulent kinetic budget indicate that the turbulent energy budget obtained on the jet centreline is different from that obtained off of the jet centreline.

scholarly journals LDV Measurement of Confined Parallel Jet Mixing

2000 ◽  
Vol 123 (3) ◽  
pp. 567-573 ◽  
Author(s):  
Robert F. Kunz ◽  
Stephen W. D’Amico ◽  
Peter F. Vassallo ◽  
Michael A. Zaccaria
Keyword(s):  
Reynolds Stress ◽  
Laser Doppler Velocimetry ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Mixing Process ◽  
Mean Velocity ◽  
Jet Mixing ◽  
Transverse Diffusion ◽  
Stress Components ◽  
Ldv Measurement

Laser Doppler Velocimetry (LDV) measurements were taken in a confinement, bounded by two parallel walls, into which issues a row of parallel jets. Two-component measurements were taken of two mean velocity components and three Reynolds stress components. As observed in isolated three-dimensional wall bounded jets, the transverse diffusion of the jets is quite large. The data indicate that this rapid mixing process is due to strong secondary flows, transport of large inlet intensities, and Reynolds stress anisotropy effects.

The Influence of Blade Wakes on the Performance of Interturbine Diffusers

1996 ◽  
Vol 118 (2) ◽  
pp. 347-352 ◽  
Author(s):  
R. G. Dominy ◽  
D. A. Kirkham
Keyword(s):  
Performance Modeling ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Two Dimensional ◽  
Correct Performance ◽  
Analysis Methods ◽  
Flow Factor ◽  
The Mean ◽  
Lp Turbine

Interturbine diffusers provide continuity between HP and LP turbines while diffusing the flow upstream of the LP turbine. Increasing the mean turbine diameter offers the potential advantage of reducing the flow factor in the following stages, leading to increased efficiency. The flows associated with these interturbine diffusers differ from those in simple annular diffusers both as a consequence of their high-curvature S-shaped geometry and of the presence of wakes created by the upstream turbine. It is shown that even the simplest two-dimensional wakes result in significantly modified flows through such ducts. These introduce strong secondary flows demonstrating that fully three-dimensional, viscous analysis methods are essential for correct performance modeling.

scholarly journals Steady flow separation patterns in a 45 degree junction

2000 ◽  
Vol 411 ◽  
pp. 1-38 ◽  
Author(s):  
C. ROSS ETHIER ◽  
SUJATA PRAKASH ◽  
DAVID A. STEINMAN ◽  
RICHARD L. LEASK ◽  
GREGORY G. COUCH ◽  
...  
Keyword(s):  
Flow Separation ◽  
Stokes Equations ◽  
Bypass Graft ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Measured Velocity ◽  
Curved Tube

Numerical and experimental techniques were used to study the physics of flow separation for steady internal flow in a 45° junction geometry, such as that observed between two pipes or between the downstream end of a bypass graft and an artery. The three-dimensional Navier–Stokes equations were solved using a validated finite element code, and complementary experiments were performed using the photochromic dye tracer technique. Inlet Reynolds numbers in the range 250 to 1650 were considered. An adaptive mesh refinement approach was adopted to ensure grid-independent solutions. Good agreement was observed between the numerical results and the experimentally measured velocity fields; however, the wall shear stress agreement was less satisfactory. Just distal to the ‘toe’ of the junction, axial flow separation was observed for all Reynolds numbers greater than 250. Further downstream (approximately 1.3 diameters from the toe), the axial flow again separated for Re [ges ] 450. The location and structure of axial flow separation in this geometry is controlled by secondary flows, which at sufficiently high Re create free stagnation points on the model symmetry plane. In fact, separation in this flow is best explained by a secondary flow boundary layer collision model, analogous to that proposed for flow in the entry region of a curved tube. Novel features of this flow include axial flow separation at modest Re (as compared to flow in a curved tube, where separation occurs only at much higher Re), and the existence and interaction of two distinct three-dimensional separation zones.

scholarly journals Incidence Angle and Pitch-Chord Effects on Secondary Flows Downstream of a Turbine Cascade

1992 ◽  
Author(s):  
A. Perdichizzi ◽  
V. Dossena
Keyword(s):  
Flow Field ◽  
Secondary Flow ◽  
Incidence Angle ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Pressure Probe ◽  
Turbine Cascade ◽  
Oil Flow ◽  
Secondary Velocity ◽  
Secondary Flow Field

This paper describes the results of an experimental investigation of the three-dimensional flow downstream of a linear turbine cascade at off-design conditions. The tests have been carried out for five incidence angles from −60 to +35 degrees, and for three pitch-chord ratios: s/c = 0.58,0.73,0.87. Data include blade pressure distributions, oil flow visualizations, and pressure probe measurements. The secondary flow field has been obtained by traversing a miniature five hole probe in a plane located at 50% of an axial chord downstream of the trailing edge. The distributions of local energy loss coefficients, together with vorticity and secondary velocity plots show in detail how much the secondary flow field is modified both by incidence and cascade solidity variations. The level of secondary vorticity and the intensity of the crossflow at the endwall have been found to be strictly related to the blade loading occurring in the blade entrance region. Heavy changes occur in the spanwise distributions of the pitch averaged loss and of the deviation angle, when incidence or pitch-chord ratio is varied.

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