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.

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.

An Eddy-Resolving Reynolds Stress Model for the Turbulent Bubbly Flow in a Square Cross-Sectioned Bubble Column

2014 ◽  
Author(s):  
Matthias Ullrich ◽  
Benjamin Krumbein ◽  
Robert Maduta ◽  
Suad Jakirlić
Keyword(s):  
Reynolds Stress ◽  
Bubble Column ◽  
Bubbly Flow ◽  
Three Dimensional ◽  
Reynolds Stress Model ◽  
Moment Closure ◽  
Numerical Code ◽  
Stress Model ◽  
Mean Flow ◽  
Second Moment Closure

An instability-sensitive, eddy-resolving Reynolds Stress Model of turbulence, employed in the Eulerian-Eulerian two-fluid framework, is formulated and validated by computing the gas-liquid bubble column in a three-dimensional square cross-sectioned configuration in the homogeneous flow regime. Interphase momentum transfer is modelled by considering drag, lift and virtual mass forces. The turbulence in the continuous liquid phase is captured by using a Second-Moment Closure model employed in the Unsteady Reynolds-Averaged Navier Stokes framework implying the solving of the differential transport equations for the Reynolds stress tensor and the homogeneous part of the inverse turbulent time scale ωh. This uiuj – ωh model is appropriately extended in accordance with the Scale-Adaptive Simulation proposal, enabling so the development of the fluctuating turbulence. The results obtained are analysed along with a reference experiment with respect to the evolution of the mean flow and turbulent quantities in both gas and liquid phases. The model described is implemented in the numerical code OpenFOAM.

scholarly journals Numerical Simulation of the Flow Through the Return Channel of Multi-Stage Centrifugal Compressors

1998 ◽  
Author(s):  
L. J. Lenke ◽  
H. Simon
Keyword(s):  
Numerical Simulation ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Reynolds Stress Model ◽  
Secondary Flows ◽  
Low Flow ◽  
Load Range ◽  
Design Point ◽  
Multi Stage ◽  
Return Channel

The numerical simulation of the flow within a return channel is reported in this paper. The investigated return channel is typically to join the exit from one stage of a centrifugal machine to the inlet of the next stage. These channel covers the range of extremely low flow coefficients. Different 3-D calculations with two different turbulence models (low-Reynolds-number k-ϵ and explicit algebraic Reynolds stress model) at the design point and part load range show the strongly three-dimensional flow structure with secondary flows on hub and shroud of the deswirl vanes. There are also significant separations downstream of the 180°-bend at suction and pressure side of the vanes. The presented numerical results are compared with experimental data in different planes and at the vane contour. The results indicate small differences between the turbulence models in the prediction of losses, flow angles and separation behavior at design point. At off-design conditions the turbulence models begin to deviate notably in their prediction of separation.

scholarly journals Analysis of Separated Flows Inside an Annular Compressor Cascade Using a Low-Re-Number k-ϵ and an Algebraic Reynolds-Stress-Model

1997 ◽  
Author(s):  
Jürgen R. Lücke ◽  
Heinz E. Gallus
Keyword(s):  
Flow Field ◽  
Reynolds Stress ◽  
Three Dimensional ◽  
Separated Flow ◽  
Reynolds Stress Model ◽  
Stress Model ◽  
Mean Flow ◽  
Compressor Cascade ◽  
Production Term ◽  
Algebraic Reynolds Stress Model

The flow field inside an annular compressor cascade is numerically investigated. The mean flow features are complex three-dimensional zones of turbulent separation at hub and shroud at high inflow angles. The flow field is investigated with an implicit three-dimensional Navier-Stokes code. To predict turbulent effects the flow solver includes two different variants of a Low-Re-number k-ϵ-model and an algebraic Reynolds-stress-model. Using the Low-Re-number model the structure of the regions of separated flow are fairly well predicted. However, intensity and size of these zones are too small compared with the experimental data. Better results are produced using the anisotropic algebraic Reynolds-stress-model combined with a stagnation point modification of the turbulent production term. Stucture and intensity of the vortex systems are simulated in more detail. Static pressure distributions and loss contours are in a very good agreement with the experiments.

Modeling of Cube Array Roughness: RANS, LES, and DNS

2021 ◽  
Author(s):  
Samuel Altland ◽  
Haosen H. A. Xu ◽  
Xiang I. A. Yang ◽  
Robert Kunz
Keyword(s):  
Reynolds Stress ◽  
Significant Degree ◽  
Reynolds Stress Model ◽  
Stress Model ◽  
Mean Velocity ◽  
Flow Features ◽  
Drag Partition ◽  
Flow Phenomena ◽  
Rans Models ◽  
Packing Densities

Abstract Flow over arrays of cubes is an extensively studied model problem for rough wall turbulent boundary layers. While considerable research has been performed in computationally investigating these topologies using DNS and LES, the ability of sublayer-resolved RANS to predict the bulk flow phenomena of these systems is relatively unexplored, especially at low and high packing densities. Here, RANS simulations are conducted on six different packing densities of cubes in aligned and staggered configurations. The packing densities investigated span from what would classically be defined as isolated, up to those in the d-type roughness regime, filling in the gap in the present literature. Three different sublayer-resolved turbulence closure models were tested for each case; a low Reynolds number k-ε model, the Menter k-ω SST model, and a full Reynolds stress model. Comparisons of the velocity fields, secondary flow features, and drag coefficients are made between the RANS results and existing LES and DNS results. There is a significant degree of variability in the performance of the various RANS models across all comparison metrics. However, the Reynolds stress model demonstrated the best accuracy in terms of the mean velocity profile as well as drag partition across the range of packing densities.

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