An Evaluation of Mean Reynolds Stress Turbulence Models: The Triple Velocity Correlation

1978 ◽  
Vol 100 (1) ◽  
pp. 47-54 ◽  
Author(s):  
D. E. Cormack ◽  
L. G. Leal ◽  
J. H. Seinfeld
Keyword(s):  
Experimental Data ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Turbulence Models ◽  
Velocity Correlation ◽  
Reynolds Stress Tensor ◽  
Closure Models ◽  
Proposed Model ◽  
The Mean ◽  
The One

A four-parameter model is presented for the triple velocity correlation which appears in the mean Reynolds stress tensor equations of turbulence. A comparison with the closure models of Hanjalic and Launder [1], Daly and Harlow [2], Wyngaard, Cote´, and Rao [3], and Shir [4], in the context of existing experimental data, indicates that the proposed model is superior. It is also demonstrated that, of the one-parameter models, the Hanjalic-Launder model best approximates the data. Due to the complexity of the four-parameter representation, it is recommended that the Hanjalic-Launder model be used for computational purposes.

scholarly journals Assessment of CFD turbulence models for free surface flow simulation and 1-D modelling for water level calculations over a broad-crested weir floodway

Water SA ◽  
2019 ◽  
Vol 45 (3 July) ◽  
Author(s):  
Ahmed M Helmi
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Water Level ◽  
Dimensional Analysis ◽  
Turbulence Model ◽  
Turbulence Models ◽  
Cfd Simulations ◽  
One Dimensional ◽  
The Mean ◽  
The One

Floodways, where a road embankment is permitted to be overtopped by flood water, are usually designed as broad-crested weirs. Determination of the water level above the floodway is crucial and related to road safety. Hydraulic performance of floodways can be assessed numerically using 1-D modelling or 3-D simulation using computational fluid dynamics (CFD) packages. Turbulence modelling is one of the key elements in CFD simulations. A wide variety of turbulence models are utilized in CFD packages; in order to identify the most relevant turbulence model for the case in question, 96 3-D CFD simulations were conducted using Flow-3D package, for 24 broad-crested weir configurations selected based on experimental data from a previous study. Four turbulence models (one-equation, k-ε, RNG k-ε, and k-ω) ere examined for each configuration. The volume of fluid (VOF) algorithm was adopted for free water surface determination. In addition, 24 1-D simulations using HEC-RAS-1-D were conducted for comparison with CFD results and experimental data. Validation of the simulated water free surface profiles versus the experimental measurements was carried out by the evaluation of the mean absolute error, the mean relative error percentage, and the root mean square error. It was concluded that the minimum error in simulating the full upstream to downstream free surface profile is achieved by using one-equation turbulence model with mixing length equal to 7% of the smallest domain dimension. Nevertheless, for the broad-crested weir upstream section, no significant difference in accuracy was found between all turbulence models and the one-dimensional analysis results, due to the low turbulence intensity at this part. For engineering design purposes, in which the water level is the main concern at the location of the flood way, the one-dimensional analysis has sufficient accuracy to determine the water level.

On the Constitutive Relation for the Reynolds Stresses and the Prandtl-Kolmogorov Hypothesis of Effective Viscosity in Axisymmetric Strained Turbulence

1999 ◽  
Vol 122 (1) ◽  
pp. 48-50 ◽  
Author(s):  
J. Jovanovic´ ◽  
I. Otic´
Keyword(s):  
Strain Rate ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Constitutive Relation ◽  
Effective Viscosity ◽  
Constitutive Relations ◽  
Reynolds Stresses ◽  
Reynolds Stress Tensor ◽  
The Mean ◽  
Mean Strain

The constitutive relation for the Reynolds stress tensor is considered for turbulence developing in axisymmetric strain fields. It is confirmed that the Reynolds stress tensor is aligned linearly with the mean strain rate. In contrast to the Prandtl-Kolmogorov, hypothesis, the effective viscosity is found to grow in proportion to the anisotropy of turbulence and the length scale based on the magnitude of the mean strain rate. Using invariant theory the effective viscosity is determined for the limiting states of turbulence. Additional analysis of the constitutive relations is supplemented for the dissipation and pressure-strain correlations. It is shown that analytical derivations are in excellent agreement with the data obtained from direct numerical simulations. [S0098-2202(00)02801-7]

On the application of successive plane strains to grid-generated turbulence

1979 ◽  
Vol 93 (3) ◽  
pp. 501-513 ◽  
Author(s):  
J. N. Gence ◽  
J. Mathieu
Keyword(s):  
Shear Flow ◽  
Detailed Analysis ◽  
Stress Tensor ◽  
Plane Strain ◽  
Reynolds Stress ◽  
Homogeneous Turbulence ◽  
Reynolds Stress Tensor ◽  
Principal Axes ◽  
The Mean

A grid-generated turbulence is subjected to a pure plane strain and the principal axes of the Reynolds stress tensor become those of the strain. This ‘oriented’ homogeneous turbulence is then submitted to a new strain the principal axes of which have a different orientation. We show that in such a situation it is possible to observe a transfer of energy from the fluctuating motion to the mean one. Such transfer is necessarily associated with a forced decay of the anisotropy of the motion. A detailed analysis of the reorientation of the principal axes of the Reynolds stress tensor in the frame of those of the second strain gives an explanation of the evolution of the principal axes of the Reynolds stress tensor in a shear flow.

scholarly journals Reynolds Stress Tensor Measurements in a Centrifugal Compressor Vaned Diffuser

1996 ◽  
Author(s):  
Ali Pinarbasi ◽  
Mark W. Johnson
Keyword(s):  
Stress Tensor ◽  
Reynolds Stress ◽  
Centrifugal Compressor ◽  
Significant Influence ◽  
Turbulence Models ◽  
Leading Edge ◽  
Exit Plane ◽  
Vaned Diffuser ◽  
Low Speed ◽  
Reynolds Stress Tensor

Measurements of the full Reynolds stress tensor have been made throughout the vaned diffuser of a low speed centrifugal compressor. Results are presented close to the impeller exit plane and the vane leading edge plane at three inter vane positions. The results show that the vanes have a significant influence on the flow in the vaneless space. The mixing out of the blade wakes is enhanced and hence the Reynolds stress levels drop rapidly between the impeller exit and the vane leading edge. The flow also exhibits high levels of anisotropicity, particularly at the mid-vane position. This suggests that standard turbulence models are inadequate for modelling these flows using CFD and full Reynolds stress turbulence models are required.

scholarly journals Kinetics of drying of basil leaves (Ocimum basilicum L.) in the infrared

2012 ◽  
Vol 16 (12) ◽  
pp. 1346-1352 ◽  
Author(s):  
Renata C. dos Reis ◽  
Ivano A. Devilla ◽  
Diego P. R. Ascheri ◽  
Ana C. O. Servulo ◽  
Athina B. M. Souza
Keyword(s):  
Experimental Data ◽  
Ocimum Basilicum ◽  
Coefficient Of Determination ◽  
Chisquare Test ◽  
The Mean ◽  
Drying Curves ◽  
The One ◽  
Increasing Temperature ◽  
Air Circulation ◽  
Kinetics Of

The objective of this paper was to model the drying curves of the leaves of basil (Ocimum basilicum L.) in the infrared at temperatures of 50, 60, 70 and 80 ºC and to evaluate the influence of drying temperature on the color of dried leaves. Drying was conducted in infrared dryer with temperature and greenhouse air circulation. Experimental data were fitted to eight mathematical models. The magnitude of the coefficient of determination (R²), the mean relative error (P), the estimated mean error (SE) and chisquare test (χ2) were used to verify the degree of fitness of the models. From the study it was concluded that: a) the behavior of the drying curves of basil leaves was similar to most agricultural products, the drying times in the infrared were less than the drying times in an oven with air circulation, b) the mathematical drying model proposed by Midilli et al. (2002) was the one which best adjusted to the experimental data, c) the diffusion coefficient ranged from 9.10 x 10-12 to 2.92 x 10-11 m² s-1 and d) the color of the samples was highly influenced by drying, becoming darker due to loss of chlorophyll with increasing temperature.

LES Investigation of Boussinesq Constitutive Relation Validity in a Corner Separation Flow

2018 ◽  
Author(s):  
Jean-François Monier ◽  
Nicolas Poujol ◽  
Mathieu Laurent ◽  
Feng Gao ◽  
Jérôme Boudet ◽  
...  
Keyword(s):  
Strain Rate ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Constitutive Relation ◽  
Strain Rate Tensor ◽  
Separation Flow ◽  
Compressor Cascade ◽  
Corner Separation ◽  
Reynolds Stress Tensor ◽  
Mean Strain

The present study aims at analysing the Boussinesq constitutive relation validity in a corner separation flow of a compressor cascade. The Boussinesq constitutive relation is commonly used in Reynolds-averaged Navier-Stokes (RANS) simulations for turbomachinery design. It assumes an alignment between the Reynolds stress tensor and the zero-trace mean strain-rate tensor. An indicator that measures the alignment between these tensors is used to test the validity of this assumption in a high fidelity large-eddy simulation. Eddy-viscosities are also computed using the LES database and compared. A large-eddy simulation (LES) of a LMFA-NACA65 compressor cascade, in which a corner separation is present, is considered as reference. With LES, both the Reynolds stress tensor and the mean strain-rate tensor are known, which allows the construction of the indicator and the eddy-viscosities. Two constitutive relations are evaluated. The first one is the Boussinesq constitutive relation, while the second one is the quadratic constitutive relation (QCR), expected to render more anisotropy, thus to present a better alignment between the tensors. The Boussinesq constitutive relation is rarely valid, but the QCR tends to improve the alignment. The improvement is mainly present at the inlet, upstream of the corner separation. At the outlet, the correction is milder. The eddy-viscosity built with the LES results are of the same order of magnitude as those built as the ratio of the turbulent kinetic energy k and the turbulence specific dissipation rate ω. They also show that the main impact of the QCR is to rotate the mean strain-rate tensor in order to realign it with the Reynolds stress tensor, without dilating it.

scholarly journals A Novel Simplification of the Reynolds-Chou-Navier-Stokes Turbulence Equations of Incompressible Flow

2018 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Velocity Field ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Incompressible Flow ◽  
Velocity Fluctuation ◽  
Explicit Representation ◽  
Navier Stokes ◽  
Mean Velocity ◽  
The Mean ◽  
Turbulence Formulations

Based on author's previous work [Sun, B. The Reynolds Navier-Stokes Turbulence Equations of Incompressible Flow Are Closed Rather Than Unclosed. Preprints 2018, 2018060461 (doi: 10.20944/preprints201806.0461.v1)], this paper proposed an explicit representation of velocity fluctuation and formulated the Reynolds stress tensor in terms of the mean velocity field. The proposed closed Reynolds Navier-Stokes turbulence formulations reveal that the mean vorticity is the key source of producing turbulence.

Sign in / Sign up

Export Citation Format

Share Document