A Note on the Empirical Constant in the Kolmogorov-Prandtl Eddy-Viscosity Expression

1975 ◽  
Vol 97 (3) ◽  
pp. 386-389 ◽  
Author(s):  
W. Rodi
Keyword(s):  
Experimental Data ◽  
Transport Equation ◽  
Reynolds Stress ◽  
Eddy Viscosity ◽  
Shear Layers ◽  
Empirical Constant ◽  
Empirical Factor

The transport equation for the Reynolds stress is simplified to yield the Kolmogorov-Prandtl eddy viscosity expression, and the conditions are studied under which the empirical factor cμ in this expression can be a constant. By reference to experimental data, it is shown that these conditions are not generally satisfied. The measured variation of cμ is given for various thin shear layers. Those flows are identified, which can be calculated with a constant value of cμ.

Numerical investigation of flow features in the vaneless region of a centrifugal pump by large eddy simulation

2018 ◽  
Vol 35 (1) ◽  
pp. 395-410 ◽  
Author(s):  
Xianbei Huang ◽  
Yaojun Li ◽  
Zhuqing Liu ◽  
Wei Yang
Keyword(s):  
Experimental Data ◽  
Transport Equation ◽  
Centrifugal Pump ◽  
Reynolds Stress ◽  
Pressure Pulsation ◽  
Third Order ◽  
Production Term ◽  
Content Type ◽  
Blade Passing Frequency ◽  
Rotor Stator Interaction

Purpose The purpose of this paper is to obtain a better understanding of the rotor–stator interaction in the vaneless region of a centrifugal pump. Design/methodology/approach A third-order sub-grid scale (SGS) model containing the rotation rate tensor named the dynamic cubic non-linear model (DCNM) is used for simulating the flow field in a centrifugal pump with a vaned diffuser. The pressure coefficient and velocity distributions are compared with the experimental data. Focusing on the vaneless region, the pressure pulsation, Reynolds stress pulsation and Reynolds stress transport equation are analyzed. Findings The comparison of the calculation results with the experimental data indicates that the DCNM can accurately capture the distributions of pressure and velocity in the vaneless region. Based on the instantaneous pressure signals, the pressure pulsation is analyzed to show that in the vaneless region, the dominant frequency near the impeller is twice the blade passing frequency, whereas it is equal to the blade passing frequency near the diffuser. Further exploration of the Reynolds stress pulsation shows the correlation between the two variables. Additionally, the extreme low frequency of Reynolds stress near the diffuser is found to be related to the rotation instability. To explore the turbulence characteristics in the vaneless region, the Reynolds stress transportation equation is studied. In the vaneless region, the rotation term of the Reynolds stress transport equation is negligible compared to the production term, although the rotation instability is obvious near the diffuser. The production of the Reynolds stress plays the role of redistributing the energy from the uu component to the vv component, except for the region near the impeller outlet. Originality/value The third-order SGS model DCNM has proved to be promising in simulating the rotor–stator interaction. The analysis of the rotation instability and the Reynolds stress transport equation shed light on the further understanding of the rotor–stator interaction.

scholarly journals Rotating Flow and Heat Transfer in Cylindrical Cavities With Radial Inflow

2012 ◽  
Author(s):  
B. G. Vinod Kumar ◽  
John W. Chew ◽  
Nicholas J. Hills
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Reynolds Stress ◽  
Integral Method ◽  
Eddy Viscosity ◽  
Reynolds Stress Model ◽  
Stress Model ◽  
Rotating Disc ◽  
Flow And Heat Transfer ◽  
Viscosity Models

Design and optimization of an efficient internal air system of a gas turbine requires thorough understanding of the flow and heat transfer in rotating disc cavities. The present study is devoted to numerical modelling of flow and heat transfer in a cylindrical cavity with radial inflow and comparison with the available experimental data. The simulations are carried out with axi-symmetric and 3-D sector models for various inlet swirl and rotational Reynolds numbers upto 2.1×106. The pressure coefficients and Nusselt numbers are compared with the available experimental data and integral method solutions. Two popular eddy viscosity models, the Spalart-Allmaras and the k-ε, and a Reynolds stress model have been used. For cases with particularly strong vortex behaviour the eddy viscosity models show some shortcomings with the Spalart-Allmaras model giving slightly better results than the k-ε model. Use of the Reynolds stress model improved the agreement with measurements for such cases. The integral method results are also found to agree well with the measurements.

scholarly journals Modeling of Flow Transition Using an Intermittency Transport Equation

2000 ◽  
Vol 122 (2) ◽  
pp. 273-284 ◽  
Author(s):  
Y. B. Suzen ◽  
P. G. Huang
Keyword(s):  
Experimental Data ◽  
Transport Equation ◽  
Eddy Viscosity ◽  
Test Cases ◽  
Flow Transition ◽  
Transitional Flows ◽  
Intermittent Behavior ◽  
Wall Flows ◽  
Sst Model ◽  
Intermittency Factor

A new transport equation for intermittency factor is proposed to model transitional flows. The intermittent behavior of the transitional flows is incorporated into the computations by modifying the eddy viscosity, μt, obtainable from a turbulence model, with the intermittency factor, γ:μt*=γμt. In this paper, Menter’s SST model is employed to compute μt and other turbulent quantities. The proposed intermittency transport equation can be considered as a blending of two models—Steelant and Dick and Cho and Chung. The former was proposed for near-wall flows and was designed to reproduce the streamwise variation of the intermittency factor in the transition zone following Dhawan and Narasimha correlation and the latter was proposed for free shear flows and a realistic cross-stream variation of the intermittency profile was reproduced. The new model was used to predict the T3 series experiments assembled by Savill including flows with different freestream turbulence intensities and two pressure-gradient cases. For all test cases good agreements between the computed results and the experimental data were observed. [S0098-2202(00)02302-6]

scholarly journals Rotating Flow and Heat Transfer in Cylindrical Cavities With Radial Inflow

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
B. G. Vinod Kumar ◽  
John W. Chew ◽  
Nicholas J. Hills
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Reynolds Stress ◽  
Integral Method ◽  
Eddy Viscosity ◽  
Reynolds Stress Model ◽  
Stress Model ◽  
Rotating Disc ◽  
Flow And Heat Transfer ◽  
Viscosity Models

The design and optimization of an efficient internal air system of a gas turbine requires a thorough understanding of the flow and heat transfer in rotating disc cavities. The present study is devoted to the numerical modeling of flow and heat transfer in a cylindrical cavity with radial inflow and a comparison with the available experimental data. The simulations are carried out with axisymmetric and 3-D sector models for various inlet swirl and rotational Reynolds numbers up to 1.2 × 106. The pressure coefficients and Nusselt numbers are compared with the available experimental data and integral method solutions. Two popular eddy viscosity models, the Spalart–Allmaras and the k-ɛ, and a Reynolds stress model have been used. For cases with particularly strong vortex behavior the eddy viscosity models show some shortcomings, with the Spalart–Allmaras model giving slightly better results than the k-ɛ model. Use of the Reynolds stress model improved the agreement with measurements for such cases. The integral method results are also found to agree well with the measurements.

scholarly journals Performance Assessment of Reynolds Stress and Eddy Viscosity Models on a Transitional DCA Compressor Blade

Aerospace ◽  
2018 ◽  
Vol 5 (4) ◽  
pp. 102
Author(s):  
Zinon Vlahostergios
Keyword(s):  
Experimental Data ◽  
Flow Field ◽  
Performance Assessment ◽  
Reynolds Stress ◽  
Eddy Viscosity ◽  
Stokes Equations ◽  
Turbulence Models ◽  
Compressor Blade ◽  
Boundary Layer Transition ◽  
Transitional Flow

In the current work a detailed investigation and a performance assessment of two eddy viscosity and two Reynolds stress turbulence models for modelling the transitional flow on a double circular arc (DCA) compressor blade is presented. The investigation is focused on the comparison of the obtained computational results with available experimental data for a specific DCA compressor blade cascade which can be found in the European Research Community on Flow, Turbulence and Combustion (ERCOFTAC) experimental database. The examined flow field is very challenging for the performance assessment of the turbulence models. The blade inlet angle departs +5° from the compressor blade design conditions resulting in a complex flow field having large regions of boundary layer transition both on the suction and pressure sides of the blade with the presence of an unsteady wake. The presented results include velocity and turbulence intensity distributions along the pressure, the suction sides, and the wake region of the blade. From the comparison with the available experimental data, it is evident that in order to accurately compute such complex velocity and turbulence fields that are met in aero engine components (compressors and turbines), it is obligatory to use more advanced turbulence models with the Unsteady Reynolds Averaged Navier Stokes Equations (URANS) adoption, or other simulation and hybrid methodologies which require unsteady calculations.

Modeling Separation-Induced Transition Using a Non-Linear Three Equation Turbulence Model and a Reynolds Stress Turbulence Model

2010 ◽  
Author(s):  
Zinon Vlahostergios ◽  
Kyros Yakinthos
Keyword(s):  
Transport Equation ◽  
Reynolds Stress ◽  
Turbulence Model ◽  
Eddy Viscosity ◽  
Turbulence Models ◽  
Viscosity Model ◽  
Transitional Flows ◽  
Eddy Viscosity Model ◽  
Non Linear ◽  
Stress Models

This paper presents an effort to model separation-induced transition on a flat plate with a semi-circular leading edge, by using two advanced turbulence models, the three equation non-linear model k-ε-A2 of Craft et al. [16] and the Reynolds-stress model of Craft [13]. The mechanism of the transition is governed by the different inlet velocity and turbulence intensity conditions, which lead to different recirculation bubbles and different transition onset points for each case. The use of advanced turbulence models in predicting the development of transitional flows has shown, in past studies, good perspectives. The k-ε-A2 model uses an additional transport equation for the A2 Reynolds stress invariant and it is an improvement of Craft et al. [12] non-linear eddy viscosity model. The use of the third transport equation gives improved results in the prediction of the longitudinal Reynolds stress distributions and especially, in flows where transitional phenomena may occur. Although this model is a pure eddy-viscosity model, it borrows many aspects from the more complex Reynolds-stress models. On the other hand, the use of an advanced Reynolds-stress turbulence model, such as the one of Craft [13], can predict many complex flows and there are indications that it can be applied to transitional flows also, since the crucial terms of Reynolds stress generation are computed exactly and normal stress anisotropy is resolved. The model of Craft [13], overcomes the drawbacks of the common used Reynolds-stress models regarding the computation of wall-normal distances and vectors in order to account for wall proximity effects. Instead of these quantities, it employs “normalized turbulence lengthscale gradients” which give the ability to identify the presence of strong inhomogeneity in a flow development, in an easier way. The final results of both turbulence models showed acceptable agreement with the experimental data. In this work it is shown that there is a good potential to model separation-induced transitional flows, with advanced turbulence modeling without any additional use of ad-hoc modifications or additional equations, based on various transition models.

Comparison of LES of Steady Transitional Flow in an Idealized Stenosed Axisymmetric Artery Model With a RANS Transitional Model

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
F. P. P. Tan ◽  
N. B. Wood ◽  
G. Tabor ◽  
X. Y. Xu
Keyword(s):  
Experimental Data ◽  
Turbulence Intensity ◽  
Eddy Viscosity ◽  
Flow Analysis ◽  
Wall Turbulence ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Turbulence Structures ◽  
Eddy Simulation ◽  
Accurate Treatment

In this study, two different turbulence methodologies are investigated to predict transitional flow in a 75% stenosed axisymmetric experimental arterial model and in a slightly modified version of the model with an eccentric stenosis. Large eddy simulation (LES) and Reynolds-averaged Navier–Stokes (RANS) methods were applied; in the LES simulations eddy viscosity subgrid-scale models were employed (basic and dynamic Smagorinsky) while the RANS method involved the correlation-based transitional version of the hybrid k-ε/k-ω flow model. The RANS simulations used 410,000 and 820,000 element meshes for the axisymmetric and eccentric stenoses, respectively, with y+ less than 2 viscous wall units for the boundary elements, while the LES used 1,200,000 elements with y+ less than 1. Implicit filtering was used for LES, giving an overlap between the resolved and modeled eddies, ensuring accurate treatment of near wall turbulence structures. Flow analysis was carried out in terms of vorticity and eddy viscosity magnitudes, velocity, and turbulence intensity profiles and the results were compared both with established experimental data and with available direct numerical simulations (DNSs) from the literature. The simulation results demonstrated that the dynamic Smagorinsky LES and RANS transitional model predicted fairly comparable velocity and turbulence intensity profiles with the experimental data, although the dynamic Smagorinsky model gave the best overall agreement. The present study demonstrated the power of LES methods, although they were computationally more costly, and added further evidence of the promise of the RANS transition model used here, previously tested in pulsatile flow on a similar model. Both dynamic Smagorinsky LES and the RANS model captured the complex transition phenomena under physiological Reynolds numbers in steady flow, including separation and reattachment. In this respect, LES with dynamic Smagorinsky appeared more successful than DNS in replicating the axisymmetric experimental results, although inflow conditions, which are subject to caveats, may have differed. For the eccentric stenosis, LES with Smagorinsky coefficient of 0.13 gave the closest agreement with DNS despite the known shortcomings of fixed coefficients. The relaminarization as the flow escaped the influence of the stenosis was amply demonstrated in the simulations, graphically so in the case of LES.

scholarly journals Reynolds averaged turbulence modelling using deep neural networks with embedded invariance

2016 ◽  
Vol 807 ◽  
pp. 155-166 ◽  
Author(s):  
Julia Ling ◽  
Andrew Kurzawski ◽  
Jeremy Templeton
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Reynolds Stress ◽  
Network Architecture ◽  
Eddy Viscosity ◽  
Deep Neural Networks ◽  
Test Cases ◽  
Neural Network Architecture ◽  
Stress Anisotropy ◽  
Anisotropy Tensor

There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property. The Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.

Gas transport in a model derived from Hansen-Ampaya anatomical data of the human lung

1976 ◽  
Vol 41 (1) ◽  
pp. 115-119 ◽  
Author(s):  
M. Paiva ◽  
L. M. Lacquet ◽  
L. P. van der Linden
Keyword(s):  
Experimental Data ◽  
Transport Equation ◽  
Satisfactory Agreement ◽  
Dead Space ◽  
Empirical Formula ◽  
Molecular Diffusion ◽  
Human Lung ◽  
Gas Transport ◽  
Gas Mixing ◽  
Anatomical Data

The anatomical data of the human lung published by Hansen and Ampaya are used in a model of gas transport in the lung. The Bohr dead space is calculated from solutions of a transport equation where diffusivity is given by an empirical formula obtained by Sherer et al. A satisfactory agreement is found with experimental data obtained from simultaneous washouts of H2 and SF6 for respiratory frequencies ranging between 15 and 60 min-1 and tidal volumes between 200 and 1,800 ml. The results support the idea that molecular diffusion is the main but not the only physical phenomenom which intervenes in gas mixing during breathing.

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