scholarly journals An Intrinsic Formulation of Incompressible Navier-Stokes Turbulent Flow

2019 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Velocity Field ◽  
Turbulent Flow ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Velocity Fluctuation ◽  
Navier Stokes ◽  
Natural Consequence ◽  
Mean Velocity ◽  
Turbulence Transition ◽  
The Mean

This paper proposed an explicit and simple representation of velocity fluctuation and the Reynolds stress tensor in terms of the mean velocity field. The proposed turbulence equations are closed. The proposed formulations reveal that the mean vorticity is the key source of producing turbulence. It is found that there are no velocity fluctuation and turbulence if there were no vorticity. As a natural consequence, the laminar- turbulence transition condition was obtained in a rational way.

scholarly journals An Intrinsic Formulation of Incompressible Navier-Stokes Turbulent Flow

2018 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Velocity Field ◽  
Turbulent Flow ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Velocity Fluctuation ◽  
Navier Stokes ◽  
Natural Consequence ◽  
Mean Velocity ◽  
Turbulence Transition ◽  
The Mean

This paper proposed an explicit and simple representation of velocity fluctuation and the Reynolds stress tensor in terms of the mean velocity field. The proposed turbulence equations are closed. The proposed formulations reveal that the mean vorticity is the key source of producing turbulence. It is found that there are no velocity fluctuation and turbulence if there were no vorticity. As a natural consequence, the laminar- turbulence transition condition was obtained in a rational way.

scholarly journals An Intrinsic Formulation of Incompressible Navier-Stokes Turbulent Flow

2018 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Velocity Field ◽  
Turbulent Flow ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Velocity Fluctuation ◽  
Navier Stokes ◽  
Natural Consequence ◽  
Mean Velocity ◽  
Turbulence Transition ◽  
The Mean

This paper proposed an explicit and simple representation of velocity fluctuation and the Reynolds stress tensor in terms of the mean velocity field. The proposed turbulence equations are closed. The proposed formulations reveal that the mean vorticity is the key source of producing turbulence. It is found that there are no velocity fluctuation and turbulence if there were no vorticity. As a natural consequence, the laminar- turbulence transition condition was obtained in a rational way.

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.

scholarly journals Reynolds' Turbulence Solution

2021 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Stress Tensor ◽  
Reynolds Stress ◽  
Velocity Fluctuation ◽  
Turbulence Modeling ◽  
Stokes Equations ◽  
Symmetric Tensor ◽  
Navier Stokes ◽  
Difficult Situation ◽  
Velocity Fluctuations ◽  
Reynolds Stress Tensor

This study revisits the Reynolds-averaged Navier--Stokes equations (RANS) and finds that the existing literature is erroneous regarding the primary unknowns and the number of independent unknowns in the RANS. The literature claims that the Reynolds stress tensor has six independent unknowns, but in fact the six unknowns can be reduced to three that are functions of the three velocity fluctuation components, because the Reynolds stress tensor is simply an integration of a second-order dyadic tensor of flow velocity fluctuations rather than a general symmetric tensor. This difficult situation is resolved by returning to the time of Reynolds in 1895 and revisiting Reynolds' averaging formulation of turbulence. The study of turbulence modeling could focus on the velocity fluctuations instead of on the Reynolds stress. An advantage of modeling the velocity fluctuations is, from both physical and experimental perspectives, that the velocity fluctuation components are observable whereas the Reynolds stress tensor is not.

scholarly journals Closed integral-differential equations of incompressible Navier-Stokes turbulent flow

2018 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Stress Tensor ◽  
Reynolds Stress ◽  
Incompressible Flows ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Fluctuation Velocity ◽  
Reynolds Stress Tensor ◽  
Mean Pressure ◽  
Integral Differential Equations ◽  
Three Components

This paper showed that turbulence closure problem is not an issue at all. All mistakes in theliterature regarding the numbers of unknown quantities in the Reynolds turbulence equations stemfrom the misunderstandings of physics of the Reynolds stress tensor, i.e., all literature has statedthat the symmetric Reynolds stress tensor has six unknowns; however, it actually has only threeunknowns, i.e., the three components of fluctuation velocity. We showed the integral-differentialequations of the Reynolds mean and fluctuation equations have exactly eight equations, which equalto the numbers of quantities in total, namely, three components of mean velocity, three componentsof fluctuation velocity, one mean pressure and one fluctuation pressure. With this understanding,the closed Reynolds Navier-Stokes turbulence equations of incompressible flows were formulated.This study may help to solve the puzzle that has eluded scientists and mathematicians for centuries.

scholarly journals The Reynolds Navier-Stokes Turbulence Equations of Incompressible Flow Are Closed Rather Than Unclosed

2018 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Stress Tensor ◽  
Reynolds Stress ◽  
Incompressible Flow ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Fluctuation Velocity ◽  
Reynolds Stress Tensor ◽  
Mean Pressure ◽  
Integral Differential Equations ◽  
Three Components

This paper shown that turbulence closure problem is not an issue at all. All mistakes in the literature regarding the numbers of unknown quantities in the Reynolds turbulence equations stem from the misunderstandings of physics of the Reynolds stress tensor, i.e., all literatures have stated that the symmetric Reynolds stress tensor has six unknowns; however, it actually has only three unknowns, i.e., the three components of fluctuation velocity. We shown the integral-differential equations of the Reynolds mean and fluctuation equations have exactly eight equations, which equal to the numbers of quantities in total, namely, three components of mean velocity, three components of fluctuation velocity, one mean pressure and one fluctuation pressure. That is why we claim in this paper, that the Reynolds Navier-Stokes turbulence equations of incompressible flow are closed rather than unclosed. This study may help to solve the puzzle that has eluded scientists and mathematicians for centuries.

Turbulent Flow Through a Ducted Elbow and Plugged Tee Geometry: An Experimental and Numerical Study

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Andrew M. Bluestein ◽  
Ravon Venters ◽  
Douglas Bohl ◽  
Brian T. Helenbrook ◽  
Goodarz Ahmadi
Keyword(s):  
Turbulent Flow ◽  
Pressure Loss ◽  
Numerical Study ◽  
Velocity Profiles ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Flow Features ◽  
Reynolds Number Effects ◽  
The Mean ◽  
Rans Simulations

An experimental and computational comparison of the turbulent flow field for a sharp 90 deg elbow and plugged tee junction is presented. These are commonly used industrial geometries with the tee often retrofitted by plugging the straight exit to create an elbow. Mean and fluctuating velocities along the midplane were measured via two-dimensional (2D) particle image velocimetry (PIV), and the results were compared with the predictions of Reynolds-averaged Navier–Stokes (RANS) simulations for Reynolds numbers of 11,500 and 115,000. Major flow features of the elbow and plugged tee were compared using the mean velocity contours. Geometry effects and Reynolds number effects were studied by examining the mean and root-mean-square (RMS) fluctuating velocity profiles at six positions. Finally, the asymmetry of the flow as measured by the position of the centroid of the volumetric flux and pressure loss data were examined to quantify the streamwise evolution of the flow in the respective geometries. It was found that in both geometries there was a large recirculation zone in the downstream leg but the RANS simulations predicted an overly long recirculation which led to significantly different mean and fluctuating velocities in that region when compared to the experiments. Comparison of velocity profiles showed that both experiments and numerics agree in the fact that the turbulence intensities were greater at higher Re downstream of the vertical leg. Finally, it was shown that the plugged tee recovered its symmetry more rapidly and created less pressure loss than the elbow.

Turbulent rotating flow calculations: An assessment of two-equation anisotropic and Reynolds stress models

1998 ◽  
Vol 212 (3) ◽  
pp. 193-212 ◽  
Author(s):  
S P Yuan ◽  
R M C So
Keyword(s):  
Stress Tensor ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Dissipation Rate ◽  
Rotating Flow ◽  
Mean Flow ◽  
Mean Velocity ◽  
Anisotropic Stress ◽  
The Mean ◽  
Anisotropic Stress Tensor

The stress field in a rotating turbulent internal flow is highly anisotropic. This is true irrespective of whether the axis of rotation is aligned with or normal to the mean flow plane. Consequently, turbulent rotating flow is very difficult to model. This paper attempts to assess the relative merits of three different ways to account for stress anisotropies in a rotating flow. One is to assume an anisotropic stress tensor, another is to model the anisotropy of the dissipation rate tensor, while a third is to solve the stress transport equations directly. Two different near-wall two-equation models and one Reynolds stress closure are considered. All the models tested are asymptotically consistent near the wall. The predictions are compared with measurements and direct numerical simulation data. Calculations of turbulent flows with inlet swirl numbers up to 1.3, with and without a central recirculation, reveal that none of the anisotropic two-equation models tested is capable of replicating the mean velocity field at these swirl numbers. This investigation, therefore, indicates that neither the assumption of anisotropic stress tensor nor that of an anisotropic dissipation rate tensor is sufficient to model flows with medium to high rotation correctly. It is further found that, at very high rotation rates, even the Reynolds stress closure fails to predict accurately the extent of the central recirculation zone.

scholarly journals Revisiting the Reynolds-averaged Navier–Stokes equations

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 853-862
Author(s):  
Bohua Sun
Keyword(s):  
Stress Tensor ◽  
Reynolds Stress ◽  
Velocity Fluctuation ◽  
Stokes Equations ◽  
Symmetric Tensor ◽  
Navier Stokes ◽  
Difficult Situation ◽  
Velocity Fluctuations ◽  
Reynolds Stress Tensor ◽  
Reynolds Averaged Navier Stokes

Abstract This study revisits the Reynolds-averaged Navier–Stokes (RANS) equations and finds that the existing literature is erroneous regarding the primary unknowns and the number of independent unknowns in the RANS. The literature claims that the Reynolds stress tensor has six independent unknowns, but in fact the six unknowns can be reduced to three that are functions of the three velocity fluctuation components, because the Reynolds stress tensor is simply an integration of a second-order dyadic tensor of flow velocity fluctuations rather than a general symmetric tensor. This difficult situation is resolved by returning to the time of Reynolds in 1895 and revisiting Reynolds’ averaging formulation of turbulence. The study of turbulence modeling could focus on the velocity fluctuations instead of the Reynolds stress. An advantage of modeling the velocity fluctuations is, from both physical and experimental perspectives, that the velocity fluctuation components are observable whereas the Reynolds stress tensor is not.

scholarly journals The Reynolds Navier-Stokes Turbulence Equations of Incompressible Flow Are Closed Rather Than Unclosed

2018 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Stress Tensor ◽  
Reynolds Stress ◽  
Incompressible Flow ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Fluctuation Velocity ◽  
Reynolds Stress Tensor ◽  
Mean Pressure ◽  
Integral Differential Equations ◽  
Three Components

This paper shown that turbulence closure problem is not an issue at all. All mistakes in the literature regarding the numbers of unknown quantities in the Reynolds turbulence equations stem from the misunderstandings of physics of the Reynolds stress tensor, i.e., all literatures have stated that the symmetric Reynolds stress tensor has six unknowns; however, it actually has only three unknowns, i.e., the three components of fluctuation velocity. We shown the integral-differential equations of the Reynolds mean and fluctuation equations have exactly eight equations, which equal to the numbers of quantities in total, namely, three components of mean velocity, three components of fluctuation velocity, one mean pressure and one fluctuation pressure. That is why we claim in this paper, that the Reynolds Navier-Stokes turbulence equations of incompressible flow are closed rather than unclosed. This study may help to solve the puzzle that has eluded scientists and mathematicians for centuries.

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