scholarly journals Deriving Six Components of Reynolds Stress Tensor from Single-ADCP Data

Water ◽  
2021 ◽  
Vol 13 (17) ◽  
pp. 2389
Author(s):  
Sergey Bogdanov ◽  
Roman Zdorovennov ◽  
Nikolay Palshin ◽  
Galina Zdorovennova
Keyword(s):  
Stress Tensor ◽  
Reynolds Stress ◽  
Energy Dissipation Rate ◽  
New Method ◽  
Shear Stresses ◽  
Depth Range ◽  
Mean Velocity ◽  
Reynolds Stress Tensor ◽  
Adcp Data ◽  
Acoustic Doppler Current Profilers

Acoustic Doppler current profilers (ADCP) are widely used in geophysical studies for mean velocity profiling and calculation of energy dissipation rate. On the other hand, the estimation of turbulent stresses from ADCP data still remains challenging. With the four-beam version of the device, only two shear stresses are derivable; and even for the five-beam version (Janus+), the calculation of the full Reynolds stress tensor is problematic currently. The known attempts to overcome the problem are based on the “coupled ADCP” experimental setup and include some hard restrictions, not to mention the essential complexity of performing experiments. In this paper, a new method is presented which allows to derive the stresses from single-ADCP data. Its essence is that interbeam correlations are taken into account as producing the missing equations for stresses. This method is applicable only for the depth range, for which the distance between the beams is comparable to the scales, where the turbulence is locally isotropic and homogeneous. The validation of this method was carried out for convectively-mixed layer in a boreal ice-covered lake. The results of computations turned out to be physically sustainable in the sense that realizability conditions were basically fulfilled. The additional verification was carried out by comparing the results, obtained by the new method and “coupled ADCPs” one.

Turbulent Friction Velocity Calculated from the Reynolds Stress Tensor

2018 ◽  
Vol 75 (4) ◽  
pp. 1029-1043 ◽  
Author(s):  
Cheryl Klipp
Keyword(s):  
Stress Tensor ◽  
Reynolds Stress ◽  
Standard Method ◽  
Friction Velocity ◽  
Full Range ◽  
New Method ◽  
Turbulent Friction ◽  
Reynolds Stress Tensor ◽  
Using Data ◽  
Standard Calculation

Abstract To eliminate the need to correct for instrument tilt, a process that can be problematic in complex terrain, a new way to calculate the turbulent friction velocity is derived based on invariants of the Reynolds stress tensor. In utilizing Reynolds stress tensor invariants, this new method eliminates the need for tilt correction. The friction velocity is calculated without any reference to the wall normal or other terrain features making this method a candidate for future use with data from complex environments. Since this new method is derived from a different theoretical basis than the well-established methods, it is evaluated using data from flat terrain to compare the new method to the standard calculation method, treated here as a baseline truth. For neutral thermal stratification the values calculated using the new method nearly identically match the control values calculated using the standard method. Although for nonneutral stratification the values calculated using the new method do not closely match the values calculated using the standard method, the new friction velocity produces the same dimensionless shear versus dimensionless height Monin–Obukhov scaling relationship over the full range of stabilities as does the standard friction velocity.

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.

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.

Law of bounded dissipation and its consequences in turbulent wall flows

2021 ◽  
Vol 933 ◽  
Author(s):  
Xi Chen ◽  
Katepalli R. Sreenivasan
Keyword(s):  
Dissipation Rate ◽  
Scaling Law ◽  
Random Variable ◽  
Energy Dissipation Rate ◽  
Shear Stresses ◽  
Mean Velocity ◽  
Wall Flows ◽  
Maximum Value ◽  
Turbulent Wall ◽  
Promising Perspective

The dominant paradigm in turbulent wall flows is that the mean velocity near the wall, when scaled on wall variables, is independent of the friction Reynolds number $Re_\tau$ . This paradigm faces challenges when applied to fluctuations but has received serious attention only recently. Here, by extending our earlier work (Chen & Sreenivasan, J. Fluid Mech., vol. 908, 2021, p. R3) we present a promising perspective, and support it with data, that fluctuations displaying non-zero wall values, or near-wall peaks, are bounded for large values of $Re_\tau$ , owing to the natural constraint that the dissipation rate is bounded. Specifically, $\varPhi _\infty - \varPhi = C_\varPhi \,Re_\tau ^{-1/4},$ where $\varPhi$ represents the maximum value of any of the following quantities: energy dissipation rate, turbulent diffusion, fluctuations of pressure, streamwise and spanwise velocities, squares of vorticity components, and the wall values of pressure and shear stresses; the subscript $\infty$ denotes the bounded asymptotic value of $\varPhi$ , and the coefficient $C_\varPhi$ depends on $\varPhi$ but not on $Re_\tau$ . Moreover, there exists a scaling law for the maximum value in the wall-normal direction of high-order moments, of the form $\langle \varphi ^{2q}\rangle ^{{1}/{q}}_{max}= \alpha _q-\beta _q\,Re^{-1/4}_\tau$ , where $\varphi$ represents the streamwise or spanwise velocity fluctuation, and $\alpha _q$ and $\beta _q$ are independent of $Re_\tau$ . Excellent agreement with available data is observed. A stochastic process for which the random variable has the form just mentioned, referred to here as the ‘linear $q$ -norm Gaussian’, is proposed to explain the observed linear dependence of $\alpha _q$ on $q$ .

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.

Experimental study of particle-driven secondary flow in turbulent pipe flows

2012 ◽  
Vol 709 ◽  
pp. 1-36 ◽  
Author(s):  
R. J. Belt ◽  
A. C. L. M. Daalmans ◽  
L. M. Portela
Keyword(s):  
Turbulent Flow ◽  
Secondary Flow ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Cross Section ◽  
Circular Pipe ◽  
Horizontal Pipe ◽  
Pipe Cross Section ◽  
Reynolds Stress Tensor ◽  
Pipe Flows

AbstractIn fully developed single-phase turbulent flow in straight pipes, it is known that mean motions can occur in the plane of the pipe cross-section, when the cross-section is non-circular, or when the wall roughness is non-uniform around the circumference of a circular pipe. This phenomenon is known as secondary flow of the second kind and is associated with the anisotropy in the Reynolds stress tensor in the pipe cross-section. In this work, we show, using careful laser Doppler anemometry experiments, that secondary flow of the second kind can also be promoted by a non-uniform non-axisymmetric particle-forcing, in a fully developed turbulent flow in a smooth circular pipe. In order to isolate the particle-forcing from other phenomena, and to prevent the occurrence of mean particle-forcing in the pipe cross-section, which could promote a different type of secondary flow (secondary flow of the first kind), we consider a simplified well-defined situation: a non-uniform distribution of particles, kept at fixed positions in the ‘bottom’ part of the pipe, mimicking, in a way, the particle or droplet distribution in horizontal pipe flows. Our results show that the particles modify the turbulence through ‘direct’ effects (associated with the wake of the particles) and ‘indirect’ effects (associated with the global balance of momentum and the turbulence dynamics). The resulting anisotropy in the Reynolds stress tensor is shown to promote four secondary flow cells in the pipe cross-section. We show that the secondary flow is determined by the projection of the Reynolds stress tensor onto the pipe cross-section. In particular, we show that the direction of the secondary flow is dictated by the gradients of the normal Reynolds stresses in the pipe cross-section, $\partial {\tau }_{rr} / \partial r$ and $\partial {\tau }_{\theta \theta } / \partial \theta $. Finally, a scaling law is proposed, showing that the particle-driven secondary flow scales with the root of the mean particle-forcing in the axial direction, allowing us to estimate the magnitude of the secondary flow.

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