Reappraisal of the velocity derivative flatness factor in various turbulent flows

2018 ◽  
Vol 847 ◽  
pp. 244-265 ◽  
Author(s):  
S. L. Tang ◽  
R. A. Antonia ◽  
L. Djenidi ◽  
L. Danaila ◽  
Y. Zhou
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Scale Effects ◽  
Nauk Sssr ◽  
Grid Turbulence ◽  
Similarity Hypothesis ◽  
Reynolds Number Effect ◽  
Pressure Diffusion ◽  
Velocity Derivative

We first analytically show, starting with the Navier–Stokes equations, that the value of the derivative flatness is controlled by pressure diffusion of energy, viscous destructive effects and large-scale effects (decay and/or production). The latter two terms tend to zero when the Taylor-microscale Reynolds number $Re_{\unicode[STIX]{x1D706}}$ is sufficiently large. We argue that the pressure-diffusion term should also tend to a constant at large $Re_{\unicode[STIX]{x1D706}}$. Available data for the velocity derivative flatness, $F$, in different turbulent flows are re-examined and interpreted in the light of the finite-Reynolds-number effect. It is found that $F$ can differ from flow to flow at moderate $Re_{\unicode[STIX]{x1D706}}$; for a given flow, $F$ may also depend on the initial conditions. The data for $F$ in various flows, e.g. along the axis in the far field of plane and circular jets, and grid turbulence, show that it approaches a constant, with a value slightly larger than 10, when $Re_{\unicode[STIX]{x1D706}}$ is sufficiently large. This behaviour for $F$ is supported, at least qualitatively, by our analytical considerations. The constancy of $F$ at large $Re_{\unicode[STIX]{x1D706}}$ violates the refined similarity hypothesis introduced by Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82–85) to account for the intermittency of the energy dissipation rate. It is not, however, inconsistent with Kolmogorov’s original similarity hypothesis (Dokl. Akad. Nauk SSSR, vol. 30, 1941, pp. 299–303), although we contend that the power-law relation $F\sim Re_{\unicode[STIX]{x1D706}}^{\unicode[STIX]{x1D6FC}_{4}}$ (Kolmogorov 1962), which is widely accepted in the literature, has in reality been almost invariably used to ‘model’ the finite-Reynolds-number effect for the laboratory data and has been strongly influenced by the weighting given to the atmospheric surface layer data. The inclusion of the latter data has misled previous investigations of how $F$ varies with $Re_{\unicode[STIX]{x1D706}}$.

scholarly journals Boundedness of the velocity derivative skewness in various turbulent flows

2015 ◽  
Vol 781 ◽  
pp. 727-744 ◽  
Author(s):  
R. A. Antonia ◽  
S. L. Tang ◽  
L. Djenidi ◽  
L. Danaila
Keyword(s):  
Turbulent Flows ◽  
Nauk Sssr ◽  
Numerical Data ◽  
Universal Constant ◽  
Energy Dissipation Rate ◽  
Small Scale ◽  
Grid Turbulence ◽  
Similarity Hypothesis ◽  
Velocity Derivative ◽  
Scale Turbulence

The variation of $S$, the velocity derivative skewness, with the Taylor microscale Reynolds number $\mathit{Re}_{{\it\lambda}}$ is examined for different turbulent flows by considering the locally isotropic form of the transport equation for the mean energy dissipation rate $\overline{{\it\epsilon}}_{iso}$. In each flow, the equation can be expressed in the form $S+2G/\mathit{Re}_{{\it\lambda}}=C/\mathit{Re}_{{\it\lambda}}$, where $G$ is a non-dimensional rate of destruction of $\overline{{\it\epsilon}}_{iso}$ and $C$ is a flow-dependent constant. Since $2G/\mathit{Re}_{{\it\lambda}}$ is found to be very nearly constant for $\mathit{Re}_{{\it\lambda}}\geqslant 70$, $S$ should approach a universal constant when $\mathit{Re}_{{\it\lambda}}$ is sufficiently large, but the way this constant is approached is flow dependent. For example, the approach is slow in grid turbulence and rapid along the axis of a round jet. For all the flows considered, the approach is reasonably well supported by experimental and numerical data. The constancy of $S$ at large $\mathit{Re}_{{\it\lambda}}$ has obvious ramifications for small-scale turbulence research since it violates the modified similarity hypothesis introduced by Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82–85) but is consistent with the original similarity hypothesis (Kolmogorov, Dokl. Akad. Nauk SSSR, vol. 30, 1941, pp. 299–303).

Parameter Extension Simulation of Turbulent Flows in a Compressor Cascade With a High Reynolds Number

2020 ◽  
Author(s):  
Yan Jin
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Simulation Method ◽  
Potential Method ◽  
Navier Stokes ◽  
Reference Solution ◽  
Compressor Cascade ◽  
High Reynolds

Abstract The turbulent flow in a compressor cascade is calculated by using a new simulation method, i.e., parameter extension simulation (PES). It is defined as the calculation of a turbulent flow with the help of a reference solution. A special large-eddy simulation (LES) method is developed to calculate the reference solution for PES. Then, the reference solution is extended to approximate the exact solution for the Navier-Stokes equations. The Richardson extrapolation is used to estimate the model error. The compressor cascade is made of NACA0065-009 airfoils. The Reynolds number 3.82 × 105 and the attack angles −2° to 7° are accounted for in the study. The effects of the end-walls, attack angle, and tripping bands on the flow are analyzed. The PES results are compared with the experimental data as well as the LES results using the Smagorinsky, k-equation and WALE subgrid models. The numerical results show that the PES requires a lower mesh resolution than the other LES methods. The details of the flow field including the laminar-turbulence transition can be directly captured from the PES results without introducing any additional model. These characteristics make the PES a potential method for simulating flows in turbomachinery with high Reynolds numbers.

scholarly journals Reynolds number effect on the velocity derivative flatness factor

2018 ◽  
Vol 856 ◽  
pp. 426-443 ◽  
Author(s):  
M. Meldi ◽  
L. Djenidi ◽  
R. Antonia
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Nauk Sssr ◽  
Quantitative Agreement ◽  
Homogeneous Isotropic Turbulence ◽  
Simulation Data ◽  
Akad Nauk Sssr ◽  
Analytic Expression ◽  
Velocity Derivative ◽  
Flatness Factor

This paper investigates the effect of a finite Reynolds number (FRN) on the flatness factor ($F$) of the velocity derivative in decaying homogeneous isotropic turbulence by applying the eddy damped quasi-normal Markovian (EDQNM) method to calculate all terms in an analytic expression for $F$ (Djenidi et al., Phys. Fluids, vol. 29 (5), 2017b, 051702). These terms and hence $F$ become constant when the Taylor microscale Reynolds number, $Re_{\unicode[STIX]{x1D706}}$ exceeds approximately $10^{4}$. For smaller values of $Re_{\unicode[STIX]{x1D706}}$, $F$, like the skewness $-S$, increases with $Re_{\unicode[STIX]{x1D706}}$; this behaviour is in quantitative agreement with experimental and direct numerical simulation data. These results indicate that one must first ensure that $Re_{\unicode[STIX]{x1D706}}$ is large enough for the FRN effect to be negligibly small before the hypotheses of Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941a, pp. 301–305; Dokl. Akad. Nauk SSSR, vol. 32, 1941b, pp. 16–18; J. Fluid Mech., vol. 13, 1962, pp. 82–85) can be assessed unambiguously. An obvious implication is that results from experiments and direct numerical simulations for which $Re_{\unicode[STIX]{x1D706}}$ is well below $10^{4}$ may not be immune from the FRN effect. Another implication is that a power-law increase of $F$ with respect to $Re_{\unicode[STIX]{x1D706}}$, as suggested by the Kolmogorov 1962 theory, is not tenable when $Re_{\unicode[STIX]{x1D706}}$ is large enough.

scholarly journals The emergence of localized vortex–wave interaction states in plane Couette flow

2013 ◽  
Vol 721 ◽  
pp. 58-85 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall ◽  
Andrew Walton
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
High Reynolds Number ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Critical Layer ◽  
Navier Stokes ◽  
Turbulent Spots ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractThe recently understood relationship between high-Reynolds-number vortex–wave interaction theory and computationally generated self-sustaining processes provides a possible route to an understanding of some of the underlying structures of fully turbulent flows. Here vortex–wave interaction (VWI) theory is used in the long streamwise wavelength limit to continue the development found at order-one wavelengths by Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). The asymptotic description given reduces the Navier–Stokes equations to the so-called boundary-region equations, for which we find equilibrium states describing the change in the VWI as the wavelength of the wave increases from $O(h)$ to $O(Rh)$, where $R$ is the Reynolds number and $2h$ is the depth of the channel. The reduced equations do not include the streamwise pressure gradient of the perturbation or the effect of streamwise diffusion of the wave–vortex states. The solutions we calculate have an asymptotic error proportional to ${R}^{- 2} $ when compared to the full Navier–Stokes equations. The results found correspond to the minimum drag configuration for VWI states and might therefore be of relevance to the control of turbulent flows. The key feature of the new states discussed here is the thickening of the critical layer structure associated with the wave part of the flow to completely fill the channel, so that the roll part of the flow is driven throughout the flow rather than as in Hall & Sherwin as a stress discontinuity across the critical layer. We identify a critical streamwise wavenumber scaling, which, when approached, causes the flow to localize and take on similarities with computationally generated or experimentally observed turbulent spots. In effect, the identification of this critical wavenumber for a given value of the assumed high Reynolds number fixes a minimum box length necessary for the emergence of localized structures. Whereas nonlinear equilibrium states of the Navier–Stokes equations are thought to form a backbone on which turbulent flows hang, our results suggest that the localized states found here might play a related role for turbulent spots.

Hot-Wire Measurements in a Plane Turbulent Jet

1965 ◽  
Vol 32 (4) ◽  
pp. 721-734 ◽  
Author(s):  
Gunnar Heskestad
Keyword(s):  
Reynolds Number ◽  
Energy Balance ◽  
Turbulent Jet ◽  
Turbulent Intensity ◽  
Turbulent Motion ◽  
Hot Wire ◽  
Reynolds Number Effect ◽  
Mach Numbers ◽  
Velocity Derivative ◽  
Flatness Factor

Results from hot-wire measurements in a plane turbulent jet of air are reported. The jet was found to be approximately self-preserving sufficiently far downstream where measurements of intermittency and data for calculating the energy balance of the turbulent motion were obtained. Measurements were also made of the effect of the jet speed (assumed equivalent to a Reynolds-number effect for the low Mach numbers used) on the centerline development of turbulent intensity and the flatness factor of the velocity derivative at a fixed downstream centerline location.

Turbulent Flow in Two-Inlet Channels

1993 ◽  
Vol 115 (4) ◽  
pp. 638-645 ◽  
Author(s):  
Hsiao C. Kao
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
High Reynolds Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Flow Properties ◽  
Navier Stokes Equations ◽  
High Reynolds ◽  
Inflow Conditions ◽  
Number Form

The problem of turbulent flows in two-inlet channels has been studied numerically by solving the Reynolds-averaged Navier-Stokes equations with the k–ε model in a mapped domain. Both the high Reynolds number and the low Reynolds number form were used for this purpose. In general, the former predicts a weaker and smaller recirculation zone than the latter. Comparisons with experimental data, when applicable, were also made. The bulk of the present computations used, however, the high Reynolds number form to correlate different geometries and inflow conditions with the flow properties after turning.

Large Eddy Simulation of a Free Circular Jet

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Trushar B. Gohil ◽  
Arun K. Saha ◽  
K. Muralidhar
Keyword(s):  
Reynolds Number ◽  
Large Eddy Simulation ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Experimental Results ◽  
Entrainment Rate ◽  
Smagorinsky Model ◽  
Potential Core ◽  
Eddy Simulation ◽  
Large Eddy

A large eddy simulation (LES) of an incompressible spatially developing circular jet at a Reynolds number of 10,000 is performed. The shear-improved Smagorinsky model (Lévêque et al., 2007, “A Shear-Improved Smagorinsky Model for the Large-Eddy Simulation of Wall-Bounded Turbulent Flows,” J. Fluid Mech., 570, pp. 491–502) is used for the resolution of the subgrid stress tensor within the filtered three-dimensional unsteady Navier–Stokes equations. Higher-order spatial and temporal discretization schemes are used for capturing the details of the turbulent flow field. With the help of instantaneous and time-averaged flow data, the spatial transition from the laminar state to the turbulent is analyzed. Flow structures are visualized using isosurfaces of the Q-criterion. Instantaneous flow patterns show single tearing and multiple pairing processes. Tracing individual vortex rings over a longer time period, a detailed understanding of the vortex interaction is revealed. The observed trends and the length of the potential core are in conformity with the findings of earlier experiments. The time-averaged axial velocity profile shows that the jet attains self-similarity and the computed profile matches well with the experimental results of Hussein et al. (1994, “Velocity Measurements in a High-Reynolds-Number, Momentum-Conserving, Axisymmetric, Turbulent Jet,” J. Fluid Mech., 258, pp. 31–75). The centerline decay of the velocity and entrainment rate are in agreement with published experiments. The Reynolds stress components u'u'¯, v'v'¯, and u'v'¯ and the third-order velocity moment are in good agreement with thr experimental results, thus confirming the validity of the present simulation.

scholarly journals The effort of increasing Reynolds number in POD-Galerkin Reduced Order Methods: from laminar to turbulent flows

2018 ◽  
Author(s):  
Shafqat Ali ◽  
Saddam Hijazi ◽  
Sokratia Georgaka ◽  
Francesco Ballarin ◽  
Giovanni Stabile ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Finite Element ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Reduced Order ◽  
Volume Method ◽  
Reduced Order Methods

We present different strategies to be able to increase Reynolds number in Reduced Order Methods (ROMs), from laminar to turbulent flows, in the context of the incompressible parametrised Navier-Stokes equations. The proposed methodologies are based on different full order discretisation techniques: the finite element method and the finite volume method. For what concerns finite element full order discretisations which in this work aim to be used from low to moderate Reynolds numbers the

scholarly journals Intermittency in solutions of the three-dimensional Navier–Stokes equations

2003 ◽  
Vol 478 ◽  
pp. 227-235 ◽  
Author(s):  
J. D. GIBBON ◽  
Charles R. DOERING
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Average Width ◽  
Binary Character ◽  
Spatio Temporal ◽  
High Reynolds

Dissipation-range intermittency was first observed by Batchelor & Townsend (1949) in high Reynolds number turbulent flows. It typically manifests itself in spatio-temporal binary behaviour which is characterized by long, quiescent periods in the signal which are interrupted by short, active ‘events’ during which there are large excursions away from the average. It is shown that Leray's weak solutions of the three-dimensional incompressible Navier–Stokes equations can have this binary character in time. An estimate is given for the widths of the short, active time intervals, which decreases with the Reynolds number. In these ‘bad’ intervals singularities are still possible. However, the average width of a ‘good’ interval, where no singularities are possible, increases with the Reynolds number relative to the average width of a bad interval.

scholarly journals Velocity and temperature derivatives in high-Reynolds-number turbulent flows in the atmospheric surface layer. Part 1. Facilities, methods and some general results

2007 ◽  
Vol 589 ◽  
pp. 57-81 ◽  
Author(s):  
G. GULITSKI ◽  
M. KHOLMYANSKY ◽  
W. KINZELBACH ◽  
B. LÜTHI ◽  
A. TSINOBER ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Surface Layer ◽  
Turbulent Flows ◽  
Atmospheric Surface Layer ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Taylor Hypothesis ◽  
High Reynolds

This is a report on a field experiment in an atmospheric surface layer at heights between 0.8 and 10m with the Taylor micro-scale Reynolds number in the range Reλ = 1.6−6.6 ×103. Explicit information is obtained on the full set of velocity and temperature derivatives both spatial and temporal, i.e. no use of Taylor hypothesis is made. The report consists of three parts. Part 1 is devoted to the description of facilities, methods and some general results. Certain results are similar to those reported before and give us confidence in both old and new data, since this is the first repetition of this kind of experiment at better data quality. Other results were not obtained before, the typical example being the so-called tear-drop R-Q plot and several others. Part 2 concerns accelerations and related matters. Part 3 is devoted to issues concerning temperature, with the emphasis on joint statistics of temperature and velocity derivatives. The results obtained in this work are similar to those obtained in experiments in laboratory turbulent grid flow and in direct numerical simulations of Navier–Stokes equations at much smaller Reynolds numbers Reλ ~ 102, and this similarity is not only qualitative, but to a large extent quantitative. This is true of such basic processes as enstrophy and strain production, geometrical statistics, the role of concentrated vorticity and strain, reduction of nonlinearity and non-local effects. The present experiments went far beyond the previous ones in two main respects. (i) All the data were obtained without invoking the Taylor hypothesis, and therefore a variety of results on fluid particle accelerations became possible. (ii) Simultaneous measurements of temperature and its gradients with the emphasis on joint statistics of temperature and velocity derivatives. These are reported in Parts 2 and 3.

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