Freely decaying turbulence in a finite domain at finite Reynolds number

2020 ◽  
Vol 32 (9) ◽  
pp. 095109
Author(s):  
Mohammad Anas ◽  
Pranav Joshi ◽  
Mahendra K. Verma
Keyword(s):  
Reynolds Number ◽  
Finite Domain ◽  
Decaying Turbulence

scholarly journals Direct Numerical Simulation in Two Dimensional Homogeneous Isotropic Turbulence Using Spectral Method

2013 ◽  
Vol 5 (3) ◽  
pp. 435-445
Author(s):  
M. S. I. Mallik ◽  
M. A. Uddin ◽  
M. A. Rahman
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Flow Field ◽  
Direct Numerical Simulation ◽  
Spectral Method ◽  
Isotropic Turbulence ◽  
Qualitative Behavior ◽  
Two Dimensional ◽  
Homogeneous Isotropic Turbulence ◽  
Decaying Turbulence

Direct numerical simulation (DNS) in two-dimensional homogeneous isotropic turbulence is performed by using the Spectral method at a Reynolds number Re = 1000 on a uniformly distributed grid points. The Reynolds number is low enough that the computational grid is capable of resolving all the possible turbulent scales. The statistical properties in the computed flow field show a good agreement with the qualitative behavior of decaying turbulence. The behavior of the flow structures in the computed flow field also follow the classical idea of the fluid flow in turbulence. Keywords: Direct numerical simulation, Isotropic turbulence, Spectral method. © 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi:http://dx.doi.org/10.3329/jsr.v5i3.12665 J. Sci. Res. 5 (3), 435-445 (2013)  

LATTICE BOLTZMANN SIMULATION OF TWO-DIMENSIONAL WALL BOUNDED TURBULENT FLOW

2010 ◽  
Vol 21 (05) ◽  
pp. 669-680 ◽  
Author(s):  
GÁBOR HÁZI ◽  
GÁBOR TÓTH
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Lattice Boltzmann ◽  
Numerical Study ◽  
Power Laws ◽  
Energy Spectra ◽  
Small Scale ◽  
Two Dimensional ◽  
Lattice Boltzmann Simulation ◽  
Decaying Turbulence

This paper reports on a numerical study of two-dimensional decaying turbulence in a square domain with no-slip walls. The generation of strong small-scale vortices near the no-slip walls have been observed in the lattice Boltzmann simulations just like in earlier pseudospectral calculations. Due to these vortices the enstrophy is not a monotone decaying function of time. Considering a number of simulations and taking their ensemble average, we have found that the decay of enstrophy and that of the kinetic energy can be described well by power-laws. The exponents of these laws depend on the Reynolds number in a similar manner than was observed before in pseudospectral simulations. Considering the ensemble averaged 1D Fourier energy spectra calculated along the walls, we could not find a simple power-law, which fits well to the simulation data. These spectra change in time and reveal an exponent close to -3 in the intermediate and an exponent -5/3 at low wavenumbers. On the other hand, the two-dimensional energy spectra, which remain almost steady in the intermediate decay stage, show clear power-law behavior with exponent larger than -3 depending on the initial Reynolds number.

scholarly journals The Jeffery–Hamel similarity solution and its relation to flow in a diverging channel

2011 ◽  
Vol 687 ◽  
pp. 404-430 ◽  
Author(s):  
P. E. Haines ◽  
R. E. Hewitt ◽  
A. L. Hazel
Keyword(s):  
Reynolds Number ◽  
Symmetry Breaking ◽  
Similarity Solution ◽  
Pitchfork Bifurcation ◽  
Numerical Results ◽  
Finite Domain ◽  
Infinite Domain ◽  
Neutral Curves ◽  
Diverging Channel ◽  
Radial Outflow

AbstractWe explore the relevance of the idealized Jeffery–Hamel similarity solution to the practical problem of flow in a diverging channel of finite (but large) streamwise extent. Numerical results are presented for the two-dimensional flow in a wedge of separation angle $2\ensuremath{\alpha} $, bounded by circular arcs at the inlet/outlet and for a net radial outflow of fluid. In particular, we show that in a finite domain there is a sequence of nested neutral curves in the $(\mathit{Re}, \ensuremath{\alpha} )$ plane, each corresponding to a midplane symmetry-breaking (pitchfork) bifurcation, where $\mathit{Re}$ is a Reynolds number based on the radial mass flux. For small wedge angles we demonstrate that the first pitchfork bifurcation in the finite domain occurs at a critical Reynolds number that is in agreement with the only pitchfork bifurcation in the infinite-domain similarity solution, but that the criticality of the bifurcation differs (in general). We explain this apparent contradiction by demonstrating that, for $\ensuremath{\alpha} \ll 1$, superposition of two (infinite-domain) eigenmodes can be used to construct a leading-order finite-domain eigenmode. These constructed modes accurately predict the multiple symmetry-breaking bifurcations of the finite-domain flow without recourse to computation of the full field equations. Our computational results also indicate that temporally stable, isolated, steady solutions may exist. These states are finite-domain analogues of the steady waves recently presented by Kerswell, Tutty, & Drazin (J. Fluid Mech., vol. 501, 2004, pp. 231–250) for an infinite domain. Moreover, we demonstrate that there is non-uniqueness of stable solutions in certain parameter regimes. Our numerical results tie together, in a consistent framework, the disparate results in the existing literature.

Examination of hypotheses in the Kolmogorov refined turbulence theory through high-resolution simulations. Part 1. Velocity field

1996 ◽  
Vol 309 ◽  
pp. 113-156 ◽  
Author(s):  
Lian-Ping Wang ◽  
Shiyi Chen ◽  
James G. Brasseur ◽  
John C. Wyngaard
Keyword(s):  
Reynolds Number ◽  
High Resolution ◽  
Probability Distribution ◽  
Similarity Theory ◽  
Turbulence Theory ◽  
Inertial Subrange ◽  
Velocity Increments ◽  
Decaying Turbulence ◽  
Log Normal ◽  
Local Reynolds Number

The fundamental hypotheses underlying Kolmogorov-Oboukhov (1962) turbulence theory (K62) are examined directly and quantitutivezy by using high-resolution numerical turbulence fields. With the use of massively parallel Connection Machine-5, we have performed direct Navier-Stokes simulations (DNS) at 5123 resolution with Taylor microscale Reynolds number up to 195. Three very different types of flow are considered: free-decaying turbulence, stationary turbulence forced at a few large scales, and a 2563 large-eddy simulation (LES) flow field. Both the forced DNS and LES flow fields show realistic inertial-subrange dynamics. The Kolmogorov constant for the k−5/3 energy spectrum obtained from the 5123 DNS flow is 1.68 ±.15. The probability distribution of the locally averaged disspation rate εr, over a length scale r is nearly log-normal in the inertial subrange, but significant departures are observed for high-order moments. The intermittency parameter p, appearing in Kolmogorov's third hypothesis for the variance of the logarithmic dissipation, is found to be in the range of 0.20 to 0.28. The scaling exponents over both εr, and r for the conditionally averaged velocity increments $\overline{\delta_ru|\epsilon_r}$ are quantified, and the direction of their variations conforms with the refined similarity theory. The dimensionless averaged velocity increments $(\overline{\delta_ru^n|\epsilon_r})/(\epsilon_rr)^{n/3}$ are found to depend on the local Reynolds number Reεr = ε1/3rr4/3/ν in a manner consistent with the refined similarity hypotheses. In the inertial subrange, the probability distribution of δru/(εrr)1/3 is found to be universal. Because the local Reynolds number of K62, Rεr = ε1/3rr4/3/ν, spans a finite range at a given scale r as compared to a single value for the local Reynolds number Rr = ε−1/3r4/3/ν in Kolmogorov's (1941a,b) original theory (K41), the inertial range in the K62 context can be better realized than that in K41 for a given turbulence field at moderate Taylor microscale (global) Reynolds number Rλ. Consequently universal constants in the second refined similarity hypothesis can be determined quite accurately, showing a faster-than-exponential growth of the constants with order n. Finally, some consideration is given to the use of pseudo-dissipation in the context of the K62 theory where it is found that the probability distribution of locally averaged pseudo-dissipation ε′r deviates more from a log-normal model than the full dissipation εr. The velocity increments conditioned on ε′r do not follow the refined similarity hypotheses to the same degree as those conditioned on εr.

scholarly journals ENTROPIC LATTICE BOLTZMANN SIMULATION OF THE FLOW PAST SQUARE CYLINDER

2004 ◽  
Vol 15 (03) ◽  
pp. 435-445 ◽  
Author(s):  
SANTOSH ANSUMALI ◽  
SHYAM SUNDER CHIKATAMARLA ◽  
CHRISTOS EMMANOUIL FROUZAKIS ◽  
KONSTANTINOS BOULOUCHOS
Keyword(s):  
Reynolds Number ◽  
Lattice Boltzmann ◽  
Large Scale ◽  
Stokes Equations ◽  
Coarse Grained ◽  
Navier Stokes ◽  
Square Cylinder ◽  
Flow Past ◽  
Lattice Boltzmann Simulation ◽  
Decaying Turbulence

Minimal Boltzmann kinetic models, such as lattice Boltzmann, are often used as an alternative to the discretization of the Navier–Stokes equations for hydrodynamic simulations. Recently, it was argued that modeling sub-grid scale phenomena at the kinetic level might provide an efficient tool for large scale simulations. Indeed, a particular variant of this approach, known as the entropic lattice Boltzmann method (ELBM), has shown that an efficient coarse-grained simulation of decaying turbulence is possible using these approaches. The present work investigates the efficiency of the entropic lattice Boltzmann in describing flows of engineering interest. In order to do so, we have chosen the flow past a square cylinder, which is a simple model of such flows. We will show that ELBM can quantitatively capture the variation of vortex shedding frequency as a function of Reynolds number in the low as well as the high Reynolds number regime, without any need for explicit sub-grid scale modeling. This extends the previous studies for this set-up, where experimental behavior ranging from Re ~O(10) to Re ≤1000 was predicted by a single simulation algorithm.1–5

A Comparison of Three Approaches to Compute the Effective Reynolds Number of the Implicit Large-Eddy Simulations

2016 ◽  
Vol 138 (7) ◽  
Author(s):  
Ye Zhou ◽  
Ben Thornber
Keyword(s):  
Reynolds Number ◽  
Critical Evaluation ◽  
Reynolds Numbers ◽  
Complex Flows ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Induced Flow ◽  
Decaying Turbulence ◽  
High Reynolds ◽  
Effective Reynolds Number

The implicit large-eddy simulation (ILES) has been utilized as an effective approach for calculating many complex flows at high Reynolds number flows. Richtmyer–Meshkov instability (RMI) induced flow can be viewed as a homogeneous decaying turbulence (HDT) after the passage of the shock. In this article, a critical evaluation of three methods for estimating the effective Reynolds number and the effective kinematic viscosity is undertaken utilizing high-resolution ILES data. Effective Reynolds numbers based on the vorticity and dissipation rate, or the integral and inner-viscous length scales, are found to be the most self-consistent when compared to the expected phenomenology and wind tunnel experiments.

Kármán–Howarth solutions of homogeneous isotropic turbulence

2021 ◽  
Vol 932 ◽  
Author(s):  
L. Djenidi ◽  
R.A. Antonia
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Three Dimensional ◽  
Order Moment ◽  
Homogeneous Isotropic Turbulence ◽  
The Difference ◽  
Decaying Turbulence ◽  
The Impact ◽  
Good Agreement

The Kármán–Howarth equation (KHEq) is solved using a closure model to obtain solutions of the second-order moment of the velocity increment, $S_2$ , in homogeneous isotropic turbulence (HIT). The results are in good agreement with experimental data for decaying turbulence and are also consistent with calculations based on the three-dimensional energy spectrum for decaying HIT. They differ, however, from those for forced HIT, the difference occurring mainly at large scales. This difference is attributed to the fact that the forcing generates large-scale motions which are not compatible with the KHEq. As the Reynolds number increases, the impact of forcing on the small scales decreases, thus allowing the KHEq and spectrally based solutions to agree well in the range of scales unaffected by forcing. Finally, the results show that the two-thirds law is compatible with the KHEq solutions as the Reynolds number increases to very large, if not infinite, values.

scholarly journals The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 2. Simulations with gravitational effects

2016 ◽  
Vol 796 ◽  
pp. 659-711 ◽  
Author(s):  
Peter J. Ireland ◽  
Andrew D. Bragg ◽  
Lance R. Collins
Keyword(s):  
Reynolds Number ◽  
Single Particle ◽  
Isotropic Turbulence ◽  
Distribution Functions ◽  
Particle Collision ◽  
Collision Kernel ◽  
Finite Domain ◽  
Inertial Particles ◽  
Inertial Particle ◽  
Wide Range

In Part 1 of this study (Ireland et al., J. Fluid Mech., vol. 796, 2016, pp. 617–658), we analysed the motion of inertial particles in isotropic turbulence in the absence of gravity using direct numerical simulation (DNS). Here, in Part 2, we introduce gravity and study its effect on single-particle and particle-pair dynamics over a wide range of flow Reynolds numbers, Froude numbers and particle Stokes numbers. The overall goal of this study is to explore the mechanisms affecting particle collisions, and to thereby improve our understanding of droplet interactions in atmospheric clouds. We find that the dynamics of heavy particles falling under gravity can be artificially influenced by the finite domain size and the periodic boundary conditions, and we therefore perform our simulations on larger domains to reduce these effects. We first study single-particle statistics that influence the relative positions and velocities of inertial particles. We see that gravity causes particles to sample the flow more uniformly and reduces the time particles can spend interacting with the underlying turbulence. We also find that gravity tends to increase inertial particle accelerations, and we introduce a model to explain that effect. We then analyse the particle relative velocities and radial distribution functions (RDFs), which are generally seen to be independent of Reynolds number for low and moderate Kolmogorov-scale Stokes numbers $St$. We see that gravity causes particle relative velocities to decrease by reducing the degree of preferential sampling and the importance of path-history interactions, and that the relative velocities have higher scaling exponents with gravity. We observe that gravity has a non-trivial effect on clustering, acting to decrease clustering at low $St$ and to increase clustering at high $St$. By considering the effect of gravity on the clustering mechanisms described in the theory of Zaichik & Alipchenkov (New J. Phys., vol. 11, 2009, 103018), we provide an explanation for this non-trivial effect of gravity. We also show that when the effects of gravity are accounted for in the theory of Zaichik & Alipchenkov (2009), the results compare favourably with DNS. The relative velocities and RDFs exhibit considerable anisotropy at small separations, and this anisotropy is quantified using spherical harmonic functions. We use the relative velocities and the RDFs to compute the particle collision kernels, and find that the collision kernel remains as it was for the case without gravity, namely nearly independent of Reynolds number for low and moderate $St$. We conclude by discussing practical implications of the results for the cloud physics and turbulence communities and by suggesting possible avenues for future research.

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