Showing papers on "K-epsilon turbulence model published in 2018"

Homogeneous Turbulence Dynamics

Abstract: 1. Introduction 2. Statistical analysis of homogeneous turbulent flows: reminders 3. Incompressible homogeneous isotropic turbulence 4. Incompressible homogeneous anisotropic turbulence: pure rotations 5. Incompressible homogeneous anisotropic turbulence: strain 6. Incompressible homogeneous anisotropic turbulence: pure shear 7. Incompressible homogeneous anisotropic turbulence: buoyancy and stable stratification 8. Coupled effects: rotations, stratification, strain and shear 9. Compressible homogeneous isotropic turbulence 10. Compressible homogeneous anisotropic turbulence 11. Isotropic turbulence/shock interaction 12. Linear interaction approximation for shock/perturbation interaction 13. Linear theories - from rapid distortions theory to WKB variants 14. Anisotropic nonlinear triadic closures 15. Conclusions and perspectives.

Viscoelastic Pipe Flow is Linearly Unstable.

Abstract: Newtonian pipe flow is known to be linearly stable at all Reynolds numbers. We report, for the first time, a linear instability of pressure-driven pipe flow of a viscoelastic fluid, obeying the Oldroyd-B constitutive equation commonly used to model dilute polymer solutions. The instability is shown to exist at Reynolds numbers significantly lower than those at which transition to turbulence is typically observed for Newtonian pipe flow. Our results qualitatively explain experimental observations of transition to turbulence in pipe flow of dilute polymer solutions at flow rates where Newtonian turbulence is absent. The instability discussed here should form the first stage in a hitherto unexplored dynamical pathway to turbulence in polymer solutions. An analogous instability exists for plane Poiseuille flow.

Exact law for homogeneous compressible Hall magnetohydrodynamics turbulence.

Abstract: We derive an exact law for three-dimensional (3D) homogeneous compressible isothermal Hall magnetohydrodynamic turbulence, without the assumption of isotropy. The Hall current is shown to introduce new flux and source terms that act at the small scales (comparable or smaller than the ion skin depth) to significantly impact the turbulence dynamics. The law provides an accurate means to estimate the energy cascade rate over a broad range of scales covering the magnetohydrodynamic inertial range and the sub-ion dispersive range in 3D numerical simulations and in in situ spacecraft observations of compressible turbulence. This work is particularly relevant to astrophysical flows in which small-scale density fluctuations cannot be ignored such as the solar wind, planetary magnetospheres, and the interstellar medium.

Turbulence Effects of Collision Efficiency and Broadening of Droplet Size Distribution in Cumulus Clouds

Abstract: This paper aims to investigate and quantify the turbulence effect on droplet collision efficiency and explore the broadening mechanism of the droplet size distribution (DSD) in cumulus clouds. The sophisticated model employed in this study individually traces droplet motions affected by gravity, droplet disturbance flows, and turbulence in a Lagrangian frame. Direct numerical simulation (DNS) techniques are implemented to resolve the small-scale turbulence. Collision statistics for cloud droplets of radii between 5 and 25 μm at five different turbulence dissipation rates (20–500 cm2 s−3) are computed and compared with pure-gravity cases. The results show that the turbulence enhancement of collision efficiency highly depends on the r ratio (defined as the radius ratio of collected and collector droplets r/R) but is less sensitive to the size of the collector droplet investigated in this study. Particularly, the enhancement is strongest among comparable-sized collisions, indicating that turbulence c...

A comprehensive two-phase flow model for unidirectional sheet-flows

Abstract: In this paper a comprehensive one-dimensional two-phase flow model for sediment transport under sheet-flow conditions is presented. The model is based on the dense granular flow rheology for the intergranular stresses and on a mixing length model for the Reynolds shear stress. A drift velocity model is introduced to represent the vertical dispersion effects. Recent experimental data are used to improve the mixing length model and the numerical model is validated for four configurations. The model is further assessed by comparing the dependence of the sediment transport rate and the sheet layer thickness on the Shields number. The good agreement with experimental data confirms the capability of the model formulation to reproduce unidirectional sheet-flows. The agreement with the latest kinetic theory of granular flows based model demonstrate that the dense granular flow rheology can be used as an alternative approach to kinetic theory in two-phase flow models.

Numerical investigation of kinetic turbulence in relativistic pair plasmas - I. Turbulence statistics

Abstract: We describe results from particle-in-cell simulations of driven turbulence in collisionless, magnetized, relativistic pair plasma. This physical regime provides a simple setting for investigating the basic properties of kinetic turbulence and is relevant for high-energy astrophysical systems such as pulsar wind nebulae and astrophysical jets. In this paper, we investigate the statistics of turbulent fluctuations in simulations on lattices of up to $1024^3$ cells and containing up to $2 \times 10^{11}$ particles. Due to the absence of a cooling mechanism in our simulations, turbulent energy dissipation reduces the magnetization parameter to order unity within a few dynamical times, causing turbulent motions to become sub-relativistic. In the developed stage, our results agree with predictions from magnetohydrodynamic turbulence phenomenology at inertial-range scales, including a power-law magnetic energy spectrum with index near $-5/3$, scale-dependent anisotropy of fluctuations described by critical balance, log-normal distributions for particle density and internal energy density (related by a $4/3$ adiabatic index, as predicted for an ultra-relativistic ideal gas), and the presence of intermittency. We also present possible signatures of a kinetic cascade by measuring power-law spectra for the magnetic, electric, and density fluctuations at sub-Larmor scales.

Vortex dynamics and Lagrangian statistics in a model for active turbulence

Abstract: Cellular suspensions such as dense bacterial flows exhibit a turbulence-like phase under certain conditions. We study this phenomenon of “active turbulence” statistically by using numerical tools. Following Wensink et al. (Proc. Natl. Acad. Sci. U.S.A. 109, 14308 (2012)), we model active turbulence by means of a generalized Navier-Stokes equation. Two-point velocity statistics of active turbulence, both in the Eulerian and the Lagrangian frame, is explored. We characterize the scale-dependent features of two-point statistics in this system. Furthermore, we extend this statistical study with measurements of vortex dynamics in this system. Our observations suggest that the large-scale statistics of active turbulence is close to Gaussian with sub-Gaussian tails.

Turbulence kinetic energy exchanges in flows with highly variable fluid properties

Abstract: This paper investigates the energy exchanges associated with the half-trace of the velocity fluctuation correlation tensor in a strongly anisothermal low Mach fully developed turbulent channel flow. The study is based on direct numerical simulations of the channel within the low Mach number hypothesis and without gravity. The overall flow behaviour is governed by the variable fluid properties. The temperature of the two channel walls are imposed at 293 K and 586 K to generate the temperature gradient. The mean friction Reynolds number of the simulation is 180. The analysis is carried out in the spatial and spectral domains. The spatial and spectral studies use the same decomposition of the terms of the evolution equation of the half-trace of the velocity fluctuation correlation tensor. The importance of each term of the decomposition in the energy exchanges is assessed. This lets us identify the terms associated with variations or fluctuations of the fluid properties that are not negligible. Then, the behaviour of the terms is investigated. The spectral energy exchanges are first discussed in the incompressible case since the analysis is not present in the literature with the decomposition used in this study. The modification of the energy exchanges by the temperature gradient is then investigated in the spatial and spectral domains. The temperature gradient generates an asymmetry between the two sides of the channel. The asymmetry can in a large part be explained by the combined effect of the mean local variations of the fluid properties and a Reynolds number effect.

Dominant features in three-dimensional turbulence structure: comparison of non-uniform accelerating and decelerating flows

Abstract: The results are presented from an experimental study to investigate three-dimensional turbulence structure profiles, including turbulence intensity and Reynolds stress, of different non-uniform open channel flows over smooth bed in subcritical flow regime. In the analysis, the uniform flow profiles have been used to compare with those of the non-uniform flows to investigate their time-averaged spatial flow turbulence structure characteristics. The measured non-uniform velocity profiles are used to verify the von Karman constant κ and to estimate sets of log-law integration constant Br and wake parameter П, where their findings are also compared with values from previous studies. From κ, Br and П findings, it has been found that the log-wake law can sufficiently represent the non-uniform flow in its non-modified form, and all κ, Br and П follow universal rules for different bed roughness conditions. The non-uniform flow experiments also show that both the turbulence intensity and Reynolds stress are governed well by exponential pressure gradient parameter β equations. Their exponential constants are described by quadratic functions in the investigated β range. Through this experimental study, it has been observed that the decelerating flow shows higher empirical constants, in both the turbulence intensity and Reynolds stress compared to the accelerating flow. The decelerating flow also has stronger dominance to determine the flow non-uniformity, because it presents higher Reynolds stress profile than uniform flow, whereas the accelerating flow does not.

Investigation of the small-scale statistics of turbulence in the Modane S1MA wind tunnel

Abstract: This article describes the planning, set-up, turbulence characterization and analysis of measurements of a passive grid turbulence experiment that was carried out in the S1MA wind-tunnel from ONERA in Modane, in the context of the ESWIRP European project. This experiment aims at a detailed investigation of the statistical properties of turbulent flows at large Reynolds numbers. The primary goal is to take advantage of the unequaled large-scale dimensions of the ONERA S1MA wind-tunnel facility, to make available to the broad turbulence community high-quality experimental turbulence data with unprecendented resolution (both spatial and temporal) and accuracy (in terms of statistical convergence). With this goal, we designed the largest grid-generated turbulence experiment planned and performed to date. Grid turbulence is a canonical flow known to produce almost perfectly homogeneous and isotropic turbulence (HIT) which remains a unique framework to investigate fundamental physics of turbulent flows. Here, we present a brief description of the measurements, in particular those based on hot-wire diagnosis. By comparing results from classical hot-wires and from a nano-fabricated wire (developed at Princeton University), we show that our goal of resolving down to the smallest dissipative scales of the flow has been achieved. We also present the full characterization of the turbulence here, in terms of turbulent energy dissipation rate, injection and dissipation scales (both spatial and temporal) and Reynolds number.

DNS of a turbulent Couette flow at constant wall transpiration up to

Abstract: We present a new set of direct numerical simulation data of a turbulent plane Couette flow with constant wall-normal transpiration velocity , i.e. permeable boundary conditions, such that there is blowing on the lower side and suction on the upper side. Hence, there is no net change in flux to preserve periodic boundary conditions in the streamwise direction. Simulations were performed at with varying transpiration rates in the range to 0.085. Additionally, a classical Couette flow case at is presented for comparison. As a first key result we found a considerably extended logarithmic region of the mean velocity profile, with constant indicator function as transpiration increases. Further, turbulent intensities are observed to decrease with increasing transpiration rate. Mean velocities and intensities collapse only in the cases where the transpiration rate is kept constant, while they are largely insensitive to friction Reynolds number variations. The long and wide characteristic stationary rolls of classical turbulent Couette flow are still present for all present DNS runs. The rolls are affected by wall transpiration, but they are not destroyed even for the largest transpiration velocity case. Spectral information indicates the prevalence of the rolls and the existence of wide structures near the blowing wall. The statistics of all simulations can be downloaded from the webpage of the Chair of Fluid Dynamics.

The effect of heat release on the entrainment in a turbulent mixing layer

Abstract: Direct numerical simulations of a temporally evolving compressible reacting mixing layer have been performed to study the entrainment of the irrotational flow into the turbulent region across the turbulent/non-turbulent interface (TNTI). In order to study the effects of heat release and interaction of the flame with the TNTI on turbulence several cases with different heat release levels, corresponding to hydrogen combustion in air. The combustion is mimicked by a one-step irreversible global reaction, and infinitely fast chemistry approximation is used to compute the species mass fractions. Entrainment is studied via two mechanisms: nibbling, considered as the vorticity transport across the TNTI, and engulfment, the drawing of the pockets of the outside irrotational fluid into the turbulent region. As the level of heat release increases, the total entrained mass flow rate into the mixing layer decreases. In a reacting mixing layer by increasing the heat release rate, the mass flow rate due to nibbling is shown to decrease mostly due to a reduction of the local entrainment velocity, while the surface area of the TNTI does not change significantly. It is also observed that nibbling is a viscous dominated mechanism in non-reacting flows, whereas it is mostly carried out by inviscid terms in reacting flows with high level of heat release. The contribution of the engulfment to entrainment is small for the non-reacting mixing layers, while mass flow rate due to engulfment can constitute close to 40 % of the total entrainment in reacting cases. This increase is primarily related to a decrease of entrained mass flow rate due to nibbling, while the entrained mass flow rate due to engulfment does not change significantly in reacting cases. It is shown that the total entrained mass flow rate in reacting and non-reacting compressible mixing layers can be estimated from an expression containing the convective Mach number and the density change due to heat release.

Transition to turbulence in shear flows

Abstract: We review recent work on the transition to turbulence in shear flows, in particular plane Couette flow. In the linearized system the non-normality of the linear operator gives rise to non-orthogonal eigenvectors and to a significant amplification of noise. We present a typical result for a Fokker-Planck equation with non-normal relaxation matrix. As the driving becomes stronger, further stationary states are born in a saddle node bifurcation. This is observed in a two degree of freedom phenomenological model, in the a few mode approximation to a simple shear flow and in full numerical studies of plane Couette flow. The stationary states give rise to a fractal border between decaying and turbulent states.

Method to measure efficiently rare fluctuations of turbulence intensity for turbulent-laminar transitions in pipe flows.

Abstract: The fluctuations of turbulence intensity in a pipe flow around the critical Reynolds number is difficult to study but important because they are related to turbulent-laminar transitions. We here propose a rare-event sampling method to study such fluctuations in order to measure the time scale of the transition efficiently. The method is composed of two parts: (i) the measurement of typical fluctuations (the bulk part of an accumulative probability function) and (ii) the measurement of rare fluctuations (the tail part of the probability function) by employing dynamics where a feedback control of the Reynolds number is implemented. We apply this method to a chaotic model of turbulent puffs proposed by Barkley and confirm that the time scale of turbulence decay increases super exponentially even for high Reynolds numbers up to Re $=2500$, where getting enough statistics by brute-force calculations is difficult. The method uses a simple procedure of changing Reynolds number that can be applied even to experiments.

Energy production and self-sustained turbulence at the Kolmogorov scale in Couette flow

Abstract: Several recent studies have reported that there exists a self-similar form of invariant solutions down to the Kolmogorov microscale in the bulk region of turbulent Couette flow. While their role in a fully-developed turbulent flow is yet to be identified, here we report that there exists a related mechanism of turbulence production at the Kolmogorov microscale in the bulk region of turbulent Couette flow by performing a set of minimalspan direct numerical simulations up to friction Reynolds number Reτ ≃ 800. This mechanism is found to essentially originate from the non-zero mean shear in the bulk region of the Couette flow, and involves the eddy turn-over dynamics remarkably similar to the so-called self-sustaining process (SSP) and/or vortex-wave interaction (VWI). A numerical experiment that removes all the other motions except in the core region is also performed, which demonstrates that the eddies at a given wall-normal location in the bulk region are sustained in the absence of other motions at different wall-normal locations. It is proposed that the self-sustaining eddies at the Kolmogorov microscale correspond to those in uniform shear turbulence at transitional Reynolds numbers, and a quantitative comparison between the eddies in uniform shear and near-wall turbulence is subsequently made. Finally, it is shown that the turbulence production by the selfsustaining eddies at the Kolmogorov microscale is much smaller than that of full-scale simulations, and that the difference between the two increases with Reynolds number.

Turbulence in the rotating-disk boundary layer investigated through direct numerical simulations

Abstract: Turbulence in the rotating-disk boundary layer investigated through direct numerical simulations

The Cospectrum of Stress-Carrying Turbulence in the Presence of Surface Gravity Waves

Abstract: The cospectrum of the horizontal and vertical turbulent velocity fluctuations, an essential tool for understanding measurements of the turbulent Reynolds shear stress, often departs in the ocean from the shape that has been established in the atmospheric surface layer. Here, we test the hypothesis that this departure is caused by advection of standard boundary layer turbulence by the random oscillatory velocities produced by surface gravity waves. The test is based on a model with two elements. The first is a representation of the spatial structure of the turbulence, guided by rapid distortion theory, and consistent with the one-dimensional cospectra that have been measured in the atmosphere. The second model element is a map of the spatial structure of the turbulence to the temporal fluctuations measured at fixed sensors, assuming advection of frozen turbulence by the velocities associated with surface waves. The model is adapted to removal of the wave velocities from the turbulent fluctuations u...

Comparison of turbulence profiles in high Reynolds number turbulent boundary layers and validation of a predictive model

Abstract: The modified Townsend-Perry attached eddy model of Vassilicos et al (2015) combines the outer peak/plateau behaviour of rms streamwise turbulence velocity profiles and the Townsend-Perry log-decay of these profiles at higher distances from the wall. This model was validated by these authors for high Reynolds number tur- bulent pipe flow data and is shown here to describe equally well and with about the same parameter values turbulent boundary layer flow data from four different facilities and a wide range of Reynolds numbers. The model has predictive value as, when extrapolated to the extremely high Reynolds numbers of the SLTEST data obtained at the Great Salt Lake Desert atmospheric test facility, it matches these data quite well.

A K-Epsilon RANS turbulence model for incompressible MHD flow at high Hartmann number in fusion liquid metal blankets

Abstract: Summary As fusion liquid metal blankets work under strong magnetic fields, the liquid metal would form magnetohydrodynamics (MHD) flow of high Hartmann number in ducts. With the anisotropic suppression effect of magnetic field towards turbulence fluctuation, MHD turbulence becomes quasi-2 dimensional, whose characteristics of heat and mass transfer are different from common turbulence. Present MHD turbulence models can not accurately predict this suppression effect. In this paper, a K-Epsilon RANS turbulence model was developed for incompressible MHD flow at high Hartmann number in fusion liquid metal blankets. According to the characteristic magnetic braking time of isotropic turbulence in MHD duct flows, the effectiveness of the electromagnetic damping process was simulated. Turbulence in MHD rectangular duct flow of high Hartmann number and Reynolds number with strong sidewall jets was chosen to benchmark the model. The MHD turbulent velocity and turbulent kinetic energy were compared between the model and the experiment. The benchmark of MHD duct flow showed that the model could accurately simulate the instability location formed by MHD jets, the distribution of turbulent kinetic energy, and variation of MHD quasi-2-dimensional turbulence strength with magnetic fields.

Turbulence radiation interaction in channel flow with various optical depths

Abstract: The present work consists of an investigation of the turbulence radiation interaction (TRI) in a radiative turbulent channel flow of grey gas bounded by isothermal hot and cold walls. The optical thickness of the channel is varied from 0.1 to 10 to observe different regimes of TRI. A high-resolution finite volume method for radiative heat transfer is employed and coupled with the direct numerical simulation (DNS) of the flow. The resulting effects of TRI on temperature statistics are strongly dependent on the considered optical depth. In particular, the contrasting role of emission and absorption is highlighted. For a low optical thickness the effect of radiative fluctuations on temperature statistics is low and causes the reduction of temperature variance through the dissipating action of emission. On the other hand, while increasing optical thickness to relatively high levels, the dissipation of temperature variance is balanced, at low wavenumbers in the turbulence spectrum, through the preferential action of absorption, which increases the large-scale temperature fluctuations. A significant rise in the effect of radiation on the temperature variance can be observed as a consequence of the reduction of radiative heat transfer length scales.

Interaction between waves and gravity currents: description of turbulence in a simple numerical model

Abstract: Effects of surface waves on gravity current propagation are studied by means of a numerical model. The adopted modeling approach couples a Boussinesq-type of model for surface waves and a gravity current model for stratified flows. In particular two different turbulence closure models are introduced which take into account subgrid turbulence and an additional depth-constant eddy-viscosity. The turbulence parameters are calibrated by means of experimental data on the time evolution of the heavy front, obtained both in the absence and in the presence of regular surface waves. Velocity fields, heavy and light front position, shear stresses, vorticity and entrainment calculated by the model are analyzed. The turbulence closure which includes both uniform and Smagorinsky type eddy viscosity allows a better description of the actual gravity current propagation. In particular, the results highlight the fact that the presence of the oscillatory motion causes, simultaneously, a reduction in turbulence and an increase in the mixing of heavy and light fluids. Such a result is in agreement with the experimental observations.