scholarly journals Scale dependence and cross-scale transfer of kinetic energy in compressible hydrodynamic turbulence at moderate Reynolds numbers

2021 ◽  
Vol 6 (4) ◽  
Author(s):  
Petr Hellinger ◽  
Andrea Verdini ◽  
Simone Landi ◽  
Emanuele Papini ◽  
Luca Franci ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Reynolds Numbers ◽  
Scale Dependence ◽  
Hydrodynamic Turbulence

Fully developed MHD turbulence near critical magnetic Reynolds number

1981 ◽  
Vol 104 ◽  
pp. 419-443 ◽  
Author(s):  
J. Léorat ◽  
A. Pouquet ◽  
U. Frisch
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Mhd Equations ◽  
Liquid Sodium ◽  
Turbulent Heat ◽  
Mhd Turbulence

Liquid-sodium-cooled breeder reactors may soon be operating at magnetic Reynolds numbers RM where magnetic fields can be self-excited by a dynamo mechanism (as first suggested by Bevir 1973). Such flows have kinetic Reynolds numbers RV of the order of 107 and are therefore highly turbulent.This leads us to investigate the behaviour of MHD turbulence with high RV and low magnetic Prandtl numbers. We use the eddy-damped quasi-normal Markovian closure applied to the MHD equations. For simplicity we restrict ourselves to homogeneous and isotropic turbulence, but we do include helicity.We obtain a critical magnetic Reynolds number RMc of the order of a few tens (non-helical case) above which magnetic energy is present. RMc is practically independent of RV (in the range 40 to 106). RMc can be considerably decreased by the presence of helicity: when the overall size of the flow L is much larger than the integral scale l0, RMc can drop below unity as suggested by an α-effect argument. When L ≈ l0 the drop can still be substantial (factor of 6) when helicity is a maximum. We examine how the turbulence is modified when RM crosses RMc: presence of magnetic energy, decreased kinetic energy, steepening of kinetic-energy spectrum, etc.We make no attempt to obtain quantitative estimates for a breeder reactor, but discuss some of the possible consequences of exceeding RMc, such as decreased turbulent heat transport. More precise information may be obtained from numerical simulations and experiments (including some in the subcritical regime).

Large-scale modes of turbulent channel flow: transport and structure

2001 ◽  
Vol 448 ◽  
pp. 53-80 ◽  
Author(s):  
Z. LIU ◽  
R. J. ADRIAN ◽  
T. J. HANRATTY
Keyword(s):  
Shear Stress ◽  
Kinetic Energy ◽  
Shear Layer ◽  
Turbulent Kinetic Energy ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Reynolds Numbers ◽  
Upstream Region ◽  
Two Dimensional ◽  
Normal Plane

Turbulent flow in a rectangular channel is investigated to determine the scale and pattern of the eddies that contribute most to the total turbulent kinetic energy and the Reynolds shear stress. Instantaneous, two-dimensional particle image velocimeter measurements in the streamwise-wall-normal plane at Reynolds numbers Reh = 5378 and 29 935 are used to form two-point spatial correlation functions, from which the proper orthogonal modes are determined. Large-scale motions – having length scales of the order of the channel width and represented by a small set of low-order eigenmodes – contain a large fraction of the kinetic energy of the streamwise velocity component and a small fraction of the kinetic energy of the wall-normal velocities. Surprisingly, the set of large-scale modes that contains half of the total turbulent kinetic energy in the channel, also contains two-thirds to three-quarters of the total Reynolds shear stress in the outer region. Thus, it is the large-scale motions, rather than the main turbulent motions, that dominate turbulent transport in all parts of the channel except the buffer layer. Samples of the large-scale structures associated with the dominant eigenfunctions are found by projecting individual realizations onto the dominant modes. In the streamwise wall-normal plane their patterns often consist of an inclined region of second quadrant vectors separated from an upstream region of fourth quadrant vectors by a stagnation point/shear layer. The inclined Q4/shear layer/Q2 region of the largest motions extends beyond the centreline of the channel and lies under a region of fluid that rotates about the spanwise direction. This pattern is very similar to the signature of a hairpin vortex. Reynolds number similarity of the large structures is demonstrated, approximately, by comparing the two-dimensional correlation coefficients and the eigenvalues of the different modes at the two Reynolds numbers.

Two-dimensional turbulence near the viscous limit

1974 ◽  
Vol 62 (2) ◽  
pp. 273-287 ◽  
Author(s):  
J. S. A. Green
Keyword(s):  
Steady State ◽  
Kinetic Energy ◽  
Body Force ◽  
Reynolds Numbers ◽  
Rapid Decrease ◽  
Two Dimensional ◽  
Turbulent Stress ◽  
Viscous Limit ◽  
External Body

Two-dimensional incompressible motion is generated by a steady external body force varying sinusoidally with a transverse co-ordinate. Such flow is found to be unstable for Reynolds numbers greater than 2½, and under these conditions evolves towards a new steady state. This ‘steady-eddy’ state is itself unstable in a sense, and its breakdown suggests the catastrophic onset of a cascade of turbulence. The mechanics of this cascade can be represented by a kind of recursion system in which the turbulence dynamics of one scale is repeated in the next, and a law of turbulent stress results. The spectrum of kinetic energy generated by a steady input of momentum at a discrete wavelength shows a rapid decrease (as k−5) towards shorter wavelengths but a much slower decrease (as k) towards longer wavelengths.

scholarly journals A Warm Rain Microphysics Parameterization that Includes the Effect of Turbulence

2008 ◽  
Vol 65 (6) ◽  
pp. 1795-1816 ◽  
Author(s):  
Charmaine N. Franklin
Keyword(s):  
Kinetic Energy ◽  
Size Distribution ◽  
Turbulent Kinetic Energy ◽  
Dissipation Rate ◽  
Drop Size ◽  
Reynolds Numbers ◽  
Liquid Water Content ◽  
Drop Size Distribution ◽  
Collision Kernel ◽  
Warm Rain

Abstract A warm rain parameterization has been developed by solving the stochastic collection equation with the use of turbulent collision kernels. The resulting parameterizations for the processes of autoconversion, accretion, and self-collection are functions of the turbulent intensity of the flow and are applicable to turbulent cloud conditions ranging in dissipation rates of turbulent kinetic energy from 100 to 1500 cm2 s−3. Turbulence has a significant effect on the acceleration of the drop size distribution and can reduce the time to the formation of raindrops. When the stochastic collection equation is solved with the gravitational collision kernel for an initial distribution with a liquid water content of 1 g m−3 and 240 drops cm−3 with a mean volume radius of 10 μm, the amount of mass that is transferred to drop sizes greater than 40 μm in radius after 20 min is 0.9% of the total mass. When the stochastic collection equation is solved with a turbulent collision kernel for collector drops in the range of 10–30 μm with a dissipation rate of turbulent kinetic energy equal to 100 cm2 s−3, this percentage increases to 21.4. Increasing the dissipation rate of turbulent kinetic energy to 500, 1000, and 1500 cm2 s−3 further increases the percentage of mass transferred to radii greater than 40 μm after 20 min to 41%, 52%, and 58%, respectively, showing a substantial acceleration of the drop size distribution when a turbulent collision kernel that includes both turbulent and gravitational forcing replaces the purely gravitational kernel. The warm rain microphysics parameterization has been developed from direct numerical simulation (DNS) results that are characterized by Reynolds numbers that are orders of magnitude smaller than those of atmospheric turbulence. The uncertainty involved with the extrapolation of the results to high Reynolds numbers, the use of gravitational collision efficiencies, and the range of the droplets for which the effect of turbulence has been included should all be considered when interpreting results based on these new microphysics parameterizations.

scholarly journals Turbulent fluid flow and heat transfer analysis of heated rectangular blocks encountered in electronics enclosures

2020 ◽  
Vol 184 ◽  
pp. 01027
Author(s):  
B Ch Nookaraju
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Kinetic Energy ◽  
Vertical Channel ◽  
Reynolds Numbers ◽  
Heat Transfer Analysis ◽  
Computational Investigation ◽  
Turbulent Fluid Flow ◽  
Flow And Heat Transfer ◽  
Pressure Fall

Computational investigation of steady, two-dimensional heat transfer attributes for forced convective chaotic discharge in a vertical channel of cluster of heated rectangular sections is performed. The discharge is deemed to be periodic fully developed so that the issue is determined for two extending zone and explanation is developed to more number of sections. This structure reproduces the driven convective cooling of a cluster of engraved circuit panels confronted in computerize belongings. Two mathematical statements for k- ℇ model is used for modeling for the turbulence and the finite volume methodology is used. Computations are performed for Reynolds numbers ranging from 6000-12000, Prandtl number of 0.7 and various geometric parameters characterizing the problem. As Reynolds number steps up the Nusselt Number increases. Re-circulations undermine the local Nusselt number when matched with comparing variation from a identical plate. The velocity contours, temperature distributions, variation of turbulent kinetic energy and kinetic energy dissipation rates in a vertical channel is found. With the blocks in the cluster, pressure fall is higher in resemblance to plane duct.

Fluid Flow Analysis in a Pebble Bed Modular Reactor Using RANS Turbulence Models

2008 ◽  
Author(s):  
Margaret Mkhosi ◽  
Richard Denning ◽  
Audeen Fentiman
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulence Intensity ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Pebble Bed ◽  
Rans Turbulence Models ◽  
Flow Domain

The computational fluid dynamics code FLUENT has been used to analyze turbulent fluid flow over pebbles in a pebble bed modular reactor. The objective of the analysis is to evaluate the capability of the various RANS turbulence models to predict mean velocities, turbulent kinetic energy, and turbulence intensity inside the bed. The code was run using three RANS turbulence models: standard k-ε, standard k-ω and the Reynolds stress turbulence models at turbulent Reynolds numbers, corresponding to normal operation of the reactor. For the k-ε turbulence model, the analyses were performed at a range of Reynolds numbers between 1300 and 22 000 based on the approach velocity and the sphere diameter of 6 cm. Predictions of the mean velocities, turbulent kinetic energy, and turbulence intensity for the three models are compared at the Reynolds number of 5500 for all the RANS models analyzed. A unit-cell approach is used and the fluid flow domain consists of three unit cells. The packing of the pebbles is an orthorhombic arrangement consisting of seven layers of pebbles with the mean flow parallel to the z-axis. For each Reynolds number analyzed, the velocity is observed to accelerate to twice the inlet velocity within the pebble bed. From the velocity contours, it can be seen that the flow appears to have reached an asymptotic behavior by the end of the first unit cell. The velocity vectors for the standard k-ε and the Reynolds stress model show similar patterns for the Reynolds number analyzed. For the standard k-ω, the vectors are different from the other two. Secondary flow structures are observed for the standard k-ω after the flow passes through the gap between spheres. This feature is not observable in the case of both the standard k-ε and the RSM. Analysis of the turbulent kinetic energy contours shows that there is higher turbulence kinetic energy near the inlet than inside the bed. As the Reynolds number increases, kinetic energy inside the bed increases. The turbulent kinetic energy values obtained for the standard k-ε and the RSM are similar, showing maximum turbulence kinetic energy of 7.5 m2·s−2, whereas the standard k-ω shows a maximum of about 20 m2·s−2. Another observation is that the turbulence intensity is spread throughout the flow domain for the k-ε and RSM whereas for the k-ω, the intensity is concentrated at the front of the second sphere. Preliminary analysis performed for the pressure drop using the standard k-ε model for various velocities show that the dependence of pressure on velocity varies as V1.76.

The Drag on Spheres and Cylinders in a Stream of Dust-Laden Air

1959 ◽  
Vol 26 (4) ◽  
pp. 584-586
Author(s):  
Thomas Gillespie ◽  
A. W. Gunter
Keyword(s):  
Particle Size ◽  
Reynolds Number ◽  
Kinetic Energy ◽  
Drag Coefficient ◽  
Flow Pattern ◽  
Reynolds Numbers ◽  
Dust Concentration ◽  
Phase System ◽  
Two Phase ◽  
Coefficient Versus

Abstract A system has been developed for measuring the drag on small spheres and cylinders in a stream of dust-laden air. The drag was found to be proportional to the kinetic energy of the air plus the kinetic energy of the dust, and to be independent of particle size for particles having diameters in the range of 50 to 400μ. The well-known drag-coefficient versus Reynolds-number plots are the same for dust-free and dust-laden air provided the drag coefficient is calculated using the density of the two-phase system and the Reynolds numbers are calculated using the density of air alone. This suggests that the dust has little effect on the flow pattern. The results indicate that an instrument utilizing the drag principle to measure dust concentration could be developed.

Experimental Measurements of the Wake of a Sphere at Subcritical Reynolds Numbers

2021 ◽  
Vol 143 (6) ◽  
Author(s):  
Robert Muyshondt ◽  
Thien Nguyen ◽  
Y. A. Hassan ◽  
N. K. Anand
Keyword(s):  
Reynolds Number ◽  
Spectral Analysis ◽  
Kinetic Energy ◽  
Cross Correlation ◽  
Reynolds Numbers ◽  
Velocity Fields ◽  
Stereoscopic Particle Image Velocimetry ◽  
Recirculation Region ◽  
Flow Structures ◽  
Vortex Identification

Abstract This work experimentally investigated the flow phenomena and vortex structures in the wake of a sphere located in a water loop at Reynolds numbers of Re = 850, 1,250, and 1,700. Velocity fields in the wake region were obtained by applying the time-resolved stereoscopic particle image velocimetry (TR-SPIV) technique. From the acquired TR-SPIV velocity vector fields, the statistical values of mean and fluctuating velocities were computed. Spectral analysis, two-point velocity–velocity cross-correlation, proper orthogonal decomposition (POD) and vortex identification analyses were also performed. The velocity fields show a recirculation region that decreases in length with an increase of Reynolds numbers. The power spectra from the spectral analysis had peaks corresponding to a Strouhal number of St = 0.2, which is a value commonly found in the literature studies of flow over a sphere. The two-point cross-correlation analysis revealed elliptical structures in the wake, with estimated integral length scales ranging between 12% and 63% of the sphere diameter. The POD analysis revealed the statistically dominant flow structures that captured the most flow kinetic energy. It is seen that the flow kinetic energy captured in the smaller scale flow structures increased as Reynolds number increased. The POD modes contained smaller structure as the Reynolds number increased and as mode order increased. In addition, spectral analysis performed on the POD temporal coefficients revealed peaks corresponding to St = 0.2, similar to the spectral analysis on the fluctuating velocity. The ability of POD to produce low-order reconstructions of the flow was also utilized to facilitate vortex identification analysis, which identified average vortex sizes of 0.41D for Re1, 0.33D for Re2, and 0.32D for Re3.

Sensitivity of stratified turbulence to the buoyancy Reynolds number

2013 ◽  
Vol 725 ◽  
pp. 1-22 ◽  
Author(s):  
P. Bartello ◽  
S. M. Tobias
Keyword(s):  
Reynolds Number ◽  
Energy Spectrum ◽  
Kinetic Energy ◽  
Numerical Simulations ◽  
Froude Number ◽  
Relative Size ◽  
Stratified Flow ◽  
Reynolds Numbers ◽  
Stratified Turbulence ◽  
Integral Scale

AbstractIn this article we present direct numerical simulations of stratified flow at resolutions of up to $204{8}^{2} \times 513$, to explore scalings for the dynamics of stably stratified turbulence. Recent work suggests that for strong enough stratification, the vertical integral scale of the turbulence adjusts to yield a vertical Froude number, ${F}_{v} $, of order unity at high enough Reynolds number, whilst the horizontal Froude number, ${F}_{h} $, decreases as stratification is increased. Our numerical simulations are consistent with predictions by Lindborg (J. Fluid Mech., vol. 550, 2006, pp, 207–242), and with numerical simulations at lower resolution, in that the horizontal kinetic energy spectrum follows a Kolmogorov spectrum (after replacing the wavenumber with the horizontal wavenumber) and that the horizontal potential energy spectrum similarly follows the Corrsin–Obukhov spectrum for a passive scalar. Most importantly, we build upon these previous results by thoroughly exploring the dependence of the horizontal spectrum of horizontal kinetic energy on both the stratification and the relative size of the vertical dissipation terms, as quantified by the buoyancy Reynolds number. Our most important result is that variations in the power-law exponent scale entirely with the buoyancy Reynolds number and not with the stratification itself, lending considerable support to the Lindborg (2006) hypothesis that horizontal spectra are independent of stratification at large Reynolds numbers. We further demonstrate that even at the large numerical resolution of this study, the spectrum and hence the dynamics are affected by the buoyancy Reynolds number unless it is larger than $O(10)$, indicating that extreme care must be taken when assessing claims made from previous numerical simulations of stratified flow at low or moderate resolution and extrapolating the results to geophysical or astrophysical Reynolds numbers.

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