Pseudo-turbulent gas-phase velocity fluctuations in homogeneous gas–solid flow: fixed particle assemblies and freely evolving suspensions

2015 ◽  
Vol 770 ◽  
pp. 210-246 ◽  
Author(s):  
M. Mehrabadi ◽  
S. Tenneti ◽  
R. Garg ◽  
S. Subramaniam
Keyword(s):  
Kinetic Energy ◽  
Phase Velocity ◽  
Turbulent Kinetic Energy ◽  
Gas Phase ◽  
Reynolds Stress ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Velocity Fluctuations ◽  
The Mean ◽  
Particle Assemblies

Gas-phase velocity fluctuations due to mean slip velocity between the gas and solid phases are quantified using particle-resolved direct numerical simulation. These fluctuations are termed pseudo-turbulent because they arise from the interaction of particles with the mean slip even in ‘laminar’ gas–solid flows. The contribution of turbulent and pseudo-turbulent fluctuations to the level of gas-phase velocity fluctuations is quantified in initially ‘laminar’ and turbulent flow past fixed random particle assemblies of monodisperse spheres. The pseudo-turbulent kinetic energy $k^{(f)}$ in steady flow is then characterized as a function of solid volume fraction ${\it\phi}$ and the Reynolds number based on the mean slip velocity $\mathit{Re}_{m}$. Anisotropy in the Reynolds stress is quantified by decomposing it into isotropic and deviatoric parts, and its dependence on ${\it\phi}$ and $Re_{m}$ is explained. An algebraic stress model is proposed that captures the dependence of the Reynolds stress on ${\it\phi}$ and $Re_{m}$. Gas-phase velocity fluctuations in freely evolving suspensions undergoing elastic and inelastic particle collisions are also quantified. The flow corresponds to homogeneous gas–solid systems, with high solid-to-gas density ratio and particle diameter greater than dissipative length scales. It is found that for the parameter values considered here, the level of pseudo-turbulence differs by only 15 % from the values for equivalent fixed beds. The principle of conservation of interphase turbulent kinetic energy transfer is validated by quantifying the interphase transfer terms in the evolution equations of kinetic energy for the gas-phase and solid-phase fluctuating velocity. It is found that the collisional dissipation is negligible compared with the viscous dissipation for the cases considered in this study where the freely evolving suspensions attain a steady state starting from an initial condition where the particles are at rest.

scholarly journals The Effects of Curved Blade Turbine on the Hydrodynamic Structure of a Stirred Tank

2020 ◽  
Author(s):  
Bilel Ben Amira ◽  
Mariem Ammar ◽  
Ahmad Kaffel ◽  
Zied Driss ◽  
Mohamed Salah Abid
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Mean Square ◽  
Velocity Fluctuations ◽  
Stirred Vessel ◽  
Image Velocimetry ◽  
Trailing Vortices ◽  
Curved Blade ◽  
Blade Tip ◽  
Hydrodynamic Structure

This work is aimed at studying the hydrodynamic structure in a cylindrical stirred vessel equipped with an eight-curved blade turbine. Flow fields were measured by two-dimensional particle image velocimetry (PIV) to evaluate the effect of the curved blade turbine. Velocity field, axial and radial velocity distribution, root mean square (rms) of the velocity fluctuations, vorticity, and turbulent kinetic energy were presented. Therefore, two recirculation loops were formed close to the free surface and in the bottom of the tank. Moreover, the highest value area of the vorticity is localized in the upper region of the tank which follows the same direction of the first circulation loop. The turbulent kinetic energy is maximum at the blade tip following the trailing vortices.

scholarly journals Diurnal Dynamics of the Umov Kinetic Energy Density Vector in the Atmospheric Boundary Layer from Minisodar Measurements

Atmosphere ◽  
2021 ◽  
Vol 12 (10) ◽  
pp. 1347
Author(s):  
Alexander Potekaev ◽  
Nikolay Krasnenko ◽  
Liudmila Shamanaeva
Keyword(s):  
Energy Density ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Energy Flux ◽  
Wind Effect ◽  
Kinetic Energy Density ◽  
Near Surface ◽  
Density Vector ◽  
The Mean ◽  
Umov Vector

The diurnal hourly dynamics of the kinetic energy flux density vector, called the Umov vector, and the mean and turbulent components of the kinetic energy are estimated from minisodar measurements of wind vector components and their variances in the lower 200-meter layer of the atmosphere. During a 24-hour period of continuous minisodar observations, it was established that the mean kinetic energy density dominated in the surface atmospheric layer at altitudes below ~50 m. At altitudes from 50 to 100 m, the relative contributions of the mean and turbulent wind kinetic energy densities depended on the time of the day and the sounding altitude. At altitudes below 100 m, the contribution of the turbulent kinetic energy component is small, and the ratio of the turbulent to mean wind kinetic energy components was in the range 0.01–10. At altitudes above 100 m, the turbulent kinetic energy density sharply increased, and the ratio reached its maximum equal to 100–1000 at altitudes of 150–200 m. A particular importance of the direction and magnitude of the wind effect, that is, of the direction and magnitude of the Umov vector at different altitudes was established. The diurnal behavior of the Umov vector depended both on the time of the day and the sounding altitude. Three layers were clearly distinguished: a near-surface layer at altitudes of 5–15 m, an intermediate layer at altitudes from 15 m to 150 m, and the layer of enhanced turbulence above. The feasibility is illustrated of detecting times and altitudes of maximal and minimal wing kinetic energy flux densities, that is, time periods and altitude ranges most and least favorable for flights of unmanned aerial vehicles. The proposed novel method of determining the spatiotemporal dynamics of the Umov vector from minisodar measurements can also be used to estimate the effect of wind on high-rise buildings and the energy potential of wind turbines.

An explicit algebraic Reynolds-stress and scalar-flux model for stably stratified flows

2013 ◽  
Vol 723 ◽  
pp. 91-125 ◽  
Author(s):  
W. M. J. Lazeroms ◽  
G. Brethouwer ◽  
S. Wallin ◽  
A. V. Johansson
Keyword(s):  
Heat Flux ◽  
Kinetic Energy ◽  
Temperature Gradient ◽  
Reynolds Stress ◽  
Turbulent Heat Flux ◽  
Turbulent Heat ◽  
Homogeneous Shear ◽  
Self Consistent ◽  
The Mean ◽  
Homogeneous Shear Flow

AbstractThis work describes the derivation of an algebraic model for the Reynolds stresses and turbulent heat flux in stably stratified turbulent flows, which are mutually coupled for this type of flow. For general two-dimensional mean flows, we present a correct way of expressing the Reynolds-stress anisotropy and the (normalized) turbulent heat flux as tensorial combinations of the mean strain rate, the mean rotation rate, the mean temperature gradient and gravity. A system of linear equations is derived for the coefficients in these expansions, which can easily be solved with computer algebra software for a specific choice of the model constants. The general model is simplified in the case of parallel mean shear flows where the temperature gradient is aligned with gravity. For this case, fully explicit and coupled expressions for the Reynolds-stress tensor and heat-flux vector are given. A self-consistent derivation of this model would, however, require finding a root of a polynomial equation of sixth-order, for which no simple analytical expression exists. Therefore, the nonlinear part of the algebraic equations is modelled through an approximation that is close to the consistent formulation. By using the framework of a$K\text{{\ndash}} \omega $model (where$K$is turbulent kinetic energy and$\omega $an inverse time scale) and, where needed, near-wall corrections, the model is applied to homogeneous shear flow and turbulent channel flow, both with stable stratification. For the case of homogeneous shear flow, the model predicts a critical Richardson number of 0.25 above which the turbulent kinetic energy decays to zero. The channel-flow results agree well with DNS data. Furthermore, the model is shown to be robust and approximately self-consistent. It also fulfils the requirements of realizability.

Evaluation of Turbulent Kinetic Energy Dissipation Rate in a Free Jet Flow from PIV Measurements

2012 ◽  
Vol 7 (1) ◽  
pp. 53-69
Author(s):  
Vladimir Dulin ◽  
Yuriy Kozorezov ◽  
Dmitriy Markovich
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Turbulent Velocity ◽  
Small Scale ◽  
Velocity Fluctuations ◽  
Piv Measurements ◽  
Free Jet

The present paper reports PIV (Particle Image Velocimetry) measurements of turbulent velocity fluctuations statistics in development region of an axisymmetric free jet (Re = 28 000). To minimize measurement uncertainty, adaptive calibration, image processing and data post-processing algorithms were utilized. On the basis of theoretical analysis and direct measurements, the paper discusses effect of PIV spatial resolution on measured statistical characteristics of turbulent fluctuations. Underestimation of the second-order moments of velocity derivatives and of the turbulent kinetic energy dissipation rate due to a finite size of PIV interrogation area and finite thickness of laser sheet was analyzed from model spectra of turbulent velocity fluctuations. The results are in a good agreement with the measured experimental data. The paper also describes performance of possible ways to account for unresolved small-scale velocity fluctuations in PIV measurements of the dissipation rate. In particular, a turbulent viscosity model can be efficiently used to account for the unresolved pulsations in a free turbulent flow

Analysis of Turbulent Thermal Convection Between Horizontal Plates

1983 ◽  
Vol 105 (4) ◽  
pp. 789-794 ◽  
Author(s):  
M. Kaviany ◽  
R. Seban
Keyword(s):  
Temperature Distribution ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Thermal Convection ◽  
Equation Model ◽  
Experimental Results ◽  
Mixing Length ◽  
Mean Temperature ◽  
The Mean ◽  
The One

The one-equation model of turbulence is applied to the turbulent thermal convection between horizontal plates maintained at constant temperatures. A pseudo-three-layer model is used consisting of a conduction sublayer adjacent to the plates, a turbulent region within which the mixing length increases linearly, and a turbulent core within which the mixing length is a constant. It is assumed that the Nusselt number varies with the Rayleigh number to the one-third power. As a result, the steady-state distributions of the turbulent kinetic energy and the mean temperature are obtrained and presented in closed forms. These results include the effects of Prandtl number. The predictions are compared with the available experimental results for different Prandtl and Rayleigh numbers. Also included are the predictions of Kraichnan, which are based on a less exact analysis. The results of the one-equation model are in fair agreement with the experimental results for the distribution of the turbulent kinetic energy and the mean temperature distribution. The predictions of Kraichnan are in better agreement with the experimental results for the mean temperature distribution.

On the structure of shear stress and turbulent kinetic energy flux across the roughness layer of a gravel-bed channel flow

2009 ◽  
Vol 638 ◽  
pp. 423-452 ◽  
Author(s):  
EMMANUEL MIGNOT ◽  
D. HURTHER ◽  
E. BARTHELEMY
Keyword(s):  
Shear Stress ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Channel Flow ◽  
Mean Flow ◽  
Local Flow ◽  
Gravel Bed ◽  
Wall Flows ◽  
The Mean ◽  
Conditional Statistics

This study examines the structure of shear stress and turbulent kinetic energy (TKE) flux across the roughness layer of a uniform, fully rough gravel-bed channel flow (ks+ ≫ 100, δ/k = 20) using high-resolution acoustic Doppler velocity profiler measurements. The studied gravel-bed roughness layer exhibits a complex random multi-scale roughness structure in strong contrast with conceptualized k- or d-type roughness in standard rough-wall flows. Within the roughness layer, strong spatial variability of all time-averaged flow quantities are observed affecting up to 40% of the boundary layer height. This variability is attributed to the presence of bed zones with emanating bed protuberances (or gravel clusters) acting as local flow obstacles and bed zones of more homogenous roughness of densely packed gravel elements. Considering the strong spatial mean flow variability across the roughness layer, a spatio-temporal averaging procedure, called double averaging (DA), has been applied to the analysed flow quantities. Three aspects have been addressed: (a) the DA shear stress and DA TKE flux in specific bed zones associated with three classes of velocity profiles as previously proposed in Mignot, Barthélemy & Hurther (J. Fluid Mech., vol. 618, 2009, p. 279), (b) the global and per class DA conditional statistics of shear stress and associated TKE flux and (c) the contribution of large-scale coherent shear stress structures (LC3S) to the TKE flux across the roughness layer. The mean Reynolds and dispersive shear structure show good agreement between the protuberance bed zones associated with the S-shape/accelerated classes and recent results obtained in standard k-type rough-wall flows (Djenidi et al., Exp. Fluids, vol. 44, 2008, p. 37; Pokrajac, McEwan & Nikora, Exp. Fluids, vol. 45, 2008, p. 73). These gravel-bed protuberances act as local flow obstacles inducing a strong turbulent activity in their wake regions. The conditional statistics show that the Reynolds stress contribution is fairly well distributed between sweep and ejection events, with threshold values ranging from H = 0 to H = 8. However, the TKE flux across the roughness layer primarily results from the residual shear stress between ejection and sweep of very high magnitude (H = 10–20) and of small turbulent scale. Although LC3S are seen to penetrated the interfacial roughness layer, their TKE flux contribution is found to be negligible compared to the very energetic small-scale sweep events. These sweeps are dominantly produced in the bed zones of local gravel protuberances where the velocity profiles are inflexional of S-shape type and the mean flow properties are of mixing-layer flow type as previously shown in Mignot et al. (2009).

Dynamics of homogeneous bubbly flows Part 2. Velocity fluctuations

2002 ◽  
Vol 466 ◽  
pp. 53-84 ◽  
Author(s):  
BERNARD BUNNER ◽  
GRÉTAR TRYGGVASON
Keyword(s):  
Kinetic Energy ◽  
Reynolds Stress ◽  
Void Fraction ◽  
Three Dimensional ◽  
Bubbly Flows ◽  
Rise Velocity ◽  
Velocity Fluctuations ◽  
Kinetic Energy Spectrum ◽  
Average Rise ◽  
High Wavenumbers

Direct numerical simulations of the motion of up to 216 three-dimensional buoyant bubbles in periodic domains are presented. The bubbles are nearly spherical and have a rise Reynolds number of about 20. The void fraction ranges from 2% to 24%. Part 1 analysed the rise velocity and the microstructure of the bubbles. This paper examines the fluctuation velocities and the dispersion of the bubbles and the ‘pseudo-turbulence’ of the liquid phase induced by the motion of the bubbles. It is found that the turbulent kinetic energy increases with void fraction and scales with the void fraction multiplied by the square of the average rise velocity of the bubbles. The vertical Reynolds stress is greater than the horizontal Reynolds stress, but the anisotropy decreases when the void fraction increases. The kinetic energy spectrum follows a power law with a slope of approximately −3.6 at high wavenumbers.

Pseudo-turbulent heat flux and average gas–phase conduction during gas–solid heat transfer: flow past random fixed particle assemblies

2016 ◽  
Vol 798 ◽  
pp. 299-349 ◽  
Author(s):  
Bo Sun ◽  
Sudheer Tenneti ◽  
Shankar Subramaniam ◽  
Donald L. Koch
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Gas Phase ◽  
Volume Fraction ◽  
Turbulent Heat Flux ◽  
Turbulent Heat ◽  
Fluid Temperature ◽  
Bulk Fluid ◽  
The Mean ◽  
Temperature Equation

Fluctuations in the gas-phase velocity can contribute significantly to the total gas-phase kinetic energy even in laminar gas–solid flows as shown by Mehrabadi et al. (J. Fluid Mech., vol. 770, 2015, pp. 210–246), and these pseudo-turbulent fluctuations can also enhance heat transfer in gas–solid flow. In this work, the pseudo-turbulent heat flux arising from temperature–velocity covariance, and average fluid-phase conduction during convective heat transfer in a gas–solid flow are quantified and modelled over a wide range of mean slip Reynolds number and solid volume fraction using particle-resolved direct numerical simulations (PR-DNS) of steady flow through a random assembly of fixed isothermal monodisperse spherical particles. A thermal self-similarity condition on the local excess temperature developed by Tenneti et al. (Intl J. Heat Mass Transfer, vol. 58, 2013, pp. 471–479) is used to guarantee thermally fully developed flow. The average gas–solid heat transfer rate for this flow has been reported elsewhere by Sun et al. (Intl J. Heat Mass Transfer, vol. 86, 2015, pp. 898–913). Although the mean velocity field is homogeneous, the mean temperature field in this thermally fully developed flow is inhomogeneous in the streamwise coordinate. An exponential decay model for the average bulk fluid temperature is proposed. The pseudo-turbulent heat flux that is usually neglected in two-fluid models of the average fluid temperature equation is computed using PR-DNS data. It is found that the transport term in the average fluid temperature equation corresponding to the pseudo-turbulent heat flux is significant when compared to the average gas–solid heat transfer over a significant range of solid volume fraction and mean slip Reynolds number that was simulated. For this flow set-up a gradient-diffusion model for the pseudo-turbulent heat flux is found to perform well. The Péclet number dependence of the effective thermal diffusivity implied by this model is explained using a scaling analysis. Axial conduction in the fluid phase, which is often neglected in existing one-dimensional models, is also quantified. As expected, it is found to be important only for low Péclet number flows. Using the exponential decay model for the average bulk fluid temperature, a model for average axial conduction is developed that verifies standard assumptions in the literature. These models can be used in two-fluid simulations of heat transfer in fixed beds. A budget analysis of the mean fluid temperature equation provides insight into the variation of the relative magnitude of the various terms over the parameter space.

Seasonal Variability of Mesoscale Instabilities in the Azores Current System

2020 ◽  
Author(s):  
João Bettencourt ◽  
Carlos Guedes Soares
Keyword(s):  
Kinetic Energy ◽  
Reynolds Stress ◽  
North Atlantic ◽  
Current System ◽  
Baroclinic Instability ◽  
Primitive Equation ◽  
The Mean ◽  
Eastern North Atlantic ◽  
Jet Axis ◽  
Mean Kinetic Energy

<p>The Azores Current-Front system coincides with the northern limit of the subtropical gyre in  the Eastern North Atlantic. The mean zonal jet is positioned south of the Azores archipelago  and extends from west of the mid-atlantic ridge to the Gulf of Cadiz, where it partially  turns south. North of the main jet, a sub-surface counter-current is found, flowing westwards. The associated thermal front separates the warm subtropical waters from the colder subpolar waters. The instantaneous flow in the Azores Current/Front system is characterized by the presence of meandering currents with length scales of 200 km that regularly shed anticyclonic warm water and cyclonic cold water eddies to the north and south of the mean jet axis, respectively, due to vortex stretching and the planetary beta effect. The time scale of eddy shedding is 100-200 days. On the meandering arms of the current, downwelling <br>and upwelling cells are found and sharp thermal gradients are formed and a residual poleward heat transport is observed. The instability cycle that originates the mesoscale meanders and the eddies is well-known from quasi-geostrophic and primitive equation models initialized from a basic baroclinic state: a first phase of baroclinic instability feeds on available potential energy to raise eddy kinetic energy levels, that, in a second phase feed the mean kinetic energy by Reynolds stress convergence. The cycle repeats itself as long as the APE reservoir is filled at the end of each cycle.</p><p>However, seasonal variability of the zonal jet dynamics has not been addressed before and it can provide valuable insights in to the variations of the Eastern North Atlantic between the subtropical and subpolar gyres. We use a primitive equation regional ocean model of the Eastern Central North Atlantic with realistic climatological wind and thermal forcing to study the yearly cycle of meandering, eddy shedding and restoration of the mean jet in the Azores/Current system. We observe an semi-annual cycle in the jet's kinetic energy with maxima in Summer/Winter and minima in early Spring/Autumn. Potential energy conversion by baroclinic instability occurs throughout the year but is predominant in the first half of the year. The mean kinetic energy draws from the turbulent kinetic energy through Reynolds stress convergence in periods of 50 - 100 days, that are followed by short barotropic instability periods. During Winter, Reynolds stress convergence, and thus mean jet reinforcement from the mesoscale eddy field, occurs along the jet meridional extent, in the top 500 m of the water column, but from Spring to Autumn it is observed only in the southern flank of the mean jet axis.</p>

A revisit of the equilibrium assumption for predicting near-wall turbulence

2014 ◽  
Vol 760 ◽  
pp. 304-312 ◽  
Author(s):  
Farid Karimpour ◽  
Subhas K. Venayagamoorthy
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Turbulent Viscosity ◽  
Wall Turbulence ◽  
Wall Region ◽  
Turbulence Decay ◽  
Prime 2 ◽  
Near Wall Turbulence ◽  
Near Wall

AbstractIn this study, we revisit the consequence of assuming equilibrium between the rates of production ($P$) and dissipation $({\it\epsilon})$ of the turbulent kinetic energy $(k)$ in the highly anisotropic and inhomogeneous near-wall region. Analytical and dimensional arguments are made to determine the relevant scales inherent in the turbulent viscosity (${\it\nu}_{t}$) formulation of the standard $k{-}{\it\epsilon}$ model, which is one of the most widely used turbulence closure schemes. This turbulent viscosity formulation is developed by assuming equilibrium and use of the turbulent kinetic energy $(k)$ to infer the relevant velocity scale. We show that such turbulent viscosity formulations are not suitable for modelling near-wall turbulence. Furthermore, we use the turbulent viscosity $({\it\nu}_{t})$ formulation suggested by Durbin (Theor. Comput. Fluid Dyn., vol. 3, 1991, pp. 1–13) to highlight the appropriate scales that correctly capture the characteristic scales and behaviour of $P/{\it\epsilon}$ in the near-wall region. We also show that the anisotropic Reynolds stress ($\overline{u^{\prime }v^{\prime }}$) is correlated with the wall-normal, isotropic Reynolds stress ($\overline{v^{\prime 2}}$) as $-\overline{u^{\prime }v^{\prime }}=c_{{\it\mu}}^{\prime }(ST_{L})(\overline{v^{\prime 2}})$, where $S$ is the mean shear rate, $T_{L}=k/{\it\epsilon}$ is the turbulence (decay) time scale and $c_{{\it\mu}}^{\prime }$ is a universal constant. ‘A priori’ tests are performed to assess the validity of the propositions using the direct numerical simulation (DNS) data of unstratified channel flow of Hoyas & Jiménez (Phys. Fluids, vol. 18, 2006, 011702). The comparisons with the data are excellent and confirm our findings.

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