On Two-Way Coupling in Gas-Solid Turbulent Flows

2003 ◽  
Author(s):  
Olivier Simonin ◽  
Kyle D. Squires
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Point Force ◽  
Turbulent Motion ◽  
Computational Techniques ◽  
Dispersed Phase ◽  
Turbulent Fluctuation ◽  
Momentum Exchange ◽  
Energy Transfers

An analysis of kinetic energy transfer in particle-laden turbulent flows is presented. The present study focuses on the subset in which dispersed-phase motion is restricted to particles in translation, particle diameters are smaller than the smallest lengthscales in the turbulent carrier flow, and the dispersed phase is present at negligible volume fraction. An analysis of the separate and exact two-fluid mean and turbulent kinetic energy transport equations shows that momentum exchange between the phases results in a transfer of kinetic energy from the mean to the fluctuating motion of the two-phase mixture. The source term accounting for fluid-particle coupling in the fluid turbulent kinetic energy equation is written as the sum of three parts, the first part representing the production of velocity fluctuations in the particle wake (“pseudo turbulence”), the second and third contributions — which act primarily on the larger scales of the fluid turbulent motion — representing a damping effect due to the turbulent fluctuation of the drag force and the effect of the transport of the particles by the fluid turbulence against their mean relative motion. A schematic representation of the energy transfers in particle-laden mixtures is also presented for the simplified systems under consideration, consistent with the separation of scales between perturbations introduced at the scale of the particle and the large, energy-containing scales of fluid turbulent motion. Implications of the energy transfers for ensemble-averaged modeling approaches are discussed, along with computational techniques that account for the back-effect of the particles on the flow using the point-force approximation. It is shown that the point-force approximation as typically implemented only accounts for the modulation of the large eddies, the contribution to wake production is not included, being implicitly assumed to be in local equilibrium with the corresponding viscous dissipation.

Turbulent kinetic energy production and flow structures in flows past smooth and rough walls

2019 ◽  
Vol 866 ◽  
pp. 897-928 ◽  
Author(s):  
P. Orlandi
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Energy Production ◽  
Compressive Strain ◽  
Turnover Time ◽  
Flow Structures ◽  
Wall Region ◽  
Rate Of Dissipation

Data available in the literature from direct numerical simulations of two-dimensional turbulent channels by Lee & Moser (J. Fluid Mech., vol. 774, 2015, pp. 395–415), Bernardini et al. (J. Fluid Mech., 742, 2014, pp. 171–191), Yamamoto & Tsuji (Phys. Rev. Fluids, vol. 3, 2018, 012062) and Orlandi et al. (J. Fluid Mech., 770, 2015, pp. 424–441) in a large range of Reynolds number have been used to find that $S^{\ast }$ the ratio between the eddy turnover time ($q^{2}/\unicode[STIX]{x1D716}$, with $q^{2}$ being twice the turbulent kinetic energy and $\unicode[STIX]{x1D716}$ the isotropic rate of dissipation) and the time scale of the mean deformation ($1/S$), scales very well with the Reynolds number in the wall region. The good scaling is due to the eddy turnover time, although the turbulent kinetic energy and the rate of isotropic dissipation show a Reynolds dependence near the wall; $S^{\ast }$, as well as $-\langle Q\rangle =\langle s_{ij}s_{ji}\rangle -\langle \unicode[STIX]{x1D714}_{i}\unicode[STIX]{x1D714}_{i}/2\rangle$ are linked to the flow structures, and also the latter quantity presents a good scaling near the wall. It has been found that the maximum of turbulent kinetic energy production $P_{k}$ occurs in the layer with $-\langle Q\rangle \approx 0$, that is, where the unstable sheet-like structures roll-up to become rods. The decomposition of $P_{k}$ in the contribution of elongational and compressive strain demonstrates that the two contributions present a good scaling. However, the good scaling holds when the wall and the outer structures are separated. The same statistics have been evaluated by direct simulations of turbulent flows in the presence of different types of corrugations on both walls. The flow physics in the layer near the plane of the crests is strongly linked to the shape of the surface and it has been demonstrated that the $u_{2}$ (normal to the wall) fluctuations are responsible for the modification of the flow structures, for the increase of the resistance and of the turbulent kinetic energy production.

A k-ε Model for Particle-Laden Turbulent Flows

2009 ◽  
Author(s):  
J. D. Schwarzkopf ◽  
C. T. Crowe ◽  
P. Dutta
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Carrier Phase ◽  
Critical Role ◽  
New Production ◽  
Mean Velocity ◽  
Production Term ◽  
Dissipation Term ◽  
Velocity Gradients

A dissipation transport equation for the carrier phase of particle-laden turbulent flows was recently developed. This equation shows a new production of dissipation term due to the presence of particles that is related to the velocity difference between the particle and the surrounding fluid. In the development, it was assumed that each coefficient was the sum of the coefficient for single phase flow and a coefficient quantifying the contribution of the particulate phase. The coefficient for the new production term (due to the presence of particles) was found from homogeneous turbulence generation by particles and the coefficient for the dissipation of dissipation term was analyzed using DNS. A numerical model was developed and applied to particles falling in a channel of downward turbulent air flow. Boundary conditions were also developed to ensure that the production of turbulent kinetic energy due to mean velocity gradients and particle surfaces balanced with the turbulent dissipation near the wall. The turbulent kinetic energy is compared with experimental data. The results show attenuation of turbulent kinetic energy with increased particle loading; however the model does under predict the turbulent kinetic energy near the center of the channel. To understand the effect of this additional production of dissipation term (due to particles), the coefficients associated with the production of dissipation due to mean velocity gradients and particle surfaces are varied to assess the effects of the dispersed phase on the carrier phase turbulent kinetic energy across the channel. The results show that this additional term plays a significant role in predicting the turbulent kinetic energy and a reason for under predicting the turbulent kinetic energy near the center of the channel is discussed. It is concluded that the dissipation coefficients play a critical role in predicting the turbulent kinetic energy in particle-laden turbulent flows.

scholarly journals Dissipation rate of turbulent kinetic energy in stably stratified sheared flows

2018 ◽  
Author(s):  
Sergej Zilitinkevich ◽  
Oleg Druzhinin ◽  
Andrey Glazunov ◽  
Evgeny Kadantsev ◽  
Evgeny Mortikov ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Atmospheric Chemistry ◽  
Dissipation Rate ◽  
Stable Stratification ◽  
Turbulence Closure ◽  
Atmospheric Measurements ◽  
Precise Knowledge ◽  
Budget Equation

Abstract. Over the years, the problem of dissipation rate of turbulent kinetic energy (TKE) in stable stratification remained unclear because of the practical impossibility to directly measure the process of dissipation that takes place at the smallest scales of turbulent motions. Poor representation of dissipation causes intolerable uncertainties in turbulence-closure theory and, thus, in modelling stably stratified turbulent flows. We obtain theoretical solution to this problem for the whole range of stratifications from neutral to limiting stable; and validate it via (i) direct numerical simulation (DNS) immediately detecting the dissipation rate and (ii) indirect estimates of dissipation rate retrieved via the TKE-budget equation from atmospheric measurements of other components of the TKE-budget. The proposed formulation of dissipation rate will be of use in any turbulence-closure models employing the TKE budget equation and in problems requiring precise knowledge of the high-frequency part of turbulence spectra in atmospheric chemistry, aerosol science and microphysics of clouds.

Grid Requirements for Multiscale Resolution in Separated Unsteady High Speed Turbulent Flows

2006 ◽  
Author(s):  
D. Basu ◽  
A. Hamed ◽  
K. Das
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Sound Pressure Level ◽  
High Speed ◽  
Sound Pressure ◽  
Pressure Fluctuations ◽  
Pressure Level ◽  
Navier Stokes ◽  
Detached Eddy Simulation

This study deals with the computational grid requirements in multiscale simulations of separated turbulent flows at high Reynolds number. The two-equation k-ε based DES (Detached Eddy Simulation) model is implemented in a full 3-D Navier-Stokes solver and numerical results are presented for transonic flow solution over an open cavity. Results for the vorticity, pressure fluctuations, SPL (Sound Pressure level) spectra and for modeled and resolved TKE (Turbulent Kinetic Energy) are presented and compared with available experimental data and with LES results. The results indicate that grid resolution significantly influences the resolved scales and the peak amplitude of the unsteady sound pressure level (SPL) and turbulent kinetic energy spectra.

Groove-induced changes of discharge in channel flows

2016 ◽  
Vol 799 ◽  
pp. 297-333 ◽  
Author(s):  
Yu Chen ◽  
J. M. Floryan ◽  
Y. T. Chew ◽  
B. C. Khoo
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Flow Regime ◽  
Turbulent Flows ◽  
Arbitrary Form ◽  
Reynolds Stresses ◽  
Bulk Fluid ◽  
Geometry Model ◽  
Smooth Channel ◽  
Channel Configuration

The changes in discharge in pressure-driven flows through channels with longitudinal grooves have been investigated in the laminar flow regime and in the turbulent flow regime with moderate Reynolds numbers ($Re_{2H}\approx 6000$) using both analytical and numerical methodologies. The results demonstrate that the long-wavelength grooves can increase discharge by 20 %–150 %, depending on the groove amplitude and the type of flow, while the short-wavelength grooves reduce the discharge. It has been shown that the reduced geometry model applies to the analysis of turbulent flows and the performance of grooves of arbitrary form is well approximated by the performance of grooves whose shape is represented by the dominant Fourier mode. The flow patterns, the turbulent kinetic energy as well as the Reynolds stresses were examined to identify the mechanisms leading to an increase in discharge. It is shown that the increase in discharge results from the rearrangement of the bulk fluid movement and not from the suppression of turbulence intensity. The turbulent kinetic energy and the Reynolds stresses are rearranged while their volume-averaged intensities remain the same as in the smooth channel. Analysis of the interaction of the groove patterns on both walls demonstrates that the converging–diverging configuration results in the greatest increase in discharge while the wavy channel configuration results in a reduction in discharge.

scholarly journals Dissipation rate of turbulent kinetic energy in stably stratified sheared flows

2019 ◽  
Vol 19 (4) ◽  
pp. 2489-2496 ◽  
Author(s):  
Sergej Zilitinkevich ◽  
Oleg Druzhinin ◽  
Andrey Glazunov ◽  
Evgeny Kadantsev ◽  
Evgeny Mortikov ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Atmospheric Chemistry ◽  
Dissipation Rate ◽  
Stable Stratification ◽  
Turbulence Closure ◽  
Atmospheric Measurements ◽  
Precise Knowledge ◽  
Budget Equation

Abstract. Over the years, the problem of dissipation rate of turbulent kinetic energy (TKE) in stable stratification remained unclear because of the practical impossibility to directly measure the process of dissipation that takes place at the smallest scales of turbulent motion. Poor representation of dissipation causes intolerable uncertainties in turbulence-closure theory and thus in modelling stably stratified turbulent flows. We obtain a theoretical solution to this problem for the whole range of stratifications from neutral to limiting stable; and validate it via (i) direct numerical simulation (DNS) immediately detecting the dissipation rate and (ii) indirect estimates of dissipation rate retrieved via the TKE budget equation from atmospheric measurements of other components of the TKE budget. The proposed formulation of dissipation rate will be of use in any turbulence-closure models employing the TKE budget equation and in problems requiring precise knowledge of the high-frequency part of turbulence spectra in atmospheric chemistry, aerosol science, and microphysics of clouds.

Direct Numerical Simulation of Homogeneous Turbulent Shear Flow Containing Bubbles

2006 ◽  
Author(s):  
T. Kawamura ◽  
T. Nakatani
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Production Rate ◽  
Turbulent Flows ◽  
Reynolds Numbers ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Hypothetical Model ◽  
Turbulent Reynolds Number

Direct numerical simulations of homogeneous shear turbulent flows containing deformable bubbles were carried out for clarifying the mechanism of drag reduction by microbubbles. The results show that presence of bubbles can suppress or enhance the development of turbulence depending on condition. The dissipation rate of turbulent kinetic energy is always increased by bubbles, while the production rate can be either increased or decreased depending on the turbulent and shear Reynolds numbers. As a result, the growth rate of turbulent kinetic energy can be either increased or decreased by bubbles depending on conditions. It was shown that the production rate tends to decrease at smaller shear Reynolds number, at larger turbulent Reynolds number, and at larger Weber number. Based on the results, a hypothetical model to explain the dependency on the Reynolds numbers has been proposed.

scholarly journals Accelerated wind conditions: spectral shape evolution and turbulent kinetic energy dissipation from laboratory and field measurements

2020 ◽  
Author(s):  
Lucia Robles-Diaz ◽  
Francisco J. Ocampo-Torres ◽  
Hubert Branger
Keyword(s):  
Wind Speed ◽  
Kinetic Energy ◽  
Momentum Transfer ◽  
Turbulent Kinetic Energy ◽  
Field Data ◽  
Wind Wave ◽  
Wave Spectrum ◽  
Sampling Rate ◽  
Momentum Exchange ◽  
Free Surface Displacement

<div> <div> <div> <p>A determined shape of the energy wave spectrum can be estimated from a given fetch and wind speed. Also, several studies have characterized the balance of the turbulent kinetic energy under the effect of waves and currents under constant wind conditions. However, deeper research is needed in order to characterize the wind-wave generation processes under non-stationary wind conditions. In this way, to be able to determine the uncertainty on not considering accelerated wind events in the air-sea momentum exchange estimations.</p> <p>Periods of accelerated winds were analyzed from experimental and field data. On one hand, several laboratory experiments were carried out in a large wind-wave facility at the Institut Pytheas (Marseille-France). Momentum fluxes were estimated from hot wire anemometry and, the free surface displacement was measured along the wave tank by resistance and capacitance wire probes. Also, the surface drift current was measured from a profiling acoustic velocimeter. During these experiments, the wind speed goes from 2 m/s to reach the maximum wind speed of 13 m/s. A constant wind acceleration characterizes each test. On the other hand, the field data were obtained from an Oceanographic and Marine Meteorology Buoy (BOMM) located in the Gulf of Mexico, from July 2018 to February 2019. The BOMM was equipped with a sonic anemometer, capacitance wires, and an inertial motion unit. Both sets of data are characterized by a high sampling rate that allows us to directly estimate the wind stress over the sea surface. Also, provide us with useful information about the evolution of the wave spectra and enable us to determine the dissipation rate of turbulent kinetic energy. It was observed that the wind acceleration has a direct effect on the momentum transfer efficiency from the wind to the wave field and that the momentum transfer is reduced as wind acceleration increases.</p> </div> </div> </div>

scholarly journals Experimental study on two oscillating grid turbulence with viscoelastic fluids based on PIV

2017 ◽  
Vol 95 (12) ◽  
pp. 1271-1277 ◽  
Author(s):  
Yue Wang ◽  
Wei-Hua Cai ◽  
Xin Zheng ◽  
Hong-Na Zhang ◽  
Feng-Chen Li
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Isotropic Turbulence ◽  
Critical Concentration ◽  
Reduction Rate ◽  
Small Scale ◽  
Grid Turbulence ◽  
Viscoelastic Effect ◽  
Oscillating Grid

In this paper, to study the viscoelastic effect on isotropic turbulence without wall effects, a two oscillating grid turbulence is built to investigate this phenomenon using particle image velocimetry. In the experiments, the classical drag-reducing additives are chosen: polyacrylamide (PAM) and cetyltrimethyl ammonium chloride (CTAC), which have shown remarkable drag-reducing effect in wall-bounded turbulent flows. The results show that the existence of drag-reducing additives makes velocity field more anisotropic and reduces turbulent kinetic energy. We propose an intuitive and natural definition for a reduction rate of turbulent kinetic energy to show viscoelastic effect. It suggests that there exists a critical concentration for the reduction rate of turbulent kinetic energy in the CTAC solution case. Also, the small-scale vortex structures are inhibited, which suggests the drag-reducing mechanism in grid turbulence without wall effect.

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