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.

Application of a Volume Averaged k-ε Model to Particle-Laden Turbulent Channel Flow

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
J. D. Schwarzkopf ◽  
C. T. Crowe ◽  
P. Dutta
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Carrier Phase ◽  
Critical Role ◽  
Turbulent Channel Flow ◽  
Mean Velocity ◽  
Closed Set ◽  
Production Term ◽  
Velocity Gradients ◽  
Additional Production

A closed set of volume averaged equations for modeling turbulence in the carrier phase of particle-laden flows is presented. The equations incorporate a recently developed dissipation transport equation that contains an additional production of dissipation term due to particle surfaces. 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. To assess the effects of this additional production term, a numerical model was developed and applied to particles falling in a channel of downward turbulent air flow. Boundary conditions were 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 coefficients associated with the production of dissipation due to mean velocity gradients and particle surfaces were varied to assess the effects of the dispersed phase on the carrier phase turbulent kinetic energy across the channel. The results show that the model predicts a decrease in turbulent kinetic energy near the wall with increased particle loading, and that the dissipation coefficients play a critical role in predicting the turbulent kinetic energy in particle-laden turbulent flows.

Interaction between a spatially growing turbulent boundary layer and embedded streamwise vortices

1996 ◽  
Vol 326 ◽  
pp. 151-179 ◽  
Author(s):  
Junhui Liu ◽  
Ugo Piomelli ◽  
Philippe R. Spalart
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Turbulent Kinetic Energy ◽  
Vortex Core ◽  
Eddy Viscosity ◽  
Shear Stresses ◽  
Streamwise Vortices ◽  
Mean Velocity ◽  
Production Term

The interaction between a zero-pressure-gradient turbulent boundary layer and a pair of strong, common-flow-down, streamwise vortices with a sizeable velocity deficit is studied by large-eddy simulation. The subgrid-scale stresses are modelled by a localized dynamic eddy-viscosity model. The results agree well with experimental data. The vortices drastically distort the boundary layer, and produce large spanwise variations of the skin friction. The Reynolds stresses are highly three-dimensional. High levels of kinetic energy are found both in the upwash region and in the vortex core. The two secondary shear stresses are significant in the vortex region, with magnitudes comparable to the primary one. Turbulent transport from the immediate upwash region is partly responsible for the high levels of turbulent kinetic energy in the vortex core; its effect on the primary stress 〈u′v′〉 is less significant. The mean velocity gradients play an important role in the generation of 〈u′v′〉 in all regions, while they are negligible in the generation of turbulent kinetic energy in the vortex core. The pressure-strain correlations are generally of opposite sign to the production terms except in the vortex core, where they have the same sign as the production term in the budget of 〈u′v′〉. The results highlight the limitations of the eddy-viscosity assumption (in a Reynolds-averaged context) for flows of this type, as well as the excessive diffusion predicted by typical turbulence models.

LDV Measurements of Periodic Fully Developed Main and Secondary Flows in a Channel With Rib-Disturbed Walls

1993 ◽  
Vol 115 (1) ◽  
pp. 109-114 ◽  
Author(s):  
T.-M. Liou ◽  
Y.-Y. Wu ◽  
Y. Chang
Keyword(s):  
Kinetic Energy ◽  
Secondary Flow ◽  
Turbulent Kinetic Energy ◽  
Secondary Flows ◽  
Laser Doppler Velocimeter ◽  
Parameter Distribution ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Production Term ◽  
Basic Assumptions

Laser-Doppler velocimeter measurements of mean velocities, turbulence intensities, and Reynolds stresses are presented for periodic fully developed flows in a channel with square rib-disturbed walls on two opposite sides. Quantities such as the vorticity thickness and turbulent kinetic energy are used to characterize the flow. The investigated flow was periodic in space. The Reynolds number based on the channel hydraulic diameter was 3.3×104. The ratios of pitch to rib-height and rib-height to chamber-height were 10 and 0.133, respectively. Regions where maximum and minimum Reynolds stress and turbulent kinetic energy occurred were identified from the results. The growth rate of the shear layers of the present study was compared with that of a backward-facing step. The measured turbulence anisotropy and structure parameter distribution were used to examine the basic assumptions embedded in the k–ε and k–ε–A models. For a given axial station, the peak axial mean-velocity was found not to occur at the center point. The secondary flow was determined to be Prandtl’s secondary flow of the second kind according to the measured streamwise mean vorticity and its production term.

PIV Investigation of Separated and Reattached Turbulent Flows Over Ribs of Various Aspect Ratio

2014 ◽  
Author(s):  
Kathryn M. Atamanchuk ◽  
Mark F. Tachie
Keyword(s):  
Kinetic Energy ◽  
Aspect Ratio ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Reynolds Shear Stress ◽  
Separated Flow ◽  
Particle Image Velocimetry System ◽  
Shear Stresses ◽  
Mean Velocity ◽  
Freestream Velocity

An experimental study is undertaken to investigate the features of separated and reattached flow over surface mounted traverse ribs of varying aspect ratio (1:1, 1:2, and 1:4) in a recirculating open channel turbulent flow. A particle image velocimetry system was used to conduct the velocity measurements. Upstream conditions were kept consistent among all three test cases. The reattachment length of the separated flow was found to decrease as rib aspect ratio increased, primarily as a result of a secondary separation reattachment formation on the ribs of increased aspect ratio. Contour plots of mean velocities, turbulence intensities, turbulent kinetic energy and Reynolds shear stresses, as well as one-dimensional profiles of streamwise mean velocity, turbulent kinetic energy and Reynolds shear stress in the recirculation and reattachment region are presented and discussed. The results show that maximum wall-normal mean velocities are approximately 40% of the approach freestream velocity. The results also indicate that the turbulence levels downstream of the block tend to decrease as the rib aspect ratio increases.

Spectra and Cospectra Over Flat Uniform Terrain

1994 ◽  
Author(s):  
J. C. Kaimal ◽  
J. J. Finnigan
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Energy Equation ◽  
Spatial Scales ◽  
Random Forcing ◽  
Dissipation Term ◽  
Turbulent Kinetic Energy Equation

Turbulent flows like those in the atmospheric boundary layer can be thought of as a superposition of eddies—coherent patterns of velocity, vorticity, and pressure— spread over a wide range of sizes. These eddies interact continuously with the mean flow, from which they derive their energy, and also with each other. The large “energy-containing” eddies, which contain most of the kinetic energy and are responsible for most of the transport in the turbulence, arise through instabilities in the background flow. The random forcing that provokes these instabilities is provided by the existing turbulence. This is the process represented in the production terms of the turbulent kinetic energy equation (1.59) in Chapter 1. The energy-containing eddies themselves are also subject to instabilities, which in their case are provoked by other eddies. This imposes upon them a finite lifetime before they too break up into yet smaller eddies. This process is repeated at all scales until the eddies become sufficiently small that viscosity can affect them directly and convert their kinetic energy to internal energy (heat). The action of viscosity is captured in the dissipation term of the turbulent kinetic energy equation. The second-moment budget equations presented in Chapter 1, of which (1.59) is one example, describe the summed behavior of all the eddies in the turbulent flow. To understand the conversion of mean kinetic energy into turbulent kinetic energy in the large eddies, the handing down of this energy to eddies of smaller and smaller scale in an “eddy cascade” process, and its ultimate conversion to heat by viscosity, we must isolate the different scales of turbulent motion and separately observe their behavior. Taking Fourier spectra and cospectra of the turbulence offers a convenient way of doing this. The spectral representation associates with each scale of motion the amount of kinetic energy, variance, or eddy flux it contributes to the whole and provides a new and invaluable perspective on boundary layer structure. The spectrum of boundary layer fluctuations covers a range of more than five decades: millimeters to kilometers in spatial scales and fractions of a second to hours in temporal scales.

Rotating Effect on Fluid Flow in a Smooth Duct With a 180-Deg Sharp Turn

2000 ◽  
Author(s):  
Chung-Chu Chen ◽  
Tong-Miin Liou
Keyword(s):  
Heat Transfer ◽  
Kinetic Energy ◽  
Secondary Flow ◽  
Turbulent Kinetic Energy ◽  
Turbine Blades ◽  
Outer Part ◽  
Intensity Level ◽  
Mean Velocity ◽  
High Heat Transfer ◽  
Sharp Turn

Laser-Doppler velocimetry (LDV) measurements are presented of turbulent flow in a two-pass square-sectioned duct simulating the coolant passages employed in gas turbine blades under rotating and non-rotating conditions. For all cases studied, the Reynolds number characterized by duct hydraulic diameter (Dh) and bulk mean velocity (Ub) was fixed at 1 × 104. The rotating case had a range of rotation number (Ro = ΩDh/Ub) from 0 to 0.2. It is found that both the skewness of streamwise mean velocity and magnitude of secondary-flow velocity increase linearly, and the magnitude of turbulence intensity level increases non-linearly with increasing Ro. As Ro is increased, the curvature induced symmetric Dean vortices in the turn for Ro = 0 is gradually dominated by a single vortex most of which impinges directly on the outer part of leading wall. The high turbulent kinetic energy is closely related to the dominant vortex prevailing inside the 180-deg sharp turn. For the first time, the measured flow characteristics account for the reported spanwise heat transfer distributions in the rotating channels, especially the high heat transfer enhancement on the leading wall in the turn. For both rotating and non-rotating cases, the direction and strength of the secondary flow with respect to the wall are the most important fluid dynamic factors affecting local heat transfer distributions inside a 180-deg sharp turn. The role of the turbulent kinetic energy in affecting the overall enhancement of heat transfer is well addressed.

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.

scholarly journals Discussion on improved method of turbulence model for supercritical water flow and heat transfer

2020 ◽  
Vol 24 (5 Part A) ◽  
pp. 2729-2741
Author(s):  
Zhenchuan Wang ◽  
Guoli Qi ◽  
Meijun Li
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulence Model ◽  
Buoyancy Effect ◽  
Improved Method ◽  
Production Term ◽  
Flow And Heat Transfer ◽  
Effect Model

The turbulence model fails in supercritical fluid-flow and heat transfer simulation, owing to the drastic change of thermal properties. The inappropriate buoyancy effect model and the improper turbulent Prandtl number model are several of these factors lead to the original low-Reynolds number turbulence model unable to predict the wall temperature for vertically heated tubes under the deteriorate heat transfer conditions. This paper proposed a simplified improved method to modify the turbulence model, using the generalized gradient diffusion hypothesis approximation model for the production term of the turbulent kinetic energy due to the buoyancy effect, using a turbulence Prandtl number model for the turbulent thermal diffusivity instead of the constant number. A better agreement was accomplished by the improved turbulence model compared with the experimental data. The main reason for the over-predicted wall temperature by the original turbulence model is the misuse of the buoyancy effect model. In the improved model, the production term of the turbulent kinetic energy is much higher than the results calculated by the original turbulence model, especially in the boundary-layer. A more accurate model for the production term of the turbulent kinetic energy is the main direction of further modification for the low Reynolds number turbulence model.

Coherent Velocity Structures in the Mixed Layer: Characteristics, Energetics, and Turbulent Kinetic Energy Budget

2021 ◽  
Author(s):  
Ewa Jarosz ◽  
Hemantha W. Wijesekera ◽  
David W. Wang
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Mixed Layer ◽  
Vertical Velocity ◽  
Mixed Layer Depth ◽  
Vertical Transport ◽  
Rate Of Change ◽  
Production Term ◽  
Forcing Mechanisms ◽  
Surface Buoyancy

AbstractVelocity, hydrographic, and microstructure observations collected under moderate to high winds, large surface waves, and significant ocean-surface heat losses were utilized to examine coherent velocity structures (CVS) and turbulent kinetic energy (TKE) budget in the mixed layer on the outer shelf in the northern Gulf of Mexico in February 2017. The CVS exhibited larger downward velocities in downweling regions and weaker upward velocities in broader upwelling regions, elevated vertical velocity variance, vertical velocity maxima in the upper part of the mixed layer, and phasing of crosswind velocities relative to vertical velocities near the base of the mixed layer. Temporal scales ranged from 10 min to 40 min and estimated lateral scales ranged from 90 m to 430 m, which were 1.5 – 6 times larger than the mixed layer depth. Nondimensional parameters, Langmuir and Hoenikker numbers, indicated that plausible forcing mechanisms were surface-wave driven Langmuir vortex and destabilizing surface buoyancy flux. The rate of change of TKE, shear production, Stokes production, buoyancy production, vertical transport of TKE, and dissipation in the TKE budget were evaluated. The shear and Stokes productions, dissipation, and vertical transport of TKE were the dominant terms. The buoyancy production term was important at the sea surface, but it decreased rapidly in the interior. A large imbalance term was found under the unstable, high wind, and high-sea state conditions. The cause of this imbalance cannot be determined with certainty through analyses of the available observations; however, our speculation is that the pressure transport is significant under these conditions.

Rotating Effect on Fluid Flow in Two Smooth Ducts Connected by a 180-Degree Bend

2003 ◽  
Vol 125 (1) ◽  
pp. 138-148 ◽  
Author(s):  
Tong-Miin Liou ◽  
Chung-Chu Chen ◽  
Meng-Yu Chen
Keyword(s):  
Heat Transfer ◽  
Kinetic Energy ◽  
Secondary Flow ◽  
Turbulent Kinetic Energy ◽  
Separation Bubble ◽  
Turbine Blades ◽  
Outer Part ◽  
Intensity Level ◽  
Mean Velocity ◽  
Sharp Turn

Laser Doppler velocimetry (LDV) measurements are presented of turbulent flow in a two-pass square-sectioned smooth duct simulating the coolant passages employed in gas turbine blades under rotating and nonrotating conditions. For all cases studied, the Reynolds number characterized by duct hydraulic diameter and bulk mean velocity was fixed at 1×104. The rotation number Ro was varied from 0 to 0.2. It is found that as Ro is increased, both the skewness (SK) of streamwise mean velocity and magnitude of secondary-flow velocity increase linearly, SK=2.3 Ro and U2+V2¯/Uh=2.3 Ro+0.4, and the magnitude of turbulence intensity level increases exponentially. As Ro is increased, the curvature induced symmetric Dean vortices in the turn for Ro=0 is gradually dominated by a single vortex most of which impinges directly on the outer part of leading wall. The high turbulent kinetic energy is closely related to the dominant vortex prevailing inside the 180-deg sharp turn. The size of separation bubble immediately after the turn is found to diminish to null as Ro is increased from 0 to 0.2. A simple correlation is developed between the bubble size and Ro. A critical range of Ro responsible for the switch of faster moving flow from near the outer wall to the inner wall is identified. For both rotating and nonrotating cases, the direction and strength of the secondary flow with respect to the wall are the most important fluid dynamic factors affecting local the heat transfer distributions inside a 180-deg sharp turn. The role of the turbulent kinetic energy in the overall enhancement of heat transfer is well addressed.

Sign in / Sign up

Export Citation Format

Share Document