The evolution of a uniformly sheared thermally stratified turbulent flow

1997 ◽  
Vol 334 ◽  
pp. 61-86 ◽  
Author(s):  
PAUL PICCIRILLO ◽  
CHARLES W. VAN ATTA
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Richardson Number ◽  
Initial Conditions ◽  
Velocity Shear ◽  
Spectral Energy ◽  
Small Scale ◽  
Mean Flow ◽  
Mean Velocity ◽  
Small Scales

Experiments were carried out in a new type of stratified flow facility to study the evolution of turbulence in a mean flow possessing both uniform stable stratification and uniform mean shear.The new facility is a thermally stratified wind tunnel consisting of ten independent supply layers, each with its own blower and heaters, and is capable of producing arbitrary temperature and velocity profiles in the test section. In the experiments, four different sized turbulence-generating grids were used to study the effect of different initial conditions. All three components of the velocity were measured, along with the temperature. Root-mean-square quantities and correlations were measured, along with their corresponding power and cross-spectra.As the gradient Richardson number Ri = N2/(dU/dz)2 was increased, the downstream spatial evolution of the turbulent kinetic energy changed from increasing, to stationary, to decreasing. The stationary value of the Richardson number, Ricr, was found to be an increasing function of the dimensionless shear parameter Sq2/∈ (where S = dU/dz is the mean velocity shear, q2 is the turbulent kinetic energy, and ∈ is the viscous dissipation).The turbulence was found to be highly anisotropic, both at the small scales and at the large scales, and anisotropy was found to increase with increasing Ri. The evolution of the velocity power spectra for Ri [les ] Ricr, in which the energy of the large scales increases while the energy in the small scales decreases, suggests that the small-scale anisotropy is caused, or at least amplified, by buoyancy forces which reduce the amount of spectral energy transfer from large to small scales. For the largest values of Ri, countergradient buoyancy flux occurred for the small scales of the turbulence, an effect noted earlier in the numerical results of Holt et al. (1992), Gerz et al. (1989), and Gerz & Schumann (1991).

A turbulent patch arising from a breaking internal wave

2011 ◽  
Vol 677 ◽  
pp. 103-133 ◽  
Author(s):  
SERGEY N. YAKOVENKO ◽  
T. GLYN THOMAS ◽  
IAN P. CASTRO
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Internal Gravity Wave ◽  
Density Fluctuations ◽  
Transport Processes ◽  
Velocity Shear ◽  
Mean Velocity ◽  
Bottom Part ◽  
Developed Turbulence ◽  
Turbulence Generation

Results of direct numerical simulations of the development of a breaking internal gravity wave are presented. The wave was forced by the imposition of an appropriate bottom boundary shape (a two-dimensional cosine hill) within a density-stratified domain having a uniform upstream velocity and density gradient. The focus is on turbulence generation and maintenance within the turbulent patch generated by the wave breaking. Pathlines, density contours, temporal and spatial spectra, and second moments of the velocity and density fluctuations and turbulent kinetic energy balance terms obtained from the data averaged over the span in the mixed zone are all used in the analysis of the flow. Typical Reynolds numbers, based on the vertical scale of the breaking region and the upstream velocity, were around 6000 and the fully resolved computations yielded sufficient resolution to capture the fine-scale transition processes as well as the subsequent fully developed turbulence. It is shown that globally, within the turbulent patch, there is an approximate balance in the production, dissipation and transport processes for turbulent kinetic energy, so that the patch remains quasi-steady over a significant time. Although it is far from being axially homogeneous, with turbulence generation occurring largely near the upstream bottom part of the patch where the mean velocity shear is particularly large, it has features not dissimilar to those of a classical turbulent wake.

Experimental investigation of jets in a crossflow

1984 ◽  
Vol 138 ◽  
pp. 93-127 ◽  
Author(s):  
J. Andreopoulos ◽  
W. Rodi
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Velocity Ratio ◽  
Three Dimensional ◽  
Turbulent Shear ◽  
Shear Stresses ◽  
Hot Wire ◽  
Mean Flow ◽  
Mean Velocity ◽  
Turbulent Kinetic Energy Equation

The paper reports on measurements in the flow generated by a jet issuing from a circular outlet in a wall into a cross-stream along this wall. For the jet-to-crossflow velocity ratios R of 0.5, 1 and 2, the mean and fluctuating velocity components were measured with a three-sensor hot-wire probe. The hot-wire signals were evaluated to yield the three mean-velocity components, the turbulent kinetic energy, the three turbulent shear stresses and, in the case of R = 0.5, the terms in the turbulent-kinetic-energy equation. The results give a quantitative picture of the complex three-dimensional mean flow and turbulence field, and the various phenomena as well as their dependence on the velocity ratio R are discussed in detail.

Comparison of Turbulence Modeling Strategies for Indoor Flows

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Ammar M. Abdilghanie ◽  
Lance R. Collins ◽  
David A. Caughey
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Constant Coefficient ◽  
Turbulence Modeling ◽  
Intermittent Flow ◽  
Turbulence Level ◽  
Mean Flow ◽  
Mean Velocity ◽  
Slow Development ◽  
Inlet Conditions

Turbulence modeling techniques are compared for the simulation of low speed indoor air flow in a simple room. The effect of inlet turbulence intensity on the flow field is investigated using the constant coefficient large eddy simulation (LES) model with uniform mean inlet conditions at several levels of inlet turbulence intensities. The results show significant differences between the simulations with laminar inflow conditions and those in which turbulence was introduced at the inlet. For simulations with turbulent inlet conditions, it is noticed that the jet transitions to a state of fully developed turbulence wherein the dynamics of the flow become nearly insensitive to any further increase in the level of inlet turbulence. For laminar flow conditions, it is seen that the jet slowly spreads and mixes with the quiescent room air. As a result, the jet reaches a fully developed turbulent state further away from the inlet relative to the simulations with inlet turbulence. The effect of using experimental inlet profiles is also investigated. It is seen that, close to the inlet, the flow is sensitive to the inflow details, whereas further away from the inlet, these effects become less pronounced. The results from the constant coefficient and the dynamic LES models are compared. The most noticeable differences in the flow occur at the locations where the subgrid-scale’s contribution to the turbulent kinetic energy is highest. Finally, the results from the dynamic LES and the k-ϵ models are compared. It is found that there are significant differences between the two models for the zero inlet turbulence limit where the flow is most probably transitional in nature and turbulence has not yet reached a fully developed state. It is seen that in the laminar inflow case the k-ϵ model predicts a fully turbulent jet very close to the inlet and thus fails to capture the slow development of the jet found in LES. Accordingly, the k-ϵ model results are nearly insensitive to the level of inlet turbulence especially far from the origin of the flow. It is also seen that for cases with nonzero inlet turbulence level, the k-ϵ model predicts the general features of the mean flow reasonably well; however, the k-ϵ model overpredicts the jet spreading rate and the turbulent kinetic energy close to the inlet. Furthermore, the k-ϵ model under predicts the turbulence level near the corner of the ceiling as it fails to capture the complicated mean velocity and turbulent kinetic energy, most likely because of the highly intermittent flow pattern found there in LES.

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.

A theory of turbulence in stratified fluids

1970 ◽  
Vol 42 (2) ◽  
pp. 349-365 ◽  
Author(s):  
Robert R. Long
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Density Profile ◽  
Richardson Number ◽  
Mixed Volume ◽  
Volume Of Fluid ◽  
Velocity Shear ◽  
Mean Velocity ◽  
Large Wave ◽  
The Mean

An effort is made to understand turbulence in fluid systems like the oceans and atmosphere in which the Richardson number is generally large. Toward this end, a theory is developed for turbulent flow over a flat plate which is moved and cooled in such a way as to produce constant vertical fluxes of momentum and heat. The theory indicates that in a co-ordinate system fixed in the plate the mean velocity increases linearly with heightzabove a turbulent boundary layer and the mean density decreases asz3, so that the Richardson number is large far from the plate. Near the plate, the results reduce to those of Monin & Obukhov.Thecurvatureof the density profile is essential in the formulation of the theory. When the curvature is negative, a volume of fluid, thoroughly mixed by turbulence, will tend to flatten out at a new level well above the original centre of mass, thereby transporting heat downward. When the curvature is positive a mixed volume of fluid will tend to fall a similar distance, again transporting heat downward. A well-mixed volume of fluid will also tend to rise when the density profile is linear, but this rise is negligible on the basis of the Boussinesq approximation. The interchange of fluid of different, mean horizontal speeds in the formation of the turbulent patch transfers momentum. As the mixing in the patch destroys the mean velocity shear locally, kinetic energy is transferred from mean motion to disturbed motion. The turbulence can arise in spite of the high Richardson number because the precise variations of mean density and mean velocity mentioned above permit wave energy to propagate from the turbulent boundary layer to the whole region above the plate. At the levels of reflexion, where the amplitudes become large, wave-breaking and turbulence will tend to develop.The relationship between the curvature of the density profile and the transfer of heat suggests that the density gradient near the level of a point of inflexion of the density curve (in general cases of stratified, shearing flow) will increase locally as time goes on. There will also be a tendency to increase the shear through the action of local wave stresses. If this results in a progressive reduction in Richardson number, an ultimate outbreak of Kelvin–Helmholtz instability will occur. The resulting sporadic turbulence will transfer heat (and momentum) through the level of the inflexion point. This mechanism for the appearance of regions of low Richardson number is offered as a possible explanation for the formation of the surfaces of strong density and velocity differences observed in the oceans and atmosphere, and for the turbulence that appears on these surfaces.

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

Les travaux sur la turbulence : les origines, Toucans, Cost-ES0905 et influence de l'entropie

2021 ◽  
pp. 079
Author(s):  
Ivan Bašták Ďurán ◽  
Pascal Marquet
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Richardson Number ◽  
Stable Stratification ◽  
Turbulence Energy ◽  
Third Order ◽  
Length Scales ◽  
Gradient Richardson Number ◽  
Turbulence Length ◽  
Consistent Treatment

Le schéma de turbulence Toucans est utilisé dans la configuration opérationnelle Alaro du modèle Aladin depuis début 2015. Son développement a été initié, guidé et en grande partie conçu par Jean-François Geleyn. Ce développement a commencé avec le prédécesseur du schéma Toucans, le schéma « pseudo-pronostique » en énergie cinétique turbulente, lui-même basé sur l'ancien schéma de turbulence de Louis, mais étendu dans Toucans à un schéma pronostique. Le schéma Toucans a pour objectif de traiter de manière cohérente les fonctions qui dépendent de la stabilité verticale de l'atmosphère, de l'influence de l'humidité et des échelles de longueur de la turbulence (de mélange et de dissipation). De plus, de nouvelles caractéristiques ont été ajoutées : une représentation améliorée pour les stratifications très stables (absence de nombre de Richardson critique), une meilleure représentation de l'anisotropie, un paramétrage unifié de la turbulence et des nuages par l'ajout d'une deuxième énergie turbulente pronostique et la paramétrisation des moments du troisième ordre. The Toucans turbulence scheme is a turbulence scheme that is used in the operational Alaro configuration of the Aladin model since early 2015. Its development was initiated, guided and to a large extend authored by Jean-François Geleyn. The development started with the predecessor of the Toucans scheme, the "pseudo-prognostic" turbulent kinetic energy scheme which itself was built on the "Louis" turbulence scheme, but extended to a prognostic scheme. The Toucans scheme aims for a consistent treatment of stability dependency functions, influence of moisture, and turbulence length scales. Additionally, new features were added to the turbulence scheme: improved representation of turbulence in very stable stratification (absence of critical gradient Richardson number), better representation of anisotropy, unified parameterization of turbulence and clouds via addition of second prognostic turbulence energy, and parameterization of third order moments.

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.

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.

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