Evolution and modelling of subgrid scales during rapid straining of turbulence

1999 ◽  
Vol 387 ◽  
pp. 281-320 ◽  
Author(s):  
SHEWEN LIU ◽  
JOSEPH KATZ ◽  
CHARLES MENEVEAU
Keyword(s):  
Constant Coefficient ◽  
Mixed Model ◽  
Isotropic Turbulence ◽  
A Priori ◽  
Constant Strain Rate ◽  
Water Tank ◽  
Smagorinsky Model ◽  
Mean Velocity ◽  
Similarity Model ◽  
The Mean

The response, evolution, and modelling of subgrid-scale (SGS) stresses during rapid straining of turbulence is studied experimentally. Nearly isotropic turbulence with low mean velocity and Rλ˜290 is generated in a water tank by means of spinning grids. Rapid straining (axisymmetric expansion) is achieved with two disks pushed towards each other at rates that for a while generate a constant strain rate. Time-resolved, two-dimensional velocity measurements are performed using cinematic PIV. The SGS stress is subdivided to a stress due to the mean distortion, a cross-term (the interaction between the mean and turbulence), and the turbulent SGS stress τ(T)ij. Analysis of the time evolution of τ(T)ij at various filter scales shows that all scales are more isotropic than the prediction of rapid distortion theory, with increasing isotropy as scales decrease. A priori tests show that rapid straining does not affect the high correlation and low square-error exhibited by the similarity model. Analysis of the evolution of total SGS energy dissipation reveals, surprisingly, that the Smagorinsky model with a constant coefficient (determined from isotropic turbulence data) underpredicts the dissipation during rapid straining. While the partial dissipation −〈τ(T)ijS˜ij〉 (due only to the turbulent part of the stress) is overpredicted by the Smagorinsky model, addition of the cross-terms reverses the trend. The similarity model with a constant coefficient appropriate for isotropic turbulence, on the other hand, overpredicts SGS dissipation. Owing to these opposite trends a linear combination of both models (mixed model) provides better prediction of SGS dissipation during rapid straining. However, the mixed model with coefficients determined from dissipation balance underpredicts the SGS stress.

scholarly journals WKB theory for rapid distortion of inhomogeneous turbulence

1999 ◽  
Vol 390 ◽  
pp. 325-348 ◽  
Author(s):  
S. NAZARENKO ◽  
N. K.-R. KEVLAHAN ◽  
B. DUBRULLE
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Two Dimensional ◽  
Turbulent Spot ◽  
Mean Flow ◽  
Mean Velocity ◽  
Inhomogeneous Turbulence ◽  
Large Scale Vortex ◽  
The Mean ◽  
Mean Strain

A WKB method is used to extend RDT (rapid distortion theory) to initially inhomogeneous turbulence and unsteady mean flows. The WKB equations describe turbulence wavepackets which are transported by the mean velocity and have wavenumbers which evolve due to the mean strain. The turbulence also modifies the mean flow and generates large-scale vorticity via the averaged Reynolds stress tensor. The theory is applied to Taylor's four-roller flow in order to explain the experimentally observed reduction in the mean strain. The strain reduction occurs due to the formation of a large-scale vortex quadrupole structure from the turbulent spot confined by the four rollers. Both turbulence inhomogeneity and three-dimensionality are shown to be important for this effect. If the initially isotropic turbulence is either homogeneous in space or two-dimensional, it has no effect on the large-scale strain. Furthermore, the turbulent kinetic energy is conserved in the two-dimensional case, which has important consequences for the theory of two-dimensional turbulence. The analytical and numerical results presented here are in good qualitative agreement with experiment.

Turbulent Statistics of Nearly Isotropic Turbulence Generated by Four Rotating Grids and the Mean Falling Velocity of Particle Through Turbulence

2007 ◽  
Author(s):  
Tatsuo Ushijima ◽  
Osami Kitoh
Keyword(s):  
Isotropic Turbulence ◽  
Terminal Velocity ◽  
Mean Velocity ◽  
Velocity Autocorrelation ◽  
Air Turbulence ◽  
Turbulent Statistics ◽  
Experimental Apparatus ◽  
Particle Property ◽  
The Mean ◽  
Lda Measurement

Box air turbulence is experimentally generated in a rectangular box by using four counter-rotating grids installed inside. Turbulence statistics are obtained from one-point measurement of LDA. Nearly isotropic turbulence with zero-mean velocity is realised in the midst of four rotating grids. The dissipation rate is estimated from the Taylor time microscale of velocity autocorrelation obtained from LDA measurement, since Taylor’s frozen turbulence hypothesis is not applicable. From this estimation, the Reynolds number based on the Taylor length microscale becomes about 200 at maximum in the present experimental apparatus. The mean falling velocity of small particle in turbulent flow is measured in the box turbulence. It is found that the mean falling velocity of the inertia particle could be smaller or larger than the terminal velocity, depending on the particle property, if the ratios of particle response time to turbulence time scale are the same.

Estimation of the Mean Velocity of Acoustic Signal Propagation for Sea Operations

1983 ◽  
Vol 105 (1) ◽  
pp. 68-72
Author(s):  
H. C. Menck
Keyword(s):  
Velocity Profile ◽  
Acoustic Signal ◽  
A Priori ◽  
Three Dimensional ◽  
Signal Propagation ◽  
Accurate Estimate ◽  
Mean Velocity ◽  
The Mean ◽  
Polynomial Surface ◽  
Device Tracking

A representative velocity profile and a priori bathymetric information about possible undersea device depths are the only data required to generate coefficients for a three-dimensional quadric polynomial surface which then expresses an accurate estimate of the mean velocity of acoustic signal propagation as a function of measured travel time and receiver depth. The resultant polynomial estimator is easily implemented in real-time navigating, station keeping, and undersea device tracking software to account for the variable refraction effects on mean velocities encountered in raypath trajectories that extend from the vertical out to and including the limiting direct raypaths.

Explicit algebraic subgrid stress models with application to rotating channel flow

2009 ◽  
Vol 639 ◽  
pp. 403-432 ◽  
Author(s):  
LINUS MARSTORP ◽  
GEERT BRETHOUWER ◽  
OLOF GRUNDESTAM ◽  
ARNE V. JOHANSSON
Keyword(s):  
Dynamic Model ◽  
Reynolds Stress ◽  
Channel Flow ◽  
Stress Model ◽  
Smagorinsky Model ◽  
Mean Velocity ◽  
The Mean ◽  
Stress Models ◽  
Subgrid Stress ◽  
Rotating Channel

New explicit subgrid stress models are proposed involving the strain rate and rotation rate tensor, which can account for rotation in a natural way. The new models are based on the same methodology that leads to the explicit algebraic Reynolds stress model formulation for Reynolds-averaged Navier–Stokes simulations. One dynamic model and one non-dynamic model are proposed. The non-dynamic model represents a computationally efficient subgrid scale (SGS) stress model, whereas the dynamic model is the most accurate. The models are validated through large eddy simulations (LESs) of spanwise and streamwise rotating channel flow and are compared with the standard and dynamic Smagorinsky models. The proposed explicit dependence on the system rotation improves the description of the mean velocity profiles and the turbulent kinetic energy at high rotation rates. Comparison with the dynamic Smagorinsky model shows that not using the eddy-viscosity assumption improves the description of both the Reynolds stress anisotropy and the SGS stress anisotropy. LESs of rotating channel flow at Reτ = 950 have been carried out as well. These reveal some significant Reynolds number influences on the turbulence statistics. LESs of non-rotating turbulent channel flow at Reτ = 950 show that the new explicit model especially at coarse resolutions significantly better predicts the mean velocity, wall shear and Reynolds stresses than the dynamic Smagorinsky model, which is probably the result of a better prediction of the anisotropy of the subgrid dissipation.

Three-Dimensional Laser Anemometer Measurements in an Annular Seal

1991 ◽  
Vol 113 (3) ◽  
pp. 421-427 ◽  
Author(s):  
G. L. Morrison ◽  
M. C. Johnson ◽  
G. B. Tatterson
Keyword(s):  
Reynolds Stress ◽  
Isotropic Turbulence ◽  
Three Dimensional ◽  
Mean Velocity ◽  
Anisotropic Turbulence ◽  
Laser Anemometer ◽  
Annular Seal ◽  
The Mean ◽  
Tensor Distributions ◽  
Anemometer System

The flow field inside an annular seal with a 1.27 mm clearance is investigated using a 3-D laser Doppler anemometer system. Through the use of this system, the mean velocity vector and the entire Reynolds stress tensor distributions are measured for the entire length of the seal (37.3 mm). The seal is operated at a Reynolds number of 18,600 and a Taylor number of 4500. The annular seal is found to produce anisotropic turbulence since the Reynolds stress measurements show the flow entering the seal with isotropic turbulence but exiting the seal with anisotropic turbulence.

Rapid distortion of turbulence into an open turbine rotor

2017 ◽  
Vol 825 ◽  
pp. 764-794 ◽  
Author(s):  
J. M. R. Graham
Keyword(s):  
Isotropic Turbulence ◽  
Strain Analysis ◽  
Turbine Rotor ◽  
Small Scale ◽  
Mean Flow ◽  
Mean Velocity ◽  
Actuator Disc ◽  
Tidal Turbine ◽  
Tidal Stream ◽  
The Mean

Rapid distortion of turbulence (RDT) theory is applied to homogeneous, isotropic turbulence incident on a horizontal axis turbine rotor such as a wind turbine or tidal-stream turbine. The mean flow field of the rotor which distorts the turbulence is represented by the commonly used axisymmetric actuator disc model due to Betz and Joukowski. The fluctuating streamwise component of the turbulence distorted by this field is calculated at the actuator disc plane. Turbulence velocity intensities and spectra are evaluated for general ratios of turbulence integral length scale to the rotor diameter, including the small-scale limit for which the original homogeneous strain analysis of Batchelor and Proudman may be applied. The distortion of the mean velocity profile of an incident rotor wake which may be considered a zero frequency disturbance relevant to wind and tidal turbine operation in large arrays is also analysed by the same method, treating it as a deterministic disturbance in the incident flow.

On the motion of gas bubbles in homogeneous isotropic turbulence

1997 ◽  
Vol 336 ◽  
pp. 221-244 ◽  
Author(s):  
P. D. M. SPELT ◽  
A. BIESHEUVEL
Keyword(s):  
Turbulent Flows ◽  
Isotropic Turbulence ◽  
Gas Bubbles ◽  
Numerical Data ◽  
Equation Of Motion ◽  
Equivalent Diameter ◽  
Approximate Analysis ◽  
Homogeneous Isotropic Turbulence ◽  
Mean Velocity ◽  
The Mean

This paper is concerned with the motion of small gas bubbles, equivalent diameter about 1.0 mm, in isotropic turbulent flows. Data on the mean velocity of rise and the dispersion of the bubbles have been obtained numerically by simulating the turbulence as a sum of Fourier modes with random phases and amplitudes determined by the Kraichnan and the von Kármán–Pao energy-spectrum functions, and by calculating the bubble trajectories from a reasonably well-established equation of motion. The data cover the range β[les ]1, where β is the ratio between the turbulence intensity and the velocity of rise of the bubbles in still fluid. An approximate analysis based on the assumption that β is small yields results that compare favourably with the numerical data, and clarifies the important role played by the lift forces exerted by the fluid.

A shear-free turbulent boundary layer

1967 ◽  
Vol 28 (4) ◽  
pp. 803-821 ◽  
Author(s):  
T. Uzkan ◽  
W. C. Reynolds
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Isotropic Turbulence ◽  
Wall Turbulence ◽  
Statistical Features ◽  
Homogeneous Isotropic Turbulence ◽  
Mean Velocity ◽  
Velocity Gradients ◽  
The Mean

A simple wall-turbulence interaction has been studied experimentally. In the idealized model an infinite flat plate is suddenly inserted into a pre-existing field of homogeneous isotropic turbulence, and subsequent changes in the turbulence field examined. The experiment involved passing grid-produced turbulence over a wall moving at the mean speed. Mean velocity gradients vanish in both the model and experiment, and hence production of new turbulence is absent. This allowed the inhibiting effects of the wall to be studied separately. The growth of the ‘inhomogeneity layer’ into the impressed turbulence field and other statistical features of the turbulence were measured.

The effect of jet injection geometry on two-dimensional momentumless wakes

1991 ◽  
Vol 224 ◽  
pp. 29-47 ◽  
Author(s):  
W. J. Park ◽  
J. M. Cimbala
Keyword(s):  
Turbulence Intensity ◽  
Isotropic Turbulence ◽  
Initial Conditions ◽  
Spreading Rate ◽  
Two Dimensional ◽  
Jet Injection ◽  
Mean Velocity ◽  
Rate Of Decay ◽  
The Mean ◽  
Momentumless Wake

It is shown experimentally that a two-dimensional momentumless wake is strongly dependent on the jet injection configuration of the model. Namely, the decay rate of mean velocity overshoot ranged from x−0.92 to x−2.0 for three different configurations, while the spreading rate ranged from x0.3 to x0.46 for those same configurations. The magnitude of axial turbulence intensity was also found to depend on model configuration. On the other hand, the rate of decay of axial turbulence intensity was the same (x−0.81) for all three models. In all cases the mean shear and Reynolds stress decayed rapidly, leaving nearly isotropic turbulence beyond 30 or 40 model diameters.Appropriate length- and velocity scales are identified which normalize the mean velocity profiles into self-similar form. The shape of the normalized profile, however, was different for each configuration, indicating again that the initial conditions are felt very far downstream.

Implication of Mismatch Between Stress and Strain-Rate in Turbulence Subjected to Rapid Straining and Destraining on Dynamic LES Models

2005 ◽  
Vol 127 (5) ◽  
pp. 840-850 ◽  
Author(s):  
Jun Chen ◽  
Joseph Katz ◽  
Charles Meneveau
Keyword(s):  
Strain Rate ◽  
Momentum Flux ◽  
Stress And Strain ◽  
Time Lags ◽  
Water Tank ◽  
Subgrid Scale ◽  
Smagorinsky Model ◽  
Mean Velocity ◽  
Stress And Strain Rate ◽  
The Impact

Planar straining and destraining of turbulence is an idealized form of turbulence-meanflow interaction that is representative of many complex engineering applications. This paper studies experimentally the response of turbulence subjected to a process involving planar straining, a brief relaxation and destraining. Subsequent analysis quantifies the impact of the applied distortions on model coefficients of various eddy viscosity subgrid-scale models. The data are obtained using planar particle image velocimetry (PIV) in a water tank, in which high Reynolds number turbulence with very low mean velocity is generated by an array of spinning grids. Planar straining and destraining mean flows are produced by pushing and pulling a rectangular piston towards and away from the bottom wall of the tank. The velocity distributions are processed to yield the time evolution of mean subgrid dissipation rate, the Smagorinsky and dynamic model coefficients, as well as the mean subgrid-scale momentum flux during the entire process. It is found that the Smagorinsky coefficient is strongly scale dependent during periods of straining and destraining. The standard dynamic approach overpredicts the dissipation based Smagorinsky coefficient, with the model coefficient at scale Δ in the standard dynamic Smagorinsky model being close to the dissipation based Smagorinsky coefficient at scale 2Δ. The scale-dependent Smagorinsky model, which is designed to compensate for such discrepancies, yields unsatisfactory results due to subtle phase lags between the responses of the subgrid-scale stress and strain-rate tensors to the applied strains. Time lags are also observed for the SGS momentum flux at the larger filter scales considered. The dynamic and scale-dependent dynamic nonlinear mixed models do not show a significant improvement. These potential problems of SGS models suggest that more research is needed to further improve and validate SGS models in highly unsteady flows.

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