Chenning Tong

On passive scalar derivative statistics in grid turbulence

The probability density function, and related statistics, of scalar (temperature) derivative fluctuations in decaying grid turbulence with an imposed cross‐stream, passive linear temperature profile, is studied for a turbulence Reynolds number range, Rel, varying from 50 to 1200, (corresponding to a Taylor Reynolds number range 30<Rλ<130). It is shown that the temperature derivative skewness in the direction of the mean gradient, Sθy has a value of 1.8±0.2 (twice the value observed in shear flows), and has no significant variation with Reynolds number. The ratio of the temperature derivative standard deviation along the gradient to that normal to it is approximately 1.2±0.1 also, with no variation with Re. The kurtosis of the derivatives increases approximately as Re0.2l. The results show that the rare, intense temperature deviations that produce the skewed scalar derivative, increase in frequency, but their area fraction (of the total field) becomes smaller as the Reynolds number increases. Thus, since S...

Passive scalar dispersion and mixing in a turbulent jet

The dispersion and mixing of passive scalar (temperature) fluctuations is studied in a turbulent jet. The temperature fluctuations were produced by heated fine wire rings placed axisymmetrically in the flow. Typically the ring diameters were of the same order as the jet, D j , and they were placed in the self-similar region. However, other initial conditions were studied, including a very small diameter ring used to approximate a point source. Using a single ring to study dispersion (which is analogous to placing a line source in a planar flow such as grid turbulence), it was found that the intense local thermal field close to the ring disperses and fills the whole jet in approximately 1.5 eddy turnover times. Thereafter the thermal field evolves in the same way as for the traditional heated jet experiments. Two heated rings were used to study the mixing of two independently introduced scalar fields. Here an inference method (invoking the principle of superposition) was used to determine the evolution of the cross-correlation coefficient, ρ, and the segregation parameter, α, as well as the coherence and co-spectrum. While initially strongly dependent on ring locations and spacing, ρ and α reached asymptotic values of 1 and 0.04, respectively, also in about 1.5 eddy turnover times. These results are contrasted with mixing and dispersion in grid turbulence where the evolution is slower. Measurements in the far field of the jet (where ρ = 1) of the square of the scalar derivative conditioned on the scalar fluctuation itself, as well as other conditional statistics, showed strong dependence on the measurement location, as well as the direction in which the derivative was determined. The cross-correlation between the square of the scalar derivative and the signal showed a clear Reynolds-number trend, decreasing as the jet Reynolds number was varied from 2800 to 18 000. The far-field measurements, using the heated rings, were corroborated by new heated jet experiments.

Measurements of conserved scalar filtered density function in a turbulent jet

Conserved scalar (temperature) filtered density function (FDF) is studied experimentally in the fully developed region of a turbulent jet with Taylor-microscale Reynolds numbers of 293 and 190. We obtain the FDFs using one-dimensional box filters of widths Δ ranging from 30 to 248 scalar dissipation scales (ηφ) as well as a two-dimensional box filter (Δ/ηφ=90) which consists of three discrete sensors. Taylor’s hypothesis is used to perform streamwise filtering operations. The mean conserved scalar FDF conditioned on the resolvable-scale scalar fluctuations 〈φ〉L and the subgrid scale (SGS) variance 〈φ″2〉L (log-normally distributed) is found to be bimodal when 〈φ″2〉L/〈φ″2〉 is large, indicating that the conditional SGS mixing is nearly binary. For small 〈φ″2〉L/〈φ″2〉 (<1) the conditional FDF is approximately Gaussian. The kurtosis of the conditional FDF decreases with increasing SGS variance and is independent of the filter widths for large SGS variance. The bimodal distribution can be symmetric or asymmetric...

Experimental Study of the Subgrid-Scale Stresses in the Atmospheric Surface Layer

In a large eddy simulation of the atmospheric boundary layer, results near the surface suffer from major deficiencies of the subgrid-scale (SGS) model due to inherently insufficient resolution there. However, efforts to develop improved models have been partially hampered by the lack of experimental data. In this paper SGS stress is studied experimentally using two-dimensional velocity fields measured with a newly developed array technique that combines a sonic array in the lateral direction with Taylor’s hypothesis in the streamwise direction. Detailed analyses show that, under convective conditions, the subgrid velocities are statistically independent of the resolvable-scale horizontal velocities; thus the large-scale eddies advect the SGS eddies but do not directly interact with them. As a result, the SGS stress components that involve resolvable-scale horizontal velocity components have strong statistical dependence on these velocity components. These SGS stress components also have the largest variances. Other SGS stress components involve only velocities whose length scales are comparable to the filter scale and are statistically dependent on the resolvable-scale vertical velocity but are statistically independent of the resolvable-scale horizontal velocities. Furthermore, these two types of SGS stress terms are independent of each other. The present study suggests that the two types of SGS stress components are related to the dynamics at the largest scales and at the filter scale, respectively, and need to be modeled separately to capture their distinct statistical characteristics.

Conditionally filtered scalar dissipation, scalar diffusion, and velocity in a turbulent jet

Conditionally filtered conserved scalar (temperature) dissipation (CFD), diffusion, and conditionally filtered velocity are studied experimentally in the fully developed region of a turbulent jet with a jet Reynolds number Rej=UjDj/ν of 40 000. These variables are the unclosed terms in the transport equation of the conserved scalar filtered density function. One-dimensional box filters of widths Δ ranging from 30 to 496 scalar dissipation scales (ηφ) as well as a two-dimensional box filter (Δ/ηφ=90) which consists of three discrete sensors are used to obtain filtered variables. Taylor’s hypothesis is used to perform the streamwise filtering. The means of these conditionally filtered variables conditional on the resolvable-scale scalar fluctuations 〈φ〉L and the subgrid-scale (SGS) variance 〈φ″2〉L indicate two regimes of the SGS scalar mixing. For large SGS variance (〈φ″2〉L/〈φ″2〉>1) the SGS scalar exhibits similarities to scalars in initially binary mixing at early times, suggesting existence of diffusion-l...

On temperature spectra in grid turbulence

This paper reports wind tunnel measurements of passive temperature spectra in decaying grid generated turbulence both with and without a mean transverse temperature gradient. The measurements cover a turbulence Reynolds number range 60<Rel<1200. It is shown that for a linear temperature profile the temperature spectrum has a scaling exponent close to −5/3 and that its dilation is consistent with Kolmogorov–Obukhov–Corrsin (KOC) scaling, i.e., the width of the scaling region increases approximately as Re3/4l. The remarkably low Reynolds number onset (Rel∼70) of Kolmogorov–Obukhov–Corrsin scaling in isotropic grid turbulence is contrasted to the case of scalars in (anisotropic) shear flows where KOC scaling only appears at very high‐Reynolds numbers (Rel∼105). It is also shown that when the temperature fluctuations are inserted very close to the grid in the absence of a gradient (by means of a mandoline), the temperature spectrum behaves in a similar way to the linear gradient case, i.e., a spectrum with a ...

Experimental study of velocity filtered joint density function for large eddy simulation

The velocity filtered joint density function (VFJDF) used in large eddy simulation and the structure of the subgrid-scale (SGS) velocity are studied experimentally. Measurements are made in the fully developed region of an axisymmetric turbulent jet (with jet Reynolds number UjDj/ν=40 000) using an array consisting of three X-wire probes. Filtering in the cross-stream and streamwise directions is realized by using the array and by invoking Taylor’s hypothesis, respectively. On the jet centerline the means of the VFJDF conditional on the SGS turbulent kinetic energy are found to be close to joint normal when the SGS energy is small compared to its mean but has a uniform portion when the SGS energy is large. The latter distribution has not been observed previously and suggests that the SGS velocity contains approximately linear structures and is under local rapid distortion. The results at off-centerline positions are also consistent with the existence of linear structures. Further analyses show that the SG...

Experimental investigation of scalar-scalar-dissipation filtered joint density function and its transport equation

The filtered joint density function (FJDF) of a conserved scalar and its dissipation rate and the FJDF transport equation are studied experimentally in the fully developed region of a turbulent jet with a jet Reynolds number Rej=UjDj/ν of 40 000. Filtered variables are obtained by a two-dimensional box filter having a size of 90 scalar dissipation scales, realized by using three discrete sensors aligned in the cross-stream direction and by invoking Taylor’s hypothesis. One-dimensional filters are also used to examine the effects of filter scales. The results show that for small and large subgrid-scale (SGS) scalar variance the FJDF and its dynamics have qualitatively different characteristics. The conditional mean FJDF for small SGS variance is generally unimodal and the dependence of the dissipation on the SGS scalar is moderate. The dissipation rate is diffused toward its conditional mean and its production rate is generally smaller than its destruction rate. These characteristics are similar to those o...

Turbulence suppression in a jet by means of a fine ring

Studied are the effects on the velocity field of a fine circular wire ring placed axisymmerically downstream of an air jet of Reynolds number 1.4×104. When placed close to the jet exit (x/Dj<3 where Dj is the jet diameter) the ring caused a pronounced reduction in the rms longitudinal velocity fluctuations, the maximum reduction (of approximately 30% based on the peak value) occurring when the ring is very close to the jet (x/Dj=0.07) and in the shear layer although rings of smaller diameter located in the core also produced the same qualitative effect. The ring also caused a shift in the virtual origin of the mean flow and an increase of the momentum thickness of the shear layer. There resulted a reduction of the magnitude of the fundamental roll‐up frequency, and it saturated later than for the undisturbed flow. The spatial growth rate of the disturbances in the shear layer were also drastically reduced. Spectra showed that vortex pairing was inhibited by the ring and there was an earlier transition to ...

Investigation of the subgrid-scale stress and its production rate in a convective atmospheric boundary layer using measurement data

The subgrid-scale (SGS) stress in the atmospheric surface layer is studied using measurement data. Field measurements employing a novel array technique were conducted to provide data for obtaining resolvable- and subgrid-scale variables. We analyse the conditional SGS stress and the conditional stress production rate conditional on the resolvable-scale velocity, which must be reproduced by the SGS model for large-eddy simulation (LES) to predict correctly the one-point resolvable-scale velocity statistics. The results show that both buoyancy and shear play important roles in the physics of the SGS stress. Strong buoyancy and vertical shear associated with updrafts and positive streamwise velocity fluctuations cause conditional forward energy transfer and strong anisotropy in the conditional SGS stress. Downward returning flows associated with large convective eddies result in conditional energy backscatter and much less anisotropic SGS stress. Predictions of the conditional SGS stress and the conditional stress production rate predicted using several SGS models are compared with measurements. None of those models are able to predict correctly the trends of both statistics. The Smagorinsky and one nonlinear model under-predict the anisotropy and the variations of the anisotropy, whereas the other nonlinear model and the mixed model over-predict both. The deficiencies of the SGS models that cause inaccurate LES statistics, such as the over-prediction of the mean shear and under-prediction of the vertical velocity skewness, are identified. The present study shows that analyses of conditional SGS stress and conditional SGS stress production provide a systematic approach for studying SGS physics and evaluating SGS models and can potentially be used to target specific aspects of LES that are important for a given application.