The mixing of passive helium and temperature fluctuations in grid turbulence

1982 ◽  
Vol 120 ◽  
pp. 475-504 ◽  
Author(s):  
A. Sirivat ◽  
Z. Warhaft
Keyword(s):  
Cross Correlation ◽  
Temperature Fluctuations ◽  
Thermal Fluctuations ◽  
Length Scale ◽  
Unexpected Finding ◽  
Grid Turbulence ◽  
Scalar Flux ◽  
Inference Method ◽  
Temperature Variance ◽  
Variance Decay

By producing thermal fluctuations with a mandohe and helium fluctuations with chimneys attached to the grid bars, the mixing of temperature and helium fluctuations as well as the decay of temperature and helium variance and their flux is investigated in decaying grid-generated turbulence. The helium, temperature and velocity fluctua- tions were measured with a modified ‘Way-Libby’ interference probe (Way & Libby 1970, 1971). It is shown that, as for temperature variance, the helium-variance decay rate is a function the ratio of the helium length scale to the velocity length scale. It is also shown that the decay of the cross-correlation between temperature and helium fluctuations is slow if both scalars are introduced close to the grid, but rapid if each scalar is introduced at a different distance from the grid, and hence at different scales. The results corroborate those of the inference method of Warhaft (1981), which is extended here to examine other cases. A particularly unexpected finding is that under certain circumstances the two-scalar cross-correlation may actually increase with distance from the grid, although the scalar covariance decreases. The return to isotropy of helium flux and temperature flux is also investigated and is shown to be slow if the scalar flux is produced near the grid bars, but faster if the flux is produced further downstream. For all the measurements helium and temperature were passive additives.

Passive scalar dispersion and mixing in a turbulent jet

1995 ◽  
Vol 292 ◽  
pp. 1-38 ◽  
Author(s):  
Chenning Tong ◽  
Z. Warhaft
Keyword(s):  
Reynolds Number ◽  
Cross Correlation ◽  
Thermal Field ◽  
Temperature Fluctuations ◽  
Passive Scalar ◽  
Turbulent Jet ◽  
Grid Turbulence ◽  
Far Field ◽  
The Cross ◽  
Heated 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, Dj, 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.

The interference of thermal fields from line sources in grid turbulence

1984 ◽  
Vol 144 ◽  
pp. 363-387 ◽  
Author(s):  
Z. Warhaft
Keyword(s):  
Line Source ◽  
Cross Correlation ◽  
Thermal Field ◽  
Grid Turbulence ◽  
Inference Method ◽  
Thermal Fields ◽  
Downstream Distance ◽  
Scalar Variance ◽  
Rate Of Decay ◽  
Total Temperature

The interference of passive thermal fields produced by two (and more) line sources in decaying grid turbulence is studied by using the inference method described by Warhaft (1981) to determine the cross-correlation coefficient ρ between the temperature fluctuations produced by the sources. The evolution of ρ as a function of downstream distance, for 0.075 < d/l < 10, where d is the wire spacing and l is the integral lengthscale of the turbulence, is determined for a pair of sources located at various distances from the grid. It is found that ρ may be positive or negative (thereby enhancing or diminishing the total temperature variance) depending on the line-source spacing, their location from the grid and the position of measurement. It is also shown that the effects of a mandoline (Warhaft & Lumley 1978) may be idealized as the interference of thermal fields produced by a number of line sources. Thus new light is shed on the rate of decay of scalar-variance dissipation. The thermal field of a single line source is also examined in detail, and these results are compared with other recent measurements.

The use of dual heat injection to infer scalar covariance decay in grid turbulence

1981 ◽  
Vol 104 ◽  
pp. 93-109 ◽  
Author(s):  
Z. Warhaft
Keyword(s):  
Cross Correlation ◽  
Isotropic Turbulence ◽  
Thermal Fluctuations ◽  
Grid Turbulence ◽  
Mixing Rate ◽  
Quantitative Measurements ◽  
Power Law Decay ◽  
Covariance Term ◽  
Heat Injection ◽  
Grid Mesh

Thermal fluctuations introduced into decaying grid turbulence at two different downstream locations are shown to be initially correlated and this correlation decays with distance from the grid. The fluctuations are introduced by placing two mandolines (Warhaft & Lumley 1978) at different distances downstream from the grid. The sum of the thermal variances produced by each mandoline operating separately, $\overline{\theta^2_1}+\overline{\theta^2_2}$, is significantly less than the total variance produced by both mandolines operating simultaneously, $\overline{(\theta_1+\theta_2)^2} = \overline{\theta^2_1} + \overline{\theta^2_2} + \overline{2\theta_1\theta_2} $, i.e. the deficit is due to the covariance term $\overline{2\overline{\theta_1\theta_2}}$. This covariance is responsible for a cross-correlation, $\rho = \overline{\theta_1\theta_2}/(\overline{\theta_1^2}\overline{\theta^2_2})^{\frac{1}{2}}$, as great as 0·6. The decay of $\overline{\theta_1\theta_2} $ and ρ is studied for various initial input thermal scale sizes and for various input locations. It is shown that the covariance follows a power-law decay, the exponent varying from - 5·5 if the thermal fluctuations are introduced close to the grid where the turbulence dissipation rate is large and the flow is inhomogeneous to - 4 if they are introduced further downstream (x/M ≥ 10, where x is the distance from the grid and M is the grid mesh length) in the region where the approximately isotropic turbulence is beginning to develop. The decay rate of $\overline{\theta_1\theta_2} $ and ρ was insensitive to the intensity of the thermal fluctuations. In all these experiments the cross-correlation between velocity and temperature fluctuations was very small (∼ − 0·05) and temperature was a passive additive. The results, which appear to be the first quantitative measurements of the rate of destruction of scalar covariance and hence of the mixing rate between two scalars, are shown to provide good confirmation of recent predictions of the decay of ρ by the second-order closure techniques of Lumley (1978 a, b).

An experimental study of the effect of uniform strain on thermal fluctuations in grid-generated turbulence

1980 ◽  
Vol 99 (3) ◽  
pp. 545-573 ◽  
Author(s):  
Z. Warhaft
Keyword(s):  
Heat Flux ◽  
Decay Rate ◽  
Time Scale ◽  
Cross Correlation ◽  
Thermal Fluctuation ◽  
Thermal Fluctuations ◽  
Length Scale ◽  
Scale Size ◽  
Velocity Scale ◽  
Scale Ratio

The effect of homogeneous strain on passive scalar fluctuations, and the resultant evolution of the scalar field when the strain is removed, is experimentally studied by passing thermal fluctuations in decaying grid turbulence through a four-to-one axisymmetric contraction. Using amandoline(Warhaft & Lumley 1978a) to vary the scale size of the initial thermal fluctuations and hence the pre-contraction mechanical/thermal time-scale ratio,r, it is shown, for values ofrgreater than unity, that asris increased so is the post-contraction thermal decay rate, i.e. the contraction does not cause the thermal-fluctuation decay rate to equilibrate to a constant value. In these experiments the post-contraction thermal decay rate is always greater than the pre-contraction decay rate, i.e. the contraction accelerates the thermal-fluctuation decay. Moreover, the mechanical/thermal time-scale ratio in the post-contraction region is driven further from unity. In terms of scale size the uniform strain has the effect of increasing the thermal length scale by an amount equal in value to the contraction ratio if the pre-contraction thermal length scale is comparable to that of the pre-contraction velocity scale. However, if the pre-contraction thermal length scale is smaller than the pre-contraction velocity scale then the effect of the contraction on the thermal scale is less marked. The contraction induces significant negative cross-correlation ρuθbetween the longitudinal velocityuand thermal fluctuations θ even if the pre-contraction cross-correlation is close to zero. The magnitude of ρuθand hence the post-contraction heat flux is varied and the coherence structure is studied. It is shown that the thermal-fluctuation decay rate is insensitive to the magnitude of the heat flux, the latter of which decays rapidly compared to the relatively slow decay of turbulence energy in the post-contraction region. It is also shown that ρuθtends towards zero in this axisymmetric homogeneous flow at a faster rate than in isotropic turbulence. In accord with previous investigations, the return toward isotropy of the velocity field is very slow.

Flow Control by Pulso Width Modulation

1972 ◽  
Vol 5 (4) ◽  
pp. 142-146
Author(s):  
M S Beck ◽  
N E Gough ◽  
J N Smithies
Keyword(s):  
Cross Correlation ◽  
Pulse Width Modulation ◽  
Correlation Method ◽  
Temperature Fluctuations ◽  
Flow Rates ◽  
Start Up ◽  
On Line ◽  
Measured Flow ◽  
Novel Method ◽  
Modulation Control

A novel method of controlling the flow rates of fluids has been devised which is particularly suitable for highly erosive fluids and slurries. The width of pulses in a pulse train actuating an on-off valve is modulated according to the error between the desired and measured flow rates and thus the ratio of the total times the valve spends in its ‘on’ and ‘off’ states is varied. The method has been tested with an on-line computer which was used to measure the flow rate of water by a cross-correlation method to determine the transit time of temperature fluctuations between two thermocouples in the pipe, and to implement the pulse width modulation control. Satisfactory results have been obtained for start-up, set-point changes and load disturbances for flow rates in the turbulent region (Re > 3 600). Future development includes the use of a fluidic diverter as the on-off device.

Evaluating and Improving Parameterizations of the Variance of Temperature Fluctuations Over Heterogeneous Landscapes for Surface Boundary Conditions in Atmospheric Models

2021 ◽  
Author(s):  
Tyler Waterman ◽  
Gabriel Katul ◽  
Andy Bragg ◽  
Nathaniel Chaney
Keyword(s):  
Energy Balance ◽  
Boundary Conditions ◽  
Weather Prediction ◽  
Potential Temperature ◽  
Temperature Fluctuations ◽  
Higher Order ◽  
Parameterization Scheme ◽  
Surface Boundary ◽  
Local Energy ◽  
Temperature Variance

&lt;p&gt;The implementation of higher-order turbulence closure schemes in Earth system models (e.g., the Cloud Layers Unified by Binormals; CLUBB) aims to improve the modeling of convection and radiative transfer in numerical weather prediction and climate models. However, the added value of these schemes is constrained by the specification of boundary conditions on higher-order statistics. At the land surface, many of the higher order turbulence statistics that are required as boundary conditions are parameterized using formulations more appropriate for stationary and planar-homogeneous flow in the absence of subsidence. A case in point is the variance of the potential temperature fluctuations.&amp;#160; Because of the additive nature of variances arising from non-uniformity in surface heating, current parameterizations are not readily generalizable. The current scheme used in CLUBB, as well as other models, relies on limited studies over uniform terrain, with the variance entirely determined by local sensible heat flux, friction velocity, and the Obukhov stability parameter without regard to local site characteristics. This presentation aims to address this weakness by leveraging the National Ecological Observation Network (NEON) network of eddy covariance towers to validate the current parameterization scheme for potential temperature variance, as well as propose improvements for more heterogeneous terrain.&lt;/p&gt;&lt;p&gt;The turbulence fluctuations of temperature at 39 NEON sites are processed and quality controlled, removing points occurring at night, while precipitation is falling, and with sub-zero temperatures. Results overall indicate the current scheme performs well, especially over flat homogeneous terrain where local flux relationships dominate. When there is sufficiently heterogeneous, rough terrain or non-closure of the local energy balance, however, existing schemes fail to accurately estimate the variances in temperature. In these cases, the parameterization needs to be modified, and initial results suggest simple adjustments can yield improvements and reduce error close to that of the uniform sites with local energy balance closure. The successful improvement of the temperature variance parameterization scheme implies high potential for similar, new, empirically derived parameterizations for the surface boundaries for other higher order turbulent statistics (e.g. temperature skewness) in atmospheric turbulence models.&lt;/p&gt;

Thermal dispersion from a line source in the shearless turbulence mixing layer

1990 ◽  
Vol 216 ◽  
pp. 35-70 ◽  
Author(s):  
S. Veeravalli ◽  
Z. Warhaft
Keyword(s):  
Heat Flux ◽  
Line Source ◽  
Large Scale ◽  
Mixing Layer ◽  
Distinct Region ◽  
Grid Turbulence ◽  
Fine Scale ◽  
Temperature Variance ◽  
Turbulence Mixing ◽  
The Mean

We experimentally investigate dispersion from a heated line source placed in the central region of a turbulence mixing layer. Recently described by Veeravalli & Warhaft (1989) the mixing layer has no mean shear and consists of gradients in the velocity variance and scale; it is formed from a composite grid of constant solidity from which two distinct velocity scales are formed, one on either side of the stream. Mixing is effected by intermittent turbulent penetration and diffusion. The dispersion measurements were carried out in the convective regime where both plume flapping and fine-scale turbulent mixing play a role, the latter becoming more dominant as the plume evolves. The mean and variance temperature profiles are strongly skewed (with larger tails on the low turbulence side of the flow) in the earlier stages of the plume development. Here, in the convective range, the median and peak of the mean plume are deflected toward the large-scale region. As the flow evolves the profiles become more symmetrical but as the plume enters the turbulent diffusive stage there is evidence that the profiles again became asymmetric but now with longer tails in the high turbulence side of the flow (owing to the higher diffusivity). The temperature variance and heat flux budgets are highly asymmetric but tend to exhibit many of the characteristics of the budget of a line source in decaying homogeneous grid turbulence which is also presented here. However, a distinct region of negative production (counter-gradient heat flux) is found in the temperature variance budget and this is shown to be a consequence of the asymmetry of the transverse velocity probability density function in the mixing layer. Temperature spectra, both of the time series and of the intermittency function, across the plume are described. They are shown to peak at high wavenumbers in the centre and edge of the plume and at lower wavenumbers in the intermediate region. Their form is shown to change as the plume develops fine-scale structure and flapping becomes less important.

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