Thermal Dissipation Field Research Articles

Test of the anomalous scaling of passive temperature fluctuations in turbulent Rayleigh–Bénard convection with spatial inhomogeneity

AbstractThe scaling properties of the temperature structure function (SF) and temperature–velocity cross-structure function (CSF) are investigated in turbulent Rayleigh–Bénard convection (RBC). The measured SFs and CSFs exhibit good scaling in space and time and the resulting SF and CSF exponents are obtained both at the centre of the convection cell and near the sidewall. A universal relationship between the CSF exponent and the thermal dissipation exponent is found, confirming that the anomalous scaling of passive temperature fluctuations in turbulent RBC is indeed caused by the spatial intermittency of the thermal dissipation field. It is also found that the difference in the functional form of the measured SF and CSF exponents at the two different locations in the cell is caused by the change of the geometry of the most dissipative structures in the (inhomogeneous) temperature field from being sheetlike at the cell centre to filament-like near the sidewall. The experiment thus provides direct evidence showing that the universality features of turbulent cascade are linked to the degree of anisotropy and inhomogeneity of turbulent statistics.

Analysis of scalar mixing dynamics in LES using high-resolution imaging of laser Rayleigh scattering in turbulent non-reacting jets and non-premixed jet flames

Imaging of turbulent jet flames has provided insights into the dynamic structure of the thermal dissipation field. These insights motivated studies of scalar mixing in non-reacting jets, with emphasis on comparing measurements to large eddy simulations (LES). We use a progressively refined set of calculations to investigate how filter size affects the LES representations of scalar mixing. Results are analyzed using three grids that are successively refined by a factor of two in space and time. The coarsest grid contains 1.3-million cells and provides resolution similar to that used in current LES. The refined grids contain 10- and 82-million cells. Imaging measurements of the instantaneous mixture fraction and dissipation fields provide insights into scalar mixing dynamics and key length scales. They show that dissipation structures reside on the resolved- and subgrid-scales of the LES, and they provide order of magnitude estimates of the relationship between the dissipation layer thickness (the smallest relevant mixing scale), the integral scale (the largest relevant mixing scale), and the filter width. For all grid distributions, the longitudinal dimension of the dissipation layers spans multiple cells, but the ratio of the layer thickness to filter width is of order 1, which is not consistent with typical modeling assumptions. Measurements of mixture fraction were filtered to isolate the effects of spatial averaging on the dissipation field from the combined effects of spatial and temporal averaging. Statistical analysis reveals that the average mixture fraction and dissipation fields for the coarsest grid deviate significantly from the measured profiles as the flow evolves. On the finest grid, however, good agreement is obtained. Trends suggest that temporal damping and dispersion errors compound as the flow evolves downstream, which is directly related to the relationship between the dissipation layer thickness, filter width, and integral scale of the local mixing field.

Measurements of the thermal dissipation field in turbulent Rayleigh-Bénard convection

A systematic study of the thermal dissipation field and its statistical properties is carried out in turbulent Rayleigh-Bénard convection. A local temperature gradient probe consisting of four identical thermistors is made to measure the normalized thermal dissipation rate epsilonN(r) in two convection cells filled with water. The measurements are conducted over varying Rayleigh numbers Ra (8.9x10(8)<approximately Ra<approximately 9.3x10(9)) and spatial positions r across the entire cell. It is found that epsilonN(r) contains two contributions; one is generated by thermal plumes, present mainly in the plume-dominated bulk region, and decreases with increasing Ra. The other contribution comes from the mean temperature gradient, being concentrated in the thermal boundary layers, and increases with Ra. The experiment provides a complete physical picture about the thermal dissipation field and its statistical properties in turbulent convection.

Spatial scales of extinction and dissipation in the near field of non-premixed turbulent jet flames

Simultaneous high-resolution Rayleigh scattering imaging and planar laser-induced fluorescence (PLIF) of OH are combined to measure the dissipative scales associated with thermal mixing and the structure and scales of extinguished regions of the reaction zone. Measurements are performed throughout the near field ( x/ d = 5, 10, 15, 20) of two turbulent, non-premixed methane/hydrogen/nitrogen jet flames with Re = 15,200 and 22,800 (flames DLR-A and DLR-B of the TNF workshop). Locally extinguished regions are identified by discontinuities in the OH layers, and the extinction hole sizes are measured. For each flame, the probability density function of the hole sizes is very similar throughout the entire near field, with the most likely hole size being 1.9 mm in DLR-A and 1.1 mm in DLR-B. Extinction events are equally probable at all measurement locations in DLR-A. In the DLR-B flame, there is a progression from frequent extinction close to the nozzle to more continuous reaction zones further downstream. The approximate instantaneous location of the stoichiometric contour is determined using the OH-PLIF images, enabling statistical analysis of dissipative scales conditioned on rich and lean conditions. The widths of the thin, elongated structures that dominate the thermal dissipation field are measured. Statistics of this microscale are qualitatively similar in both flames, with the higher Reynolds number producing smaller scales throughout the flow field. For dissipation layers in rich regions, the layer widths increase significantly with increasing temperature, while on the lean side the layer widths decrease with increasing temperature.

Fine-scale statistics of temperature and its derivatives in convective turbulence

We study the fine-scale statistics of temperature and its derivatives in turbulent Rayleigh–Bénard convection. Direct numerical simulations are carried out in a cylindrical cell with unit aspect ratio filled with a fluid with Prandtl number equal to 0.7 for Rayleigh numbers between 107 and 109. The probability density function of the temperature or its fluctuations is found to be always non-Gaussian. The asymmetry and strength of deviations from the Gaussian distribution are quantified as a function of the cell height. The deviations of the temperature fluctuations from the local isotropy, as measured by the skewness of the vertical derivative of the temperature fluctuations, decrease in the bulk, but increase in the thermal boundary layer for growing Rayleigh number, respectively. Similarly to the passive scalar mixing, the probability density function of the thermal dissipation rate deviates significantly from a log-normal distribution. The distribution is fitted well by a stretched exponential form. The tails become more extended with increasing Rayleigh number which displays an increasing degree of small-scale intermittency of the thermal dissipation field for both the bulk and the thermal boundary layer. We find that the thermal dissipation rate due to the temperature fluctuations is not only dominant in the bulk of the convection cell, but also yields a significant contribution to the total thermal dissipation in the thermal boundary layer. This is in contrast to the ansatz used in scaling theories and can explain the differences in the scaling of the total thermal dissipation rate with respect to the Rayleigh number.

High-resolution imaging of dissipative structures in a turbulent jet flame with laser Rayleigh scattering

High-resolution 2-D imaging of laser Rayleigh scattering is used to measure the detailed structure of the thermal dissipation field in a turbulent non-premixed CH4/H2/N2 jet flame. Measurements are performed in the near field (x/d = 5–20) of the flame where the primary combustion reactions interact with the turbulent flow. The contributions of both the axial and radial gradients to the mean thermal dissipation are determined from the 2-D dissipation measurements. The relative contributions of the two components vary significantly with radial position. The dissipation field exhibits thin layers of high dissipation. Noise suppression by adaptive smoothing enables accurate determination of the dissipation-layer widths from single-shot measurements. Probability density functions (PDF) of the dissipation-layer widths conditioned on temperature are approximately log-normal distributions. The conditional layer width PDFs are self-similar functions with the layer widths scaling with temperature to the 0.75 power. The high signal-to-noise ratio of the Rayleigh scattering images coupled with an interlacing technique for noise suppression enable fully resolved measurements of the mean power spectral density (PSD) of the temperature gradients. These spectra are used to determine the turbulence microscales by measuring a cutoff wavelength, λC, at 2% of the peak PSD. The Batchelor scale is estimated from λC, and the results are compared with estimates from scaling laws in non-reacting flows. At x/d = 20, the different approaches to determining the Batchelor scale are comparable on the jet centerline. However, the estimates from non-reacting flow scaling laws are significantly less accurate in off-centerline regions and at locations closer to the nozzle exit. Throughout the near field of the jet flame, the measured ratio of a characteristic dissipation-layer width to the local Batchelor scale is larger than values previously reported for the far field of non-reacting flows.

Measured Thermal Dissipation Field in Turbulent Rayleigh-Bénard Convection

The time-averaged local thermal dissipation rate epsilonN(r) in turbulent convection is obtained from direct measurements of the temperature gradient vector in a cylindrical cell filled with water. It is found that epsilonN(r) contains two contributions. One is generated by thermal plumes, present mainly in the plume-dominated bulk region, and decreases with increasing Rayleigh number Ra. The other contribution comes from the mean temperature gradient, being concentrated in the thermal boundary layers, and increases with Ra. The experiment thus provides a new physical picture about the thermal dissipation field in turbulent convection.