Thermal Dissipation Rate Research Articles

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.

Analysis of the thermal plumes in turbulent Rayleigh–Bénard convection based on well-resolved numerical simulations

In this study, direct numerical simulations and high-resolved large eddy simulations of turbulent Rayleigh–Bénard convection were conducted with a fluid of Prandtl number Pr = 0.7 in a long rectangular cell of aspect ratio unity in the cross-section and periodic boundaries in a horizontal longitudinal direction. The analysis of the thermal and kinetic energy spectra suggests that temperature and velocity fields are correlated within the thermal boundary layers and tend to be uncorrelated in the core region of the flow. A tendency of decorrelation of the temperature and velocity fields is also observed for increasing Ra when the flow has become fully turbulent, which is thought to characterize this regime. This argument is also supported by the analysis of the correlation of the turbulent fluctuations |u|′ and θ′. The plume and mixing layer dominated region is found to be separated from the thermal dissipation rates of the bulk and conductive sublayer by the inflection points of the probability density function (PDF). In order to analyse the contributions of bulk, boundary layers and plumes to the mean heat transfer, the thermal dissipation rate PDFs of four different Ra are integrated over these three regions. Hence, it is shown that the core region is dominated by the turbulent fluctuations of the thermal dissipation rate throughout the range of simulated Ra, whereas the contributions from the conductive sublayer due to turbulent fluctuations increase rapidly with Ra. The latter contradicts results by He, Tong &amp; Xia (Phys. Rev. Lett., vol. 98, 2007). The results also show that the plumes and mixing layers are increasingly dominated by the mean gradient contributions. The PDFs of the core region are compared to an analytical scaling law for passive scalar turbulence which is found to be in good agreement with the results of the present study. It is noted that the core region scaling seems to approach the behaviour of a passive scalar as Ra increases, i.e. it changes from pure exponential to a stretched exponential scaling.

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.

Ultimate-state scaling in a shell model for homogeneous turbulent convection

An interesting question in turbulent convection is how the heat transport depends on the strength of thermal forcing in the limit of very large thermal forcing. Kraichnan predicted [Phys. Fluids 5, 1374 (1962)] that for fluids with low Prandtl number (Pr), the heat transport measured by the Nusselt number (Nu) would depend on the strength of thermal forcing measured by the Rayleigh number (Ra) as Nu approximately Ra(1/2) with logarithmic corrections at very high Ra. According to Kraichnan, the shear boundary layers play a crucial role in giving rise to this so-called ultimate-state scaling. A similar scaling result is predicted by the Grossmann-Lohse theory [J. Fluid Mech. 407, 27 (2000)], but with the assumption that the ultimate state is a bulk-dominated state in which both the average kinetic and thermal dissipation rates are dominated by contributions from the bulk of the flow with the boundary layers either broken down or playing no role in the heat transport. In this paper, we study the dependence of Nu and the Reynolds number (Re) measuring the root-mean-squared velocity fluctuations on Ra and Pr, for low Pr, using a shell model for homogeneous turbulent convection where buoyancy is acting directly on most of the scales. We find that Nu approximately Ra(1/2)Pr(1/2) and Re approximately Ra(1/2)Pr(-1/2) , which resemble the ultimate-state scaling behavior for fluids with low Pr, and show that the presence of a drag acting on the large scales is crucial in giving rise to such scaling. As a large-scale drag cannot exist by itself in the bulk of turbulent thermal convection, our results indicate that if buoyancy acts on most of the scales in the bulk of turbulent convection at very high Ra, then the ultimate state cannot be bulk dominated.

Analysis of sheet-like thermal plumes in turbulent Rayleigh–Bénard convection

Sheet-like thermal plumes are investigated using time-dependent and three-dimensional flow fields obtained from direct numerical simulations and well-resolved large-eddy simulations of turbulent Rayleigh–Bénard convection in water (Prandtl number Pr=5.4) in a cylindrical container with the aspect ratio Γ=1 and for the Rayleigh numbers Ra=2×109 and 2×1010.To analyse quantitatively the physical properties of the sheet-like thermal plumes and the turbulent background and to obtain the temperature threshold which separates these two different flow regions, the temperature dependences of the conditionally averaged local heat flux, thermal dissipation rate and selected components of the velocity and vorticity fields are studied. It is shown that the sheet-like plumes are characterized by high values of the local heat flux and relatively large absolute values of the vertical components of the vorticity and velocity fields. The borders of these plumes are indicated by large values of the thermal dissipation rate and large absolute values of the horizontal vorticity components. In contrast to the sheet-like thermal plumes, the turbulent background is characterized by low values of the thermal dissipation rate, local heat flux and vertical vorticity component. The highest values of the local heat flux and the highest absolute values of the vertical vorticity component are found in the regions where the sheet-like plumes strike against each other. Fluid swirling at these places forms the stems of the mushroom-like thermal plumes which develop in the bulk of the Rayleigh–Bénard cell.Further, formulae to calculate the curvature, thickness and length of the plumes are introduced. Geometrical properties such as plume area, diameter, curvature, thickness and aspect ratio together with the physical properties of the sheet-like plumes such as temperature, heat flux, thermal dissipation rate, velocity and vorticity are investigated.

Turbulent time scales in a nonpremixed turbulent jet flame by using high-repetition rate thermometry

High-repetition-rate (10-kHz), single-point laser Rayleigh scattering thermometry was used to measure temperature and thermal dissipation rate fluctuations in a turbulent nonpremixed jet flame at a Reynolds number of 15,200. The measurements were made along the jet-flame centerline for downstream locations in the vicinity of the flame tip and were aimed at obtaining one-dimensional (1D) energy and dissipation spectra and estimates of the integral and Batchelor scales. The signal-to-noise ratios of the measured correlations, energy spectra, and dissipation spectra were significantly improved by using two detectors to measure redundant scattering signals from the same point, followed by computing the cross-correlation of these signals. Measurements of the integral scales show good agreement with measurements in isothermal jets except near the stoichiometric flame length, where the flame scales are smaller. These smaller scales are attributed to the state relationship between temperature and mixture fraction. The cutoff frequency of the dissipation range (i.e., the Batchelor frequency) is determined from the 1D thermal dissipation spectra. The experimentally determined cutoff frequencies agree with those estimated using nonreacting jet scaling laws, provided an appropriate local Reynolds number is used that is significantly smaller than the jet exit Reynolds number. The resulting 1D energy and dissipation spectra at all downstream stations collapse when properly normalized and fit well to model spectra at a Taylor Reynolds number near 55. This Reynolds number is considerably smaller than the corresponding nonreacting jet value of 150. The measured energy and dissipation spectra exhibit significant overlap at intermediate frequencies, which indicates that the largest scales of the dissipation range may be significantly influenced by the large, energy containing scales. The time-series data are also used to determine the influence of the probe resolution on the temperature variance and mean 1D thermal dissipation rate. It is shown that the resolution requirements are similar to those in nonreacting jet flows, provided the difference in the local Reynolds number is considered.

Local heat fluxes in turbulent Rayleigh-Bénard convection

The vertical turbulent heat flux Ω in Rayleigh-Bénard convection, its spatial distribution, and some mean characteristics are investigated by means of direct numerical simulations for the Rayleigh numbers Ra=106 and 107 and well resolved large-eddy simulations for Ra=108. All simulations were performed for Prandtl number Pr=0.7 and aspect ratio of a cylindrical container Γ=5. Analyzing the spatial distribution of Ω, it is shown that the fluid volume with negative Ω values increases with Ra and reaches one-third of the total volume for Ra=108. The spread in the local heat flux values expands with increasing distance from the top or the bottom plates. For example, for Ra=107, about 31% and 19% of the center horizontal cross section reflects, respectively, negative and large positive (⩾2Nu) values of Ω, while at the plates the local heat flux values vary basically between 0 and 2Nu. Further, it is shown that with growing Rayleigh numbers, the zones of higher values of the time-averaged local heat flux move toward the corners, where horizontal and vertical walls intersect. Analytical relations between the components of Ω and the thermal dissipation rates, proven in the paper, show that the square root of the thermal dissipation rate describes well the spatial distribution of the local heat transport close to the top or the bottom plates.

Photoprotection processes under water stress and recovery in Mediterranean plants with different growth forms and leaf habits

The response of photoprotection mechanisms to a short‐term water stress period followed by rewatering, to simulate common episodic water stress periods occurring in Mediterranean areas, was studied in 10 potted plants representative of different growth forms and leaf habits. During water stress and recovery, relative water content, stomatal conductance, leaf pigment composition, electron transport rates, maximum quantum efficiency of PSII photochemistry (Fv/Fm), thermal energy dissipation and photorespiration rates (Pr) were determined. All the species analyzed proved to be strongly resistant to photoinactivation of PSII under the imposed water stress conditions. The responses of the analyzed parameters did not differ largely among species, suggesting that Mediterranean plants have similar needs and capacity for photoprotection under episodic water stress periods regardless of their growth form and leaf habit. A general pattern of photoprotection emerged, consisting in maintenance or increase of Pr at mild stress and the increase of the thermal energy dissipation at more severe stress. Adjustments in pigment pool sizes were not an important short‐term response to water stress. The increase of thermal energy dissipation because of water stress depended mostly on the de‐epoxidation state of xanthophylls, although the slope and kinetics of such relationship strongly differed among species, suggesting species‐dependent additional roles of de‐epoxidated xanthophylls. Also, small decreases in Fv/Fm at predawn during water stress were strongly correlated with maintained de‐epoxidation of the xanthophylls cycle, suggesting that a form of xanthophyll‐dependent sustained photoprotection was developed during short‐term water stress not only in evergreen but also in semideciduous and annual species.

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.

Analysis of thermal dissipation rates in turbulent Rayleigh–Bénard convection

Direct numerical simulations (DNS) of turbulent Rayleigh–Bénard convection in a wide cylindrical container (aspect ratio are defined to determine quantitatively the role of the turbulent background. Evaluating these functions from the DNS data, it is shown that the turbulent background pushes the thermal plumes back and that its contribution to the volume-averaged thermal dissipation rate increases with the Rayleigh number. Further, it is proven analytically that the ratio of the area-averaged (over the top or the bottom plates) to the volume-averaged thermal dissipation rate is greater than or equal to the Nusselt number for all aspect ratios, and Prandtl and Rayleigh numbers.

Forced convection cooling enhancement for rectangular blocks using a wavy plate

Heat transfer enhancement using a wavy plate in a channel containing heated blocks is numerically studied. The finite-element method is utilized to solve the problem. The blocks simulate an electronic package with a high thermal dissipation rate. The considered assembly consists of a channel formed by two plates with heated blocks attached to both internal walls and a wavy plate installed at the centerline of the channel. The wavy plate enhances heat transfer from the blocks through the modification of the flow pattern in the channel. The effect of the Reynolds number, waviness of the wavy plate, and blocks' spacing on the Nusselt number and maximum temperature of the blocks is investigated. Heat transfer enhancement of the blocks with a wavy plate is evaluated by comparing their thermal characteristics to blocks with a zero waviness plate. The results show that the wavy plate enhances heat flow out of the blocks and reduces their temperature up to 23%.

Finescale Structure of the T–S Relation in the Eastern North Atlantic

Abstract Distributions of temperature (T) and salinity (S) and their relationship in the oceans are the result of a balance between T–S variability generated at the surface by air–sea fluxes and its removal by molecular dissipation. In this paper the role of different motions in setting the cascade of T–S variance to dissipation scales is quantified using data from the North Atlantic Tracer Release Experiment (NATRE). The NATRE observational programs include fine- and microscale measurements and provide a snapshot of T–S variability across a wide range of scales from basin to molecular. It is found that microscale turbulence controls the rate of thermal dissipation in the thermocline. At this level the T–S relation is established through a balance between large-scale advection by the gyre circulation and small-scale turbulence. Further down, at the level of intermediate and Mediterranean waters, mesoscale eddies are the rate-controlling process. The transition between the two regimes is related to the presence of a strong salinity gradient along density surfaces associated with the outflow of Mediterranean waters. Mesoscale eddies stir this gradient and produce a rich filamentation and salinity-compensated temperature inversions: isopycnal stirring and diapycnal mixing are both required to explain the T–S relation at depth.

Rayleigh and Prandtl number scaling in the bulk of Rayleigh–Bénard turbulence

The Ra and Pr number scaling of the Nusselt number Nu, the Reynolds number Re, the temperature fluctuations, and the kinetic and thermal dissipation rates is studied for (numerical) homogeneous Rayleigh–Bénard turbulence, i.e., Rayleigh–Bénard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature field by a mean gradient. This system serves as model system for the bulk of Rayleigh–Bénard flow and therefore as model for the so-called “ultimate regime of thermal convection.” With respect to the Ra dependence of Nu and Re we confirm our earlier results [D. Lohse and F. Toschi, “The ultimate state of thermal convection,” Phys. Rev. Lett. 90, 034502 (2003)] which are consistent with the Kraichnan theory [R. H. Kraichnan, “Turbulent thermal convection at arbitrary Prandtl number,” Phys. Fluids 5, 1374 (1962)] and the Grossmann–Lohse (GL) theory [S. Grossmann and D. Lohse, “Scaling in thermal convection: A unifying view,” J. Fluid Mech. 407, 27 (2000); “Thermal convection for large Prandtl number,” Phys. Rev. Lett. 86, 3316 (2001); “Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection,” Phys. Rev. E 66, 016305 (2002); “Fluctuations in turbulent Rayleigh–Bénard convection: The role of plumes,” Phys. Fluids 16, 4462 (2004)], which both predict Nu∼Ra1∕2 and Re∼Ra1∕2. However the Pr dependence within these two theories is different. Here we show that the numerical data are consistent with the GL theory Nu∼Pr1∕2, Re∼Pr−1∕2. For the thermal and kinetic dissipation rates we find ϵθ∕(κΔ2L−2)∼(RePr)0.87 and ϵu∕(ν3L−4)∼Re2.77, both near (but not fully consistent) the bulk dominated behavior, whereas the temperature fluctuations do not depend on Ra and Pr. Finally, the dynamics of the heat transport is studied and put into the context of a recent theoretical finding by Doering et al. [“Comment on ultimate state of thermal convection” (private communication)].

Nonpremixed Flamelet Statistics at Flame Base of Lifted Turbulent Jet Nonpremixed Flames

Nonpremixed flamelet statistics at the flame base of lifted turbulent nonpremixed flames are investigated experimentally using a planar temperature Rayleigh scattering method. A methane/hydrogen mixture is supplied from a tube of 3.2mm I.D. into the surrounding air flow so as to form two lifted turbulent nonpremixed flames having exit velocities of 50m/s (Re=4200) and 80m/s (Re=6700), respectively. Temperature data are related to maximum temperature at several flame positions based on the instantaneous flame base tip as containing information on the reaction region of each nonpremixed flamelet at each position. The statistics in terms of maximum temperature, thermal dissipation rate, scalar dissipation rate, and flame brush are discussed with reference to the modeling of the flame base structure. The scalar dissipation rate has log-normal statistics and the quenching scalar dissipation rate is lower than the critical value predicted using the uniformly strained counter nonpremixed flame. These statistics are compared to those obtained using a model proposed by Muller et al., which combines the flamelet model and the scalar field variable to predict lifted turbulent nonpremixed flames. The comparison has shown that the model can qualitatively predict lifted turbulent nonpremixed flames, but modification is required in order to obtain more accurate quantitative prediction taking into account the edge flame structure, the statistics of scalar dissipation rate, and the statistics of flame brush.

High-repetition rate measurements of temperature and thermal dissipation in a non-premixed turbulent jet flame

High-repetition rate laser Rayleigh scattering is used to study the temperature fluctuations, power spectra, gradients, and thermal dissipation rate characteristics of a non-premixed turbulent jet flame at a Reynolds number of 15,200. The radial temperature gradient is measured by a two-point technique, whereas the axial gradient is measured from the temperature time-series combined with Taylor’s hypothesis. The temperature power spectra along the jet centerline exhibit only a small inertial subrange, probably because of the low local Reynolds number ( Re δ ≈ 2000), although a larger inertial subrange is present in the spectra at off-centerline locations. Scaling the frequency by the estimated Batchelor frequency improves the collapse of the dissipation region of the spectra, but this collapse is not as good as is obtained in non-reacting jets. Probability density functions of the thermal dissipation are shown to deviate from lognormal in the low-dissipation portion of the distribution when only one component of the gradient is used. In contrast, nearly log-normal distributions are obtained along the centerline when both axial and radial components are included, even for locations where the axial gradient is not resolved. The thermal dissipation PDFs measured off the centerline deviate from log-normal owing to large-scale intermittency. At one-half the visible flame length, the radial profile of the mean thermal dissipation exhibits a peak off the centerline, whereas farther downstream the peak dissipation occurs on the centerline. The mean thermal dissipation on centerline is observed to increase linearly with downstream distance, reach a peak at the location of maximum mean centerline temperature, and then decrease for farther downstream locations. Many of these observed trends are not consistent with equivalent non-reacting turbulent jet measurements, and thus indicate the importance of understanding how heat release modifies the turbulence structure of jet flames.

Fluctuations in turbulent Rayleigh–Bénard convection: The role of plumes

Our unifying theory of turbulent thermal convection [Grossmann and Lohse, J. Fluid. Mech. 407, 27 (2000); Phys. Rev. Lett. 86, 3316 (2001); Phys. Rev. E 66, 016305 (2002)] is revisited, considering the role of thermal plumes for the thermal dissipation rate and addressing the local distribution of the thermal dissipation rate, which had numerically been calculated by Verzicco and Camussi [J. Fluid Mech. 477, 19 (2003); Eur. Phys. J. B 35, 133 (2003)]. Predictions for the local heat flux and for the temperature and velocity fluctuations as functions of the Rayleigh and Prandtl numbers are offered. We conclude with a list of suggestions for measurements that seem suitable to verify or falsify our present understanding of heat transport and fluctuations in turbulent thermal convection.

Microstructure Measurements from a Towed Undulating Platform

MicroSoar, an undulating profiler capable of measuring turbulence parameters such as Thorpe scales and thermal dissipation rate while being towed at speeds of up t o4ms 21, offers the possibility of obtaining a closeto-synoptic image of mixing over large spatial areas. In this paper, the method of calculating Thorpe scales from the high-frequency MicroSoar data is developed, and results from data taken off the coast of Oregon during the summer of 2001 are presented. Large Thorpe scales and elevated measurements of the thermal dissipation rate are shown to be associated with shear at the edge of the coastal jet. It is further shown that using MicroSoar data rather than Sea-Bird conductivity‐temperature‐depth data extends the range of measurable overturns to smaller scales, particularly in regions of low stratification.

Direct numerical simulation of VHF radar measurements of turbulence in the mesosphere

We simulate very high frequency (VHF) radar backscatter from turbulent irregularities in the mesosphere and examine the process of calculating key turbulence parameters from radar Doppler spectral moments. Mesospheric turbulence is represented by a three‐dimensional (3‐D) direct numerical simulation (DNS) of a turbulent layer generated by Kelvin–Helmholtz instability, which exhibits inertial range turbulence characteristics. A subgrid‐scale turbulence advection model is used to parameterize the unresolved small‐scale structure of mesospheric temperature, ion species, and electron mixing ratios and to derive the radar backscatter cross sections. Energy and thermal dissipation rates are calculated from the 3‐D velocity and temperature derivatives of the DNS. Doppler spectral widths relevant to various mesospheric radar observations are then determined from explicit calculation of spectral moments. We then present a comparison between the turbulence parameters calculated from the DNS and those calculated from the Doppler spectral moments.

Antioxidants and xanthophyll cycle-dependent energy dissipation in Cucurbita pepo L. and Vinca major L. acclimated to four growth PPFDs in the field

The acclimation of photochemistry, xanthophyll cycledependent energy dissipation, and antioxidants was characterized in leaves of Cucurbita pepo L. and Vinca major L. that developed under photosynthetic photon flux densities (PPFDs) ranging from deep shade to full sunlight in the field. The predominant acclimatory response of leaf pigment composition was an increase in the xanthophyll cycle pool size with increasing growth PPFD. In both species, the estimated rate of thermal energy dissipation at midday increased with increasing PPFD and midday levels of zeaxanthin and antheraxanthin per chlorophyll were closely correlated with the levels of non-photochemical fluorescence quenching under all growth PPFD regimes. However, at full sunlight there appeared to be considerably higher levels of xanthophyll cycle-dependent energy dissipation in V. major compared with pumpkin while estimated rates of photochemistry exhibited the reverse trend. Leaf activities of the antioxidant enzymes ascorbate peroxidase and superoxide dismutase, as well as ascorbate content, increased with increasing growth PPFD in both plant species. Activities/contents were higher under 100% full sunlight and increased more strongly from intermediate growth PPFDs to 100% full sunlight in V. major than in C. pepo. These patterns of acclimation are similar to those exhibited by xanthophyll cycle-dependent energy dissipation. The patterns of acclimation of glutathione reductase are discussed in the context of the multiple roles for reduced glutathione. Catalase acclimated in a manner consistent with its role in scavenging H2O2 generated via photo respiration and/or mitochondrial respiration. Leaf α-tocopherol did not exhibit growth PPFD-dependent trends.

On the analysis of temperature dissipation in a turbulent jet propane flame

The analysis of a turbulent jet flame of propane in still air is reported with the aim of contributing to a better understanding of the interaction between chemistry and the turbulent structure of the flow in non-premixed combustion systems. The emphasis is put on time-resolved two-point temperature measurements, from which the dissipation of the temperature fluctuations was obtained. The results quantify the correlation of thermal dissipation with the fluctuations of the temperature, which suggest the likely influence of large scales mixing on the anisotropy of the thermal dissipation rate. In addition, the experiments reported here demonstrate the ability of compensated fine wire thermocouples to measure the dissipation rate of temperature in strongly radiating flames, where the use of optical techniques may be limited.