Eddy Diffusivity Of Heat Research Articles

Lateral velocity fluctuations and dissipation time scale ratios for prediction of mean and fluctuating temperature fields

Further testing of a previously developed diffusivity-based model for predicting mean and fluctuating temperatures in water and liquid sodium flows downstream of a multi-bore jet block in which one jet is heated is performed but using air as the working fluid. The apparatus used enabled geometric similitude with the previous studies. The previous model used longitudinal turbulence intensities and longitudinal integral length scales to estimate values of the eddy diffusivity of heat. Measurement of lateral velocities in the present work allowed a significant improvement to be made in the modelling procedure. It was found that the lateral turbulence intensity was a more effective velocity scale to use and a length scale based on lateral velocity fluctuations was more apt. The Prandtl number effect on temperature dissipation rates found previously in water and sodium is extended by the results using air, leading to a simple algebraic relation between the Prandtl number and dissipation time scale ratio. The non-isotropic nature of the flow is identified and is seen to influence the results.

Turbulent heat flux in the upper ocean under sea ice

Turbulence data from three Arctic drift station experiments demonstrate features of turbulent heat transfer in the oceanic boundary layer. Time series analysis of several w′T′ records shows that heat and momentum flux occur at nearly the same scales, typically by turbulent eddies of the order of 10–20 m in horizontal extent and a few meters in vertical extent. Probability distribution functions of w′T′ have large skewness and kurtosis, where the latter confirms that most of the flux occurs in intermittent “events” with positive and negative excursions an order of magnitude larger than the mean value. An estimate of the eddy heat diffusivity in the outer (Ekman) part of the boundary layer, based on measured heat flux and temperature gradient during a diurnal tidal cycle over the Yermak Plateau slope north of Fram Strait, agrees reasonably well with the eddy viscosity, with values as high as 0.15 m2 s−1. An analysis of measurements made near the ice‐ocean interface at the three stations shows that heat flux increases with both temperature elevation above freezing and with friction velocity at the interface. It also reveals a surprising uniformity in parameters describing the heat and mass transfer: e.g., the thickness of the “transition sublayer” (from a modified version of the Yaglom‐Kader theory) is about 10 cm at all three sites, despite nearly a fivefold difference in the under‐ice roughness z0, which ranges from approximately 2 to 9 cm. A much simplified model for heat and mass transfer at the ice‐ocean interface, suggested by the relative uniformity of the heat transfer coefficients at the three sites, is outlined.

Experimentally determined turbulent Prandtl numbers in liquid sodium at low Reynolds numbers

Turbulent Prandtl numbers have been deduced from measurements of mean velocity and mean temperature distributions and their half value radii for a liquid sodium jet discharging into essentially still fluid. Results obtained indicate a velocity dependence and are similar to those reported in the literature for pipe flows. The velocity dependence, which is assumed to be due to transition to an inertial-conductive flow regime where turbulent diffusion of heat inherent in the turbulent Prandtl number no longer exists, becomes pronounced at low velocities. Combination of the new jet flow and existing pipe flow data for liquid sodium leads to a simple functional relationship between turbulent Prandtl number and eddy diffusivity of heat which may be readily solved for ε H once ε M is known. The combined results show that, for liquid sodium, significant increases in turbulent Prandtl number occur when flow conditions lead to ε H α < 2.5 , that is, when ε M/gn < 2 Pr .

Experimental Study of Turbulent Heat Transfer in a Two-Dimensional Curved Channel. Time-Mean Temperature and Multiple Temperature/Velocity Correlations in the Entrance Section.

Full measurements of thermal field were made for a turbulent flow of air in the entrance section of a two-dimensional curved channel. The wall heat flux develops more rapidly than the mean temperature distribution, decreasing and increasing on the inner and outer walls, respectively. Locations at which the mean temperature gradient and the radial component of turbulent heat flux become zero do not coincide in this case, and the eddy diffusivity of heat becomes negative in a region of about 20% of the channel width. In the vicinity of the wall, the temperature fluctuation intensity normalized by the friction temperature is not affected by the wall curvature, whereas the cross correlation coefficients between velocity and temperature fluctuations, the skewness and the flatness are appreciably affected by it. The triple correlations relating to the transverse diffusion decrease and increase remarkably in the inner and outer sides of the channel, respectively.

Numerical Prediction of Turbulent Heat Transfer in High-Prandtl-Number Fluids.

A two-equation heat-transfer model for high-Prandtl-number fluid flows has been developed from the scope of the original (t2)^^- et model of Nagano and Kim (1988). The proposed model has been appraised in comparison mainly with the existing experiments on water (Pr=5.9), aqueous ethylene glycol (Pr=14.3) and oil (Pr=95). It is shown that the present model predicts quite well the experimental behavior of fundamental quantities in turbulent heat transfer, i.e., the Nusselt or Sherwood number, temperature profiles and intensity of temperature fluctuations. Especially, the prediction of the r.m.s. intensity of temperature fluctuations is in good agreement with the most recent and reliable experimental data of water. Furthermore, we have investigated the Prandtl-number dependency of the turbulence quantities in thermal fields such as Nusselt number, temperature profile, temperature variance and eddy diffusivity for heat. Since the two-equation heat-transfer model provides information on temperature fluctuations, which cannot be obtained by the conventional model based on the assumption of the turbulent Prandtl number, the present model provides a powerful tool for critical design of thermal equipments.

A Two-Equation Model for Heat Transport in Wall Turbulent Shear Flows

A new proposal for closing the energy equation is presented at the two-equation level of turbulence modeling. The eddy diffusivity concept is used in modeling. However, just as the eddy viscosity is determined from solutions of the k and ε equations, so the eddy diffusivity for heat is given as functions of temperature variance t2, and the dissipation rate of temperature fluctuations εt, together with k and ε. Thus, the proposed model does not require any questionable assumptions for the “turbulent Prandtl number.” Modeled forms of the t2 and εt equations are developed to account for the physical effects of molecular Prandtl number and near-wall turbulence. The model is tested by application to a flat-plate boundary layer, the thermal entrance region of a pipe, and the turbulent heat transfer in fluids over a wide range of the Prandtl number. Agreement with the experiment is generally very satisfactory.

The stably stratified boundary layer over the great plains

We present airplane measurements of the stably stratified nocturnal boundary layer obtained during the Severe Environmental Storms and Mesoscale Experiment (SESAME) in 1979. The cases presented here were obtained over rolling terrain in central Oklahama, with a mean slope of about 0.003. The results are in general agreement with previous modeling and observational studies for the mean and turbulence structure of the nocturnal boundary layer, with the exception that the eddy diffusivity of heat, and consequently the flux Richardson number are less than expected.

A two-equation model for heat transport in wall turbulent shear flows.

A new proposal for closing the energy equation is presented at the two-equation level of turbulence modelling. The eddy diffusivity concept is used in modelling. However, just as the eddy viscosity is determined from solutions of the k- and e-equations, so the eddy diffusivity for heat is given as functions of temperature variance, ^-, and the dissipation rate of temperature fluctuations, et, together with k and e. Thus, the proposed model does not require any questionable assumptions for the Prandtl Modelled forms of the ^-- and et-equations are developed to account for the physical effects of molecular Prandtl number and near-wall turbulence. The model is tested by application to a flat plate boundary layer, the thermal entrance region of a pipe, and the turbulent heat transfer in fluids over a wide range of the Prandtl number. Agreement with experiment is generally very satisfactory.

Experiments on scalar dispersion within a model plant canopy part II: An elevated plane source

An experiment is reported in which heat was released as a passive tracer from an elevated lateral line source within a model plant canopy, with hs = 0.85 hc (hs and hc being the source and canopy heights, respectively). A sensor assembly consisting of three coplanar hot wires and one cold wire was used to measure profiles of mean temperature % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikamaana% aabaGaeqiUdehaaiaacMcaaaa!390C!\[(\overline \theta )\], temperature variance (Σθ2), vertical and streamwise turbulent heat fluxes, and third moments of wind and temperature fluctuations. Conclusions were: (i) Despite the very heterogeneous flow within the canopy, the observed dispersive heat flux (due to spatial correlation between time-averaged temperature and vertical velocity) was small. However, there is evidence from the plume centroid (which was lower than hs at the source) of systematic recirculating motions within the canopy. (ii) The ratio % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS% baaSqaaiabeI7aXjaab2gacaqGHbGaaeiEaaqabaGccaGGVaWaa0aa% aeaacqaH4oqCaaWaaSbaaSqaaiaab2gacaqGHbGaaeiEaaqabaaaaa!41DF!\[\sigma _{\theta {\text{max}}} /\overline \theta _{{\text{max}}} \] (of maximum values on vertical profiles) decreased from 1 near the source to an asymptotic value of 0.4 far downstream, in good agreement with previous experimental and theoretical work for concentration fluctuations in the surface layer well above the canopy. (iii) The eddy diffusivity for heat from the line source (KHL) increased, downstream of the source, to a nearly constant ‘far-field’ vertical profile. Within the canopy, the far-field KHL was an order of magnitude larger than KHP, the equivalent diffusivity for a plane source; well above the canopy, the two were equal. The time scale defined by (far-field KHL)/(vertical velocity variance) was independent of height within the canopy. (iv) Budgets for temperature variance, vertical heat flux and streamwise heat flux are remarkably similar to the equivalent budgets for an elevated line source in the surface layer well above the canopy, except in the lower part of the canopy in the far field, where vertical transport is much more important than in the surface layer. (v) A random flight simulation of the mean height and depth of the temperature plume was generally in good agreement with experiment. However, details of the temperature and streamwise turbulent heat flux profiles were not correct, suggesting that the model formulation needs to be improved.

Extrapolation of the nocturnal temperature inversion from ground-based measurements

The characteristics of a nocturnal temperature inversion and their relationship to the atmospheric eddy heat diffusion and ground radiated heat flux are discussed. A method to extrapolate the temperature profile from ground-based measurements based on a theory described by Anfossi et al is introduced ( 1976, Q. Jl R. met. Soc. 102, 173–180). Experimental evidence shows the technique to give a useful degree of accuracy.

The influence of faculae on sunspot heat blocking

We study the influence of faculae on sunspot heat blockage using a thermal model based on eddy heat diffusion through the convection zone. The facula is represented as a localized area of excess emission surrounding the sunspot, which is represented as a thermal plug. Our computations using a range of reasonable combinations of spot and facular depths show no significant influence of the facula on the long storage times of heat blocked by sunspots. However, the local cooling of surface layers produced by excess facular emission in this model propagates globally within the convection zone in a similar way to the heating produced by a spot. The net effect of spots and faculae on L⊙ over time scales longer than an active region lifetime should thus be determined by the global sum of sunspot flux deficits and facular excesses.

Mercury-argon two-phase heat transfer in a vertical annulus under transverse magnetic field

This paper presents experimental data of local properties and heat transfer of mercury-argon two-phase bubbly flow with small gas flow rate in a vertical annulus in the presence of transverse magnetic field. The two-phase Nusselt number decreases as well as single phase mercury heat transfer with increasing Hartmann number at the fixed Peclet number, but its decrease becomes smaller than the single phase as the quality is increased. Discussions are presented on contributions of effective thermal conductivity, eddy diffusivity of heat and liquid velocity to the two-phase heat transfer.

Buoyancy effects on turbulent transport in combined free and forced convection between vertical parallel plates

Turbulent mixed flow of free and forced convection was investigated experimentally and theoretically. Experiments were carried out in the upward turbulent flow between vertical parallel plates at different wall temperatures. In this condition, the aiding and opposing flows arose simultaneously on the heated and cooled sides, respectively, and a fully developed condition was established.Buoyancy effects on the mean velocity and temperature profiles, eddy diffusivities of heat and momentum, Nusselt number and friction factor, as well as the intensity of velocity and temperature fluctuations were examined, and the substantial effects of the buoyancy force were confirmed.In addition, an analytical model was proposed, based upon the damping factor concept of the turbulent fluctuations due to viscous action and buoyancy force. It is confirmed that the analytical model predicts the experimental results for the buoyancy effects on the turbulent transport process, and also partly explains the behavior of the turbulent properties.

Diffusion of Bubbles in Two-Phase Flow : 2nd Report, Diffusion of a Single Bubble and Eddy Diffusivity of Heat in Single-Phase Turbulent Flow

In this second report, we investigate the relation between the turbulent diffusion of a bubble and eddy diffusivity of heat in the core of a fully developed pipe flow. As a result, it is found that the diffusivity of bubbles is smaller than the eddy diffusivity of heat, and can be divided into three regions, corresponding to the distribution of terminal velocities of bubbles in water against the size of bubbles.

Gas temperature distribution and eddy diffusivity of heat in gaseous suspension flow.

Two mathematical models are proposed to represent gas temperature distributions in suspension flows heated at the tube wall. These models are quite different from each other in the turbulent mixing mode of solid particles. Two parameters in these models were determined from experimental measurement of temperature distribution by using a parameter estimation technique. These models express observed temperature distributions well, especially when the loading ratio is smaller than unity. Mean gas eddy diffusivity and Nusselt number were calculated from these two parameters, which could be correlated well with a single nondimensional parameter that represents the operating conditions. By using this correlation and the models, temperature distributions can be easily predicted in the usual practical operating conditions of industrial suspension flows.

Heat transfer for turbulent flow with injection in a porous tube.

The effect of injection on the eddy diffusivity of heat in the turbulent core region and the heat transfer rate in the thermally fully developed region was analyzed using a simple model. The analytical results were tested in experiments on the heat transfer of turbulent flows of water in a circular tube of porous wall through which heated water was injected. Measurements of heat transfer rate and temperature profile were made far downstream from the entrance. The experiments were performed for Reynolds numbers of the main flow ranging from 6, 000 to 34, 000 and for injection rates of m=-0.004 to -0.0004. It was found that the measured heat transfer rates and the eddy diffusivities of heat could be correlated well by the expressions obtained from the analysis. The j-factor of heat transfer divided by the dimensionless pressure gradient and the eddy diffusivity of heat normalized by Re(-dp*/dx*) were expressed as the sum of the linear function and the hyperbola of the injection rate parameter, m/(-dp*/dx*). In the range of 0>m/(-dp*/dx*)>-0.08 the Chilton-Colburn analogy was found to hold even in the presence of injection.

大気境界層の乱流パラメタリゼーションについてのノート

A simple turbulent energy equation based on semi-empirical turbulence theory was used to parameterize the vertical eddy exchange processes in the atmospheric boundary layer. Numerical experiments with a one-dimensional version of the Techniques Development Laboratory boundary layer model were conducted to evaluate the parameters employed in the turbulent energy equation. These parameters include the ratio αT between eddy diffusivity for heat and that for momentum, and the turbulence length scale l.The study concludes that while specification of l has a great effect on the wind speed, values of αT affect the prediction of temperature substantially. With a proper choice of l and aT, the turbulent energy parameterization scheme may be useful for modeling detailed structures of the boundary layer. Results with four different specification of l and αT are presented and compared with observations. Recommendations are made on the proper specification of l and αT for use in the turbulent energy equation.

Comments on a paper by B. B. Hicks: ‘A procedure for the formulation of bulk transfer coefficients over water’

In formulating bulk transfer coefficients over water, Hicks (1975) assumes that an appropriate temperature roughness parameter, zH, may be derived with a method proposed by Sheppard (1958). The assumption is questioned in this note. For simplicity, the discussion is restricted to sensible heat transfer, and stability dependence is ignored. The ratio of the eddy diffusivity for heat to that for momentum, cx, is included in the calculations. Hicks considers only Q = 1. Usual eddy diffusivity assumptions for the neutral surface layer lead to

An Investigation of the Occurrence of Oceanic Turbulence with Respect to Finestructure

Abstract Data obtained from the cycling mode of a towed system operated in the North Pacific are used to investigate the relationship of small-scale mixing to the finestructure which seems to be such a common characteristic of vertical profiles of oceanic water properties. The signal from a high-frequency response platinum-film thermometer is used, with the local mean vertical temperature gradient, to produce variables proportional to heat flux and an eddy diffusivity for heat. Along with measured values for the local vertical salinity and density gradients, this information is used to examine some questions of interest in the general understanding of turbulence and finestructure. First, it is shown that in regions where the vertical density structure is distinctly layered, there is no noticeable tendency for mixing to occur preferentially on “sheets,” the high-density-gradient regions which separate “layers of lower density gradient. Instead, mixing events seem to occur at random with respect to the den...

Turbulent velocity and temperature distribution in the central subchannel of rod bundles

In this paper a method is given for solving the momentum and heat transfer equations for the central subchannel of a reactor subassembly in general curvilinear orthogonal coordinates. For turbulent flow, the eddy diffusivities are determined by Prandtl's ‘mixing length’ hypothesis. A new method is proposed to determine eddy diffusivities parallel to the wall. The eddy diffusivities of heat are calculated from those of momentum using the relations obtained by various authors, and the results are compared in the case of sodium. To show the capability of the computer codes developed, the three-dimensional temperature field is calculated in the central subchannel of a fuel element cooled by sodium and helium. The agreement between calculated and experimental results is satisfactory.