Turbulent Diffusion Of Heat Research Articles

NUMERICAL COMPUTATION OF HEAT AND MOMENTUM TRANSFER IN TURBULENT FLOWS ALONG A PLATE USING LARGE TRANSVERSAL INTERVALS

A hybrid computational method has been developed for the step-by-step calculation of both momentum and heat transfer in turbulent boundary layer flows along flat plates. Basically, the proposed procedure relies on the method of lines (MOL), which replaces a partial differential equation in two independent variables by an appropriate system of ordinary differential equations in one of these variables. This convenient transformation is accomplished by constructing a “control volume” being infinitesimal in the axial direction and finite in the transversal direction of the fluid stream. Using the customary assumptions for modellirg the turbulent diffusivity of momentum and heat for gases, the resulting system of ordinary differential equations of first order may be readily integrated utilizing a fourth-order Runge-Kutta algorithm. In general, for a typical boundary layer calculation, a maximum number of sixteen lines is necessary at the trailing edge of the flat plate. As a consequence, computing time and sto...

Physical interactions within a coupled climate model over the last glacial–interglacial cycle

ABSTRACTA two-dimensional (2-D) seasonal model has been developed for simulating the transient response of the climate system to the astronomical forcing. The atmosphere is represented by a zonally averaged quasi-geostrophic model which includes accurate treatment of radiative transfer. The atmospheric model interacts with the other components of the climate system (ocean, sea-ice and land surface covered or not by snow and ice) through vertical fluxes of momentum, heat and humidity. The model explicitly incorporates surface energy balances and has snow and sea-ice mass budgets. The vertical profile of the upper-ocean temperature is computed by an interactive mixed-layer model which takes into account the meridional turbulent diffusion of heat. This model is asynchronously coupled to a model which simulates the dynamics of the Greenland, the northern American and the Eurasian ice sheets. Over the last glacial–interglacial cycle, the coupled model simulates climatic changes which are in general agreement with the low frequency part of deep-sea, ice and sea-level records. However, after 6000 yBP, the remaining ice volume of the Greenland and northern American ice sheets is overestimated in the simulation. The simulated climate is sensitive to the initial size of the Greenland ice sheet, to the ice-albedo positive feedback, to the precipitation-altitude negative feedback over the ice sheets, to the albedo of the aging snow and to the insolation increase, particularly at the southern edge of the ice sheets, which is important for their collapse or surge.

Climate studies with a coupled atmosphere-upper-ocean-ice-sheet model

A two-dimensional zonally averaged model has been developed for simulating the seasonal cycle of the climate of the Northern Hemisphere. The atmospheric component of the model is based on the two-level quasi-geostrophic potential vorticity system of equations. At the surface, the model has land—sea resolution and incorporates detailed snow and sea-ice mass budgets. The upper ocean is represented by an integral mixed-layer model that takes into account the meridional advection and turbulent diffusion of heat. Comparisons between the computed present-day climate and climatological data show that the model does reasonably well in simulating the seasonal cycle of the temperature field. In response to a projected CO 2 trend based on the scenario of Wuebbles et al. (DOE/ NBB-0066 Technical Report 15 (1984)), the modelled annual hemispheric mean surface temperature increases by 2 °C between 1983 and 2063. In the high latitudes, the response undergoes significant seasonal variations. The largest surface warmings occur during autumn and spring. The model is then asynchronously coupled to a model that simulates the dynamics of the Greenland, the Eurasian and the North American ice sheets in order to investigate the transient response of the climate to the long-term insolation anomalies caused by orbital perturbations. Over the last interglacial-glacial cycle, the coupled model produces continental ice-volume changes that are in general agreement with the low-frequency part of palaeoclimatic records.

Measuring distributions of diffusivity in turbulent fluids with magnetic-resonance imaging.

This paper describes a method for measuring distributions of turbulent diffusivity in less than an hour. The measurement is rapid enough to aid in designing devices that make use of the turbulent diffusion of mass, heat, or momentum. It may be useful as a measurement of the degree of turbulence in the blood of patients with cardiovascular diseases. It consists of subtracting the natural logarithms of the pixel values of a magnetic-resonance image of turbulent fluid from those of stationary fluid. The pixel values of the resulting image are multiplied by a constant to yield diffusivities. The accuracy of the measurement is within the range of diffusivities (1) upstream as far as the speed of the fluid multiplied by the time ${T}_{E}$ between exciting the spin system and recording the signal, (2) in the direction of the gradient of diffusivity as far as ${T}_{E}$ multiplied by 5 times the gradient of the diffusivity, and (3) in the direction of the phase-encoding magnetic field gradient as far as the negative of the component of velocity in the phase-encoding direction multiplied by the time between phase encoding and recording the signal. In a 32\ifmmode\times\else\texttimes\fi{}32-${\mathrm{cm}}^{2}$ image of a jet of water with a nozzle velocity of 4.5 m ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and Reynolds number of 18 000, made with a ${T}_{E}$ of 15 ms, the distance of (1) ranged from 0 to 6.7 cm, of (2) ranged from 0 to 0.3 cm, and of (3) ranged from 0 to 0.4 cm. These distances are bounds; the actual spatial misregistration was less. The signal-to-noise ratio ranged from 10 to 15 for diffusivities from 0.02 to 0.7 ${\mathrm{cm}}^{2}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$. .AE

Seasonal variability of temperature, salinity, velocity, vorticity and sea level in the central Gulf of California, as inferred from historical data

AbstractHistorical data from 17 cruises into the Guaymas basin, central part of the Gulf of California, are globally analysed. Temperature, across‐gulf integrated velocity, sea level, and salinity have a significant seasonal cycle. The last variable has an important semi‐annual component, presenting four extremes per year. The others are mainly annual, reaching their maximum values in summer and their minima in winter.By interaction with the atmosphere, the central gulf is gaining heat and losing fresh water during the whole year, on a monthly‐mean time scale (the only exception is an unimportant gain of fresh water in August). This implies net heat and salinity fluxes into the open ocean, through the gulf's mouth.Temperature and salinity vertical gradients at the surface are well correlated with atmospheric forcing, through turbulent diffusion of heat and salt. Average velocity correlates with the along‐gulf wind stress with zero lag, as if frictionally dragged in a surface layer, with a short relaxation time. Seasonal sea‐level changes are mainly caused by the thermal expansion of the water column.Horizontal processes (advection and diffusion) are as important as, or more important than, vertical diffusion for both heat and salt balances in the upper layers.Vorticity, the across‐gulf derivative of the velocity field, does not show a seasonal cycle. Its contribution to the instantaneous geostrophic velocity and surface elevation near each coast is larger than that due to the across‐gulf average velocity.

A two-dimensional time-dependent model for surface shear and buoyancy-driven flows in domains with large aspect ratio

A two-dimensional numerical model has been developed for studying flows in enclosures having a large length-to-depth ratio. The model solves the two-dimensional Navier-Stokes and energy equations subject to hydrostatic, Boussinesq, and rigid-lid assumptions. Turbulent momentum and heat diffusion are incorporated using variable eddy coefficients. The flow is driven by surface wind shear and heat transfer. Two cases were run for a rectangular domain, subject to a suddenly imposed surface shear stress while the surface and bottom were mainained at two different but constant temperatures. The difference between the cases was the formulation used for predicting the eddy viscosities and diffusivities. The variations of velocities and temperatures with time were studied. Both velocities and temperatures were found to undergo a sudden rapid change, after an initial period of slow change, before attaining steady state. This has been explained in light of the differences in the convective and diffusive time scales and the nature of coupling between the governing equations.

Turbulent diffusion of heat in dilute disperse flows

On the basis of inserting random terms in the heat-transfer equations in a gas suspension, the influence of particles on turbulent heat diffusion and the behavior of spectral functions of turbulent temperature fluctuations are investigated.

Theory of trapped-particle-induced resistive fluid turbulence

A theory of anomalous electron heat transport, evolving from trapped-particle-induced resistive interchange modes, is proposed. The latter are a new branch of the resistive interchange-ballooning family of instabilities, destabilized when the pressure carried by the unfavorably drifting trapped particles is sufficiently large to overcome stabilizing contributions coming from favorable average curvature. Expressions for the turbulent heat diffusivity and anomalous electron thermal conductivity at saturation are derived for two regimes of trapped-particle energy: (i) a moderately energetic regime, which is ‘‘fluidlike’’ in the sense that the unstable mode grows faster than the time that it takes for particles in this energy range to precess once around the torus, and (ii) a highly energetic regime, where the trapped species has sufficiently high energy as to be able to interact resonantly with the mode. Unlike previous theories of anomalous transport, the estimates of diffusion and transport obtained here are self-consistent since the trapped particles do not ‘‘see’’ the magnetic flutter due to their rapid bounce motion. The theory is valid for moderate electron-temperature, high ion-temperature (auxiliary heated) plasmas and as such, is relevant for present- and future-generation experimental fusion devices.

Conventional and conditional Prandtl number in a turbulent plane wake

Conventional and conditional measurements of several turbulence quantities and particularly of the turbulent Prandtl number are presented for the nearly self-preserving region of a slightly heated wake of a circular cylinder. To verify that the measurements were made in the self-preserving region, and to also serve as a check on measurement accuracy, three stations in the wake were used. The identification of the turbulent regions in the outer part of the wake was based on the behaviour of the probability density function of the temperature fluctuation. Conventional distributions of the turbulent diffusivities of momentum and heat vary considerably in the outer part of the wake. This variation is not reduced when only turbulent zone averages are considered. The turbulent Prandtl number varies significantly in the turbulent part of the flow.

A two-dimensional time-dependent model for surface shear and buoyancy-driven flows in domains with large aspect ratio

A two-dimensional numerical model has been developed for studying flows in enclosures having a large length-to-depth ratio. The model solves the two-dimensional Navier-Stokes and energy equations subject to hydrostatic, Boussinesq, and rigid-lid assumptions. Turbulent momentum and heat diffusion are incorporated using variable eddy coefficients. The flow is driven by surface wind shear and heat transfer. Two cases were run for a rectangular domain, subject to a suddenly imposed surface shear stress while the surface and bottom were maintained at two different but constant temperatures. The difference between the cases was the formulation used for predicting the eddy viscosities and diffusivities. The variations of velocities and temperatures with time were studied. Both velocities and temperatures were found to undergo a sudden rapid change, after an initial period of slow change, before attaining steady stage. This has been explained in light of the differences in the convective and diffusive time scales and the nature of coupling between the governing equations.

Observations of internal gravity waves under the Arctic pack ice

Internal gravity waves measured under the Arctic pack ice were strikingly different from measurements at lower latitudes. The total wave energy, integrated over the internal wave frequency band, was lower by a factor of 0.03–0.07, and the spectral slope at high frequency was nearly −1 in contrast to the − 2 observed at lower latitudes. This result has implications for theoretical investigations of the generation, evolution, and destruction of internal waves and is also important for other processes, such as the propagation of sound, and the wave‐induced turbulent diffusion of heat, plankton, and chemical tracers.

Modelling the Propagation of Atmospheric Tides from the Lower to the Middle and Upper Atmosphere

Upward propagating tides make an important contribution to the momentum budget of the lower thermosphere, and significantly modify ionized and neutral structures at higher levels, accounting for such phenomena as the midnight collapse of the ionosphere over Arecibo, and the midnight temperature anomaly. Modelling the thermospheric penetration of upward propagating tides excited in the lower atmosphere can be approached by (a) numerical solution of the governing tidal equations from ground level, taking into account realistic thermal forcing and the non-classical effects of turbulent diffusion of momentum and heat, zonal mean winds, and latitudinal temperature gradients; or (b) the utilization of meteor, M.F. and Thomson scatter radar data to specify tidal oscillations at the lower boundary (ca. 95 km) of a thermosphere general circulation model (TGCM). In this paper the main physical processes affecting the propagation of tides from the lower to middle and upper atmosphere are reviewed, as well as existing models used to simulate tidal propagation. In addition, new theoretical work is presented which quantifies the effects of mean winds and dissipation on the diurnal propagating tide in the mesosphere and lower thermosphere, and a new method is proposed whereby the lower boundary specification of the semidiurnal perturbation geopotential for TGCM's can be analytically specified through utilization of radar wind data and classical tidal theory.

Analysis of model relations for turbulent heat diffusion as applied to the calculation of wake flows

An experimental test of the known approximations is made and a new relation is proposed for turbulent diffusion of heat or of a passive admixture.

On self-preserving, variable-density, turbulent free jets

Appropriately defined Gaussian error-functions are shown to represent closed-form solutions of self-preserving, axisymmetric, variable density, free turbulent jets. The turbulent diffusivities of momentum, mass or heat associated with such solutions are found to vary both in the streamwise and radial directions, and are different from each other. An entrainment function for the jet can also be derived from the present analysis. The entrainment coefficient is found to be uniquely related to the turbulent Reynolds number, Re t , of the jet, which is one of the two parameters in the closed-form solutions. Inverse centreline values of velocity, density, mass fraction and temperature are found to be linearly proportional to the streamwise coordinate as are the spread of velocity and scalar. If the two parameters are determined from jet spread data, the resulting closed-form solutions are in good agreement with measurements.

Turbulent diffusion in rod arrays with sodium coolant

The authors estimate transfer processes in the rod arrays with sodium coolant and discuss the forms of turbulent radial and turbulent azimuthal momentum diffusions; a diagram of turbulent heat diffusion is presented. Many equations are analyzed.

Mathematical modelling of buoyancy-induced smoke flow in enclosures

A computational procedure for predicting velocity and temperature distributions in enclosures containing a fire source is reported. The procedure is based on the solution, in finite-difference form, of the 2-dim. equations for the conservation of mass, momentum, energy, turbulence energy and eddy dissipation rate, with closing expressions for the turbulent viscosity and heat diffusivity. Effects of buoyancy on the turbulence model have been included. The results are shown to be in reasonable agreement with experimental data.

A method of evaluating local turbulent diffusivity of heat in a gridded fuel subassembly

Abstract In evaluating the turbulent diffusivity of heat associated with the coolant flow past a grid spacer within an FBR fuel subassembly, a heat diffusion technique is usually employed. However, measurement of subchannel bulk coolant temperature using thermocouples usually involves difficulty due to a steep and non-linear temperature gradient in the subchannels adjacent to a heater pin. A series solution of the heat conduction equation for the coolant flow in subchannels past a grid spacer and a heated section of a dummy fuel pin was derived under a slug flow approximation where the boundary conditions on dummy fuel pins were satisfied by means of the point-matching technique. The solution may be utilized in analyzing the turbulent diffusivity of heat within subchannel coolant flow as a function of distance from a grid spacer based on the measured temperature distribution on the wall of dummy fuel pins, which may be obtained without affecting the subchannel coolant temperature. In an illustrative example, the turbulent diffusivity of heat was most exaggerated at about 50 mm beyond a grid spacer and was approximately five times larger than the corresponding diffusivity without a grid spacer.

Experimental Investigation of Heat and Mass Diffusion in a Porous Tube-Generated Flowfield

Flow of laser gas and a saturable absorber gas generated by two adjacent grids of porous tubes provides a fiav$ scheme for windowless gain isolation of large CO2 laser amplifiers. Turbulent mixing at the interface of the two parallel flows causes laser beam degradation, and a reduction in the available active laser volume due to mass diffusion. In the present study, hot wire anemometry, species concentration measurements, and interferometry were used to investigate and to visualize the turbulent diffusion of mass and heat at the interface between the laser and saturable absorber gas flows. The results show that the growth of the mixing zone is linear, a = 0.1, and the spreading of heat and mass are mutually equal. The interferometric data show that for CO2 wavelength radiation (10.6 /*) the turbulent mixing at the interface has little effect on the optical quality of the porous tube-generated flowfield for differences in /3 up to about

Numerical modeling of land and sea breeze circulation along a complex coastline

The wind distribution in the atmospheric boundary layer is affected by air motions on all scales. In low-latitude coastal areas, however, the wind flows generally are dominated by the diurnally varying land and sea breezes. These flow patterns have been known to exert great influence on local environments by spreading wind-driven brish fires, for example, or dispersing natural or man-made air pollutants. The purpose of this paper is to present a mathematical model that can simulate land and sea breezes in coastal areas. The model equations, based on the primitive equations for the planetary boundary layer with the hydrostatic approximation, are solved numerically with appropriate initial and boundary conditions obtained from interpolation of observational data. Turbulent diffusion of momentum and heat is parameterized through the use of similarity theory for the surface layer supplemented by empirical relationships. This model has been applied to the Tampa Bay area along the Gulf of Mexico. The computed wind field not only simulates the strong land-bound sea breeze at the surface during the day and a weak return flow during the night, but it also retrieves the essential features of land/sea breeze along a complex coastline.

Turbulent diffusion of heat between connected flow passages Part 2: Predictions using the “κ-ϵ” turbulence model

Axial velocity contours, temperature contours and the amount of inter-subchannel mixing by turbulent diffusion and secondary flow for turbulent flow in ducts simulating smooth bare rod bundles have been investigated both experimentally and analytically. This paper, part 2, deals with the computer prediction of the turbulent flow in three duct configurations simulating pitch to diameter ratios of 1.833, 1.375 and 1.1; in part 1 the problem was outlined and detailed measurements were reported for the three ducts. The analytical work has been performed by solving the basic differential equations of the turbulent flow and heat flux using the “κ-ϵ” turbulence model and the “Gosman” numerical integration procedure. This is believed to be the first application of these procedures to the prediction of inter-subchannel mixing. A detailed comparison between the computer predictions and the results of the experimental work revealed that secondary flows were not an important determinant in the mixing rate and did not allow agreement to be obtained with the measured axial velocity and temperature contours. Predictions assuming that the effective diffusivity was isotropic, produced gap Stanton numbers an order less than those measured. To obtain gap stanton numbers of the correct order it was found necessary to use anisotropic effective diffusivities in which the anisotropy distribution rose sharply near the walls to very high values (≈50).