Local Energy Flux Research Articles

Measurement of magnetic fluctuation-induced heat transport in tokamaks and RFP

The local electron energy flux produced by magnetic fluctuations has been measured directly in the edge plasma of the Madison symmetric torus (MST) reversed field pinch (RFP), continuous current tokamak (CCT), and the scrape-off layer of the TEXT-U tokamak. The flux produced by electrons travelling parallel to a fluctuating magnetic field is obtained from correlation between the fluctuations in the parallel heat flux and the radial magnetic field. The fluctuations in the parallel heat flux were measured with a fast insertable pyrobolometer. The measurements reveal fundamental differences in the nature of electron energy transport in the RFP and the tokamak. In the RFP the fluctuation-induced energy flux is large (, comparable to the total ohmic heating power) inside the reversal surface where the magnetic field is expected to be stochastic, and small in the edge. The magnetic fluctuation induced radial energy flux Q and radial particle flux (measured independently) are related by a `convective' formula . The electron heat transport is significantly lower than the value predicted by the Rechester - Rosenbluth transport model. This feature of the electron energy transport can be explained using self-consistent calculations that account for clumping of electrons streaming along the magnetic field. In the tokamak the magnetic fluctuations do not contribute to the total energy transport except in the vicinity of the q = 2 magnetic surface, where the transport is associated with large amplitude Mirnov oscillations.

Computation of Sea-Wave Direction of Propagation of Random Waves

In the last 20 years, the application of the random wave theory in maritime engineering has been given the utmost importance, especially for evaluating design wave conditions, loads on structures, and sand littoral drift. The aim of the paper is to present a general expression for the evaluation of the local energy flux vector of random waves. This expression can be used for computing a representative direction of propagation of the wave spectrum in the presence of any scattering source. The effectiveness of the presented expression is shown by a numerical experiment. Moreover the expression is compared with the relationship that is normally used in field observations to represent the mean wave direction of a two-dimensional spectrum. The results of the comparison, carried out with a measured directional wave spectrum, are discussed.

Model and computer simulation of friction

AbstractA model, consisting of the stochastic formulae which describe the relationship between the friction coefficient and the parameters known to be significant in dry friction, is proposed for dry sliding friction between two randomly rough surfaces. The model considers the frictional phenomena which dominate in energy dissipation and which may occur simultaneously between contacting elements. The kind of interaction in a given spot of asperity contact depends on the local energy flux density. The effect of several parameters on the friction coefficient, the real area of contact, and the number of contact spots can be calculated with the FRI‐SIM program. A comparison of the simulation and experimental data shows a convergence of results.

Local energy flux and the refined similarity hypothesis

In this paper we demonstrate the locality of energy transport for incompressible Euler equations both in space and in scale. The key to the proof is the proper definition of a “local subscale flux,”Π t (r), which is supposed to be a measure of energy transfer to length scales <l at the space point r. Kraichnan suggested that for such a quantity the ”refined similarity hypothesis” will hold, which Kolmogorov originally assumed to hold instead for volume-averaged dissipation. We derive a local energy-balance relation for the large-scale motions which yields a natural definition of such a subscale flux. For this definition a precise form of the “refined similarity hypothesis” is rigorously proved as a big-O bound. The established estimate isΠ t (r)=O(l3h-1) in terms of the local Holder exponenth at the point r, which is also the estimate assumed in the Parisi-Frisch “multifractal model.” Our method not only establishes locality of energy transfer, but it also clarifies the physical reason that convection effects, which naively violate locality, do not contribute to the subscale flux. In fact, we show that, as a consequence of incompressibility, such effects enter into the local energy balance only as the divergence of a spatial current. Therefore, they describe motion of energy in space and cancel in the integration over volume. We also discuss theorems of Onsager, Eyink, and Constantinet al. on energy conservation for Euler dynamics, particularly to explain their relation with the Parisi-Frisch model. The Constantinet al. proof may be interpreted as giving a bound on the total flux,Π t =∫d d rΠ t (r), of the formΠ t (r)=O(lz3h-1), wherez3 is the third-order scaling exponent (or Besov index), in agreement with the “multifractal model.” Finally, we discuss how the local estimates are related to the results of Caffarelli-Kohn-Nirenberg on partial regularity for solutions of Navier-Stokes equations. They provide some heuristic support to a scenario proposed recently by Pumir and Siggia for singularities in the solutions of Navier-Stokes with small enough viscosity.

Measurement of magnetic fluctuation induced energy transport.

The local electron energy flux produced by magnetic fluctuations has been measured directly in the MST reversed field pinch (over the radial range r/a&gt;0.75).The flux, produced by electrons traveling parallel to a fluctuating magentic field, is obtained from correlation between the fluctuations in the parallel heat flux and the radial magnetic field. The fluctuation induced flux is large (100 kW/${\mathrm{cm}}^{2}$) in the ``core'' (r/a0.85) and small (10--30 kW/${\mathrm{cm}}^{2}$) in the edge.

Non-equilibrium molecular dynamics calculation of heat conduction in liquid and through liquid-gas interface

This paper presents a new algorithm for non-equilibrium molecular dynamics, where a temperature gradient is established in a system with periodic boundary conditions. At each time step in the simulation, a fixed amount of energy is supplied to a hot region by scaling the velocity of each particle in it, subject to conservation of total momentum. An equal amount of energy is likewise withdrawn from a cold region at each time step. Between the hot and cold regions is a region through which an energy flux is established. Two configurations of hot and cold regions are proposed. Using a stacked layer structure, the instantaneous local energy flux for a 128-particle Lennard-Jones system in liquid was found to be in good agreement with the macroscopic theory of heat conduction at stationary state, except in and near the hot and cold regions. Thermal conductivity calculated for the 128-particle system was about 10% smaller than the literature value obtained by molecular dynamics calculations. One run with a 1024-...

Radiation boundary conditions for the two-dimensional wave equation from a variational principle

A variational principle is used to derive a new radiation boundary condition for the two-dimensional wave equation. This boundary condition is obtained from an expression for the local energy flux velocity on the boundary in normal direction. The wellposedness of the wave equation with this boundary condition is analyzed by investigating the energy of the system. Results obtained with this (nonlinear) boundary condition are compared with those obtained with the (linear) first-order absorbing boundary condition suggested by Higdon. In an accompanying paper the underlying theory is presented.

A Linear Stability Analysis of the Stratospheric and Mesospheric Zonal Mean State in Winter and Summer

Abstract The linear normal modes of large-scale atmospheric motions are computed in a spherical quasi-geostrophic model extending from the surface up to 80 km to investigate the stability of zonal motions in the stratosphere and mesosphere. The basic states are taken from the Northern Hemisphere winter and summer solstitial conditions. The winter basic state is able to generate growing planetary waves 1 and 2, which extend into the stratosphere and the mesosphere at high latitudes. They are identified as Green modes which propagate very slowly. The structure of the Green mode compares favorably with the observed quasi-stationary planetary waves. Waves 4–6, generated in the troposphere, can also penetrate into the lower stratosphere but an trapped them and resemble Charney modes. Energetics analysis indicates that the ratio of the local energy conversion versus energy flux from below is about 1:2 for the Omen modes waves 1 and 2 in the stratosphere while the mean flow and the planetary waves in the mesosph...

The Suitability of Routine Weather Data for Estimating Local Estuarine Heat Energy Fluxes

Meteorological data and water temperatures from a 98-day period during the summer of 1980 are used to examine the suitability of routine weather observations for quantifying the heat energy budget of a shallow lagoon on the Atlantic coast of Florida. Hourly cloud-cover observations are used to calculate incoming solar radiation, and results are compared with pyranometer readings. The standard error of the estimate is 26% of the mean daily accumulation for simulations of one day, but this decreases to only 0.3% of the total accumulation for simulations of 21 days. Wind speeds recorded at a weather station 4 km from the study site must be modified by a site-specific wind ratio before they can be used to calculate latent and sensible heat fluxes. Even with site-specific corrections to routine weather data, the standard deviation of simulated temperatures is 2 to 3 times that of observed temperatures. Cloud cover and wind speed are the two variables most difficult to incorporate into the simulations.

Local inhomogeneities in a Robertson-Walker background. III - Elementary growth rates in a flat background with a relativistic equation of state

view Abstract Citations (4) References (12) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Local inhomogeneities in a Robertson-Walker background. III - Elementary growth rates in a flat background with a relativistic equation of state Helaby, C. ; Lake, K. Abstract An examination is undertaken of a class of inhomogeneities, embedded in a spatially flat Robertson-Walker background, which is restricted by the simplifying assumption that isotropic pressure equals local energy flux. Both a noninteracting mixture of blackbody photons and dust, and a baryon-conserving equilibrium mixture of blackbody photons and a neutral, two-component, relativistic Maxwell-Boltzmann gas, are used to describe the background. It is demonstrated through a comparison of the resultant mass of the inhomogeneities with the Jeans and particle horizon mass scales that varying the initial photon-to-baryon ratio in the background has a critical effect on all masses. Publication: The Astrophysical Journal Pub Date: December 1981 DOI: 10.1086/159480 Bibcode: 1981ApJ...251..429H Keywords: Background Radiation; Cosmology; Inhomogeneity; Relativity; Baryons; Black Body Radiation; Dust; Equations Of State; Photons; Astrophysics full text sources ADS |

Structure of a Turbulent Thermal Plume Rising along an Isothermal Wall

The weakly buoyant region of a turbulent thermal plume formed by a line heat source along the base of a vertical isothermal wall was investigated. The turbulence quantities: u′, v′, w′, t′, u′v′, u′t′, and v′t′ were measured, supplementing existing measurements of mean quantities in this flow. The plumes exhibited local similarity in terms of local plume thermal energy flux and height above the source. In the outer portions of the flow, the shear stress agreed with conventional mixing length models and the turbulent Prandtl number approached 0.5. Near the wall, however, turbulent stress and transport quantities do not approach zero when gradients in mean quantities are zero and eddy viscosity models do not properly represent the turbulence characteristics. Predictions of mean quantities were examined using a local similarity hypothesis and various eddy viscosity models. The theoretical results are in fair agreement with the measurements, in spite of the inaccurate representation of turbulence quantities near the wall. The theory indicates that local similarity for mean quantities is only approximately observed, and suggests the presence of systematic Grashof number effects that were not apparent in the measurements due to data scatter.

Turbulent wall fires

Turbulent natural convection fires at the base of a vertical wall were considered. The burning surface was simulated by 51–305 mm high wicks soaked with methanol, ethanol or 1-propanol. Measurements were made of burning rates in the pyrolysis zone; radiative and convective heat fluxes to the wall (and radiative heat flux to the ambiance) in the wall plume above the pyrolysis zone; and profiles of mean velocity, temperature and concentrations in all regions of the flow. The measurements are compared with solutions of the laminar boundary layer equations, solutions of the turbulent boundary layer equations employing a mixing length model, and integral models approximating the more complete theories. The theoreis provided a unified correlation of laminar and turbulent burning rate measurements from both the present and earlier studies. The correlation was relatively insensitive to the radiant heat flux from the flame to the burning surface, which varies in the range 0–86 percent of the total surface heat flux; this behavior is convenient, but has not been fully explained and deserves further attention. Laminar wall flames are 2–3 times longer than turbulent wall flames, when length is normalized by the length of the pyrolysis zone; theory provides good length predictions in both cases. The soot content of the flames was low for the present tests and radiation comprised only 10–20% of the heat flux to the surface; the flux of radiation to the ambiance was larger than the wall component. Predicted wall heat fluxes were within 20% of the measurements. Predictions in the noncombusting portion of the plume employed earlier results for weakly buoyant plumes using average physical properties at each wall position; profiles of mean velocity and temperature approximated local similarity, based on local plume energy flux and height along the wall; however, effects of combustion near the flame tip, variable property effects, and an additional Rayleigh number dependence were observed.

Fusion reactor first-wall cooling for very high energy fluxes

A study has been made of the feasibility of a protective first-wall shield between the plasma and the containment vessel for early experimental controlled thermonuclear fusion machines. The proposed first-wall shield is a water-cooled array of thin-walled tubes designed to take very high local energy fluxes originating from the neutral beam injectors. Detailed computer calculations reveal that heat flux capabilities of 3300 W/cm 2 are possible with first-wall shield sections made up of tubes 1 m long of Ta-10W alloy (with tubes of 10 mm i.d. and tube wall thickness of 0.5 mm) with a structural safety factor of about four. Required pumping powers on the order of 1 MW/m 2 of first-wall area exposed to these high energy fluxes are predicted for flow in the non-boiling regime. If operation in the subcooled nucleate boiling regime can be achieved without oscillations or instabilities, the required pumping power is shown to decrease by about an order of magnitude.

Second Sound in Superfluid Helium

The problem of the propagation of second sound in superfluid helium is studied. The second sound wave is assumed to be described by a set of variables, the local energy and local energy flux densities. Relaxation function expressions are obtained for the thermal con­ ductivity X which is analogous to the normal thermal conductivity /CT, as is distinct from the abnormal thermal· conductivity due to the counterflow of the super and normal components, and also for the kinetic coefficients (1) (3, (4. It is pointed out that, to the thermal conduc­ tivity. x, a restoring force due to temperature is essential. 1 ) first recognized that another wave motion, in which the density and pressure remain practically in local equilibrium values but in which entropy (or temperature) fluctuates, is also possible. This leads to an essential condition fol,' its existence; There must be a sufficient number of interactions between excitations, so that such a local equilibrium can be established within distances which are small compared with the wavelength of second sound. That is, an inequality (1)f<l must be satisfied, where (1) is the frequency of second sound, f a relaxation time of the system. The relaxation time is determined by a momentum-and-energy-conserving scatte~ing process. Landau 2 ) . showed that the unique properties of superfluid helium could be explained by describing the atomic motion in terms of elementa:ry excitations. These excitations are phonons and rotons. There are several scattering processes. These situationsm<ike it complex to discuss the propagation of sound in superfluid helium. Analysing these scattering processes, Khalatnikov and Chernikova 3 ) es­ tablished a unified derivation of expressions for the velocity of sound wave and the attenuation which is valid for both large and small values of (1)f. In their theory dynamical variables are the fluctuation of mass density, the deviation of temperature of the roton gas from an equilibrium value, the roton part of the mass current, and (1)r = jVnr - vsj, where Vnr - Vs is a relative velocity of the roton gas.

Energy-Flux Operator for a Lattice

A systematic derivation of the energy-flux operator for a three-dimensional lattice is given. The treatment is based on the general expressions for the energy flux which are valid for all phases of matter; a short derivation of these expressions, making no restrictions to two-body forces, is presented. The average energy flux is transformed to the phonon representation, and it is shown that the diagonal contribution from the harmonic forces has the familiar form $\ensuremath{\Sigma}{\mathrm{k}s}^{}{N}_{\mathrm{k}s}\ensuremath{\hbar}{\ensuremath{\omega}}_{\mathrm{k}s}{\mathrm{v}}_{\mathrm{k}s}$. There are, in addition, nondiagonal contributions to the energy flux, even in the harmonic approximation. The significance of these corrections is discussed. The contributions to the average flux from the anharmonic forces and from lattice imperfections are also treated. Finally, the problem of forming wave packets of the plane-wave normal modes to obtain an expression for the local energy flux is considered.