Total Energy Dissipation Rate Research Articles

Energy analysis of substorms based on remote sensing techniques, solar wind measurements, and geomagnetic indices

Observations from the Polar Ionospheric X‐ray Imaging Experiment (PIXIE) and the Ultraviolet Imager (UVI) on board the Polar satellite have been used to examine the energy deposition in the Northern Hemisphere by precipitating electrons for seven substorms during 1997. By combining the results from these two remote sensing techniques we derive the 5 min average electron energy distributions from 100 eV to 100 keV with a spatial resolution of ∼700 km. During growth phase we find that most of the energy is carried by electrons below 10 keV. The study shows that the maximum intensity of the substorm is mostly defined by the flux of electrons below 10 keV. In contrast, the electrons above 10 keV show a greater intensification at substorm onset and are more confined azimuthally during the expansion phase. By using the most appropriate parameterized methods to estimate the energy increase of the ring current (UR) and the Joule heating rate in both hemispheres (UJ) and by adding the rate of energy deposition in both hemispheres by precipitating electrons (UA), we estimate the total energy dissipation rate during substorms (UT). Our estimate of UA is a factor 2–4 larger than that reported in earlier studies. We find that the contributions to the total time‐integrated energy dissipation over the duration of the substorm, W(UT), from W(UR), W(UJ), and W(UA) on average are 15%, 56%, and 29%. Comparing W(UT) and the time‐integrated ϵ parameter, W(ϵ), which approximates the solar wind input due to dayside reconnection, we find that the ϵ parameter does not always provide enough energy into the magnetosphere to balance W(UT). An additional energy transfer mechanism is needed to balance the energy budget. We find that a viscous interaction that transfers 0.17% of the solar wind kinetic energy in addition to the energy transfer due to dayside reconnection, estimated by the ϵ parameter, is sufficient to balance the total energy dissipation UT.

Single phase flow modeling in packed beds: discrete cell approach revisited

A discrete cell model (DCM), based on the minimization of the total rate of energy dissipation, is applied to compute the fluid velocity field in two-dimensional packed beds. The analysis of the individual terms of the energy dissipation rate equation is also presented. The results obtained by DCM are validated both by comparing them with the solutions of ensemble-averaged momentum and mass conservation equations (CFDLIB code) and by available experimental results. The differences between DCM and CFD simulations were found to be confined to within a 10% band over a wide range of Reynolds numbers ( Re′=5–171). Thus, a reasonable agreement between the predictions of the two methods can be claimed for engineering applications. An acceptable agreement of DCM/CFD predictions and the available experimental data in the literature is also achieved. The presented case studies justify the use of DCM for predicting the fluid velocity fields in packed beds with complex internal structures and with irregular distributed gas feeding points.

Wind Sea Growth and Dissipation in the Open Ocean

Abstract Wind sea growth and dissipation in a swell-dominated, open ocean environment is investigated to explore the use of wave parameters in air–sea process modeling. Wind, wave, and whitecap observations are used from the Gulf of Alaska surface scatter and air–sea interaction experiment (Critical Sea Test-7, Phase 2), conducted 24 February through 1 March 1992. Wind sea components are extracted from buoy directional wave spectra using an inverted catchment area approach for peak isolation with both wave age criteria and an equilibrium range threshold used to classify the wind sea spectral domain. Dimensionless wind sea energy is found to scale with inverse wave age independently of swell. However, wind trend causes significant variations, such as underdeveloped seas during rising winds. These important effects are neglected in wind-forced air–sea process models. The total rate of wave energy dissipation is conveniently estimated using concepts from the Phillips equilibrium range theory. Replacing wind ...

Shear-induced particle migration in a polydisperse concentrated suspension

The shear-induced particle migration in a polydisperse concentrated suspension is described using migration potentials for the various particle size fractions. The model is applied to solve the flow patterns and the particle concentration distributions in bidisperse suspensions in various viscometric flows. For the case of a continuous particle size distribution a formulation of this model in terms of concentration distribution moments is presented. The model predicts the total migration of the particles in the various flow devices and the size segregation of the various fractions. The calculations capture well the few experimental observations reported so far. It is found that in all calculated cases the total energy dissipation rate and, therefore, the power required to drive the flow were diminished considerably at steady state.

Influence of a propeller on Saccharomyces cerevisiae fermentations in a pilot scale airlift bioreactor

The hydrodynamics (sectional gas holdup and liquid velocities) and oxygen transfer performance of a conventionally operated multiconfigurable pilot scale (0.25 m3) concentric airlift bioreactor containing baker's yeast were significantly improved by operating a marine propeller to draw liquid down the draft tube and aid recirculation at the base of the vessel. Propeller operation reduced the severe DOT heterogeneity of the reactor, which gave DOT values below 1% air saturation in the riser, by producing DOTs above 40% around the vessel at maximum energy dissipation rate. As a consequence the overall oxygen uptake rate (OUR) of the baker's yeast increased up to 3 fold with the total energy dissipation rate into the reactor until the lowest DOTs of the vessel were at or above 10%. The different degrees of heterogeneity generated by the two reactor configurations enabled the reactor to be used as a scale down tool to study the impact of heterogeneity on the physiology of fermentation broths. Comparison of the hydrodynamics and oxygen transfer between tall and short reactor heights revealed that the faster circulation times of the short reactor produced a greater improvement in the OUR with propeller operation even though similar DOT changes occurred around both sizes of reactor. This indicated that the yeast cells were responding to the rapid DOT changes around the vessel.

Simulation of Coating Layer Evolution and Drop Formation on Horizontal Cylinders

The lubrication form of the equations governing the flow of a thin liquid film on a horizontal right circular cylinder is derived. The equations are discretized and solved numerically using an alternating-direction implicit algorithm. Simulations demonstrate that the transition from a uniform coating to a final configuration of distinct drops follows a similar evolution for a wide range of cylinder radii. Initially gravity-driven drainage from the top and sides of the cylinder dampens the formation of any axial disturbances; only when this drainage slows do longitudinal waves begin to develop along the bottom of the cylinder. These waves grow rapidly and a series of alternating primary and satellite drops form during the transition from a linear to a nonlinear wave growth regime. This is followed by a slow drainage between adjacent drops as the drop pattern approaches an equilibrium state where surface tension forces exactly balance gravitational forces in each discrete drop. For large cylinder radii, these drops are localized on the bottom of the cylinder, while, for sufficiently small cylinder radii, these drops may wrap around the entire circumference of the cylinder. Integral measures of the evolving coating profile, such as the total energy and viscous dissipation rate, clearly show these growth phases. The equilibrium shape of large-amplitude pendant drops and the maximum sustainable drop volume for various cylinders are also considered.

Surface wave parameters for the prediction of breaking waves and acoustic backscatter

Results from the acoustic surface reverberation experiment (ASREX) and critical sea test 7 (CST-7 phase 2) are examined to determine if surface wave parameters can be used to augment wind speed in air–sea process models. The wave parameters are extracted from directional wave spectra using a fully automated spectral partitioning approach. Isolated directional wind–sea spectra provide the basis for estimating the total rate of energy dissipation by breaking waves. The method employs Phillips’ equilibrium range theory and extends Felizardo and Melville’s recent work obtaining wave dissipation estimates from one-dimensional wave spectra. Preliminary results are encouraging; wave dissipation reduces the scatter in whitecap fraction observations by several orders of magnitude when wind speed is replaced with wave dissipation as the independent variable in the standard power-law model for whitecap fraction. It will be demonstrated that the success of this approach is partially attributed to a wind history bias that is automatically compensated for in the wave parameters. Results of similar on-going investigations using an extensive ambient noise and surface scatter observation set, collected during ASREX by the University of Miami, will also be discussed. [Work supported by ONR Code 32OA.]

Effect of unstable density gradients on back‐mixing in a reciprocating plate column

AbstractAxial dispersion coefficients were measured in the continuous phase in a 5‐cm‐dia. Karr column, operated cocurrently with the system kerosene(d)‐water(c). The effect of unstable density gradient in the continuous phase was studied by injecting a steady stream of sodium chloride solution as a tracer near the top of the column. The effects of energy dissipation due to unstable density gradient, mechanical agitation, and the flow of the dispersed phase were investigated as the three principal variables, and two plate spacings (2.55 and 5.10 cm) were also employed. The axial dispersion results were correlated in terms of a weighted power‐law model based on Kolmogoroff's mixing length concept and incorporating contributions due to each of the three modes of energy dissipation. Axial mixing was significantly increased in the presence of unstable density gradients even though these contributed very little (typically less than 1 mW/kg) to the total specific energy dissipation rate.

Energy deposition due to the dissipation of dust-acoustic waves

We calculate the total energy dissipation rate of a dust-acoustic wave on a uniform background medium, in which the dust is not a dominant charge carrier, as a function of the dust-acoustic wavelength and dust parameters and give results for the deposition rates in each of the dust, ion and electron fluids.

Double-core evolution. 5: Three-dimensional effects in the merger of a red giant with a dwarf companion

The evolution of the common envelope phase of a binary system consisting of a 4.67 solar mass red giant and a 0.94 solar mass dwarf is studied using smoothed particle hydrodynamics. We demonstrate that the three-dimensional effects associated with the gravitational tidal torques lead to a rapid decay of the orbit on timescales approximately less than 1 yr. The relative orbit of the two cores in the common envelope is initally eccentric and tends to circularize as the orbital separation of the two cores decreases. The angular momentum lost from the orbital motion is distributed throughout the common envelope, and the double core does not evolve to a state of co-rotation for the evolutionary time followed. The energy dissipated from the relative orbit and deposited in the common envelope results in the ejection of approximately 13% of the mass of the envelope. The mass is ejected in all directions, but there is a preference for mass ejection in the orbital plane of the binary system. For example, approximately 80% of the ejected mass lies within 30 deg of the binary orbital plane. Because gravitational forces are long range, most of the energy and angular momentum is imparted to a small fraction of the common envelope resulting in an efficiency of the mass ejection process of approximately 15%. The core of the red giant executes significant displacement with respect to the center of mass of the system and contributes nearly equally to the total energy dissipation rate during the latter phases of the evolution. The degree of departure from synchronism of the initial binary system can be an important property of the system which can affect the outcome of the common envelope phase.

Energy Loss by Breaking waves

Observations of the frequency of wind wave breaking in deep water are combined with laboratory estimates of the rate of energy loss a from single breaking wave to infer the net rate of energy transfer to the mixed layer from breaking waves, as a function of wind speed. Breaking waves with wavelengths much shorter than the dominant waves can contribute energy at a rate that is a significant fraction of the total turbulent kinetic energy dissipation rate in the ocean surface mixed layer.

Bulging and folding-over in plane-strain upset forging

In many industrial metal-forming processes, bulging of free workpiece surfaces occures. At the same time these surfaces may fold over and come into contact with the dies. These kind of phenomena are often neglected in metal-forming analyses. The present work deals with the problem of bulging and folding over in plane-strain upset forging. It is a basic work which is meant for a deeper understanding of the problem, and for future utilisation in more complicated simulations such as that of filling of die cavities in the closed-die forging of long components. A computer program has been developed by means of which it is possible to study the influence of workpiece geometry and friction. The analysis is carried out with the upper-bound method for a rigid-perfectly plastic material. A flexible velocity field is utilised and a rigid region of variable shape is supposed to be in contact with the dies. By minimizing the total rate of energy dissipation the best velocity field is obtained. The shape and extension of the dead region is found to be influenced heavily by friction. Theoretically and experimentally obtained fold-overs, free surface shapes and grid network distortions are in satisfactory agreement.

Evaluation of the drag force by integrating the energy dissipation rate in stokes flow for 2D domains using the FEM

AbstractThe total drag force on the surface of a body, which is the sum of the form drag and the skin friction drag in a 2D domain, is numerically evaluated by integrating the energy dissipation rate in the whole domain for an incompressible Stokes fluid. The finite element method is used to calculate both the energy dissipation rate in the whole domain as well as the drag on the boundary of the body. The evaluation of the drag and the energy dissipation rate are post‐processing operations which are carried out after the velocity field and the pressure field for the flow over a particular profile have been obtained. The results obtained for the flow over three different but constant area profiles—a circle, an ellipse and a cross‐section of a prolate spheroid—with uniform inlet velocity are presented and it is shown that the total drag force times the velocity is equal to the total energy dissipation rate in the entire finite flow domain. Hence, by calculating the energy dissipation rate in the domain with unit velocity specified at the far‐field boundary enclosing the domain, the drag force on the boundary of the body can be obtained.

Rheological Properties of Sericite Suspensions

Shear stress of sericite suspensions was measured against shear rate in the range of 16 to 650s-1 using a rotational viscometer. Mineral compositions of two kinds of clay particles (AT-S, AT-K), which were obtained by elutriation from two different kinds of powdered Amakusa pottery stones, were mainly sericite and a few amount of kaolin mineral and quartz. Rheological properties of these sericite suspensions were approximated as Bingham body and analysed using DLVO theory of coagulation and dispersion. The results were summarized as follows;(1) Bingham yield stress (BYS) values obtained from the relation between shear stress and shear rate became higher with increasing the volume fractions of AT-S and AT-K suspensions from 1.8% to 6.9%. BYS values of two suspensions were nearly zero at pH 7, increased from pH 6 to pH 5, and decreased at pH 4.(2) Total potential energy of interaction between two flat clay particles and Bingham yield stress (BYS) of clay suspensions were calculated using the estimated edge and face potentials of sericite on the basis of DLVO theory and the equation of total energy dissipation rate. The calculated results showed that BYS values of both sericite suspensions became zero at pH 7, then had finite values at pH 6 and pH 4, and had a maximum at pH 5 because these calculated values were brought about from the different association modes such as face to edge and edge to edge. These changes of calculated BYS values with pH explained well those of measured ones. It was also made clear that the thickness of sericite gave a great effect on BYS values.

Helical, dissipative, magnetohydrodynamic states with flow.

It is shown that for an axially periodic column of magnetofluid driven by an applied axial electric field, the total rate of energy dissipation (Ohmic plus viscous) can be lowered by permitting a helical component with vortical flow in the solution. The principle of minimum energy-dissipation rate suggests that this partially helical state will be preferred to the axisymmetric one that exists for the same parameters. The result is consistent with the repeated appearance of such partially-helical states in several fully three-dimensional numerical computations and is not inconsistent with the data from some confinement experiments.

Energy Dissipation and Upwelling in a Western Boundary Current

Abstract Energy dissipation in a western boundary current begins with the conversion of mean potential energy into kinetic energy of “primary” eddies. The rate of this energy conversion is taken to equal the total energy dissipation rate, in analogy with the energy cascade of laboratory turbulence. The growth of primary eddies is due to baroclinic instability, and implies the rising of relatively light fluid, sinking of heavy fluid. An inviscid, nondiffusive model adequately describes this process and yields a quantitative relationship between the dissipation rate and upward-downward motions. In statistically steady flow, an eddy mass transport arises from the correlation of cross-stream velocity and isentropic layer thickness which is proportional to the energy dissipation rate. In this manner, the rate of upwelling of upper thermocline fluid and/or the downwelling of heavier fluid comes to determine the energy dissipation rate. Conversely, a given energy dissipation rate implies upwelling or downwelling...

Three-Dimensional Analysis of Closed-Die Forging Processes: Part 1: Formulation

In this series of papers, a theoretical model based on the upper bound elemental technique is presented for prediction of forging load and metal flow in three-dimensional closed-die forging processes. Three basic elements are introduced in order to partition a forging into simple elementary regions. An optimum velocity distribution within the forging is obtained by minimizing the total rate of energy dissipation using a simplex optimizing procedure. Applications of the proposed model are discussed in Part 2.

Energy dissipation associated with crack extension in an elastic-plastic material

Crack extension in elastic-plastic material involves energy dissipation through the creation of new crack surfaces and additional yielding around the crack front. An analytical procedure, using a two-dimensional elastic-plastic finite element method, was developed to calculate the energy dissipation components during a quasi-static crack extension. The Fracture of an isotropic compact specimen was numerically simulated using the critical crack-tip-opening-displacement (CTOD) growth criterion. Two specimen sizes were analyzed for three values of critical CTOD. Results from the analysis showed that the total energy dissipation rate consisted of three components: (1) the crack separation energy rate G s , (2) the plastic energy dissipation rate G p and (3) the residual strain energy rate G rs . All three energy dissipation components and the total energy dissipation rate initially increased with crack extension and finally reached constant values. For ductile materials (larger CTOD), G p becomes dominant (more than 70% of the total), whereas G rs remained constant (about 6%). Furthermore. G p appeared to vary linearly with the plastic zone height. G s is linearly proportional to the critical CTOD.

Electrical changes of the polar ionosphere during magnetospheric substorms

Changes of the distribution of the potential, electric fields, ionospheric currents, field‐aligned currents, the Joule heat production rate, the particle energy injection rate and the total energy dissipation rate are examined in detail by comparing them at a presubstorm epoch and the maximum epoch for several substorms on March 17, 18, and 19, 1978. The data sets are obtained on the basis of the magnetic records from the six International Magnetospheric Study meridian chains of observatories by using the computer code developed by Kamide et al. (1981) and the conductivity model developed by Ahn et al. (1983b). A number of global features that are found to be common to most of the substorms examined in this study include the following: (1) The positive potential cell in the morning sector extends into the evening sector during substorms. (2) When it is intensified, the westward electrojet on the nightside tends to flow equatorward of the positive potential ridge. (3) The so‐called “Harang discontinuity” may be identified as the ridge of the negative potential cell. (4) The distribution of field‐aligned currents determined by our method is more complicated than the statistical pattern obtained by polar orbiting satellites. (5) The basic ionospheric current pattern is fundamentally the same during a fairly quiet period, a slightly disturbed period and a substorm period. (6) The highest Joule heat production occurs along the westward extension of the westward electrojet, while the particle energy injection rate is high along the westward electrojet in the morning sector.

An Analytical Study of Deformation Behavior of Porous Metals in Uniaxial Tension and Compression

On the basis of an upper-bound approach, deformation behavior of porous metals is considered. A model for porous metals is employed to describe a kinematically admissible velocity field for uniaxial deformation. By minimizing the total energy dissipation rate obtained from the velocity field, the yield strength, deformation behavior of porous metals, and also distortion of pores are evaluated. In the analysis, porosity, geometry of pores, and environmental hydrostatic pressure are taken into consideration. Calculated results are compared with experimental and/or other theoretical ones and show good agreement.