Form Of Balance Research Articles

Note on “Dynamics of inertia dominated binary drop collisions” [Phys. Fluids 16, 3438 (2004)

The analytical approach shown in the paper [I. V. Roisman, “Dynamics of inertia dominated binary drop collisions,” Phys. Fluids 16, 3438 (2004)] has been found not to yield physically consistent results, for which the theoretically predicted initial kinetic energy of the radially expanding lamella is negative. Such theoretical predictions do not allow the ensuing computation of the flow field. The code for the numerical predictions of the evolution of the drop diameter includes a computational bug with which only a quarter of the dissipated energy is accounted for. Three possible sources of the error are identified: the assumed velocity field in the lamella, the shape of the lamella at the initial phase of drop deformation, and the energy balance formulation of the problem. A possible way for the improvement of the modeling of the dynamics of the initial stage of drop collision is proposed.

A satellite-based Daily Actual Evapotranspiration estimation algorithm over South Florida

Water resources and agricultural applications require the knowledge of evapotranspiration ( ET) over a range of spatial and temporal scales. Due to paucity of surface based hydro-meteorological stations, the spatial resolution of ET estimates is fairly coarse and is not particularly suitable or reliable for hydrologic modeling, water resources planning and decision making. An ET estimation algorithm has been developed by combining data from satellite and ground observations. The method extends the applicability of a commonly used energy balance formulation of ET and utilizes the contextual relationship between remotely sensed surface temperature and vegetation index. The required parameters are derived from the Advanced Very High Resolution Radiometer (AVHRR) aboard NOAA-14 satellite. First, the Evaporative Fraction ( EF) is estimated by utilizing the relationship between a vegetation index and radiometric surface temperature observed from AVHRR for each day. Then spatio-temporal interpolation and filtering techniques are applied to obtain daily EF values for cloudy pixels to produce the EF map for the entire region. Daily Actual ET ( DAET) maps are derived from these EF maps and net radiation maps obtained from ground-based observations. The comparisons between satellite derived DAET and ground measurements showed overall low bias and root-mean-square-error for both clear and cloudy days at South Florida in 1998 and 1999. The proposed satellite-based DAET (SatDAET) algorithm has its EF component primarily estimated from satellite data and the resulting DAET has been validated using multi-year ground observations over the South Florida region. The SatDAET algorithm appears to be robust and has the potential to provide near real-time land surface evapotranspiration monitoring over large heterogeneous areas at a very fine spatial and temporal resolution.

A Frequency- and Space-Domain Series-Expansion Approach for Efficient Numerical Modeling of Semiconductor Devices

In this paper, an approach is described that combines frequency-domain Fourier series expansion and space-domain polynomial expansion of the physical quantities inside the semiconductor, for an efficient numerical modeling of high-frequency active devices, based on the solution of the physical transport equations in the semiconductor. The unknowns of the problem are the coefficients of the expansions of the physical quantities in the device channel: electrostatic potential and electron density, velocity, and energy. The frequency- and space-domain expansions drastically reduce the number of time and space sampling points where the equations are computed, greatly reducing the computational burden with respect to classical finite-difference approaches. Moreover, the frequency-domain technique eliminates the need for time-to-frequency transforms for a spectral solution and allows for the easy inclusion of frequency-dependent parameters of the semiconductor that are particularly important at very high frequencies (e.g., dielectric constant). In addition, the coupling with an EM program, for a global modeling simulator, becomes straightforward, due to the reduced interconnection nodes with the physical simulator. A demonstrator for PC implementing a quasi-2-D model with a hydrodynamic formulation with the first three moments of Boltzmann's transport equation is given, and its results are compared with a standard finite-difference time-domain approach and with a standard Harmonic Balance formulation.

Comments on a paradox of viscous dissipation and its relation to the Oberbeck–Boussinesq approach

Some reflections are made about the object of a recent debate on the role played by the viscous dissipation term in the local energy balance equation. The debate regards both clear fluids and fluid saturated porous media. A strong accent has been placed on the role played by the pressure work term in the local energy balance. In the present brief contribution, it is suggested that the focus on the pressure work is not the most convincing escape from the possible paradoxes of viscous dissipation. On the other hand, another focus is proposed, namely the most appropriate formulation of the energy balance in the framework of the Oberbeck–Boussinesq approach to the description of buoyant flows.

Strong Imbalanced Turbulence

We consider stationary, forced, imbalanced, or cross helical MHD Alfvenic turbulence where the waves traveling in one direction have higher amplitudes than the opposite waves. This paper is dedicated to so-called strong turbulence, which cannot be treated perturbatively. Our main result is that the anisotropy of the weak waves is stronger than the anisotropy of strong waves. We propose that critical balance, which was originally conceived as a causality argument, has to be amended by what we call a propagation argument. This revised formulation of critical balance is able to handle the imbalanced case and reduces to the old formulation in the balanced case. We also provide a phenomenological model of energy cascading and discuss the possibility of self-similar solutions in a realistic setup of driven turbulence.

Estimation of large‐scale evaporation fields based on assimilation of remotely sensed land temperature

Many Earth system science and environmental applications require knowledge of mapped evaporation. Satellite remote sensing can indirectly provide these measurements with a spatial coverage that is logistically and economically impossible to obtain through ground‐based observation networks. Here a model for surface energy fluxes estimation based on the assimilation of land surface temperature from satellite is presented. The data assimilation scheme provides a useful framework that allows us to combine measurements and models to produce an optimal and dynamically consistent estimate of the evolving state of the system. The assimilation scheme can take advantage of the synergy of multisensor‐multiplatform observations in order to obtain estimations of surface fluxes, flux partitioning, and surface characteristics. The model is based on the surface energy balance and bulk transfer formulation. A simplified soil wetness model, which is a filter of antecedent precipitation, is introduced in order to develop a more robust estimation scheme. This approach is implemented and tested over the Southern Great Plain field experiment domain. Comparisons with observed surface energy fluxes and soil moisture maps have shown that this assimilation system can estimate, when compared with the ground truth observations, the surface energy balance and its partitioning among turbulent heat fluxes. The introduction of the simplified soil wetness model forced by precipitation data improved evaporative fraction estimation. Further research is still required to analyze the reliability of retrieved fluxes in periods where radiation is the limiting factor for latent heat flux.

Re-evaluation of the Nusselt number for determining the interfacial heat and mass transfer coefficients in a flow-through monolithic catalytic converter

The two-equation porous medium model has been widely employed for modeling the flow-through monolithic catalytic converter. In this model, the interfacial heat and mass transfer coefficients have been usually obtained using the asymptotic Nusselt and Sherwood numbers with some suitable assumptions. However, previously it seemed that there existed some misunderstanding in adopting these Nusselt and Sherwood numbers. Up to now, the Nusselt number based on the fluid bulk mean temperature has been used for determining the interfacial heat and mass transfer coefficients. However, the mass and energy balance formulations in the two-equation model indicate that the Nusselt number should be evaluated based on the fluid mean temperature instead of the fluid bulk mean temperature. Therefore, in this study, to correctly model the heat and mass transfer coefficients, the Nusselt number based on the fluid mean temperature was newly obtained for the square and circular cross-sections under two different thermal boundary conditions (i.e., constant heat flux and constant temperature at the wall). In order to do that, the present study employed the numerical as well as analytical method.

Exergetic and thermoeconomic analyses of diesel engine powered cogeneration: Part 1 – Formulations

This paper is part 1 of the study on the energy, exergy, and exergoeconomic analysis of diesel engine powered cogeneration (DEPC). Part 1 presents the formulation developed for such a comprehensive analysis while part 2 is an application of the developed formulation that considers an actual cogeneration power plant. Compression ignition engine powered cogeneration application is among the most efficient simple cycle power generation plants where the efficiencies are around 50%. The DEPC is mostly preferred in regions where natural gas is not available or not preferable because of high unit prices. In this paper, a DEPC plant is considered with all associated components. Mass, energy, and exergy balances are applied to each system component and subsystem. Exergy balance formulations are aimed to yield exergy destructions. Various efficiencies based on both energy and exergy methods and the performance assessment parameters are defined for both the system components and the entire cogeneration plant. The formulations for the cost of products, and cost formation and allocation within the system are developed based on both energy and exergy (i.e., exergoeconomic analysis). The cost analyses formulated here have significant importance to obtain the optimum marketing price of the product of thermal systems to maximize the benefit and/or minimize the cost.

Sublethal toxic effects in a simple aquatic food chain

In this paper, we study the sublethal effect of toxicants on the functioning (biomass production, nutrient recycling) and structure (species composition and complexity) of a simple aquatic ecosystem in a well-mixed environment (chemostat reactor). The modelled ecosystem consists of a nutrient consumed by a prey ( e.g. bacteria, algae) which, in turn, is consumed by a predator ( e.g. ciliates, daphnia) population. The dynamic behaviour of this ecosystem is described by a set of ordinary differential equations (ODE)s: one for the nutrient and one for each population. The system is stressed by a toxicant dissolved in the in-flowing water. The transport of the toxicant is modeled using a mass balance formulation leading to an ODE. Bioaccumulation in the prey and predator populations is via uptake from the water, in case of the predator also via consumption of contaminated prey. Mathematically, this process is described by a one-compartment model for the kinetics of the toxicant: uptake (from water and food) and elimination. The toxicant affects individuals which make up populations. In the model the physiological parameters depend on the internal concentration of the toxicant in individuals. Examples of physiological parameters are cost for growth and maintenance, and assimilation efficiency. In this paper, we use bifurcation theory to analyse the long-term dynamics of the models. In this way, the parameter space is divided into regions with qualitatively different asymptotic dynamic behaviour of the system. As logical choice for bifurcation parameters are the input rate of the nutrient and toxicant. The dynamic behaviour of the stressed ecosystem can be much more complicated than that of the unstressed system. For instance, the nutrient–prey–toxicant system can show bi-stability and oscillatory dynamics. Due to the toxic effects a total collapse (both prey and predator population go extinct) of the nutrient–prey–predator–toxicant system can occur after invasion of a predator.

A Model for Estimating the Dynamic Contact Angle with Molecular Dynamics Simulation

The microscopic configuration of fluid interface near the wetting or dewetting front (i.e., moving contact line) is of significant interest in relation to many industrial processes. In this paper we report on molecular dynamics (MD) simulations conducted for investigation of the dependence of the microscopic contact angle θ on the speed of contact line relative to the solid surface, ΔV. Our simulations were made for a Couette flow geometry where two Lennard-Jones (LJ) liquids are sheared between two solid walls moving at a speed V in opposite directions. The two liquids are immiscible and have different wall-wetting properties. The liquid configuration remains unchanged with time, since ΔV=V at all the contact lines, for V below a certain critical value. The contact angle θ measured under such steady conditions varies monotonically with ΔV. Above the critical wall speed, however, the flow at the receding contact line, where the more wetting liquid of the two is being replaced by the less wetting one, starts becoming unsteady, as ΔV remains smaller than the critical wall speed. We show that the viscous and pressure forces measured from the MD simulation results can be reproduced by the Stokes flow model of Huh and Scriven (1971) using the MD-predicted value of θ at the given ΔV. It follows that, by the aid of Qian et al.'s formulation (2003) of the stress balance at the moving contact line, and by using the MD-predicted proportionality constant between the total wall-tangential force and ΔV, this model can reproduce the MD-predicted dependence of θ on ΔV. The model predictions, furthermore, give insight into the reason why the contact line flow becomes unsteady above the critical wall speed.

Scaling of capillary, gravity and viscous forces affecting flow morphology in unsaturated porous media

Interplay between capillary, gravity and viscous forces in unsaturated porous media gives rise to a range of complex flow phenomena affecting morphology, stability and dynamics of wetting and drainage fronts. Similar average phase contents may result in significantly different fluid distribution and patterns affecting macroscopic transport properties of the unsaturated medium. The formulation of general force balance within simplified pore spaces yields scaling relationships for motion of liquid elements in which gravitational force in excess of capillary pinning force scales linearly with viscous force. Displacement fluid front morphology is described using dimensionless force ratios expressed as Bond and Capillary numbers. The concise representations of a wide range of flow regimes with scaling relations, and predictive capabilities of front morphology based on dimensionless numbers lend support to certain generalizations. Considering available experimental data, we are able to define conditions for onset of unstable and intermittent flows leading to enhanced liquid and gas entrapment. These results provide a basis for delineation of a tentative value of Bo ∼ 0.05 as an upper limit of applicability of the Richards equation (at pore to sample scales) and related continuum-based flow models.

Phase and Amplitude Noise Analysis in Microwave Oscillators Using Nodal Harmonic Balance

In this paper, a nodal harmonic balance (HB) formulation is presented for the phase and amplitude noise analysis of free-running oscillators. The implications of using different constraints in the resolution of the perturbed-oscillator equations are studied. The obtained formulation allows the prediction of the possible spectrum resonances without ill conditioning at low frequency offset from the carrier. The noise spectrum is meaningfully expressed in terms of the eigenvalues of a newly defined matrix, obtained from the linearization of the nodal HB system about the steady-state solution. The cases of real or complex-conjugate dominant eigenvalues are distinguished. The developed phase-noise formulation is extended to a system of two coupled oscillators. The phase and amplitude noise analyses have been applied to a push-push oscillator at 18 GHz, a bipolar oscillator at 1 GHz, and a coupled system of two field-effect transistor oscillators at 6 GHz.

A novel harmonic balance analysis for the Van Der Pol oscillator

This study focuses on a novel harmonic balance formulation, the high-dimensional harmonic balance method. To investigate a non-linearity in the damping term, the system chosen for study is the Van der Pol's oscillator. Both unforced and forced oscillators are analyzed. The results from the analysis are compared with those obtained from the classical harmonic balance and the time marching (Runge–Kutta) methods.

Simulation of true moving bed adsorptive reactor: Detailed particle model and linear driving force approximations

A new true moving bed (TMB) adsorptive reactor model with a detailed particle approach is presented introducing the formulation of the mass balance for the solid phase in counter-current moving systems. The system studied here is the enzymatic inversion of sucrose into fructose and glucose and subsequent separation of glucose/fructose; the reaction occurs both in the outer fluid phase and inside particles. Model equations include film mass transfer, intra-particle diffusion resistance, axial dispersion for the outer fluid phase, plug flow of the solid phase and linear adsorption equilibrium of glucose/fructose. This new model is compared with previous LDF-type approximations for reactive systems and applied to pure separative TMB process. The numerical solution of model equations is obtained for transient and steady state with commercial and public domain packages (gPROMS and COLNEW). The influence of the particle size and reaction rate constant is analyzed in the ( γ 2 × γ 3 ) reactive/separation region.

Evaporation and Precipitation Surface Effects in Local Mass Continuity Laws of Moist Air

Abstract The local mass balance equations of cloudy air are formulated for a model system composed of dry air, water vapor, and four categories of water condensate particles, as typically adopted for numerical weather prediction and climate models. The choice of the barycentric velocity as reference motion provides the most convenient form of the total mass continuity equation. Mass transfer across the earth’s surface due to precipitation and evaporation causes a nonvanishing barycentric vertical velocity ws and is proportional to the local difference between evaporation rate and rain plus snow rate. Hence ws vanishes only in the special situation that evaporation and precipitation balance exactly. Alternative concepts related to different reference motions are reviewed. However, the choice of the barycentric velocity turns out to be advantageous for several reasons. The implication of the nonvanishing total mass transport across the earth’s surface is estimated from model simulations for two extreme weather situations: a polar cold air outbreak and a tropical cyclone. While the effect is small in the first case, it is important in the latter. The large precipitation rates in the tropical cyclone case cause a loss of atmospheric mass, which corresponds to a vertical velocity at the surface larger than −20 mm s−1, and an instantaneous drop in pressure, which if sustained for 6 h, would correspond to about 49 hPa; this demonstrates the necessity of using the correct formulation of the mass balance in simulation models for moist air.

A study of the collisional fragmentation problem using the Gamma distribution approximation

The nonlinear fragmentation population balance formulation has been elevated in recent years from a prototype for studying nonlinear integro-differential equations to a vehicle for analyzing and understanding several physicochemical processes of technological interest. The so-called pure collisional fragmentation, which is the particular mode of nonlinear fragmentation induced by collisions between particles, is studied here. It is shown that the corresponding population balance equation admits large time asymptotic (self-similarity) solutions for homogeneous fragmentation and collision functions (kernels). The self-similar solutions are given in closed form for some simple kernels. Based on the shape of the self-similar solutions the method of moments with Gamma distribution approximation is employed for transient solution (from initial state to establishment of the asymptotic shape) of the collisional fragmentation equation. These solutions are presented for several sets of parameters and their behavior is discussed rather extensively. The present study is similar to the one has already been performed for the case of the much simpler linear fragmentation equation [G. Madras, B.J. McCoy, AIChE J. 44 (1998) 647].

Subharmonic resonances of a mechanical oscillator with periodically time-varying, piecewise-nonlinear stiffness

The subharmonic (period- η, η>1) motions of a piecewise-nonlinear (PN) mechanical oscillator having parametric and external excitations are investigated. The system is formed by a viscously damped, single-degree-of-freedom oscillator subjected to a periodically time-varying, PN stiffness defined by a clearance surrounded by continuous forms of nonlinearity. A multiterm harmonic balance formulation in conjunction with discrete Fourier transforms is used to determine steady-state period- η motions of the system near the parametric instability regions. The accuracy of analytical solutions is verified through a comparison with direct numerical integration results. A parametric study is also presented to demonstrate the combined influence of a clearance and of cubic nonlinearities on period- η motions within typical ranges of system and excitation parameters.

The Relationship between Intermodel Differences and Surface Energy Balance Complexity in the Rhône-Aggregation Intercomparison Project

Abstract Six modes of complexity of the Chameleon land surface model (CHASM) are used to explore the relationship between the complexity of the surface energy balance (SEB) formulation and the capacity of the model to explain intermodel variations in results from the Rhône-Aggregation Intercomparison Project (Rhône-AGG). At an annual time scale, differences between models identified in the Rhône-AGG experiments in the partitioning of available energy and water at the spatial scale of the Rhône Basin can be reproduced by CHASM via variations in the SEB complexity. Only two changes in the SEB complexity in the model generate statistically significant differences in the mean latent heat flux. These are the addition of a constant surface resistance to the simplest mode of CHASM and the addition of tiling and temporally and spatially variable surface resistance to produce the most complex model. Further, the only statistically significant differences in runoff occur following the addition of a constant surface resistance to the simplest mode of CHASM. As the time scale is reduced from annual to monthly, specific mechanisms begin to dominate the simulations produced by each Rhône-AGG model and introduce parameterization-specific behavior that depends on the time evolution of processes operating on longer time scales. CHASM cannot capture all this behavior by varying the SEB complexity, demonstrating the contribution to intermodel differences by hydrology and snow-related processes. Despite the increasing role of hydrology and snow in simulating processes at finer time scales, provided the constant surface resistance is included, CHASM's modes perform within the range of uncertainty illustrated by other Rhône-AGG models on seasonal and annual time scales.

Ice-sheet modelling characteristics in sea-level-based temperature reconstructions over the last glacial cycle

AbstractA widely used method for investigating palaeotemperatures is to analyze local proxy records (e.g. ice cores or deep-sea sediment cores). The interpretation of these records is often not straightforward, and global or hemispheric means cannot be deduced from local estimates because of large spatial variability. Using a different approach, temperature changes over the last glacial cycle can be estimated from sea-level observations by applying an inverse method to an ice-sheet model. In order to understand the underlying physical mechanisms, we used a 1-D ice-sheet model and a 3-D coupled thermodynamic ice-sheet–ice-shelf–bedrock model to investigate the importance of several physical processes for the inverse temperature reconstructions. Results show that (i) temperature reconstructions are sensitive to the employed formulation of mass balance, (ii) excluding thermodynamics in the ice sheet leads to a smaller temperature amplitude in the reconstruction and (iii) hysteresis in the non-linear relation between sea level and temperature occurs as a consequence of ice redistribution in the process of merging and separation of ice sheets. The ice redistribution does not occur if the geometry does not support the formation of a relatively flat dome, which tends to be preserved in warming conditions.

A comparison of classical and high dimensional harmonic balance approaches for a Duffing oscillator

The present study focuses on a novel harmonic balance formulation, which is much easier to implement than the standard/classical harmonic balance method for complex nonlinear mathematical models and algorithms. Both harmonic balance approaches are applied to Duffing’s oscillator to demonstrate the advantages and disadvantages of the two approaches. A fundamental understanding of the difference between these two methods is achieved, and the properties of each method are analyzed in detail.