Flux Balance Equation Research Articles

Topography optimisation using a reduced-dimensional model for transient conjugate heat transfer between fluid channels and solid plates with volumetric heat source

Consideration of transient effects is important for industrial applications of heat transfer structure optimisation studies; however, the huge computational cost associated with transient problems is a pressing concern. This paper proposes an extension of a previous reduced-dimensional model to transient conjugate heat transfer between a fluid flow and solid-heated plates in a plate heat exchanger. The extended reduced-dimensional model introduces the temperature field of the plate governed by the heat conduction equation, which is coupled to the temperature field of the fluid, governed by the convection-diffusion equation, through the heat flux balance equation at the contact surface. The model is based on assumptions of fully developed flow and constant temperature profile, reducing the three-dimensional problem to a planar problem and significantly reducing computational costs. The accuracy of the model for the simulation of transient heat transfer is verified by comparison with a three-dimensional model. In this paper, the topography of the heat exchanger plate is optimised for both steady-state and transient conditions by applying the reduced-dimensional model. The effectiveness of the optimised design was demonstrated by the cross-check of both the reduced-dimensional and full three-dimensional models. Furthermore, this work considers the effect of time-independent boundary conditions and time-dependent boundary conditions on transient optimisation. The transient and steady-state optimised designs are analysed and compared for both conditions, and the necessity of transient optimisation is discussed.

Flat from anti de Sitter

Ricci-flat solutions to Einstein’s equations in four dimensions are obtained as the flat limit of Einstein spacetimes with negative cosmological constant. In the limiting process, the anti-de Sitter energy-momentum tensor is expanded in Laurent series in powers of the cosmological constant, endowing the system with the infinite number of boundary data, characteristic of an asymptotically flat solution space. The governing flat Einstein dynamics is recovered as the limit of the original energy-momentum conservation law and from the additional requirement of the line-element finiteness, providing at each order the necessary set of flux-balance equations for the boundary data. This analysis is conducted using a covariant version of the Newman-Unti gauge designed for taking advantage of the boundary Carrollian structure emerging at vanishing cosmological constant and its Carrollian attributes such as the Cotton tensor.

A new model for quantifying wave damping by vegetation in combined wave–current flow

The propagation of waves in nearshore areas is often accompanied by the presence of tidal currents, which have an impact on the dissipation of wave energy in coastal vegetation regions. However, the existing models generally do not consider the in-canopy velocity, resulting incomplete energy dissipation terms and thus inaccurate estimation of drag coefficients. In this study, we developed a new analytical model to incorporate vertical velocity distribution and full energy dissipation terms in energy flux balance equation. This model is applied to interpret the data from a new flume experiment of vegetation in combined wave-current flows. New CD-Re relationships were derived by applying the new model. Additionally, we extracted the wave energy passage time and decay rate from both the experimental data and the model results, which shows that the wave energy passage time of opposing currents is up to 75% longer than that of following currents. This disparity in passage time is the primary factor contributing to the greater wave dissipation observed in the cases of opposing currents. This study offers novel insights into the process of wave dissipation, and can potentially improve our capability in predicting wave dissipation.

The asymptotic tails of limit distributions of continuous-time Markov chains

AbstractThis paper investigates tail asymptotics of stationary distributions and quasi-stationary distributions (QSDs) of continuous-time Markov chains on subsets of the non-negative integers. Based on the so-called flux-balance equation, we establish identities for stationary measures and QSDs, which we use to derive tail asymptotics. In particular, for continuous-time Markov chains with asymptotic power law transition rates, tail asymptotics for stationary distributions and QSDs are classified into three types using three easily computable parameters: (i) super-exponential distributions, (ii) exponential-tailed distributions, and (iii) sub-exponential distributions. Our approach to establish tail asymptotics of stationary distributions is different from the classical semimartingale approach, and we do not impose ergodicity or moment bound conditions. In particular, the results also hold for explosive Markov chains, for which multiple stationary distributions may exist. Furthermore, our results on tail asymptotics of QSDs seem new. We apply our results to biochemical reaction networks, a general single-cell stochastic gene expression model, an extended class of branching processes, and stochastic population processes with bursty reproduction, none of which are birth–death processes. Our approach, together with the identities, easily extends to discrete-time Markov chains.

A new scheme for simulating diffusion-controlled growth in multi-component alloys

Simulation of diffusion-controlled phase growth has long been practiced by strictly following Fick-Onsager-Darken law for diffusion under the assumptions of local equilibrium and sharp interface. However, a major pain point is the difficulty of finding operating tie-lines at the interface for multi-component alloys. In the present work, a new scheme is presented to deal with this difficulty by extending from Larsson and Reed scheme (Larsson and Reed, Acta Mater. 56 (2008) 3754–3760). The flux balance equations are rewritten to enhance the accuracy and fulfilled from the very beginning of simulations. The simulation results of the Fe-Mn-Mo and Fe-C-Mn ternary systems, as well as high-order systems, demonstrate the applicability and robustness of the new scheme. The simulation of the Fe-C-Mn system reveals the details of the early stages of the bcc phase growth, showing a shrink of bcc before its growth with two growth modes smoothly switched.

Synthesis of PWM Converters From Conversion Ratios Using Flux- or Charge-Balance Equations

To cater to the heterogeneity in emerging applications, researchers have constantly been driven to invent novel dc–dc converter topologies. A review of prior art in dc–dc converter synthesis methods shows that many converter choices are available for a given input and output specification. This article quantifies the number of these choices using the flux balance equation (FBE). As the number of state variables that can be used to derive the FBE is limited, it is possible to find out the total number of possible FBEs available for a given voltage conversion ratio. Once the FBEs are known, synthesizing a converter is carried out as an inverse problem. Three different strategies to solve this inverse problem of converter synthesis and some critical synthesis results are summarized in this article. The dual synthesis of current-fed topologies with given current conversion ratios based on the charge balance equation (CBE) is also demonstrated. Four novel topologies were synthesized to illustrate the effectiveness of the CBE-based synthesis method. The mathematical formulation of the CBE-based inverse problem and the quantification of complexities in solving it are also reported.

On symplectic form for null boundary phase space

To formulate gravity in spacetimes bounded by a null boundary, an arbitrary hypothetical null surface, boundary degrees of freedom (d.o.f) should be added to account for the d.o.f and dynamics in the spacetime regions excised behind the null boundary. In the D dimensional example, boundary d.o.f are labelled by D charges defined at D-2 dimensional spacelike slices at the null boundary. While boundary modes can have their own boundary dynamics, their interaction with the bulk modes is governed by flux-balance equations which may be interpreted as a diffusion equation describing "dissolution" of bulk gravitons into the boundary. From boundary viewpoint, boundary d.o.f obey local thermodynamical equations at the boundary. Our description suggests a new "semiclassical" quantization of the system in which boundary d.o.f are quantized while bulk is classical. This semiclassical treatment may be relevant to questions in black hole physics.

Synthesis of DC–DC Converters From Voltage Conversion Ratio and Prescribed Requirements

This article proposes a systematic synthesis method to identify the optimum converter topology for a specified voltage conversion ratio. This gain-oriented converter synthesis is formulated as an inverse problem around the inductor flux balance equations. The proposed synthesis method consists of two processes. A set of distinct converter topologies is first synthesized from the specified voltage conversion ratio by obtaining the solutions for a set of six inverse equations in twelve unknowns. The optimal topology for any intended application can be identified based on the desired performance metrics. The complete synthesis method is illustrated with quadratic buck-boost gain as an example. In total, 25 distinct topologies are synthesized using the first process, and their feasibility is validated by PLECS simulation. In total, three case studies are reported to explain the second process. Ground-referenced output and the minimum number of switches are used as the first two selection criteria in all the case studies. Minimum peak inductor current, minimum component stress factor, and minimum voltage and current stress are the third selection criterion in Case Studies-1, 2, and 3, respectively. The steady-state operations of two optimal converters selected in Case Study-1 were verified experimentally.

Gravitational radiation from inspiralling compact objects: Spin-spin effects completed at the next-to-leading post-Newtonian order

Using the gravitational potential and source multipole moments bilinear in the spins, first computed to next-to-leading order (NLO) in the post-Newtonian (PN) expansion within the effective field theory (EFT) framework, we complete here the derivation of the dynamical invariants and flux-balance equations, including energy and angular momentum. We use these results to calculate spin-spin effects in the orbital frequency and accumulated phase to NLO for circular orbits. We also derive the linear momentum and center-of-mass fluxes and associated kick-velocity, to the highest relevant PN order. We explicitly demonstrate the equivalence between the quadratic-in-spin source multipoles obtained using the EFT formalism and those rederived later with more traditional tools, leading to perfect agreement for spin-spin radiative observables to NLO among both approaches.

A control volume method based interface movement equation for one-dimensional Stefan problem achieving mass conservation

For heat-transfer-controlled or diffusion-controlled phase transformation simulations, the movement of the interface between different phases needs to be determined, which is commonly called the Stefan problem. Various numerical methods have been developed for this and the movement of the interface is conventionally calculated by a flux balance equation, which is usually called the Stefan condition equation. However, mass conservation errors have been reported in the literature for some of the numerical methods. In this research, a control volume method based interface movement equation was proposed to achieve mass conservation during calculation. The obtained maximum relative mass conservation error for the new interface movement equation is less than 10−13 and the total mass is constant to the machine precision. This is much smaller than that of the Stefan condition discrete equation, which is in the order of 10−2. It was also found that the mass conservation accuracy of the numerical methods partly depends on the choice of the interface movement equation. The mass change term in the Stefan condition discrete equation is only a part of the whole mass change during interface movement, leading to the mass non-conservation found in the literature. In contrast, the piecewise integration treatment in the proposed interface movement equation in this research gives a more accurate mass change description during the interface movement. The correctness of the proposed interface movement equation was also proved by a comparison with the analytical solutions.

Tidal effects in the gravitational-wave phase evolution of compact binary systems to next-to-next-to-leading post-Newtonian order

We compute the gravitational-wave (GW) energy flux up to the next-to-next-to-leading (NNL) order of tidal effects in a spinless compact binary system on quasi-circular orbits. Starting from an effective matter action, we obtain the stress-energy tensor of the system, which we use in a GW generation formalism based on multipolar-post-Minkowskian (MPM) and post-Newtonian (PN) approximations. The tidal contributions to the multipole moments of the system are first obtained, from which we deduce the instantaneous GW energy flux to NNL order (formally 7PN order). We also include the remaining tidal contributions of GW tails to the leading (formally 6.5PN) and NL (7.5PN) orders. Combining it with our previous work on the conservative equations of motion (EoM) and associated energy, we get the GW phase and frequency evolution through the flux-balance equation to the same NNL order. These results extend and complete several preceding results in the literature.

DC-DC Converter Synthesis: An Inverse Problem

The inverse problem for the dc–dc converters refers to synthesizing converter topologies from a specified voltage gain expression. Though the flux balance principle is widely used in the analysis of dc–dc converters, its application as a synthesis tool has not been explored. This letter describes a mathematical approach to synthesize converter topologies from a required voltage gain expression by utilizing the principle of inductor flux balance. At first, the general form of gain expression for second-order converters is derived. From the general form of gain expression, the inverse problem is formulated by identifying the governing equations. The mathematical formulation of the inverse problem and highlighting challenges involved in solving it are the primary subjects of this article. To outline these challenges, a probable solution strategy of this inverse problem is presented. In order to derive a converter topology, at first, the appropriate flux balance equations are determined, and then the circuit topology is derived to establish the required flux balance. In contrast to the forward problem, the solution to the inverse problem is neither direct nor unique. Hence, getting the optimum closed-form solution to this inverse problem is an open-ended challenge with many possible approaches.

A Theory to Synthesize Nonisolated DC–DC Converters Using Flux Balance Principle

This paper describes a theory to synthesize nonisolated dc–dc converters. It uses the fundamental flux balance equation across the inductors of a converter as a starting point in this synthesis process. The flux balance equations are the linear equations of the input voltage, capacitor voltages, and duty cycle (D). The coefficients of these linear equations can be selected from a finite set of choices. These choices define the converter topologies that are subsequently used to synthesize a converter. The synthesis procedure applies to a converter of multiple order. All the possible converters are identified for a first-order topology. In the case of second-order converters, all the choices of the flux balance equation are defined. Based on these choices, three new quadratic topologies are derived and verified to demonstrate the effectiveness of the theory. The procedure to synthesize a converter from a given voltage conversion ratio is also outlined.

Flux-balance equations for linear momentum and center-of-mass position of self-gravitating post-Newtonian systems

We revisit the problem of flux-balance equations for isolated post-Newtonian matter systems due to the emission of gravitational waves. In particular we show by a local derivation confined to the system, using the expression of radiation-reaction forces up to the 3.5 PN order, that not only the energy, angular momentum and linear momentum of the system, but also the position of its center of mass, obey some (non-trivial) flux-balance equations. The balance equation for the center-of-mass position completes the description of the secular evolution by gravitational waves of relativistic post-Newtonian isolated matter systems. We then confirm this result by a direct computation of the gravitational-wave fluxes at future null infinity, obtaining the full multipole-moment expansion of the flux associated with the center-of-mass position (probably new with this paper), and rederiving as well the known multipole-moment expansions of the fluxes of energy, angular momentum and linear momentum. We also check our analysis by a direct calculation of radiation-reaction effects in the case of compact binary systems.

A phenomenological description of charge transfer within polaron-containing films with unramified polymer chains

According to the existing modified electrode theory, both radical-cations (polarons) and reduced quasi-particles of conducting polymer films include the same number of repeat units of polymer chains. As opposed to such supposition, any reduced repeat unit of polymer chains is assumed to be a separate quasiparticle in scope of the recently proposed approach to treating the conductance of polaron-containing films. To say nothing of the obtained new results of such approach, it is necessary to indicate that its applications have been restricted so far to the cases of either a homogeneous polaron population, which means the absence of any polaron transformations (for example, into bipolarons), or the presence of such transformations proceeding in equilibrium conditions. The main purpose of the presented communication is to derive charge carrier fluxes and material balance equations valid for non-equilibrium conditions and accounting for the above transformations and translocations of quasi-particles along polymer chains. Consecutive acts of any type of the indicated processes are treated as sequences of similar reactions proceeding in the film interior. This allows one to apply the Bronsted rule of linear correlation between activation energies of such reactions and their generalized heat effects, in order to express the reaction rate as a function of the local electric field. Using a lattice model of films formed by unramified polymer chains, non-stationary flux and material balance equations have been obtained. A comparison between the derived results and those conformed to the existing theory shows their significant difference. Some other inferences from the description carried out and possible prospects of its development are discussed.

Condensation models for the water–steam interface and the volume of fluid method

We assess the quantitative capabilities of three condensation models. These models are: (1) Numerical iteration technique; (2) heat flux balance equation; (3) phase field. The numerical iteration technique introduces a mass and energy transfer at the interface, if the temperature of the corresponding cell differs from the saturation value. The second approach solves the heat flux balance equation at the interface, hence, the resolution of the thermal boundary layer around the liquid-vapor interface is necessary to obtain an accurate value for the condensation rate. The third technique is based on a recently derived phase field model for boiling and condensation phenomena. The models were implemented in FLUENT and the interface was tracked explicitly with the volume of fluid (VOF) method. The models were tested on the LAOKOON facility, which measured direct contact condensation in a horizontal duct. The results showed that the phase field model fit best the experimental results.

GIS induced current analysis in multipoint grounding systems by using 3-D finite element method

For a good understanding of EHV GIS external induced currents in multipoint grounding systems, generation mechanism, distribution characteristics and influence factors analysis of the induced currents have been proposed in this paper. According to the structural characteristics of the multipoint gr ounding system, self and mutual inductances in GIS were calculated by using Biot-Savart Law. Based on Lenz's law, external flux balance equation of GIS was proposed, which can be used to calculate the induced circuiting currents. And the composition of induced currents in different locations of EHV GIS has been analyzed. Furthermore, 3-D analytical models of GIS were established. And the finite element method (FEM) was used to analyze the influence factors and the distribution characteristics of induced currents. Not only the amplitude but also the phase angles of the induced currents were analyzed in this paper.

A model for pressurized hydrogen induced thin film blisters

We introduce a model for hydrogen induced blister formation in nanometer thick thin films. The model assumes that molecular hydrogen gets trapped under a circular blister cap causing it to deflect elastically outward until a stable blister is formed. In the first part, the energy balance required for a stable blister is calculated. From this model, the adhesion energy of the blister cap, the internal pressure, and the critical H-dose for blister formation can be calculated. In the second part, the flux balance required for a blister to grow to a stable size is calculated. The model is applied to blisters formed in a Mo/Si multilayer after being exposed to hydrogen ions. From the model, the adhesion energy of the Mo/Si blister cap was calculated to be around 1.05 J/m2 with internal pressures in the range of 175–280 MPa. Based on the model, a minimum ion dose for the onset of blister formation was calculated to be d = 4.2 × 1018 ions/cm2. From the flux balance equations, the diffusion constant for the Mo/Si blister cap was estimated to be DH2=(10±1)×10−18 cm2/s.

A new approach to calculation of flue gas scrubbing efficiency in electrostatic precipitators

The majority of existing approaches to computation of electrostatic precipitator (ESP) efficiency do not take into account particle reentrainment from collecting electrodes. The first attempts to take into consideration particle reentrainment were made only recently. However, the existing reentrainment models for ESP are not sufficiently substantiated. A general model, which takes into account precipitation of particles, entering the ESP inlet (direct precipitation), as well as precipitation of reentrained particles (secondary precipitation), is presented in the paper. The model describes physical processes in an ESP using three integral parameters. These parameters are direct precipitation coefficient, secondary precipitation coefficient, and reentrainment coefficient, which is the ratio of reentrained particle flux to precipitation flux. An improved technique for computation of direct precipitation that takes into account particle charge distribution function is proposed. The influence of gas flow turbulence on charge distribution function parameters, as well as on other parameters of precipitation phenomena, is taken into account. The method has low computational costs. The secondary precipitation coefficient is also computed using this method. The most difficult task is calculation of the reentrainment coefficient. We suggest using data of periodical ESP testing to determine the reentrainment coefficient. The analysis of experimental data indicates that a fly ash layer on collecting electrodes is of paramount importance. It has been shown that the flux per unit length of particles falling into hoppers is proportional to weight (thickness) per unit length of the fly ash layer. Distributions of precipitation flux, flux into hoppers, reentrained particle flux along the ESP duct, and particle penetration through the ESP are computed using experimental data. A novel model that is based on a flux balance equation for each length element of an ESP duct is presented. The model has the form of a connection between physical phenomena that take place on two successive length elements of the collecting electrode. The model qualitatively agrees with experimental data. However, correction of the secondary precipitation coefficient and the reentrainment coefficient is required for quantitative agreement. In this regard, a model of layer growth and determination of functional relations between layer weight, hopper flux, and particle penetration play a key role.

Simulation of Radiant Syngas Coolers and Comparison with Various Arrangements of the Entrained‐Flow Gasifier

AbstractA 3D numerical model was developed for studying the multiphase flow and heat transfer process in a radiant syngas cooler (RSC). Realizable k‐ϵ turbulent and discrete random walk models were adopted to simulate gas phase and particle phase flow fields, respectively. The surface temperature of the membrane wall was calculated by heat flux balance equations. The calculated temperature distribution was validated by comparing calculated values with measured data of an industrial RSC. Four different membrane wall arrangements of RSC, namely, ordinary membrane wall (OMW), partial division wall (PDW), annular division wall (ADW), and fin division wall (FDW), were designed for a specific condition.