A weight-function approach for determining watershed initial conditions for combustion waves

Homogeneous versus heterogeneous lunar mantle: Constraints from secondary crust production

Combustion and pressure wave interaction in enclosed mixtures initiated by temperature nonuniformities

Transport simulation of ECRH H-mode experiments on HL-2A tokamak is carried out using ONETWO code, the GLF23 and PEDESTAL models, along with TORAY code for ECRH. It is found that the initial electron and ion temperature profiles affect L-H transition significantly, and larger initial temperature gradient at the edge plasma benefits the transition. The simulation results show that it is possible to achieve ECRH H-mode with appropriate initial electron and ion temperature profiles under present discharge conditions on HL-2A tokamak. In addition, the pedestal density, electron temperature and pedestal width are predicted, and the evolutions of electron and ion temperature profile are calculated.

Quite a lot of design parameters exist when the designer designs the best performance impeller and guidevane. Finally, it is necessary to decide the detail 3D shape of impeller and guidevane. The best flow conditions of the flow velocity and the flow angle at the impeller inlet and outlet are designed as first step before impeller detailed 3D shape is designed. The detailed 3D shape is not necessary in this study. The optimum meridian shape has been found, assuming that the total loss head is addition of the blade-to-blade diffusion loss head and the hub-tip axial-symmetrical annular surface friction loss head. That is, the meridian shape is mainly decided depending on the blade-to-blade flow condition on hub surface, mean surface and tip surface. Main design parameters that decide the meridian shape is built in the loss head equation by diffusion factor and all the design parameters relate closely respectively. The value of the design parameters can be set at random for loss head calculation in a usual optimization technique. But, the loss head in the combination of the limited value design parameters can be calculated in this method. Therefore, the great change of design parameter value is not permitted in this optimum process, and the increment of all the design parameters is set respectively and the optimization of the design parameter is advanced from an initial value of the design parameters changing the value of design parameters little by little. Therefore, there is a possibility that the best solution becomes a local best solution and the influence of an initial condition value cannot be removed. In this method, it is necessary for coming out from the local best solution that the value of all the design parameters changes from an initial value to a largely different value. The specific speed influences all the other design parameters. So, the specific speed is changed gradually in restriction optimum process. In FEDSM2014-21030, the impeller blade number was assumed to be a variable real number design parameter and the specific speed that was the specification as constant value become a variable design parameter equally to other design parameters. In AJK2015-09034, the impeller outlet diameter and impeller rotational speed were assumed to be a variable optimum design parameters. As a result, all the design parameters became variable. Optimization was executed from two different initial conditions to study the initial value dependency whether the obtained two optimum solution became the same. In FEDSM2016-7518, one initial value of the specific speed was assumed to be 916 and it was confirmed to obtain the solution from the specific speed 200 to the specific speed 3000 as the variable wide range design parameter by restriction. The design parameter of mixed flow angle of impeller inlet was not change at the beginning of calculation and changed rapidly in the latter half of the calculation. The cause of the mixed flow angle of impeller inlet value jump was uncertainty. In FEDSM2017-69024, the influence of the surface roughness of the axial-symmetrical hub and tip wall was examined. The impeller blade number, the guidevane blade number and mixed flow angle of impeller inlet were able to change by restriction, and the influence of the impeller blade number and the guidevane blade number was examined. The mixed flow angle of impeller inlet was assumed 0 degrees (axial-flow) to avoid the parameter value jump. In this paper, the specific speed design parameter become the restriction design parameter. The specific speed as restriction parameter has been changed from the lower bound value to the upper bound value to come out from a local best solution. The efficiency extended to the specific speed whole area is able to be improved by the influence of the another middle specific speed with the highest efficiency. It is found that the value of the change increment at the specific speed as restriction parameter is important very much executed by the several kind of specific speed increment. In order to improve the design parameters of traditional impeller and guidevane in the future, it is convenient that total head and flow rate are new optimum design parameters instead of impeller outlet diameter and impeller rotational speed. The impeller rotational speed can be calculated by specific speed and total head.

Combining the principles of dynamic inversion and optimization theory, a new approach is presented for stable control of a class of one-dimensional nonlinear distributed parameter systems with a finite number of actuators in the spatial domain. Unlike the existing 'approximate-then-design' and 'design-then-approximate' techniques, this approach does not use any approximation either of the system dynamics or of the resulting controller. The formulation has more practical significance because one can implement a set of discrete controllers with relative ease. To demonstrate the potential of the proposed technique, a real-life temperature control problem for a heat transfer application is solved through simulations. Numerical results are presented which show that the desired temperature profile can be achieved starting from any initial temperature profile.

The temperature distribution in ice sheets is worthy of attention given the strong relation with ice dynamics and the intrinsic information about past surface temperature variations. Here we refine the classical analysis of free oscillations in an ice sheet by analytically solving the thermal evolution of an ice column. In so doing, we provide analytical solutions to the one-dimensional Fourier heat equation over a finite motionless ice column for a general boundary condition problem. The time evolution of the temperature profiles appears to be strongly dependent on the column thickness L and largely differs from previous studies that assumed an infinite column thickness. Consequently, the time required for the column base to thaw depends on several factors: the ice column thickness L, the initial temperature profile and the boundary conditions. This timescale is classically considered to be the period of a binge-purge oscillator, a potential mechanism behind the Heinrich Events. Our analytical solutions show a broad range of periods for medium-size column thicknesses. In the limit of L → ∞, the particular values of the prescribed temperature at the top of the column become irrelevant and the reference value of ~7000 years, previously estimated for an idealised infinite domain, is retrieved. More generally, we prove that solutions with different upper boundary conditions, yet covered by our formulation, converge to the same result in such a limit. These results ultimately manifest a subtle connection between internal free and externally-driven (in the sense of a time-dependent boundary condition at the top) mechanisms caused by the finitude of the domain. Thermomechanical instabilities, inherent to internal free oscillations, are in fact sensitive to the particular climatic forcing imposed as a boundary condition at the top of the ice column. Lastly, analytical solutions herein presented are applicable in any context where our general boundary problem is satisfied.

<strong class="journal-contentHeaderColor">Abstract.</strong> The temperature distribution in ice sheets is worthy of attention given the strong relation with ice dynamics and the intrinsic information about past surface temperature variations. Here we refine the classical analysis of free oscillations in an ice sheet by analytically solving the thermal evolution of an ice column. In so doing, we provide analytical solutions to the one-dimensional Fourier heat equation over a finite motionless ice column for a general boundary condition problem. The time evolution of the temperature profiles appears to be strongly dependent on the column thickness <em>L</em> and largely differs from previous studies that assumed an infinite column thickness. Consequently, the time required for the column base to thaw depends on several factors: the ice column thickness <em>L</em>, the initial temperature profile and the boundary conditions. This timescale is classically considered to be the period of a binge-purge oscillator, a potential mechanism behind the Heinrich Events. Our analytical solutions show a broad range of periods for medium-size column thicknesses. In the limit of <em>L</em> &rarr; &infin;, the particular values of the prescribed temperature at the top of the column become irrelevant and the reference value of ~7000 years, previously estimated for an idealised infinite domain, is retrieved. More generally, we prove that solutions with different upper boundary conditions, yet covered by our formulation, converge to the same result in such a limit. These results ultimately manifest a subtle connection between internal free and externally-driven (in the sense of a time-dependent boundary condition at the top) mechanisms caused by the finitude of the domain. Thermomechanical instabilities, inherent to internal free oscillations, are in fact sensitive to the particular climatic forcing imposed as a boundary condition at the top of the ice column. Lastly, analytical solutions herein presented are applicable in any context where our general boundary problem is satisfied.

Finite element analysis of thermoforming simulation based on isothermal as well as non-isothermal initial conditions has been applied successfully for predicating final thickness distributions. For these simulations, it is assumed that the initial sheet temperature is known and does not change significantly during forming at a rapid stretch rate. For a non-isothermal analysis, the temperature dependent material properties are necessary. In this paper sample results are presented for the so-called inverse thermoforming problem, where an initial temperature distribution is sought numerically that will result in a specific final thickness distribution. Thus, a finite element simulation is combined with an iterative algorithm to obtain inverse solutions for a thermoformed part. In this example, the required initial temperature distributions that result in a uniform final thickness are determined for a thermoformed part. It is shown that the calculated results are quite sensitive to perturbations in the specified initial temperature profile and thus the practical application of optimal temperature distributions may require high precision thermal sensors and controls. This initial temperature distribution can then be used for the determination of desired heating patterns on zone-controlled heaters of a thermoforming machine using transient heat transfer analysis.

RIFT, a model of sedimentary basin evolution by finite rate, non-uniform, pure shear extension of the lithosphere

The theory of a constant pressure vapor bubble growing in a liquid with both superheat and sub‐cooling is presented. In the case where the initial temperature profile is purely radial, bubble radius‐time curves and temperature profile near the bubble are calculated. For the case of the hemispherical bubble growing on a plane heater surface with initially plane parallel temperature distribution, it is shown that the problem may be reduced to that of radial temperature profile if the inverse thickness of the superheated layer measured along the radius vector is averaged over the surface of the bubble. It is further shown that in the latter case vaporization is always present at the foot of the bubble, but condensation may occur near the top where the bubble penetrates furthest into the subcooled liquid.

We study the evolution of initial temperature profiles in a two-dimensional isolated harmonic graphene lattice. Two heat transfer problems are solved analytically and numerically. In the first problem, the evolution of a spatially sinusoidal initial temperature profile is considered. This profile is usually generated in real experiments based on the transient thermal grating technique. It is shown that at short times the amplitude of the profile decreases by an order magnitude and then it performs small decaying oscillations. A closed-form solution, describing the decay of the amplitude at short times is derived. It shows that due to symmetry of the lattice, the anisotropy of the ballistic heat transfer is negligible at short times, while at large times it is significant. In the second problem, a uniform spatial distribution of the initial temperature in a circle is specified. The profile is the simplest model of graphene heating by an ultrashort localized laser pulse. The corresponding solution has the symmetry of the lattice and many local maxima. Additionally, we show that each atom has two distinct temperatures corresponding to motions in zigzag and armchair directions. Presented results may serve for proper statement and interpretation of laboratory experiments and molecular dynamics simulations of unsteady heat transfer in graphene.

Abstract. The process of thermocline evolution under the action of turbulent stream in the upper layer is investigated in laboratory experiment in thermally stratified tank, the initial temperature profile with pronounced thermocline being similar to that observed in tropic seas. The mean velocity and turbulent energy spatial distributions have been shaped to model the hydrological conditions in strong oceanic currents or wind-induced drag currents. The experiment demonstrates the gradual deepening and transformation of thermocline in a case where no global instability took place (i.e., with Richardson numbers always exceeding 0.3-0.4). The process of thermocline evolution resulted also in recurring "bursts" of microstructure. A numerical experiment based on equations of semi-empirical theory of turbulence shows quantitative agreement with experimental data. Moreover, simple analytical solutions and numerical results show that a layer with marginal stability is formed with Richardson numbers being very close to the stability threshold, so that quite small disturbances in thermocline can result in appearance of internal waves and bursts of turbulence.

The stability of the front to infinitely small distor� tions was analyzed under the assumption that the reac� tor channel width is infinitely large in comparison with the combustion zone thickness (5). It was concluded that the plane filtration combustion wave may be unstable. The experimental investigation of the filtra� tion combustion wave stability confirmed (6) that the propagation of a plane filtration combustion front may be unstable and may be accompanied by the formation of structures similar to Saffman-Taylor fingers, which were observed as a highviscosity liquid was displaced by a lowviscosity liquid (7). In this work, for the first time, we made mathemat� ical modeling of twodimensional unsteady filtration combustion during the forced oxidant filtration in the combustion wave direction. The purposes of the study was to determine the conditions for the occurrence of filtration combustion with a stable plane front in chan� nels of finite width and investigate the filtration com� bustion wave propagation modes in the range of insta� bility of the plane reaction front. The physical formulation of the problem is the fol� lowing. A gas mixture with oxidant concentration a0 is fed to a reactor filled with a porous mixture containing a fuel component. The gas flow rate at the inlet (x = 0) is maintained constant (G0). Reaction initiation with a hightemperature source leads to reaction front prop� agation in the х direction at rate u. As the fuel is burned out, the structure of the porous medium changes, because of which the porosity, thermal diffusivity, and permeability of the combustion products may differ from the respective characteristics of the initial reac� tion mixture. The problem is considered in the plane geometry under the assumption that the reactor is shaped as a thin slitlike channel. If the reaction front propagation velocities are low, which is characteristic of filtration combustion waves, the difference between the temperatures of the parti� cles and the gas can be ignored and the porous medium can be considered locally uniform in temper� ature and concentration. Under this assumption, the dimensionless system of equations describing filtra� tion combustion has the form (1, 2)

A theoretical study of combustion in porous media driven by a gravity induced gas flux is conducted. Filtration of the oxidizer carrying gas arises in response to heating of the gas due to exothermic conversion of the solid fuel. Specifically, we consider a reaction front propagating through a porous matrix consisting of reactive (fuel) and inert components. Gas, consisting of both oxidizer and inert components, filters through the matrix and reacts with the solid fuel. The hot gases in the medium rise due to buoyancy, thus drawing in fresh gas from below. We employ approximate analytical methods and numerical simulations to analyze all the basic combustion phenomena, including self ignition, external ignition, both upward and downward as well as adiabatic and nonadiabatic propagating combustion waves. Our simulations also describe the dynamics of buoyancy driven combustion waves. In conventional combustion systems the combustion waves are traveling waves, whose wave characteristics, e.g., propagation velocity and shape, are constant, and the time and length scales for the ignition period are independent of the length L of the sample. In contrast, here the waves are not traveling waves. Rather, they are quasisteady waves, whose characteristics do depend on L. Thus, knowledge of the combustion characteristics determined from experiments on a specific sample of a given size can not be generalized to samples of larger size as is the case in conventional combustion. We derive estimates for the dependence of various combustion characteristics on L. Finally, suggestions for the experimental verification of some of the qualitative results of our analysis are presented.

Quantum vortex dynamics in Bose-Einstein condensates or superfluid helium can be informatively described by the Gross-Pitaevskii (GP) equation. Various approximate analytical formulae for a single stationary vortex are recalled and their shortcomings demonstrated. Significantly more accurate two-point [2/2] and [3/3] Pade' approximants for stationary vortex profiles are presented. Two straight, singly quantized, antiparallel vortices, located at a distance d apart, form a vortex dipole, which, in the GP model, can either annihilate or propagate indefinitely as a `solitary wave'. We show, through calculations performed in a periodic domain, that the details and types of behavior displayed by vortex dipoles depend strongly on the initial conditions rather than only on the separation distance (as has been previously claimed). It is found, indeed, that the choice of the initial two-vortex profile (i.e., the modulus of the `effective wave function'), strongly affects the vortex trajectories and the time scale of the process: annihilation proceeds more rapidly when low-energy (or `relaxed') initial profiles are imposed. The initial `circular' phase distribution contours, customarily obtained by multiplying an effective wave function for each individual vortex, can be generalized to explicit elliptical forms specified by two parameters; then by `tuning' the elliptical shape at fixed d, a sharp transition between solitary-wave propagation and annihilation is captured. Thereby, a `phase diagram' for this `AnSol' transition is constructed in the space of ellipticity and separation and various limiting forms of the boundary are discussed.