Recovering an Initial Temperature Profile from Finite Linear Time Sampling

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.

Alternative thermal histories of Earth-like planets: Influence of key parameters

The Simulation-based High-efficiency Advanced Reactor Prototyping (SHARP) toolkit is under development by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) Campaign of the U.S. Department of Energy, Office of Nuclear Energy. To better understand and exploit the benefits of advanced modeling simulations, the NEAMS Campaign initiated the “Sodium-Cooled Fast Reactor (SFR) Challenge Problems” task, which include the assessment of hot channel factors (HCFs) and the demonstration of zooming capability using the SHARP toolkit. If both challenge problems are resolved through advanced modeling and simulation using the SHARP toolkit, the economic competitiveness of a SFR can be significantly improved. The efforts in the first year of this project focused on the development of computational models, meshes, and coupling procedures for multi-physics calculations using the neutronics (PROTEUS) and thermal-hydraulic (Nek5000) components of the SHARP toolkit, as well as demonstration of the HCF calculation capability for the 100 MWe Advanced Fast Reactor (AFR-100) design. Testing the feasibility of the SHARP zooming capability is planned in FY 2018. The HCFs developed for the earlier SFRs (FFTF, CRBR, and EBR-II) were reviewed, and a subset of these were identified as potential candidates for reduction or elimination through high-fidelity simulations. A one-way offline coupling method was used to evaluate the HCFs where the neutronics solver PROTEUS computes the power profile based on an assumed temperature, and the computational fluid dynamics solver Nek5000 evaluates the peak temperatures using the neutronics power profile. If the initial temperature profile used in the neutronics calculation is reasonably accurate, the one-way offline method is valid because the neutronics power profile has weak dependence on small temperature variation. In order to get more precise results, the proper temperature profile for initial neutronics calculations was obtained from the STAR-CCM+ calculations. The HCFs of the peak temperatures at cladding outer surface, cladding inner wall surface, and fuel centerline induced by cladding manufacturing tolerance and uncertainties on the cladding, coolant, and fuel properties were evaluated for the AFR-100. Some assessment on the effect of wire wrap configuration and size of the bundle shows that it is practical to use the 7-pin bare rod bundle to calculate the HCFs. The resulting HCFs obtained from the high-fidelity SHARP calculations are generally smaller than those developed for the earlier SFRs because the most uncertainties involved in the modeling and simulations were disappeared. For completeness, additional investigations are planned in FY 2018, which will use random sampling techniques.

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.

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.

<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.

Homogeneous versus heterogeneous lunar mantle: Constraints from secondary crust production

The transient temperature profile across a commercial wafer temperature sensor device in an inductively coupled Ar plasma is reported. The measured temperatures are compared to model predictions, based on a coupled plasma-wafer model. The radial temperature profile is the result of the radial profile in the ion energy flux. The ion energy flux profile is obtained by combining the Langmuir probe measurement, the ion wall flux probe measurement, and a plasma model. A methodology to estimate the ion flux profile using the sensor measurements has been validated by combining the plasma measurements, the wafer temperature measurements, and the plasma-wafer model. It is shown that with minimal heat transfer between the wafer and the chuck, the initial transient wafer temperature profile after plasma ignition can be used to estimate the ion energy flux profile across the wafer.

The momentum and energy integral method of von Karman and Pohlhausen is used to solve the entrance heat transfer problem for a non‐Newtonian fluid in a flat duct. The initial temperature and velocity profiles are assumed to be flat. The fluid is assumed to obey the Ostwald‐de Wael model and its physical properties are assumed to be constant. Dimensionless expressions for temperature and velocity profiles are obtained by numerical methods.The results of this investigation indicate that, similar to the case of Newtonian fluid, the parameters which influence entrance heat transfer are x/b ratio, Reynolds number and Prandtl number, provided these groups are properly defined.

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.

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.

Over the past two decades, a coherent picture has emerged of the atmospheric dynamics of hot Jupiters from a combination of three-dimensional general circulation models (GCMs) and astronomical observations. This paradigm consists of hot Jupiters being spin-synchronized due to their close-in orbit, with a resulting large day-to-night irradiation gradient driving a day-to-night temperature contrast. This day-to-night temperature contrast in turn raises day-to-night pressure gradients that are balanced by a circulation with wind speeds on the order of km/s. The dominant feature of this circulation is a superrotating equatorial jet, maintained by eddy-mean flow interactions that pump momentum into the jet. In this work, I explore the dependence of this circulation paradigm on the initial thermal and dynamical conditions in atmospheric circulation models of &amp;#160;hot Jupiters. To do so, I conduct MITgcm simulations of the atmospheric circulation of hot Jupiters with both varying initial wind directions and initial temperature profiles. I find that the results are ubiquitously insensitive to the initial conditions, implying that the current paradigm of hot Jupiter circulation exhibits at most limited hysteresis. I demonstrate that there is a single characteristic wind speed of hot Jupiters for given planetary and atmospheric parameters using an idealized scaling theory, and discuss implications for the interpretation of hot Jupiter observations.

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.

In many generic combustion models, one finds that a combustion wave will develop with a specific wave speed. However, there are possible initial temperature profiles which do not evolve into such waves, but rather die out to the ambient temperature. There can exist, in some models, a clear distinction between those initial conditions that do evolve into combustion waves and those that do not; this is sometimes referred to as the watershed initial condition. When fuel consumption is considered to be negligible, analytical methods can be used to obtain the exact watershed. In this paper, we consider the problem of determining pseudo-watersheds and ascertaining the relationship between these pseudo-watersheds and the exact watersheds. In the process a novel weight-function approach for infinite spatial domains is developed.