A Hybrid Second Moment Method for Thermal Radiative Transfer
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A comprehensive discussion of heat transfer by thermal radiation is presented, including the radiative behavior of materials, radiation between surfaces, and gas radiation. Among the topics considered are property prediction by electromagnetic theory, the observed properties of solid materials, radiation in the presence of other modes of energy transfer, the equations of transfer for an absorbing-emitting gas, and radiative transfer in scattering and absorbing media. Also considered are radiation exchange between black isothermal surfaces, radiation exchange in enclosures composed of diffuse gray surfaces and in enclosures having some specularly reflecting surfaces, and radiation exchange between nondiffuse nongray surfaces. The use of the Monte Carlo technique in solving radiant-exchange problems and problems of radiative transfer through absorbing-emitting media is explained.
Thermal radiative heat transfer in absorbing, emitting, and scattering media
Thermal radiative transfer in nonuniform anisotropic magnetoactive plasma, correcting term of Zheleznyakov equation
This book first reviews the overall aspects and background information related to thermal radiation heat transfer and incorporates new general information, advances in analytical and computational techniques, and new reference material. Coverage focuses on radiation from opaque surfaces, radiation interchange between various types of surfaces enclosing a vacuum or transparent medium, and radiation including the effects of partially transmitting media, such as combustion gases, soot, or windows. Boundary conditions and multiple layers are discussed with information on radiation in materials with nonunity refractive indices.
Thermal radiation exchange between surfaces and enclosures
Radiative heat transfer and thermal structure of planetary atmospheres
A model for numerical simulation of stratus cloud layers is constructed by combining a second-order closure, turbulent transfer model with a thermal radiative transfer model. The turbulent transfer model allows water vapor saturation. The combined turbulence-radiation model is applied to both a horizontally uniform one-dimensional case and a horizontally nonuniform two-dimensional case. In the latter, the dynamics of mesoscale circulations are also incorporated. Results of the two-dimensional simulation show that the layer cloud instability occurs where the sea surface temperature is high and the large-scale subsidence is weak. The simulated instability is analyzed in view of an instability criterion, the eddy kinetic energy budget, and evaporative cooling near the cloud top.
Thermal effect of radiative transfer in atomic oxygen line
This report documents the time and space discretizations for grey flux-limited diffusion applied to the thermal radiative transfer (TRT) equations. We begin with a description of the physics being solved before moving into the diffusion approximation. Once we have the TRT system, we show a finite-volume-inspired discretization from Jim Morel (Texas A&M University, NUEN 627 class notes, lecture 8). As systems become hotter they emit more photons in the form of blackbody radiation. Because average photon energy of the blackbody source is proportional to the temperature of the system, we call these thermal photons or thermal radiation. As material temperatures increase, increasing fractions of the total energy in the system go into the radiation field. In addition, radiation can deposit energy and momentum non-locally, making it an important phenomenon for heating and impulse. In order to accurately study systems at high temperatures, we wish to add the physics of thermal radiation to our hydrodynamic system. In practice, coupling radiation and hydrodynamics is often done by operator-splitting each timestep into two consecutive, non-overlapping phases: (1) update the hydrodynamics for a fixed radiation state (2) update the radiation and internal energy for an otherwise fixed hydrodynamic state. Because of this clean separation of physics updates, in this report we show only the latter phase, which involves solely the TRT equations.
The thermal radiative transfer equations (TRT) model many important phenomena of interest at LANL. The TRT equations model time-dependent thermal radiation through a medium, i.e., how thermal radiation loses energy by absorption, gains energy via emission processes, and redistributes energy via scattering.
The radiosity method is introduced to plant canopy reflectance modeling. We review the physics principles of the radiosity method which originates in thermal radiative transfer analyses when hot and cold surfaces are considered within a given enclosure. The radiosity equation, which is an energy balance equation for discrete surfaces, is described and contrasted with the radiative transfer equation, which is a volumetric energy balance equation. Comparing the strengths and weaknesses of the radiosity method and the radiative transfer method, we conclude that both methods are complementary to each other. Results of sample calculations are given for canopy models with up to 20,000 discrete leaves.
A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor) equations for moments of the radiation intensity and (ii) the normalized Boltzmann transport equation (BTE). The multilevel system of moment equations is derived by projection of the BTE onto a sequence of subspaces which represent elements of the phase space of the problem. Exact closure for the moment equations is provided by the Eddington tensor. A Petrov-Galerkin (PG) projection of the normalized BTE is formulated using a proper orthogonal decomposition (POD) basis representing the normalized radiation intensity over the whole phase space and time. The Eddington tensor linearly depends on the solution of the normalized BTE. By linear superposition of the POD basis functions, a low-rank expansion of the Eddington tensor is constructed with coefficients defined by the PG projected normalized BTE. The material energy balance (MEB) equation is coupled with the effective gray low-order equations which exist on the same dimensional scale as the MEB equation. The resulting TRT ROM is structure and asymptotic preserving. A detailed analysis of the ROM is performed on the classical Fleck-Cummings (F-C) TRT multigroup test problem in 2D geometry. Numerical results are presented to demonstrate the ROM's effectiveness in the simulation of radiation wave phenomena. Importantly, the ROM is shown to produce solutions with sufficiently high accuracy while using low-rank approximation of the normalized BTE solution. Essential physical characteristics of supersonic radiation wave are preserved in the ROM solutions.
A summary of the work involving the Monte Carlo method in the solution of problems in thermal radiation transfer is presented, which indicates general methods previously used for solving problems in which radiation is coupled with other modes of energy transfer. Previous work involving radiation in absorbing-emitting media is included. An example is outlined to indicate the use of the Monte Carlo method in the design of a space radiator. Suggestions are given for solution of a complex case incorporating the effects of coupled conduction, convection and radiation, wavelength dependent and selective surfaces, nonisothermal conditions, and strongly directional or nondiffuse emitting and reflecting surfaces. A discussion is given of the factors that may affect convergence, running time, and accuracy of the Monte Carlo solutions and of the advantages and disadvantages of this approach for practical problems. Also discussed are the case of programming for complex problems and the probable machine time requirements of the method.
The role of clouds remains the largest uncertainty in climate projections. They influence solar and thermal radiative transfer and the earth's water cycle. Therefore, there is an urgent need for accurate cloud observations to validate climate models and to monitor climate change. Passive satellite imagers measuring radiation at visible to thermal infrared (IR) wavelengths provide a wealth of information on cloud properties. Among others, the cloud top height (CTH) - a crucial parameter to estimate the thermal cloud radiative forcing - can be retrieved. In this paper we investigate the skill of ten current retrieval algorithms to estimate the CTH using observations from the Spinning Enhanced Visible and InfraRed Imager (SEVIRI) onboard Meteosat Second Generation (MSG). In the first part we compare ten SEVIRI cloud top pressure (CTP) data sets with each other. The SEVIRI algorithms catch the latitudinal variation of the CTP in a similar way. The agreement is better in the extratropics than in the tropics. In the tropics multi-layer clouds and thin cirrus layers complicate the CTP retrieval, whereas a good agreement among the algorithms is found for trade wind cumulus, marine stratocumulus and the optically thick cores of the deep convective system. In the second part of the paper the SEVIRI retrievals are compared to CTH observations from the Cloud-Aerosol LIdar with Orthogonal Polarization (CALIOP) and Cloud Profiling Radar (CPR) instruments. It is important to note that the different measurement techniques cause differences in the retrieved CTH data. SEVIRI measures a radiatively effective CTH, while the CTH of the active instruments is derived from the return time of the emitted radar or lidar signal. Therefore, some systematic differences are expected. On average the CTHs detected by the SEVIRI algorithms are 1.0 to 2.5 kilometers lower than CALIOP observations, and the correlation coefficients between the SEVIRI and the CALIOP data sets range between 0.77 and 0.90. The average CTHs derived by the SEVIRI algorithms are closer to the CPR measurements than to CALIOP measurements. The biases between SEVIRI and CPR retrievals range from −0.8 kilometers to 0.6 kilometers. The correlation coefficients of CPR and SEVIRI observations vary between 0.82 and 0.89. To discuss the origin of the CTH deviation, we investigate three cloud categories: optically thin and thick single layer as well as multi-layer clouds. For optically thick clouds the correlation coefficients between the SEVIRI and the reference data sets are usually above 0.95. For optically thin single layer clouds the correlation coefficients are still above 0.92. For this cloud category the SEVIRI algorithms yield CTHs that are lower than CALIOP and similar to CPR observations. Most challenging are the multi-layer clouds, where the correlation coefficients are for most algorithms between 0.6 and 0.8. Finally, we evaluate the performance of the SEVIRI retrievals for boundary layer clouds. While the CTH retrieval for this cloud type is relatively accurate, there are still considerable differences between the algorithms. These are related to the uncertainties and limited vertical resolution of the assumed temperature profiles in combination with the presence of temperature inversions, which lead to ambiguities in the CTH retrieval. Alternative approaches for the CTH retrieval of low clouds are discussed.
We apply a nonlinearly preconditioned, quasi-Newton framework to accelerate the numerical solution of the thermal radiative transfer (TRT) equations. This framework was inspired by the unpublished method that has existed for years in Teton, Lawrence Livermore National Laboratory’s deterministic TRT code. In this paper, we cast this iteration scheme within a formal nonlinear preconditioning framework and compare its performance against other iteration schemes in the framework. With proper choices of iteration controls for the various levels of the solver, we can recover the standard linearized one-step method, a full nonlinear Newton scheme, as well as the method in Teton. In brief, the nonlinear preconditioning TRT scheme formally eliminates the material temperature equation from the nonlinear system in a nonlinear analog of a Schur complement. This nonlinear elimination step involves solving a decoupled nonlinear equation for each spatial degree of freedom and is therefore inexpensive. By applying a quasi-Newton iteration scheme on the new system, we obtain a three-level iteration scheme that is at least as efficient as commonly used TRT schemes. The new method allows full convergence to the nonlinear backward Euler time-discretized system, increasing accuracy and robustness, while using a similar number of linear iterations as the more common linearized one-step methods Eq. (4).