Radiative Transfer Equation Model Research Articles

Fully Coupled Material Response and Internal Radiative Heat Transfer for Three-Dimensional Heat Shield Modeling

A material response code is strongly coupled with a radiative transfer equation (RTE) to evaluate the effect of a spectrally resolved heat flux on the thermal response of a heat shield. A P1 approximation model of RTE is used to account for radiation heat transfer within the material. First, the RTE model is verified by comparing the numerical results with the analytical solution. Next, the coupling scheme is verified by comparing the temperature histories computed by the pure conduction scheme with the ones computed by conduction coupled with radiative emission. The verification study is conducted using test cases from the literature (radiant heating, arc jet heating, and space shuttle entry) as well as on a 3D Block, a 2D IsoQ sample, and the Stardust Return Capsule. The verification results are satisfactory for all cases. Thus, the verification results indicate that the coupling approach can accurately simulate the thermal response of the material. The coupling scheme was then used to simulate a laser heating experiment that studied the impact of spectral radiative heat transfer on ablative material. The results from the laser ablation simulations exhibit a behavior analogous to the experimental observations, indicating the importance of spectral radiative flux on the material response.

An Illustration of FY-3E GNOS-R for Global Soil Moisture Monitoring.

An effective soil moisture retrieval method for FY-3E (Fengyun-3E) GNOS-R (GNSS occultation sounder II-reflectometry) is developed in this paper. Here, the LAGRS model, which is totally oriented for GNOS-R, is employed to estimate vegetation and surface roughness effects on surface reflectivity. Since the LAGRS (land surface GNSS reflection simulator) model is a space-borne GNSS-R (GNSS reflectometry) simulator based on the microwave radiative transfer equation model, the method presented in this paper takes more consideration on the physical scattering properties for retrieval. Ancillary information from SMAP (soil moisture active passive) such as the vegetation water content and the roughness coefficient are investigated for the final algorithm's development. At first, the SR (surface reflectivity) data calculated from GNOS-R is calculated and then calibrated, and then the vegetation roughness factor is achieved and used to eliminate the effects on both factors. After receiving the Fresnel reflectivity, the corresponding soil moisture estimated from this method is retrieved. The results demonstrate good consistency between soil moisture derived from GNOS-R data and SMAP soil moisture, with a correlation coefficient of 0.9599 and a root mean square error of 0.0483 cm3/cm3. This method succeeds in providing soil moisture on a global scale and is based on the previously developed physical LAGRS model. In this way, the great potential of GNOS-R for soil moisture estimation is presented.

Numerical Study of Radiation and Fuel–Air Unmixedness on the Performance of a Dry Low NOx Combustor

Abstract The development of gas turbine combustors is expected to consider the effects of radiation heat transfer in modeling. However, this is not always the case in many studies that neglect this for adiabatic conditions. The effect of radiation is substantiated here, concerning the impact on the performance, mainly the emissions. Also, the fuel–air unmixedness (mixing quality) influenced by the combustor design and operational settings has been investigated with regard to the emissions. The work was conducted with a Mitsubishi-type dry low NOx combustor developed and validated against experimental data. This 3D computational fluid dynamics study was implemented using Reynolds-averaged Navier Stokes simulation and the radiative transfer equation model. It shows that NO, CO, and combustor outlet temperature reduce when the radiative effect is considered. The reductions are 17.6% and below 1% for the others, respectively. Thus, indicating a significant effect on NO. For unmixedness across the combustor in a non-reacting simulation, the mixing quality shows a direct relationship with the turbulence kinetic energy (TKE) in the reacting case. The most significant improvements in unmixedness are shown around the main burner. Also, the baseload shows better mixing, higher TKE, and lower emissions (particularly NO) at the combustor outlet, compared to part-load.

Output tracking for a radiative density optical communication system with unknown disturbance

This paper deals with boundary tracking problem for a radiative density parabolic equation (RDE) coming from an optical communication system. First, the radiative intensity is modeled by a radiative transfer equation (RTE). The idea of this work is to use the fact that the signal sent by the laser beam is collimated in consideration of the radiative density flux. Therefore, the control problem of the RTE model is transformed into a boundary control for an RDE based on the time-dependent SPN approximation. Then, we investigate a boundary output tracking problem of one dimensional parabolic density equation where the unknown disturbance enters the system from one part of the boundary. By utilizing one side boundary measurement, we construct an extended state observer to estimate the system state and the external disturbance. An output feedback boundary control is then designed using the states of the servo system and observer. It is shown that the closed-loop system and the control are uniformly bounded with output being tracking the reference and the closed-loop is internally exponentially stable. The numerical simulations are presented to illustrate the effectiveness of the proposed output feedback method.

A Forward GPS Multipath Simulator Based on the Vegetation Radiative Transfer Equation Model.

Global Navigation Satellite Systems (GNSS) have been widely used in navigation, positioning and timing. Nowadays, the multipath errors may be re-utilized for the remote sensing of geophysical parameters (soil moisture, vegetation and snow depth), i.e., GPS-Multipath Reflectometry (GPS-MR). However, bistatic scattering properties and the relation between GPS observables and geophysical parameters are not clear, e.g., vegetation. In this paper, a new element on bistatic scattering properties of vegetation is incorporated into the traditional GPS-MR model. This new element is the first-order radiative transfer equation model. The new forward GPS multipath simulator is able to explicitly link the vegetation parameters with GPS multipath observables (signal-to-noise-ratio (SNR), code pseudorange and carrier phase observables). The trunk layer and its corresponding scattering mechanisms are ignored since GPS-MR is not suitable for high forest monitoring due to the coherence of direct and reflected signals. Based on this new model, the developed simulator can present how the GPS signals (L1 and L2 carrier frequencies, C/A, P(Y) and L2C modulations) are transmitted (scattered and absorbed) through vegetation medium and received by GPS receivers. Simulation results show that the wheat will decrease the amplitudes of GPS multipath observables (SNR, phase and code), if we increase the vegetation moisture contents or the scatters sizes (stem or leaf). Although the Specular-Ground component dominates the total specular scattering, vegetation covered ground soil moisture has almost no effects on the final multipath signatures. Our simulated results are consistent with previous results for environmental parameter detections by GPS-MR.

Diffusive to quasi-ballistic random laser: incoherent and coherent models

We study the crossover between the diffusive and quasi-ballistic regimes of random lasers. In particular, we compare incoherent models based on the diffusion equation and the radiative transfer equation (RTE), which neglect all wave effects, with a coherent wave model for the random laser threshold. We show that both the incoherent and the coherent models predict qualitatively similar thresholds, with a smooth transition from a diffuse to a quasi-ballistic regime. The shape of the intensity distribution in the sample as predicted by the RTE model at threshold is also in good agreement with the coherent model. The approximate incoherent models thus provide useful analytical predictions for the threshold of random lasers as well as the shape of the random laser modes at threshold.

Dual phase lag model-based thermal analysis of tissue phantoms using lattice Boltzmann method

The present study is concerned with the development and application of Lattice Boltzmann method-based numerical scheme for investigating the thermal response of laser irradiated biological tissue phantom during laser-based photo-thermal therapy. The Lattice Boltzmann Method (LBM) has been employed for analyzing the transport of short-pulse radiation within the body of the tissue phantom that has been considered as the participating medium. In order to determine the two-dimensional temperature distribution inside the tissue medium, the transient form of radiative transfer equation (RTE) has been coupled with the energy equation modeled based on dual phase lag (DPL) heat conduction framework. The LBM-based solution of the coupled RTE and DPL-based numerical model has been benchmarked against the results available in the literature. Results have been presented in the form of two-dimensional temperature distributions, spatial and temporal profiles of temperatures within the body of the laser-irradiated biological tissue phantoms. Effects of phase lags associated with the heat flux (τq) and temperature gradients (τT) on the resultant temperature distributions inside the laser irradiated tissue phantom have also been analyzed and discussed. Thereafter, the temperature distribution inside the biological tissue phantom embedded with optical inhomogeneities has been determined using the DPL-based model. Results of the study clearly reveal the successful implementation of LBM-based numerical approach in analyzing the thermal response of laser-irradiated biological tissue phantoms. The inherent properties associated with non-Fourier heat conduction models have also been explicitly brought out in the context of photo-thermal therapy.

Numerical developments for short-pulsed Near Infra-Red laser spectroscopy. Part II: inverse treatment

Indirect optical spectroscopy or tomography, that is, mapping of optical properties in scattering and absorption inside a medium given a set of measurements at the boundaries, is highly dependent on the radiative transfer model used to track radiative energy propagation in semi-transparent materials. In the first part of this study, a numerical tool adapted for treating radiative transfer in the frame of short-pulsed laser beam interaction with non-homogeneous matter has been presented. In this paper, it is intended to show how such numerical tools can undergo inversion through adjoint treatment or reverse differentiation. Adjoint models, as well as reverse differentiation, are used in order to allow an efficient computation of the gradient, in the unknown optical parameters space, of an objective or cost function estimating the residual between data obtained at the boundary and predictions by numerical simulations. This gradient is a crucial indication as to update, through line minimization, the set of internal optical properties of the medium. First, the theoretical background of the inverse treatments, both reverse differentiation and adjoint model, for the transient radiative transfer equation model introduced in Part I is developed. Second, different reconstruction configurations are presented. Time-dependent sampling and time filtering effects of the measurements are addressed. Image reconstructions from simulated data are achieved for material phantoms of simple geometry.

Design of an inversion-based precipitation proflie retrieval algorithm using an explicit cloud model for initial guess microphysics

This paper describes the design and validation of the FSU precipitation profile retrieval algorithm for applications with SSM/I passive microwave measurements. The algorithm employs the principles of multifrequency inversion based on forward radiative transfer modeling. A Sobolev 2-stream solution to the radiative transfer equation (RTE) is used as the forward RTE model and is described herein. The method is shown to be very accurate, retaining the same degree of computational efficiency inherent to simpler 2-stream flux models. Tests of the model against more detailed multistream, adding-doubling models demonstrate that the Sobolev solution produces radiance accuracies of approximately 1%. An advantage of the Sobolev approach is that the intensity field can be expanded in a mathematically consistent fashion, an essential feature in applications with the off-nadir SSM/I microwave measurements. A 4-dimensional non-hydrostatic cloud model provides the microphysical underpinnings of the algorithm, and is used to generate the initial guess profiles for the inversion procedure. The various stages of the algorithm are described, as well as two different methods of computational implementation for storm-scale and global-scale applications. The paper also summarizes a number of different rainrate validation analyses that have been carried out at the two scales, as well as examining the capabilities of the algorithm in diagnosing the vertical latent heating structure. The validation results represent a mixture of quantitative comparisons to radar and raingage datasets, and more qualitative comparisons to the numerical modeling results of other investigators. Because of known uncertainties in the validation data in terms of their accuracy and representativeness, and the underlying problems with time-space matching of the comparisons, it is not yet possible to place absolute confidence limits on the retrievals. However, taken as a whole, the rainrate validation analyses and the estimated latent heating profiles present solid evidence that the profile approach is returning credible rainfall estimates whose uncertainnes are commensurate with those of current validation data.