Radiative transfer in particulate medium is encountered in wide variety of applications such as pigmented coatings, nano-composites, remote sensing and astrophysics. For many of these problems radiative transfer theory and radiative transfer equation (RTE) is used for efficient computation to enable rigorus design or characterization processes. When the medium is dense, dependent scattering prevails and must be considered while estimating the radiative transfer properties.
Updated scattering regime map
Transition from independent to dependent scattering regime is defined by scattering regime map proposed by Tien's group in late 1980s based on measured reflectance/transmittance data. Recently, Mishchenko et al. (2013) experimentally showed that the map was erroneous and needs an update.
In our research, we showed that a regime map established based on transport or reduced scattering coefficient as a metric of transition is consistent with a reflectance based map. Transport scattering coefficient is defined based on scattering coefficient and asymmetry factor, and we also showed that Static Structure Factor (SSF) can be used for correcting prediction of transport scattering coefficient based on independent scattering approximation (ISA) using Lorenz-Mie Theory (LMT) for dielectric particles. The resulting revised map aligns with all known experimental data.
Please feel free to contact us if you have or aware of experimental data that is not considered in our studies. The study was carried out as Aristo Taufiq's MS thesis research and was funded by Tubitak 1001 program.
Applicability of radiative transfer equation for dense medium
Mishchenko (2013) also outlined that applicability of RTE under dependent and multiple scattering must be questioned and its applicability limits must be identified. In our research we are trying to address these questions, trying to define the applicability limits of RTE by comparing its predictions with rigorous solution of Maxwell's equations. We have been focusing on dielectric particulate medium and we are using SSF and LMT for predicting radiative transfer properties under dependent scattering. Random particle systems are mostly polydisperse and the particle size distribution for most systems is defined by a log-normal distribution. However, SSF have been formulated either for monodisperse particulate systems or polydisperse systems with different size distributions such as Schulz distribution. Therefore, we are currently developing a formulation for SSF for a log-normal distribution so that we can validate our dense medium radiative transfer (DMRT) model that is comprised of SSF and LMT for predicting radiative transfer properties and Monte Carlo method as a RTE solver, against T-matrix solutions. Through these comparisons, we will be able to define the applicability limits of DMRT.
Applicability of effective medium theory for interfacial properties
Related publications:
Particle Characterization:
Non-intrusive characterization of nano-sized particles is critical in many different fields for characterization and diagnostics in combustion systems, biomedical, materials science and manufacturing. Non-invasive optical characterization relying on measurement of light scattering pattern and inferring the particle or particle cluster’s characteristics has been investigated by researchers. Here, the characterization problem can be formulated as an inverse problem that is solved by various methods relying on optimization techniques, Bayesian approaches. Our research focuses on the problem and expands the existing state of the art by introducing advanced mathematical tools for improved characterization. We have implemented global search algorithms, Bayesian inference and approximate Bayesian computation techniques for the solution of the problem. Our research continues in this field.
Related publications:
Ericok OB, and Erturk H, "Inverse Characterization of Nanoparticle Clusters using Unpolarized Optical Scattering without Ex-Situ Measurements", Journal of Quantitative Spectroscopy and Radiative Transfer, vol.198, pp.117-129. (SCI) (link to article)
Ericok OB, and Erturk H, 2016, “Chracterization of Nanoparticle Aggregates Using Bayesian Inference via Light Scattering Experiments”, 2016 ASME International Mechanical Engineering Conference and Exhibition, Phoenix, AZ.
Ericok OB, and Erturk H, 2016, "Inverse Characterization of Nanoparticle Clusters using Unpolarized Optical Scattering without Ex-Situ Measurements", 8th International Symposium on Radiative Transfer, June 5-10, Cappadocia, Turkey.
Inverse design of thermal systems and materials:
Thermal processing systems are built to satisfy conditions demanded by various processes such as semiconductor rapid thermal processing (RTP), industrial baking, glass or wire annealing processes. These applications require precise thermal processing that is very critical for sustaining high quality and yield, and improving the energy efficiency of the process at the same time that makes design and control of thermal processing systems a more challenging task than ever. The challenge lies in three coupled problems: the design and control of thermal processing equipment, and accurate thermal sensing necessary for the control.
Design:
The design goal for such thermal equipment is to determine the “ideal” system with the optimal geometry, materials, configuration and the necessary input for the devices such as surface heaters, lamps, burners, fans or other cooling components used in the system to satisfy the needs of the process in a feasible manner. In general, the overall design process involves a number of design iterations of prototype building and testing, and any means of using numerical simulations techniques can help in reducing the number of iterations required and the associated costs.
The boundary condition design is an inverse problem where a desired effect is known from the design objective and the necessary cause is sought. It is a well-known fact that the inverse problems result in ill-posed systems, where the solutions are unstable. The traditional way to solve such a design problem is to guess an input for the energy supply devices used in the system and then use mathematical models to check whether the desired conditions in the design environment are satisfied. The guessed value is modified based on the preceding results until the desired conditions are reached. Such trial-and-error methods are computationally expensive; moreover, it can be difficult to obtain smooth and physically reasonable or feasible solutions.
Inverse formulation can be implemented to estimate the unknown heater input required directly from the information available in the “design object” or the processed object. In the inverse formulation the system is represented by a system of discretized Fredholm equation of the first kind that is ill-posed. Mathematically, the system is unstable with no unique solution; whereas physically, the solution might not have any physically meaningful solution such as negative emissive powers. However, a solution with regularization of the system is possible using techniques such as truncated singular value decomposition (TSVD), modified TSVD, conjugate gradient method, and Tikhonov regularization.
Control:
Once the system is designed, its operation must also be controlled to precisely follow the process recipe. Although necessary heater settings can be estimated using inverse formulation or optimization using mathematical models, some discrepancies will be observed between what is estimated by the model and how the physical system responds. These are due to; errors due to approximations in mathematical models, numerical error, error due to uncertainty in the properties used for the model. These must be corrected by some means of a control algorithm. We have shown that artificial neural networks can be used for controlling such a system. Robust control algorithms can also be employed.
Remote Thermal Sensing:
In order to ensure precise control of the thermal processing system accurate monitoring of temperature is necessary. For semiconductor thermal processing non-intrusive, accurate, and precise temperature measurement metrologies that are capable of measuring up to ±1.5oC at 1000oC must be used for high precision thermal control. Light-pipe radiation thermometers (LPRT) have been used as an industrial tool to fulfill this task. The errors associated with light-pipe measurements are great concerns across the industry. Modeling of the light-pipes has helped in understanding the signal transport process and errors associated with the light pipe measurements. However, due to the smaller size of the light-pipe sensor area with respect to the total system area, full scale modeling of such a system including the light pipe thermometer has not been possible due to the computational demand. We have overcome this problem to improve the computational efficiency using reverse Monte Carlo method that can be used to model the signal transport through a light-pipe thermometer used in a RTP system considering the spectral and angular dependent optical properties of the chamber and probe materials.
Aside from the research programs mentioned, we have been working on applications such as inverse design of system for renewable energy harvesting, and non-destructive fault detection in electronics packaging. The research in these fields has been utilizing optimization/minimization or regularization for achieving a reasonable solution. More details about the research in these fields are posted under the relevant pages that can be accessed through the links.
Related publications:
Erturk, H. and Howell, J. R., 2010, “Efficient Signal Transport Model for Remote Thermometry in Full Scale Systems”, IEEE Transactions on Semiconductor Manufacturing, vol.23, no.1., pp.132-140. (SCI) (link to article)
Erturk, H. and Howell, J. R., 2008, “Complete Modeling of a Light-pipe Radiation Thermometer in a Rapid Thermal Processing System”, Proceedings of 2008 ASME International Mechanical Engineering Conference and Exhibition, Boston, MA, USA.
Erturk, H., Ezekoye, O. A., and Howell, J. R., 2008, “Reverse Monte Carlo Modeling of Signal Transport in Light-pipe Radiation Thermometers”, Proceedings of 2008 ASME Summer Heat Transfer Conference, Jacksonville, FL, USA.
Erturk, H., Gamba, M., Ezekoye, O.A., and Howell, J.R., 2008, “Validation of Inverse Boundary Condition Design in a Thermometry Test Bed”, Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 109, pp.317-326. (SCI) (link to article)
Erturk, H., Ezekoye, O. A., and Howell, J. R., 2004, “Boundary Condition Design to Heat a Moving Object at Uniform Transient Temperature”, ASME Journal Manufacturing Science and Engineering, vol. 126, pp.619-626. (SCI) (link to article)
Howell, J. R., Daun, K. J., Erturk, H., Gamba, M. and Hosseini Sarvari, M., 2003, “The Use of Inverse Methods for the Design and Control of Radiant Sources”, JSME International Journal, Series B, Fluid and Thermal Engineering, vol. 46, pp.470-478. (SCI-E) (link to article)
Daun, K. J., Erturk, H. and Howell, J. R., 2002, “Inverse Methods for High Temperature Systems”, Arabian Journal for Science and Engineering, vol. 27, no 2C, pp. 3-48. (SCI-E) (link to article)
Erturk, H., Ezekoye, O. A., and Howell, J. R., 2002, “The Application of An Inverse Formulation In The Design of Boundary Conditions for Transient Radiating Enclosures”, ASME Journal of Heat Transfer, vol.124, pp. 1095-1102. (SCI) (link to article)
Erturk, H., Ezekoye, O. A., and Howell, J. R., 2002, “Comparison of Three Regularized Solution Techniques in a Three-Dimensional Inverse Radiation Problem”, Journal of Quantitative Spectroscopy and Radiative Transfer, vol.73, pp. 307-316. (SCI) (link to article)
Gamba, M., Erturk, H., Ezekoye, O. A., and Howell, J. R., 2002, “Modeling of a Radiative RTP-type Furnace through an Inverse Design: Mathematical Model and Experimental Results”, Proceedings of 2002 ASME International Mechanical Engineering Conference and Exhibition, New Orleans, LA.
Erturk, H., Gamba, M., Ezekoye, O. A., and Howell, J. R., 2002, “Design of A Rapid Thermal Processing Chamber Using an Inverse Formulation”, Proceedings of 2002 ASME/AIAA Joint Thermophysics and Heat Transfer Conference, St. Louis, MO.
Erturk, H., Ezekoye, O. A., and Howell, J. R., 2002, “The Use of Inverse Formulation in Design and Control of Transient Radiant Systems”, Proceedings of 2002 International Heat Transfer Conference, Grenoble, France.
Erturk, H., Ezekoye, O. A., and Howell, J. R., 2001, “Inverse Design of a Three-Dimensional Furnace with Moving Design Environment”, Proceedings of 2001 ASME International Mechanical Engineering Conference and Exhibition, New York City, NY.
Erturk, H., Ezekoye, O. A., and Howell, J. R., 2001, “Comparison of Three Regularized Solution Techniques in a Three-Dimensional Inverse Radiation Problem”, Proceedings of ICHMT Third International Symposium on Radiative Heat Transfer, Antalya, Turkey, eds. M. P. Mengüç and N. Selçuk, Begell House, New York.
Erturk, H., Ezekoye, O. A., and Howell, J. R., 2001, “Inverse Transient Boundary Condition Estimation Problem in a Radiating Enclosure”, Proceedings of 2001 ASME National Heat Transfer Conference, Anaheim, CA.
Erturk, H., Ezekoye, O. A., and Howell, J. R., 2000, “Inverse Solution of Radiative Transfer in Two-Dimensional Irregularly Shaped Enclosures”, Proceedings of 2000 ASME International Mechanical Engineering Conference and Exhibition, Orlando, FL.