Abstract 675 – Monte Carlo modeling of the thermal radiative behavior of rough coatings

Presented in the session Photothermal Techniques. Theory and Modeling at the 18th European Conference on Thermophysical Properties, Pau, France 31 Aug-4 Sep 2008
Mr Hector Gomarta*+
Dr Benoit Rousseaua
Dr Domingos De Sousa Menesesa
Dr Patrick Echeguta

a CNRS Orléans
Site Haute Température
1D avenue de la Recherche Scientifique
45071 cedex 02, France

*: Corresponding author
+: Presenting author


Surface roughness plays a crucial role in the thermal radiative properties of industrial systems, such as infrared heaters, plate near blackbody references used to calibrate a pyrometric setup. Nevertheless literature usually reports radiative properties simulations only for several wavelengths. In this study, we focus on modeling emissivity over a wide IR-spectral range for surfaces either measured by profilometry or numerically rebuild.

A Monte Carlo Ray Tracing (MCRT) program has been developed to predict the thermal radiative properties of rough opaque materials from the unique knowledge of their complex refractive index and the surface geometry. The evaluation of the directional spectral emissivity can be performed by using the Kirchhoff laws, an indirect method based on energy balance and the knowledge of the directional hemispherical spectral reflectivity. The computing procedure is based on a ray tracing model which assumes that the propagation of the photons at the surface sample follows the geometrical optic approximation. Multiple reflections can occur but neither interference, nor diffraction effects are taking into account.

This approach is applied to rough samples of graphite (C) with different roughness, for which the statistical parameters of the surface are compatible with the application of the geometrical optic approximation, defined by Tang and Buckius, 1998. The statistical analysis of a large set of z-data acquired with an optical profilometer allowed us to characterize the surface roughness that exhibits a near normal height distribution and is nearly isotropic. Slope root mean square of graphite surfaces are contained between 0.15 and 0.8. Rough 3D-surfaces with gaussian height distribution have been numerically generated up to a rms slope equal to 2. This method, proposed by Wu, 2000, rests on FFT of spectral density or auto-correlation function. In our case, a gaussian correlation function, which properly fits the real surface one, is implemented and allows us to generate rough surfaces with controlled parameters such as the height root mean square, the correlation length and slope root mean square.

The complex refractive index takes both material crystallography and temperature effects into account. It plays a crucial role in the MCRT procedure, since it allows calculation of the Fresnel’s coefficient, which governs the ray propagation at the surface. Moreover, the high level of extinction coefficient makes medium opaque for considered wavelengths. The values of the optical index are assessed by a modified form of Drude model, presented by Rousseau et al., 2005. The optical index values of the bulk material are measured for a wide infrared spectral range [20 – 5 000 cm-1 i.e. 500 – 2 µm], at T = 300 K.

In this work we present the evolution of normal spectral emissivity for controlled surface roughness parameters by ray tracing. In order to validate our technique, we have compared simulations for copper 3D-surfaces with those of Bergström et al., 2007, that carried out MCRT for 2D-surfaces with different slope degrees. Both results exhibit a good agreement. In our case, MCRT simulations are applied on graphite numerical surfaces with different roughness in a large spectral domain at room temperature. The normal spectral emissivity of these surfaces is compared with z-data measured from optical profilometry. Normal spectral emissivity of the material obviously increases with slope roughness. However the behavior of emissivity in function of roughness shows that emissivity raises up very slowly for the high values of the rms slope, in particular for the mid-IR domain. Therefore, the influence of slope roughness on emissivity and its spectral response will be discussed.

1. K. Tang, R.O. Buckius, Regions of validity of the geometric optics approximation for angular scattering from very rough surfaces, International Journal of Heat and Mass Transfer, 41, 1998.
2. J.-J. Wu, Simulation of rough surfaces with FFT, Tribology International, 33, 2000.
3. B. Rousseau, D. De Sousa Meneses, A. Blin, P. Echegut, M. Chabin, P. Odier and F. Gervais, High-temperature behavior of infrared conductivity of a Pr2NiO4+? single crystal, Physical Review B, 72, 2005.
4. D. Bergström, J. Powell and A.F.H. Kaplan, A ray-tracing analysis of the absorption of light by smooth and rough metal surfaces, Journal of Applied Physics, 101, 2007.