Monte Carlo Modeling of Effective Emissivities of Blackbody Radiators

To satisfy the computational needs of blackbody-related projects, a range of Monte Carlo modeling codes that allow calculating the spectral effective emissivities of blackbody cavities have been developed. The modeling programs use the ray-tracing engine of a commercial software STEEP3 modified to avoid restriction on cavity axial symmetry. Two reflection models are currently supported - uniform specular-diffuse (specular component does not depend on incidence angle) and Lambertian-Fresnelian (specular component varies according to Fresnel's equations). Temperature distribution is set by values entered for the arbitrary arranged nodes.

Certain commercial software is identified on this web page in order to specify the computational procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the software identified is necessarily the best available for the purpose.

Example 1: Cylindrical Blackbody cavity with conical bottom.

Numerical modeling was performed for a graphite cavity - crucible used for fixed-point blackbodies [1]. The cavity is nearly isothermal and has cylindro-conical shape with the cross section as shown below.

Fixed-Point Blackbody Crucible with Cylindro-Conical Cavity

Figure 1. Fixed-Point Blackbody Crucible with Cylindro-Conical Cavity

The computed dependences of normal effective emissivity on diffusity (ratio of diffusely reflected flux to its total value) of the cavity internal surface for various values of emissivity are shown in the right-hand graph.

Effective Emissivity Computed for Various Combinations of Reflectance and Diffusity of Internal Surface of Isothermal Cylindro-Conical Cavity

Example 2: Cylindrical Blackbody cavity with Inclined Bottom

The Monte Carlo method was also applied to the modeling of the radiative properties of a specular-diffuse isothermal blackbody cavity shaped by a cylindrical generatrix, a flat inclined bottom and a flat diaphragm. The European Standard EN 12470-5:2003 prescribes this shape for blackbody radiation sources intended for calibration of clinical ear thermometers.

Cylindrical Cavity with an Inclined Bottom

The dependences of the normal effective emissivity on the bottom inclination angle were studied for different cavity depths and various values of the diffuse component of the cavity wall reflectance. The distributions of the local normal effective emissivity over the cavity aperture (see right-hand pictures) and the dependences of the integrated effective emissivity on the distance between the aperture and the radiation detector were computed. The numerical experiments performed enable selection of optimal geometrical parameters for improving the radiometric performance of such blackbodies [2].

Specular Cavity with Inclined Bottom

Diffuse Cavity with Inclined Bottom

Distributions of the local normal effective emissivity over the cavity aperture for β = 30°, R = 1, Ra = 0.5, H = 8, ε = 0.5, D = 0 (top) and D = 1(bottom). Because of symmetry, only the right halves of the distributions are shown.

Example 3: V-grooved flat plate Blackbody

Emitters with grooved surfaces are widely used as reference sources in radiation thermometry and radiometry. In the design phase of such devices it is important to be able to predict their performance. Monte Carlo based modeling software has been developed for effective emissivity of radiators with concentric grooves of trapezoidal and triangular profiles.

Thermal Radiator with Concentric V-Grooves

The angular dependences of effective emissivity of a radiator with concentric triangular and trapezoidal grooves have been computed for various values of the diffuse component. The dependences of normal effective emissivity on the angle β for triangular and trapezoidal grooves with different values of diffusity are shown in the right-hand graphs.

Grooves with isothermal and non-isothermal walls were modeled [3]. It was shown that a temperature drop towards the peak of a groove might lead to substantially decreased effective emissivity.

The Normal Effective Emissivity of Isothermal Grooves vs. Groove Angle

The normal effective emissivity of isothermal grooves vs. angle β: (a) and (b) - triangular grooves (ft = fb = 0); (c) and (d) - trapezoidal grooves (ft = fb = 0.1); (a) and (c) - diffusity D of groove walls is independent of incidence angle; (b) and (d) - diffusity D ranges from the values of 0, 0.25, 0.5, 0.75, 1, respectively for normal incidence and linearly decreases down to 0 for the incidence angle of 90°. For all cases ε = 0.7.

References

Effective emissivity of a cylindrical cavity with an inclined bottom: I. Isothermal cavity,
A.V. Prokhorov and L.M. Hanssen,
Metrologia 41 (2004) 421-431

Emissivity modeling of thermal radiation sources with concentric grooves,
A.V. Prokhorov, S.N. Mekhontsev, and L.M. Hanssen,
High Temp. High Pres. 35-36(2), 199-207 (2003-2004).

Radiation properties of IR calibrators with V-grooved surfaces,
A.V. Prokhorov, L.M. Hanssen, and S.N. Mekhontsev, Thermosense XXVIII, ed. by J.J. Miles, G.R. Peacock, and K.M. Knettel,
Proc. of SPIE 6205, 620505 (2006).