Three-dimensional combined pyrometric sizing and velocimetry of combusting coal particles I Velocimetry

Three-dimensional combined pyrometric sizing and velocimetry of combusting coal particles II: Pyrometry

“…In the current formulation, the term R m refers to an aggregate spectral transfer function of all optical elements between the sensor and imaged object. Following Part I [31] of this work, it is easy to understand that R m most importantly describes the mirrors used in the optical setup. ϵ is the emissivity of the particle and Pλ; T ; t is the Planck radiation emitted by the particle at temperature T , wavelength λ and time instant t. Equation (1) assumes Lambertian char or coal particle surfaces and can be simplified further by introducing the following additional assumptions:…”

“…Radiation from individual char particles can be closely localized in the obtained images. In other words, A s can be substituted with sensor area in the close vicinity of identified particle streaks, as shown in Part I [31], and with a typical setup, the size of the neighborhood depends mainly on the point spread function (PSF) of the imaging system and the size and shape of the imaged particle. More specifically, the integral R A s f cal C λ dA s in Eq.…”

“…(1) becomes the volume under the particle streak model g s x 0 ; y 0 . The assumption of close localization is expected to be valid for fully focused images, which are subsequently preferred with the proposed method (see Part I [31]). …”

“…Equation (2) holds for spherical particles; for aspherical particles, τ h is typically higher than that predicted for spheres. The 1 ms exposure time used in this study (see Part I [31]) seems appropriate for assuming constant particle temperature during exposures. A characteristic time for particle size change is more difficult to derive, but it seems intuitive that, unless a singular event (particle breakup) happens, particle size remains fairly constant during such short times in typical pulverized coal flames.…”

“…Similarly to the techniques cited in Part I [31], apart from digital holography, all of the above mentioned methods operate in small measurement volumes, typically analyzing a single particle. Even with digital holography, the measurement volume is not larger than 10 cm 3 [32].…”