Terahertz Radar Inversion for Range-Resolved Solids Concentration Profiling in Gas--Solid Flows

Abstract: A stable inversion method is developed to reconstruct millimeter-scale solids-concentration profiles in particulate suspensions from monostatic sub-terahertz frequency-modulated continuous-wave (FMCW) radar measurements. In industrial particulate flows, cumulative attenuation renders the direct inversion of the path-integrated volume-scattering radar equation ill-conditioned. The method resolves this by an ensemble-averaged Mie-scattering closure coupled to a stable backward-integration scheme, yielding an analytical solution for the range-resolved solids concentration without case-specific parameter fitting against reference concentration measurements. The required range-dependent system response is determined by absolute near- and far-field calibration via external substitution with an electrically large metallic sphere. The method was evaluated against solids-volume-fraction estimates derived from differential-pressure measurements in a 3.1 m-tall circulating fluidized-bed riser operated with ambient air and copper powder (median diameter 32.6 $μ$m, density 8920 kg m$<sup>{-3}$). The radar-derived and pressure-derived profiles agreed well across three superficial gas velocities producing distinct axial solids distributions, and the radar indicates sensitivity down to solids volume fractions of order $10<sup>{-6}$.