Millimeter-Wave Interferometry for Opaque Particle-Laden Flows

A novel method to measure the concentration of particles in optically opaque particle-laden flows is presented. This method is based on the principle of millimeter wave interferometry, using a fully-integrated frequency modulated continuous-wave (FMCW) radar operating between 77 and 81 GHz to measure path-integrated particle concentrations between the radar and a reflector. The instrument is capable of quantitative, high-speed (20 kHz) path-integrated concentration measurements in dispersed multiphase flows with concentrations one to two orders of magnitude higher than those at reach with state-of-the-art optical methods. The interferometer was demonstrated and calibrated for path-integrated number concentrations up to $(4.36 \pm 0.24) \times 10^8 \mathrm{~m}^{-2}$ using glass microspheres with a mean diameter of $109.2 \mu \mathrm {m}$ . Two independent measurements of particle size distribution (PSD) were performed using X-ray microtomography and dry sieving. The calibration setup relied on high-resolution particle shadowgraphy applied to individual thin particle streams and used multistreams superposition to reproduce large optical depths in a controlled particle-air mixture. The instrument exhibited excellent linearity and low error during the calibration, with a phase shift-to-number concentration slope of $(1.378 \pm 0.043) \times 10^{-7} \mathrm{~m}^2$ , validating the measurement concept and paving the way for practical applications. The leading uncertainties are discussed, providing guidelines for exploiting the measurement concept without necessarily performing a direct calibration.