Higher order statistical analysis of Eulerian particle velocity data in CFB risers as measured with high speed particle imaging

Abstract Velocities of individual particles have been measured in gas-particle flow fields within the risers of two circulating fluidized bed (CFB), one with a 0.305 m diameter riser at the National Energy Technology Laboratory (NETL) and one with a 0.20 m diameter riser at Particle Solid Research Inc. (PSRI). The risers were operated at moderate to high particle concentrations (solid fluxes up to 400 kg/m2s). The NETL riser was operated in the core–annulus regime. The PSRI riser was operated in both the core–annulus and dense up-flow regimes. HDPE particles with a mean diameter of 800 μm were used in the NETL riser and FCC particles with a mean diameter of 80 μm were used in the PSRI riser. Particle velocities were measured with a high speed particle imaging velocimetry (HSPIV) system developed by the NETL. The HSPIV measurement technique has the ability to measure the velocities and trajectories of thousands of particles simultaneously in flows of high particle concentration. In this study, particle velocities are measured in a small two-dimensional field-of-view with dimensions in the range of 1–5 mm wide by 1–10 mm high, with a depth of about 1 mm. The size of the field-of-view is chosen to be similar to the size of CFD grid cells in models used by NETL and small enough that gradients of the mean particle velocity are small over the field-of-view, but large enough to achieve high data sample rates (at least ten velocity vectors per camera frame). In this study sample rates for particle velocity vectors were in the range of 0.1 to 1 million per second. This sample rate provides the high temporal resolution necessary to resolve the complete temporal domain of particle velocity. Particle velocities in each camera frame (at each point in time) are averaged to yield a pointwise instantaneous particle velocity. Using a recently developed particle velocity decomposition technique (Gopalan and Shaffer, 2011 [15]) the pointwise particle velocity time series is decomposed into a varying mean Eulerian component and a random fluctuating component. Statistics of the Eulerian velocity, namely the mean, RMS, skewness and kurtosis, and the granular temperature of the random fluctuating component are presented in this study. Results show that the vertical component of the overall mean Eulerian velocity decreases with increasing mass flux in both the core–annulus and dense up-flow regimes. The root mean square (RMS) of the Eulerian velocity in the horizontal direction is independent of the radial location in the NETL riser. In the PSRI riser, for both the core–annulus and dense upflow regime, the RMS of the horizontal Eulerian velocity decreases monotonically from the center of the riser to the wall. The radial profile of the RMS of the vertical Eulerian velocity for the PSRI riser is parabolic with a peak near r/R ~ 0.5–0.6 for the dense upflow regime. For the core–annulus regime the radial profile of the RMS of the vertical Eulerian velocity is relatively flat for both the NETL and PSRI risers, with a slight decrease near the wall in the PSRI riser. The skewness of the PDF of Eulerian velocity is near zero in the horizontal direction for the dense upflow regime in the PSRI riser, the only Eulerian velocity distribution for which the Gaussian approximation is appropriate. The skewness trends of the vertical velocity distribution are more complex and require further experimental confirmation. The kurtosis of the PDF of the Eulerian velocity is always higher in the horizontal direction than the vertical direction except at the wall of the riser. The 80 μm FCC particles in the PSRI riser showed much higher granular temperature than the 800 μm particles in the NETL riser. The granular temperature decreases monotonically for all conditions from the center of the riser to the wall. granular temperature is anisotropic for all conditions in both risers. The radial profile of anisotropy of granular temperature is relatively flat over most of the NETL and PSRI risers with values in the range of 0.3 to 0.6. Near the wall it decreases for the PSRI riser, while increasing for the NETL riser.