(143a) A New Method for Decomposition of High Speed PIV Data and Calculation of Granular Temperature for High Concentration Particle Flows

A high speed particle image velocimetry (PIV) system has been developed by the USDOE National Energy Technology Laboratory (NETL) to observe and measure particle flow fields at high particle concentrations. Previous techniques for simultaneous measurement of particle velocity and concentration in particle flow fields acquired particle velocity data at sample rates (for velocity vectors) in the range of 100 to 1000 samples per second. The NETL high speed PIV system achieves sustained sample rates in the range of 100,000 to 1 million samples per second. With higher sampling rates, the full range of temporal scales of particle flow fields can be resolved for flow fields up to 100 m/s. CFD models of particle flow fields often use methods similar to the Reynolds Decomposition for single phase flows to decompose particle velocity time series data into mean and random fluctuating components. The fluctuating component is used to calculate important modeling parameters such as granular temperature and particle stresses. In the past, the random fluctuating component of velocity was calculated by subtracting individual particle velocities from either the total average velocity or a frame averaged velocity (an average of all velocity vectors in a camera frame). However, both lead to unacceptable uncertainties. Using the total average includes low-frequency flow structures and using a frame averaged velocity undersamples the velocity data. Even at the highest sampling rates achieved, the number of velocity vectors in each frame is often too low to yield an accurate local average. The decomposition method developed in this work decomposes particle velocity into several components that describe the full range of temporal structures in a particle flow field. A small averaging window is used to calculate a local average velocity for use in velocity decomposition. The size of the local averaging window (in number of camera frames) must be large enough to include enough velocity samples to calculate an accurate local average, but small enough to exclude low frequency fluctuations caused by larger flow structures, such as particle clusters. Decomposition of HSPIV measurements of particle flow fields in several risers at two different laboratories produces the expected Gaussian or exponential distributions of random fluctuating velocity. This indicates that the local averaging method developed in this work accurately decomposes particle velocity measurements.