Mixing quantification by visual imaging analysis

This paper reports on development of a method for quantifying two measures of mixing, the scale and intensity of segregation, through flow visualization, video recording, and software analysis. This non-intrusive method analyzes a planar cross section of a flowing system from an instantaneous data record, thereby eliminating the need for statistical analysis of a large number of point measurements at multiple locations throughout the system to characterize the mixing. The method is applied to a cold flow model of a high temperature, gas/solid reactor so that reactor design and operation can be optimized to promote reaction efficiency. This method may be useful for studying a variety of mixing systems in which multiphase components or tracers are visually distinguishable.List of symbols mixing coefficient (defined by Eq. (17)) - standard deviation - a mixing coefficient (defined by Eq. (16)) - C(k, m) sample grayscale covariance (defined by Eq. (3)) - d distance (defined by Eq. (8)) - D divisor (defined by Eq. (3)) - d^* value of d for which R_I(d) approaches zero - D₅₀ mass median diameter - I intensity of segregation (defined by Eq. (20)) - M sample size (defined by Eq. (16)) - n number of contiguous pixels - n^* value of n for which SSE_Q/SSE_L is maximized - n_c number of columns of pixels - N_R number of rows of pixels - P number of pixels per linear distance - r radius of Cold Flow Model - R(k, m) sample correlation function (defined by Eq. (5)) - R_C(k) column correlation function (defined by Eq. (7)) - R_I(d) isotropic correlation function (defined by Eq. (9)) - R_R(m) row correlation function (defined by Eq. (6)) - SSE_Q residual sum of squared errors from the least squares fit of the quadratic model to Eq. (14) - SSE_L residual sum of squared errors from the least squares fit of the linear model to Eq. (14) - S_y² sample grayscale variance (defined by Eq. (2)) - S_c column scale of segregation (defined by Eqs. (7) and (13)) - S_D Danckwerts' scale of segregation (defined by Eq. (10)) - S_R row scale of segregation (defined by Eqs. (6) and (13)) - S_s scale measure developed in this paper (defined by Eq. (13)) - V_n sample variance of contiguous pixels (defined by Eq. (11)) - V_n^* normalized variance function (defined by Eq. (12)) - sample grayscale mean (defined by Eq. (1)) - Y_i,j grayscale value at pixel (i,j)