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
Gt G a C(k, m) d D d* Dso I M n n* Nc NR P r R(k, m) Rc(k) Rl(d) RR(m) SSEQ SSEL Sc So SR Ss mixing coefficient (defined by Eq. ( )) standard deviation mixing coefficient (defined by Eq. ( )) sample grayseale covariance (defined by Eq. ( )) distance (defined by Eq. ( )) divisor (defined by Eq. ( )) value of d for which Rt(d) approaches zero. mass median diameter intensity of segregation (defined by Eq. ( )) sample size (defined by Eq. ( )) number of contiguous pixels value of n for which SSEQ/SSEL is maximized number of columns of pixels number of rows of pixels number of pixels per linear distance radius of Cold Flow Model sample correlation function (defined by Eq. ( )) column correlation function (defined by Eq. ( )) isotropic correlation function (defined by Eq. ( )) row correlation function (defined by Eq. ( )) residual sum of squared errors from the least squares fit of the quadratic model to Eq. ( ) residual sum of squared errors from the least squares fit of the linear model to Eq. ( ) sample grayscale variance (defined by Eq. ( )) column scale of segregation (defined by Eqs. ( ) and ( )) Danckwerts' scale of segregation (defined by Eq. ( )) row scale of segregation (defined by Eqs. ( ) and ( )) scale measure developed in this paper (defined by Eq. ( ))
Correspondence to: B. K. Gullett Y Yi.j sample variance of contiguous pixels (defined by Eq. ( )) normalized variance function (defined by Eq. ( )) sample grayscale mean (defined by Eq. ( )) grayscale value at pixei (i,j)