Analysis and correlation of fluid acceleration with vorticity and Liutex (Rortex) in swirling jets

The characteristics of acceleration a and its correlation with vortex core in swirling flow have been analyzed in detail. Swirling flows of four swirl numbers (Sn = 0, 0.1, 0.2, 0.36) are simulated by direct numerical simulation, and a number of fluid mass particles issued from the inlet of swirling flow have been traced as a database for current study. Correlations of acceleration a with vortex identification criteria of R and ω have been quantified. Herein R is the ‘Liutex’-method proposed by Prof. Liu, and its early version is ‘Rortex’. The probability density functions of included angles of a ∼ R and a ∼ ω are computed which are used to clarify the geometrical configuration between a and R. The covariance coefficients between a and various vortex core criteria (Q, λ2, ΩL, ΩR, ω and R) have been computed and their relative levels of correlation are compared. Compared to velocity, the expectation and r.m.s of acceleration magnitudes and its projections on R and the plane perpendicular to R are computed for better explain the correlation features between a and R. It is found that a and R are always either perpendicular or parallel to each other with quantized included angles of ∠(a, R) = π/2, (k = 0, 1, 2). This confirms the role of R which works as the axis of vortex exclusively.