In the fast reaction category, the turbulent reactive mixing strongly affects the reaction products yield and distribution. The present work adopts a high-efficiency vortex structure induced by a novel static mixer hollow cross disk (HCD) to enhance the turbulent reactive mixing within the tubular turbulent flow. Specifically, the direct quadrature method of moments (DQMoM) coupled with the interaction-by-exchange-with-the-mean model (IEM) is utilized to simulate the consecutive competitive reactions system in this tubular turbulent flow. In order to quantitatively evaluate the enhanced mixing effect of the HCD, the turbulent reacting flows in the Kenics static mixer and coaxial jet mixer have also been studied. A combining analysis of turbulent flow field and the chemical species distribution indicates that the turbulent mixing enhancement mechanisms of these two static mixers. The simulation suggests that the sinusoidal wave structure in the HCD generate an important flow structure-counter vortex pairs (CVPs), which increases the momentum exchange between the near-wall region and the flow core. Moreover, the spatial distribution of the mixture fraction and reaction product concentration in these configurations agrees well with its turbulent flow field characteristics. The improved turbulent mixing initially is located at the jet periphery when at 0 < z/D < 2, which fits well with the HCD's longitudinal evolution of turbulent energy dissipation. Whereas at z/D > 2, CVPs of the HCD ameliorate the near-wall area's turbulent mixing and thus increase the reaction productivity and selectivity. Additionally, the effects of flow rate on segregation index are studied to suggest that the improvement of Xs for HCD is of about 35% relative to the original tubular flow.