Flow-field and steady state

Simulations made with the full transient approach are carried on in time until convergence of the flow field to a pseudo-steady state is achieved. Pseudo-steady state corresponds to a periodic steady state in which only periodic fluctuations of the flow field are observed that depend on the blade frequency. The behavior of the CSTR is characterized with reference to this condition. Figures 4.5, 4.6 and  4.7 show the flow field for the different simulations when pseudo steady state is achieved. Radial and vertical components of velocity are presented for a section of the reactor that contains the baffle. Simulations are presented for increasing Reynolds number. For each simulation, the flow field in the vertical section ($v_r$ and $v_z$ components), the rotational motion ($v_{\theta}$ component) and the upflow profile calculated for the cylindrical body are shown. Flow field representations can be directly compared for the different simulations, since the same scale is used for the velocity vectors and for the velocity contours. Vector fields are used to represent the intensity and extent of the secondary circulation flow within the reactor. Contour plots are used to represent the primary circulation. From these pictures, the relative intensity of the secondary circulation with respect to the flow field in the rest of vessel can be appreciated even if the impeller is not in the same position for the different simulations. The vortical structures developing from the discharge jets generated from the impeller are responsible for the propagation of the flow to the rest of the vessel. A larger region in the vessel is stirred when the value of the angular velocity is larger (simulations S2, S4 and S6). The same behavior is found for the primary circulation. For each fluid examined (glycerol, water and glycerol solution and water), rotation of the impeller is transferred to larger regions of the vessel if the angular velocity is increased. Furthermore, a larger extension of these regions is found as the viscosity of the fluids is reduced. Simulation S6 shows that rotation of the impeller is transferred to the entire vessel when the Reynolds number is 108000.

Direct comparison of the generated flow fields can be made also by comparison of the upflow curves. The mass of fluid moving upward across a section normal to the rotation axis (x axis) is shown versus the distance of the section from the bottom of the vessel (y axis).

Upflow calculations are made only for sections in the cylindrical body of the vessel. The shape of upward profile is different for the different simulations. The absolute value of upward flow is a function of the rotation speed (larger values are found for simulations S2, S4 and S6, for which rotation speeds are 200, 180 and 200 RPM, respectively). For simulations S1, S2, S3 and S4, for which the Reynolds number is less than 4600, a sudden drop is observed in the upflow profile when z is around $0.20-0.25~m$. In the upper part of the reactor, only weak flow fields are produced for values of the Reynolds number less than $4600$. This can be observed from the flow field distribution within the vessel. Only for simulations S5 and S6, significant values of velocity field are found up to the upper part of the vessel.