Hopper-Standpipe-Discharger Flow

As mentioned, the flow rate in a standpipe depends on the solid feed device as well as the flow control valve. In this section, we discuss the gas-solid flows in a simple standpipe system where the feed device is a mass flow hopper and the solid flow regulator is a discharge orifice [Chen et al., 1984]. As shown in Fig. 8.15, the entrance of the vertical standpipe is connected to a conical hopper feeder of half angle pw, while a discharge orifice is located at the bottom of the standpipe. Here, two representative solids flow patterns are considered. One is a dilute suspension flow, and the other is a solid moving bed. In this case, the following additional assumptions are needed  

In the transition region I (2-3), the mass balance of solids requires (1 - a3 Mzp3As = -(1 - a2 MRP2Ach 

Note that wRp2 is the radial velocity in spherical coordinates while Mzp3 is the axial velocity in cylindrical coordinates 2 = amb and Ach is the surface area of the spherical cap near the exit of the hopper, whereas As represents the cross-sectional area of the standpipe. Ach is related to As by 

Similarly, the mass balance of gas (assumed incompressible in this region) requires 

By neglecting the wall friction in the transition region, the momentum balance of solids in the axial direction is given by 

---

In this section, we introduce the theories of moving bed flows in hoppers and general standpipes. The hopper flow theory may be extended to the cases of moving bed flows through a discharge valve. A unique hopper-standpipe-discharger flow system is then discussed as an example of the application of these theories. Multiplicity of steady flows in a standpipe system is also illustrated. 

---