3.1.3 Cavity under different gas superficial velocities
The cavity appears in the upper of the gas upstream. Its size grows when the gas superficial velocity increases(Fig 3 and Fig.7).
The cavity formation is analyzed by the particle normal forces inx and z directions. In the x direction, the gas-solid force pushes the particles away from the gas upstream of the bed. The particle normal force in x direction in the gas upstream when cavity appears. Many researches distinguish the appearance of the cavity by this method. In the z direction, the gas flows upward near the gas upstream in the feed influence zone. The gas-solid force stops the particles from moving down. In this paper, can also be taken as the signal of the cavity occurrence.
(a) Particle normal force in x direction
The particle normal force in x direction is taken to be zero when cavity appears. Under the same gas superficial velocity, the gas-solid force seems to be unvaried. As the bed width of left/right area in Type RB is smaller than Type RA, the particles have low movement in axial direction in Type RB.
As the particle normal force in x direction is hardly measured in experiment, it is mainly discussed by theoretical method, which is described in Appendix . In type RA, the cavity is firstly assumed to occur before the pinning. The pressure drop is 437 Pa by computation when in equation (A13) of Appendix , corresponding to 0.15 m/s. In this condition, the pinning appears according to equation (2). The assumption is invalid and then the cavity appears after the pinning. In equation (A14) of Appendix , the critical pressure drop is 630 Pa, corresponding to 0.23 m/s.
In the same way, the critical pressure drop can also be determined in type RB. Through calculation, the pinning happens before the cavity. The cavity appears when pressure drop is 660+660 Pa (left and right beds), corresponding to 0.39 m/s.
Under the same conditions, the critical gas superficial velocity of cavity is improved from about 0.23 to 0.39 m/s. The experimental results is 0.29 to 0.39 m/s, which has the same trends with the calculation results. The cavity is eliminated by the gas-solid baffles in type RB in terms of the particle normal force in x direction, especially when the baffles located at x /L =0.5.
(b) Particle normal force in z direction
One signal of the cavity occurrence is the particle normal force in z direction becomes zero at the ends of the gas upstream Johnson net.
The gas axial velocity distribution can be computed by CPP method30, which is explained in Appendix . Indicated by Fig.8, near the gas upstream Johnson net x /L =0, the gas axial velocity has a maximum value. It increases with the growing of the gas superficial velocity. Meanwhile, the gas axial velocity decreases greatly when the gas-solid baffles are used. It denotes the baffles restrain the gas axial velocity in the feed influence zone and then the cavity is eliminated.
In detail, the particle normal force in z direction is mainly influenced by the gas-solid drag, the particle gravity and the particle-wall frictional forces. The equivalent particle acceleration is introduced to considering the active forces: gas-solid drag, the particle gravity. Only when the , (equation (5)), the cavity may occurs. The equivalent particle acceleration is computed by equation (6). The coefficient C 2 is introduced to consider the difference between the average and local gas velocity, the experimental error. The computed critical gas superficial velocity of cavity improved from about 0.29 to 0.52 m/s when C 2=2.56. Through calculation, the baffles have greatest effects on cavity when placed atx /L =0.5.
(5)
, (6)