(150h) Kutta-Joukowski Force: The Radial Distribution of Particles Concentration in a Riser

The most desirable gas-solid
distribution in a riser is quite uniform in both axial and radial directions.
However, the particle concentration presents quite dense in the wall area while
dilute comparatively in the riser center. In other words, it assumes a typical
annular-core structure. The annular-core is obviously disadvantageous to the
contacting of gas-solids two phases in the riser. It is necessary to explore
the occurrence mechanism of the annular-core in order to further improve the
gas-solid contacting condition.

Researches covering the
occurrence mechanism of the annular-core are quite limited. Except for some
qualitative description, the occurrence of the core-annular structure was
usually simply contributed to the velocity gradient in the boundary layer or
drag force. However, these researches do NOT analyze the force(s) exerted on
the particle(s) in the riser.

In this paper, the
aerodynamic theory is used in the two-phase flow analysis. A transverse force
on the particles, the Kutta-Joukowski force, is introduced to explain and
quantify the formation of the core-annulus in riser. This force is the function
of particle velocity curl, the slip velocity and the gas density.

The mechanism of the
Kutta-Joukowski Lift is the same as that of the Magnus force. However,
combining it with the Stokes theorem in classical single-phase hydrodynamics,
the scale of the object can be extended from an individual particle to a
particle group that is enclosed by any closed curve.

In a riser, the
Kutta-Joukowski force exerts on a group of particles per unit length is
expressed by Eq.(1)

                                                                                             
                     (1)

The Kutta-Joukowski
force can be used to explain the generation of the annular-core flow in a
riser. As shown in Fig.1, consider the direction of the slip velocity, the
relative velocity between the particles and the gas is illustrated by the arrow
CD. In the fully developed zone of a riser, the gradients of particle velocity conform
to =0 and <0, then >0. The vortex
strength is positive, corresponding to an anti-clockwise velocity circulation
as illustrated by the circle 1 in Figure 1. Therefore, the direction of the Kutta-Joukowski force on particles is towards the riser wall. The
annular-core structure is then formed by this force.

In this paper, the
particle velocity gradient was obtained with fiber-optical probe. As to the
slip velocity, the formula proposed by Yang (1993) was used.

Fig.1 Kutta-Joukowski force on particles in a riser

In the cold model
experiment, the riser is a plexiglass pipe with an ID of 100 mm and its height
is 11m. The lift gas and the fluidizing gas are atmospheric air and are all
supplied by the Roots blowers. Their flowrates are controlled by a series of
rotameters. The superficial velocity of the riser ranges from 6.02~12.03m/s;
while the solid flux in the riser is controlled in a range from0~155kg/m²s.The
particles are typical FCC catalysts. The particle density is 1500kg/m³,
while the mean diameter is 60¦Ìm.

A PV-6 Particle Velocity/Concentration
Analyzer connecting with a small probe was used to determine the local solids volume
fraction and particle velocity simultaneously.

Based on the measured
distributions of the local particle velocity and concentration, the
Kutta-Joukowski force on the particles per unit area is then computed.

It is clear seen that
the local density has close relationship to the Kutta-Joukowski force. Local
density assumes an evident monotonic functional relation to Kutta-Joukowski
force. This force increases with r/R and reaches a maximum near the
riser wall. In the area r/R=0~0.5, the values of both Kutta-Joukowski
force and the local solids holdup are relatively low while they increase
sharply in r/R =0.5~1 with a similar gradient. It demonstrated that the
Kutta-Joukowski force directly contributed to the annular-core structure.

Furthermore, based on
the experimental results, the empirical correlations for Kutta-Joukowski force
are proposed.