Additional Hydraulic Loss Caused by AF Solid in Impeller

I. Dynamic Balance Equation of Particles in Impeller Channel

When the solid-liquid mixture moves in the rotating channel, the particles whose size is larger than the critical ruler are separated obviously. Smaller particles participate in turbulent mixing, and their presence does not affect hydraulic loss.

The mixing process of Zhengxin is mostly Eastward-Moving and does not coincide with the flow line in the impeller passage along the volume and liquid rest: the work consumed by the solid particles relative to the fluid-carrying motion is determined under the particles moving along the trajectory. Firstly, the relative motion of a single solid particle in the flow passage between blades is studied, which is a stable motion. The force acting on the particles is projected to the tangent direction of the relative trajectory.

The volume and density of solid particles are expressed by QT and PR respectively. The velocity of particles along the relative trajectory is wt. Write out the dynamic equilibrium equation of solid particles, i.e.

In this formula, the projection of inertia force of solid particles in relative velocity direction is considered on the left side, and the sum of forces produced by centrifugal force, pressure gradient and the force produced by the head-on resistance of particles in relative fluid motion is considered on the right side.

Because the motion of solid particles along their trajectories is studied, wrdt = ds, DWR / dt = dScosg / 2 = dR (in formula, DS is the small length of solid particle trajectories).

Thus, the particle dynamic equilibrium equation can be written as

In the range of parameters from impeller inlet to impeller outlet, the upper integral is obtained.

Relative velocity of solid particles at impeller outlet and inlet;

The functional OT representation of the head-on drag of solid particles moving along relative trajectories is obtained.

This part of the work determines the hydraulic loss, which is related to the solid particles moving along their respective trajectories (not coinciding with the liquid streamlines) and not participating in the turbulent mixing process. In the obtained formula, the pressure drop (pr-P!) is replaced by its expression.

Work consumed to overcome head-on resistance

2. Total loss in impeller

The total loss of HX of solid-liquid mixture flowing in impeller is the sum of the loss of HN in impeller when pumping fluid and the additional loss of Ohx caused by the relative motion of solid particles re-participating in turbulent mixing. Therefore, HK = HXO + Ohr.

The volume concentration of particles which continue to move with the mixture and participate in turbulent mixing is expressed by P1, while the volume concentration of particles whose size is larger than the critical size and moves along its own trajectory is expressed by P2, and the total volume concentration of solid particles in the mixture is P=P1+P2.

The number of particles passing through the impeller in a unit time is equal to P2Qr/qT (in this case, Qr is the flow rate of the pump). The corresponding work consumed per unit time is equal to P:QraT/gr.

Work done to overcome the head-on resistance of solid particles that do not participate in turbulent mixing and to transport solid-liquid mixtures per unit weight

The ratio of work is the additional head loss of impeller, which is related to the solid particles existing in the carrier fluid and the relative motion of the fluid in the impeller channel. So, get it.

By using formula (3-5-7), the following formula can be obtained.

The following conclusions can be drawn from formula (3-5-8):

(1) The gradation of suspended solids plays an important role in determining head hydraulic loss. When suspended solids are composed of particles larger than critical particles, i.e. P, = 0, the gradation does not affect the additional head loss, which is related to the presence of solid particles in the mixture.

(2) When the pump head increases, i.e. (u3-uf)/2z term increases, the additional head loss in impeller increases.

(3) It should be noted that the second and third terms in the brackets on the right side of the formula are much smaller than the first term, so the additional head loss in the impeller changes little when the flow rate of the pump changes.

(4) When the suspended solids are pumped, when all the particles are smaller than the critical particles, i.e. P:=P, there is no additional loss. At this time, the mixture can be regarded as homogeneous liquid.