Section 2.1.1 - Centrifugal Pump Theory - Predicting Axial Thrust

Predicting Axial Thrust   The prediction of pump performance is not truly complete
without the corresponding prediction of the hydrodynamic axial and radial thrust that the
impeller(s) can be expected to encounter. A comprehensive treatment of radial thrust
appears in Section 2.1.3, and a review of axial thrust and thrust balancing devices is covered
in Section 2.2.1. However, obscure flow phenomena can profoundly affect the radial
distributions of pressure on the outside surfaces of a shrouded impeller that give rise
to the net axial thrust. These phenomena become even more complex when discharge
recirculation occurs and can cause adverse mechanical response in high-energy pumps,
as will be explained further on. As a basis for tackling such problems, the fundamentals
of axial thrust are presented in Table 4 for shrouded centrifugal impellers that have
leaking fluid flowing in the gaps between the impeller shrouds and the adjacent casing
walls. The positive direction of the thrust T is taken toward the suction or eye of the single-
suction impeller shown. The incoming axial momentum pQV_{z, 1} is generally quite
small for radial impellers and has been omitted from the Table. It serves, however, to
reduce T.

The centrifugal effect of the fluid spinning in the sidewall gaps causes a reduction
in static pressure from the outer periphery (OD) of the impeller to the sealing ring, and
this is quantified in the expressions given for the swirl velocity component V_θ. These

expressions are curve fits to experimental data for the leakage flowing radially inward on
either or both sides of the impeller⁵⁰ and for outflowing leakage as occurs on the back side
(away from the “front” or suction side) of multistage pump impellers due to the higher
pressure arising from the diffusing system downstream of each impeller⁵¹. In the absence
of leakage, the fluid in the sidewall gap rotates at about half the local impeller wheel
speed; that is,V_θ = Ωr/2, and this half speed is typical of the gap flow near the impeller OD,
even in the presence of leakage. The greater the inflow leakage, the lower the pressure
becomes at the entrance to the ring clearance. The major effect is that of swirl or the tangential
component of velocity V_θ, which varies inversely with radius; although casing wall
drag tends to slow it toward half speed. More leakage flow is less influenced by this drag
and so experiences a greater centrifugal effect. This in turn means more pressure drop
from OD to ring. (The leakage rate, of course, is affected, the solutions for both leakage and
pressure distribution being linked and usually requiring iteration.) The opposite effect
happens for outflow on the back side of multistage pump impellers. Here the fluid enters
the sidewall gap at a small radius (see Section 2.2.1) and so with negligible swirl. It flows
outward without picking up much swirl, especially if there is substantial radial outflow
leakage, which means the centrifugal effect is small, yielding a nearly constant pressure
versus radius. The overall result is more net thrust toward suction than might be expected
from a cursory look at the pressure-loaded surfaces.

If wear ring clearances increase during the life of the pump, the net thrust of multi-stage
pump impellers increases. Likewise, unequal ring wear leads to uncertain changes
in the thrust of a “balanced” single- or double-suction impeller with inflow to wear rings
on both sides. Similarly, these theories can be applied to balancing drums and other such
devices described in Section 2.2.1.

Integration of the pressure equation in Table 4 becomes a chore unless the whole theory
is computerized. A quick estimate of the thrust is possible, however, if the distributions of
pressure in the separable domains of the surfaces are assumed to be linear; in that case,
the integration is simple and yields the closed-form results of Table 5. This table also

indicates how to account for each element of the thrust, including the axial momentum
terms, which become significant for higher-specific-speed mixed-flow impellers. In all
cases, in order to proceed with the calculation, the static pressure at the impeller OD must
be known, as it is from the boundary condition imposed at the OD that the rest of the pressure
distribution emerges. Even for substantial leakage, the pressure drop of the fluid
entering the sidewall gaps from the impeller exit is small or negligible; therefore, the
impeller pressure essentially applies in the gap (at the OD) as well. The foregoing methods
of predicting pump head also yield the impeller OD pressure, which is usually between
75 and 80% of the stage pressure rise above inlet.

Thrust computations can therefore be coupled with the head-curve prediction scheme
being employed for the pump, thereby yielding predicted thrust curves together with the
predictions of hydraulic performance.

Predicting Axial Thrust   The prediction of pump performance is not truly complete
without the corresponding prediction of the hydrodynamic axial and radial thrust that the
impeller(s) can be expected to encounter. A comprehensive treatment of radial thrust
appears in Section 2.1.3, and a review of axial thrust and thrust balancing devices is covered
in Section 2.2.1. However, obscure flow phenomena can profoundly affect the radial
distributions of pressure on the outside surfaces of a shrouded impeller that give rise
to the net axial thrust. These phenomena become even more complex when discharge
recirculation occurs and can cause adverse mechanical response in high-energy pumps,
as will be explained further on. As a basis for tackling such problems, the fundamentals
of axial thrust are presented in Table 4 for shrouded centrifugal impellers that have
leaking fluid flowing in the gaps between the impeller shrouds and the adjacent casing
walls. The positive direction of the thrust T is taken toward the suction or eye of the single-
suction impeller shown. The incoming axial momentum pQV_z,...