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the impact of the gap between the impeller
and shroud on the performance of single-
blade impellers. These studies demonstrate
that a well-maintained gap minimizes effi-
ciency losses, emphasizing the importance of
regular gap adjustments throughout the
pump’s lifecycle. Yang Y. et al. [4] further in-
vestigated the effects of tip clearance in
three-blade impellers, describing the forma-
tion of vortices due to leakage flows. Their
research suggests that adjusting the clear-
ance can influence pump performance.
Overall, while the use of a stationary front
shroud may slightly decrease efficiency, its
benefits in preventing blockages make it
a valuable component in many sewage
pump designs.
Reducing the number of blades is benefi-
cial for increasing free passage, but it pres-
ents challenges during the design stage.
Standard design theories often assume uni-
form flow patterns, which are not present in
two-blade or single-blade impellers. Mini-
mizing the number of blades is associated
with several issues, including high levels of
fluid-induced vibrations that increase as the
blade count decreases. Furthermore, vibra-
tions induced by the fluid in one-blade and
two-blade impellers can overlap with vibra-
tions caused by mechanical faults, such as
unbalance, bearing misalignment, and
cocked bearings, at synchronous (1x) and
twice synchronous (2x) frequencies. Tan L. et
al. [5] investigated the influence of blade
wrap angle on the hydrodynamic radial
force of asingle-blade impeller. They found
that increasing the wrap angle improved
head and efficiency but narrowed the high-
efficiency operating range. The radial forces
were strongly dependent on the wrap angle,
with asignificant decrease observed as the
wrap angle increased. However, this study
primarily focused on energy characteristics
and did not include experimental validation
of the predicted radial forces or vibration
levels. Wang C. et al. [6] explored the impact
of rotation center eccentricity on radial force
in asingle-blade impeller, aiming to mitigate
large fluctuating forces. While they found that
eccentricity can effectively reduce radial
forces, their study also lacked experimental
validation of the predicted force reductions
and their impact on vibration levels. Kim et al.
[7, 8, 9, 10, 11] and Nguyen et al. [12] opti-
mized asingle-channel impeller to improve
efficiency and reduce unsteady radial forces,
thereby mitigating flow-induced vibrations.
Their optimization process involved modify-
ing the impeller and volute shapes using
Stepanoff’s theory and employing ahybrid
particle swarm optimization and genetic al-
gorithm coupled with surrogate modelling.
CFD simulations, including both steady and
unsteady Reynolds-Averaged Navier-Stokes
equations, were used to evaluate the de-
signs. The optimized design demonstrated
improved efficiency and reduced variable
radial forces, with experimental results con-
firming increased efficiency and decreased
vibration at the blade passing frequency
(BPF). Tan L. et al. [13] investigated asingle-
blade impeller using numerical simulations,
performance tests, and particle image velo-
cimetry (PIV). Their study focused on charac-
terizing secondary flows within the impeller,
including jet-wake structures at the impeller
outlet, which are known to contribute to
losses and induce vibrations. Cui et al. [14]
investigated the correlation between radial
forces, total entropy generation (TEG), en-
tropy generation rate (EGR), and flow-in-
duced vibrations in a single-stage, low-
speed centrifugal pump with a5-blade im-
peller across various operating conditions.
They employed CFD and fluid-structure inter-
action (FSI) analyses and validated their nu-
merical model through experimental mea-
surements of vibrations and energy parame-
ters. The results demonstrated that radial
force, TEG, EGR, and vibration levels were
minimized at the pump’s optimal efficiency
point and increased as operating conditions
deviated from this point. This finding supports
the use of radial force, TEG, and EGR as in-
dicators of flow-induced pump vibrations.
The study also confirmed the previously ob-
served phenomenon of changes in radial
force vector direction with variations in effi-
ciency. Pei et al. [15] utilized FSI simulations
with strong two-way coupling to investigate
unsteady flow-induced impeller oscillations
in a single-blade pump under off-design
conditions. To validate their CFD-FSI model,
they employed proximity sensors to measure
shaft and impeller deformations in the radial
direction and conducted experiments under
various operating conditions. While the strain
values obtained from FSI and experiments
showed good agreement, a phase shift of
half a shaft revolution was observed be-
tween the predicted and measured strain
values. Song et al. [16] investigated pressure
oscillations and radial forces in centrifugal
pumps with single and double-suction impel-
lers. Their results demonstrated good agree-
ment between CFD simulations and experi-
mental data in terms of Q-H characteristics
and pressure oscillations around the spiral
circumference. Furthermore, the study
showed that double-suction impellers effec-
tively reduce pressure oscillations and radial
forces. It is important to note that vibration
problems are not limited to single-blade im-
pellers. Two-blade impellers are also suscep-
tible to significant vibration levels, and exist-
ing research on this specific configuration is
relatively limited. Ma et al. [17] conducted
amulti-objective optimization of atwo-blade
sewage pump impeller, focusing on maxi-
mizing free passage, head, and efficiency.
The optimization variables included impeller
blade angle and volute cross-sectional area,
determined using Stepanoff’s theory. The
optimization process utilized CFD methods in
conjunction with amachine-learning-based
artificial neural network. While the study
achieved improvements in the target hydrau-
lic parameters, it did not explicitly consider
flow-induced vibrations, acritical factor for
two-blade impeller designs. Ren Y. et al. [18]
employed a genetic algorithm to optimize
atwo-blade sewage pump impeller, consid-
ering head, efficiency, and average wear
depth as optimization objectives. Their ap-
proach utilized a coupled Computational
Fluid Dynamics-Discrete Element Method
(CFD-DEM) simulation.
As demonstrated by these previous studies,
effective methodologies for designing two-
blade impellers that simultaneously achieve
increased free passage, high efficiency, and
reduced vibrations are currently lacking. This
research addresses this gap by presenting
a multi-objective optimization framework for
two-blade impellers based on logarithmic
curves (curves with aconstant beta angle).
Methods
A Hydro-Vacuum S.A. pump model
FZF.5.21, equipped with aDN 150 inlet and
aDN 125 outlet in accordance with the EN-
1092 standard, was used for the tests. The
impeller was modified, while the mechanical
drive, volute, and stationary front shroud re-
mained unchanged. Figure 1 illustrates the
Figure 1.
Meridional section and axial view with marked maximum free passage value
Rysunek 1. Przekrój merydionalny iwidok na płaszczyznę prostopadłą do osi zzaznaczoną mak-
symalną wartością swobodnego przelotu
Księga3_25.indb 55Księga3_25.indb 55 20.03.2025 11:39:2520.03.2025 11:39:25