Improving the Characteristics of Two-Stage Fuel Pump
by Optimizing the Blades Geometry
Oleg Baturin, Daria Kolmakova, Grigorii Popov and Vasilii M. Zubanov
Department of Aircraft Engine Theory, Samara National Research University, Samara, Russian Federation
Keywords: Screw Centrifugal Pump, Blade, CFD, Optimization.
Abstract: The article presents a refining method for a two-stage screw centrifugal pump by the joint usage of
optimization software IOSO, meshing complex NUMECA and CFD software ANSYS CFX. The pump main
parameters: high-pressure stage rotor speed was 13300 rpm; low-pressure rotor speed was 3617 rpm by
gearbox; inlet total pressure was 0.4 MPa; outlet mass flow was 132.6 kg/s at the nominal mode. This article
describes the process of simplifying the calculation model for the optimization. The parameters of camber
lines of the low-pressure impeller, transition duct, and high-pressure impeller blades for two sections (hub
and shroud) were chosen as optimization parameters. The optimization goal was the increase of the pump
efficiency with preservation or slight increase in the pressure head. The efficiency was increased by 3%.
1 INTRODUCTION
Pumps are the integral part of both industrial
production and everyday human life (Andronov,
2004), centrifugal pumps are used in water supply and
disposal systems. A special place is occupied by the
screw centrifugal pumps as the devices for supplying
liquid components to the rocket engine. In this case,
the turbo-pump unit requires both high performance
and high reliability of operation. It is known
(Ivanov, 2006), more than 70% of crashes of liquid
propellant rocket engines occurred due to the
breakdown in the turbo-pump units.
Currently used turbo-pump units for liquid
propellant rocket engines (LPRE) were designed in
the 1960-1970. The geometry of the pumps was
projected initially by theoretical and empirical
dependencies, and they were designed by expensive
experimental development of the engine/pumps.
A modern CFD programs allows the simulation of
the pump workflow. After validating the simulation
results, these CFD models can be used to study the
effect of the pump parameters on its performance. It
is also possible to optimize the pump using verified
CFD model as a "black box".
An optimization of the pump geometry is carried
out for the following purposes:
1) improvement of the pump performance while
maintaining the pump reliability.
2) providing the same pump performance with
the reduced pump rotor speed. In this case, the
load on the rotor elements of the turbo-pump
unit will be decreased;
3) the combination of the first two approaches.
Investigation of the working process in previous
studies (Zubanov, 2015; Zubanov, 2016) showed the
presence of vortex zones in the high-performance
pumps. The high-performance fuel pump was
adopted as the study subject (Figure 1, 2).
The fuel pump main parameters with water as the
working fluid (based on experiment data) were the
following:
high-pressure stage rotor speed was 13300 rpm,
low-pressure rotor speed was 3617 rpm by
gearbox;
inlet total pressure was 0.4 MPa;
outlet mass flow was 132.6 kg/s at nominal
mode.
Figure 3 shows the meridional section of the fuel
pump, in which vortex zones present in the following
regions:
the periphery of the inlet edge of the low-
pressure screw (LPS) and high-pressure screw
(HPS) (areas 1 and 4);
the periphery of the leading edge of the low-
pressure impeller (LPI) (area 2);
the area closer to LPI stage outlet at the hub
(area 3);
Baturin, O., Kolmakova, D., Popov, G. and Zubanov, V.
Improving the Characteristics of Two-Stage Fuel Pump by Optimizing the Blades Geometry.
DOI: 10.5220/0006889903570364
In Proceedings of 8th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2018), pages 357-364
ISBN: 978-989-758-323-0
Copyright © 2018 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
357
the stagnation zone of the vortex near HPI hub
(area 5).
Vortices in regions 1 and 4 are due to the design
of the screws. But vortices 2, 3 and 5 in the pump are
undesirable. Thus, the decrease of the intensity of
vortices 2, 3, and 5 will increase the efficiency and
pressure head of the pump. This can be achieved by
changing the geometry of LPI, TP and HPI blades.
2 NOMENCLATURE
These are abbreviations of the pump parts (Figure 2):
KID - Knee Inlet Duct;
LPS - Low Pressure Screw passage;
LPI - Low Pressure Impeller passage;
TP - Transferring Passage;
HPS - High Pressure Screw passage;
HPI - High Pressure Impeller passage;
VOD - Volute Outlet Duct.
Figure 1: 3D view of the pump under investigation.
Figure 2: Meridional section of the pump.
Figure 3: The pump meridional section with vortex zones.
3 METHODOLOGY
A proven CFD model will be used from the previous
study (Zubanov, 2016). Water was used as the
working fluid because the experimental test data for
water were available. The proven CFD model ensures
a coincidence of Pressure Head value with
experimental data with the accuracy of 6.9% at
nominal mode, and of Internal Efficiency - 2.0%. The
experimental data are presented in the form of points.
The IOSO program was used as an optimizer
(IOSO, 2017). The optimization algorithm requires
multiple iterations with CFD-model. The mesh model
size has a direct impact on the speed of calculation.
For optimization, it is important to have a mesh model
with the smallest number of elements, which
adequately repeats the pressure and efficiency
characteristics of the pump. This article describes the
process of simplifying the calculation model for the
optimization. A calculation will be performed with
the settings of the basic mesh model for the final
optimal variant of the pump design.
The physical processes in the pump are non-
stationary (Pinho, 2014; Reboud, 2003; NUMECA,
2017). While calculations in a stationary statement
are sufficient for most engineering tasks, the
parameters of efficiency and pressure head vary by
iterations in high-performance pumps for stationary
calculation. It was found in previous studies the time-
averaged parameters of efficiency and pressure head
for non-steady-state calculations coincide with the
parameters averaged over iterations for stationary
calculation. Therefore, further calculations will be
carried out in the stationary statement, with averaging
the last 100 iterations by a specially script. To
calculate one task 600 iterations were used, while the
oscillation of parameters remained constant after 400
iterations (Figure 4). The maximum level of
parameter variation for the last 100 iterations was also
controlled by a special script.
Figure 4: The internal efficiency parameter by the
accumulated time step.
4 OPTIMIZATION ALGORITHM
AND DESCRIPTION OF BLADE
PARAMETERIZATION
IOSO software was used as optimization program
(IOSO, 2017). This program has proven itself in
SIMULTECH 2018 - 8th International Conference on Simulation and Modeling Methodologies, Technologies and Applications
358
many research studies (Jha, 2015; Matveev, 2014;
Yang, 2016). The optimization algorithm for the
investigated pump is shown in Figure 5.
At each step of optimization, the optimizer IOSO
PM generates a Vector of variable parameters x
1
, x
2
,
x
3
, …, x
n
. The Vector describes the geometry of the
LPI, TP and HPI blades in a parametric form. The
Vector of variable parameters is transferred to the
reprofiling block, at which Numeca
AutoBlade (ANSYS CFX-Solver Modeling
Guide, 2011) program perform a conversion of the
blades by Vector data and save them in the form of
geometry files in a *.GeomTurbo format. Then, the
mesh model is created in the Numeca AutoBlade 5
program using new blades. At the next step, the CFD
calculation is performed with the new mesh model.
The processing of CFD-results is carried out by a
special script. As a result, several output files are
created containing pump operation parameters in the
text format. These parameters are then passed to the
optimizer IOSO.
The optimization goal was the increase of the
pump efficiency with preservation or slight increase
in the pressure head. This will reduce the load of the
main gas turbine. It is necessary because the main gas
turbine of the turbopump unit operates in oxidizing
environment (the mass ratio at the gas generator is
more than 56 for oxygen/kerosene components).
Figure 5: The optimization algorithm of the investigated
pump.
The blades fitting was performed in the Numeca
AutoBlade. The parameters of camber lines of the
LPI, TP and HPI blades for two sections (hub and
shroud) were chosen as optimization parameters.
Figure 6 shows the parameterization scheme of the
LPI blades. The camber lines of the LPI, TP and HPI
blades are described by Bezier curves. The camber
line of the LPI blade is described by three points-
poles, while the camber lines of the TP and HPI
requires at least four point-poles. This is due to the
large length of the TP and HPI blades. The
distribution of the cross sections along the blade
height was carried out according to the linear law.
The total number of independent variables was 22.
The pump model with fitted blades was called v0,
and a comparison of its characteristics with the basic
values shows the pressure head differs from the basic
value by 20 m, or 1%, and the efficiency differs by
0.013 or 2%. A good match of the mesh B2Bm2 level
with a mesh B2B0 level is revealed.
Figure 6: 2D parameterization of the LPI blades.
5 SIMPLIFICATION OF THE
PUMP MODEL FOR
OPTIMIZATION
Simplification of the pump model is necessary to
reduce the estimated time of CFD-calculation.
Simplified models were calculated with the
Mass Flow boundary condition, since changing the
geometry of the LPI, TP, and especially of the HPI
can lead to a displacement of the pump
characteristics.
The simplification of the pump model included:
comparison of the results of simulations with
cavitation and without one;
comparison of the results of stationary and
transient simulations of pump workflows;
a study of the pump characteristics behavior,
depending on the mesh model level in the
blades passages (B2B section) and on the
flowpath amounts.
5.1 Simulations Results Comparison
with Cavitation and without One
The phenomenon of cavitation should be considered
in hydrodynamic investigations of the pumps,
because the water hammer effect, arising from the
cavitation, poses a serious risk to the pump reliability.
Also, neglecting the cavitation simulation in pumps
Improving the Characteristics of Two-Stage Fuel Pump by Optimizing the Blades Geometry
359
can lead to obtaining characteristics with a
sufficiently large error of 10-15% (Ding, 2011;
Athavale, 2002). To estimate this error for the pump,
the modeling of working processes with cavitation
was carried out. The simulation was performed with
the basic mesh model. Cavitation settings were the
following:
doubled fluids: primary – liquid, secondary –
vapor;
homogeneous model of multiphase;
cavitation model of Rayleight-Plesset;
bubbles mean diameter is 2 microns;
saturation pressure is 3169 Pa;
volume fraction at inlet: “1” for liquid, “0” for
vapor.
The results of comparison of efficiency are shown
in Figure 7. The pressure head characteristics are
practically the same, and the efficiency with
cavitation is lower by 1.0-2.9%.
Simulation of the pump considering cavitation
took in 1.9 times more processor-hours than
simulations without cavitation. The pressure and
efficiency characteristics are equidistant in the near-
nominal mode. Therefore, the modeling of workflows
in the pump was carried out without considering
cavitation for further research.
Figure 7: The internal efficiency characteristic of the
investigated pump without and with cavitation modeling.
5.2 Comparison of the Results of
Stationary and Transient
Simulations of Pump Workflows
In the «Methodology» section, the specific decision
on stationary modeling with averaging the last 100
iterations was mentioned. This section contains the
rationale for such approach.
The simulation was performed with the basic
mesh model. Settings for the transient modeling:
the time step is 3.7594e-005 seconds. This
value corresponds to 1/10 of the transit time of
the HPI blade channel;
Maximum Number of Coefficient Loops is 10;
Number of Timesteps is 600.
The sustained operation of the pump required 300
iterations. The last 300 iterations (of total 600) were
used for averaging the transient results.
Figure 8 show the pump efficiency for stationary
and transient tasks that differ by less than 0.3%.
The simulation of non-stationary pump operation
was very resource-intensive task by 2.7 times more
than for the stationary simulation without cavitation.
Regarding the foregoing, the simulation of working
processes in the pump was carried out in the steady
state without cavitation for further investigations.
Figure 8: The internal efficiency characteristic of the
investigated pump for steady and transient cases.
5.3 Investigation of the Pump
Characteristics Dependence on the
Mesh Model
The basic mesh model of the vane units contained
2.81 million elements with 81 flowpaths by height.
The number of elements in the B2B section of the
vanes of the basic model was adopted as B2B0 level.
Two levels of B2B meshes were created with a
reduced number of points: B2Bm1 and B2Bm2. The
B2B levels differed by ~1.3 times according to the
recommendations given in (ANSYS CFX-Solver
Modeling Guide, 2011; Marchukov, 2017;
Jha, 2015). The number of points in 3D meshes
depending on B2B level and flowpaths number,
which are presented in Table 1.
Table 1: The number of points in the 3D mesh, X10
6
.
B2B
level
Flowpaths number
81 73 65 57
B2B0 3.08 2.80 2.51 2.22
B2Bm1 2.28 2.10 1.85 1.64
B2Bm2 1.77 1.60 1.44 1.27
All mesh models adequately predict the values
and behavior of the pressure head and internal
efficiency characteristics. Figures 9 and 10 show the
SIMULTECH 2018 - 8th International Conference on Simulation and Modeling Methodologies, Technologies and Applications
360
pressure head and efficiency characteristics of the
investigated pump for several mesh models. The
internal efficiency and pressure head values were
determined at the outlet of HPI stage, to determine the
influence of only the mesh parameters of the blade
elements on the pump characteristics.
The maximum difference of the pressure head at
the nominal mode for B2Bm2_flowpath57 mesh
model was 1% relative to the basic value, and of the
internal efficiency - 0.2% for the for
B2B0_flowpath57 mesh model. The mesh model
B2Bm2_flowpath57 was chosen for the optimization
task because it provides the fastest possible solution
time with the adequate prediction of the pump
characteristics.
Figure 9: The pressure head characteristic of the
investigated pump for several mesh models determined at
the outlet of the HPI stage.
Figure 10: The internal efficiency characteristic of the
investigated pump for several mesh models determined at
the outlet of the HPI stage.
6 OPTIMIZATION RESULTS
The optimization task was performed using B2Bm2
mesh model of blades and mesh models of KID and
VOD from rough mesh of previous study (Zubanov,
2015).
The optimization task of the pump had criteria:
increase in the internal efficiency;
preservation or a slight increase the pressure
head.
The optimization of the pump required more than
200 iterations. The Pareto front «efficiency-pressure
head» was obtained. For a detailed analysis, 2 points
were selected from the Pareto front:
v33 is the variant of the pump with increased
internal efficiency by 3.3% and increased
pressure head by 6.8% at B2Bm2 mesh level
relative to variant v0;
v41 is the variant of the pump with increased
internal efficiency by 5.4% and increased
pressure head by 0.2% at B2Bm2 mesh level
relative to variant v0.
Then calculations of variants v33 and v41 were
performed at B2B0 mesh level. The internal
efficiency and pressure head characteristics with
boundary condition Mass Flow at the outlet are
shown in Figures 11-12. The pressure head of pump
variant v41 is below the basic value at the parity level
of the internal efficiency in comparison with pump
variant v33. In addition, the internal efficiency of the
pump is sharper in the field of high mass flows. The
pump variant v33 seems preferable.
The internal efficiency of the pump variant v33
has the increased value by 3.1% and the increased
pressure head by 0.4% at nominal mode relative to the
basic values.
Figure 13 shows the blade-to-blade sections of
LPI, TP and HPI pump blades of basic and optimized
(v33) versions. LPI blade became more elongated
closer to the exit, the blade of the TP became more
curved, and provides a certain flow angle for the HPS.
The HPI blade underwent major change closer to the
outlet of HPI stage, especially at the shroud. It seems,
that such shape of the HPI blade ensures
compensation of Pressure Head losses in the
periphery of the HPS blade.
Figure 11: The pressure head characteristic of the pump
with boundary condition Mass Flow.
Improving the Characteristics of Two-Stage Fuel Pump by Optimizing the Blades Geometry
361
Figure 12: The internal efficiency characteristic of the
pump with boundary condition Mass Flow.
Figure 13: Blade-to-blade sections of LPI, TP and HPI
pump blades of base and optimized (v33) versions.
Analysis of the pressure head and efficiency
parameters by the pump parts was carried out for the
basic pump, v33 and v41 variants. Changing the
parameters of internal efficiency and pressure
recovery coefficient is shown in Figure 14. The
greatest change occurred in the TP part of the pump.
The pump variant v41 has higher efficiency for
the impeller than the pump variant v33, but v41 has
lower pressure recovery coefficient for the VOD.
Apparently, the calculation on the fine B2B0 mesh
level allowed to calculate the vortices shown in
Figure 3 more detailed.
Since only the LPI, TP and HPI blades were
subject to optimization, the efficiency of the LPS and
HPS blades should remain at the same level or
slightly change. The efficiency of the LPS blades
slightly increased due to the change in the shape of
the LPI blades. At the same time the efficiency of the
HPS blades decreased because of the change in the
velocity triangles associated with the change in the
shape of the TP and HPI blades. In general, the
efficiency of the pump increased by 3.1% with the
increased pressure head by 0.4% due to the
coordinated work of the stages (Popov, 2016).
Figure 14: The parameters of internal efficiency and
pressure recovery coefficient determined for the pump
parts.
7 STRENGTH ANALYSIS OF HPI
BLADE OPTIMAL GEOMETRY
The geometry of the HPI blades was significantly
changed during the optimization. To evaluate the
effect of loads acting on the optimized variant of
geometry, calculations are made to determine the
maximum equivalent stresses in the basic geometry
and in the optimized variant of the high-pressure
impeller. The calculation was carried out in ANSYS
Mechanical. Computational model was the impeller
sector, the cyclic symmetry condition was used. The
calculation did not consider the material ductility.
The pressure values on the solid surfaces were
interpolated from the CFD calculation. The
temperature field was 25 °C, given as constant for the
entire calculation model.
As a result of the calculation of two impeller
variants, the values of the maximum equivalent
stresses were obtained. For the basic variant the
maximum value of equivalent stress
σ_(von Mises stress)_base was 961.6 MPa, for the
optimized variant v33 - σ_(von Mises stress)_opt was
1038.3 MPa.
The material of HPI is chromium-nickel steel
VNL-1. It has the specific stress limit of 1079 MPa
(VIAM, 2017). According to J. E. Shigley
«stress-concentration factors need not be employed
when the material is ductile, and the loads are static»
(Shigley, 2001). According to the recommendations
in (VIAM, 2017) and (ANSYS Mechanical User's
Guide, 2013) «failure is most often declared if
yielding occurs across a complete section».
Therefore, the equivalent stresses region near the
maximum value was considered. A region occupying
1/4 of the maximum stress scale for each case was
SIMULTECH 2018 - 8th International Conference on Simulation and Modeling Methodologies, Technologies and Applications
362
adopted as such region. The equivalent stresses for
the selected region was 722.3 MPa for the basic HPI
blade version and 779.2 MPa – for the optimized v33
version. Then the safety factor for the basic version is
1.49, and for the optimized version is 1.38.
8 CONCLUSIONS
Two optimization studies of powerful fuel pump were
performed. The first optimization task with CFD-
model, which does not contain KID and VOD parts
of the pump, did not allow to significantly increase
the pressure head and internal efficiency.
Nevertheless, optimization with the first CFD-model
correctly predicted the trends in the geometry
variation of the LPI and TP blades. Thus, it is possible
to perform optimization of the pump blades without
VOD part, while maintaining the geometry of the
blades in the stage before the output device. This can
be important for the gradual improvement of the
pump geometry, especially if the number of variable
parameters is limited by the capabilities of an
optimizer program.
The second optimization task provided the pump
with re-profiling geometry of the blades, which allow
to obtain the increased internal efficiency by 3.1%
and the increased pressure head by 0.4% at nominal
mode relative to the basic values.
The strength analysis of the HPI blade was
performed since the HPI blades were greatly changed
at the HPI stage exit area. The maximum equivalent
stresses increased by 76.7 MPa, and the safety factor
of HPI decreased from 1.49 to 1.38.
The obtained reserve can be used to boost the
rocket engine, and/or to reduce the loading of the
main turbine, which operates in aggressive oxidizing
environment.
Further optimization is planned for 3-4 sections
for all blade stages, including screws. Also, conjugate
optimization is planned to consider the strength
model.
ACKNOWLEDGEMENTS
This work was financially supported by the Ministry
of education and science of the Russian Federation in
the framework of the implementation of the Program
“Research and development on priority directions of
scientific-technological complex of Russia for 2014-
2020”.
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