Rotordynamic Force Coefficients for Open and Shrouded Impellers

Rotordynamic Force Coefficients for
Open and Shrouded Impellers

Pascal Jolly, Olivier Bonneau, and Mihai Arghir

1 Introduction

Rocket engine turbopumps are very complex rotating machines with a very low
mass-to-power ratio. This power concentration requires designers to continuously
improve the performance and the reliability of the mechanical components compos-
ing the turbopumps, including impellers. Indeed, the principle of impeller operation
requires the use of gaps – flow paths – where leaks affect both the efficiency of
the turbopump and its stability. In the case of a LH2 turbopump, the pressure rise
provided by each compressor stage must be of several MPa, while the shaft has
to cross critical speeds to reach the operating speed. Therefore, design of LH2
turbompump requires a rigorous rotordynamic characterization in its whole [1]
by providing rotordynamic force coefficients for the rotating parts, among which
bearings, seals, and impellers. Among the available solutions to reduce the cost of
turbopumps, an open (face) impeller can be used instead of a shrouded impeller [2].
The present paper aims to compare experimental rotordynamic force coefficients
produced by both type of impellers, as well as the performance curves.

2 Tested Impellers

The measurements were carried out using the BALAFRE test rig which is dedicated
to the identification of dynamic force coefficients of thin fluid film components.
The test rig, as well as the method used to identify rotordynamic force coefficients,

P. Jolly () · O. Bonneau · M. Arghir
Institut Pprime, CNRS – Université de Poitiers – ISAE ENSMA, Poitiers, France
e-mail: pascal.jolly@univ-poitiers.fr

© Springer Nature Switzerland AG 2021                                            107
S. Oberst et al. (eds.), Vibration Engineering for a Sustainable Future,
https://doi.org/10.1007/978-3-030-46466-0_15

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Fig. 1 Schematic view of the test section with an open impeller

has been described in a previous work [3], so only few details will be given
hereafter. The test facility is mainly composed of a test cell, an electric motor
(180 kW, 6000 rpm max), a hydraulic closed circuit with hot water (50 ◦ C max)
pressurized at 0.5 MPa (with various pumps and tanks), and a programmable logic
controller associated with a DAQ device. The maximum pressure differential is
4.5 MPa. The tested component can have a nominal diameter up to 350 mm. In
many works, known orbiting motions are imposed to the impeller (whirling motion
is produced by an eccentric drive mechanism), and resulting hydrodynamic forces
are measured [4–6]. In [7], measurements are performed using a hydraulic exciter
to impose transient excitations (up to 50 Hz) to the impeller in one direction of
motion (vertical translation). In the present work, the impeller is fixed on the rotor
of a double conical hydrostatic thrust bearing (cf. Fig. 1) that transmits the dynamic
displacements applied by 8 piezoelectric shakers, mounted 4 by 4 in its forward
and rear planes. The volute casing is fixed on a rigid part which is mounted on the
frame of the test cell via three piezoelectric force transducers which constitute a
force balance.
    Two types of centrifugal impellers were tested: open (unshrouded) and closed
(front shrouded). Although the impellers were designed to work with a cryogenic
fluid, water was used as working fluid. All the tests were conducted with a vaned
diffuser. The flowrate of water passing through the diffuser is measured by a Venturi
flowrate meter located at the outlet of the volute. Since the inlet flowrate is also
measured, the leakage between the back shroud and the casing is also estimated.
The open impeller has been tested first in order to set the pressure loss to install
downstream of the volute casing to reach a given flow rate at 4000 rpm (Best

Rotordynamic Force Coefficients for Open and Shrouded Impellers                           109

Table 1 Tested                        Configuration name    Eye packing seal    Front casing
Combinations of eye-packing
seal and front casing                 Open                  No seal/no shroud   Smooth
                                      AS-S                  Annular seal        Smooth
                                      FS-S                  Face seal           Smooth
                                      LS-S                  Labyrinth seal      Smooth
                                      AS-T                  Annular seal        Textured
                                      FS-T                  Face seal           Textured
                                      LS-T                  Labyrinth seal      Textured

Efficiency Point – BEP).1 Then, the closed impeller has been tested with the
pressure loss obtained previously and by combining three types of eye-packing seal
and two types of front casing (smooth and textured), as listed in Table 1. For all the
tests, the flow coefficient φ is of the order of 0.15.
   The volute casing is equipped with six eddy current proximity probes which
are positioned three by three, for measuring radial and axial displacements of the
impeller relatively to the casing, respectively. Before each test, a dedicated part
is used to calibrate in situ and simultaneously the response (gain and offset) of
these sensors. The tests are performed by imposing only two translation degrees of
freedom, from a centered position and without misalignment. For each rotor speed
Ω, experimental data (displacements, forces, pressures, flowrates, temperatures,
torque) are recorded for steady-state static case and dynamic excitations. The tests
conditions are:
• Rotor speed Ω: 2000, 3000, 4000 and 5000 rpm
• Excitations frequencies ω: 20, 30, 40, 50, 60, 70, 80, 90 and 110 Hz
• Water supply pressure Ps : 0.6 MPa

3 Results and Discussion

3.1 Performance Curves

Figure 2 shows the performance curves, for each combination listed in Table 1,
where the pressure rise (differential head) is defined as the difference between the
inlet pressure of the impeller and the outlet pressure of the diffuser. Pressure and
flowrate at BEP are used to normalize the corresponding data.
    Experimental points for the open impeller are the closer from the computed
efficiency curve (reference), except at 5000 rpm where the measured pressure rise
is lower than predicted. The shrouded impeller configurations LS − T and AS − T

1 Ariane Group has proceeded to many CFD simulations, using FINE/Turbo, in order to define the
theoretical performance curves.

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Fig. 2 Performance curves in centered position for the two types of impellers

better fit the reference curve. In the next section, only these two configurations for
the shrouded impeller will be used.

3.2 Experimentally Identified Rotordynamic Force Coefficients

According to Childs [8], and as mentioned in [9], the present experimental dynamic
force coefficients of impellers are made nondimensional as follows:

                                                                          Kij
                Dimensionless stiffness coefficients         Kij∗ =
                                                                       πρb2 r22 Ω 2
                                                                                                (1)
                                                                          Cij
                 Dimensionless damping coefficients           Cij∗ =
                                                                        πρb2 r22 Ω

where ρ = mass density of pumped liquid, r2 = impeller outer (discharge) radius,
and b2 = impeller discharge width including impeller side plate. For various shaft
speeds, Fig. 3 shows the evolution of the four terms Kij∗ of the stiffness matrix for
the three configurations mentioned above (open impeller, shrouded impeller LS −T
and AS − T ). The open impeller produces the lower stiffness coefficients, with
negative values of Kxx   ∗ for the three rotating speed, while they are positive for

the shrouded impeller equipped with an annular seal. For both types of impellers,
present experimental results do not provide equal values for the direct stiffness
coefficients while the assumption Kxy   ∗ = −K ∗ is almost verified. The amplitude
                                                  yx
                           ∗                                                       ∗
of the latter, as well as Kyy , decrease with increasing Ω while the amplitude of Kxx
increase with increasing Ω.

Rotordynamic Force Coefficients for Open and Shrouded Impellers                               111

Fig. 3 Dimensionless identified stiffness coefficients Kij∗ for the open impeller and two configu-
rations of shrouded impeller

   For open and closed impellers, the normalized damping coefficients (Fig. 4) are
almost constant in the range of rotating speeds, while the cross-coupled damping
coefficients are of the same order. The open impeller produces the lower direct
damping coefficients.
   The shrouded impeller provides higher direct stiffness and damping coefficients
than the open impeller because of the eye packing seal (or wear ring seal) that is
mounted on its front side.

4 Conclusion

A test rig dedicated to the identification of rotordynamic force coefficients of thin
fluid film components is used for testing two types of impellers: open and shrouded.
An open impeller, which is less expensive to manufacture with respect to the front
shrouded type, would produce lower direct stiffness and direct damping coefficients
compared to the latter, which is fitted with an eye-packing seal. Stiffness and
damping cross-coupled coefficients are almost the same for both types of impellers.

112                                                                                      P. Jolly et al.

Fig. 4 Dimensionless identified damping coefficients Cij∗ for the open impeller and two configu-
rations of shrouded impeller

Acknowledgments The authors are grateful to Centre National d’Etudes Spatiales (CNES) and
to ARIANE GROUP for using the BALAFRE test rig and for their agreement to present this
experimental work. This work was partially funded by the French Government “Investments for
the Future” program (EQUIPEX GAP, PIA, ANR-11-EQUIPEX-0018).

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