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This paper presents acoustic and flowdynamic investigations of large-scale instabilities in a radial pump with a vaned diffuser. Pressure fluctuations were measured with transducers placed flush at the inlet duct, at the impeller discharge, and in the vane diffuser walls. Two impeller rotation speeds were analyzed in the study, at design, and at off-design flow rates. A spectral analysis was carried out on the pressure signals in frequency and in time-frequency domains to identified precursors, inception, and evolution of the pressure instabilities. The results highlighted the existence of a rotating pressure structure at the impeller discharge, having a fluid-dynamical origin and propagating both in the radial direction and inside the impeller. The experimental data were then compared with the results obtained with help of ANSYS CFX computer code; focusing on the changing flow field at part load. Turbulence was reproduced by DES model.

Flow in the diffuser pump is dominated by unsteady interactions due to the relative motion and close proximity between the rotating impeller and stationary diffuser, thus, resulting in pressure and velocity fluctuations both upstream and downstream. In the literature, different analytical and experimental approaches were used to investigate the mutual influence of the impeller and its surroundings.

Experiments were
conducted to measure pressure fluctuations in diffuser radial pumps by
Arndt et al. [

The noise spectral content for studying the
unsteady phenomena developing in the impeller passages and at the flow
discharge was also considered by researchers.
Cumpsty [

Notwithstanding Ferrara et al. [

The objective of this research was to identify and characterize the unsteady phenomena produced in a centrifugal pump, utilizing the Fourier approach and the time-frequency analysis. A correlation between the fluid dynamics and the emitted noise was investigated in order to define the characteristic frequencies of the unsteady stator/rotor interaction.

The paper reports time-resolved fluctuations of pressure upstream and downstream of a radial vaned pump at design flow rate and at low-flow rates. Particular emphasis was dedicated to understand the source of the pitch-wise variations at the impeller outlet and in the diffuser channels.

Furthermore, this paper discusses the numerical data obtained with the ANSYS CFD 11 code, and shows comparison between the theoretical and experimental results on the impeller model equipped with vaned diffuser.

The experimental analysis was performed in the Open
Turbomachinery Facility (OTF), in the Department of Mechanical Engineering, University of Padua. The OTF is a water test rig
designed for testing the influence of several parameters on the overall
performances of both pumps and turbines. The analyzed pump had an original
configuration, constituted by a 3D impeller, coupled with a vaned diffuser and
a vaned return channel, reproducing the first stage of a two-stage pump turbine
(

Impeller data | ||||
---|---|---|---|---|

400 | 40 | 7 | 26.5 | .125 |

Adjustable guide-diffuser vanes data | ||||

410 | 40 | 22 | 21.8 |

Pressure transducers, placed flush with the
wall, at different positions carried out measurements of the unsteady pressure.
Figure

Scheme of the impeller and the vaned diffuser.

three
traverse planes, 68 mm upstream the impeller, in the inlet duct (positions 10,
11, and 12—white marks in Figure

a
traverse plane, 2 mm downstream the impeller (position 20—green mark in
Figure

twelve
pressure points in the mid height (Figure

Scheme of the diffuser blade with the 12 micro transducers, 7 of them numbered.

Piezoelectric dynamic pressure transducers (sensitivity of 76.89 V/Pa) were placed circumferentially equidistant in the inlet duct (positions 10, 11, and 12); and a piezoelectric transducer (sensitivity of 7.62 V/Pa) was located 2 mm downstream the impeller (position 20). Miniaturized piezoresistive transducers (sensitivity of about 0.29 V/Pa) were placed in the diffuser vane. The sensors’ combined nonlinearity, hysteresis, and repeatability were better than ±0.1%.

The vibrations of the rig were also measured by
accelerometers fixed at the inflow and outflow pump casing, and in the dynamo
that powered the pump (charge sensitivity of

The pump inflow was connected to a water reservoir, filled continuously to a weir brim by an external pump, so that the water level change during operations could be considered negligible. The vibrations of the tank were monitored by an accelerometer.

The data were simultaneously acquired from all the channels at a sampling rate of 2048 Hz and recorded by a workstation controlled transient data recorder, with a dynamic range of 24 bit. The outputs from the transducers channel were conditioned with a low-pass filter at 1024 Hz.

Design and off-design conditions, and two
impeller rotation speeds (

The pressure signals were analyzed both in the frequency domain and in the time-frequency domains.

Auto-spectral and cross-spectral matrices were
computed by partitioning each time signal into 256, nonoverlapping segments of

The coherence function

The signal processing in the frequency domain
allows finding and analyzing the spectral components contained in the measured
pressure signals, but it does not allow an assignment of these spectral
components to time. In order to provide information about their time evolution,
a time-frequency analysis was carried out by means of the wavelet transforms.
For the time-frequency analysis the continuous wavelet transform

In order to determine the relation between two
pressure signals

Finally, the wavelet coherence function,
measuring the coherence between two sampled signals

The commercial software package ANSYS CFX 11.0 was used for performing the numerical simulations on the entire machine. On both blades and wall surfaces, the boundary layer was assumed fully turbulent.

The detached eddy simulation (DES)
model was chosen as turbulence
model. The shear stress transport

Since one of the interesting analysis aspects is the possible prediction of noise and vibrations due to stator-rotor interaction, the LES peculiarity of providing information on turbulent flow structures and spectral distribution is useful.

An unsteady model was used for all the computations. For the interface between stator/rotor blocks, the standard transient sliding interface approach was chosen.

The scheme adopted for the time discretization
was a second-order implicit time stepping. The time step definition was based
on the impeller rotation and it was of about one degree. So, the RMS courant number
was CFL = 2.04. A maximum number of five iterations were fixed for each time step,
resulting in a mass residue of

The numerical data were acquired between the 2nd and 3rd impeller revolution subsequent to the cyclic behavior of the residual plots obtained after about 3 impeller revolutions.

An H-type grid was used for the impeller,
whereas an O-type grid was adopted for the diffuser. The leakage from the
labyrinth seal was also considered and several H-blocks were built to describe
the cavities. The grid, globally of

As regards the boundary conditions, mass flow rates were prescribed with stochastic fluctuations of the velocities with 5% free-stream turbulence intensity at the pump inlet. At the pump outlet the average static pressure was fixed.

Stator rotor interaction gave rise to a complex pressure pulsation system.

Figures

Power spectrum of the pressure measured at the pump inlet and outlet at 500 rpm.

Power spectrum of the pressure measured in the diffuser vane at 500 rpm.

Power spectrum of the pressure measured in the diffuser vane at 600 rpm.

The spectra were dominated by
the blade passage frequency BPF

Table

Some identified nonlinear interaction components.

500 rpm | 600 rpm | ||||||
---|---|---|---|---|---|---|---|

St | Nonlinear components | St | Nonlinear components | St | Nonlinear components | St | Nonlinear components |

0.064 | 1.093 | 0.164 | 1.021 | ||||

0.336 | 1.264 | 0.336 | 1.164 | ||||

0.493 | 1.157 | 0.521 | 1.185 | ||||

0.750 | 1.664 | 0.736 | 1.664 | ||||

0.835 | 2.227 | 0.807 | 2.300 | ||||

0.971 | 2.328 | 0.971 | 2.328 | ||||

0.899 | 2.664 | 1.014 | 2.664 |

The pressure pulsation at a frequency of 5 Hz
was independent of the impeller velocity and it was also identified with the
impeller not running (Figure

Wavelet
magnitude

The pressure pulsation at

Wavelet
magnitude

Wavelet
magnitude

The fluid-dynamical unsteadiness is well
highlighted by the time-frequency analysis at all the flow rates. For

Wavelet
magnitude

Wavelet
magnitude

The passage of an energy core, having a varying energy level was supposed to generate the pulsating behavior of the structure, as seen by the wavelet analysis. The energy core was associated with one of the zones of jet and wake, localized at the impeller discharge. As these zones pass over the transducers, they could be perceived as pressure fluctuations, pulsating in time and rotating around the impeller discharge.

The numerical analysis showed that at low flow rate the wake zone was
characterized by sequences of vortices.
The vortices, originated at about mid cord, evolved growing along the blade
length up to a maximum to be reabsorbed subsequently (Figure

Vector plot at 10% blade height

It seemed that the modes, constituting the
unsteady pattern, interfered with one another alternately in a constructive and
destructive way. The resulting structure was not frozen in time, but it changed
with a pulsating behavior, appearing and disappearing, depending on the
interference of its modes (Figure

At design flow rate, the numerical analysis did
not highlight a well-defined wake zone, but the investigation of the impeller
blade load showed pressure fluctuations due to both the stator rotor
interaction and an independent source. In Figure

Pressure
evolution in the impeller mid height for

In the relative system of reference, the Strouhal
number could be expressed by

Cavazzini [

The mode of each
blade interfered weakly with the others constituting a well-defined global
pattern (Figure

The frequency of the unsteady
pattern (

Coherence
level between inlet (traverse 10) and impeller discharge (traverse 20)

The presence of the BPF was not always well
defined, and its magnitude was often less than that of the other frequencies (Figures

In regards to the phase displacement, Figure

Cross-wavelet transform between the pressure transducers in
traverse 20 and in position 4 for

Experimental and numerical analyses were carried out on the flow field instability in an impeller, coupled with a vaned diffuser to study the characteristics and the development of the unsteady phenomena. Acoustic measurements were acquired by means of pressure transducers, placed in the inlet duct and at the impeller discharge, and in a diffuser vane, for two different impeller rotation velocities, in order to identify the pulsating phenomena, to define their characteristics, and to evaluate their evolution and the influence of the impeller rotation velocity on their characteristics.

The pressure signals were processed by the spectral analysis in the frequency and in the time-frequency domains to obtain information about the evolution at the time of the phenomena.

The analysis of the pressure signals highlighted
the presence of a first pulsating phenomenon with a low frequency (

On the other side, at the impeller discharge, a
rotating structure of pressure pulsations was identified with the fundamental
frequency at

Interaction with both the blade passage frequency and with the system fluctuations generated nonlinear interaction components in the spectra, appearing and disappearing in time with regular intervals. The resulting structure was not frozen in time; it changed with a pulsating behavior, depending on the constructive or destructive interference of its constituting modes.

The numerical analyses seem to confirm the existence of this unsteady pattern and to detect the fluid-dynamical origin in the blade load as in the jet-wake instability.

Width [m]

Axial, meridional, and radial absolute velocity components, respectively [m/s]

Diameter [m]

Frequency [Hz]

Gravitational
constant [

Elements of the cross-spectra matrices

Pump head [m]

Azimuthal mode number [-]

Shaft
speed [

Number of time history segments

Number of blades [-]

Specific speed [

Pressure [Pa]

Flow
rate [

Strouhal number based on the impeller tip speed [-]

Peripheral velocity [m/s]

Fourier transform data segment

Nondimensional variable based on the distance from the wall to the first node [-]

Continuous wavelet transform

Weighting constant corresponding to the Hanning window

Cross-wavelet spectrum

Relative flow angle [rad]

Phase
angle [

Coherence function

Overall efficiency [-]

Flow coefficient [-]

Cross-wavelet phase difference

Angular
rotation speed [

Angular propagation speed [

Time delay [s].

Rotor blade leading edge

Rotor blade trailing edge

Diffuser blade leading edge

Of the blade mean line

Design

Indices in equations

Indication of a discrete-time signal; also specific time index of such a signal.