=Paper=
{{Paper
|id=Vol-2298/paper14
|storemode=property
|title=Validation of a CFD Model of a Single Stage Centrifugal Compressor by Local Flow Parameters
|pdfUrl=https://ceur-ws.org/Vol-2298/paper14.pdf
|volume=Vol-2298
|authors=Sergey Bogdanets,Vitaly Blinov,Vyacheslav Sedunin,Oleg Komarov,Alexander Skorohodov
}}
==Validation of a CFD Model of a Single Stage Centrifugal Compressor by Local Flow Parameters==
https://ceur-ws.org/Vol-2298/paper14.pdf
Validation of a CFD Model of a Single Stage Centrifugal Compressor
by Local Flow Parameters
Sergey Bogdanets Vitaly Blinov Vyacheslav Sedunin
Ural Federal University named Ural Federal University named Ural Federal University named
after the first President of Russia after the first President of Russia after the first President of Russia
B.N. Yeltsin B.N. Yeltsin B.N. Yeltsin
Yekaterinburg, Russia Yekaterinburg, Russia Yekaterinburg, Russia
bogdanec1996@rambler.ru vithomukyn@mail.ru lerr@bk.ru
Oleg Komarov Alexander Skorohodov
Ural Federal University named Ural Federal University named
after the first President of Russia after the first President of Russia
B.N. Yeltsin B.N. Yeltsin
Yekaterinburg, Russia Yekaterinburg, Russia
ov_komarov@mail.ru skorohodov@gmail.com
Abstract
In this article, CFD model validation results of a single-stage centrifugal
compressor is presented. Based on a local parameters comparison for static
pressure, meridional velocity and flow angles in absolute motion, the paper
describes aerodynamic flow features in the flow path, both those adequately
predicted and those that not.
1 Introduction
This work is devoted to the verification of a computational model of a centrifugal compressor with an axial inlet
impeller and a vaneless diffuser. These types of stages become necessary when the rotational speed of the drives is
constantly increasing [1]. The advantage of axial inlet impeller is in greater total head compared to simple radial designs
with identical circumferential speeds [2]. For the design of centrifugal compressors with a high efficiency, it is
necessary to consider the three-dimensional physical effects occurring in its passage. At present, the application of the
methods of computational fluid dynamic (CFD) has become an integral part of various researches, and requirements to
accuracy of such results are also increasing. Paper [3] summarizes results of numerous fluid dynamics studies in
centrifugal compressors.
The flow in the centrifugal wheel is described by the jet-wake model, which Dean first described in [4]. Later, this
model was experimentally confirmed by Eckardt [5]. The appearance and development of a wake zone can be highly
dependent on the tip flow above unshrouded impeller. Many numerical investigations determine and establish jet-wake
flow model [6,7]. In an investigation [8] basic mechanism leading to the formation of the jet/wake flow structure in
centrifugal machines is given. Numerous numerical simulations were made, on basic of which vortexes, vortices and
leakage flows were described and studied.
The compressor of interest is shown in Fig. 1 and it consists of an unshrouded impeller and a vaneless diffuser.
Experimental data for comparison was taken from [5].
Figure 1. Impeller of centrifugal compressor a) - a photo of Eckardt impeller [5], b) - 3D model, c) Main dimensions and
measuring points positions, measurements in mm
2 Statement research
The experimental results, obtained by D. Eckardt et.al. in [4] were used for verification. An in-house code was used to
create a 3D model of the compressor flow path (Figure 1a), geometry data from the report, partially shown on Figure 1b.
Figure 2. Boundary conditions of numerical model
Figure 2 shows the types of boundary conditions at surfaces of domain. It was as: a total pressure of 101325 Pa and
total temperature of 288K at the inlet and mass flow at the diffuser outlet. These boundary condition were chosen in order
to have stable convergence above the design operating point. The radial tip with relative magnitude of about 0.5% to
2.6% was simulated by the GGI interface. Periodic boundary conditions were applied at the side faces of the model. To
study the mixing of the jet-wake in the diffuser, a frozen rotor interface was set between rotating and stationary domains.
The turbulence model k-ε allows to reduce computational cost due to the coarser grid. Fluid – air ideal gas. Mesh size for
both domains is 540,000 elements. Convergence criteria: below than 10-6 and stabilized value of the compressor
efficiency.
3 Processing results
3.1 Validation by mass-averaged parameters
Computed performance of the compressor is plotted on Figure. 3a. It shows that the numerical model predicts less
loading coefficient and earlier stability loss. When the shaft speed is low, the speed lines better match with the
experimental ones, but as the rpm goes up, computed lines appear to have counterclockwise turn compared to the
experiment.
Figure 3. a) - Performance characteristic of a compressor pressure ratio versus mass flow and b) - Performance
characteristic of a compressor loading coefficient versus flow coefficient. 1– lines of constant rotational speed in
experiment, 2 – lines of constant rotational speed in numerical simulation, 3 – throttle ring curve, 4 – surge limit
Figure 3b shows that the pressure ratio increases linearly with decreasing flow, up to a certain value, which
determines the onset of stall. Lines with lower rpm have bigger slope. This is explained by large change in the deviation
angle in the speed lines at a higher rate. At the nominal speed line, the deviation angle increases by 4 degrees, between
speed lines of 0.67 and 0.56 by 2 degrees. Analysis of Mach number distribution (Figure 4) revealed that a sharp drop in
pressure ratio is due to the formation of vortices behind the trailing edge and from overflow through the radial clearance
at the inlet. This vortex causes a decrease in the flow rate at the shroud, which increases the angle of attack at the shroud
and a small separation on the back of the blade. Also, as the flow rate decreases, the losses in the diffuser increase non-
linearly (Figure 5).
Figure 4. a) - Mach number contour at the surface span=0.95 and b) - at the meridional section. c) - Static entropy
contour at the meridional section. Stall mode at nominal rotating speed.
Figure 5. a) - Total pressure loss coefficient versus flowing coefficient. b) - The entropy gain (2) in the impeller and in
the diffuser versus flowing coefficient at the nominal rotating speed c) - at the 0.56 nominal rotating speed
Figure 5 shows that the dependence of the total pressure loss coefficient in the diffuser, which is calculated based on
expression (1) for identical flow coefficient at all speed lines. At the operating points away from surge, losses in the
diffuser are almost independent of the mass flow. With lowering flow there is even a slight decrease in losses, but after a
certain flow a rapid loss gain happens.
P4t P2t
] diff (1)
P2t P1t
Where ζdiff is the total pressure loss coefficient into diffuser, P4t, P2t, P1t are total pressure at diffuser outlet, impeller
outlet and impeller inlet respectively.
From the analysis of Figures 3b and 5a it can be seen that the shift of the performance characteristic (Fig. 3a) is
caused by a change in the losses in the diffuser. This can also explain almost horizontal slope of the speed lines as for
ψТ=f(φ2). The high speed line has a horizontal dependence ψТ=f(φ2), and the worst qualitative coincidence with the
experimental speed line.
Total pressure ratio of the impeller (section 0-2) in computation is less, static pressure ratio is greater. The difference
between the total pressure ratio between the 0-2 and 0-4 sections in the computation is less, which indicates a lower total
pressure loss in the diffuser compared to the experiment. Total pressure ratio of the stage is lower than in the experiment,
because of the lower total pressure ratio of the impeller.
Losses in the impeller and diffuser are determined as entropy gain ΔS. The entropy gain in the impeller and in the
vaneless diffuser versus the mass flow is shown in Fig. 5b,5c and is calculated based on expressions (2). This dependence
has character of changing like the total pressure loss coefficient.
§T · §P ·
'S c p *ln ¨ 2t ¸ R *ln ¨ 2t ¸ (1)
© T1t ¹ © P1t ¹
Where cp is specific heat at constant pressure, R is gas constant, T2t, T1t are total temperature at impeller outlet and
impeller inlet respectively.
The main loss source in the impeller is expected to be due to the tip leakage flows (Figure 4c). These losses are less
for lower rotor speeds [3]. The error in verification decreases with decreasing rotational speed, which may be caused by a
more accurate prediction of the vortex at the shroud.
3.2 Validation by local flow parameters at the design speed
The following comparison is presented for the design operating point. Based on his results Eckardt presents a flow
pattern in the radial part of the blade channel, which is shown in Figure 6A. Figure 6B shows for comparison similar
scheme of the velocity vector pitch wise components on the circumferential surface x/s=0.87 based on computation. It
can be seen that in the numerical simulation the vortex occupies a large area and is shifted to the pressure side. This
vortex must form a "wake", which affects the distribution of parameters across the section.
Figure 6. Secondary flow pattern in the radial part of the impeller blade channel x/s=0.87
a) - Eckardt [1]; b) - numerical simulation
Figure 7. Streamlines from the radial tip a) - contour Сr/U2; b) - contour Рt3/Рt0;
c) - streamlines from the middle of blade Сr/U2 R/R2=1.017
The image of the streamlines together with the contour of Сr/U2 and Рt3/Рt0 (Figure 7) makes it possible to determine
the causes of the zones with low parameters near the front wall and suction side (in the pictures this area is bottom right).
These zones are due to tip flow. The vortex appearing at the tip near outlet defines the boundaries of these zones (Figure
7A).
3.3 Validation by local flow parameters at the rotational speed of 0.78
Figure 8 shows the sections in which the data sets were measured for plotted contours of velocity and flow angle.
Figure 8. Location of the measuring sections
Figure 9. Contours Сm/U2 at the various sections
Figure 10. Contour Сm/U2 at the section R/R2=1.151. a) - experiment; b) - numerical simulation
Figures 9 and 10 show contours of meridional velocity to blade velocity ratio after impeller Сm/U2 at different
sections (Figure 8).
In section 7 the shape of the meridional velocity distribution coincides with experiment. A similar qualitative
agreement was found in section 10. This section is the last for the axial part of the impeller. The core of the stream is at
the suction side close to casing, the stream has not yet been divided into jet and wake zones.
Section 11 is diagonal, in which the core flow has not yet shifted to the hub surface, but a vortex has already appeared
from the tip leakage. Therefore a starting position of this vortex is predicted more or less correctly.
Section 13 is located on the radial section of the impeller and there is a developed tip vortex. The core has shifted to
the suction side, both in experiment and in computation. In this section, the flow is described by a jet-wake model and
there are differences between computation and experiment. The core in the computation is stretched over the suction side
because the tip vortex stays at the middle of the channel.
The flow core in section 14 is shifted to the rear wall, which is caused by a flow turning from axial to radial direction.
Considering the thickness of the radial tip and nonzero dimensions of a pitot tube in the experiment, one can draw an
approximate line behind which the experimental data was not obtained. Then, comparing the contours, it can be seen that
the jet-wake zones in the computation and in the experiment are qualitative agreed. The flow core at the computation
extends over a larger area, being also in the middle of the channel. Section 14 is located after the trailing edge.
The contour in the section of diffuser R/R2 = 1.151 shows increasing of the vortex size and mixing of the one with the
flow in the tangential direction, which does not happen in the experiment.
In the computation, the boundary layer is very thin as compared with the experiment. Therefore, area of the flow core
in computation is bigger which cause a change in the mass averaged velocity diagram.
In computation, the vortex from the radial tip proceeds to the pressure side direction, although in the experiment the
vortex moves towards the hub direction along the suction side right after exiting the tip.
Figure 11 shows distributions of the flow exit angle in absolute frame - α2. The representation of the distributions in
the form of constant value lines allows for a quantitative comparison. A decreased angle α2 indicates the increased radial
absolute velocity Сr, when other velocity components remain equal. Decreased С2r along the wall indicates that the
causes a slowing of the flow. Therefore, the contour α2 in the section R/R2=1,017 shows that in the computation the
thickness of the boundary layer at the hub is smaller than one in the experiment.
Figure 11. Contours of the flow exit angle in the absolute frame α2 a), c)- numerical simulation; b), d)- experiment
The contour of α2 in the section of R/R2=1,017 allows to estimate quantitative difference. The zone of angles by 25º-
20º in the computation and the experiment beat a qualitative similarity. An absence of a developed boundary layer near
the hub is the difference. The presence of this layer would allow this zone (angles by 25º-20º) to expand like in the
experiment and, perhaps, would shift the flow core (30-35º) toward the pressure side. In computation compared to the
experiment, there is no zone of angles > 35º. Therefore, area of the flow core in the computation is larger due to
negligibly small boundary layer. The zone of angles below 10 degrees is defined by a vortex and has the biggest
difference compared to the experiment: the gradient is higher in the computation.
In the section R/R2=1,151, the zone of angles more than> 35 º is appeared. In the computation there is an intense
tangential mixing of the zones by 5º-25º, compared to the experiment. The numerical model predicts the undeveloped
boundary layer near the hub. The mixing of the flow behind the impeller is faster than in the experiment.
4 Conclusion
It was found that for the design operating point the difference in the integral characteristics between the numerical
simulation and the experiment is less than 1.2%. Main conclusions are drawn from comparison of local flow parameters
at different sections at different operating conditions:
1. It was shown that the vortex is formed at the same place where Dean determined in his work [4]. But the numerical
simulation predicts the vortex being stretched along the front wall. This vortex doesn’t move into the flow path as it was
seen in the experiment.
2. Underestimation of the boundary layer on solid surfaces affect the flow pattern in the numerical simulation. This
causes increased diffusivity and earlier onset of stall. Therefore, the surge limit in the computation is shifted to the right
due to earlier prediction of flow separation at the angle between the shroud and the trailing edge. Increased diffusivity in
the computation provides more effective deceleration of the flow in the impeller. This leads to a less density of the
working fluid. Provided that the air flow is the same, computed exit speed is lower, which cause less hydraulic losses.
This explains greater efficiency in the computation.
3. In the numerical simulation zones of jet and wake mix earlier at the diffuser, therefore pressure losses in the
diffuser are lower.
4. The slope shift of the computed characteristics compared to the experimental ones was observed especially with
increasing rotational speed. Improving convergence of computed and experimental speed lines at lower speeds is a
consequence of better prediction of the deviation angle and losses from the dissipation of the radial tip vortex. Also, the
supersonic flow at the casing at higher speeds adds complexity to the model.
5.The numerical model is reasonably good at prediction of overall performance and flow features occurring in the
flow path at the design operating point. Further away from the nominal, accumulation of numerical errors leads to bigger
errors. These errors must be investigated to improve the quality of numerical simulations.
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