JOURNAL OF THE GLOBAL POWER AND PROPULSION SOCIETY
journal.gpps.global

Generation mechanism of diffuser stall in a centrifugal
compressor with vaneless diffuser
Original article

Nobumichi Fujisawa1,*, Kenta Tajima1, Hiroshi Miida1, Yutaka Ohta1
1

Waseda University, Tokyo, Japan

Article history:
Submission date: 23 September 2020
Accepted date: 27 October 2020
Publication date: 4 December 2020
This is the updated version of a paper
originally presented at the Global Powerand Propulsion Virtual TechnicalConference, GPPS Chania20, Sept. 7–9
2020.

*Correspondence:
NF: nobumichi-fuji@akane.waseda.jp

Peer review:
Single blind

Copyright:© 2020 Fujisawa et al.

This is an open

access article distributed under the Creative
Commons Attribution License (CC-BY 4.0),
which permits unrestricted use, distribution,and reproduction in any medium, provided
the original work is properly cited and its
authors credited.

Abstract
The generation mechanism of a diffuser stall in a centrifugal compressor
with a vaneless diffuser was experimentally and computationally investigated, and the main ﬁndings are presented in this paper. Diffuser stall isgenerated when the mass ﬂow through the compressor decreases andapproaches the compressor surge limit. It was observed that diffuser stallcells rotate at 25–30% of the impeller rotational speed, with diffuser stall
ﬂuctuations observed at 180° from the cutoff (volute tongue). It was foundthat the magnitude of the diffuser stall ﬂuctuation gradually increased near
the cutoff. According to the CFD analysis, the mass ﬂow ﬂuctuations at the
diffuser exit showed a low mass ﬂow region, rotating at approximately 25%of the impeller rotational speed. The diffuser stall ﬂuctuations began at 180°from the cutoff and developed as this region approached the cutoff.
Therefore, the diffuser stall could be simulated by CFD analysis. First, thediffuser stall cell originated at 180° from the cutoff by the hub side boundary layer separation. Then, the diffuser stall cell further developed by theboundary layer separation accumulation and the induced low velocity area.
The low velocity region formed a blockage across the diffuser passage
span. The diffuser stall cell expanded due to the boundary layer separations
occurring on the shroud and hub wall by turns. Finally, the diffuser stall cell
vanished when it passed the cutoff, because the mass ﬂow recovery
occurred. The current paper presented the main results of this phenomenaof great importance in centrifugal compressors.

Keywords:
centrifugal compressor; vaneless diffuser;
CFD; DES; rotating stall; internal ﬂow

Citation:
Fujisawa N., Tajima K., Miida H., and Ohta Y.
(2020). Generation mechanism of diffuser
stall in a centrifugal compressor withvaneless diffuser. Journal of the Global
Power and Propulsion Society. 4: 190–201.
https://doi.org/10.33737/jgpps/128974

Introduction
A centrifugal compressor is mostly used in a wide range of applications
due to a high pressure ratio and small size. Centrifugal compressors witha vaneless diffuser are often employed due to their wider stability range,
compared to those with a vaned diffuser. However, the operating range
is limited by the onset of rotating stall and surge. Prior to the onset ofthe surge, the rotating stall was generally occurred. Therefore, toenhance the operating range and suppress the surge onset, one should
must focus on understanding the rotating stall generation mechanism.
Numerous researchers have reported rotating stall behavior in centrifugal compressors with vaneless diffuser. The tornado-type separationvortex caused by full blade leading-edge separation was observed under
the ﬂow ﬁeld of a developed rotating condition (Iwakiri et al., 2009).
Zhang et al. investigated the volute inﬂuence on stall inception onset
and development. Under the volute inﬂuence, the spillage vortices at aleading edge of impeller blades were developed by a static pressure peaknear the tongue (Zhang et al., 2019). Therefore, the centrifugal compressor impeller stall was strongly related to a suction side separation and

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tip-leakage vortex. Additionally, many reports discuss a diffuser stall behavior in a vaneless diffuser. Senoo et al.
were the ﬁrst to investigate the relationship between reverse ﬂow and the initiation of a vaneless diffuser rotatingstall in a centrifugal blower. They proposed initiation criteria for a vaneless diffuser rotating stall (Senoo et al.,
1977; Senoo and Kinoshita, 1978). Ohuchida et al. suggested both a boundary layer separation pattern and astall propagation mechanism in a vaneless diffuser by PIV experiments (Ohuchida et al., 2013). They indicatedthat a rotating reverse ﬂow disturbance in the diffuser was related to developing of a rotating stall cell, blocking
interior diffuser ﬂow at near-surge. However, the detailed diffuser stall generation mechanism in a vaneless diffuser was not completely understood.
Previous publications revealed the mechanism of rotating stall in the centrifugal compressor with vaned diffuser (Fujisawa and Ohta, 2017; Fujisawa et al., 2019a,b). The current study is focused on the generation mechanism of a diffuser stall in vaneless diffuser. Both experimental and numerical analysis were conducted on stall
inception of centrifugal compressor with vaneless diffuser. The unsteady velocity was measured in circumferential
and meridional direction within vaneless diffuser. Furthermore, Detached Eddy Simulation (DES) analysis overthe entire compressor region, including the volute, was performed to reveal more detailed diffuser stall cell
behavior.

Experimental apparatus and procedure
The tested centrifugal compressor schematic view for this study is shown in Figure 1. The test rig at Waseda
University was used for a shipboard turbocharger, consisting of an impeller, vaneless diffuser, and volute. The
impeller is equipped with seven full blades and seven splitter blades. The geometry details, as well as key parameters, of the tested compressor are summarized in Table 1. The impeller is an open-type impeller with a tip
clearance that is 1.0% of the impeller blade width at B1 = 105.6 mm. The impeller rotational speed was set to6,000 min−1.
The steady pressure was measured at the compressor exit by a differential pressure transducer (Yamatake
JTD920A). The oriﬁce ﬂow meter was set at the outlet duct to measure the steady mass ﬂow rate. Velocity ﬂuctuations, which deﬁned as the difference between the time averaged value and the peak one, were measured on
the test rig using a hot-wire anemometer (DANTEC, 55R57). The circumferential measurement points wereplaced at ﬁve positions (0°, 90°, 150°, 180° and 240°), respectively as shown in Figure 1. The meridional velocity
measurement points were at the diffuser inlet (D.I.), diffuser midsection (D.M.), and diffuser exit (D.E.). The
hot-wire probes traversed in the spanwise direction in 5% increments of the diffuser width. The probe body is a
2.3 mm diameter, which is about 10% of the diffuser passage width. Although this probe size slightly inﬂuenced
on the ﬂow blockage, the scale of stall behavior would be greatly larger compared with the velocity ﬂuctuationinduced by the probe effect.

Figure 1. Experimental Apparatus and Procedure.
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Table 1. Dimensions of tested compressor.
Tested Centrifugal Compressor

Diffuser

Rotational Speed

N

6,000 min−1

Inlet Diameter

D3

328 mmMass Flow Rate (design point)G

1.64 kg/s

Outlet Diameter

D4

559 mmPressure Ratio (design point)

p5/p1

1.1

Diffuser Width

B4

19.55 mmZ

14

Impeller
Number of Blades(Main + Splitter)(7 + 7)

Inlet Diameter

D1

248 mmOutlet Diameter

D2

328 mmExit Blade Width

B2

26.14 mm

CFD methodology
A detached eddy simulation (DES) code was developed for investigating the internal ﬂow. The Computational
Fluid Dynamics (CFD) code was constructed to solve the three-dimensional compressible Navier-Stokes equations. The convective ﬂux was evaluated using the ﬂux difference splitting (FDS) method and extended to thethird-order MUSCL interpolation. The viscous ﬂux was evaluated as a second-order central difference. The
Matrix Free Gauss-Seidel (MFGS) implicit algorithm was employed for time integration. The shear stress transport (SST) k-ω turbulence model was used in this code and applied to DES. This model depends on the local
turbulent length scale and grid spacing size. The dissipation term in the k-equation of the SST k-ω turbulencemodel is modiﬁed as follows:k
DDES¼ ρk 3=2 =el(1)

el ¼ min(lkω , CDES Δ)(2)

where l is the turbulent length scale, Δ is the local grid spacing, and the model’s constant coefﬁcient CDES was
set to the recommended value by the report (Strelets, 2001). The several studies reported that DES analysis is
more suitable than URANS for detailed ﬂow ﬁeld investigations near stall in both axial and centrifugal compressor (Im et al., 2012; Yamada et al., 2017). Our In-house code was successfully validated for unsteady ﬂow ﬁelds
of various turbomachinery ﬂows (Fujisawa et al., 2019b; Zhang et al., 2020).
The computational domains applied in the numerical simulations are illustrated in Figure 2. The grid system
included 14 impeller passages, vaneless diffuser, and a volute. The impeller (including clearance region) andvaneless diffuser systems had 32.0 and 11.0 million cells, respectively. The volute region had 22.0 million cells.
In total, the computational grid had 65.0 million cells. The wall cell width was 0.1 μm, corresponding to a y+parameter, equal to approximately one along all solid surfaces. At the inﬂow boundary, the total pressure andtemperature were ﬁxed, while mass ﬂow rates were ﬁxed at the outﬂow boundary. Across a sliding boundary separating the moving impeller and stationary diffuser frames, the most recent data on one side were interpolated toobtain opposite side data by using an unsteady simulation sliding mesh. Nonslip and adiabatic conditions wereadopted for the wall conditions. The main CFD setup was summarized in Table 2.
Compressor performance and stall characteristics
The experimental and numerical compressor performance results are shown in Figure 3. The numerical totalpressure-rise characteristics were obtained from the time-averaged results of unsteady DES analysis and steady
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Figure 2. Numerical Mesh.

Table 2. Computational setup.
Numerical Scheme
Convective Term

FDS (MUSCL 3rd-order Interpolation)

Viscous Term

2nd-order Central Differential Method

Time Integral

MFGS

Turbulence Model

SST k-ω Turbulence Model (DES)

Boundary Conditions
Inlet Boundary

Total Pressure and Temperature Fixed

Outlet Boundary

Mass Flow Rate Fixed

RS Boundary

Sliding MeshTime Steps

5,000 step/rev

Mesh
Impeller Region

32.0 million cells

Diffuser Region

11.0 million cells

Volute Region

22.0 million cells

Wall y+<1

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Figure 3. Compressor Performance.

RANS analyses. The ﬂow and total pressure-rise coefﬁcients are deﬁned as follows:
ϕ¼
Ψt ¼

Q
π 2 D22 B2 (N =60)Δpt
22
ρπ D2 (N =60)2 =2

(3)

(4)

The unsteady simulations were conducted at the operational design point (ϕ = 0.24), and two off-design
points (ϕ = 0.10 and 0.08). The steady simulations were conducted at three operational points from ϕ = 0.24 toϕ = 0.14. The steady RANS analysis results were in good agreement with measured results. The unsteady CFD
results were overestimated particularly at the off-design points as compared with the test results. The mixing loss
especially within scroll passages was assumed to be underpredicted at near stall point, but the main factor of overprediction of pressure rise coefﬁcient still was not conﬁrmed. However, the relative error between experimental
and unsteady CFD results at off design points was within 5%, as shown in Figure 3. Therefore, it was noproblem to investigate the characteristics of a diffuser stall because the relative error was small.
To investigate the unsteady rotating stall characteristics, the radial velocity ﬂuctuation of impeller discharge
ﬂow was measured with a split-ﬁlm anemometer at ϕ = 0.08. The radial velocity was measured at D.I.0, 90, 180
and 240, which were indicated in Figure 1. The fast Fourier transformation (FFT) spatial distribution results ateach measurement point in the spanwise direction are shown in Figure 4. The vertical axis represents the radial
velocity ﬂuctuation magnitude. From Figure 4, two types of velocity ﬂuctuations were observed. One occurred ataround 58 Hz and the other occurred at around 25–30 Hz. Based on previous report (Fujisawa et al., 2016),
the unsteady phenomena at around 58 Hz were caused by a rotating stall within the impeller passages. On theother hand, the lower frequency ﬂuctuation at around 25–30 Hz, was equivalent to 25–30% of the impeller
rotating speed, and was caused by a rotating stall within the vaneless diffuser. Particularly, focusing on the diffuser stall, its characteristics varied depending on the circumferential position. From Figure 4(i), the small velocity ﬂuctuation magnitudes caused by diffuser stall were observed near the shroud wall at D.I.0. Whereas, from
Figure 4(ii), the large velocity ﬂuctuation magnitude around 28 Hz was observed near the hub wall at D.I.90.
Furthermore, Figure 4(iii) and (iv) show that the largest velocity ﬂuctuation magnitude caused by the diffuser
stall was observed near both shroud and hub walls at D.I.180 and 240, located near the cutoff. The mass ﬂow
ﬂuctuations at the diffuser exit obtained from CFD analysis are shown in Figure 5. The red colored line indicatedlow mass ﬂow regions and this rotational speed was about 25% of the impeller rotation speed. Therefore, the redcolored low mass ﬂow regions was assumed to be caused by the rotating diffuser stall, which rotated at 25% of
the impeller rotation speed. This low mass ﬂow region appeared at 90° and disappeared after passing the cutoff.
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Figure 4. Distributions of Velocity Fluctuation in Spanwise Direction at Diffuser Inlet (EXP:ϕ = 0.08).

Both experiment and CFD analysis indicated that the diffuser rotating stall initiated at 90° and developed further
as the diffuser stall cell approached the cutoff. After passing the cutoff, the diffuser rotating stall was attenuated.
The detailed unsteady diffuser stall behavior is discussed later.
Generation mechanism of diffuser stall
To investigate the detailed unsteady diffuser stall behavior, an unsteady DES analysis was conducted. First, tounderstand the ﬂow ﬁeld, Figure 6 shows the distributions of radial velocity ﬂuctuation within the diffuser
passage obtained by CFD analysis. The radial velocity ﬂuctuation was deﬁned as follows:
ΔVr (t) ¼ Vr (t)  Vr ave(5)

Vr_ave indicates the time-averaged radial velocity. The red color indicates the large magnitudes of radial velocity
ﬂuctuations. The region indicated by the white dashed circle is the diffuser stall cell that induced the largest massﬂow ﬂuctuations in Figure 5. Furthermore, the time-averaged mass ﬂow rate of impeller discharge ﬂow obtained
from CFD analysis at ϕ = 0.08 is shown in Figure 7. The impeller exit plane mass ﬂow rate was calculated on
sections obtained by dividing the diffuser inlet into 32 circumferential sections. At t* = 2.2, the region with thelarge velocity ﬂuctuations, as shown in Figure 6, was ﬁrst generated at around 45°, where a strong circumferential

Figure 5. Mass Flow Fluctuation at Diffuser Exit (CFD:ϕ = 0.08).
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Figure 6. Distribution of Radial Velocity Fluctuations (CFD:ϕ = 0.08).

adverse pressure gradient is observed, as depicted in Figure 8. Then, the large ﬂuctuations region was formed at
the diffuser exit area by the accumulation of several small backﬂow regions at t* = 2.9. After that, the diffuser
stall cell expanded both radially and circumferentially as it approached the cutoff at t* = 3.7 and 4.2. Finally, thestall cell size reduced after passing the cutoff at t* = 5.4 due to increased impeller discharge mass ﬂow rate at near
the cutoff, as shown in Figure 7.
The circumferential static pressure distributions at ϕ = 0.24 and ϕ = 0.08 obtained from the CFD analysis areshown in Figure 8. The static pressure was measured at shroud wall D.M. From this ﬁgure, at around 300°, thestatic pressure at off-design point ϕ = 0.08 was the same level as that at design point ϕ = 0.24. However, from 0°
to the cutoff, the static pressure at ϕ = 0.08 was higher than that of ϕ = 0.24. The magnitude of circumferential
adverse pressure gradient was strong near 0° for ϕ = 0.08. Therefore, the diffuser stall was initiated at around 45°.
Furthermore, the time-averaged meridional distribution of radial velocity and streamlines at 0°, 45°, and 240° areshown in Figure 9. The boundary layer separation occurred at hub and shroud wall by turns at 240deg, withnumerous papers reporting the same phenomena (Van den Braembussche, 2019). From this paper, the spanwisepressure gradient induced the ﬂow concentration on the side with the highest pressure. In addition, the spanwisepressure gradient inversion was generated once separation occurred, and this pressure gradient change continued
until ﬂow reversal took place on the other side. Therefore, the separations generated at both hub and shroud byturns. First, the ﬂow concentrated on the shroud side where the total pressure was highest and boundary layer

Figure 7. Distribution of Mass Flow at Impeller Exit (CFD:ϕ = 0.08).
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Figure 8. Distribution of Static Pressure in Circumferential Direction (CFD:ϕ = 0.24 and 0.08).

Figure 9. Meridional Distribution of Radial Velocity and Streamlines (CFD:ϕ = 0.08).

separation occurred on the hub side at 240deg ( point (a)), as shown in Figure 9. At point (b), the pressure gradient inversion occurred and the ﬂow concentrated on the hub side. Therefore, the next boundary layer separation
occurred at the opposite wall. Particularly, at 45deg, the separation region was observed near the diffuser inlet
shroud wall. Accordingly, the hub side boundary layer separations at around 45°, triggering the diffuser stall cell
generation, were caused by the shroud side separation region at the diffuser inlet and a large circumferential
adverse pressure gradient. Figure 10 shows the time-averaged limiting streamlines on hub wall obtained by measurement and CFD analysis. In the experiment, the limiting streamlines were visualized by using an oil ﬁlm
method. The limiting hub wall streamlines were bent at around 45° where a small backﬂow region generated.
For improved understanding of the diffuser stall cell generation mechanism, the unsteady ﬂow ﬁeld was visualized. The instantaneous ﬂow ﬁeld at two different times are shown in Figure 11. The distributions of radial velocity ﬂuctuation within the diffuser passage at each time are shown. The developing behavior of diffuser stall cell

Figure 10. Limiting streamlines on hub wall (EXP and CFD:ϕ = 0.08).
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Figure 11. Instantaneous Radial Velocity Fluctuation at t* = 2.13 and 3.00 (CFD:ϕ = 0.08).

was investigated from Figures 12 and 13. Figures 12(i) and 13(i) show the meridional radial velocity distribution
around the region A and B at t* = 2.13 and 3.00. Figures 12(ii) and 13(ii) show the iso-surface of Vr = −10 m/s
colored by the distance from the hub wall. From Figure 12, the hub wall boundary layer separation initiated ataround 45°. Then, this hub wall separation induced the next shroud wall separation because of a spanwise pressure gradient, as shown in Figure 13. The boundary layer separations on the shroud wall developed, as it can beseen by the low velocity region at diffuser exit. The hub side Backﬂow Region I was the impeller wake. Fromnumerical results, the impeller wake mainly expanded on the hub side from 90° to the cutoff. The shroud side
Backﬂow Region II consisted of the boundary layer separations. The region indicated by the black circle was thelow velocity region. Backﬂow Region I rotated faster than Backﬂow Region II, as shown in Figure 13a and b.
Therefore, Region I caught up with Region II and induced the boundary layer separation enlargement on the
shroud wall (Region II). Furthermore, the shroud wall boundary layer separations (Region II) induced the next
hub wall boundary layer separations (Region III) because of a spanwise pressure gradient. The low velocity region
within vaneless diffuser developed due to the boundary layer separations occurring on the shroud and hub wallby turns. Finally, the low velocity region formed the entire diffuser passage span blockage.
In order to validate the numerical results, the radial velocity ﬂuctuation of impeller discharge ﬂow was measured at the meridional direction (D.I.150, D.M.150 and D.E.150), as shown in Figure 14. The diffuser stall
ﬂuctuations were observed near hub side at D.I.150. On the other hand, the region with large magnitudes of the
diffuser stall was shifted to the shroud side at D.M.150 and D.E.150. It is because the diffuser stall was consistedof the boundary layer separations occurring on the shroud and hub wall by turns. Therefore, the boundary layer
separations occurring on the shroud and hub wall were considered as the key factors contributing to the diffuser
stall generation by both experimental and CFD results. In our future work, the general generation mechanism of

Figure 12. Generation Mechanism of Diffuser Stall Cell at t* = 2.13 (CFD:ϕ = 0.08).
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Figure 13. Development of Diffuser Stall Cell at t* = 2.88 and 3.00 (CFD:ϕ = 0.08).

the boundary layer separations, which occurred at the hub and then the shroud end wall, will be revealed byseveral CFD investigations.

Conclusions
The generation mechanism of a diffuser rotating stall in a centrifugal compressor with a vaneless diffuser wasinvestigated by experiments and CFD analysis. The results can be summarized as follows:
1. In the test compressor, ﬂuctuations occurred at around 25–30 Hz, were caused by diffuser stall at off design
point ϕ = 0.08. The ﬂuctuation magnitude varied depending on circumferential position with the largest ﬂuctuations observed near the cutoff.
2. The diffuser stall behavior varied depending on circumferential position. First, the boundary layer separations
initiated on the hub wall at around 45° where a large circumferential adverse pressure gradient magnitude wasobserved. Next, the hub side separations induced the next shroud wall boundary layer separations. The
shroud side boundary layer separations developed and induced a low velocity region located at the diffuser
stall cell center.
3. The diffuser stall cell developed further as it approached the cutoff. The boundary layer separations developedon both shroud and hub walls by turns due to the impeller wake interaction that developed on the hub side.
The boundary layer separations occurring on the shroud and hub wall were considered as the key factors contributing to the diffuser stall generation by both experimental and CFD results.

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Figure 14. Distributions of Velocity Fluctuation in Meridional Direction (EXP:ϕ = 0.08).

Nomenclature
B diffuser passage height (m)D diameter (m)G mass ﬂow rate (kg/s)
N rotational speed (min−1)
Q volume ﬂow rate (m3/s)
Vr radial velocity (m/s)
p static pressure (Pa)pt total pressure (Pa)t time (s)trev one impeller revolution time (s)t* non-dimensional time (=t/trev)
Z number of impeller bladesρ air density (kg/m3)
ϕ ﬂow coefﬁcient
ψt total pressure rise coefﬁcient
1 impeller inlet
2 impeller outlet
3 diffuser inlet
4 diffuser outlet

Funding sources
Grant-in-Aid for Early-Career Scientists No.19K14894.

Competing interests
Nobumichi Fujisawa declares that he has no conﬂict of interest. Kenta Tajima declares that he has no conﬂict of interest.
Hiroshi Miida declares that he has no conﬂict of interest. Yutaka Ohta declares that he has no conﬂict of interest.
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