Journal of Applied Fluid Mechanics, Vol. 10, No. 1, pp. 143-155, 2017.

Available online at www.jafmonline.net, ISSN 1735-3572, EISSN 1735-3645.

DOI: 10.18869/acadpub.jafm.73.238.26476

Flow Characteristics of a Pipe Diffuser for Centrifugal

Compressors
Z. Sun, X. Zheng† and Z. Linghu
Turbomachinery Laboratory, State Key Laboratory of Automotive Safety and Energy, Tsinghua University,
Beijing, 100084, China.

†Corresponding Author Email: zhengxq@tsinghua.edu.cn

(Received April 29, 2016; accepted July 30, 2016)

ABSTRACT

The pipe diffuser, an efficient kind of radial bladed diffuser, is widely used in centrifugal compressors for gas
turbine engines. This paper investigates flow characteristics of a pipe diffuser for centrifugal compressors by
solving three-dimensional Reynolds-averaged Navier-Stokes equations. The results show that the pipe diffuser
is adaptable to high Mach number incoming flows, and its unique leading edge could uniform the flow
distortion. Numerical analysis indicates that the choke in pipe diffuser occurs suddenly, which leads to the
dramatically steep performance curves near choke condition. Besides, it is found that the first half flow passage
is particularly important to the pipe diffuser performance as it influences the choking behavior, the static
pressure distribution, and the matching, so more attention should be paid to this region when designing or
optimizing a pipe diffuser. Two counter-rotating vortices generated in the diffuser inlet region are captured by
numerical simulation, and they can exist in the downstream of the diffuser passage. More detailed analysis
show that these two vortices dominate the flow structure in the whole diffuser passage by shifting flow to
certain positions and forming high-momentum flow cells and wake flow cells. The leading edge formed by the
intersection of adjacent diffuser passages significantly affects this pair of vortices. In addition, these two
vortices also affect the flow separation in pipe diffuser flow passages, they suppress separation near the front
wall and back wall while facilitate separation at center locations. Therefore, it is recommended to design the
leading edge of the pipe diffuser carefully to control the vortices and obtain a better flow field.
Key Words: Pipe diffuser; Centrifugal compressor; Flow characteristics; Counter-rotating vortices; CFD; Flow
separation.

NOMENCLATURE

A area x the abscissa of the reference frame

cp pressure recovery y the ordinate of the reference frame
l distance from diffuser throat to diffuser y non-dimensional wall distance of first node
outlet
m mass flow rate Subscripts
Ma absolute Mach number 0 total parameter
N rotation speed 1 pipe diffuser inlet
p pressure 2 pipe diffuser outlet
 loss coefficient

1. INTRODUCTION components: the impeller and the diffuser.

Researches have devoted to the design and the
Centrifugal compressors are widely used in gas improvement of diffusers to obtain higher stage
turbine engines, as they can achieve high pressure efficiency, and the pipe diffuser introduced by Kenny
ratio and enable engines to be more compact. At the (1969) and Runstadler et al. (1969) turns out to be an
same time, centrifugal compressors often suffer low efficient design. Compared with conventional vane
stage efficiency on account of the long flow path and island diffusers, the pipe diffuser has many
strengthened secondary flow phenomena, especially advantages. Bennett et al. (2000) point out that the
in diffusion components. A centrifugal compressor pipe diffuser has higher stage efficiency and fewer
applied in jet engines primarily consists of two friction losses. Moreover, the pipe diffuser is able to
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handle highly distorted inlet flow and gain superior relationship between the flow characteristics and the
performance at high inlet Mach numbers. The geometric features of the pipe diffuser performance
pioneering researches by Kenny (1969, 1970 & is unclear. In this paper, flow characteristics of a pipe
1972) show that pipe diffusers have lower diffuser for centrifugal compressors are investigated
manufacturing cost, superior efficiency with by solving three-dimensional Reynolds-averaged
supersonic inlet flow, and smaller throat blockage Navier-Stokes equations, and the underlying
compared with alternative designs. The pipe diffuser mechanism of the flow characteristics associated
has been applied in industrial products by General with the geometry features is revealed.
Electric and Pratt and Whitney in North America
(Bennett et al. 2000, Kenny 1972), and it is likely to 2. GEOMETRY CHARACTERISTICS
play a more important role in compressors where the
Mach number is high at the diffuser inlet (Kenny The pipe diffuser is essentially a kind of radial bladed
1970, Zachau 2008). diffuser. Its geometry and structure are similar to that
Due to the data protection for commercial security, of a channel diffuser or a wedge diffuser. The
open literature and available information about pipe geometry characteristics of pipe diffusers have been
diffusers are limited. Some researches are carried out described in previous studies (Kenny 1970, Reeves
to investigate the key parameters and their influences 1977, and Salvage 1997). An array of radial diffusion
on the performance of pipe diffusers. Reeves (1977) pipe passages is spaced uniformly in circumferential
compares the performance of pipe diffusers with direction in the diffuser ring, and all centerlines of
different inlet cross-sections. He proposes that the pipe passages are tangent to a common tangency
incidence at the inlet could have a considerable effect circle whose diameter is substantially identical to
on the performance of pipe diffusers, and an that of the periphery of the impeller. The fluid
optimum incidence for best performance is negative particles leave the center region of impeller blades at
3 degrees. Researches on the pipe diffuser throat angles above tangential whereas fluid particles near
have been done by Bennett et al. (2000). They the front and back shrouds leave at angles quite near
investigate pipe diffusers with different throat cross- the tangential. Therefore, an appropriate incidence at
sectional shapes and proposes an optimum ‘side-wall the diffuser inlet is achievable when passage center
expansion’. Besides, they introduce a design lines are tangent to the same tangency circle. Pipe
criterion for the throat size.The number of passages diffuser passages are made to intersect with adjacent
in the whole 360 degrees is another crucial ones and in this way the leading edges with elliptical
parameter. The works by Groh et al. (1970) show that ridges (Fig. 1) are formed (Kenny 1969, Zachau
increasing the passage number of pipe diffusers 2008, Grates et al. 2014, Zachau et al. 2009, and
extends the stable operation range without Kunte et al. 2013). At the same time, the beginning
decreasing efficiency. However, the results from and the cusp (shown in Fig. 2) of the elliptical ridges
Bennett et al. (1998) suggest that pipe diffusers with are located in two circles outside the tangency circle,
a low number of passages can get wider operating respectively. Finally, as presented in Fig. 2, three
range at the cost of increased unsteadiness and flow different spaces are formed between the tangency
distortion. The length of the flow passage also circle and the diffuser throat. Regions inside the cusp
influences the performance of pipe diffusers, and it of the elliptical ridges are called vaneless space while
is studied by Kunte et al. (2013), and they truncate regions outside the beginning of elliptical ridges
the pipe diffuser and observes an increase of 0.3% in (leading edge radius) are semi-vaneless space.
stage isentropic efficiency. Moreover, the flow angle Between them is the pseudo-vaneless space.
at the pipe diffuser outlet changes when the pipe
diffuser is truncated.
Some investigations are focused on the flow
structures and flow characteristics of the pipe
diffuser. Zachau (2008) studies the three-
dimensional flow phenomena with PIV technology,
and results show that streamlines are pushed to the
suction side (SS) of the passage and flow separation
occurs in regions near the pressure side (PS). Grates
et al. (2014) reveal that the fluid flow inside impeller
and pipe diffuser is highly unsteady. In the inlet
domain, the leading edge of the pipe diffuser
generates a pair of vortices, and it can help mix the Fig. 1. The inlet region of a pipe diffuser.
non-uniform inlet flow better (Zachau 2008, Gates et
al. 2014, and Zachau et al. 2009). Grates et al. (2014) Downstream of the semi-vaneless space is the throat
also investigate the generation process of the vortices of a pipe diffuser, a short region of constant cross-
by unsteady CFD and notices that the intensity of the section area (shown in the enlarged view in Fig. 3).
vortex near impeller hub is constant in time while the The streamwise length of the throat affects the stage
other one is oscillating. performance. According to Han at el. (2014),
Previous research on pipe diffusers provides useful increasing the throat length decreases the efficiency
information about the critical parameters, the flow and pressure ratio at design point while it improves
field, and the vortices. The geometry information is the performance at near surge point.
introduced in some papers and patents. However, the The diffusion law of the passage is a unique feature

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of the pipe diffuser geometry. To express this law 3. SIMULATION MODEL AND
clearly, a reference frame is established as shown in VALIDATION
Fig. 3. Its origin is located at the center point of the
diffuser throat inlet, and the distance from throat inlet To investigate the detailed flow field of the pipe
to diffuser passage outlet is denoted as l. Based on diffuser by numerical methods, a simulation model is
this frame, the distribution of the cross-section area established first. In this investigation, based on the
of the diffuser passage from the throat inlet to the three-dimensional steady compressible finite
diffuser outlet (0 < x/l < 1) is displayed in Fig. 4. volume, the Reynolds-averaged Navier-Stokes
According to the inclination of the area distribution equations are solved. Fourth order Runge-Kutta
curve, the cross-section area increases slowly near scheme and Central scheme are used for temporal
diffuser throat but much more quickly at the rear discretization and spatial discretization, respectively.
parts. The main reason for such a diffusion law lies The Shear Stress Transport (SST) turbulence model
in the requirements of controlling reverse static is applied for turbulence closure. A multigrid
pressure gradient, which is demonstrated in the later procedure is applied to accelerate the convergence.
part of this paper.
As for boundary conditions, the solid wall is set to be
non-slip and adiabatic. Total pressure, total
temperature as well as velocity directions are
imposed as inlet boundary condition. Outlet
conditions are changed depending on the operation
condition. At near choke conditions, static pressure
is imposed at the diffuser outlet while, at other
conditions, averaged mass flow rate is imposed at the
diffuser outlet. Besides, the frame change between
the rotational impeller and stationary diffuser is
achieved by the method of “Stage” supplied in
ANSYS CFX, which is actually a method of “Full
Non Matching Mixing Plane”.

Fig. 2. Schematic of the pipe diffuser inlet region.

Fig. 5. The mesh of a single passage mesh in the

compressor stage.

The impeller used in this investigation consists of

Fig. 3. Schematic of the diffuser passage and the 19 main blades and 19 splitter blades, and the pipe
reference frame. diffuser has 30 flow passages. The meshed domain
only contains one single passage of the impeller
and the pipe diffuser, which is adequate for the
simulation requirements of this investigation. It is
widely acknowledged that the spatial
discretization error is directly related to the grid
number. Usually, a higher grid number is needed
for higher calculation accuracy, but it inevitably
occupies more CPU time and storing memories.
To determine the optimum grid number that can
ensure both the accuracy and the acceptable time
and memory requirements, several meshes with
different grid numbers are tested. The results show
that 500,000 nodes in a single impeller passage
and 500,000 nodes in a pipe diffuser passage is a
satisfying choice that meets all the simulation
Fig. 4. Cross-section areas distribution along the requirements. The mesh finally used is shown in
center line of the diffuser passage.

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Fig. 5. For the impeller passage, a structured grid validation. The comparison between numerical
is created, and the mesh contains 546,819 nodes and experimental total pressure ratio at 80%
with 512,860 elements. For the pipe diffuser rotating speed is shown in Fig. 7. It can be seen
passage, there are 512,860 nodes, but more that experimental and numerical results agree well
elements (2,080,072 elements) because an in tendency as the largest relative difference is less
unstructured grid is used due to the complex than 5%, the CFD can predict the characteristics
geometry of the pipe diffuser. To get the suitable of the overall performance well despite the small
value of y+, the mesh height of the first layer is set flaw that the CFD underestimates the total
as 0.001 mm, and seven prism layers are imposed pressure ratio slightly when the compressor
near the pipe diffuser solid wall. As shown in Fig. operates at conditions near choke, while it
6, the y+ for all solid wall is less than 3.0, which overestimates the total pressure ratio slightly at
is an acceptable range for the application of SST near surge conditions.
turbulence model to obtain credible results
(Vaughn at el. 2007).

Fig. 7. Total pressure ratio comparison between

experiment and CFD at 80% speed.

Fig. 6. Distribution of y+ on all solid walls. Two measurement locations named as 2M' and 4M
are selected to compare the detailed flow inside
the compressor. As shown in Fig. 8, 2M' locates
As the purpose of this paper lies not only on the
near the outlet of the impeller and intersects with
overall stage performance of the compressor with a
the trailing edge of the impeller blade, while the
pipe diffuser, but also on certain details of the flow
measurement plane 4M locates at the inlet of the
and interaction, it is appropriate to validate the
wedge diffuser. The comparison in detailed flow is
numerical method at the level of both overall
carried out at the similar operation condition
performance and detailed flow field. To do this, the
marked as “CP” with a dash circle in Fig.7, where
overall and detailed experimental results of the
the mass flow rate is 87.5% of the choke mass flow
compressor case “Radiver” is used to validate the
rate, and the results of velocity comparison at 80%
accuracy of the simulation method. “Radiver” is a
rotational speed are shown in Fig. 9 and Fig. 10.
centrifugal compressor with wedge diffuser
developed by the Institute of Jet Propulsion and According to Fig. 9, accurate prediction of the
Turbomachinery of the RWTH Aachen. The reason relative velocity at 2M’ measurement plane is
of selecting this compressor for numerical validation obtained with CFD as the distribution of the
is because of abundant flow details inside this magnitude of the relative velocity is quite similar
compressor obtained by advanced visual between numerical and experimental results. It can
experiments. As for “Radiver”, the distance between be seen that the flow field at 2M’ is characterized
wedge diffuser inlet and impeller outlet is adjustable, by an area of low relative velocity near the shroud
here we chose the results of case “rle / rte = 1.04” for side, but this area is a little larger in the numerical
validation as this ratio almost equals to the ratio of result than that in the experimental result. In
the investigated pipe diffuser in this paper (rte and rle addition, high relative velocity areas are detected
stands for the radius of impeller trailing edge and by both CFD and experiment at corners between
diffuser leading edge, respectively). Detailed the hub and the impeller blade. Obviously, the
introduction about the compressor “Radiver” and flow structure at 2M’ is of great agreement
related experimental information could be found between CFD and experiment and the CFD
easily in published literatures (Ziegler et al. 2002, method used in this paper is capable to catch the
Ziegler et al. 2003, Weiß et al. 2003, and Ziegler detailed flow in the impeller.
2003).
When it comes to measurement location 4M, the
When simulating the case “Radiver”, the distribution of absolute velocity is compared
numerical model is set to be the same as the one between CFD and experiment. From Fig. 10 one can
used for the centrifugal compressor with pipe see that the numerical prediction of the flow field
diffuser to ensure the scientificity of the structure is again quite good. At areas near the

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Fig. 8. Schematic of measurement locations in the compressor “Radiver”

(Ziegler et al. 2003, and Ziegler 2003).

Fig. 9. Comparison of relative velocity at 2M’ at the operating point “CP”.

Fig. 10. Comparison of absolute velocity at 4M at the operating point “CP”.

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leading edge of the wedge diffuser (marked by the 4.1 Characteristics Related to Different
vertical dash lines), low absolute velocity is shown Mass Flow Rates
by both numerical and experimental results, and high
absolute velocity areas appear in the middle region The stage performance curve is one of the most
between two adjacent diffuser vanes. Again the flow significant characteristics of a compressor stage,
structure obtained by CFD and experiment at 4M from which a lot of useful information can be
shows great agreement, indicating the CFD can obtained immediately. Fig. 11 (a) and (b) show
capture the main characteristics of the flow field. curves of total pressure ratio and isentropic
efficiency versus normalized mass flow rate. Both
The CFD results show a good agreement with the two curves are steep when the normalized mass flow
experimental results of the compressor “Radiver” in rate is nearly 1.0 (choke condition). Once the mass
terms of overall stage performance and detailed flow flow rate decreases slightly, however, the curves
field, especially the flow structure inside the become flat immediately, and total pressure ratio and
impeller and diffuser. In spite of the acceptable small isentropic efficiency change slowly with further
deviations in overall performance prediction decrease in mass flow rate. This characteristic is
(relative difference less than 5%), the numerical quite different from that of conventional vaned
method is still capable to predict the overall diffusers or vaneless diffusers, and it indicates that
performance and the main characteristics of the flow the choke in the pipe diffuser happens suddenly. This
field. Therefore, it can be concluded that the characteristic is owed to the special geometric
numerical method used in this study is adequate for structure in the inlet region. At the upstream of the
this investigation. pipe diffuser throat, adjacent passages intersect in the
inlet region and form sharp leading edges with
4. NUMERICAL RESULTS AND elliptical ridges. This leading edge is a ‘swallow-tail’
ANALYSIS type of geometry, and it allows the pipe diffuser to
swallow a highly non-uniform flow (Cumpsty 2004,
The stage performance and the inside flow of the and Krain 2003). When the impeller discharge flow
investigated centrifugal compressor with a pipe passing through the inlet region and arriving at the
diffuser are obtained by numerical methods. To study diffuser inlet, it becomes much more uniform.
the relationship between the flow characteristics and Therefore, at choke condition, most of the flow in the
the geometric features in the pipe diffuser, the diffuser throat accelerates and reaches a speed of
operating condition of design speed is simulated, and sound simultaneously, and when mass flow rate
the simulation results are shown from different decreases, the pipe diffuser could free from the choke
aspects as follows. easily. Fig. 12 presents the Mach number distribution
at the diffuser throat. The proportion of the throat
area where the Mach number is less than 1.0 is no
more than 20% at choke condition (Fig. 12 (a)),
which means most of the flow passing the throat
reaches the speed of sound simultaneously. However,
at the near-choke condition (mass flow rate decreases
by 1.0%), the Mach number at all the throat cross-
section is less than 1.0 (Fig. 12 (b)), implying the
pipe diffuser no longer suffers from the choke after a
slight decrease in mass flow rate.
To investigate the characteristics of diffusion ability
and loss generation in the pipe diffuser, the pressure
recovery and the loss coefficient are used. These two
parameters are defined as Eqs. (1) and (2). The
definitions reveal that pressure recovery stands for
the diffusion ability. Larger pressure recovery means
more static pressure is obtained from decelerating the
flow. Meanwhile, the loss coefficient represents the
loss in total pressure, the smaller it is, the fewer
losses are generated.
Pressure recovery:
p2  p1
cp  (1)
p01  p1
Loss coefficient:
p01  p02
 (2)
p01  p1
The curves of loss efficient and pressure recovery for
Fig. 11. Compressor map for (a) total pressure the investigated pipe diffuser are shown in Fig. 13 (a)
ratio and (b) isentropic efficiency. and (b). With the decline of the normalized mass

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Fig. 12. Mach number at diffuser throat cross-section: (a) choke condition; (b) near-choke condition.

flow rate, the pressure recovery increases rapidly to pressure by decelerating the high-speed flow
a certain value, then slightly decreases. The loss discharged from the impeller outlet. The static
coefficient presents an opposite tendency, as it pressure distribution along the flow passage is
decreases to a certain value and then slightly important for the diffuser performance. Regarding
increases. According to Fig. 13 (a) and (b), 95% to the diffuser passage as a one-dimensional flow
98% of the choke mass flow rate is an optimum channel, the reference frame shown in Fig. 2 can be
operation flow range where the pipe diffuser can used to display the static pressure distribution along
obtain high pressure recovery and low loss the diffuser center line. The results of the
coefficient, which means obtaining high static investigated pipe diffuser are presented in Fig. 14.
pressure without generating high losses. Obviously the distribution changes under different
operating conditions.
Stable flow range (SFR) is another
importantparameter of a compressor that stands for Comparing the static pressure distribution at the
the stability. Its definition is expressed in Eq. (3) choke condition and the peak-efficiency condition
(both conditions are marked in Fig. 11), the biggest
m choke  m surge difference occurs in the throat region and the rear
SFR  ( ) N const  100% (3)
m choke region (where 0 < x/l < 0.2). As shown in Fig. 14
(a), the static pressure changes acutely in this
 choke and m surge are the mass flow rate at
where m region when the pipe diffuser operates at the choke
choke and surge point respectively. The SFR of the condition. The static pressure decreases abruptly
investigated pipe diffuser can be obtained from Fig. first and then increases sharply after the nadir
11 and Fig. 13, and its value is near 8%. To ensure which locates at the downstream of the throat
sufficient surge margin, the pipe diffuser should not where x/l is about 0.1. Nevertheless, the static
operate at conditions near surge. So the suitable pressure at the peak-efficiency condition increases
operating flow range for a pipe diffuser is suggested smoothly at this region (shown in Fig. 14 (b)). The
to be 96% to 98% of the choke mass flow rate. difference is mainly because of the incoming flow.
Within this flow range, the pipe diffuser could According to the absolute Mach number
balance the static pressure rise, the loss generation, distribution shown in Fig. 15, at the choke
and the surge margin. Bennett et al. (2000) introduce condition (Fig. 15 (a)) where the mass flow rate is
a design criterion for the design of the diffuser throat relatively high, the flow accelerates to supersonic
size, he suggests that the design mass flow rate of the flow quickly when passing through the throat
compressor stage should be 96% to 98% of the choke region. The supersonic flow continues to accelerate
mass flow rate of the pipe diffuser. Therefore, when in the diffusion passage after the throat. Thus, the
designing a pipe diffuser, it is better to set the throat acceleration results in great and steep decrease in
to such a size that the mass flow rate of the design static pressure. Then the flow suffers a shock wave
point is 96% to 98% of the choke mass flow rate. at the position where x/l is about 0.1. The shock
wave heavily compresses the flow and increases the
4.2 Static Pressure Distribution along static pressure sharply. At the peak-efficiency
Diffuser Passage condition (Fig. 15 (b)) where the mass flow rate is
relatively low, the flow passing the passage is
The function of a diffuser is increasing the static subsonic. Therefore, no supersonic acceleration or

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shock wave appears, and no abrupt change happens At both the choke condition and the peak-efficiency
in static pressure. conditions, the static pressure increases more rapidly
in the first half of the diffusion passage than the
second half, and this can be verified from the slopes
of the curves in Fig. 14. This is an inherent feature in
a centrifugal diffuser, and some previous studies
prove the reality. Zachau (2008) draws a similar
conclusion from the experimental results in his
investigation on the pipe diffuser, and Grates et al.
(2014) present similar numerical and experimental
results when investigating the static pressure
distribution at the diffuser shroud. The increasing
rate, however, cannot be too high, or the flow would
suffer a great adverse static pressure gradient which
exacerbates the instability of the flow field. So when
designing a pipe diffuser, the increasing rate of the
cross-section area of the diffusion passage is well
controlled (shown in Fig. 4), especially at the first
half of the passage. A pipe diffuser usually operates
at 96% to 98% of the choke mass flow rate,
indicating that the operating condition is close to the
choke condition. At the first half of the passage, the
absolute Mach number is close to 1.0, and a small
change in cross-section area would cause a
significant change in static pressure. The explanation
is as follows.

Fig. 13. Characteristics of (a) loss coefficient and

(b) pressure recovery of the investigated pipe
diffuser.

Fig. 15. Absolute Mach number distribution at

50% span at (a) choke condition and (b) peak-
efficiency condition.

Regarding the diffuser passage as a pseudo one-

dimensional heat-insulated pipe, and assuming that
the flow inside is steady isentropic inviscid flow, a
correlation can be expressed as Eq. (4).
du dA du 1 dA (4)
( Ma 2  1)   
u A u Ma 2  1 A
where Ma denotes the local Mach number, u denotes
the flow velocity along the center line, and A denotes
Fig. 14. Static pressure distribution along the the cross-section area of the diffuser passage.
diffuser passage center line at (a) choke
condition and (b) peak-efficiency condition. According to Eq. (4), when Mach number is close

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to 1.0, the velocity will change a lot with a small moves towards the suction side (SS). Because of the
change in cross-section area, then great change deflection effect of the passage wall, the main flow
occurs in the static pressure. So at the first half of turns towards the front wall along SS, then it is
the passage, the increasing rate of the cross-section redirected again near the front wall and moves
area must be small to avoid an abrupt change in towards the pressure side (PS) along the front wall.
static pressure. Therefore, the cross-section area of In this way, a vortex is generated near the front wall.
the diffusion passage in a pipe diffuser increases This vortex also occurs in other radial bladed
slowly in the first half of the passage while diffusers applied in centrifugal compressors. Ziegler
increases much faster in the second half, as et al. (2003) studied the unsteadiness of this vortex
described in Fig. 4. in a wedge-type diffuser, and Stahlecker et al. (1998)
detected the vortex in a vaned diffuser by
The first half of the diffusion passage of a pipe experimental methods. The vortex near the back wall
diffuser is significant as it has predominant can be seen clearly in plane02, implying that it is
influences on the performance of a pipe diffuser. The fully generated before entering the diffuser throat.
flow phenomena are complex here, shock wave and After the elliptical ridge, the flow suffers an abrupt
supersonic flow often occur, and the cross-section expansion and forms a backflow area at the corner
area determines the static pressure distribution. So it between the back wall and the PS. The vortex near
is recommended that improvement investigations the back wall is generated by the interaction between
should focus more on this area. the flow passing over the ridges and the flow in the
4.3 Vortices and Total Pressure Distribution backflow area. More detailed perspective about the
generation process of the pair vortices is presented
As mentioned in many publications (Gates et al. 2014, by Grates et al. (2014).
and Kunte et al. 2013), there is a pair of counter-
rotating vortices inside the pipe diffuser passages, one Besides the difference in locations and generations,
is near the front wall (near impeller shroud) while the the two vortices also differ in their sizes and moving
other one is near the back wall (near impeller hub), and trajectories. According to the streamlines in Fig. 17,
this is a unique flow characteristic of the pipe diffuser. both two vortices can be seen at the diffuser outlet,
In this investigation, vortices are detected by steady and the vortex near the front wall is larger than the
simulation. To track their development in the flow one near the back wall in all eight planes. According
direction, eight cross-sections of the diffuser passage to the streamlines from plane01 to plane08 shown in
are selected to display the shapes and locations of the Fig. 17, the relative position of the two vortices
two counter-rotating vortices. As exhibited in Fig. 16, varies at different locations. From diffuser inlet to
these cross-sections are named from plane01 to outlet, the larger vortex moves from the front wall to
plane08. Plane01 is located on the leading edge of the the back wall, and is finally located in the middle
diffuser elliptical ridges while plane08 is close to the area near the PS. Meanwhile, the smaller vortex
outlet of diffuser passage. Plane02 and plane03 locates moves from the PS to the SS along the back wall, and
at the throat inlet and outlet respectively. is finally located in the corner between the back wall
and the SS.
The pair of vortices can affect the flow field inside
the pipe diffuser significantly because they
transform and redistribute the flow. Fig. 18 shows
the total pressure distribution in different locations,
and these distributions are directly related to this
pair of vortices. At diffuser inlet regions (plane01
to plane04), the main flow from impeller outlet first
rushes to SS, and then vortices shift it. As the vortex
near the front wall is much larger and stronger, it
plays a predominant role in shifting the flow. As a
result, most of the high-momentum flow gathering
near the SS is shifted by the larger vortex and
Fig. 16. Selected cross-sections in the pipe moves towards the front wall along the SS. At
diffuser passage. regions further downstream, the larger vortex
continues shifting the high-momentum flow from
the SS to the PS along the front wall (from plane04
Streamline projections in these cross-sections are
to plane08 in Fig. 18), and finally the high-
shown in Fig. 17 to illustrate the vortices. In plane01,
momentum flow comes to the corner between the
the streamlines are greatly influenced by the
front wall and the PS. Meanwhile, the smaller
elliptical ridges. The elliptical ridges function as a
vortex also transports some high-momentum flow
vortex generator in pipe diffusers. At the corner
from the SS to the PS along the back wall. As a
between the back wall and the PS, the velocity of the
result, high-momentum flow is brought to the PS
flow is low because of the passage expansion after
by the pair of vortices and re-energizes the wake
the elliptical ridges, this flow interacts with the main
flow on the PS, thus reducing the aerodynamic
flow passing over the elliptical ridges and generates
loading. The vortices also shift wake flow to the
the vortex near back wall. For the other vortex near
center of the passage. In plane07 and plane08, an
the front wall, it can be greatly influenced by the
area filled with the low-momentum flow is clearly
elliptical ridges, but it has a different generation
presented in the center regions.
process. After leaving the impeller, the main flow

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Fig. 17. Streamlines in different cross-sections at peak-efficiency condition (color stand for the
amplitude of the flow velocity).

Fig. 18. Total pressure distribution in different cross-sections at peak-efficiency condition.

The transportation of flow by the pair vortices 4.4 Flow Separations

leads to two consequences: 1). A low-momentum
flow cell is formed in the center area at the second Flow separation in the pipe diffuser often occurs in
half of the passage, and it is surrounded by an the PS at the downstream of the diffuser throat
energy-rich flow-layer near the passage wall. 2). (Zachau 2008) and is greatly affected by the vortices.
Boundary layer loading on the PS is reduced, and Flow separation is much focused, especially at near
the flow stability is improved because the flow surge conditions, because it affects both the stability
separation is suppressed on the PS by re- and efficiency of the compressor stage. According to
energizing the wake flow. Fig. 11 (b), the peak-efficiency condition is very
close to the surge line, so it is selected here to analyze
In fact, vortices are often used to control flow the separated flow. To investigate the flow separation
separation and improve the stability of compressors. inside the pipe diffuser, four planes parallel to the
For example, Hasegawa et al. (2008) study front wall and the back wall are created, as shown in
adaptive separation control system using vortex Fig. 19. The two planes near the back wall cut the
generator jets for time-varying flow and get pipe diffuser passages at 10% span and 30% span
some good results. while the other two cut the pipe diffuser passages at
60% span and 90% span. As the flow separation is
The pair of vortices is generated in the inlet region more likely to happen in areas where the flow
and they exist in the whole passage. By transferring momentum is low, the 30% span and the 60% span
the flow to certain positions, they can greatly are of more possibility to detect flow separations
influence the flow behavior and dominant the flow because they interact with the wake flow cells in the
field, further influence the performance of the pipe diffuser passage (shown in Fig. 19).
diffuser. As the spatial structure of the inlet region,
especially the structure of the elliptical ridges, has a Streamline projections in the four planes at peak-
great effect on the vortices in the process of efficiency condition are shown in Fig. 20. According
improving the performance of the pipe diffuser, to the streamline distribution, flow separations
many works could be done on the elliptical ridges to happen near the PS at positions 1 and 2 in the 30%
control the vortices and improve the flow field. span and the 60% span, and streamlines tend to

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Fig. 20. Streamline projections in planes located in different spans (Peak-efficiency condition).

deflect towards the SS once separation occurs. The There remains a difference between separations in
experimental results from Zachau (2008) present position 1 and 2. Flow in position 2 is of low-
comparable flow phenomena. He studies the momentum (see plane07 in Fig. 18) and suffers from
separation in different operating conditions and heavy separation and reverse flow. By contrast, flow
concludes that flow only separates near the PS in all in position 1 separates slightly, and the separated
investigated conditions. The flow separations flow even reattaches to the PS wall downstream at
areessentially related to the pair vortices generated in 60% span. In fact, the flow in position 1 is less likely
diffuser inlet region. As what has been mentioned to separate because its momentum is relatively
when discussing the results in Fig. 18, the higher, and the reverse static pressure gradient is well
transportation effect of the two vortices redistributes controlled by the passage expansion rate. It is the
the flow and forms wake flow cells in the diffuser vortices that stimulate the slight separation. As
passages. Position 1 and 2 at the 30% span and the shown in Fig. 21, the vortices shift flow from the PS
60% span are within or near these wake flow cells to the SS in the 30% span and the 60% span, flow in
(Fig. 19), so the flow here is easier to separate. position 1 is driven away from the PS wall. As a
result, slight separation occurs here.

.
Fig. 21. Velocity vectors in plane04 at peak-
efficiency condition.

Unlike at 30% and 60% span, no separation happens

Fig. 19. Locations of planes parallel to the front at 10% span and 90% span (Fig. 20), and this is the
wall and back wall. benefit of the vortices. Velocity vectors at plane04

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(Fig. 21) show that vortices shift high-momentum dominate the flow structure in the whole diffuser
flow from PS to SS along the front wall or the back passages by shifting flows to certain locations
wall, thus the wake flow near PS is re-energized and and forming high-momentum flow cells and
the boundary layer loading near the PS is reduced. In wake flow cells. Because the leading edge
this way, the vortices improve the stability of the formed by the intersection of the adjacent
flow near the front wall and the back wall. Grates et diffuser passages significantly affects the
al. (2014) also attribute the absence of flow generation of vortices, it is effective to optimize
separation in the front region of the PS to the this region to control the vortices and improve
transportation effects of the vortices. the structure of the flow field.
In summary, it is obvious that the vortices have a dual (4) The two counter-rotating vortices have
effect on the flow separation in a pipe diffuser. suppression effect and facilitation effect on the
Results from Zachau (2008) and results in Fig. 20 flow separation in a pipe diffuser. Near the front
indicate that flow separations in pipe diffuser occur wall and back wall, the vortices shift high-
in the PS, so the separated flow moves from the PS momentum flow from the suction side to the
towards the SS. According to Fig. 21, the vortices pressure side, and reduce aerodynamic loading
facilitate the flow separated from the PS at the on the pressure side and suppress the flow
middle regions of the passage, like 30% and 60% separation. However, they move the high-
span. Meanwhile, it helps the flow to attach to the PS momentum flow away from the pressure side at
at regions near the back wall and the front wall, like center locations and facilitate the flow
10% and 90% span. Therefore, such avortices are separation. In the process of designing a pipe
wanted, which can suppress the flow separation at diffuser, one of the key issues is to balance the
near wall regions without greatly stimulating flow suppression effect and the facilitation effect on
separation in the middle regions. So the inlet region the flow separation.
and the elliptical ridges need to be carefully designed
to obtain a pair of vortices that can balance both the ACKNOWLEDGMENTS
two opposite sides.
This research is supported by the National Natural
5. CONCLUSIONS AND REMARKS Science Foundation of China (Grant No. 51176087).
Authors of this paper would like to give sincere
A three-dimensional numerical investigation has appreciation to the Institute of Jet Propulsion and
been carried out on a pipe diffuser to analyze the Turbomachinery of the RWTH Aachen for providing
relationship between the flow characteristics and the the test case “Radiver” whose experimental results
geometric features. The following conclusions can are used to validate the CFD method in this
be drawn from the results: investigation.
(1) The pipe diffuser inlet region composed of the
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