Experimental Study on Performance of Centrifugal

Compressor Exposed to Pulsating Backpressure

Mengying Shua, Mingyang Yanga,*, Kaiyue Zhanga, Kangyao Denga, Bijie Yangb, Ricardo Martinez-Botasb

a Shanghai Jiao Tong University, Shanghai, 200240, China

b Imperial College London, London, SW7 2AZ, UK

Abstract

Pressure fluctuations in intake manifold of Internal Combustion Engine introduce a pulsating boundary condition

to the centrifugal compressor. In this study, the performance of centrifugal compressor exposed to pulsating

backpressure is experimentally investigated. Unsteady performance and surge characteristic of the compressor at

different pulsating conditions are analyzed. Results show that instantaneous performance of the compressor forms a

hysteresis loop encapsulating steady performance. A correlation of compressor unsteadiness with pulse frequency,

magnitude, and local slope of the characteristic curve is obtained based on measurements. Cycle-average performance

of the compressor is notably lower than that at constant conditions. Specifically, the averaged peak efficiency at

pulsating condition drops 3%~7%. Fast Fourier Transformation method is applied to study surge characteristics at

pulsating conditions. Results manifest that compressor surge is postponed remarkably by pulsating backpressure at all

conditions. As the compressor approaches to small mass flow rate, flow fluctuations decay quickly and then increase

dramatically when the surge happens, forming the variation with ‘V-shape’ for frequency domains. This phenomenon

is resulted from the influence of the slope of characteristic curve on the filling-empty and compressor stability. Smaller

slope produces less filling-empty and hence smaller size of the loop, but reduces the stability of compressing system

and initiates surge.

Keywords: Centrifugal compressor; Pulsating backpressure; Unsteady performance; Surge;

Nomenclatures

A = area, m2

a = sonic speed, m/s

f = frequency, Hz

* Corresponding author

Email: myy15@sjtu.edu.cn

l = length, m

M = pulse magnitude

m = mass flow rate, kg/s

N = rotational speed, RPM

P = pressure, kPa

PR = pressure ratio

S = absolute value of slope of performance curve

St = Strouhal number

T = temperature, K

t* = non-dimensional time

t = time, s

V = volume, m3

ΔSL = shift of surge limit

η = efficiency

κ = adiabatic index

Ω = size of hysteresis loop

Ψ = unsteadiness coefficient

Subscripts

ave = average

c = constant condition

corr = corrected

i = instantaneous

in = inlet

max = maximum

min = minimum

out = outlet

p = pulsating condition

ref = reference

1. Introduction

Turbocharging is the key technology for power recovery of Internal Combustion Engine (ICE) at high altitude

for long endurance unmanned aerial vehicle (UAV) [1, 2]. Centrifugal compressor is the core component of a

turbocharger. The performance of the compressor, including pressure ratio, efficiency, and aerodynamic stability, has

remarkable influence on the altitude adaptability and the endurance of the vehicle [3, 4]. Because ICE works in

reciprocating way, the intake valves are operated intermittently and result in pulsating environment downstream the

compressor in the intake manifold. Furthermore, the pulsating environment is further enhanced as the boosting level

increases to achieve better altitude adaptability. Consequently, the centrifugal compressor is exposed to pulsating

backpressure, and its performance is inevitably influenced by the highly unsteady condition. On the other hand, the

performance of a centrifugal compressor for turbocharging is normally obtained and studied with constant

backpressure instead of the pulsating one at real engine conditions. Therefore, it is necessary to obtain the knowledge

of centrifugal compressor exposed to the pulsating backpressure.

Pioneering experimental studies have been carried out on the influence of pulsating backpressure on the

performance of centrifugal compressor in recent decade [5-7]. The pulsating backpressure is produced by a pulse

generator which is installed downstream the compressor to simulate the intake valves. It is confirmed that pulsating

backpressure has notable influence on compressor performance and the aerodynamic stability. Different from the

performance at constant backpressure condition, the trace of instantaneous pressure ratio versus mass flow rate

encapsulates the steady performance, forming an evident hysteresis loop. Moreover, the size and the shape of the loop

are strongly influenced by the frequency and magnitude of the pulse, the location of the loop, and compressor

rotational speed. Particularly, the loop is enlarged as the pulse magnitude and the rotational speed increase [8, 9]. In

fact, similar phenomenon has been observed and comprehensively studied in turbine at pulsating incoming flow

conditions [10-12]. It is concluded that the filling-empty effect and wave dynamics are the reasons for different

behaviors of loops. In order to quantitatively evaluate the unsteadiness of turbine performance, dimensionless

coefficients as Strouhal number and pulse magnitude are introduced and theoretically proved to be related with instant

mass imbalance in the turbine system. Furthermore, Cao and Yang have shown that the local gradient of the pressure

fluctuation is the fundamental reason for the mass accumulation and performance unsteadiness at pulsating condition

[13, 14]. These studies on the turbine can enlighten the understanding of the compressor performance exposed to

pulsating backpressure. However, there are profound differences between the turbine and the compressor. Firstly, the

pulsating condition is upstream of inlet of turbine, while it is downstream the exit of compressor. The filling-empty

and wave dynamics may be evidently different due to different characteristics of the devices and bulk flow velocity.

Secondly, the swallowing capacity of turbine is not sensitive to rotational speeds when compared with that of

centrifugal compressor. As a result, the influence of rotational speeds on the unsteadiness of turbine performance at

pulsating conditions can’t be observed. Thirdly, although the mass accumulation has been proposed as an index of the

performance unsteadiness, it has never been experimentally validated in the studies of turbine, not to mention in the

centrifugal compressor. Finally but the most importantly, the surge which is the most important performance of the

compressor can’t be studied in turbine.

Surge limit determines the available operational range of compressor and hence the altitude-adaptability.

Compressor surge is a self-maintained oscillating flow phenomenon [15, 16]. Interest of research arises immediately

that how the compressor surge is affected when the compressor is exposed to forced pulsating backpressure. Few

researches have been carried out on quantitative analysis on the influence of surge characteristics by pulsating

backpressure so far. Galindo et.al [17] shows in the experiment that remarkable improvement of surge margin up to

15% can be achieved by the pulsating backpressure depending on the rotational speed of the compressor. Barrera-

Medrano et.al [18] further demonstrates that the influence is also coupled with the volume of pipes at compressor exit.

More benefits on the surge limit can be achieved by the increase of the volume. Positive effects on the surge limit by

pulsating backpressure have been observed in both researches, but few discussions have been carried out on the

mechanism of the influence. Moreover, it is worth mentioning that the frequency of surge is at the same order of the

pulse frequency and possibly similar strength of fluctuations. New methodology with good reliability has to be

developed to identify the initiation of surge at the pulsating conditions for the credible comparison among different

cases. In order to understand compressor instability exposed to pulsating backpressure, more detailed investigations

are necessary and valuable on the influence of pulsating backpressure on surge behaviors hiding in the pulsating

environment.

In this paper, behaviors of a centrifugal compressor under different pulsating backpressure conditions are studied

by experimental method. The paper is mainly organized in three sections. Firstly, experiment facilities and methods

of the study are introduced. Following that, instantaneous characteristic together with cycle averaged performance at

different pulsating conditions are analyzed and the evaluation method of performance unsteadiness of the compressor

is proposed based on the measurements. In the last section, surge characteristics of compressor exposed to pulsating

backpressure are discussed.

2. Experimental Facilities

2.1 Layout of test rig

Compressor performance at pulsating backpressure conditions is experimentally studied on the centrifugal

compressor test rig in Shanghai Jiao Tong University. The layout of the test rig is shown in Fig. 1. The centrifugal

compressor is driven by an ABB variable frequency motor through a belt and planetary gear box. The maximum

rotational speed of the investigated compressor is 90 kRPM. The inlet of the compressor is exposed to ambient

condition via a pipe with bell mouth. The compressed air from compressor exit is throttled by an electric-control

regulating valve before discharged to atmosphere. Pulsating flow is generated by a motor-driven rotating disk

downstream the compressor exit. At the meantime, the regulating valve is used to control mass flow rate of the

compressor. There are two branches in the exit piping system, which are used to study the performance of

intake/exhaust manifolds of internal combustion engine. They are closed by valve-A and valve-B (as shown in Fig. 1)

during compressor experiments.

Fig. 1 Layout of centrifugal compressor test rig

The maximum frequency of the pulse generator is 200 Hz, which corresponds to the pressure pulse in a 4-cylinder

engine operating at rotational speed 6000 RPM. Therefore, the frequency of pulsating backpressure in normal

operational range of a typical internal combustion engine can be generated by the device. Moreover, the pressure pulse

generated by the rig is compared with the one measured on an engine operated at rated condition, as shown in Fig. 2.

It can be seen that the shape of two pulses is quite similar, although moderate discrepancies are observed on the

amplitudes between the two pressure pulses. Therefore, the rig is considered to be capable to replicate the pulsating

environment of the centrifugal compressor in a real engine.

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.96

0.99

1.02

1.05

1.08N

on

-dim

ensi

on

al p

ress

ure

(-)

Non-dimensional time (-)

engine

pulse generator

Fig. 2 Comparison between pressure pule on engine and test rig.

The centrifugal compressor investigated in this paper is shown in Fig. 3. There are 7 main blades and 7 splitters in

the impeller, as demonstrated in subfigure (a). The exit diameter of the impeller is 110mm. The volute is shown in

subfigure (b). More detailed geometrical parameters are listed in Table 1.

(a) Impeller

(b) Volute

Fig. 3 Investigated centrifugal compressor.

Table 1 Geometrical parameters of compressor

Compressor geometries Value

Blade number 7+7

Impeller inlet hub radius 10.2 mm

Impeller inlet shroud radius 35.0 mm

Impeller exit radius 55.0 mm

Blade sweep angle 56.0 deg

Impeller exit width 5.4 mm

Diffuser exit radius 59.3 mm

A/R of volute 27.9 mm

2.2 Experimental method

Compressor performance at both constant and pulsating backpressure conditions are measured at three rotational

speeds as 25, 30, and 35 kRPM. The rotational speed of compressor is controlled by an ABB inverter and the accuracy

of speed is ±0.3 RPM for the motor, corresponding to ±9 RPM for the compressor. A photoelectric speed sensor is

installed to measure the speed of the pulley of the gear box, thus the compressor speed is obtained conveniently

according to the gear ratio.

For constant backpressure condition, steady mass flow rate is measured by a Venturi flow meter (V-cone) with an

accuracy of 0.5%FS at compressor inlet, as shown in Fig. 1. Steady static pressure is obtained by a 16-channel

scannivalve PSI 9116, with an accuracy of 0.05%FS at both inlet and outlet of compressor. The temperature is

measured by K-type thermocouples with the uncertainty of 1.5K at experiment temperature range. For pulsating

backpressure conditions, instantaneous flow parameters including mass flow rate and pressure are measured at

compressor inlet and exit. Specifically, instantaneous pressure is measured by fast response transducer (HM90) with

an accuracy of 0.4%FS. Transient mass flow rate is measured by 1D constant temperature hotwire anemometer

(Dantec 55P11) together with a 6-channel constant temperature anemometer (CTA) system at both compressor inlet

and exit. The response frequency of the hotwire is 10 kHz, which is fast enough to capture details of the pulsating flow

parameter. The measurement method of mass flow rate is well calibrated against the method via the V-cone at constant

backpressure conditions which cover the range of mass flow rate variations experienced at pulsating conditions. The

effect of temperature variation on hotwire is also considered by introducing a temperature-corrected coefficient in the

King’s law [19]. The measurement method of instant mass flow rate has already been well confirmed in the researches

of turbine under pulsating conditions [10, 12]. In particularly, the uncertainty of the calibration is limited in 5%.

Finally, the instantaneous temperature is calculated by instantaneous pressure and steady temperature based the

adiabatic process assumption which has been proved to be reasonable [20], as shown in Eq. (1).

1

ii steady

steady

PT T

P

−

=

(1)

The performance of compressor is defined by Eq. (2) ~ (4):

,

,

t in ref

corr

t in ref

m T Tm

P P

= (2)

,

,

t out

t in

PPR

P=

(3)

( )

1

( 1)in

out in

T PR

T T

−

−=

− (4)

where mcorr is corrected mass flow rate. PR and η is the pressure ratio and the isentropic efficiency. Pt and Tt is

total pressure and total temperature.

The time averaged performance of centrifugal compressor is also studied in this paper. The flow parameters in a

pulse period are obtained by the averaged values over 50 continuous pulses to alleviate the influence of random noise.

Cycle-average performance of compressor at pulsating backpressure condition is evaluated by Eq. (5) ~ (7):

i

Tave

m dt

mT

=

(5)

i i

Tave

i

T

PR m dt

PRm dt

=

(6)

( )

1

, ,

, , , ,

1in i i in i

T

ave

out i out i in i in i

T

T PR m dt

T m T m dt

− −

=−

(7)

Data acquiring is achieved via NI PXIe-1078 chassis containing a 16-channel NI-PXIe-6361 card, with a total

bandwidth 2MS/s for all 16 simultaneously data acquisition. The sample frequencies of all channels are set to 12 kHz,

in order to capture the details of pulsating flow parameters in the centrifugal compressor.

Based on the accuracy of sensors and the definitions of compressor performance, the uncertainty of the

measurement is evaluated according to the error transfer function. The maximum uncertainty of pressure ratio

measurement at steady state condition is 0.2%, while the uncertainty of instantaneous pressure ratio is 1.6%.

The compressor performance is measured from choke to surge by gradually closing the main valve with the

resolution of 1 degree. Compressor surge is detected by pressure fluctuations at compressor outlet during experiment.

Usually, the frequency of surge is at order of 10, which is similar with the frequency of the pulsating backpressure.

Furthermore, the magnitudes of the two oscillations are also comparable. As a result, it is difficult to identify the surge

from the pulsating backpressure by checking the scrutiny of flow fluctuations. However, the frequency of the pulsating

backpressure is set during the test and the frequency of the surge is the natural frequency of the compressing system.

Therefore, the initiation of the surge can be observed by the appearance of the frequency component which is close to

natural frequency of the system. Specifically, it is identified carefully by checking frequency domains of pressure

signal at compressor exit by Fast Fourier Transformation method (FFT).

3. Results and discussions

3.1 Instantaneous flow and performance at pulsating backpressure conditions

Compressor map at constant backpressure conditions is firstly obtained at three rotational speeds (25, 30, and 35

kRPM) for the comparison between pulsating and constant cases. Following steady tests, instantaneous performance

of the compressor is measured at pulsating back pressure. For each speed, three pulse frequencies, 80, 100, and 120

Hz are investigated, equivalent to the engine speed 2400, 3000, and 3600 RPM based on a four-stroke, four-cylinder

engine.

Fig. 4 demonstrates fluctuations of mass flow rate and pressure, normalized by average value, at both compressor

inlet and outlet at near choke condition. The fluctuations of pressure at compressor inlet reduces dramatically by 83%

when it propagates from the exit to the inlet. This is expectable because that the inlet pipe is directly exposed to the

atmosphere where the pressure is constant. However, the fluctuations of mass flow rate at the compressor inlet are

still remarkable, as demonstrated in the lower part of the figure. The magnitude reduces by less than 50% compared

with the one at the exit. Consequently, the inlet flow conditions are expected to fluctuate notably resulted from the

pulsating backpressure although the pressure is relatively stable. Moreover, it is observed that there is an evidently

phase difference (0.48 pulse period) between inlet and outlet pulses for both the pressure and mass flow rate.

Obviously, the phase shift is caused by the wave dynamics of the pulse from the exit to the inlet. Assuming the

propagation dominates the wave dynamics, the speed of the propagation can be evaluated as 353m/s by the phase shift

together with the length between two measurement locations, which is similar as the relative speed of averaged sonic

speed to the bulk flow velocity in the compressor.

Fig. 4 Fluctuations of pressure and mass flow rate at compressor inlet and exit (N=35 kRPM, f=80 Hz).

Because the fluctuations of mass flow rate are evidently different in terms of magnitude, shape, and phase at the

inlet and the exit, the hysteresis loops of the mass flow rate versus pressure ratio are different by using the mass flow

rate at two locations. Fig. 5 compares hysteresis loops of the mass flow rate at the inlet and exit at rotational speed 35

kRPM. Both the shape and the size of loops of the exit are notably different for the case of inlet. Interestingly, the

direction of hysteresis loops is anti-clockwise at compressor inlet, but it becomes clockwise at compressor outlet, as

shown by the arrows in the figure. It is the direct result of the large phase difference of the mass flow rate at the two

locations.

Fig. 5 Instantaneous pressure ratio versus mass flow rate at inlet and outlet (N=35 kRPM, f=80 Hz).

The performance of centrifugal compressor is sensitive to the inlet flow condition especially the flow angle.

Because the inlet mass flow rate fluctuates remarkably due to the pulsating backpressure, the inlet flow angle of the

impeller will be influenced inevitably. Fig. 6 manifests inlet flow angle at mean blade height in three periods at near

choke, peak efficiency and near surge at rotational speed 35 kRPM and pulse frequency 80 Hz. Specifically, the flow

angle is evaluated by mass flow rate, the density, and the area of the inlet duct with the blockage coefficient as 0.05.

The fluctuations of inlet flow angle caused by pulsating backpressure can be clearly observed. The amplitude of flow

angle pulse is about 4 degrees at near choke condition, then it decreases to around 2 degrees at peak efficiency and

near surge due to the shrinking of the hysteresis loops, as shown in Fig. 5. It is worth mentioning that the incidence

angle is more sensitive to the variation of mass flow rate at low mass flow rate condition due to the flatter velocity

triangle. Therefore, the fluctuation magnitude of inlet flow angle is still notable even the loop shrinks remarkably at

small mass flow rate. Considering that the sensitivity of compressor performance to the inlet flow angle, it is more

meaningful to apply the instant mass flow rate at the compressor inlet to evaluate its behaviors under pulsating

backpressure. This method of the performance evaluation is going to be applied in the following sections.

Fig. 6 Fluctuations of inlet flow angle (N=35 kRPM, f=80 Hz).

Fig. 7 demonstrates compressor instantaneous characteristic at two rotational speeds and frequencies. Four mass

flow rates are chosen on every speed for the discussion, which are near choke, peak efficiency, low mass flow rate,

and near surge point. Hysteresis loops encapsulating the steady characteristic curve are clearly seen in the figures. The

direction of hysteresis loops keeps the same for at all operational conditions, as indicated by arrows in the plots. It can

also be observed that the size and the shape of hysteresis loops vary significantly with the pulse parameters, the

location on the steady curve, and the rotational speed of the compressor. Specifically, the size of the loop enlarges

evidently as either the mass flow rate or the rotational speed increases. Moreover, the pulse frequency also has notable

influence on the shape as well as the size of the loops. Larger hysteresis loops are obtained at higher frequency near

choke condition. However, the size doesn’t increase with the frequency at smaller mass flow rate. It indicates that

other factors may contribute to the variation of the hysteresis loops.

0.00 0.05 0.10 0.15 0.20 0.25 0.30

1.00

1.05

1.10

1.15

1.20

1.25

Pre

ssure

rat

io (

-)

Corrected mass flow rate (kg/s)

N=35 kRPM

N=25 kRPM

f = 80Hz

(a) f=80 Hz

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

1.00

1.05

1.10

1.15

1.20

1.25

Pre

ssure

rat

io (

-)

Corrected mass flow rate (kg/s)

N=35 kPRM

N=25 kPRM

f = 120Hz

(b) f =120 Hz

Fig. 7 Instantaneous performance at pulsating backpressure conditions.

In fact, the hysteresis loop at pulsating condition is caused by both the filling-empty effect and wave dynamics in

the compressor. This phenomenon has been previously observed and comprehensively studied in the turbine exposed

to pulsating incoming flow in literatures [20, 21]. In the studies, it has been confirmed that the mass imbalance in the

turbine is a reasonable criteria to evaluate the unsteadiness of the turbine performance under pulsating incoming flow

[13]. Moreover, the quantity of the mass imbalance can be directly evaluated by the size of hysteresis loop of

swallowing capacity. Enlightened by the study in turbine, the relationship between the unsteadiness of the compressor

and the size of the hysteresis loop is going to be studied in the following contents.

Size of loop can be calculated by the integration of pressure ratio along the loop and non-dimensionalized by the

area of map, as in Eq. (8):

100%loop

PRds

PR m =

(8)

In order to quantitatively evaluate the unsteadiness of the compressor performance at pulsating backpressure

condition, the coefficient of the unsteadiness Ψ is defined by the difference of pressure ratio between the one at

pulsating condition and quasi-steady condition. The quasi-steady performance of the compressor is conveniently

calculated by the steady characteristic. Therefore, the unsteadiness coefficient is evaluated as Eq. (9):

=

i i steady

T

steady

T

PR m PR m dt

PR mdt

−

(9)

The correlation of the unsteadiness coefficient with the size of the loop is manifested in Fig. 9 where all the

experimentally measured data at different conditions are plot together. It is clearly seen from the figure that all the

data fall in the linear band. As a result, a linear correlation can be used for a good approximation to describe the

relationship of the unsteadiness of the compressor and the size of the loop, as shown by the black dashed line in the

figure. The results prove solidly that the unsteadiness of the compressor is proportionally correlated with the size of

the loop. Therefore, it is reliable to employ the size of the loop to evaluate the unsteadiness of the compressor at

pulsating backpressure.

Fig. 8 Relationship between loop size and performance discrepancies.

According to the analysis above, the size of the loop is mainly influenced by mass flow rate, frequency, and

rotational speed. It has already been confirmed in the study of turbine that Strouhal number instead of the frequency,

which reflects the relation between the time of pulse propagation and the pulse period, is a more fundamental

coefficient to evaluate the unsteadiness of turbine [22]. At the meantime, the pulse magnitude and the turbine load are

also key factors contributing to turbine unsteadiness. Specifically, larger magnitude and higher load result in more

mass imbalance in the turbine and hence larger size of the loop. Moreover, the variation of the slope of the steady

characteristic is considered to be the root for the influence of turbine load [13]. In fact, the mechanism of the

phenomenon in turbine is also considered valid for the compressor exposed to the pulsating backpressure. Filling-

empty effect is enhanced by larger magnitude and higher frequency of pulse because of larger local gradient of pressure

variation. Furthermore, as the compressor approaches to choke where the slope is large, the discharged mass from the

compressor is saturated while instant intake flow keeps increase at compressor inlet, resulting more evident filling and

empty effect. As been mentioned previously, the rotational speed has much smaller influence on the swallowing

capacity of the turbine compared with that of the centrifugal compressor. As a result, the influence of the rotational

speed on the size of the loop is much more evident in the compressor. In fact, the influence of rotational speed on

hysteresis loop are also considered to be mainly contributed to the slope of the steady characteristic curves.

According to the analysis above, in order to correlate the three key factors with the unsteadiness of the compressor

at pulsating backpressure, the size of the loop is plot versus Strouhal number, magnitude of the pulse, and the local

slope of the steady characteristic based on the experimental measurement, as demonstrated in Fig. 9. The logarithmic

function is used on the size of the loop, the product of Strouhal number, and the magnitude which has been proposed

in the study of turbine, and the slope of the steady characteristic. It can be clearly observed that the points fall on or

near a plane at all pulsating conditions. The coefficient of goodness to fit is 0.85, which shows a reasonably good

fitting. This figure demonstrates that the logarithmic function of the size of the loop (thus the unsteadiness of the

compressor) is approximately proportional correlated to the logarithmic function of St∙M and the slope.

Fig. 9 Relationship among the size of loop, pulse parameters and operational point.

Therefore, the correlation of the unsteadiness of the compressor with the pulse parameters and the steady

characteristic can be concluded as Eq. (10):

( )1 2log log logk St M k S + (10)

where St=fL⁄a, f is pulse frequency, L is characteristic length of compressing system, and a is sonic speed. M represents

the magnitude of outlet pressure pulse; S is the absolute value of local slope of the steady characteristic evaluated by

the cycle-averaged performance. Two constants k1 and k2 are considered to be influenced by the specific compressor

configuration. More compressors are needed to be investigated in future to obtain and validate the values of these two

constants.

This correlation demonstrates clearly the relation of the unsteadiness of compressor performance with the pulse

parameters and compressor characteristic at pulsating backpressure conditions. Therefore, the unsteadiness of the

compressor performance can be evaluated conveniently based on the pulsating conditions and the steady performance.

3.2 Cycle-average performance at pulsating conditions

The time-average performance of compressor at pulsating backpressure is essential to the engine performance.

Therefore, cycle-average performance of the compressor at pulsating condition is discussed in more details in this

section. Definitions of cycle-average performance is given in Eq. (5) to (7). The uncertainty of pressure ratio

measurement is 0.2% and 1.6% for constant and pulsating backpressure conditions, respectively. Fig. 10 manifests

averaged pressure ratio versus the mass flow rate at three rotational speeds and three pulse frequencies. The

performance at constant condition is also overlapped in the figure for the comparison. It is observed that the

performance at pulsating backpressure is notably lower by about 2%~3% than the one at constant condition in general.

Furthermore, the cycle averaged performance is influenced remarkably by the pulse frequency, but there is no

consistent rule of the influence according to the comparison. As been discussed in previous section, the pulse

frequency is the one among three key factors influencing the performance of the compressor. The discrepancies of the

performance at different frequencies manifested in the figure are actually contributed by the pulse magnitude,

frequency as well as the slope together.

0.00 0.05 0.10 0.15 0.20 0.25 0.30

1.00

1.05

1.10

1.15

1.20

1.25

Constant condition

f=80Hz

f=100Hz

f=120Hz

Pre

ssu

re r

atio

(-)

Corrected mass flow (kg/s) Fig. 10 Cycle-average pressure ratio at pulsating conditions.

Fig. 11 further compares the efficiency at three rotational speeds. Evident discrepancies are observed between

efficiencies at pulsating and constant conditions. Particularly, the performance is consistently lower at most of

pulsating backpressure conditions, especially near the peak efficiency locations. Specifically, the peak efficiency

decreases by about 7%, 5%, and 3% at 25, 30, and 35 kRPM, respectively. Moreover, the deterioration of the efficiency

at pulsating conditions reduces gradually as the operational point deviates from the peak point. For the operational

points with high or low mass flow rates near two ends of the curves, the efficiency is almost overlapped with or even

higher than the values at constant conditions, as shown in the figure. The efficiency of the compressor is determined

by the flow field in the component, and the incidence angle of the compressor is the main factor influencing the flow

field. Therefore, in order to study the reason for the behaviors of compressor efficiency at pulsating backpressure, the

inlet flow angle at the peak points are calculated via the method mentioned previously and demonstrated in Fig. 12.

For constant backpressure condition, the optimum incidence angle corresponding to the peak efficiency is 33 degrees.

However, when the compressor is operated at pulsating backpressure near the peak point, the incidence angle

fluctuates notably at the vicinity of the optimum value. The amplitudes of flow angle fluctuations are 3, 4, and 6

degrees for three pulse frequencies (80 Hz, 100 Hz, and 120 Hz), respectively. The performance deteriorates when the

flow angle deviates from the optimum value. Consequently, the cycle-average efficiency is inevitably lower than the

peak value of the constant backpressure condition.

Fig. 11 Cycle-average efficiency at pulsating conditions.

Fig. 12 Variation of incidence angle at pulsating and constant backpressure conditions.

3.3 Surge characteristic

The aerodynamic stability, mainly referring to the surge, is one of the most important performance of the

compressor. It can be observed from Fig. 11 that some averaged mass flow rates at pulsation cases are considerably

smaller than the minimum value of constant cases where surge initiates. This strongly suggested that the stability of

the centrifugal compressor is influenced by the pulsating backpressure conditions.

In order to compare the surge limit of the pulsating condition with that of the constant condition, the change of

surge limit is defined as Eq. (11):

,min ,min

,max ,min

100%c p

c c

m mSL

m m

− =

− (11)

where the subscript c and p means constant and pulsating condition, respectively.

Fig. 13 shows the cycle-averaged pressure ratio versus the mass flow rate at three speeds. The uncertainty of mass

flow rate measurement is plot in the zoom-in subfigure. The smallest mass flow rate for each case is ‘near surge’ point,

which means that surge is not initiated at this point but happens when the mass flow rate slightly further decreases by

closing the throttling valve at step of 1 degree. Comparing with the constant case, it is observed that the surge is

notably delayed by the pulsating backpressure at all frequencies and speeds. Specifically, for the rotational speed as

30 kRPM, the maximum improvement of surge limit is 8.4% which is achieved at 120 Hz, followed by 5.2% and 4%

at 100 Hz and 80 Hz, respectively.

Fig. 13 Surge limit at pulsating backpressure conditions.

To further investigate the surge characteristic of the compressor, Fast Fourier Transformation method (FFT) is

employed to analyze the frequency domain of the signal of compressor exit pressure and mass flow rate. Fig. 14 shows

frequency domains of the pressure and mass flow rate fluctuations when surge is just initiated at three rotational speeds

at constant backpressure condition. It can be seen that the frequency domains are very similar for the signal of mass

flow rate and pressure except the magnitude. Specifically, an evidently large magnitude of frequency component

appears around 10 Hz to 15 Hz at all speeds for both the mass flow rate and the pressure. It is apparently the initiation

of the compressor surge, which can be solidly confirmed by the natural frequency of the compressing system. As

studied by previous research [23, 24], the flow oscillates at the natural frequency of the compressing system when the

surge happens. Therefore, the surge frequency can be estimated by the value of Helmholtz frequency, as in Eq. (12):

2

a Af

V l=

(12)

where a is sonic speed, A is the throttle area of pipe system. V and l represents the characteristic volume and length of

exit pipe, respectively.

According to the equation, Helmholtz frequency of the investigated compressing system is calculated to be about

11 Hz, which is in good accordance with the surge frequency shown in Fig. 14. Moreover, it is suggested from the

figure that the information of the frequency domains of mass flow rate and pressure relating with the compressor surge

is similar. Therefore, only the pressure fluctuations are applied for the discussions on surge characteristics in following

contents.

(a) Pressure

(b) Mass flow rate

Fig. 14 Signals FFT of outlet pressure and mass flow rate at constant conditions.

Fig. 15 demonstrates the variations of frequency domains of outlet pressure with mass flow rate at two pulsating

backpressure and two rotational speeds. Two principal events can be clearly identified in all the plots including surge

and pulsating backpressure. The magnitude of pulsating backpressure is large at high mass flow rate condition. As the

mass flow rate reduces, the magnitude of the event reduces sharply and almost disappears at the relatively small mass

flow rate. However, the magnitude of the fluctuation increases sharply again as the mass flow rate further reduces.

Apparently, this ‘shoot-up’ of the magnitude at small mass flow rate is caused by the initiation of compressor surge.

In order to manifest the influence on the surge limit by pulsating backpressure, the mass flow rate when the surge

happens at constant backpressure is plot in back curve in all the subfigures. It can be clearly seen that no sign of surge

is observed on these curves at all pulsating conditions. Again it is solidly confirmed that the surge is delayed by

introducing the pulsating backpressure. Furthermore, comparing with the information shown in Fig. 14, the surge

frequency at pulsating and constant cases are the same for both rotational speeds, indicating that the surge frequency

of compressor is independent of the pulsating backpressure. The surge frequency mainly depends on the configuration

of the compressing system, and the intermittent throttling of pulse generator at pulsating conditions does not affect

the natural frequency of the system.

(a) N=25 kRPM, f=80Hz

(b) N=35 kRPM, f=80Hz

(c) N=25 kRPM, f=120Hz

(d) N=35 kRPM, f=120Hz

Fig. 15 Frequency domain of signal of exit pressure pulse.

In fact, the phenomenon of ‘reduce-increase’ of the frequency domain as the mass flow rate reduces from choke

to surge is mainly resulted from the variation of the slope of the characteristic curve. The filling-empty effect is greatly

enhanced near choke because of the large slope (steep curve), which has already been discussed in previous section.

As the mass flow rate reduces, the curve becomes flatter gradually and the slope (absolute value) becomes smaller,

therefore the filling-empty effect is alleviated, resulting a smaller hysteresis loop and weaker pulsation. The loop

shrinks dramatically and almost collapses into a point when the slope is near zero, which has been demonstrated in

Fig. 7. Consequently, the frequency domains demonstrate the dramatic decaying of pulse fluctuations as the mass flow

rate reduces from choke condition. On the other hand, the compressor stability is also determined by the slope of the

characteristic curve. The smaller the slope is, the more unstable the compressor is. Particularly, the compressing

system is considered to be at critical status of the stability when the slope is zero. The disturbance can’t be damped

when the slope is positive and the system becomes unstable. Therefore, the compressor surge is expected to happen

when the slope of the characteristic curve reduces to the value around zero, as manifested in Fig. 15. When the surge

happens, the classic hysteresis loop of surge with evident size appears again and the ‘shoot-up’ of fluctuation

magnitude appears in the frequency domains. In conclusion, the ‘V-shape’ of the magnitude variation of frequency

domain is resulted from the trade-off between the two unsteady flow phenomena: forced-oscillating pulsating

backpressure and self-oscillating surge. Moreover, the trade-off is resulted by the influence of slope of characteristic

curve on the filling-empty effect and the stability of the system.

In conclusion, the complete evolution of instantaneous pressure ratio versus mass flow rate from choke to surge

region is manifested in Fig. 16. The hysteresis loops caused by the pulsating backpressure are demonstrated in blue

curves, while the loop caused by the surge is demonstrated by the red curve.

Fig. 16 Instantaneous performance at pulsation.

4. Conclusions

A centrifugal compressor in a turbocharger is exposed to pulsating backpressure because of the reciprocated

internal combustion engine, and its performance is inevitably influenced by the pulsating conditions. Performance of

centrifugal compressor at pulsating backpressure conditions is experimentally studied via the centrifugal compressor

test rig in Shanghai Jiao Tong University. The influence of the pulsating backpressure on unsteady performance and

surge characteristics of the compressor are discussed in details. Three main conclusions can be drawn as following:

The size of hysteresis loop for pressure ratio versus mass flow rate is proposed to evaluate the performance

unsteadiness of centrifugal compressor under pulsating backpressure conditions. A linear correlation is obtained by

the experiment, which correlates the performance unsteadiness with Strouhal number, the pulse magnitude, and the

local slope of the characteristic curve.

Cycle-average performance of the compressor at pulsating backpressure is notably different from that at constant

conditions. Specifically, the averaged pressure ratio is about 2~3% lower than the steady performance, and the peak

efficiency is about 3~7% lower than the steady performance. Moreover, the fluctuations of incidence angle is

considered to contribute to the deterioration of the efficiency.

Fast Fourier Transformation method is employed to analyze surge characteristics at pulsating backpressure

conditions. Surge limit is confirmed to be notably delayed by pulsating backpressure at all rotational speeds. As the

mass flow rate reduces from choke condition, the magnitude of flow fluctuation reduces quickly and then increases

suddenly indicating the initiation of compressor surge, forming the ‘reduce-increase’ phenomenon in the frequency

domains. Moreover, this ‘V-shape’ of the frequency domain is resulted from the trade-off effect by the slope of the

characteristic curve on the filling-empty and compressor stability.

Funding

This research is supported by Natural Science Foundation of China (NSFC) (Grant No. 51606121).

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