Effects of volute’s asymmetry on the performance of a ... · volute constricted the stable ﬂow range by up to 47% at design speed, and the maximum eﬃciency wasfound to decrease

Original Article

Effects of volute’s asymmetry onthe performance of a turbochargercentrifugal compressor

Xinqian Zheng, Yun Lin and Zhenzhong Sun

Abstract

The effects of the volute’s asymmetry on the performance of a turbocharger centrifugal compressor were studied using

steady simulations and theoretical analysis. According to the steady simulation results, it is found that the volute’s

asymmetry has significant influence on the performance of the centrifugal compressor. The variation of the stage effi-

ciency due to volute’s asymmetry is up to 4%. Meanwhile, the volute’s asymmetry restricts the compressor stable flow

range by imposing a distorted outlet pressure condition and forcing some certain impeller passages to suffer from a

worse flow than the others. These certain passages are likely to stall first and trigger the surge, as the stage flow rate

further decreases. In other words, the local stall triggers the surge. The relevant flow mechanisms were given to explain

the effects based on the three-dimensional flow field, and a new model was developed to demonstrate how the local stall

induced by the volute’s asymmetry triggers the system instability.

Keywords

Centrifugal compressor, stability, turbocharger, volute, asymmetry

Date received: 11 March 2016; accepted: 24 August 2016

Introduction

A centrifugal compressor for turbocharger applica-tions consists of a radial impeller, a diffuser, and avolute. The first two components are axisymmetric,while the latter is spiral-shaped. The volute is usuallydesigned to distribute a circumferentially constantstatic pressure at the design point. At off-design con-ditions, the flow in volute will accelerate at higher flowrates, and decelerate at lower flow rates, causing a pres-sure distortion in the diffuser outlet. This phenomenonhas long been recognized in both experiments andnumerical simulations,1–3 and its effects on the perform-ance of centrifugal compressors were widely studied.4–6

The experiments and numerical simulations con-ducted by Yang et al.4 confirmed that the pressuredistortion induced by the volute extended upstreamto the impeller inlet, implying that the impeller wassubjected to varying inlet and exit conditions, whichled to the deterioration of the performance. Zhenget al.5 compared performance of a high pressure-ratio centrifugal compressor with and without thevolute using three-dimensional viscous computationalfluid dynamics (CFD). The volute was found to harmthe flow stability severely. The relative constriction instable flow range was up to 42% at the design speed.Lin et al.6 developed an experimental method toevaluate the impact of the volute’s asymmetry on

the performance of a high pressure-ratio turbochargercompressor, and it was found that the deterioratingimpact of the volute’s asymmetry on the performancebecame much severer at higher rotating speed. Thevolute constricted the stable flow range by up to 47%at design speed, and the maximum efficiency was foundto decrease by 4.8%. Furthermore, some novel flowcontrol methods were proposed to alleviate the nega-tive effect of the volute’s asymmetry on the compressorperformance. Partially decoupling the impeller and thedownstream distortion by casing treatments is provedto be an effective way to alleviate the effect of thevolute, as reported in Hunziker et al.7 Alternatively,both the volute tongue and the diffuser can be carefullydesigned to minimize the magnitude of the pressuredistortion induced by the volute, as reported in Xuand Amano,8 Xu and Mueller,9 and Zheng et al.10

The effectiveness of these measures in turn indicatedthe significant influence of the volute’s asymmetry onthe compressor performance, especially the stability.

Proc IMechE Part G:

J Aerospace Engineering

0(0) 1–12

! IMechE 2016

Reprints and permissions:

sagepub.co.uk/journalsPermissions.nav

DOI: 10.1177/0954410016670418

uk.sagepub.com/jaero

State Key Laboratory of Automotive Safety and Energy, Tsinghua

University, Beijing, China

Corresponding author:

Xinqian Zheng, State Key Laboratory of Automotive Safety and Energy,

Tsinghua University, Beijing 100084, China.

Email: [email protected]

at Tsinghua University on October 1, 2016pig.sagepub.comDownloaded from

http://pig.sagepub.com/

Flow instability is always the focus of the researcheson turbomachinery. Intensive studies have reportedvarieties of instability phenomena in compressors.11–13

Generally, these phenomena can be categorized intosurge and stall. Surge is characterized as a large amp-litude oscillation of the total annulus averaged flowthrough the system, and it is determined not only bythe compressor but the volume and the throttle char-acteristics of the compression system. Stall can happenin any component of the compressor, and when inimpeller, the most mentioned form is the rotatingstall. During rotating stall, one to several stall cellswould rotate around the annulus, while the annulusaveraged mass flow maintains constant. In general,there are two approaches to study this issue. The firstapproach applies the numerical simulations and experi-ments to explore the multi-dimensional flow field, andattempts are made to capture and explain the flow fea-tures during instability process. The second method,which is more theoretical, uses one (or two) dimen-sional lumped parameter models to analyze theinstability of the compression system. The classicworks using the latter approach can be referred tothe early works of Greitzer14,15 and Stenning16 andmore recent works of Spakovszky and Roduner.17,18

However, few theoretical models account for theimportant role the volute’s asymmetry plays in the sta-bility of the compression system.

In this work, the effects of the volute’s asymmetryon the performance of a turbocharger centrifugalcompressor were studied using numerical simulationand a developed theoretical model. Numerical simu-lations were conducted to study the detailed flow fieldand the relevant mechanism, and a lumped parametermodel was developed to take into account the effect ofthe volute’s asymmetry on the stability.

Numerical approach

Three-dimensional steady simulation was employed inthis work. The simulation was done with NUMECAEURANUSTM solver. The Spalart–Allmaras (S-A)one-equation model was chosen for turbulence clo-sure. A central scheme was applied for spatial discret-ization and a fourth-order Runge–Kutta schemewas used for temporal discretization. The frozen-rotor method was applied to deal with rotor–statorinteractions. The rotor–stator interface was locatedat 1.03 times of the tip radius (R2). Simulations withdifferent blades’ meshed angular positions relative tothe volute were conducted (referring to Zheng et al.5),and it was found that this position has little influenceon the performance of the compressor (less than0.2%).

The main parameters of the compressor are listedin Table 1. The Mach number based on rotor inlet tipMach number (Mu) is defined as

Mu ¼ U1=a1

The flow coefficient (�) is defined as

� ¼ C1x=U1

where U1 is the blade tip speed at impeller inlet; a1 isthe speed of sound at impeller inlet; C1x is the axialcomponent of the absolute flow velocity at impellerinlet. A volute with approximately elliptical cross sec-tions was designed to create a circumferentially con-stant static pressure along the volute inlet at thedesign point. No casing treatment was employed.

The mesh including all the whole impeller, the vane-less diffuser, and the volute is shown in Figure 1(a).

Table 1. Main parameters of the compressor.

Parameters Value (unit)

Design pressure ratio 4.0

Mu at design point 1.05

� at design point 0.43

Blade number 6/6 main/splitter blades

Impeller inlet diameter 40.9 mm

Impeller outlet diameter 62.15 mm

Impeller backswept angle 30�

Diffuser inlet diameter 70 mm

Diffuser outlet diameter 100 mm

Diffuser width 3.13 mm

Figure 1. Mesh and passage numbering: (a) structural mesh

topology; (b) passage numbering.

2 Proc IMechE Part G: J Aerospace Engineering 0(0)



Structural girds were employed, and grid indepen-dency assessment was carried out and the finalmodel consisted of about 16,000,000 surface cells(or 5,200,000 volume cells) in order to attain a highresolution of flow quantities. The grid exhibited anacceptable quality as defined by measures of orthogon-ality (minimum 10�), relative grid spacing in boundarylayers (expansion ratio <6), and grid skewness (aspectratio <1600). The nondimensional distance of the firstgrid point from the wall yþ1 was kept under 5.

Boundary conditions were set in accordance with the1D characteristic theories. Total pressure of 100kPa,and total temperature of 298 K together with the axialvelocity direction were imposed as the inlet boundaryconditions. The static pressure was imposed as the outletboundary condition. Nonslip and adiabatic conditionswere imposed on all the solid walls.

Simulation results and analysis

Prototype

For the convenience of data processing, the wholeimpeller is divided into 12 passages, each of which isencompassed by the surfaces of the two adjacentblades, and is numbered as shown in Figure 1(b).The computing characteristics of the whole compres-sor are shown in Figure 2. It should be noted that theminimum mass flow point is not the surge point,since the steady simulation is not capable of capturingthe exact surge point and therefore no effort was madefor this. The impeller outlet static pressure distribu-tions (measured at R¼ 1.01R2) for different mass flowrate points are shown in Figure 3. The pressure dis-tortions are apparent, and vary with the flow rate.As the volute is designed to give a constant velocityin the volute at the design point, in this circumstancethe flow rate into the volute is identical at every angu-lar location, which gives (Figure 4)

_m� ¼ �CudA ¼�

2�_m

where _m� is the mass flow rate going into the shadedpart of the volute, and _m is the total mass flow rate ofthe impeller. Therefore, at design point, the incrementof volute cross-sectional area of volute is consistentwith the volute inflow, the A–� curve overlaps with the_m�–� curve, as shown in Figure 4. However, with thegiven geometry, at lower mass flow rate, the inflow ofthe volute grows lower than the cross-sectional area

0.45

0.50

0.55

0.60

0.65

0.70

2.0

2.5

3.0

3.5

4.0

0.7 0.8 0.9 1

Stag

e ef

ficie

ncy

Tota

l pre

ssur

e ra

tio

m /m ref

Pressure ratio

Efficiency

Figure 2. Stage performance characteristics.

0.55

0.65

0.75

0.85

0.95

1.05

1 2 3 4 5 6 7 8 9 10 11 12

P/P

ref

Passage number

1.000

0.997

0.984

0.920

0.801

0.753

m /mref

Figure 3. Static pressure distributions at R¼ 1.01R2.

Figure 4. Schematic diagram of volute.

Zheng et al. 3



and the flow in the volute will decelerate; while thesituation is contrary at higher mass flow rate. Thevolute tongue is the connection of the exit pipe andthe scroll section, where considerable local pressuregradients exit at off-design points. At lower massflow rate, part of the flow in the exit pipe is droveinto the scroll section through the tongue, whichincreases the local _m�, leading to the local flow accel-eration and therewith decreasing pressure down-stream of the tongue. Therefore, the pressureminimum happens downstream of the tongue, asshown in Figure 3.

Yang et al.4 compared the static pressure distribu-tion in the vaneless diffuser and the impeller capturedby steady simulation with frozen-rotor method andS-A model, and experimental measurements, asshown in Figure 5. It can be seen that the steady

simulation with ‘‘frozen-rotor method’’ well predictedthe phase (location of the minimum) and the magni-tude of the static pressure distribution at the impelleroutlet (Figure 5(a)), as well as the magnitude of thestatic pressure distribution within the impeller(Figure 5(b)). Besides, the phase of the pressure dis-tribution within the impeller could not be capture pre-cisely by this simulation method, due to the unsteadyeffects. However, well predicting the phase is not sorelevant with this work. Therefore, it can be con-cluded that the steady simulation with ‘‘frozen-rotormethod’’ can to some extent predict the effects of vol-ute’s asymmetry on the impeller.

The performance characteristics of each passage areshown in Figure 6. For the calculations of the char-acteristics of each passage, the outflow parameterswere calculated near the impeller outlet (at 1.01R2),

Figure 5. Pressure coefficient distributions comparison (from Yang et al.4): (a) at impeller outlet and diffuser outlet; (b) near the

leading edge of the splitter blades.




while the inflow parameters were set as the same withthe compressor inlet boundary conditions (i.e. a totalpressure of 100 kPa, and total temperature of 298 K),since it is unlikely to identify the exact inlet region ofeach passage, and also the inlet flow variations is quitesmall. It can be seen that the odd passages andthe even passage have different maximum flow ratesdue to the design of the main and the splitter blades.The performance of each passage varies significantlywith respect to either total pressure ratio or isentropicefficiency.

Using the slope of the pressure–flow rate curve as acriterion on assessing the stability,19 it can be foundthat although the stage pressure characteristic presenta negative slope (which means the flow is stable) at thepresented flow range, some passages, such as passages3 and 4, possess positive slope at about left half ofthe flow range. It is indicated that these passages aresuffering a likely unstable process. Meanwhile,the pressure characteristics of most passages stillhave negative slope.

Furthermore, the correlations between the per-formance characteristics of each passage and thepassage outlet static pressure distribution are clear.The passages, which possess a positive slope atabout left half of the pressure characteristic, are cor-responding to relative lower outlet static pressure.Therefore, it can be deduced that the volute’s asym-metry restricts the compressor stable flow range byimposing a distorted outlet pressure conditions andforcing some certain impeller passages to suffer froma worse flow than the others. These certain passagesare likely to stall first and trigger the surge, asthe stage flow rate further decreases. In other words,the local stall triggers the surge.

An attempt was made to explore the flow mechan-isms by looking at the flow fields of the minimumflow rate point (m=mf ¼ 0:753), as the performancedeviations between different passages are the mostapparent at this point. The entropy contour at 95%span (Figure 7) highlights the high loss regionsoccupying the rear of the impeller passages. Figure 7also shows the streamlines going through theseregions at passages 3 and 4. It is found that the highloss region is attributed to the peripheral flow (redstreamlines in Figure 7) in the vicinity of the impelleroutlet and the tip clearance flow (blue streamlines inFigure 7) at the rear of the blade. Since the outletstatic pressure of passages 3 and 4 are relativelylower, the peripheral flow tends to be drew in thepassage and impinges on the blade surface, whichcauses a considerable blockage therein. Meanwhile,the blockage also changes the path of the tip clearanceflow. The tip clearance flow has to detour along alonger spiral route before brought out of the passageby the main stream, which further aggravates theblockage in the rear of the passages, and induced asignificant loss as indicated in Figure 7. Due to theblockage, the inflow will have a larger deflection(and therewith also a larger incidence), and acceleratemuch severer at the front part of the main blade suc-tion surface. This can be seen from the relative Machnumber contour in Figure 7. The shock wave at pas-sage 4 is the strongest, indicating severer local flowacceleration therein. The severer acceleration at thesuction surface will increase the pressure difference(as shown in Figure 7), which induces a stronger tipclearance flow and contributes to high entropy regionat the inlet of passage 4, as marked in Figure 7.What’s more, the shock wave at passage 4 is located

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

4.6

4.8To

tal p

ress

ure

ratio

m /mref

m /mref

m /mref

m /mref

P1

P3

P5

P7

P9

P11

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

4.6

Tota

l pre

ssur

e ra

tio

P2 P4 P6

P8 P10 P12

0.60

0.64

0.68

0.72

0.76

0.80

0.84

Isen

trop

ic e

ffic

ienc

y

P1

P3

P5

P7

P9

P11

0.60

0.64

0.68

0.72

0.76

0.80

0.84

0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09

Isen

trop

ic e

ffic

ienc

y

P2 P4 P6

P8 P10 P12

0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09

0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09

0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09

(a)

(b)

(c)

(d)

Figure 6. Performance characteristics of each passage: (a)

total pressure ratio of odd passages; (b) total pressure ratio of

even passages; (c) isentropic efficiency of odd passages; (d)

isentropic efficiency of even passages.

Zheng et al. 5



more upstream, and will enhance the interactionsbetween the shock wave, the boundary flow at thesuction surface and the tip clearance flow, which isusually believed to be highly relative to the stabilityof high pressure-ratio centrifugal compressors.

Modified cases

In order to further assess the effects of volute’s asym-metry on the compressor performance, four caseswere developed. The only difference between thesefour cases is the circumferential distribution of dif-fuser width, as shown in Figure 8. So, just by rotatingthe diffuser of any of the four modified cases by acertain degree, it can become any one of the others.

These cases were designed based on the followingidea: assuming the volute’s asymmetry has no effectson the compressor performance, the performance ofthese four cases should be strictly identical. Otherwiseany performance differences between these four casesprove the existence of effects of the volute’s asym-metry on the compressor performance.

Figure 9 shows the performance characteristics ofthe four cases. Once again note that the minimummass flow point is not the surge point, since thesteady simulation is not capable of accurately captur-ing the exact surge point and, therefore, no effort wasmade for this.

It can be seen that the performance deviations doexist, which confirms the effects of the volute’s asym-metry on the compressor performance. The variationof the stage efficiency is up to 4%, while the variationof impeller efficiency is about 1%. The relativelylarger deviation of the stage performance impliesthat the matching between vaneless diffuser and thevolute is of significant importance. It should alsobe noted that these four diffuser designs are intendedto assess the volute’s effect, and the relevant designparameters were determined without consideringthe performance simultaneously, therefore the devi-ations of the stage performance would somehow beexaggerated.

Among these four cases, Case B is the best, andCase D is the worst. It is also interesting that these

Figure 7. Flow field: static pressure contour, entropy contour, and streamlines.

0.6

0.8

1.0

1.2

1.4

1.6

0 45 90 135 180 225 270 315 360

b/b r

ef

Circumferential angle (deg)

Prototype Case A Case B

Case C Case D

Figure 8. Diffuser width distributions of the four modified

cases.




two cases have opposite distributions of diffuserwidth, as shown in Figure 8. The maximum widthof Case B is located at 90�, where Case D has theminimum width. Figure 10 shows the static pressureat impeller outlet (R¼ 1.01R2) of the minimum flowrate points of the three cases (Figure 9(a)). It canbe seen that the pressure valley shifts in Cases B andD compared with the prototype. This is the couplingeffect of the asymmetrical volute and diffuser.

By modifying the circumferential distributions of thediffuser width, the impeller outlet pressure distortioncan be changed. For Case B, the original pressurevalley is almost eliminated. However, a new pressurevalley forms at the outlet of passage 10 to 12, prob-ably due to the width contraction of Case B thereby.For Case D the pressure distortion is considerablyenlarged, and passages 5 and 6 have the poorest per-formance. Similar to the prototype, for both cases, thepassages whose outlets are within the pressure valleyhave poorer performance, as shown in Figure 11.

When comparing the passage performance ofCases B and D, it can be found that the minimumpassage flow rate of Case D is relatively smaller,implying that Case D is likely to stall first, althoughthe stage flow rate at the points be analyzed ofthese two cases are almost the same, as shown inFigure 9(a).

In conclusion, these modified cases reproducethe process of ‘‘local stall triggering the surge’’, andthe location of the ‘‘local stall’’ depends on the pres-sure distortion induced by the volute’s asymmetry(in these cases also by the diffuser’s asymmetry), anda severer asymmetry will causes the premature of the‘‘local stall’’. Based on this knowledge, it is supposedthat with a careful design of the diffuser width,the static pressure distortion induced by the volutecan be eliminated, and some performance benefitcan be obtained.

It is worth pointing out that the above analysis isbased on the rotating reference frame, and thereforefrom a steady view. In fact the impeller is rotating,while the location of the pressure valley is fixed due toa given volute geometry. Hence during one rotatingcycle, each passage will go through different outletpressure conditions. At relative small mass flowrates, the volute will cause a valley in the impelleroutlet static pressure distribution. When one passageencounters this valley, the flow inside it tends to beunstable, and then recover when it passes the valley.However, it can be expected that if this pressure dis-tortion is large enough, or the flow situation ofthe passage is not well before it enters into thevalley (e.g. in the case when the stage flow rate is

(d)

0.78

0.79

0.80

0.81

0.82

0.83

0.84

Effic

ienc

y

Prototype Case A

Case B Case C

Case D

2.0

2.5

3.0

3.5

4.0

0.7 0.8 0.9 1

Tota

l pre

ssur

e ra

tio

m /mref

Prototype

Case A

Case B

Case C

Case D

0.50

0.55

0.60

0.65

0.70

Effic

ienc

y

Prototype

Case A

Case B

Case C

Case D

3.8

4.0

4.2

4.4

4.6

4.8

5.0

Tota

l pre

ssur

e ra

tio

Prototype

Case A

Case B

Case C

Case D

(a)

(b)

(c)

0.7 0.8 0.9 1m /mref

0.7 0.8 0.9 1m /mref

0.7 0.8 0.9 1m /mref

Figure 9. Performance characteristics of the four cases: (a)

stage pressure characteristics; (b) stage efficiency characteris-

tics; (c) impeller pressure characteristics; (d) impeller efficiency

characteristics.

0.78

0.88

0.98

1.08

1.18

1 2 3 4 5 6 7 8 9 10 11 12

P/P

ref

Passage number

Prototype

Case B

Case D

Figure 10. Static pressure distributions at R¼ 1.01R2.

Zheng et al. 7



quite small and, therefore, the flow incidence is large),the passage may not be able to recover in time, thelocal stall will extend to the whole impeller, and leadto the surge of the compression system. This profilesthe ‘‘local stall triggering the surge’’ process in reality.

A developed stability model

The above analysis makes clear the considerable effectsof the volute’s asymmetry on the stability of compres-sors. However, this important factor is missing in the

conventional theoretical models. In this work, alumped parameter model was proposed to considerthe effects of the volute’s asymmetry on the compressorstability. The compression system comprises four com-ponents: compressor, duct (to give flow inertia),plenum (to give transient mass storage), and throttle,as shown in Figure 12. In the conventional models(such as the model developed by Stenning16), thewhole compressor was characterized as a pressure–mass flow curve, so the deviations of the passage per-formance are missing. In this model, the compressormodule is divided into several sub-components corres-ponding to different impeller passages, and each sub-component is characterized by its own pressure–massflow characteristics. For simplicity, only two passagesare included in this model, as shown in Figure 12.

The flow is treated as one-dimensional. The flowparameters are taken to vary about the time-meanvalues, and the variation is assumed to be relativelysmall.

The compressor

There is assumed to be no inertia or mass storage inthe compressor, so that

mp1 þmp2 ¼ m3 ð1Þ

The compressor is divided into two passages withdifferent performance, and for a given rotationalspeed the pressure rise–mass flow characteristic is spe-cified by

Pp1 � P01 ¼ Cp1ðmp1Þ ð2Þ

Pp2 � P01 ¼ Cp2ðmp2Þ ð3Þ

Assuming the flows from the two passage havefully mixed before they enter the duct, so that

P3 ¼ "Pp1 þ ð1� "ÞPp2 ð4Þ

where " is a constant characterizing the mixingprocess.

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

4.6

4.8

0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09

Tota

l pre

ssur

e ra

tio

m /m ref

P1 P2P3 P4P5 P6P7 P8P9 P10P11 P12

0.60

0.64

0.68

0.72

0.76

0.80

0.84

Effic

ienc

y

P1 P2 P3 P4P5 P6 P7 P8P9 P10 P11 P12

3.0

3.5

4.0

4.5

5.0

5.5

Tota

l pre

ssur

e ra

tio

P1 P2P3 P4P5 P6P7 P8P9 P10P11 P12

0.55

0.60

0.65

0.70

0.75

0.80

0.85

Tota

l pre

ssur

e ra

tio

P1 P2 P3 P4P5 P6 P7 P8P9 P10 P11 P12

0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09m /mref

0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09m /mref

0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09m /mref

(a)

(b)

(c)

(d)

Figure 11. Passage characteristic of Cases B and D: (a) pas-

sage total pressure ratio of Case B; (b) passage efficiency of

Case B; (c) passage total pressure ratio of Case D; (d) passage

total pressure ratio of Case D.

Figure 12. Simplified compression system.




Therefore

P3 � P01 ¼ "Cp1ðmp1Þ þ ð1� "ÞCp2ðmp2Þ ð5Þ

Consider small variation about the time-mean flowsuch that

Pp1 ¼ �Pp1 þ �Pp1 ð6Þ

Pp2 ¼ �Pp2 þ �Pp2 ð7Þ

P3 ¼ �P3 þ �P3 ð8Þ

mp1 ¼ �mp1 þ �mp1 ð9Þ

mp2 ¼ �mp2 þ �mp2 ð10Þ

Under steady flow conditions, �mp1 þ �mp2 ¼ �m3, so

�m3 ¼ �mp1 þ �mp2 ð11Þ

In this model, the flow rate fraction i ¼ �mp1=�m3 isdefined, so that

�mp2 ¼ ð1� iÞ�m3

Linearizing the compressor characteristic (5) in thevicinity of the steady-state operation point at a spe-cific speed

ð �P3 þ �P3Þ � P01 ¼ " �Cp1 þdCp1

dmp1�mp1

� �

þ ð1� "Þ �Cp2 þdCp2

dm2�mp2

� � ð12Þ

but

�P3 � P01 ¼ " �Cp1 þ ð1� "Þ �Cp2�mp2

Therefore

�P3 ¼ " cp1�mp1 þ 1� "ð Þ cp2�mp2

¼ "i cp1 þ 1� "ð Þð1� iÞ cp2� �

�m3

ð13Þ

where cp1 ¼ dCp1=dmp1 and cp2 ¼ dCp2=dmp2.

The duct

The flow leaves the compressor and enters a duct oflength L with a constant flow area A. Neglecting axialdensity changes in the duct, the momentum equationwithin the duct is

P3 � P4 ¼L

A

dm3

dtð14Þ

Under steady flow conditions, �m3 ¼ �m4, �P3 ¼ �P4, so

ð �P3 þ �P3Þ � ð �P4 þ �P4Þ ¼L

A

dð �m3 þ �m3Þ

dt

That is

�P3 � �P4 ¼L

A

d�m3

dtð15Þ

The plenum

The compressed gas is stored in the plenum and it isassumed that the variation of mass is related to thevariation of pressure p3 by treating the process as isen-tropic. Thus

�m3 � �m4 ¼ Vd��4dt¼

V

a24

d�P4

dtð16Þ

where a4 is the speed of sound inside the plenum.

The throttle

It is assumed that the pressure difference across thethrottle is a function only of the instantaneous massflow rate through it, so

P4 � P01 ¼ Gðm4Þ ð17Þ

where G depends on the gas properties and the throt-tle area. Since P01 is constant, one obtains

�P4 ¼ g�m4 ð18Þ

where g ¼ dG=dm4

The four equations (13), (15), (16), and (18) definethe perturbations for the compression system withfour effective variables, namely �m3, �m4, �P3, and�P4. Based on these four equations, a second-orderordinary differential equation can be obtained interms of any one of the four variables as follows

LVg

Aa24

d2z

dt2þ

L

A�"i cp1 þ 1� "ð Þð1� iÞ cp2� �

gV

a24

� �dz

dt

þ g� "i cp1 � 1� "ð Þð1� iÞ cp2� �

z ¼ 0

ð19Þ

where z could be any of the four variables.The stability of the compression system can be

evaluated by examining the coefficients in equation(19). The stability of the solutions requires that thecoefficients of z and dz=dt are positive. If the coeffi-cient of z becomes negative, i.e.

g� "i cp1 � 1� "ð Þ 1� ið Þ cp240 ð20Þ

Zheng et al. 9



The system is statically unstable. If the coefficient ofdz=dt becomes negative, namely

L

A�"i cp1 þ 1� "ð Þð1� iÞ cp2� �

gV

a2440 ð21Þ

small disturbances will grow with time in an exponen-tial manner. The compression system will experiencedynamic instability.

The theoretical models can be used to judge thesurge onset and the type of instability of compressorsproviding the pressure characteristics of the compres-sor at steady conditions is available. However, theconventional models fail to consider the effect of thevolute’s asymmetry on the stability of the system.This can be understood by considering a simple exam-ple given below. Figure 13 shows the pressure oftwo compressors named as Case E and Case F,respectively. These two compressors have the samestage characteristic as shown in the left picture ofFigure 13, but they have different passage perform-ance, depending on the designs of impeller, diffuser,and volute. (It should be noted that the minimum flowrate point of stage characteristic curve (in Figure 13)is not the surge point, because Case F will surge firstand, therefore, has a larger surge mass flow rate. Soactually, the stage characteristic does not include thevery small flow rate points near the surge. This situ-ation happens when the stage characteristic isobtained by numerical simulations, which are not cap-able of capturing the surge points or by experimentswhen it is necessary for the surge to be avoided in caseof system failure. Actually this situation is quitecommon, and usually only part of the stage charac-teristic is available.) For each case, the performancevaries in different impeller passages due to the effectof the volute’s asymmetry. In the figure, only twopassages are shown for clarity, and it is assumed theperformance of the other passages fall between thesetwo lines. When examining the performance of eachpassage, it is reasonable to deduce that the volute’sasymmetry in Case F is much severer, which imposesa local stall in passage 1 and will finally trigger thesurge as the flow rate decreases further.

In such case, the conventional models will concludethat these two cases have the same stability, sincethese two cases have the same stage characteristic(providing that the other components of the compres-sion system such as duct, plenum and throttle areidentical in two cases). However, when employingthe proposed model, it will tell the stability difference.Besides, the model will show how the characteristicsof the poor passage (in this situation, it is passage 1)change the type of system instability. For this exam-ple, when

cp15g="i� 1� "ð Þ 1� ið Þ cp2="i ð22Þ

static instability occurs; and when

cp15La24

AgV"i�

1� "ð Þ 1� ið Þ cp2

"ið23Þ

dynamic instability occurs.Thus when compared with the conventional

model, the proposed model has the advantage ofassessing the system stability through the character-istics of the individual passages and, therefore, isable to account for the effects of the volute’s asym-metry on the system stability. The model also indi-cates that when either equation (22) or (23) issatisfied, the local stall in certain passage will triggerthe instability of the system.

It is worth to point out that in the above example,the local stall is caused by the impeller outlet pressuredistortion due to the volute’s asymmetry. In fact var-iety of flow distortion may exist in the compres-sor,20–22 and the proposed model can be applied toassess the effects of these distortions on the stability.However, before it comes into use, the coefficientssuch as mixing parameter " and flow fraction ishould be well calibrated. But this is not of concernin this work. The real value of this proposed model isthat it provides a link between the system stability andthe flow distortions in the compressor, which will helpto inspire researchers to think over the stability issuemore comprehensively.

Figure 13. Pressure characteristics of two compressors.




Conclusions and remarks

In this work, the effects of the volute’s asymmetry onthe performance of a turbocharger centrifugal com-pressor were studied, and several conclusions can bemade as follows:

1. The volute’s asymmetry has significant influenceon the efficiency of the centrifugal compressor.According to the steady simulations, the variationof the stage efficiency due to volute’s asymmetry isup to 4%. The impeller passages whose outlets arewithin the pressure valley have poor performance.The peripheral flow is sucked into the passage nearthe pressure valley, and interacts with the tip clear-ance flow, causing a large blockage in the rear ofthe passages, where loss is generated.

2. The volute’s asymmetry restricts the compressorstable flow range by imposing a distorted outletpressure conditions and forcing some certainimpeller passages to suffer from a worse flowthan the others. These certain passages are likelyto stall first and trigger the surge, as the stage flowrate further decreases. In other words, the localstall triggers the surge.

3. Finally, a new model was developed to accountfor the important role the volute’s asymmetryplays in the stability of the compressionsystem. The proposed model demonstrates theprocess of ‘‘local stall triggering the surge’’,and tells how the characteristics of the poor pas-sage change the type of system instability.What’s more, this model can help to assess theeffects of variety of flow distortions on the com-pressor stability.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with

respect to the research, authorship, and/or publication ofthis article.

Funding

The author(s) disclosed receipt of the following financialsupport for the research, authorship, and/or publicationof this article: This research was supported by the

National Natural Science Foundation of China (GrantNo. 51176087).

References

1. Elholm T, Ayder E and van den Braembussche RA.

Experimental study of the swirling flow in the volute ofa centrifugal pump. ASME J Turbomach 1992; 114:366–372.

2. Ayder E, van den Braembussche RA and Brasz JJ.Experimental and theoretical analysis of the flow in acentrifugal compressor volute. ASME J Turbomach1993; 115: 582–589.

3. Hillewaert K and van den Braembussche RA. Numericalsimulation of impeller-volute interaction in centrifugalcompressors. ASME J Turbomach 1999; 121: 603–608.

4. Yang MY, Zheng XQ, Zhang YJ, et al. Stabilityimprovement of high-pressure-ratio turbocharger centri-fugal compressor by asymmetric flow control—Part I:

Non-axisymmetric flow in centrifugal compressor.ASME J Turbomach 2013; 135: 021006.

5. Zheng XQ, Huenteler J, Yang MY, et al. Influence of

the volute on the flow in a centrifugal compressor of ahigh-pressure-ratio turbocharger. Proc IMechE, Part A:J Power and Energy 2010; 224: 1157–1169.

6. Lin Y, Zheng XQ, Jin L, et al. A novel experimentalmethod to evaluate the impact of the volute’s asymmetryon the performance of a high pressure-ratio turbochargercompressor. Sci China Technol 2012; 55: 1695–1700.

7. Hunziker R, Dickmann HP and Emmrich R. Numericaland experimental investigation of a centrifugal compres-sor with an inducer casing bleed system. Proc IMechE,

Part A: J Power and Energy 2001; 215: 783–791.8. Xu C and Amano R. Eliminating static pressure distor-

tion by a large cut back tongue volute. ASME Paper

No. GT2006-90001, 2006.9. Xu C and Mueller M. Development and design of a cen-

trifugal compressor volute. Int J Rotat Mach 3: 190–196.

10. Zheng XQ, Zhang YJ, Yang MY, et al. Stabilityimprovement of high-pressure-ratio turbocharger cen-trifugal compressor by asymmetric flow control—PartII: Non-axisymmetric self recirculation casing treat-

ment. ASME J Turbomach 2013; 135: 021007.11. Emmons HW, Pearson CF and Grant HP. Compressor

surge and stall propagation. Trans ASME 1955; 77:

455–469.12. Tan CS, Day I and Morris S. Spike-type compressor

stall inception, detection, and control. Annu Rev Fluid

Mech 2010; 42: 275–300.13. Camp TR and Day IJ. A study of spike and stall phe-

nomena in a low-speed axial compressor. ASME JTurbomach 1998; 120: 393–401.

14. Greitzer EM. Surge and rotating stall in axial flowcompressors—Part I: Theoretical compression systemmodel. J Eng Power 1976; 98: 190–198.

15. Greitzer EM. Surge and rotating stall in axial flowcompressors—Part II: Experimental results and com-pression. J Eng Power 1976; 98: 199–211.

16. Stenning AH. Rotating stall and surge. ASME J FluidsEng 1980; 102: 14–20.

17. Spakovszky ZS. Backward traveling rotating stall

waves in centrifugal compressors. ASME J Turbomach2004; 126: 1–12.

18. Spakovszky ZS and Roduner CH. Spike & modal stallinception in an advanced turbocharger centrifugal com-

pressor. ASME J Turbomach 2009; 131: 031012.19. Cumpsty NA. Compressor aerodynamics. Malabar, FL:

Krieger Publishing Company, 2004, pp.362–364.

20. Hah C, Rabe DC, Sullivan TJ, et al. Effects of inletdistortion on the flow field in a transonic compressorrotor. J Turbomach 1998; 120: 233–246.

21. Kim Y, Engeda A, Aungier R, et al. The influence ofinlet flow distortion on the performance of a centrifugalcompressor and the development of an improved inletusing numerical simulations. Proc IMechE, Part A: J

Power and Energy 2001; 215: 323–338.22. Erbsloh SD, Crowther WJ and Frutos JR. Control of

compressor face total pressure distortion on a high

bypass turbofan intake using air-jet vortex generators.AIAA Paper, No. 2206, 2004.

Zheng et al. 11



Appendix

Notation

a speed of soundA flow areac slope of compressor characteristicC compressor characteristic, or absolute

velocityg throttle characteristic slopeG throttle characteristicL equivalent length of the ductm mass flow rateP pressureR radius� air density

Subscripts

0 total parameter1 compressor inlet, ambient parameter2 impeller outlet, or passage outlet3 parameter in duct4 parameter in plenump1 passage 1p2 passage 2

y circumferential angle or direction




Documents

Effects of volute’s asymmetry on the performance of a ... · volute constricted the stable ﬂow range by up to 47% at design speed, and the maximum eﬃciency wasfound to decrease