research article characterization of a twin-entry radial...

Research ArticleCharacterization of a Twin-Entry Radial Turbine underPulsatile Flow Condition

Mahfoudh Cerdoun1 and Adel Ghenaiet2

1Laboratory ofThermal Power Systems AppliedMechanics EcoleMilitaire Polytechnique BP 17 Bordj-el-Bahri 16046Algiers Algeria2Laboratory of Energetics and Conversion Systems Faculty of Mechanical Engineering University of Sciences andTechnology Houari Boumediene BP 32 El-Alia Bab Ezzouar 16111 Algiers Algeria

Correspondence should be addressed to Adel Ghenaiet ag1964yahoocom

Received 19 December 2015 Revised 7 April 2016 Accepted 14 April 2016

Academic Editor Funazaki Ken-ichi

Copyright copy 2016 M Cerdoun and A GhenaietThis is an open access article distributed under theCreative CommonsAttributionLicense which permits unrestricted use distribution and reproduction in anymedium provided the originalwork is properly cited

In automotive applications radial gas turbines are commonly fitted with a twin-entry volute connected to a divided exhaustmanifold ensuring a better scavenge process owing to less interference between enginesrsquo cylinders This paper is concerned withthe study of the unsteady performances related to the pulsating flows of a twin-entry radial turbine in engine-like conditions andthe hysteresis-like behaviour during the pulses period The results show that the aerodynamic performances deviate noticeablyfrom the steady state and depend mainly on the time shifting between the actual output power and the isentropic power whichis distantly related to the apparent length The maximum of efficiency and output shaft power are accompanied by low entropygeneration through the shroud entry side and their instantaneous behaviours tend to follow mainly the inlet total pressure curveAs revealed a billow is created by the interaction between the main flow and the infiltrated flow affecting the flow incidence at rotorentry and producing high losses

1 Introduction

In standard turbochargers radial turbines are able to reachhigh expansion ratios in a short time by using the maximumenergy of the gas flow pulses to raise the air density tointernal combustion engines (ICE) However at a low enginespeed the exhaust gas flow is small and the boost pressureis low By using a twin-entry radial inflow turbine thereis a better recovery of energy inducted alternatively andintermittently into the hub and shroud entries of the voluteand subsequently the dynamic pressure of exhaust gas flowpulses is used effectively Romagnoli et al [1] comparedbetween the steady performances of two types of turbinesdouble-entry and twin-entry and showed that in the caseof a twin-entry turbine the interaction between entries issignificant and causes the flow capacity to be larger than thatwhich would be obtained by halving the mass flow in fulladmission in contrast to a double-entry turbine PischingerandWunsche [2] studied the interaction between the inlet gasflows from comparable double-entry and twin-entry volutes

under steady conditions At full admission both of themproduced a better efficiency but at partial admission theefficiency of the twin-entry volute was significantly betterwhereas at unequal inlet conditions there is a significant effecton the apparent flow characteristics and the turbine perfor-mance Also the performance of a twin-entry turbine wasmeasured by Dale andWatson [3] over a wide range of partialadmission conditions As a result the best efficiency is notunder the full admission but occurs when themass flow of theshroud-side entry ismore than the hub-side entry Steady andunsteady flow performances of an asymmetric twin-entryturbine of an automotive turbocharger were measured byCapobianco and Gambarotta [4] in both full admission andpartial admission to highlight the interaction between thetwo entries and to show the effect of each entry of the voluteon the full and partial admission conditions Romagnoli etal [5] modified a nozzleless turbine into a variable geometrysingle-entry turbine and a twin-entry turbine which weretested The steady state experiment revealed that at a vaneangle of 70 deg the effect of divider is not significant in

Hindawi Publishing CorporationInternational Journal of Rotating MachineryVolume 2016 Article ID 4618298 15 pageshttpdxdoiorg10115520164618298

2 International Journal of Rotating Machinery

terms of efficiency however a significant depreciation inefficiency was measured for a vane angle between 50 deg and40 deg Further an optimum vane angle of 60 deg was foundfor the twin-entry turbine Based on unsteady experimentsfor the same modified turbine Rajoo et al [6] showedthat the swallowing capacity of a twin-entry turbine in in-phase testing during full admission was inconsistent betweenthe two entries Contrarily during out-phase testing theswallowing capacity of both entries was found to be similarThe performance of an asymmetric twin-entry radial turbinewas investigated analytically and experimentally by Hajilouyet al [7] under steady state conditions considering the fulland partial admission As results for a very high ratio ofmass flow rates between the shroud-side and hub-side theefficiency is lower than that of the full admission

Engine exhaust pulse flows can significantly affect theturbine performance of a turbocharger hence it is necessaryto consider the pulse flow effects in the turbine designand performance analysis Many researchers were interestedin the effects of pulsatile flows such as Serrano et al [8]who determined the performance of a small radial inflowturbine working under pulsatile flows and compared withthe one measured from cold pulsating flows Iwasaki et al[9] performed steady and unsteady flow measurements ona twin-entry turbine coupled to a 6-cylinder medium dutydiesel engine They found that for a fixed turbocharger speedand expansion ratio the unsteady flow mass flow parameterwas lower than that corresponding to the steady flow valueover the tested operating range Ehrlich [10] performedmeasurements in an engine test cell on a turbochargedmedium speed 6-cylinder diesel engine with the focus onunderstanding the process of energy transport from the cylin-ders to the twin-entry turbine admission They measuredthe instantaneous total and static pressures by using in-house constructed probes connected to a high frequencydynamic pressure transducer The results indicated that thetransport mechanism of the gas pulses energy in the exhaustmanifold must be modelled as both convective and acousticpropagation of a wave Dale and Watson [3] measured theshaft power of a twin-entry turbine working in pulsatile flowand concluded that the efficiency varies with admission andthe lowest efficiency occurs when the flow enters only oneof the two entries Rajoo and Martinez-Botas [11] discussedthe performance of a twin-entry variable geometry turbinetested under the pulsating flow conditions and concludedthat the swallowing capacity during the full admission wasinconsistent and the shroud entry was more pressurizedcompared to the hub entry Owing to many difficulties inmeasuring the unsteady performance of radial turbines andthe necessity of fully understanding their internal flows CFDstudies are used to surmount the lack of data Lam et al[12] performed a numerical study of the pulsatile flow in aradial nozzled turbine based on the frozen rotor interfaceThe results show that the instantaneous performance variesslightly from the nonpulsatile flow conditions thus allowingconcluding that the rotor can be treated as a quasi-steadydomain while the volute must be treated as a non-quasi-steady flow device Also Palfreyman and Martinez-Botas[13] investigated the pulsatile flow in a medium sized mixed

flow nozzleless turbine based on URANS computationsRNG-119896120598 turbulence model and sliding mesh model (SMM)at volute-rotor interface They concluded that the agreementwith the flow field measurements for both the cycle averagedand instantaneous data was reasonable and the sliding meshmodel showed better results than themoving reference frameas adopted by Lam et al [12] Hellstrom and Fuchs [14ndash16]carried out numerical flow analyses of a nozzleless turbinein the case of pulsatile inlet conditions considering largeeddy simulations (LES) implemented in the commercial codeSTAR-CD Their first report [14] treated two cases of an ICErotational speed (1500 rpm 3000 rpm) and concluded thatthe entry of rotor into the flow angle varies from minus67 deg tominus25 deg for the second speedwhichwasmore favourable thanthe first speed where the flow angle is from minus85 deg to 60 degresulting in a drop of the peak shaft power about 4 Theresults of Palfreyman and Martinez-Botas [13] showed thatthe incidence angle varied from minus92 deg to 60 deg

Recently Padzillah et al [17] based on a full 3D CFDmodel studied the influence of the speed and the frequencyof pulses on a mixed radial turbine The temporal andspatial resolutions of the flow incidence suggested that thecircumferential variation is less than 7 compared to itsvariation in time as the pulses progressThey found that thereis no direct instantaneous relationship between the pulsatingpressure and the turbine efficiency The major difficulty inderiving the turbine performance is the shifting time betweenthe isentropic conditions upstream of the turbine and theactual output work Furthermore the expansion process ishighly unsteady as it responds to the exhaust manifoldsof an ICE and this is why its design and adaptation area very difficult task owing to its operation in off-designconditions There are still debates on the effective method ofdefining the efficiency of a turbine under the unsteady flowconditions due to the phase shifting so a question ariseshow can the time lag be evaluated To answer this questiontwo parameters should be determined such as the transportmechanism speed of pressure wave and the apparent lengthwhich represents the average distance travelled by the wavefrom a measurement plan to a supposed position at the rotorentry Three approaches have been adopted by researchersin order to estimate the time lag The first approach asproposed by Dale and Watson [3] is based on the sonictravel speed arguing that the pressure waves propagate atthis speed Karamanis et al [18] measured the static pressuredevelopment from the inlet measuring plane to the rotorentry at various locations upstream and downstream of thetongue and concluded that the only appropriate time to shiftthe signal is given by the sonic travel time such an approachwas adopted bymany workersThe second approach suggeststhat the bulk of the flow transmission is more important thanthe pressure wave transmission which was first proposed byWinterbone et al [19] and followed by other workers Thethird approach suggests that the transport mechanism mustbe modelled as both convective and acoustic propagation[10] Recently Szymko et al [20] showed that the sum ofsonic velocity and bulk flow velocity can lead to betterresults Many researchers took the apparent length as thepath length between the centres of volute sections from

International Journal of Rotating Machinery 3

the measurement plan to a point at 180 deg removed fromthe tongue Until now there is yet no agreement aboutthe approaches related to the pulses transport mechanismin order to characterize the unsteady turbine performanceHowever the unsteady flowfieldmeasurements in twin-entryturbines are rare due to great demands on the measurementtechniques especially concerning the pulsating behaviour offlows and the high fluctuations of the total inlet temperaturewith the high rotational speed The reasonable agreementbetween experiment and theory found by researches suchas in [13 21] may constitute a good support to a numericalstudy Moreover the efforts in characterizing the small radialturbines under the pulsatile flow conditions are hamperedby some difficulties in the unsteady measurements Oftenthe inlet pressure is measured as a time-varying quantity butthe total temperature the mass flow rate and the power aremeasured as time-mean quantities In his survey Baines [22]quoted very few facilities to investigate the pulsatile flows andthis is why the unsteady flow analyses based on CFD toolsbecome useful

The present paper is a contribution to predict the aero-dynamic performance of a twin-entry radial turbine underpulsating flow conditions The simulations consist in solvingthe unsteady 3D flows by means of Ansys-CFX URANSsolver considering appropriate inlet and exit boundary con-ditionsThemethod of time lag is focused on throughout thiswork Indeed there are difficulties in studying the unsteadyflows both numerically and experimentally owing to timedifference between the instantaneously measured isentropicconditions and the actual turbine conditions Furthermoreit is certain that the unsteady value of the turbine efficiencyis related to the phase shifting and hence might lead tounrealistic values as quoted by Rajoo and Martinez-Botas[23] The accuracy in estimating the time shifting may be ofgreat help for improving the enginemodels in order to predictthe real response of a turbocharger versus the pulsatile flowsand therefore possibilities of comparing between differentunsteady radial turbinesrsquo performances

2 Computational Domain

The studied twin-entry radial turbine has a rotor with 12blades having an inlet diameter of 96mm and an outletdiameter of 863mm and a shroud blade angle of 37 deg Thegeometry was obtained by means of a measuring machineequipped with a contactless optical feeler The beam of lightmoves over the mapped surfaces to reproduce the correctblade shape The nonsymmetric twin-entry volute is dividedinto two domains inlet domain and 3D spiral domain(Figure 1)The surfaces at the inlet horizontal domain remainfixed but the angles between the two slots vary becausethis domain is twisted Next there is a spiral volute wherethe angle between two plans remains constant and only thedimensions of the sides vary according to the spiral shape

The pressure boundary condition will result in thereflection of outgoing waves and subsequently the interiordomain contains spurious wave reflections Indeed the non-reflecting boundary conditions provide a special treatmentto the domain boundaries to control these spurious wave

3Dr

2Dr

Shroud entry

Hub entry

Figure 1 The twin-entry radial turbine

reflections but unfortunately these nonreflecting boundaryconditions are not available for the pressure-based solverimplemented in Ansys-CFX version 145 as a consequencean induction pipe and a diffuser of length of 2119863

119903and 3119863

119903(119863119903

represent inlet rotor (Figure 1)) respectively were added tothe inlet and outlet of this turbine to avoid any interferenceproduced by the boundaries

The computational gridswere created separately as shownby Figure 2(b) The rotor domain by means of TurboGridadopted an H-grid topology with an O-grid wrapped aroundthe rotor blades in order to minimize the skew angles Highergrid resolution was set on the blades surfaces hub andshroud with an expansion factor of 118 in order to modelthe near wall flows as accurately as possible The tip gaps areabout 011mm and 0205mm (Figure 2(a)) and used twelveuniform cells to better capture the tip leakage flows As aconsequence the total nodes used to mesh the rotor are1599684 nodes For the twin-entry volute a hexahedral meshof 1063249 nodes was generated in addition to 265006 nodesused for the exhaust To study the grid size dependency themesh distributionwas changed around the blade surfaces andalong the streamwise and spanwise directions and five newgrids were used to predict the turbine performance whichseemed to stabilize above a grid size of 41 million The flowwas solved through the volute in a stationary frame and in arotating frame for the rotor In the present simulations the119896120596-SST turbulence model with an automatic wall functionwas considered The minimum and maximum values of 119910+on the surfaces of volute and rotor in the extreme inletconditions were in between 02 and 685 because it wasdifficult to have small values near the hub and tongue When119910+

gt 2 the solver automatically uses the wall functionwhereas the low Reynolds method is used for 119910+ le 2 suchas the majority of blade surfaces

3 Pulsatile Flow Simulations

The average values of pressure and temperature at inlet andoutlet correspond to the real operating conditions obtained


Interspace I

Exit tip clearance GInlet

Rinlet

Rotation axis X

Hinlet

LMean

CMean

Xturbine

Exit tip clearance GExit

Space after trailingEdge (STE) = 040CMean

ROutletShroud

ROutletMean

ROutletHub

Space before leadingedge (SLE) = 001CMean

(a)

Tip clearance

(b)

Figure 2 (a) Rotor and volute cross sections (b) The generated meshes

with a V12 diesel engine according to Ghenaiet [24] On theother side Ehrlich [10] performed extensive measurementsof an in-line 6-cylinder medium speed diesel engine with aquite low output (59 litres peak torque 569Nm 1600 rpm)in order to analyze the on-engine turbine performanceunder pulsatile flows The instantaneous total and staticpressure at both the inlet and outlet of the twin-entryturbine were measured by constructed probes connected toa high frequency dynamic pressure transducer The exhaust

gases were ducted away from the exit of the turbochargerrsquosturbine and discharged outside the test cell The butterflyvalves installed in the air intake and the gas exhaust setan inlet restriction and an exhaust backpressure Ehrlich[10] used fine wire thermocouples to measure the significanttemperature variation over the engine cycle

In the present simulations the pulsating behaviours ofthe total temperature 119879

1015840

119905and the total pressure 119875

1015840

119905identified

by Ehrlich [10] were used and scaled (Figure 3) by the


0 120 240 360 480 600 720500

550

600

650

700

750

Hub inletShroud inlet

Crank angle (deg)

Inle

t tot

al te

mpe

ratu

re (∘

C)

(a)In

let t

otal

pre

ssur

e (ba

r)

16

18

20

22

0 120 240 360 480 600 720


Crank angle (deg)

(b)

Crank angle (deg)

Out

let s

tatic

pre

ssur

e (ba

r)

0 120 240 360 480 600 720105

110

115

120

125

130

135

(c)

Figure 3 Boundary conditions (a) inlet total pressure (b) inlet total temperature and (c) outlet static pressure

measured average values of the total pressure and tempera-ture (Ghenaiet [24])

119875119905= 1198751015840

119905+ (119875119905minus

1

2120587int

2120587

0

1198751015840

119905119889120579)

119879119905= 1198791015840

119905+ (119879119905minus

1

2120587int

2120587

0

1198791015840

119905119889120579)

(1)

At the turbine exit Ehrlich [10] showed that the staticpressure perturbation is nearly sinusoidal and characterized

by six pulses per engine cycle and each pulse correspondsto one valve event in the six-cylinder engine as mentionedabove for the total temperature and pressure the staticpressure is chosen to verify the following equation

119901 = 1199011015840

+ (119901 minus1

2120587int

2120587

0

1199011015840

119889120579) (2)

The results of the simulations in terms of shaft powerefficiency and expansion ratio will be presented in thenext section But first some parameters are introduced anddefined


For each entry the ratio of inletmass flow to the inlet totalmass flow (MFR) is given as follows

MFR119904=

119904

119904+ ℎ

MFRℎ=

ℎ

119904+ ℎ

(3)

The reduced mass flow (RMF) parameter for the case of atwin-entry radial turbine is calculated by considering thecontribution of the two entries where each entry feeds half ofthe span of the entire circumference Cumpsty and Horlock[25] suggested that the total temperature and pressure shouldbe based on a clear view of the purpose forwhich the averagedvalues are intendedTherefore the total temperature119879

119905could

be calculated as a mass weighed average value (1198791199050

= MFR119904sdot

119879119905119904+MFR

ℎsdot 119879119905ℎ) since this gives the correct value of enthalpy

flux according to ideal gas assumptions While for the totalpressure 119875

119905it is noteworthy that as the magnitude of the total

pressure is reduced the various average pressures becomemore nearly equal thus a mass weighed average is also usedfor the total pressure (119875

1199050= MFR

119904sdot 119875119905119904+ MFR

119904sdot 119875119905ℎ) The

instantaneous reduced mass flow (RMF) parameter is givenas follows

RMF = (119904+ ℎ)radicMFR

119904sdot 119879119905119904+MFR

ℎsdot 119879119905ℎ

(MFR119904sdot 119875119905119904+MFR

119904sdot 119875119905ℎ) (4)

The total-to-static instantaneous expansion ratio for eachentry and for the entire turbine is presented as follows

120587119905119904-119904 =

119875119905119904

119901out

120587119905119904-ℎ =

119875119905ℎ

119901out

120587119905119904=

1198751199050

119901out

(5)

In a turbocharger the most important figure is the actualpressure of air delivered by the compressor driven by theturbine thus the shaft power is very important and it is oneof the global parameters to be evaluated

119875 = Shaft sdot rotor (6)

where the shaft torque Shaft is obtained by integrating theelement forces due to pressure forces over the turbine rotor

Shaft = int119904

119903 times (119901 sdot ) 119889119904 (7)

The total-to-static efficiency can instead be calculated asthe ratio between the utilized power and the maximumpower variation of gases if expanding isentropically withina twin-entry radial turbine The resulting expression for theinstantaneous total-to-static efficiency is as follows

120578119905119904=

Shaft sdot rotor

119904119862119901119904sdot 119879119905119904[1 minus (119901out119875119905119904)

(120574minus1)120574

] + ℎ119862119901ℎsdot 119879119905ℎ[1 minus (119901out119875119905ℎ)

(120574minus1)120574

]

(8)

119904and

ℎare the mass flowwithin the shroud-side and hub-

side respectively 119879119905119904and 119875

119905119904are the total gas temperature

and pressure at the hub-side inlet 119879119905ℎand 119875

119905ℎare the total

gas temperature and pressure at the hub-side inlet and 119901outis the static pressure downstream of turbine 119862119901

119904and 119862119901

ℎ

are the specific heat of the gases at shroud-side and hub-side respectively and 120574 is the isentropic index Accordingto Hellstrom and Fuchs [14 16] the above definition workswell for nonpulsatile and for pulsatile flows at moderatefrequencies

4 Unsteady Performance

The results presented herein are aimed at better understand-ing the effects of pulsatile inlet conditions on the performanceof a twin-entry radial turbine especially the effect of phaseshifting Due to the huge total time required to simulatethe overall four-stroke engine a compromise between theaccuracy and CPU time is required to make computationscost-effective Thus the total time is limited to a 600 degcrank angle which corresponds to the complete two pulsesincoming from the two entries and to 622 rounds of the

turbine The performance can be expressed in terms of theoutput shaft power the efficiency and the expansion ratioAlso an analysis of the flow structures between the shroud-side and the hub-side of volute is provided at two planessituated at the voluterotor interface

41 Effect of the Pulsatile Flow The important parameters forthe current simulations are the total pressure loss factor 120577 andthe total-to-static isentropic efficiency 120578

119905-119904 which for the caseof a twin-entry turbine are defined as follows

120577 =(MFR

119904sdot 119875119905119904+MFR

119904sdot 119875119905ℎ) minus 119875t1

(MFR119904sdot 119875119905119904+MFR

119904sdot 119875119905ℎ)

120578119905-119904 =

(MFR119904sdot 119879119905119904+MFR

ℎsdot 119879119905ℎ) minus 1198791

(MFR119904sdot 119879119905119904+MFR

ℎsdot 119879119905ℎ) minus 1198791119904

(9)

where 1198751199051 1198791 and 119879

1119904refer to the total pressure static

temperature and isentropic static temperature at the voluteexit respectively Since no work is done by the volute andthe wall is assumed to be adiabatic thus the total-to-static

International Journal of Rotating Machinery 7To

tal p

ress

ure (

bar)

150

175

200

225

250

0 60 120 180 240 300 360

Crank angle (deg)

minus020

minus015

minus010

minus005

000

005

010

015

Loss

fact

or

Pt at hub inletPt at shroud inlet

Average Pt at inlet voluteLoss factor

Figure 4 Instantaneous total pressure and loss factor

Tota

l to

stat

ic effi

cien

cy

0 60 120 180 240 300 360

Crank angle (deg)

00

02

04

06

08

10

12

14

16

18

20

Figure 5 Unsteady total-to-static efficiency of the volute

efficiency of the volute can bewritten as a function of pressureratio as follows

120578119905-119904 =

1 minus (11987511198751199051)(120574minus1)120574

1 minus (11987511198751199050)(120574minus1)120574

(10)

Figures 4 and 5 show the response of the twin-entry voluteto the pulsatile flow at inlet in terms of the total pressure lossfactor and the total-to-static efficiency versus the crank angleExcept that at the beginning of simulations where the valueof total pressure loss factor is negative or exceeds unity thebehaviour of loss factor is shown to be nearly in out-phaseto the mean inlet total pressure Similarly the total-to-staticisentropic efficiency of the twin-entry volute shows a strongbehaviour during the first 60 deg of the crank angle and thentends to be in out-phase to the loss factor since low losses leadto more efficiency

The flow structures in the volute between shroud-sideand hub-side are revealed (Figure 6) by the velocity vectorssuperimposed to the plot of the total pressure at two planes

situated at the interface voluterotor (radius 1198771 = 49mm)and at an interspace plane distant from the rotor entry about15mm (radius 1198772 = 515mm) Figure 6 depicts flow struc-tures at three different instants instant of a high total pressureat the shroud-side instant of an equality of total pressureat the two entries and an instant when the volute is highlyfed through the hub-side entry Before entering into theinterspace represented by the space between the divider andthe rotor inlet (about 6mm in radial direction) the vectorsare seen to be in the circumferential directionHowever sincethe flow attains the interspace area the velocity vectors startdeviating to the radial direction (plane of radius 1198772) Theflow entering from the shroud-side is characterized by anaxial component provoked by the inclination of the two wallswhich constitute the shroud-side entryThis axial componentseems to be more accentuated in the case of a high totalpressure at the shroud-side since the flow tends to migrate tothe hub-side (Figure 6(a)) In the case of equal admission themain flowwithin the shroud-side is shown to enter parallel tothe divider whereas the flowwithin the hub-side is parallel tothe upper wall of volute (Figure 6(b)) At the instant when thevolute is highly fed through the hub-side entry (Figure 6(c))the flow entering the interspace from the hub-side tends torecover the shroud-side The flow near the tongue is firstlyaffected by the previous infiltrated flow coming downstreamof the tongue and feeding the rotor once more and secondlyby the zone of flow mixture created upstream of the tonguebetween the two incoming flows For the three instants thevelocity vectors near the tongue are shown to be inclinedto the circumferential direction and then inclined largely tothe radial direction Also the details of Figure 6 depict arapid recovery of the flow asmoving from the circumferentialdirection to the radial direction through the interspace of6mm for the three instants

42 Instantaneous Isentropic and Actual Power There is acertain distance existing between the locations of upstreamand downstream planes used for calculating the turbineperformance which gives rise to a time lag between thephases for the respective quantities under pulsating flowsThis time lag should be equal to the time taken by thepulse mechanism to travel between the two stations In thecase of a twin-entry radial turbine the estimation of phaseshift between the actual and the isentropic work seems tobe more complicated as compared to a single-entry turbinebecause of the complex geometry and the interaction betweenthe two entries There are two major problems which areinvolved to find the time lag The first is the flow velocitythrough the volute which varies considerably due to theprogressive restriction of volute section from the inlet ductto the tongue in addition to continuous variation of gas flowconditions at the inlet The second is the distance separatingthe twomeasurements planeswhich cannot be clearly definedwithout a detailed evaluation of the path-lines since the twin-entry volute feeds the rotor circumferentially around 360 degPalfreyman and Martinez-Botas [13] and Arcoumanis et al[26] showed that the time shift is mainly produced in thevolute owing to its biggest characteristic length as comparedto the rotor which may be studied as a quasi-steady pattern


R1

R2

Rotational axis X

Total pressure203e + 005

185e + 005

167e + 005

149e + 005

131e + 005

(Pa)

Rotation

Tongue position 0∘

(a)

R1

R2

Rotational axis X

Rotation


Total pressure

(Pa)

193e + 005

175e + 005

156e + 005

138e + 005

119e + 005

(b)

R1

R2

Rotational axis X

Rotation

Tongue position 0

∘

Total pressure

(Pa)

209e + 005

189e + 005

169e + 005

149e + 005

129e + 005

(c)

Figure 6 Velocity vectors over total pressure through the volute at three different instants

Shroud-side mean plane

75 of span

120593s120593s2

(a)

Hub-side mean plane

25 of span

120593h120593h2

(b)

Figure 7 Mean planes of volute (a) shroud-side and (b) hub-side

Therefore in the present study the time shift is taken as thenecessary time for the mechanism of pulse to travel from theinlet duct to the exit volute hence the time shift 120591 is expressedas

120591 =119871

119881 (11)

where 119871 represents the apparent length and 119881 the velocity ofpulse mechanism

In order to estimate the velocity used to determine thetime lag two mean planes are plotted in the two entriesas shown by Figure 7 For each entry and for each time

step corresponding to 15 deg of rotor rotation the averagearea velocities (bulk flow velocity and sonic velocity andsum of them) were evaluated By using the apparent length(assuming inlet rotor at 90 deg 180 deg 270 deg or 360 degfrom the tongue) the mean time lag related to one time stepcan be calculated for the turbine and the average of all thevalues of time lag could be taken as an approximation of theglobal time lag

The results of the simulated actual power and the isen-tropic inlet power versus the crank angle are presented inFigure 8 The unsteady isentropic power is presented as


Crank angle (deg)

Pow

er (k

W)

0 120 240 360 480 60010

15

20

25

30

35

40

45

50

Utilized powerIsentropic power (bulk velocity)Isentropic power (sonic velocity)Isentropic power (sum velocities)

No correspondence betweenisen and actu power

Correspondence

Figure 8 Simulated instantaneous isentropic and utilized power

depending on the bulk flow velocity and the sonic velocityand the sum of them in order to evaluate the time lag Themean time lag is found equal to 1723119879119903 0573119879119903 and 0494119879119903(119879119903 represents the time necessary for the rotor to revolveone round) by taking the velocity of the pulse transportmechanism as the bulk flow velocity and the sonic velocityand the sum of them respectively An equivalent value ofthe time lag expressed in terms of crank angle attributed toprevious values (1657 deg 55058 deg and 4744 deg) depictsa high difference between the mean time lag calculated usingthe bulk flow velocity and that using the sonic velocityor the sum of them Such difference could be related tothe importance of the sonic velocity resulting from a highoperating temperature Figure 8 reveals that although takinginto account the time shift in evaluating the isentropic inletpower the maximum and the minimum of isentropic inletpower do not correspond to the maximum and minimumof the actual power Thus there is a nonconstant phase shiftbetween isentropic and actual power which varies during thepulses In practice these time-dependent phase shifts maybe explained by the fact of the inertial effect of the turbinerotor causing its rotation to continue even when the inletpressure is low and this effect is not taken into account inthe present simulations because Ansys-CFX only requires aconstant rotational speed In their LES Hellstrom and Fuchs[14] captured this time-dependent behaviour and related itto the pulsatile inlet conditions where the maximum phaseshift occurs when the inlet flow changes its direction and theminimum of phase shift occurs when the mass flow reachesitsmaximumGiven the uncertainty associatedwith the valueof the time lag an alternative issue is to evaluate the radialturbine performance by cycle averaging of the inlet and outlet

parameters during one ormore pulse cycles thus avoiding thephase shifting

To identify the effect of the apparent length in theevaluation of total-to-static efficiency four apparent lengthswere tested using the sum of bulk flow velocity and sonicvelocity as the velocity of the pulses mechanism Figure 9shows that the effect of choosing the apparent length onthe total-to-static efficiency is noticeable when using theapproach based on the bulk flow velocity however this effectis not clear for the other two approaches The instantaneousshaft power and the total-to-static efficiency recorded at thebeginning of simulations exhibit abrupt variations where thevalue of shaft power doubled and that of efficiency exceededunity However the effect of pulses within the turbine impliesa dynamic process thus the instantaneous developed power isnot a simple function of the current boundary condition butdepends on the history of boundary conditions for some timeprior to themoment of calculation [24] Consequently a lapseof time corresponding to 45 deg of crank angle equivalent toa half of the complete period of pulse through the hub entryfor these simulations is required to ensure that such a historyis constituted and a periodic solution is reached

43 Instantaneous Mass Flow Rate For this twin-entry radialturbine the instantaneous inlet and exit mass flow rates ateach time step versus the crank angle are plotted as depictedin Figure 10 The instantaneous mass flow rate is derivedby the summation of the discrete mass flows through asurface of the control volume over all integration pointsat inlet or outlet of the control volume At the beginningof simulations a strong variation of the inlet and outletmass flow rates was recorded A lapse of time correspondingto 45 deg of crank angle (equivalent to a complete periodof the pulses at hub entry) was required to ensure that aperiodic solution is reached The instantaneous mass flowrate behaviour for the two entries is more irregular than thepressure trace and mainly follows the features of the pressuresignal Furthermore the inlet mass flow rate is in out-phasebetween the two entries following the imposed inlet totalpressure features Nevertheless the mass flow rate at theoutlet moves away from a sinusoidal feature as imposed atthe outlet During a fixed period from a position 120579 = 45 deg to360 deg the inlet mass flow rate fluctuates between 0257 kgsand 0344 kgs while the outlet mass flow rate fluctuates in awider range from019 kgs to 0367 kgsThemaximumoutletmass flow is higher than that at the inlet due to the emptying-filling phenomena However the volume of the twin volutecan be considered as a temporary tank in which the fluid canbe accumulated and then dischargedThrough the rise time ofthe pulse the mass flow reaches a critical value related to thechoked regime after that the rotor is incapable of dischargingthe incoming fluid before the next pulse cycle resulting fromboth sides thus causing an accumulation within the voluteInversely through the descent time of the pulse the incomingmass flow drops hence allowing the rotor to consume theexcessive fluid However the turbine has insufficient time toconsume the gas mass within the working inlet pipe beforethe next pulse cycle and storage of mass is taking placein the volute [10 27] To quantify the instantaneous rate


04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09

Apparent length at 360∘Apparent length at 180∘


0 60 120 180 240

180 210 240

300 360

(a)

04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09



180 210 240

0 60 120 180 240 300 360

(b)

Figure 9 Total-to-static efficiency evaluated for different apparent length (a) bulk flow velocity and (b) sumof sonic velocity and bulk velocityas velocity of pulse mechanisms

00

01

02

03

04

05

06

MFHMFS

MFIMFO

Crank angle (deg)

Mas

s flow

(Kg

s)

0 60 120 180 240 300 360

Figure 10 Instantaneous mass flow rate

of this mass storage Ehrlich [10] introduced the parameter((ℎ+ 119904minus out)(ℎ +

119904)) to describe the net rate of

mass entering or leaving the twin-entry radial turbine asa percentage of the total mass flow entering the turbine atany instant The surplus accumulated during the unequaladmission and partial admission could be evacuated overother portions of the ICE cycle and therefore the conservationof mass flow is respected during a complete cycle Figure 11illustrates the evolution ofmass storage parameter and revealsthat except at the beginning of the simulations the massstorage and the discharge through this twin-entry radialturbine do not exceed the value of 30 of the total mass flowentering the turbine Also the storage mass parameter shows

minus20

minus15

minus10

minus05

00

05

10

(C)(B)

(A)

0 60 120 180 240 300 360

Crank angle (deg)

m

s+m

hminusm

out

ms+m

h(

) (

)

Figure 11 Mass storage parameter

that the duration of the accumulation period representsapproximately 70 of the discharge period wherein the rotorevacuates quickly the storage mass characterized by a highpressure and stored through the volume of volute

Figure 12 depicts the distribution of static pressure atthe mid-span of hub-side and shroud-side of the volute atthree instants equivalent to maximum of mass flow rateaccumulation (instant A) maximum of mass flow dischargethrough the volute (instant C) and no storage mass flow(instant B) At the instant of no storage mass flow (instant B)the static pressure distributions at mid-span of shroud-sideand hub-side of the volute show that the volute distributesthe flow in an axisymmetric way at the entry of rotor bytransforming the potential energy of gases into kinetic energy


Maximum accumulation(A)

No mass storage(B)

Maximum discharge (C) Pressure

(Pa)

1805e + 005

1598e + 005

1391e + 005

1184e + 005

9766e + 004

(a)Pressure

(Pa)

1745e + 005

1527e + 005

1309e + 005

1090e + 005

8722e + 004

(b)

Figure 12 Static pressure distribution at mid-span (a) hub-side of volute and (b) shroud-side of volute

conformed to the free vortex design A qualitative com-parison of the flow field distributions between the shroud-side and hub-side illustrates that the conversion of energyis much more evident in the shroud-side At the instant ofmaximum of mass flow rate accumulation (instant A) theflow field shows a gradual decrease of static pressure coveringthe forward and backward directions of interspaces area(beginning of the area of interspace shown by Figures 12 and13 by a continued circle) On the other side at the instant ofmaximumdischarge (instantC) a rapid drop in static pressureis shown within the interspace due to interactions betweenthe two entries where instantaneous unequal inlet admissionis recorded at an angle of 268 deg Nonuniformities observednear the tongue and a part of crossing flow that recovers themain flow are directly transmitted to the nearest blade Theratio between this crossing flow and the instantaneous inletmass flow at the instant of maximum storage (about 25) isless than the ratio at the maximum discharge (about 3)

In steady flow the entropy rise and the total pressure losscoefficient both can be used to estimate the losses Howeverdue to the pulses through the radial turbine where both thetotal pressure and temperature highly fluctuate subsequentlythe losses should be expressed in terms of entropy MoreoverDenton [28] concluded that the most rational measure ofloss generation in an adiabatic machine is in terms ofentropy creation By referring to the discussion in Sections42 and 43 concerning (acoustic and convective and both)propagation of fluid properties it can be seen that the choicesof pulse transport mechanism are not obvious Moreoverthe effect of the pulses on the turbine performance in its

rise time or descent time is not clear in terms of losses Asmentioned above the pulse flow through the radial turbineis characterized by an accumulation and a discharge of thefluid within the volute The following paragraph quantifiesthe losses caused by the emptying and the filling effectThe distributions of the static entropy at mid-span throughthe hub-side and the shroud-side of volute are shown inFigure 13 The generated static entropy intensifies backwardof a position of 90 deg from the tongue due to a subsequentseparation as the flow is forced to return to feed the rotorespecially at the instant of no storage mass flow (instantB) However the influence of the tongue region is clearlydepicted forward to it at the instant of maximum dischargeor maximum accumulation as a consequence of the wakegenerated from the mixing between the inlet flow and thatemerging from the tongue which circled around the rotorThe impact of the wake from the tongue seems to not extendany further than an azimuth angle of 90 deg High entropygenerated at the instant of maximum discharge (instant C) ismore concentrated at the hub-side than shroud-side whereasa lower entropy is generated at the instant of maximumstorage (instant A) at the hub-side than at the shroud-side

44 Total-to-Static Efficiency versus RMF and IsentropicVelocity Ratio Figures 14 and 15 plot the evolution of thetotal-to-static efficiency versus the reduced mass flow (RMF)parameter and the isentropic velocity ratio for the cases ofsteady and pulsatile flow conditions As shown this lattervaries in a narrow range of the reduced mass flow parameterand is close to the optimum value of the isentropic velocity



No mass storage(B)

Maximum discharge (C) Static entropy

2776e + 003

2733e + 003

2691e + 003

2648e + 003

2605e + 003

(J kg

minus1

Kminus1)

(a)Static entropy

2764e + 003

2733e + 003

2701e + 003

2670e + 003

2638e + 003

(J kg

minus1

Kminus1)

(b)

Figure 13 Static entropy distribution at mid-span (a) hub-side of volute and (b) shroud-side of volute

Isentropic velocity ratio

Tota

l-to-

stat

ic effi

cien

cy

055 06 065 07 075 08 085

06

07

08

09

1

Steady stateBulk velocity

Sonic velocitySum of sonic and bulk velocity

Figure 14 Total-to-static efficiency versus isentropic velocity ratio

ratio The unsteady performance is presented using thesum of the bulk flow velocity and the sonic velocity forevaluating the time lag between the isentropic conditionand the actual condition The asymmetric twin-entry radial

Reduced mass flow

Tota

l-to-

stat

ic effi

cien

cy

35 4 45 5 55 6 65

06

07

08

09

1



Figure 15 Total-to-static efficiency versus reduced mass flowparameter

turbine with pulse flow at the two inlets indicates that theinstantaneous performance and flow characteristics deviatesubstantially from their steady state valuesThis confirms thatthe quasi-steady assumption normally used in the assessment


13

14

15

16

17

18

19

20

Crank angle (deg)

Tota

l-to-

stat

ic p

ress

ure r

atio

0

5

10

15

20

25

30

Out

let s

haft

pow

er (K

W)

(D)

(E)

0 60 120 180 240 300 360

120587ts-s

120587ts-h

120587ts

Shaft power

Figure 16 The instantaneous actual shaft power

of performance is inadequate for the characterization ofthe efficiency in a pulsating environment of an automotiveturbocharger The results show that the efficiency versusisentropic velocity ratio departs from the steady state upto +26 and minus22 whereas the efficiency versus reducedmass flow has +25 and minus21 difference For a twin-entryturbine but with a symmetric volute Dale and Watson [3]showed that the efficiency deviates with different unequaladmission conditions +5 to minus12 from the steady equaladmission line This common looping curves behaviour aswell depicted in the present numerical study was reportedin the experiments of Arcoumanis et al [26] Karamanisand Martinez-Botas [18] and Winterbone et al [19] for amixed flow turbine and Dale and Watson [3] and Ehrlich[10] for a twin-entry radial turbine This looping behaviouris attributed to the continuous filling and emptying of thevolute volume during the pulsating flow conditions thus theimbalance between the inlet and outlet mass flow during thepulse occurs as explained by Chen et al [29] and Karamanisand Martinez-Botas [18]

45 Unsteady Shaft Power and Total-to-Static Pressure RatioFigure 16 presents the behaviour of the shaft power andthe total-to-static pressure ratio versus the crank angle Asseen the shaft power is not constant when the inlet pressurethrough the hub-side entry and the shroud-side entry variesand tends to follow the trend of the mean total-to-staticpressure ratio The power shaft remains fairly flat for a mini-mum total-to-static pressure ratio related to the shroud-sideentry which is more sensitive to the inlet total pressure thanthe hub-side entry Thus through an increase of expansionratio the efficiency rises and more mass flow passes throughthe turbine The shaft power fluctuates with a frequencythat corresponds to the blade passing frequency (BPF) of12000Hz (Figure 17) andmodulated by a curve describing theinflow fluctuations Similar behaviour has been reported insome papers studying radial turbines under pulsating flowssuch as that of Palfreyman and Martinez-Botas [13] who

0

250

500

750

1000

1250

1500

1750

Frequency (Hz)

Am

plitu

de (W

att)

1 10 1000100 10000 100000

X = 151Y = 1534

X = 101Y = 472

X = 75Y = 793

X = 249Y = 470

X = 249Y = 470

X = 12001Y = 399

Figure 17 FFT spectrum of the actual shaft power signal

conducted both computations and experiments to investigatethe performance of a mixed flow turbine working underpulsatile flow conditions and showed that an oscillation witha frequency corresponding to the blade passage is superim-posed on the shaft produced power Recently Hellstrom andFuchs [14ndash16] in their LES computations highlighted thisfrequency The resulting FFT analysis of the signal of theactual shaft power reveals the domination of the frequenciesmultiple of 25Hz whichmay be related to the potential effectmarked by the interaction between the incoming flow fromthe hub-side and the shroud-side at the interspace upward tothe rotor These interactions were highlighted in a previouswork by Cerdoun and Ghenaiet [30] using the chorochronicperiodicity developed by Tyler and Sofrin [31]

For identifying the effect of these interactions Figure 18plots the flow streamlines superimposed to the static entropyat a plane around the exit of volute located in the interspace ata distance of 42mm from the divider representing 70of thedistance between the divider and the volute exit The plot isgiven for two instants at themaximumof shaftpower (D) andthe minimum of shaft power (E) The flow in the interspacepassing by the tongue depicts mixing near the divider andthe streamlines follow a form of a bulge created betweenthe main flow and the infiltrated flow owing to differencein velocities between the incoming flow through the tongueand the main flow As a consequence the flow structures inthe interspace between shroud-side and hub-side are seen tobe affected by the flow incidence at rotor entry to provokehigh losses (Figure 18) Therefore the instant (D) associatedwith the maximum of shaft power is accompanied with lowentropy generation in the shroud-side On the other hand theincrease in entropy generation in the hub-side is marked by adecrease in the shaft power

5 Conclusion

A twin-entry radial turbine operating under inlet pulsatileflows was studied considering more realistic inlet and outletboundary conditions and the time lag As a result theinstantaneous performance obtained at the design speed is


Visualization plane

Divider

70 of interspace

Volute exit

(a)

Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(b)Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(c)

Figure 18 Streamlines over static entropy in the interspace at 70 from the divider (detail (a)) and (b) instant of maximum shaft power and(c) instant of minimum shaft power

shown to depart from that of steady state The total pressureloss factor through the twin-entry volute is shown to behavein out-phase with the mean inlet total pressure whereas theshaft power tends to follow the mean total-to-static pressureratio The choice of the time lag was of a considerableimportance in evaluating the unsteady efficiency The massstorage and discharge through this twin-entry radial turbinedo not exceed 30of the entering totalmass Also the storagemass parameters show that the duration of accumulationperiod represents approximately 70 of discharge periodThe entropy generation is seen to be more marked at theperiod of discharge whereas the minimum occurs duringthe period of mass flow storage The shaft power fluctuateswith a frequency corresponding to BPF and according tothe entropy generated through hub-side and shroud-side ofvolute Moreover there is a nonconstant phase shift betweenthe isentropic and the actual power which varies with thepulses It appears that the parameters affecting the phase shiftnot only could be limited to the velocity of pulse transportmechanism but also may be extended to the pulse frequencyamplitude and temporal local gradient of mass flow andpressure wave

Notations

119875119905 Total pressure [Pa]

119879119905 Total temperature [K]

119901 Static pressure [Pa] Mass flow [kgsdotsminus1]119875 Power [Watt]119879Shaft Shaft torque [Nsdotm]119891 Force [N]119903 Radius [m]119905 Time [s]

Greek

120596 Rotational speed [radsdotsminus1]120579 Circumferential coordinate [deg]

Subscripts

ℎ Hub119904 Shroudout Outlet

Abbreviations

BPF Blade passing frequencyCFD Computational fluid dynamicMFR Mass flow ratioLES Large eddy simulationsRMF Reduced mass flow


SMM Sliding mesh modelURANS Unsteady Reynolds Average

Navier-Stokes

Competing Interests

The authors declare no competing interests

References

[1] A Romagnoli C D Copeland R F Martinez-Botas S MartinS Rajoo and A Costall ldquoComparison between the steadyperformance of double-entry and twin-entry turbochargerturbinesrdquo Journal of Turbomachinery vol 135 no 1 Article ID011042 11 pages 2012

[2] F Pischinger and A Wunsche ldquoThe characteristic behaviour ofradial turbines and its influence on the turbocharging processrdquoin Proceedings of the CIMAC Conference pp 545ndash568 TokyoJapan 1977

[3] A Dale and N Watson ldquoVaneless radial turbocharger turbineperformancerdquo in Proceedings of the IMechE C11086 pp 65ndash761986

[4] M Capobianco and A Gambarotta ldquoPerformance of a twin-entry automotive turbocharger turbinerdquo ASME Paper 93-ICE-2 1993

[5] A Romagnoli R F Martinez-Botas and S Rajoo ldquoSteadystate performance evaluation of variable geometry twin-entryturbinerdquo International Journal of Heat and Fluid Flow vol 32no 2 pp 477ndash489 2011

[6] S Rajoo A Romagnoli and R F Martinez-Botas ldquoUnsteadyperformance analysis of a twin-entry variable geometry tur-bocharger turbinerdquo Energy vol 38 no 1 pp 176ndash189 2012

[7] A Hajilouy M Rad and M R Shahhosseini ldquoModelling oftwin-entry radial turbine performance characteristics based onexperimental investigation under full and partial admissionconditionsrdquo Scientia Iranica vol 16 no 4 pp 281ndash290 2009

[8] J R Serrano F J Arnau V Dolz A Tiseira and C CervelloldquoA model of turbocharger radial turbines appropriate to beused in zero- and one-dimensional gas dynamics codes forinternal combustion engines modellingrdquo Energy Conversionand Management vol 49 no 12 pp 3729ndash3745 2008

[9] M Iwasaki N Ikeya Y Marutani and T Kitazawa ldquoCom-parison of turbocharger performance between steady flow andpulsating flow on enginesrdquo SAE Paper 940839 1994

[10] D A Ehrlich Characterisation of unsteady on-engine tur-bocharger turbine performance [PhD thesis] PurdueUniversity1998

[11] S Rajoo and R FMartinez-Botas ldquoUnsteady effect in a nozzledturbocharger turbinerdquo Journal of Turbomachinery vol 132 no3 Article ID 031001 2010

[12] J K W Lam Q D H Roberts and G T McDonnell ldquoFlowmodelling of a turbocharger turbine under pulsating flowrdquo inProceedings of the ImechE Conference Transactions from 7thInternational Conference on Turbochargers and Turbochargingpp 181ndash196 London UK May 2002

[13] D Palfreyman and R F Martinez-Botas ldquoThe pulsating flowfield in amixed flow turbocharger turbine an experimental andcomputational studyrdquo Journal of Turbomachinery vol 127 no 1pp 144ndash155 2005

[14] FHellstromandL Fuchs ldquoNumerical computations of pulsatileflow in a turbo-chargerrdquo in Proceedings of the 46th AIAA

Aerospace Sciences Meeting and Exhibit Aerospace SciencesMeetings AIAA 2008-735 2008

[15] F Hellstrom and L Fuchs ldquoEffects of inlet conditions on theturbine performance of a radial turbinerdquo ASME Paper GT2008-51088 2008

[16] F Hellstrom and L Fuchs ldquoNumerical computation of thepulsatile flow in a turbocharger with realistic inflow conditionsfrom an exhaust manifoldrdquo ASME Paper GT2009-59619 2009

[17] M H Padzillah S Rajoo and R FMartinez-Botas ldquoNumericalassessment of unsteady flow effects on a nozzled turbochargerturbinerdquo in Proceedings of the ASME Turbo Expo TurbineTechnical Conference and Exposition Paper no GT2012-69062pp 745ndash756 Copenhagen Denmark June 2012

[18] N Karamanis R F Martinez-Botas and C C Su ldquoMixedflow turbines inlet and exit flow under steady and pulsatingconditionsrdquo Journal of Turbomachinery vol 123 no 2 pp 359ndash371 2001

[19] D E Winterbone B Nikpour and G I Alexander ldquoMea-surements of the performance of a radial inflow turbine inconditional steady and unsteady flowrdquo in Proceedings of theImechE Conference Transactions 4th International ConferenceTurbocharging and Turbochargers C405015 pp 153ndash160 1990

[20] S Szymko R F Martinez-Botas and K R Pullen ldquoExperi-mental evaluation of turbocharger turbine performance underpulsating flow conditionsrdquo ASME Paper GT2005-68878 2005

[21] J K W Lam Q D H Roberts and G T Mcdonnell ldquoFlowmodelling of a turbocharger turbine under pulsating flowrdquo inTurbocharging and Turbochargers I Mech E pp 181ndash197 2002

[22] N C Baines Turbocharger Turbine Pulse Flow Performance andModellingmdash25 Years On Concepts NREC Hartford Vt USA2010

[23] S Rajoo and R Martinez-Botas ldquoMixed flow turbine researcha reviewrdquo Journal of Turbomachinery vol 130 no 4 Article ID044001 2008

[24] A Ghenaiet ldquoPredicting the aerodynamic performance ofturbocharger componentsrdquo IMechE Compressors and TheirSystems Paper C65801007 Chandos Oxford UK 2007

[25] N A Cumpsty and J H Horlock ldquoAveraging nonuniform flowfor a purposerdquo Journal of Turbomachinery vol 128 no 1 pp120ndash129 2006

[26] C Arcoumanis I Hakeem L Khezzar and R F Martinez-Botas ldquoPerformance of a mixed flow turbocharger turbineunder pulsating flow conditionsrdquo ASMEPaper 95-GT-210 1995

[27] S Marelli and M Capobianco ldquoMeasurement of instantaneousfluid dynamic parameters in automotive turbocharging circuitrdquoin Proceedings of the 9th SAE International Conference onEngines and Vehicles 2009-24-0124 2009

[28] J D Denton ldquoThe 1993 IGTI scholar lecture loss mechanismsin turbomachinesrdquo Journal of Turbomachinery vol 115 no 4pp 621ndash656 1993

[29] H Chen I Hakeem and R F Martinez-Botas ldquoModellingof a turbocharger turbine under pulsating inlet conditionsrdquoProceedings of IMechE Part A Journal of Power and Energy vol210 pp 397ndash408 1996

[30] M Cerdoun and A Ghenaiet ldquoAnalyses of steady and unsteadyflows in a turbochargerrsquos radial turbinerdquo Proceedings of IMechEPart E Proc IMechE Part E Journal of Process MechanicalEngineering vol 229 no 2 pp 130ndash145 2015

[31] J M Tyler and T G Sofrin ldquoAxial flow compressor noisestudiesrdquo SAE Transaction vol 70 pp 309ndash332 1962

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terms of efficiency however a significant depreciation inefficiency was measured for a vane angle between 50 deg and40 deg Further an optimum vane angle of 60 deg was foundfor the twin-entry turbine Based on unsteady experimentsfor the same modified turbine Rajoo et al [6] showedthat the swallowing capacity of a twin-entry turbine in in-phase testing during full admission was inconsistent betweenthe two entries Contrarily during out-phase testing theswallowing capacity of both entries was found to be similarThe performance of an asymmetric twin-entry radial turbinewas investigated analytically and experimentally by Hajilouyet al [7] under steady state conditions considering the fulland partial admission As results for a very high ratio ofmass flow rates between the shroud-side and hub-side theefficiency is lower than that of the full admission

Engine exhaust pulse flows can significantly affect theturbine performance of a turbocharger hence it is necessaryto consider the pulse flow effects in the turbine designand performance analysis Many researchers were interestedin the effects of pulsatile flows such as Serrano et al [8]who determined the performance of a small radial inflowturbine working under pulsatile flows and compared withthe one measured from cold pulsating flows Iwasaki et al[9] performed steady and unsteady flow measurements ona twin-entry turbine coupled to a 6-cylinder medium dutydiesel engine They found that for a fixed turbocharger speedand expansion ratio the unsteady flow mass flow parameterwas lower than that corresponding to the steady flow valueover the tested operating range Ehrlich [10] performedmeasurements in an engine test cell on a turbochargedmedium speed 6-cylinder diesel engine with the focus onunderstanding the process of energy transport from the cylin-ders to the twin-entry turbine admission They measuredthe instantaneous total and static pressures by using in-house constructed probes connected to a high frequencydynamic pressure transducer The results indicated that thetransport mechanism of the gas pulses energy in the exhaustmanifold must be modelled as both convective and acousticpropagation of a wave Dale and Watson [3] measured theshaft power of a twin-entry turbine working in pulsatile flowand concluded that the efficiency varies with admission andthe lowest efficiency occurs when the flow enters only oneof the two entries Rajoo and Martinez-Botas [11] discussedthe performance of a twin-entry variable geometry turbinetested under the pulsating flow conditions and concludedthat the swallowing capacity during the full admission wasinconsistent and the shroud entry was more pressurizedcompared to the hub entry Owing to many difficulties inmeasuring the unsteady performance of radial turbines andthe necessity of fully understanding their internal flows CFDstudies are used to surmount the lack of data Lam et al[12] performed a numerical study of the pulsatile flow in aradial nozzled turbine based on the frozen rotor interfaceThe results show that the instantaneous performance variesslightly from the nonpulsatile flow conditions thus allowingconcluding that the rotor can be treated as a quasi-steadydomain while the volute must be treated as a non-quasi-steady flow device Also Palfreyman and Martinez-Botas[13] investigated the pulsatile flow in a medium sized mixed

flow nozzleless turbine based on URANS computationsRNG-119896120598 turbulence model and sliding mesh model (SMM)at volute-rotor interface They concluded that the agreementwith the flow field measurements for both the cycle averagedand instantaneous data was reasonable and the sliding meshmodel showed better results than themoving reference frameas adopted by Lam et al [12] Hellstrom and Fuchs [14ndash16]carried out numerical flow analyses of a nozzleless turbinein the case of pulsatile inlet conditions considering largeeddy simulations (LES) implemented in the commercial codeSTAR-CD Their first report [14] treated two cases of an ICErotational speed (1500 rpm 3000 rpm) and concluded thatthe entry of rotor into the flow angle varies from minus67 deg tominus25 deg for the second speedwhichwasmore favourable thanthe first speed where the flow angle is from minus85 deg to 60 degresulting in a drop of the peak shaft power about 4 Theresults of Palfreyman and Martinez-Botas [13] showed thatthe incidence angle varied from minus92 deg to 60 deg

Recently Padzillah et al [17] based on a full 3D CFDmodel studied the influence of the speed and the frequencyof pulses on a mixed radial turbine The temporal andspatial resolutions of the flow incidence suggested that thecircumferential variation is less than 7 compared to itsvariation in time as the pulses progressThey found that thereis no direct instantaneous relationship between the pulsatingpressure and the turbine efficiency The major difficulty inderiving the turbine performance is the shifting time betweenthe isentropic conditions upstream of the turbine and theactual output work Furthermore the expansion process ishighly unsteady as it responds to the exhaust manifoldsof an ICE and this is why its design and adaptation area very difficult task owing to its operation in off-designconditions There are still debates on the effective method ofdefining the efficiency of a turbine under the unsteady flowconditions due to the phase shifting so a question ariseshow can the time lag be evaluated To answer this questiontwo parameters should be determined such as the transportmechanism speed of pressure wave and the apparent lengthwhich represents the average distance travelled by the wavefrom a measurement plan to a supposed position at the rotorentry Three approaches have been adopted by researchersin order to estimate the time lag The first approach asproposed by Dale and Watson [3] is based on the sonictravel speed arguing that the pressure waves propagate atthis speed Karamanis et al [18] measured the static pressuredevelopment from the inlet measuring plane to the rotorentry at various locations upstream and downstream of thetongue and concluded that the only appropriate time to shiftthe signal is given by the sonic travel time such an approachwas adopted bymany workersThe second approach suggeststhat the bulk of the flow transmission is more important thanthe pressure wave transmission which was first proposed byWinterbone et al [19] and followed by other workers Thethird approach suggests that the transport mechanism mustbe modelled as both convective and acoustic propagation[10] Recently Szymko et al [20] showed that the sum ofsonic velocity and bulk flow velocity can lead to betterresults Many researchers took the apparent length as thepath length between the centres of volute sections from







3Dr

2Dr

Shroud entry

Hub entry



119903and 3119863

119903(119863119903







Interspace I


Rinlet

Rotation axis X

Hinlet

LMean

CMean

Xturbine



ROutletShroud

ROutletMean

ROutletHub


(a)

Tip clearance

(b)





1015840


1015840

119905identified



0 120 240 360 480 600 720500

550

600

650

700

750


Crank angle (deg)

Inle

t tot

al te

mpe

ratu

re (∘

C)

(a)In

let t

otal

pre

ssur

e (ba

r)

16

18

20

22

0 120 240 360 480 600 720


Crank angle (deg)

(b)

Crank angle (deg)

Out

let s

tatic

pre

ssur

e (ba

r)

0 120 240 360 480 600 720105

110

115

120

125

130

135

(c)



119875119905= 1198751015840

119905+ (119875119905minus

1

2120587int

2120587

0

1198751015840

119905119889120579)

119879119905= 1198791015840

119905+ (119879119905minus

1

2120587int

2120587

0

1198791015840

119905119889120579)

(1)



119901 = 1199011015840

+ (119901 minus1

2120587int

2120587

0

1199011015840

119889120579) (2)




MFR119904=

119904

119904+ ℎ

MFRℎ=

ℎ

119904+ ℎ

(3)


119905could


= MFR119904sdot

119879119905119904+MFR





1199050= MFR

119904sdot 119875119905119904+ MFR

119904sdot 119875119905ℎ) The



119904sdot 119879119905119904+MFR

ℎsdot 119879119905ℎ

(MFR119904sdot 119875119905119904+MFR

119904sdot 119875119905ℎ) (4)


120587119905119904-119904 =

119875119905119904

119901out

120587119905119904-ℎ =

119875119905ℎ

119901out

120587119905119904=

1198751199050

119901out

(5)




Shaft = int119904

119903 times (119901 sdot ) 119889119904 (7)


120578119905119904=

Shaft sdot rotor

119904119862119901119904sdot 119879119905119904[1 minus (119901out119875119905119904)

(120574minus1)120574


(120574minus1)120574

]

(8)

119904and







119904and 119862119901

ℎ







120577 =(MFR

119904sdot 119875119905119904+MFR

119904sdot 119875119905ℎ) minus 119875t1

(MFR119904sdot 119875119905119904+MFR

119904sdot 119875119905ℎ)

120578119905-119904 =

(MFR119904sdot 119879119905119904+MFR

ℎsdot 119879119905ℎ) minus 1198791

(MFR119904sdot 119879119905119904+MFR

ℎsdot 119879119905ℎ) minus 1198791119904

(9)

where 1198751199051 1198791 and 119879




tal p

ress

ure (

bar)

150

175

200

225

250

0 60 120 180 240 300 360

Crank angle (deg)

minus020

minus015

minus010

minus005

000

005

010

015

Loss

fact

or




Tota

l to

stat

ic effi

cien

cy

0 60 120 180 240 300 360

Crank angle (deg)

00

02

04

06

08

10

12

14

16

18

20



120578119905-119904 =

1 minus (11987511198751199051)(120574minus1)120574

1 minus (11987511198751199050)(120574minus1)120574

(10)






R1

R2

Rotational axis X


185e + 005

167e + 005

149e + 005

131e + 005

(Pa)

Rotation


(a)

R1

R2

Rotational axis X

Rotation


Total pressure

(Pa)

193e + 005

175e + 005

156e + 005

138e + 005

119e + 005

(b)

R1

R2

Rotational axis X

Rotation

Tongue position 0

∘

Total pressure

(Pa)

209e + 005

189e + 005

169e + 005

149e + 005

129e + 005

(c)



75 of span

120593s120593s2

(a)

Hub-side mean plane

25 of span

120593h120593h2

(b)



120591 =119871

119881 (11)






Crank angle (deg)

Pow

er (k

W)

0 120 240 360 480 60010

15

20

25

30

35

40

45

50



Correspondence







04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09



0 60 120 180 240

180 210 240

300 360

(a)

04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09



180 210 240

0 60 120 180 240 300 360

(b)


00

01

02

03

04

05

06

MFHMFS

MFIMFO

Crank angle (deg)

Mas

s flow

(Kg

s)

0 60 120 180 240 300 360





minus20

minus15

minus10

minus05

00

05

10

(C)(B)

(A)

0 60 120 180 240 300 360

Crank angle (deg)

m

s+m

hminusm

out

ms+m

h(

) (

)






No mass storage(B)


(Pa)

1805e + 005

1598e + 005

1391e + 005

1184e + 005

9766e + 004

(a)Pressure

(Pa)

1745e + 005

1527e + 005

1309e + 005

1090e + 005

8722e + 004

(b)








No mass storage(B)


2776e + 003

2733e + 003

2691e + 003

2648e + 003

2605e + 003

(J kg

minus1

Kminus1)

(a)Static entropy

2764e + 003

2733e + 003

2701e + 003

2670e + 003

2638e + 003

(J kg

minus1

Kminus1)

(b)



Tota

l-to-

stat

ic effi

cien

cy

055 06 065 07 075 08 085

06

07

08

09

1





Reduced mass flow

Tota

l-to-

stat

ic effi

cien

cy

35 4 45 5 55 6 65

06

07

08

09

1






13

14

15

16

17

18

19

20

Crank angle (deg)

Tota

l-to-

stat

ic p

ress

ure r

atio

0

5

10

15

20

25

30

Out

let s

haft

pow

er (K

W)

(D)

(E)

0 60 120 180 240 300 360

120587ts-s

120587ts-h

120587ts

Shaft power




0

250

500

750

1000

1250

1500

1750

Frequency (Hz)

Am

plitu

de (W

att)

1 10 1000100 10000 100000

X = 151Y = 1534

X = 101Y = 472

X = 75Y = 793

X = 249Y = 470

X = 249Y = 470

X = 12001Y = 399




5 Conclusion



Visualization plane

Divider

70 of interspace

Volute exit

(a)

Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(b)Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(c)



Notations




Greek


Subscripts


Abbreviations




Navier-Stokes

Competing Interests


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















3Dr

2Dr

Shroud entry

Hub entry



119903and 3119863

119903(119863119903







Interspace I


Rinlet

Rotation axis X

Hinlet

LMean

CMean

Xturbine



ROutletShroud

ROutletMean

ROutletHub


(a)

Tip clearance

(b)





1015840


1015840

119905identified



0 120 240 360 480 600 720500

550

600

650

700

750


Crank angle (deg)

Inle

t tot

al te

mpe

ratu

re (∘

C)

(a)In

let t

otal

pre

ssur

e (ba

r)

16

18

20

22

0 120 240 360 480 600 720


Crank angle (deg)

(b)

Crank angle (deg)

Out

let s

tatic

pre

ssur

e (ba

r)

0 120 240 360 480 600 720105

110

115

120

125

130

135

(c)



119875119905= 1198751015840

119905+ (119875119905minus

1

2120587int

2120587

0

1198751015840

119905119889120579)

119879119905= 1198791015840

119905+ (119879119905minus

1

2120587int

2120587

0

1198791015840

119905119889120579)

(1)



119901 = 1199011015840

+ (119901 minus1

2120587int

2120587

0

1199011015840

119889120579) (2)




MFR119904=

119904

119904+ ℎ

MFRℎ=

ℎ

119904+ ℎ

(3)


119905could


= MFR119904sdot

119879119905119904+MFR





1199050= MFR

119904sdot 119875119905119904+ MFR

119904sdot 119875119905ℎ) The



119904sdot 119879119905119904+MFR

ℎsdot 119879119905ℎ

(MFR119904sdot 119875119905119904+MFR

119904sdot 119875119905ℎ) (4)


120587119905119904-119904 =

119875119905119904

119901out

120587119905119904-ℎ =

119875119905ℎ

119901out

120587119905119904=

1198751199050

119901out

(5)




Shaft = int119904

119903 times (119901 sdot ) 119889119904 (7)


120578119905119904=

Shaft sdot rotor

119904119862119901119904sdot 119879119905119904[1 minus (119901out119875119905119904)

(120574minus1)120574


(120574minus1)120574

]

(8)

119904and







119904and 119862119901

ℎ







120577 =(MFR

119904sdot 119875119905119904+MFR

119904sdot 119875119905ℎ) minus 119875t1

(MFR119904sdot 119875119905119904+MFR

119904sdot 119875119905ℎ)

120578119905-119904 =

(MFR119904sdot 119879119905119904+MFR

ℎsdot 119879119905ℎ) minus 1198791

(MFR119904sdot 119879119905119904+MFR

ℎsdot 119879119905ℎ) minus 1198791119904

(9)

where 1198751199051 1198791 and 119879




tal p

ress

ure (

bar)

150

175

200

225

250

0 60 120 180 240 300 360

Crank angle (deg)

minus020

minus015

minus010

minus005

000

005

010

015

Loss

fact

or




Tota

l to

stat

ic effi

cien

cy

0 60 120 180 240 300 360

Crank angle (deg)

00

02

04

06

08

10

12

14

16

18

20



120578119905-119904 =

1 minus (11987511198751199051)(120574minus1)120574

1 minus (11987511198751199050)(120574minus1)120574

(10)






R1

R2

Rotational axis X


185e + 005

167e + 005

149e + 005

131e + 005

(Pa)

Rotation


(a)

R1

R2

Rotational axis X

Rotation


Total pressure

(Pa)

193e + 005

175e + 005

156e + 005

138e + 005

119e + 005

(b)

R1

R2

Rotational axis X

Rotation

Tongue position 0

∘

Total pressure

(Pa)

209e + 005

189e + 005

169e + 005

149e + 005

129e + 005

(c)



75 of span

120593s120593s2

(a)

Hub-side mean plane

25 of span

120593h120593h2

(b)



120591 =119871

119881 (11)






Crank angle (deg)

Pow

er (k

W)

0 120 240 360 480 60010

15

20

25

30

35

40

45

50



Correspondence







04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09



0 60 120 180 240

180 210 240

300 360

(a)

04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09



180 210 240

0 60 120 180 240 300 360

(b)


00

01

02

03

04

05

06

MFHMFS

MFIMFO

Crank angle (deg)

Mas

s flow

(Kg

s)

0 60 120 180 240 300 360





minus20

minus15

minus10

minus05

00

05

10

(C)(B)

(A)

0 60 120 180 240 300 360

Crank angle (deg)

m

s+m

hminusm

out

ms+m

h(

) (

)






No mass storage(B)


(Pa)

1805e + 005

1598e + 005

1391e + 005

1184e + 005

9766e + 004

(a)Pressure

(Pa)

1745e + 005

1527e + 005

1309e + 005

1090e + 005

8722e + 004

(b)








No mass storage(B)


2776e + 003

2733e + 003

2691e + 003

2648e + 003

2605e + 003

(J kg

minus1

Kminus1)

(a)Static entropy

2764e + 003

2733e + 003

2701e + 003

2670e + 003

2638e + 003

(J kg

minus1

Kminus1)

(b)



Tota

l-to-

stat

ic effi

cien

cy

055 06 065 07 075 08 085

06

07

08

09

1





Reduced mass flow

Tota

l-to-

stat

ic effi

cien

cy

35 4 45 5 55 6 65

06

07

08

09

1






13

14

15

16

17

18

19

20

Crank angle (deg)

Tota

l-to-

stat

ic p

ress

ure r

atio

0

5

10

15

20

25

30

Out

let s

haft

pow

er (K

W)

(D)

(E)

0 60 120 180 240 300 360

120587ts-s

120587ts-h

120587ts

Shaft power




0

250

500

750

1000

1250

1500

1750

Frequency (Hz)

Am

plitu

de (W

att)

1 10 1000100 10000 100000

X = 151Y = 1534

X = 101Y = 472

X = 75Y = 793

X = 249Y = 470

X = 249Y = 470

X = 12001Y = 399




5 Conclusion



Visualization plane

Divider

70 of interspace

Volute exit

(a)

Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(b)Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(c)



Notations




Greek


Subscripts


Abbreviations




Navier-Stokes

Competing Interests


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Interspace I


Rinlet

Rotation axis X

Hinlet

LMean

CMean

Xturbine



ROutletShroud

ROutletMean

ROutletHub


(a)

Tip clearance

(b)





1015840


1015840

119905identified



0 120 240 360 480 600 720500

550

600

650

700

750


Crank angle (deg)

Inle

t tot

al te

mpe

ratu

re (∘

C)

(a)In

let t

otal

pre

ssur

e (ba

r)

16

18

20

22

0 120 240 360 480 600 720


Crank angle (deg)

(b)

Crank angle (deg)

Out

let s

tatic

pre

ssur

e (ba

r)

0 120 240 360 480 600 720105

110

115

120

125

130

135

(c)



119875119905= 1198751015840

119905+ (119875119905minus

1

2120587int

2120587

0

1198751015840

119905119889120579)

119879119905= 1198791015840

119905+ (119879119905minus

1

2120587int

2120587

0

1198791015840

119905119889120579)

(1)



119901 = 1199011015840

+ (119901 minus1

2120587int

2120587

0

1199011015840

119889120579) (2)




MFR119904=

119904

119904+ ℎ

MFRℎ=

ℎ

119904+ ℎ

(3)


119905could


= MFR119904sdot

119879119905119904+MFR





1199050= MFR

119904sdot 119875119905119904+ MFR

119904sdot 119875119905ℎ) The



119904sdot 119879119905119904+MFR

ℎsdot 119879119905ℎ

(MFR119904sdot 119875119905119904+MFR

119904sdot 119875119905ℎ) (4)


120587119905119904-119904 =

119875119905119904

119901out

120587119905119904-ℎ =

119875119905ℎ

119901out

120587119905119904=

1198751199050

119901out

(5)




Shaft = int119904

119903 times (119901 sdot ) 119889119904 (7)


120578119905119904=

Shaft sdot rotor

119904119862119901119904sdot 119879119905119904[1 minus (119901out119875119905119904)

(120574minus1)120574


(120574minus1)120574

]

(8)

119904and







119904and 119862119901

ℎ







120577 =(MFR

119904sdot 119875119905119904+MFR

119904sdot 119875119905ℎ) minus 119875t1

(MFR119904sdot 119875119905119904+MFR

119904sdot 119875119905ℎ)

120578119905-119904 =

(MFR119904sdot 119879119905119904+MFR

ℎsdot 119879119905ℎ) minus 1198791

(MFR119904sdot 119879119905119904+MFR

ℎsdot 119879119905ℎ) minus 1198791119904

(9)

where 1198751199051 1198791 and 119879




tal p

ress

ure (

bar)

150

175

200

225

250

0 60 120 180 240 300 360

Crank angle (deg)

minus020

minus015

minus010

minus005

000

005

010

015

Loss

fact

or




Tota

l to

stat

ic effi

cien

cy

0 60 120 180 240 300 360

Crank angle (deg)

00

02

04

06

08

10

12

14

16

18

20



120578119905-119904 =

1 minus (11987511198751199051)(120574minus1)120574

1 minus (11987511198751199050)(120574minus1)120574

(10)






R1

R2

Rotational axis X


185e + 005

167e + 005

149e + 005

131e + 005

(Pa)

Rotation


(a)

R1

R2

Rotational axis X

Rotation


Total pressure

(Pa)

193e + 005

175e + 005

156e + 005

138e + 005

119e + 005

(b)

R1

R2

Rotational axis X

Rotation

Tongue position 0

∘

Total pressure

(Pa)

209e + 005

189e + 005

169e + 005

149e + 005

129e + 005

(c)



75 of span

120593s120593s2

(a)

Hub-side mean plane

25 of span

120593h120593h2

(b)



120591 =119871

119881 (11)






Crank angle (deg)

Pow

er (k

W)

0 120 240 360 480 60010

15

20

25

30

35

40

45

50



Correspondence







04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09



0 60 120 180 240

180 210 240

300 360

(a)

04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09



180 210 240

0 60 120 180 240 300 360

(b)


00

01

02

03

04

05

06

MFHMFS

MFIMFO

Crank angle (deg)

Mas

s flow

(Kg

s)

0 60 120 180 240 300 360





minus20

minus15

minus10

minus05

00

05

10

(C)(B)

(A)

0 60 120 180 240 300 360

Crank angle (deg)

m

s+m

hminusm

out

ms+m

h(

) (

)






No mass storage(B)


(Pa)

1805e + 005

1598e + 005

1391e + 005

1184e + 005

9766e + 004

(a)Pressure

(Pa)

1745e + 005

1527e + 005

1309e + 005

1090e + 005

8722e + 004

(b)








No mass storage(B)


2776e + 003

2733e + 003

2691e + 003

2648e + 003

2605e + 003

(J kg

minus1

Kminus1)

(a)Static entropy

2764e + 003

2733e + 003

2701e + 003

2670e + 003

2638e + 003

(J kg

minus1

Kminus1)

(b)



Tota

l-to-

stat

ic effi

cien

cy

055 06 065 07 075 08 085

06

07

08

09

1





Reduced mass flow

Tota

l-to-

stat

ic effi

cien

cy

35 4 45 5 55 6 65

06

07

08

09

1






13

14

15

16

17

18

19

20

Crank angle (deg)

Tota

l-to-

stat

ic p

ress

ure r

atio

0

5

10

15

20

25

30

Out

let s

haft

pow

er (K

W)

(D)

(E)

0 60 120 180 240 300 360

120587ts-s

120587ts-h

120587ts

Shaft power




0

250

500

750

1000

1250

1500

1750

Frequency (Hz)

Am

plitu

de (W

att)

1 10 1000100 10000 100000

X = 151Y = 1534

X = 101Y = 472

X = 75Y = 793

X = 249Y = 470

X = 249Y = 470

X = 12001Y = 399




5 Conclusion



Visualization plane

Divider

70 of interspace

Volute exit

(a)

Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(b)Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(c)



Notations




Greek


Subscripts


Abbreviations




Navier-Stokes

Competing Interests


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 120 240 360 480 600 720500

550

600

650

700

750


Crank angle (deg)

Inle

t tot

al te

mpe

ratu

re (∘

C)

(a)In

let t

otal

pre

ssur

e (ba

r)

16

18

20

22

0 120 240 360 480 600 720


Crank angle (deg)

(b)

Crank angle (deg)

Out

let s

tatic

pre

ssur

e (ba

r)

0 120 240 360 480 600 720105

110

115

120

125

130

135

(c)



119875119905= 1198751015840

119905+ (119875119905minus

1

2120587int

2120587

0

1198751015840

119905119889120579)

119879119905= 1198791015840

119905+ (119879119905minus

1

2120587int

2120587

0

1198791015840

119905119889120579)

(1)



119901 = 1199011015840

+ (119901 minus1

2120587int

2120587

0

1199011015840

119889120579) (2)




MFR119904=

119904

119904+ ℎ

MFRℎ=

ℎ

119904+ ℎ

(3)


119905could


= MFR119904sdot

119879119905119904+MFR





1199050= MFR

119904sdot 119875119905119904+ MFR

119904sdot 119875119905ℎ) The



119904sdot 119879119905119904+MFR

ℎsdot 119879119905ℎ

(MFR119904sdot 119875119905119904+MFR

119904sdot 119875119905ℎ) (4)


120587119905119904-119904 =

119875119905119904

119901out

120587119905119904-ℎ =

119875119905ℎ

119901out

120587119905119904=

1198751199050

119901out

(5)




Shaft = int119904

119903 times (119901 sdot ) 119889119904 (7)


120578119905119904=

Shaft sdot rotor

119904119862119901119904sdot 119879119905119904[1 minus (119901out119875119905119904)

(120574minus1)120574


(120574minus1)120574

]

(8)

119904and







119904and 119862119901

ℎ







120577 =(MFR

119904sdot 119875119905119904+MFR

119904sdot 119875119905ℎ) minus 119875t1

(MFR119904sdot 119875119905119904+MFR

119904sdot 119875119905ℎ)

120578119905-119904 =

(MFR119904sdot 119879119905119904+MFR

ℎsdot 119879119905ℎ) minus 1198791

(MFR119904sdot 119879119905119904+MFR

ℎsdot 119879119905ℎ) minus 1198791119904

(9)

where 1198751199051 1198791 and 119879




tal p

ress

ure (

bar)

150

175

200

225

250

0 60 120 180 240 300 360

Crank angle (deg)

minus020

minus015

minus010

minus005

000

005

010

015

Loss

fact

or




Tota

l to

stat

ic effi

cien

cy

0 60 120 180 240 300 360

Crank angle (deg)

00

02

04

06

08

10

12

14

16

18

20



120578119905-119904 =

1 minus (11987511198751199051)(120574minus1)120574

1 minus (11987511198751199050)(120574minus1)120574

(10)






R1

R2

Rotational axis X


185e + 005

167e + 005

149e + 005

131e + 005

(Pa)

Rotation


(a)

R1

R2

Rotational axis X

Rotation


Total pressure

(Pa)

193e + 005

175e + 005

156e + 005

138e + 005

119e + 005

(b)

R1

R2

Rotational axis X

Rotation

Tongue position 0

∘

Total pressure

(Pa)

209e + 005

189e + 005

169e + 005

149e + 005

129e + 005

(c)



75 of span

120593s120593s2

(a)

Hub-side mean plane

25 of span

120593h120593h2

(b)



120591 =119871

119881 (11)






Crank angle (deg)

Pow

er (k

W)

0 120 240 360 480 60010

15

20

25

30

35

40

45

50



Correspondence







04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09



0 60 120 180 240

180 210 240

300 360

(a)

04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09



180 210 240

0 60 120 180 240 300 360

(b)


00

01

02

03

04

05

06

MFHMFS

MFIMFO

Crank angle (deg)

Mas

s flow

(Kg

s)

0 60 120 180 240 300 360





minus20

minus15

minus10

minus05

00

05

10

(C)(B)

(A)

0 60 120 180 240 300 360

Crank angle (deg)

m

s+m

hminusm

out

ms+m

h(

) (

)






No mass storage(B)


(Pa)

1805e + 005

1598e + 005

1391e + 005

1184e + 005

9766e + 004

(a)Pressure

(Pa)

1745e + 005

1527e + 005

1309e + 005

1090e + 005

8722e + 004

(b)








No mass storage(B)


2776e + 003

2733e + 003

2691e + 003

2648e + 003

2605e + 003

(J kg

minus1

Kminus1)

(a)Static entropy

2764e + 003

2733e + 003

2701e + 003

2670e + 003

2638e + 003

(J kg

minus1

Kminus1)

(b)



Tota

l-to-

stat

ic effi

cien

cy

055 06 065 07 075 08 085

06

07

08

09

1





Reduced mass flow

Tota

l-to-

stat

ic effi

cien

cy

35 4 45 5 55 6 65

06

07

08

09

1






13

14

15

16

17

18

19

20

Crank angle (deg)

Tota

l-to-

stat

ic p

ress

ure r

atio

0

5

10

15

20

25

30

Out

let s

haft

pow

er (K

W)

(D)

(E)

0 60 120 180 240 300 360

120587ts-s

120587ts-h

120587ts

Shaft power




0

250

500

750

1000

1250

1500

1750

Frequency (Hz)

Am

plitu

de (W

att)

1 10 1000100 10000 100000

X = 151Y = 1534

X = 101Y = 472

X = 75Y = 793

X = 249Y = 470

X = 249Y = 470

X = 12001Y = 399




5 Conclusion



Visualization plane

Divider

70 of interspace

Volute exit

(a)

Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(b)Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(c)



Notations




Greek


Subscripts


Abbreviations




Navier-Stokes

Competing Interests


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











MFR119904=

119904

119904+ ℎ

MFRℎ=

ℎ

119904+ ℎ

(3)


119905could


= MFR119904sdot

119879119905119904+MFR





1199050= MFR

119904sdot 119875119905119904+ MFR

119904sdot 119875119905ℎ) The



119904sdot 119879119905119904+MFR

ℎsdot 119879119905ℎ

(MFR119904sdot 119875119905119904+MFR

119904sdot 119875119905ℎ) (4)


120587119905119904-119904 =

119875119905119904

119901out

120587119905119904-ℎ =

119875119905ℎ

119901out

120587119905119904=

1198751199050

119901out

(5)




Shaft = int119904

119903 times (119901 sdot ) 119889119904 (7)


120578119905119904=

Shaft sdot rotor

119904119862119901119904sdot 119879119905119904[1 minus (119901out119875119905119904)

(120574minus1)120574


(120574minus1)120574

]

(8)

119904and







119904and 119862119901

ℎ







120577 =(MFR

119904sdot 119875119905119904+MFR

119904sdot 119875119905ℎ) minus 119875t1

(MFR119904sdot 119875119905119904+MFR

119904sdot 119875119905ℎ)

120578119905-119904 =

(MFR119904sdot 119879119905119904+MFR

ℎsdot 119879119905ℎ) minus 1198791

(MFR119904sdot 119879119905119904+MFR

ℎsdot 119879119905ℎ) minus 1198791119904

(9)

where 1198751199051 1198791 and 119879




tal p

ress

ure (

bar)

150

175

200

225

250

0 60 120 180 240 300 360

Crank angle (deg)

minus020

minus015

minus010

minus005

000

005

010

015

Loss

fact

or




Tota

l to

stat

ic effi

cien

cy

0 60 120 180 240 300 360

Crank angle (deg)

00

02

04

06

08

10

12

14

16

18

20



120578119905-119904 =

1 minus (11987511198751199051)(120574minus1)120574

1 minus (11987511198751199050)(120574minus1)120574

(10)






R1

R2

Rotational axis X


185e + 005

167e + 005

149e + 005

131e + 005

(Pa)

Rotation


(a)

R1

R2

Rotational axis X

Rotation


Total pressure

(Pa)

193e + 005

175e + 005

156e + 005

138e + 005

119e + 005

(b)

R1

R2

Rotational axis X

Rotation

Tongue position 0

∘

Total pressure

(Pa)

209e + 005

189e + 005

169e + 005

149e + 005

129e + 005

(c)



75 of span

120593s120593s2

(a)

Hub-side mean plane

25 of span

120593h120593h2

(b)



120591 =119871

119881 (11)






Crank angle (deg)

Pow

er (k

W)

0 120 240 360 480 60010

15

20

25

30

35

40

45

50



Correspondence







04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09



0 60 120 180 240

180 210 240

300 360

(a)

04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09



180 210 240

0 60 120 180 240 300 360

(b)


00

01

02

03

04

05

06

MFHMFS

MFIMFO

Crank angle (deg)

Mas

s flow

(Kg

s)

0 60 120 180 240 300 360





minus20

minus15

minus10

minus05

00

05

10

(C)(B)

(A)

0 60 120 180 240 300 360

Crank angle (deg)

m

s+m

hminusm

out

ms+m

h(

) (

)






No mass storage(B)


(Pa)

1805e + 005

1598e + 005

1391e + 005

1184e + 005

9766e + 004

(a)Pressure

(Pa)

1745e + 005

1527e + 005

1309e + 005

1090e + 005

8722e + 004

(b)








No mass storage(B)


2776e + 003

2733e + 003

2691e + 003

2648e + 003

2605e + 003

(J kg

minus1

Kminus1)

(a)Static entropy

2764e + 003

2733e + 003

2701e + 003

2670e + 003

2638e + 003

(J kg

minus1

Kminus1)

(b)



Tota

l-to-

stat

ic effi

cien

cy

055 06 065 07 075 08 085

06

07

08

09

1





Reduced mass flow

Tota

l-to-

stat

ic effi

cien

cy

35 4 45 5 55 6 65

06

07

08

09

1






13

14

15

16

17

18

19

20

Crank angle (deg)

Tota

l-to-

stat

ic p

ress

ure r

atio

0

5

10

15

20

25

30

Out

let s

haft

pow

er (K

W)

(D)

(E)

0 60 120 180 240 300 360

120587ts-s

120587ts-h

120587ts

Shaft power




0

250

500

750

1000

1250

1500

1750

Frequency (Hz)

Am

plitu

de (W

att)

1 10 1000100 10000 100000

X = 151Y = 1534

X = 101Y = 472

X = 75Y = 793

X = 249Y = 470

X = 249Y = 470

X = 12001Y = 399




5 Conclusion



Visualization plane

Divider

70 of interspace

Volute exit

(a)

Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(b)Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(c)



Notations




Greek


Subscripts


Abbreviations




Navier-Stokes

Competing Interests


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










tal p

ress

ure (

bar)

150

175

200

225

250

0 60 120 180 240 300 360

Crank angle (deg)

minus020

minus015

minus010

minus005

000

005

010

015

Loss

fact

or




Tota

l to

stat

ic effi

cien

cy

0 60 120 180 240 300 360

Crank angle (deg)

00

02

04

06

08

10

12

14

16

18

20



120578119905-119904 =

1 minus (11987511198751199051)(120574minus1)120574

1 minus (11987511198751199050)(120574minus1)120574

(10)






R1

R2

Rotational axis X


185e + 005

167e + 005

149e + 005

131e + 005

(Pa)

Rotation


(a)

R1

R2

Rotational axis X

Rotation


Total pressure

(Pa)

193e + 005

175e + 005

156e + 005

138e + 005

119e + 005

(b)

R1

R2

Rotational axis X

Rotation

Tongue position 0

∘

Total pressure

(Pa)

209e + 005

189e + 005

169e + 005

149e + 005

129e + 005

(c)



75 of span

120593s120593s2

(a)

Hub-side mean plane

25 of span

120593h120593h2

(b)



120591 =119871

119881 (11)






Crank angle (deg)

Pow

er (k

W)

0 120 240 360 480 60010

15

20

25

30

35

40

45

50



Correspondence







04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09



0 60 120 180 240

180 210 240

300 360

(a)

04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09



180 210 240

0 60 120 180 240 300 360

(b)


00

01

02

03

04

05

06

MFHMFS

MFIMFO

Crank angle (deg)

Mas

s flow

(Kg

s)

0 60 120 180 240 300 360





minus20

minus15

minus10

minus05

00

05

10

(C)(B)

(A)

0 60 120 180 240 300 360

Crank angle (deg)

m

s+m

hminusm

out

ms+m

h(

) (

)






No mass storage(B)


(Pa)

1805e + 005

1598e + 005

1391e + 005

1184e + 005

9766e + 004

(a)Pressure

(Pa)

1745e + 005

1527e + 005

1309e + 005

1090e + 005

8722e + 004

(b)








No mass storage(B)


2776e + 003

2733e + 003

2691e + 003

2648e + 003

2605e + 003

(J kg

minus1

Kminus1)

(a)Static entropy

2764e + 003

2733e + 003

2701e + 003

2670e + 003

2638e + 003

(J kg

minus1

Kminus1)

(b)



Tota

l-to-

stat

ic effi

cien

cy

055 06 065 07 075 08 085

06

07

08

09

1





Reduced mass flow

Tota

l-to-

stat

ic effi

cien

cy

35 4 45 5 55 6 65

06

07

08

09

1






13

14

15

16

17

18

19

20

Crank angle (deg)

Tota

l-to-

stat

ic p

ress

ure r

atio

0

5

10

15

20

25

30

Out

let s

haft

pow

er (K

W)

(D)

(E)

0 60 120 180 240 300 360

120587ts-s

120587ts-h

120587ts

Shaft power




0

250

500

750

1000

1250

1500

1750

Frequency (Hz)

Am

plitu

de (W

att)

1 10 1000100 10000 100000

X = 151Y = 1534

X = 101Y = 472

X = 75Y = 793

X = 249Y = 470

X = 249Y = 470

X = 12001Y = 399




5 Conclusion



Visualization plane

Divider

70 of interspace

Volute exit

(a)

Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(b)Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(c)



Notations




Greek


Subscripts


Abbreviations




Navier-Stokes

Competing Interests


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










R1

R2

Rotational axis X


185e + 005

167e + 005

149e + 005

131e + 005

(Pa)

Rotation


(a)

R1

R2

Rotational axis X

Rotation


Total pressure

(Pa)

193e + 005

175e + 005

156e + 005

138e + 005

119e + 005

(b)

R1

R2

Rotational axis X

Rotation

Tongue position 0

∘

Total pressure

(Pa)

209e + 005

189e + 005

169e + 005

149e + 005

129e + 005

(c)



75 of span

120593s120593s2

(a)

Hub-side mean plane

25 of span

120593h120593h2

(b)



120591 =119871

119881 (11)






Crank angle (deg)

Pow

er (k

W)

0 120 240 360 480 60010

15

20

25

30

35

40

45

50



Correspondence







04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09



0 60 120 180 240

180 210 240

300 360

(a)

04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09



180 210 240

0 60 120 180 240 300 360

(b)


00

01

02

03

04

05

06

MFHMFS

MFIMFO

Crank angle (deg)

Mas

s flow

(Kg

s)

0 60 120 180 240 300 360





minus20

minus15

minus10

minus05

00

05

10

(C)(B)

(A)

0 60 120 180 240 300 360

Crank angle (deg)

m

s+m

hminusm

out

ms+m

h(

) (

)






No mass storage(B)


(Pa)

1805e + 005

1598e + 005

1391e + 005

1184e + 005

9766e + 004

(a)Pressure

(Pa)

1745e + 005

1527e + 005

1309e + 005

1090e + 005

8722e + 004

(b)








No mass storage(B)


2776e + 003

2733e + 003

2691e + 003

2648e + 003

2605e + 003

(J kg

minus1

Kminus1)

(a)Static entropy

2764e + 003

2733e + 003

2701e + 003

2670e + 003

2638e + 003

(J kg

minus1

Kminus1)

(b)



Tota

l-to-

stat

ic effi

cien

cy

055 06 065 07 075 08 085

06

07

08

09

1





Reduced mass flow

Tota

l-to-

stat

ic effi

cien

cy

35 4 45 5 55 6 65

06

07

08

09

1






13

14

15

16

17

18

19

20

Crank angle (deg)

Tota

l-to-

stat

ic p

ress

ure r

atio

0

5

10

15

20

25

30

Out

let s

haft

pow

er (K

W)

(D)

(E)

0 60 120 180 240 300 360

120587ts-s

120587ts-h

120587ts

Shaft power




0

250

500

750

1000

1250

1500

1750

Frequency (Hz)

Am

plitu

de (W

att)

1 10 1000100 10000 100000

X = 151Y = 1534

X = 101Y = 472

X = 75Y = 793

X = 249Y = 470

X = 249Y = 470

X = 12001Y = 399




5 Conclusion



Visualization plane

Divider

70 of interspace

Volute exit

(a)

Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(b)Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(c)



Notations




Greek


Subscripts


Abbreviations




Navier-Stokes

Competing Interests


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Crank angle (deg)

Pow

er (k

W)

0 120 240 360 480 60010

15

20

25

30

35

40

45

50



Correspondence







04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09



0 60 120 180 240

180 210 240

300 360

(a)

04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09



180 210 240

0 60 120 180 240 300 360

(b)


00

01

02

03

04

05

06

MFHMFS

MFIMFO

Crank angle (deg)

Mas

s flow

(Kg

s)

0 60 120 180 240 300 360





minus20

minus15

minus10

minus05

00

05

10

(C)(B)

(A)

0 60 120 180 240 300 360

Crank angle (deg)

m

s+m

hminusm

out

ms+m

h(

) (

)






No mass storage(B)


(Pa)

1805e + 005

1598e + 005

1391e + 005

1184e + 005

9766e + 004

(a)Pressure

(Pa)

1745e + 005

1527e + 005

1309e + 005

1090e + 005

8722e + 004

(b)








No mass storage(B)


2776e + 003

2733e + 003

2691e + 003

2648e + 003

2605e + 003

(J kg

minus1

Kminus1)

(a)Static entropy

2764e + 003

2733e + 003

2701e + 003

2670e + 003

2638e + 003

(J kg

minus1

Kminus1)

(b)



Tota

l-to-

stat

ic effi

cien

cy

055 06 065 07 075 08 085

06

07

08

09

1





Reduced mass flow

Tota

l-to-

stat

ic effi

cien

cy

35 4 45 5 55 6 65

06

07

08

09

1






13

14

15

16

17

18

19

20

Crank angle (deg)

Tota

l-to-

stat

ic p

ress

ure r

atio

0

5

10

15

20

25

30

Out

let s

haft

pow

er (K

W)

(D)

(E)

0 60 120 180 240 300 360

120587ts-s

120587ts-h

120587ts

Shaft power




0

250

500

750

1000

1250

1500

1750

Frequency (Hz)

Am

plitu

de (W

att)

1 10 1000100 10000 100000

X = 151Y = 1534

X = 101Y = 472

X = 75Y = 793

X = 249Y = 470

X = 249Y = 470

X = 12001Y = 399




5 Conclusion



Visualization plane

Divider

70 of interspace

Volute exit

(a)

Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(b)Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(c)



Notations




Greek


Subscripts


Abbreviations




Navier-Stokes

Competing Interests


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09



0 60 120 180 240

180 210 240

300 360

(a)

04

06

08

10

12

14

16

Crank angle (deg)

Tota

l-to-

stat

ic effi

cien

cy

06

07

08

09



180 210 240

0 60 120 180 240 300 360

(b)


00

01

02

03

04

05

06

MFHMFS

MFIMFO

Crank angle (deg)

Mas

s flow

(Kg

s)

0 60 120 180 240 300 360





minus20

minus15

minus10

minus05

00

05

10

(C)(B)

(A)

0 60 120 180 240 300 360

Crank angle (deg)

m

s+m

hminusm

out

ms+m

h(

) (

)






No mass storage(B)


(Pa)

1805e + 005

1598e + 005

1391e + 005

1184e + 005

9766e + 004

(a)Pressure

(Pa)

1745e + 005

1527e + 005

1309e + 005

1090e + 005

8722e + 004

(b)








No mass storage(B)


2776e + 003

2733e + 003

2691e + 003

2648e + 003

2605e + 003

(J kg

minus1

Kminus1)

(a)Static entropy

2764e + 003

2733e + 003

2701e + 003

2670e + 003

2638e + 003

(J kg

minus1

Kminus1)

(b)



Tota

l-to-

stat

ic effi

cien

cy

055 06 065 07 075 08 085

06

07

08

09

1





Reduced mass flow

Tota

l-to-

stat

ic effi

cien

cy

35 4 45 5 55 6 65

06

07

08

09

1






13

14

15

16

17

18

19

20

Crank angle (deg)

Tota

l-to-

stat

ic p

ress

ure r

atio

0

5

10

15

20

25

30

Out

let s

haft

pow

er (K

W)

(D)

(E)

0 60 120 180 240 300 360

120587ts-s

120587ts-h

120587ts

Shaft power




0

250

500

750

1000

1250

1500

1750

Frequency (Hz)

Am

plitu

de (W

att)

1 10 1000100 10000 100000

X = 151Y = 1534

X = 101Y = 472

X = 75Y = 793

X = 249Y = 470

X = 249Y = 470

X = 12001Y = 399




5 Conclusion



Visualization plane

Divider

70 of interspace

Volute exit

(a)

Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(b)Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(c)



Notations




Greek


Subscripts


Abbreviations




Navier-Stokes

Competing Interests


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











No mass storage(B)


(Pa)

1805e + 005

1598e + 005

1391e + 005

1184e + 005

9766e + 004

(a)Pressure

(Pa)

1745e + 005

1527e + 005

1309e + 005

1090e + 005

8722e + 004

(b)








No mass storage(B)


2776e + 003

2733e + 003

2691e + 003

2648e + 003

2605e + 003

(J kg

minus1

Kminus1)

(a)Static entropy

2764e + 003

2733e + 003

2701e + 003

2670e + 003

2638e + 003

(J kg

minus1

Kminus1)

(b)



Tota

l-to-

stat

ic effi

cien

cy

055 06 065 07 075 08 085

06

07

08

09

1





Reduced mass flow

Tota

l-to-

stat

ic effi

cien

cy

35 4 45 5 55 6 65

06

07

08

09

1






13

14

15

16

17

18

19

20

Crank angle (deg)

Tota

l-to-

stat

ic p

ress

ure r

atio

0

5

10

15

20

25

30

Out

let s

haft

pow

er (K

W)

(D)

(E)

0 60 120 180 240 300 360

120587ts-s

120587ts-h

120587ts

Shaft power




0

250

500

750

1000

1250

1500

1750

Frequency (Hz)

Am

plitu

de (W

att)

1 10 1000100 10000 100000

X = 151Y = 1534

X = 101Y = 472

X = 75Y = 793

X = 249Y = 470

X = 249Y = 470

X = 12001Y = 399




5 Conclusion



Visualization plane

Divider

70 of interspace

Volute exit

(a)

Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(b)Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(c)



Notations




Greek


Subscripts


Abbreviations




Navier-Stokes

Competing Interests


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











No mass storage(B)


2776e + 003

2733e + 003

2691e + 003

2648e + 003

2605e + 003

(J kg

minus1

Kminus1)

(a)Static entropy

2764e + 003

2733e + 003

2701e + 003

2670e + 003

2638e + 003

(J kg

minus1

Kminus1)

(b)



Tota

l-to-

stat

ic effi

cien

cy

055 06 065 07 075 08 085

06

07

08

09

1





Reduced mass flow

Tota

l-to-

stat

ic effi

cien

cy

35 4 45 5 55 6 65

06

07

08

09

1






13

14

15

16

17

18

19

20

Crank angle (deg)

Tota

l-to-

stat

ic p

ress

ure r

atio

0

5

10

15

20

25

30

Out

let s

haft

pow

er (K

W)

(D)

(E)

0 60 120 180 240 300 360

120587ts-s

120587ts-h

120587ts

Shaft power




0

250

500

750

1000

1250

1500

1750

Frequency (Hz)

Am

plitu

de (W

att)

1 10 1000100 10000 100000

X = 151Y = 1534

X = 101Y = 472

X = 75Y = 793

X = 249Y = 470

X = 249Y = 470

X = 12001Y = 399




5 Conclusion



Visualization plane

Divider

70 of interspace

Volute exit

(a)

Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(b)Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(c)



Notations




Greek


Subscripts


Abbreviations




Navier-Stokes

Competing Interests


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










13

14

15

16

17

18

19

20

Crank angle (deg)

Tota

l-to-

stat

ic p

ress

ure r

atio

0

5

10

15

20

25

30

Out

let s

haft

pow

er (K

W)

(D)

(E)

0 60 120 180 240 300 360

120587ts-s

120587ts-h

120587ts

Shaft power




0

250

500

750

1000

1250

1500

1750

Frequency (Hz)

Am

plitu

de (W

att)

1 10 1000100 10000 100000

X = 151Y = 1534

X = 101Y = 472

X = 75Y = 793

X = 249Y = 470

X = 249Y = 470

X = 12001Y = 399




5 Conclusion



Visualization plane

Divider

70 of interspace

Volute exit

(a)

Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(b)Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(c)



Notations




Greek


Subscripts


Abbreviations




Navier-Stokes

Competing Interests


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Visualization plane

Divider

70 of interspace

Volute exit

(a)

Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(b)Static entropy

(J kg

minus1

Kminus1)

2731

2695

2660

2625

2590

(c)



Notations




Greek


Subscripts


Abbreviations




Navier-Stokes

Competing Interests


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Navier-Stokes

Competing Interests


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article characterization of a twin-entry radial...

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