optimisationanalysisofstructuralparametersofanannularslot ejector based on the coanda … · 2020....

Research ArticleOptimisationAnalysis of Structural Parameters of anAnnular SlotEjector Based on the Coanda Effect

Fengliang Wu 1 and Zhisheng Li 12

1College of Safety Science and Engineering Xirsquoan University of Science and Technology Xirsquoan 710054 China2Faculty of Geosciences and Environmental Engineering Southwest Jiaotong University Chengdu 610031 China

Correspondence should be addressed to Fengliang Wu wuflxusteducn

Received 13 March 2020 Revised 2 July 2020 Accepted 16 July 2020 Published 11 August 2020

Guest Editor Sanghyuk Lee

Copyright copy 2020 Fengliang Wu and Zhisheng Li -is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

To investigate the effect of structural parameters on the performance of an annular slot ejector a series of numericalsimulations were conducted with single-factor analysis Moreover a multifactor grey relational analysis was applied toexamine the correlations between the structural parameters and entrainment ratio Subsequently the optimised model wasverified by comparing the simulated results with experimental data Results show that the performance of the optimisedejector model was improved -e RNG k-ε turbulent transport mode can simulate the internal field characteristics of anannular slot ejector and the corresponding simulated results as verified by experiment satisfy engineering requirementsIn addition a quantitative correlation between structural parameters and entrainment ratio was obtained as follows e(nozzle clearance) gt θ (diffusing chamber angle) gtHL (mixing chamber length) gt d (throat diameter) gtKL (diffusingchamber length) -is work may provide a certain guiding significance for the design and application of annularslot ejectors

1 Introduction

An annular slot ejector is a mechanical device which isdifferent from a central jet [1ndash4] A large volume of low-pressure fluid is dragged by high-pressure fluid due to thespecial structure of the annular slot ejector [5]-e workingprinciple of an annular slot ejector is known as the Coandaeffect [6 7]-e phenomenon is described as a fluid flowingnot along the original direction but along a curved surfaceSubsequently the mainstream flow passes through thenozzle clearance it deflects and flows along the wall surfaceand then induces a large amount of air from its sur-roundings [8] Gregory-Smith and Gilchrist describedthree main features of the Coanda effect including thenonviscous effect viscous effect and a stronger entrain-ment capability [9] Besides another major feature of theCoanda effect is the Coanda flare also known as a shockwave when the high-pressure gas reaches a certain speed(Figure 1)

-e Coanda effect has received extensive attention inaviation [11] medicine [12] acoustics [8] robotics [13] andleafless fans [14] Dong-Won et al utilised a Coanda nozzleto cause jet deflection and wall shearing [15] -eir workshowed that when the pressure increases the potentialsplash zone tends to move downstream In recent years theintroduction of the Coanda effect has promoted researchinto and development of annular ejectors [10 16ndash25]

Ameri proposed a semiempirical formula for the sectionvelocity based on a new ejector model by conducting a set ofexperiments with an LDV (laser Doppler velocimeter) [26]In his study it was assumed that the flow between thepressure inlet and the nozzle must satisfy the isentropiccondition however the isentropic condition cannot beapplied at high pressures Guerriero investigated the in-fluence of structural parameters on the ejector performanceby conducting a set of experiments -ey suggested thatnozzle clearance has a significant influence on the ejectorperformance [27] and the corresponding results under the

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 8951353 11 pageshttpsdoiorg10115520208951353

same model and working conditions were verified by Kimet al employing CFD methods Moreover they pointed outthat the stagnation pressure ratio is another importantparameter affecting ejector performance [28 29] Alexandruet al developed a semiempirical formula for two-dimen-sional Coanda flow while the curvature of the tangentialmomentum equation was neglected [16] Sierra del Rio et aldesigned a two-ejector model with varying nozzle clearance(03mm and 08mm) to investigate the effect of nozzleclearance on the flow velocity by means of CFD methods[30] their results showed that the velocity increases with theincrease of nozzle clearance Similar trends were obtained byLowry et al based on a new Coanda ejector [31] Jain et aldeveloped a new ejector model with two nozzles to inves-tigate the relationship between the structural parameters(nozzle clearance and throat diameter) and the flow char-acteristic -ey also suggested that the nozzle clearance has asignificant influence on the flow velocity and the larger thethroat diameter is the faster the mixing layer is developed[10]

Although many studies have been conducted previousstudies focused on single-factor analysis and few studieswhere all structural parameters were varied simultaneouslyhave been undertaken Moreover different optimal sizes ofthe model were obtained due to the differences in thestructure being modelled Besides in the early literature onlythe nozzle clearance is deemed to have been an importantparameter that influences ejector performance but corre-lations between other geometric parameters and the en-trainment ratio were ignored In the present work a set ofnumerical simulations were conducted using single-factoranalysis and multifactor analysis to investigate annular slotejector performance including five structural parameters(namely mixing chamber length diffusion chamber length

diffusion chamber angle throat diameter and nozzleclearance) Moreover the optimised model was verified andanalysed by conducting a series of experiments to comparewith the results of numerical simulation

2 Numerical Model

21 Turbulent Model -e flow of gas inside the annularejector contains turbulence and the velocity gradient of themainstream gas at the throat of the ejector changes sig-nificantly which may generate more vortices Amel et alanalysed the variation of the flow characteristic for bothsingle-phase flow and two-phase flow mode inside theejector based on a supersonic ejector using CFD methods-ey suggested that the RNG (renormalisation group) k-εmodel be applied to simulate a supersonic ejector [32]Victor and Steven also verified the RNG k-ε turbulencemodel as being able to simulate the flow characteristic basedon a Coanda ejector -erefore in the present work theRNG k-ε double equation model [33] was applied to theannular slot ejector as follows

k equation

z(ρk)

zt+

z ρkui( 1113857

zxi

z αkμeff zkzxj1113872 11138731113872 1113873

zxj

+ Gk minus ρε (1)

where ρ is the fluid density k is the turbulent kineticenergy t is the time αk is the turbulent Prandtl numberof k μi and μeff are the viscosity coefficients xi and xj arecoordinate vectors Gk represents the turbulent kineticenergy generated by the laminar velocity gradient and εis the dissipation rateε equation

(a) (b)

Figure 1 A Coanda flare (a) contours of Mach number at the ejector throat and (b) contours of velocity [10]

2 Mathematical Problems in Engineering

z(ρε)zt

+z ρεui( 1113857

zxi

z αεμeffzεzxj1113872 1113873

zxj

+ C1ε lowastεk

Gk minus C2ερε2

k

C1ε lowast C1ε minusη 1 minus ηη0( 1113857( 1113857

1 + βη3

η 2Eij

1113969 k

ε

Eij 12

zui

zxj

+zuj

zxi

1113888 1113889

(2)

where C1ε and C2ε are constants indicating the effect ofbuoyancy on the dissipation rate and αε is the turbulentPrandtl number of ε -e values of the coefficients inthe formula are as follows

αk αε 139

β 0012

η0 4377

Cμ 00845

C1ε 142

C2ε 168

(3)

22 Modelling and Meshing for an Annular Slot EjectorAn annular slot ejector is usually an axisymmetric structurewhich includes eight parts (Figure 2) Moreover the 3Dmodel can be simplified to a 2D model according to the flowcharacteristic -e mainstream gas flows at high speed alongthe wall after passing through the nozzle clearance Mean-while a secondary flow will be induced into the mixingchamber -ereafter the mixing gas flows outward throughthe diffusion chamber however the velocity near the wall isdifferent from that near the centreline due to the Coandaeffect which causes a physical gradient inside the ejectortherefore the corresponding mesh mapped using grid-generating software (ICEM) is encrypted to guarantee theaccuracy of the numerical simulation results All elementsare quadrilaterals with about 200000 in each mesh -emesh size near the wall boundary is 01mm and it graduallyincreases to 1mm (Figure 3(a)) -e independence of thegrid has been analysed by obtaining a resulting mesh size of075mm-reemeshes (a coarse grid medium grid and finegrid) were used to evaluate grid size-independence the threegrid sizes tested were 075mm 1mm and 125mm re-spectively Figure 3(b) shows that secondary mass flow in-creases first and then decreases as the primary pressureincreases from 03MPa to 07MPa the difference in sec-ondary mass flow for the fine and medium grid is observedto be slight but there was some improvement comparedwith the case modelled using a grid size of 1mm -ereforethe simulation model with a 1-mm grid was selected to

reduce the computational time and ensure accuracy insubsequent simulations

23 Boundary Conditions -e operating fluid is a com-pressed gas and the ejector fluid is from the surrounding airIn the present work both fluids are treated as ideal gases ascarried out by other scholars [29 34] An implicit solutionmethod and a hybrid initialisation method were applied tothe flow calculation of compressible gases Both the high-pressure inlet and the low-pressure inlet of the annular slotejector were set as a pressure inlet boundary condition andthe mixed fluid outlet is configured as a pressure outletOther boundaries are wall surfaces and the insulation be-tween the wall and the environment is assumed to be adi-abatic nonpermeable and nonslip boundaries [35](Table 1)

3 Analysis of Factors AffectingEjector Performance

31 Influence ofMixingChamberLength Figure 4 shows thatthe entrainment ratio raises first and then decreases as thelength of the mixing chamber increases from 10mm to100mm and the corresponding maximum entrainmentratio is obtained when the mixing chamber length is 40mm-ere is a certain buffer developed during themixing processof primary and secondary flows More importantly whenthe mixing chamber is short mainstream gas does nottransmit momentum to the ejector fluid well resulting in theinsufficient mixing of the two fluids moreover when thelength of the mixing chamber is too large the impact loss ofthe fluid increases Figure 5 indicates that the distribution ofthe flow velocity under different primary pressures include03MPa 04MPa 05MPa 06MPa and 07MPa respec-tively It is seen that the flow velocity away from the wallshows a certain gradient and there is good turbulent mixingat the interface between the primary gas and the secondarygas [36] In addition for different primary pressures theflow velocity near the wall is always much larger than thatnear the central axis which corresponds to the main featuresof the Coanda effect [37]

32 Influence of Diffusion Chamber Length Figure 6 showsthe relationship between diffusion chamber length andentrainment ratio when the mainstream pressure is 03MPathe entrainment ratio continuously increases as the diffusionchamber length increases from 120mm to 400mm-is canbe explained by their different physical flow processes theflow of the mixed fluid in the diffusion chamber is a processin which static pressure recovery quickly and the rapiddecline of velocity and the diffusion area increases with acertain gradient during the process (Figure 7) -e high-pressure jet layer is wider when the diffusion chamber lengthis 400mm than at other sizes suggesting good turbulentmixing Moreover the diffusion area contributes to theamount of induced air during the process and it may benecessary to use more compressed gas to complete turbulentmixing with the induced fluid

Mathematical Problems in Engineering 3

33 Influence of the Diffusion Chamber Angle Figure 8 in-dicates that the entrainment ratio decreases as the angle ofthe diffusing chamber increases from 6deg to 16deg the high-pressure jet is not separated from the wall surface as theangle increases due to the Coanda effect Nevertheless thehigh-pressure jet layer becomes thinner and the corre-sponding mixed boundary layer moves towards the wallbecause the adsorption capacity decreased Moreover due tothe increase of the diffusion area the amount of induced airrises (in relative terms) and the traction force on the in-duced fluid is reduced thereby causing the entrainment ratioto decrease at the same primary pressure Figure 9 indicatesthe relationship between the velocity and the angle of the

diffusing chamber the flow velocity decreases upon wid-ening of the diffusion chamber angle Besides when thediffusion angle is large enough a local counterflow zoneappears near the inlet section of the diffusion chamber andthe surrounding countercurrent zone still contains higher-energy fluid which may cause energy loss -erefore theattenuation of the jet flow may be greater further resultingin a lower entrainment ratio

34 Influence of ltroat Diameter Figure 10 shows that themass flow both primary and secondary gas increases with theincrease of the throat diameter and the growth rate of the

x

y

z

(a)

140

145

150

155

160

165

170

175

Seco

ndar

y m

ass f

low

(Kg(

sndash1))

03 04 05 06 0702Primary pressure (MPa)

Fine grid (mesh size of 075mm)Medium grid (mesh size of 1mm)Course grid (mesh size of 125mm)

(b)

Figure 3 (a) Meshing for annular slot ejector and (b) secondary mass flow with different grid densities

Table 1 Boundary conditions

Location Pressure Turbulence intensity Hydraulic diameter (m) Total temperature (K)Primary inlet 3ndash7times105 Pa 1 0025

300Secondary inlet 1times 105 Pa 1 008Outlet 1times 105 Pa 5 016

1

2

3

46 7 8

5

(a) (b)

Figure 2 -e annular slot ejector model (a) Schematic diagram of annular slot ejector and (b) photograph of the physical model 1 High-pressure inlet 2 Secondary inlet 3 Symmetry axis 4 Outlet 5 Storage room 6 Suction 7 Mixing chamber 8 Diffusion chamber


secondary mass flow rate is significantly higher than that ofthe primary flow -is can be explained by considering thatthe aspect ratio both primary and secondary flows increaseas throat diameter rises inducing more air and resulting in agreater mass flow rate Figure 11 shows that the entrainmentratio decreases significantly as the primary pressure in-creases from 03MPa to 07MPa which can be explained bythe fact that the larger primary pressure is the more massflow is available for primary flow resulting in a lower en-trainment ratio however the entrainment ratio shows acomplicated trend in behaviour upon variation of the throatdiameter which may lie in the complex physical processesincluding turbulent flow mixing in both primary and

secondary flows In addition as the aspect ratio increasesthe more shearing force will be needed to drag the secondaryflow in -ereafter the primary and secondary flows enterthe mixing chamber to achieve static pressure matchingcompleting the mixing process of the two flows inside themixing chamber reducing the impact loss between the twofluids At the same time as the throat diameter increasesfrom 60mm to 160mm more air (by volume) is inducedinto the ejector In previous studies Kim et al analysed theinfluence of throat diameter on the ejector coefficient basedon a Coanda ejector [28] -eir results showed that thevelocity decreases when the throat diameter increases from35mm to 50mm however the higher velocity does notmean a larger mass flow due to the decline in diameterresulting in a lower flow In the present work the mixingentrainment ratio is obtained when the throat diameter is160mm under different primary pressures

4

6

8

10

12

14

16

18En

trai

nmen

t rat

io ωndash

40 50 60 7030P (MPa)

120mm160mm

200mm240mm

280mm320mm

360mm400mm

Figure 6 Diffusion chamber length v entrainment ratio

12

13

14

15

16

17

18

19

20

Entr

ainm

ent r

atio

ωndash

20 40 60 80 1000Mixing room length (mm)

ωndash

Figure 4 Mixing chamber length v entrainment ratio

350e + 02333e + 02315e + 02298e + 02280e + 02263e + 02245e + 02228e + 02210e + 02193e + 02175e + 02158e + 02140e + 02123e + 02105e + 02875e + 01700e + 01525e + 01350e + 01175e + 01000e + 00

HL = 40mm P = 07MPa

HL = 40mm P = 06MPa

HL = 40mm P = 05MPa

HL = 40mm P = 04MPa

HL = 40mm P = 03MPa

Figure 5 Velocity contours inside the ejector at different primarypressures


35 Influence of Nozzle Clearance Figure 12 shows that theentrainment ratio gradually decreases as the primary pres-sure increases from 03MPa to 07MPa When the main-stream pressure is fixed the entrainment ratio decreasescontinuously as the nozzle clearance increases from 01mmto 05mm a similar trend was obtained elsewhere [30] Italso can be seen that when the primary pressure is 03MPathe entrainment ratio increases by 423 as the nozzleclearance increases from 01mm to 015mm and the en-trainment ratio rises by 859 when the nozzle clearanceincreases from 01mm to 05mm -erefore the nozzle

clearance affects the performance of the annular slot ejectorto a significant extent

36MultifactorAnalysis ofEjectorPerformanceEmploying theGrey Relational Analysis Method -e above analysis showsthe influence of the geometry on the entrainment ratio whenone parameter changes but other parameters are fixedNozzle clearance is the more important parameter never-theless the importance of the other parameters in terms oftheir influence on ejector performance is unclear thereforeit is necessary to analyse ejector performance when the fivegeometric parameters are varied simultaneously -e greyrelational analysis method involves the analysis of an

00

02

04

06

08

10

12

14

Mas

s flo

w (K

g(sndash1

))

80 100 120 140 16060Throat diameter (mm)

Primary mass flow (p = 03MPa)Secondary mass flow (p = 03MPa)

Figure 10 -roat diameter of diffusion chamber v mass flow


KL = 400mm

KL = 360mm

KL = 320mm

KL = 280mm

KL = 240mm

KL = 200mm

Figure 7 Velocity contours inside the ejector for different dif-fusion chamber lengths

5

10

15

20

Entr

ainm

ent r

atio

ωndash

04 05 06 0703P (MPa)

θ = 6degθ = 8deg

θ = 10degθ = 12deg


Figure 8 Diffusion chamber angle v entrainment ratio


θ = 6deg P = 03MPa

θ = 8deg P = 03MPa

θ = 10deg P = 03MPa




Figure 9 Velocity contours inside the ejector for different angles


abstract system or phenomenon which makes up for thedeficiencies in systematic analysis using mathematical sta-tistical methods It is also applicable to any number ofsamples and works irrespective of a parametric distributionbeing known a priori Ju-Long [38] proposed a theoreticalmodel for analysing the correlation between samples

c0i(k)

mini

mink

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868 + ξmaxi

maxk

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868 + ξmaxi

maxk

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868

(4)

where Xi(k) is observed data on sequence k X0(k) reflectsthe behaviour of the system characteristics k can also rep-resent the time serial number and the index number c0i(k) isthe grey correlation ofXi andX0 and ξ is the resolution factor

In the present work the grey relational analysis methodwas applied to study ejector performance without fixedgeometric parameters A set of numerical simulations wereconducted to investigate the ejector performance underconstant pressure (Table 2) Taking the first set of pa-rameters from Table 2 as a reference sequence the six setsof parameters were normalised and initialised (Table 3)Finally the sensitivity of each structure parameter to theentrainment ratio was obtained (Table 4) which can besorted as follows nozzle clearance (e)gt diffusion chamberangle (θ) gtmixing chamber length (HL) gt throat diameter(d) gt diffusion chamber length (KL)

4 Experimental Optimisation Model of anAnnular Slot Ejector

41 Experiments Although a series of numerical calcula-tions were conducted to optimise the ejector structure theoptimised model still needs further experimental verifica-tion -e optimised model and dimensions were obtainedbased on the aforementioned simulated results and thecomparison between the original model and the optimisedmodel is shown in Figure 13 and Table 5 (where Dmain is thediameter of the primary inlet Dsec is the diameter of thesecondary inlet and Dout is the diameter of the outlet)

In this experiment the logarithmic linear measurementmethod [39] was used to measure the average dynamicpressure in the ejector inlet section and then the averagevelocity and mass flow of the ejector inlet section wereobtained -e experiments were conducted in a relativelyclosed indoor environment (Figure 14) An air compressorwas adopted to provide mainstream gas flow under differentpressures and to act as a buffer airflow -e gas collectiontank was used to supply a continuous flow of compressedgas Moreover the compressed air was dried before enteringthe ejector -e pressure transmitter measured the main-stream pressure and the gas turbine flowmeter was used tomeasure the primary mass flow and a Pitot tube was utilisedto measure the dynamic pressure at each measurement pointon the cross-section of the ejector exit and to obtain theaverage flow velocity and the total mass flow -ese threeparameters were transmitted through a sensor to a computerprogram for simultaneous counting with a pulse counter

42 Analysis of Experimental Results Nine groups of ex-perimental tests present a set of parameters for ejectorperformance at different primary pressures (Table 6) theprimary mass flow (G1) rises continuously while the sec-ondary mass flow (G2) tends to first increase then decreaseas the primary pressure increases from 03MPa to 07MPaMoreover the dynamic pressure and velocity in the ejectorexit show the same trend as the secondary flow this can beexplained by considering that the excessive primary pressuredeveloped poor turbulent mixing forming a local vortexthereby leading to a decrease in the secondarymass flow rate-e entrainment ratio (ϖ) decreases continuously with in-creasing primary pressure (Figure 15) Moreover there isgood consistency found by comparing simulated results and

04 05 06 0703P (MPa)

789

1011121314151617181920

Entr

ainm

ent r

atio

ωndash

d = 80mmd = 100mmd = 100mm

d = 120mmd = 140mmd = 160mm

Figure 11 -roat diameter v entrainment ratio

e = 050mme = 040mme = 030mm

e = 020mme = 015mme = 010mm

04 05 06 0703P (MPa)

0

10

20

30

40

50

Entr

ainm

ent r

atio

ω_

Figure 12 Nozzle clearance v entrainment ratio


Table 2 Preliminary calculated entrainment ratios

HL KL θ d e Entrainment ratio

10 200 6 80 01 3743120 240 8 100 015 2075640 280 10 120 02 2146160 320 12 140 03 1428680 360 14 160 04 10987100 400 16 180 05 9301

Table 3 Pretreatment results

X0 X1 X2 X3 X4 X5

1 1 1 1 1 10554514 05 0833333 075 08 06666670573346 025 0714286 06 0666667 050381654 0166667 0625 05 0571429 03333330293524 0125 0555556 0428571 05 0250248495 01 05 0375 0444444 02

Table 4 Relevance ranking results

Structural parameter Correlation RankMixing chamber length 0586878 3Diffusion chamber length 051222 5Diffusion chamber angle 066573 2-roat diameter 0563725 4Nozzle clearance 0767563 1

Original model

Optimized model

Figure 13 Comparison of annular ejector models (a) Gland (b) secondary inlet and (c) outlet

Table 5 Improved model dimensions for an annular slot ejector

Structural parameter Origin size (mm) Optimised size (mm)Dmain 25 25Dsec 80 160Dout 145 290d 80 160e 03 01θ 6deg 6degHL 20 40KL 300 400


experimental data which also indicates that the RNG-k-εturbulent transport mode can simulate the flow character-istics of the gas in the ejector Besides it could be seen thatnumerical simulation results are always slightly higher thanexperimental test values which can be explained using theBoussinesq hypothesis ensure solution closure and theworking flow was set to that of an ideal gas

5 Conclusion

To investigate the annular slot ejector performance a two-dimensional ejector structure model was constructedemploying Fluent 150 Five factors (e θ HL d andKL) wereselected to analyse ejector performance while one parameterwas changed the others were fixed -en the grey corre-lation analysis was used to study ejector performance whenthe five structural parameters were changed simultaneouslyand the correlation of the performance parameters affectingthe annular ejector was obtained Finally the optimisedmodel was verified by comparing the numerical results withexperimental data -e main conclusions were as followsϖ first rises then falls when increasing HL from 10mm

to 100mm and when HL was 40mm the maximum valueof ϖ was obtained there is a nonmonotonic trend seenwhen D rises from 80mm to 160mm When θ increasesfrom 6deg to 16deg there is a continuously decreasing trendhowever when varying KL (from 120mm to 400mm) and e(from 01mm to 05mm) ϖ increased at all times-erefore the dimensions of the optimised model were asfollows HL 40mm KL 400mm θ 6deg d 160mmand e 05mm -e grey correlation between the fivefactors and the ejector performance was obtained as fol-lows egt θ gtHL gt d gt KL therefore the nozzle clearance isthe most important parameter among the five factors af-fecting ejector performance Nine groups of primarypressure conditions (from 03MPa to 07MPa) were

P

12345

6

7 8 9

10

11

12

9

10

13

14 15

n n

Figure 14 Schematic diagram of the experimental flow regime in the annular ejector 1 Power switch 2 Starting device 3 Air compressor4 Gas tank 5 Buffer gas tank 6 Desiccator 7 Pressure transmitters 8 Gas vortex flowmeter 9 Pulse counter 10 Sensor 11 Annular slotejector 12 L-type pitot tube and differential manometer 13 Silencer 14 Monitor 15 Computer

Table 6 Experimental results

P1 (MPa) G1 (kgs) G2 (kgs) ϖ P (Pa) V (m3s)030 00234 0991 41367 10728 13154035 00276 1061 37428 12297 14083040 00298 1097 35805 13145 14561045 00341 1220 34780 16259 16194050 00375 1291 33440 18206 17136055 00409 1257 31678 17260 16685060 00435 1248 27678 17015 16566065 00463 1209 25118 15967 16048070 00576 1164 19201 14801 15451

ExperimentsCFD

04 05 06 0703P (MPa)

15

20

25

30

35

40

45

Entr

ainm

ent r

atio

ω_

Figure 15 Comparison of experimental and numerical simulationresults


analysed using a set of experiments based on the optimisedmodel to verify the accuracy of the simulated entrainmentratio the corresponding results indicated that the twomethods were consistent Besides the feasibility of the useof the RNG-k-ε turbulent transport mode was verified insimulating the flow characteristics of the gas in the ejector

Data Availability

-e data used to support the findings of this study are in-cluded within the manuscript

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (Grant nos 51974232 and 51574193)and Fundamental Research Funds of Shaanxi ProvinceChina (Grant no 2017JM5039)

References

[1] Y Han L Guo X D Wang and A C Y Yuen ldquoA steamejector refrigeration system powered by engine combustionwaste heat part 1 characterization of the internal flowstructurerdquo Applied Sciences vol 9 no 20 p 4275 2019

[2] Y Han X D Wang L Guo and A Chun ldquoA steam ejectorrefrigeration system powered by engine combustion wasteheat part 2 understanding the nature of the shock wavestructurerdquo Applied Sciences vol 9 no 20 2019

[3] Y Han X Wang A C Y Yuen et al ldquoCharacterization ofchoking flow behaviors inside steam ejectors based on theejector refrigeration systemrdquo International Journal of Re-frigeration vol 113 pp 296ndash307 2020

[4] Y Wu H Zhao C Zhang L Wang and J Han ldquoOptimi-zation analysis of structure parameters of steam ejector basedon CFD and orthogonal testrdquo Energy vol 151 pp 79ndash932018

[5] S Da-Wen andW E Ian ldquoRecent developments in the designtheories and applications of ejectors-a reviewrdquo Fuel amp EnergyAbstracts vol 36 no 5 pp 361ndash370 1995

[6] D J Pieiro ldquoHenry Marie Coanda and the ldquoCoanda effectrdquordquoRevista Portuguesa De Pneumologia vol 80 no 1 p 4 2010

[7] C Ionica D Sorin and G Virgil ldquo-eoretical approachesregarding the gasodynamic phenomena in asymmetric flowsrdquoAdvanced Material Research vol 1128 pp 364ndash371 2015

[8] C Smith ldquoOn some recent applications of the Coanda effectto acousticsrdquolte Journal of the Acoustical Society of Americavol 128 no 4 p 16 2010

[9] D G Gregory-Smith and A R Gilchrist ldquo-e compressibleCoanda wall jet--an experimental study of jet structure andbreakawayrdquo International Journal of Heat and Fluid Flowvol 8 no 2 p 9 1987

[10] S Jain Shashi and S Kumar ldquoNumerical studies on evalu-ation of smoke control system of underground metro railtransport system in India having jet injection system a casestudyrdquo Building Simulation vol 4 no 3 pp 205ndash216 2011

[11] I Cırciu and S Dinea Review of the Air Force AcademyldquoHenri Coandardquo Air Force Academy Brasov Romania 2010

[12] A Perrig F Avellan J-L KuenyM Farhat and E ParkinsonldquoFlow in a pelton turbine bucket numerical and experimentalinvestigationsrdquo Journal of Fluids Engineering vol 128 no 2pp 350ndash358 2006

[13] E Natarajan and N O Onubogu ldquoApplication of Coandaeffect in robotsndasha reviewrdquo Mechanical Engineering andTechnology vol 125 pp 411ndash418 2012

[14] L Guoqi H Yongjun and Y Yingzi ldquoInfluence of Coandasurface curvature on performance of bladeless fanrdquo Journal ofltermal Science vol 23 no 5 p 10 2014

[15] L Dong-Won H Jae-Gun K Young-Doo and K Soon-BumldquoA study on the air knife flow with Coanda effectrdquo Journal ofMechanical Science and Technology vol 21 no 12 p 7 2007

[16] D Alexandru F Frunzulica and C I Tudor MathematicalModelling and Numerical Investigations on the Coanda EffectNonlinearity Bifurcation and Chaos-lteory and ApplicationsIntech London UK 2012

[17] D Alexandru F Frunzulica F Frunzulica and T IonesculdquoCoanda effect on the flows through ejectors and channelsrdquoScientific Research and Education in the Air Force vol 20pp 161ndash174 2018

[18] A Dumitrache F Frunzulica and O Preotu ldquoFlow analysisin various ejectors configurationsrdquo in Proceedings of the 2017Fourth International Conference on Mathematics and Com-puters in Sciences and in Industry p 7 Corfu Greece August2017

[19] A Dumitrache ldquoNumerical investigation of the flow in aCoanda ejectorrdquo in Proceedings of the 4th European Con-ference For Aerospace Sciences (EUCASS) p 12 SaintPetersburg Russia July 2011

[20] V Rajalakshmi K Kavitha and D Lavanya ldquoDesign andoptimization of single head planar Coanda gripperrdquo Advancesin Natural and Applied Sciences vol 11 no 4 p 8 2017

[21] V Benche and V Benche ldquoTransient proceses for vent-ejectors assisted by Coanda effectrdquo in Proceedimgs of the 6thInternational Conference on Hydraulic Machinery and Hy-drodynamics Timisoara p 6 Timisoara Romania October2004

[22] T-H Kim A Study on the Characteristics of Coanda NozzleFlow Saga University Saga Japan 2007

[23] P M Weston V Sharifi and J Swithenbank ldquoDestruction oftar in a novel Coanda tar cracking systemrdquo Energy amp Fuelsvol 28 no 2 pp 1059ndash1065 2014

[24] H C Yang ldquoHorizontal two-phase jet behavior with anannular nozzle ejector in the water tankrdquo Journal of Visu-alization vol 18 no 2 pp 359ndash367 2014

[25] C P Lubert ldquoSome recent experimental results concerningturbulent Coanda wall jetsrdquo lte Journal of the AcousticalSociety of America vol 136 no 4 p 2137 2015

[26] A Mohammad An Experimental and lteretical Study ofCoanda ejectors Case Western Reverse University ClevelandOH USA 1993

[27] V Guerriero ldquoNumerical solutions of compressible flowmixing in Coanda ejectorsrdquo in Proceedings of the EighthSymposium on Fluid Control Measurement and VisualizationChina Society of -eoretical and Applied MechanicsChengdu ChinaChina Society of -eoretical and AppliedMechanics Chengdu China August 2005

[28] H D Kim G Rajesh T Setoguchi and S Matsuo ldquoOpti-mization study of a Coanda ejectorrdquo Journal of ltermalScience vol 15 no 4 pp 331ndash336 2006

[29] G Rajesh ldquoA computational study of the gas flow in a Coandaejectorrdquo in Proceedings of the Korean Society of MechanicalEngineers Conference Busan Korea June 2005


[30] J A Sierra del Rio J G Ardila Marin S Velez GarciaM Londontildeo and D A Hincapie Zuluaga ldquoSimulationanalysis of a coanda-effect ejector using CFDrdquo Teccienciavol 12 no 22 pp 17ndash25 2016

[31] K P Lowry R Y Coley D L Miglioretti et al ldquoEffect ofCoanda nozzle clearance on the flow characteristics of airamplifierrdquo in Proceedings of the 2014 6th InternationalSymposium on Fluid Machinery and Fluid EngineeringWuhan China March 2014

[32] H Amel F Henry and S Leclaire ldquoCFD analysis of a su-personic air ejector Part I experimental validation of single-phase and two-phase operationrdquo Applied ltermal Engi-neering vol 29 no 8 p 9 2009

[33] Y Victor and A O Steven ldquoRenormalization group analysisof turbulence I basic theoryrdquo Journal of Scientific Computingvol 1 no 1 pp 3ndash51 1986

[34] D Valentın A Guardo-Zabaleta and E Egusquiza ldquoUse ofCoanda nozzles for double glazed faccedil ades forced ventila-tionrdquo Energy amp Buildings vol 62 p 10 2013

[35] A Li A C Y Yuen T B Y Chen and C Wang ldquoCom-putational study of wet steam flow to optimize steam ejectorefficiency for potential fire suppression applicationrdquo AppliedSciences vol 9 no 7 2019

[36] E F Schum P M Bevilaqua and S V Patankar Compu-tation of the Turbulent Mixing in Curved Ejectors RockwellInternational Corporation Milwaukee WI USA 1980

[37] A R Gilchrist lte Development and Breakaway of a Com-pressible Air Jet with Streamline Curvature and its Applicationto the Coanda Durham University Durham UK 1985

[38] D Ju-Long ldquoControl problems of grey systemsrdquo Systems ampControl Letters vol 1 no 5 pp 288ndash294 1982

[39] J Zhou J Ren and C Yao ldquoMulti-objective optimization ofmulti-axis ball-end milling inconel 718 via grey relationalanalysis coupled with RBF neural network and PSO algo-rithmrdquo Measurement vol 102 p 15 2017


same model and working conditions were verified by Kimet al employing CFD methods Moreover they pointed outthat the stagnation pressure ratio is another importantparameter affecting ejector performance [28 29] Alexandruet al developed a semiempirical formula for two-dimen-sional Coanda flow while the curvature of the tangentialmomentum equation was neglected [16] Sierra del Rio et aldesigned a two-ejector model with varying nozzle clearance(03mm and 08mm) to investigate the effect of nozzleclearance on the flow velocity by means of CFD methods[30] their results showed that the velocity increases with theincrease of nozzle clearance Similar trends were obtained byLowry et al based on a new Coanda ejector [31] Jain et aldeveloped a new ejector model with two nozzles to inves-tigate the relationship between the structural parameters(nozzle clearance and throat diameter) and the flow char-acteristic -ey also suggested that the nozzle clearance has asignificant influence on the flow velocity and the larger thethroat diameter is the faster the mixing layer is developed[10]

Although many studies have been conducted previousstudies focused on single-factor analysis and few studieswhere all structural parameters were varied simultaneouslyhave been undertaken Moreover different optimal sizes ofthe model were obtained due to the differences in thestructure being modelled Besides in the early literature onlythe nozzle clearance is deemed to have been an importantparameter that influences ejector performance but corre-lations between other geometric parameters and the en-trainment ratio were ignored In the present work a set ofnumerical simulations were conducted using single-factoranalysis and multifactor analysis to investigate annular slotejector performance including five structural parameters(namely mixing chamber length diffusion chamber length

diffusion chamber angle throat diameter and nozzleclearance) Moreover the optimised model was verified andanalysed by conducting a series of experiments to comparewith the results of numerical simulation

2 Numerical Model

21 Turbulent Model -e flow of gas inside the annularejector contains turbulence and the velocity gradient of themainstream gas at the throat of the ejector changes sig-nificantly which may generate more vortices Amel et alanalysed the variation of the flow characteristic for bothsingle-phase flow and two-phase flow mode inside theejector based on a supersonic ejector using CFD methods-ey suggested that the RNG (renormalisation group) k-εmodel be applied to simulate a supersonic ejector [32]Victor and Steven also verified the RNG k-ε turbulencemodel as being able to simulate the flow characteristic basedon a Coanda ejector -erefore in the present work theRNG k-ε double equation model [33] was applied to theannular slot ejector as follows

k equation

z(ρk)

zt+

z ρkui( 1113857

zxi

z αkμeff zkzxj1113872 11138731113872 1113873

zxj

+ Gk minus ρε (1)

where ρ is the fluid density k is the turbulent kineticenergy t is the time αk is the turbulent Prandtl numberof k μi and μeff are the viscosity coefficients xi and xj arecoordinate vectors Gk represents the turbulent kineticenergy generated by the laminar velocity gradient and εis the dissipation rateε equation

(a) (b)

Figure 1 A Coanda flare (a) contours of Mach number at the ejector throat and (b) contours of velocity [10]


z(ρε)zt

+z ρεui( 1113857

zxi


zxj

+ C1ε lowastεk

Gk minus C2ερε2

k


1 + βη3

η 2Eij

1113969 k

ε

Eij 12

zui

zxj

+zuj

zxi

1113888 1113889

(2)


αk αε 139

β 0012

η0 4377

Cμ 00845

C1ε 142

C2ε 168

(3)











x

y

z

(a)

140

145

150

155

160

165

170

175

Seco

ndar

y m

ass f

low

(Kg(

sndash1))



(b)





1

2

3

46 7 8

5

(a) (b)





4

6

8

10

12

14

16

18En

trai

nmen

t rat

io ωndash

40 50 60 7030P (MPa)

120mm160mm

200mm240mm

280mm320mm

360mm400mm


12

13

14

15

16

17

18

19

20

Entr

ainm

ent r

atio

ωndash


ωndash



HL = 40mm P = 07MPa

HL = 40mm P = 06MPa

HL = 40mm P = 05MPa

HL = 40mm P = 04MPa

HL = 40mm P = 03MPa






00

02

04

06

08

10

12

14

Mas

s flo

w (K

g(sndash1

))





KL = 400mm

KL = 360mm

KL = 320mm

KL = 280mm

KL = 240mm

KL = 200mm


5

10

15

20

Entr

ainm

ent r

atio

ωndash

04 05 06 0703P (MPa)

θ = 6degθ = 8deg





θ = 6deg P = 03MPa

θ = 8deg P = 03MPa








c0i(k)

mini

mink

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868 + ξmaxi

maxk

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868 + ξmaxi

maxk

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868

(4)







04 05 06 0703P (MPa)

789

1011121314151617181920

Entr

ainm

ent r

atio

ωndash

d = 80mmd = 100mmd = 100mm

d = 120mmd = 140mmd = 160mm


e = 050mme = 040mme = 030mm

e = 020mme = 015mme = 010mm

04 05 06 0703P (MPa)

0

10

20

30

40

50

Entr

ainm

ent r

atio

ω_





10 200 6 80 01 3743120 240 8 100 015 2075640 280 10 120 02 2146160 320 12 140 03 1428680 360 14 160 04 10987100 400 16 180 05 9301


X0 X1 X2 X3 X4 X5

1 1 1 1 1 10554514 05 0833333 075 08 06666670573346 025 0714286 06 0666667 050381654 0166667 0625 05 0571429 03333330293524 0125 0555556 0428571 05 0250248495 01 05 0375 0444444 02



Original model

Optimized model






5 Conclusion



P

12345

6

7 8 9

10

11

12

9

10

13

14 15

n n




ExperimentsCFD

04 05 06 0703P (MPa)

15

20

25

30

35

40

45

Entr

ainm

ent r

atio

ω_




Data Availability




Acknowledgments


References










































z(ρε)zt

+z ρεui( 1113857

zxi


zxj

+ C1ε lowastεk

Gk minus C2ερε2

k


1 + βη3

η 2Eij

1113969 k

ε

Eij 12

zui

zxj

+zuj

zxi

1113888 1113889

(2)


αk αε 139

β 0012

η0 4377

Cμ 00845

C1ε 142

C2ε 168

(3)











x

y

z

(a)

140

145

150

155

160

165

170

175

Seco

ndar

y m

ass f

low

(Kg(

sndash1))



(b)





1

2

3

46 7 8

5

(a) (b)





4

6

8

10

12

14

16

18En

trai

nmen

t rat

io ωndash

40 50 60 7030P (MPa)

120mm160mm

200mm240mm

280mm320mm

360mm400mm


12

13

14

15

16

17

18

19

20

Entr

ainm

ent r

atio

ωndash


ωndash



HL = 40mm P = 07MPa

HL = 40mm P = 06MPa

HL = 40mm P = 05MPa

HL = 40mm P = 04MPa

HL = 40mm P = 03MPa






00

02

04

06

08

10

12

14

Mas

s flo

w (K

g(sndash1

))





KL = 400mm

KL = 360mm

KL = 320mm

KL = 280mm

KL = 240mm

KL = 200mm


5

10

15

20

Entr

ainm

ent r

atio

ωndash

04 05 06 0703P (MPa)

θ = 6degθ = 8deg





θ = 6deg P = 03MPa

θ = 8deg P = 03MPa








c0i(k)

mini

mink

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868 + ξmaxi

maxk

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868 + ξmaxi

maxk

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868

(4)







04 05 06 0703P (MPa)

789

1011121314151617181920

Entr

ainm

ent r

atio

ωndash

d = 80mmd = 100mmd = 100mm

d = 120mmd = 140mmd = 160mm


e = 050mme = 040mme = 030mm

e = 020mme = 015mme = 010mm

04 05 06 0703P (MPa)

0

10

20

30

40

50

Entr

ainm

ent r

atio

ω_





10 200 6 80 01 3743120 240 8 100 015 2075640 280 10 120 02 2146160 320 12 140 03 1428680 360 14 160 04 10987100 400 16 180 05 9301


X0 X1 X2 X3 X4 X5

1 1 1 1 1 10554514 05 0833333 075 08 06666670573346 025 0714286 06 0666667 050381654 0166667 0625 05 0571429 03333330293524 0125 0555556 0428571 05 0250248495 01 05 0375 0444444 02



Original model

Optimized model






5 Conclusion



P

12345

6

7 8 9

10

11

12

9

10

13

14 15

n n




ExperimentsCFD

04 05 06 0703P (MPa)

15

20

25

30

35

40

45

Entr

ainm

ent r

atio

ω_




Data Availability




Acknowledgments


References













































x

y

z

(a)

140

145

150

155

160

165

170

175

Seco

ndar

y m

ass f

low

(Kg(

sndash1))



(b)





1

2

3

46 7 8

5

(a) (b)





4

6

8

10

12

14

16

18En

trai

nmen

t rat

io ωndash

40 50 60 7030P (MPa)

120mm160mm

200mm240mm

280mm320mm

360mm400mm


12

13

14

15

16

17

18

19

20

Entr

ainm

ent r

atio

ωndash


ωndash



HL = 40mm P = 07MPa

HL = 40mm P = 06MPa

HL = 40mm P = 05MPa

HL = 40mm P = 04MPa

HL = 40mm P = 03MPa






00

02

04

06

08

10

12

14

Mas

s flo

w (K

g(sndash1

))





KL = 400mm

KL = 360mm

KL = 320mm

KL = 280mm

KL = 240mm

KL = 200mm


5

10

15

20

Entr

ainm

ent r

atio

ωndash

04 05 06 0703P (MPa)

θ = 6degθ = 8deg





θ = 6deg P = 03MPa

θ = 8deg P = 03MPa








c0i(k)

mini

mink

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868 + ξmaxi

maxk

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868 + ξmaxi

maxk

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868

(4)







04 05 06 0703P (MPa)

789

1011121314151617181920

Entr

ainm

ent r

atio

ωndash

d = 80mmd = 100mmd = 100mm

d = 120mmd = 140mmd = 160mm


e = 050mme = 040mme = 030mm

e = 020mme = 015mme = 010mm

04 05 06 0703P (MPa)

0

10

20

30

40

50

Entr

ainm

ent r

atio

ω_





10 200 6 80 01 3743120 240 8 100 015 2075640 280 10 120 02 2146160 320 12 140 03 1428680 360 14 160 04 10987100 400 16 180 05 9301


X0 X1 X2 X3 X4 X5

1 1 1 1 1 10554514 05 0833333 075 08 06666670573346 025 0714286 06 0666667 050381654 0166667 0625 05 0571429 03333330293524 0125 0555556 0428571 05 0250248495 01 05 0375 0444444 02



Original model

Optimized model






5 Conclusion



P

12345

6

7 8 9

10

11

12

9

10

13

14 15

n n




ExperimentsCFD

04 05 06 0703P (MPa)

15

20

25

30

35

40

45

Entr

ainm

ent r

atio

ω_




Data Availability




Acknowledgments


References












































4

6

8

10

12

14

16

18En

trai

nmen

t rat

io ωndash

40 50 60 7030P (MPa)

120mm160mm

200mm240mm

280mm320mm

360mm400mm


12

13

14

15

16

17

18

19

20

Entr

ainm

ent r

atio

ωndash


ωndash



HL = 40mm P = 07MPa

HL = 40mm P = 06MPa

HL = 40mm P = 05MPa

HL = 40mm P = 04MPa

HL = 40mm P = 03MPa






00

02

04

06

08

10

12

14

Mas

s flo

w (K

g(sndash1

))





KL = 400mm

KL = 360mm

KL = 320mm

KL = 280mm

KL = 240mm

KL = 200mm


5

10

15

20

Entr

ainm

ent r

atio

ωndash

04 05 06 0703P (MPa)

θ = 6degθ = 8deg





θ = 6deg P = 03MPa

θ = 8deg P = 03MPa








c0i(k)

mini

mink

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868 + ξmaxi

maxk

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868 + ξmaxi

maxk

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868

(4)







04 05 06 0703P (MPa)

789

1011121314151617181920

Entr

ainm

ent r

atio

ωndash

d = 80mmd = 100mmd = 100mm

d = 120mmd = 140mmd = 160mm


e = 050mme = 040mme = 030mm

e = 020mme = 015mme = 010mm

04 05 06 0703P (MPa)

0

10

20

30

40

50

Entr

ainm

ent r

atio

ω_





10 200 6 80 01 3743120 240 8 100 015 2075640 280 10 120 02 2146160 320 12 140 03 1428680 360 14 160 04 10987100 400 16 180 05 9301


X0 X1 X2 X3 X4 X5

1 1 1 1 1 10554514 05 0833333 075 08 06666670573346 025 0714286 06 0666667 050381654 0166667 0625 05 0571429 03333330293524 0125 0555556 0428571 05 0250248495 01 05 0375 0444444 02



Original model

Optimized model






5 Conclusion



P

12345

6

7 8 9

10

11

12

9

10

13

14 15

n n




ExperimentsCFD

04 05 06 0703P (MPa)

15

20

25

30

35

40

45

Entr

ainm

ent r

atio

ω_




Data Availability




Acknowledgments


References













































00

02

04

06

08

10

12

14

Mas

s flo

w (K

g(sndash1

))





KL = 400mm

KL = 360mm

KL = 320mm

KL = 280mm

KL = 240mm

KL = 200mm


5

10

15

20

Entr

ainm

ent r

atio

ωndash

04 05 06 0703P (MPa)

θ = 6degθ = 8deg





θ = 6deg P = 03MPa

θ = 8deg P = 03MPa








c0i(k)

mini

mink

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868 + ξmaxi

maxk

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868 + ξmaxi

maxk

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868

(4)







04 05 06 0703P (MPa)

789

1011121314151617181920

Entr

ainm

ent r

atio

ωndash

d = 80mmd = 100mmd = 100mm

d = 120mmd = 140mmd = 160mm


e = 050mme = 040mme = 030mm

e = 020mme = 015mme = 010mm

04 05 06 0703P (MPa)

0

10

20

30

40

50

Entr

ainm

ent r

atio

ω_





10 200 6 80 01 3743120 240 8 100 015 2075640 280 10 120 02 2146160 320 12 140 03 1428680 360 14 160 04 10987100 400 16 180 05 9301


X0 X1 X2 X3 X4 X5

1 1 1 1 1 10554514 05 0833333 075 08 06666670573346 025 0714286 06 0666667 050381654 0166667 0625 05 0571429 03333330293524 0125 0555556 0428571 05 0250248495 01 05 0375 0444444 02



Original model

Optimized model






5 Conclusion



P

12345

6

7 8 9

10

11

12

9

10

13

14 15

n n




ExperimentsCFD

04 05 06 0703P (MPa)

15

20

25

30

35

40

45

Entr

ainm

ent r

atio

ω_




Data Availability




Acknowledgments


References











































c0i(k)

mini

mink

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868 + ξmaxi

maxk

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868 + ξmaxi

maxk

X0(k) minus Xi(k)( 11138571113868111386811138681113868

1113868111386811138681113868

(4)







04 05 06 0703P (MPa)

789

1011121314151617181920

Entr

ainm

ent r

atio

ωndash

d = 80mmd = 100mmd = 100mm

d = 120mmd = 140mmd = 160mm


e = 050mme = 040mme = 030mm

e = 020mme = 015mme = 010mm

04 05 06 0703P (MPa)

0

10

20

30

40

50

Entr

ainm

ent r

atio

ω_





10 200 6 80 01 3743120 240 8 100 015 2075640 280 10 120 02 2146160 320 12 140 03 1428680 360 14 160 04 10987100 400 16 180 05 9301


X0 X1 X2 X3 X4 X5

1 1 1 1 1 10554514 05 0833333 075 08 06666670573346 025 0714286 06 0666667 050381654 0166667 0625 05 0571429 03333330293524 0125 0555556 0428571 05 0250248495 01 05 0375 0444444 02



Original model

Optimized model






5 Conclusion



P

12345

6

7 8 9

10

11

12

9

10

13

14 15

n n




ExperimentsCFD

04 05 06 0703P (MPa)

15

20

25

30

35

40

45

Entr

ainm

ent r

atio

ω_




Data Availability




Acknowledgments


References












































10 200 6 80 01 3743120 240 8 100 015 2075640 280 10 120 02 2146160 320 12 140 03 1428680 360 14 160 04 10987100 400 16 180 05 9301


X0 X1 X2 X3 X4 X5

1 1 1 1 1 10554514 05 0833333 075 08 06666670573346 025 0714286 06 0666667 050381654 0166667 0625 05 0571429 03333330293524 0125 0555556 0428571 05 0250248495 01 05 0375 0444444 02



Original model

Optimized model






5 Conclusion



P

12345

6

7 8 9

10

11

12

9

10

13

14 15

n n




ExperimentsCFD

04 05 06 0703P (MPa)

15

20

25

30

35

40

45

Entr

ainm

ent r

atio

ω_




Data Availability




Acknowledgments


References











































5 Conclusion



P

12345

6

7 8 9

10

11

12

9

10

13

14 15

n n




ExperimentsCFD

04 05 06 0703P (MPa)

15

20

25

30

35

40

45

Entr

ainm

ent r

atio

ω_




Data Availability




Acknowledgments


References











































Data Availability




Acknowledgments


References










































optimisationanalysisofstructuralparametersofanannularslot ejector based on the coanda … · 2020....

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