Optimization of Ejector's Performance With a CFD Analysis

Amanda Mattos

Karolline Ropelato

Ricardo Medronho

Introduction

• Ejectors

– Equipment industrially used and based on the Venturi phenomena;

– With a high pressure motive fluid and converging/diverging ducts it promotes the drag of a secondary fluid, usually causing vaccum on the side entrance

2

Secondary Fluid

Primary Fluid

Diffuser

Throat

Primary Nozzle Mixture

Chamber

Suction Chamber

Basic Operational Principles

• Typical Performance • Ejector’s Efficiency Evalutation

3

Discharge Pressure

Entr

ain

men

t R

ati

o Choked flow

Critical Pressure

Reversed Flow Breakdown

Pressure

▫ Choked flow

▫ Unchoked flow

▫ Reversed flow

▫ Entrainment Ratio (RM)

▫ Compression Ratio (CR)

▫ Expansion Ratio (ER)

RM = secondary fluid mass flow primary fluid mass flow

CR = mixture outlet pressure secondary fluid inlet pressure

ER = primary fluid inlet pressure secondary fluid inlet pressure

• Study of Sriveerakul et al. (2007a)

– Objective: validate a representative model through experimental data

– Model characteristics:

• Bidimensional domain with axyssimetric aproximation

• Ideal gas relation for working fluid (saturated water vapour)

• Turbulence model – realizable k-ε

• Pressure boundary conditions were adopted for both entrances and outlet, according to experimental procedure

– Observations:

• Calculated pressure profile presents the same pattern observed in experimental data

• Similarities on the ejector’s experimental behavior, regarding its performance under different geometries were observed by computational model

Pressure experimental data

Bibliographic Research

4

Computational Model

• CFD

– Objective: validate a representative model

– Geometry

• Bidimensional domain

• Axyssimetric aproximation

5

Axyssimetric

Computational Model

• CFD

– Objective: validate a representative model

– Geometry

• Bidimensional domain

• Axyssimetric aproximation

– Working Fluid

• Saturated water vapour

• Ideal gas relation for compressibility

• No phase change

– Boundary Conditions

– Model Details

• Solver density-based

• Implicit formulation

6

Saída

Fluido

Secundário

Fluido

PrimárioPrimary Fluid

Secondary

Fluid

Discharge

Axyssimetric

Computational Model

• Optimization

– Objective: maximize equipment’s efficiency

– Geometric variation and entrainment ratio analysis

– Geometric/Operation condition variations and entrainment/ compression ratios analysis

– Model Details

• Design of Experiments

(Central Composite Designs)

• Optimization Algorithm (NSGA-II)

7

3

Secondary Fluid

1

2

2

3

1 Primary Nozzle Diameter

Mixture Chamber Diameter

Throat Length

Parameter Range

Primary Nozzle Diameter 6 - 8 [mm]

Mixture Chamber Diameter 19 - 29 [mm]

Throat Length DCM - 6 DCM

Secondary Fluid Temperature 278 - 288 [K]

Secondary Fluid

Results

8

0

5

10

15

20

25

30

0 50 100 150 200 250 300 350 400

Pr

es

sã

o [

mb

ar

]

(a) Perfil de pressão na linha central

0

200

400

600

800

1000

1200

0 50 100 150 200 250 300 350 400

Ve

loc

ida

de

[m

/s]

X [mm]

(b) Perfil de velocidade na linha central

Mesh 110 Mesh 40 Mesh 13 Mesh 8

• Mesh Independency Test

– Objective: identify variations on pressure and velocity profiles under different levels of mesh refinement

– Hexaedrical mesh chosen

Pressure Profile on center line

Velocity Profile on center line

Vel

oci

ty [

m/s

] P

ress

ure

[m

bar

]

0

5

10

15

20

25

30

0 50 100 150 200 250 300 350 400

Pr

es

sã

o[m

ba

r]

0

200

400

600

800

1000

1200

0 50 100 150 200 250 300 350 400

Ve

loc

ida

de

[m

/s

]

X [mm]

Results

• CFD model validation

9

1 2

3

4 5

Pressure

Velocity

1 2 3 4 5

Primary Fluid

Secondary Fluid

Mixture

Sonic Velocity

1 2 3 4 5

First series of oblique shocks

Second series of oblique shocks

Vel

oci

ty [

m/s

] P

ress

ure

[m

bar

]

X [mm]

• CFD model valitation

– Pressure profile analysis

0

5

10

15

20

25

30

35

0 50 100 150 200 250 300 350 400

Pr

es

sã

o [

mb

ar

]

X [mm]

Pre

ssu

re [

mb

ar]

X [mm]

Results

10

• CFD model valitation

– Pressure profile analysis

– Entrainment ratio analysis

0

5

10

15

20

25

30

35

0 50 100 150 200 250 300 350 400

Pr

es

sã

o [

mb

ar

]

X [mm]

Pre

ssu

re [

mb

ar]

X [mm]

Results

11

Operation

Condition

Calculated

Entrainment Ratio

Experimental

Entrainment Ratio Error

A 0,54 0,53 -1,88%

B 0,39 0,40 1,46%

C 0,26 0,31 15,27%

• CFD model valitation

– Pressure profile analysis

– Entrainment ratio analysis

– Calculated profiles

• Supersonic flow on diverging duct

• Oblique shock wave formation

A p v T ρ c м

м> 1

(a)

(b)

(c)

(d)

Results

12

Velocity [m/s]

Absolute Pressure [mbar]

Density [kg/m3 ]

Temperature [K]

Onda de choque oblíqua

Pressões diminuindo

Lower Pressures

Oblique shock wave

Results

• CFD model valitation

– Operation condition variation

• Decreasing primary fluid pressure

– Lowers primary fluid momentum

– Restricts the expansion angle

– Larger effective area

– Major secondary fluid drag

• Decreasing secondary fluid pressure

– Larger expansion angle

– Minor effective area

– Less drag of secondary fluid

13

(a)

(b)

(c)

(a)

(b)

(c)

(a)

(b)

(c)

(a)

(b)

(c)

Standard Operation Condition

Lower primary fluid pressure

Lower secondary

fluid pressure

Operation

Condition

Calculated

Entrainment Ratio

Experimental

Entrainment Ratio Error

A 0,54 0,53 -1,88%

B 0,39 0,40 1,46%

C 0,26 0,31 15,27%

Mach Number

Optimal Point

Results

• Geometry Optimization

– Total of 150 cases

• Initial population with 15 cases

– Negative entrainment ratio

• Observed in designs of experiment

14

Design of Experiments

Simulations

Velocity [m/s] En

trai

nm

ent

Rat

io

Case DBP [mm] DCM [mm] CG [mm] Entrainment Ratio

Original 8,00 24,00 5,00* DCM 0,5400

Optimal 7,14 26,17 4,51* DCM 0,6754

Optimal Point

Simulations

Entr

ain

men

t R

atio

(a)

(b)

(a)

(b)

Resultados

• Geometry Optimization

– Total of 150 cases

• Initial population with 15 cases

– Negative entrainment ratio

• Observed in designs of experiment

– Comparison between original and optimal cases

• 25% efficiency increase

15

25% efficiency increase

Mach Number

Simulations

Entr

ain

men

t R

atio

C

om

pre

ssio

n R

atio

• Geometry and Operation Condition Optimization

– Total of 250 cases

• Initial population with 25 cases

– Conflicting objective functions

• Paretor Frontier

– Various cases with reversed flow

• Operation condition effect

– Sensibility analysis

• Effect over entrainment ratio

– 10 to 20% for geometry

– 40% to operation condition

• Effect over compression ratio

– -10 to -20% for geometry

– -100% for operation condition

Results

16

Optimal Point

Optimal Point

Compression Ratio

Entr

ain

men

t R

atio

• Geometry and Operation Condition Optimization

– Total of 250 cases

• Initial population with 25 cases

– Conflicting objective functions

• Paretor Frontier

– Various cases with reversed flow

• Operation condition effect

– Sensibility analysis

• Effect over entrainment ratio

– 10 to 20% for geometry

– 40% to operation condition

• Effect over compression ratio

– -10 to -20% for geometry

– -100% for operation condition

Results

17

Optimal Curve

Effe

ct S

ize

Ef

fect

Siz

e

Entrainment Ratio

Compression Ratio

Primary Nozzle Diameter Throat Length

Mixture Chamber Diameter Secondary Fluid Temperature

Parameter Significance for

RM

Significance for

CR

Primary Nozzle Diameter 0,0035 0,1955

Mixture Chamber Diameter 0,0374 0,4034

Throat Length 0,0362 0,2018

Secondary Fluid Temperature 0,0000 0,0000

• Geometry and Operation Condition Optimization

– Total of 250 cases

• Initial population with 25 cases

– Conflicting objective functions

• Paretor Frontier

– Various cases with reversed flow

• Operation condition effect

– Sensibility analysis

• Effect over entrainment ratio

– 10 to 20% for geometry

– 40% to operation condition

• Effect over compression ratio

– -10 to -20% for geometry

– -100% for operation condition

High values of significance

Results

18

Conclusions

• The CFD technique has proved to be useful in understanding the phenomena that occur inside the ejector, allowing the visualization of profiles calculated inside the ejector

• The mesh independency test allowed the better usage of computational resources

• The optimization process allowed the equipment behavior prediction against variations in geometry or operating condition

• Geometry’s optimization featured a 25% increase in the entrainment rate on the original ejector

• Parameters such as length throat and mixing chamber diameter can influence the entrainment rate when varied simultaneously

• The operating condition adopted strongly influences the efficiency of the equipment

• The efficiency rates analyzed have a conflicting relationship which can be characterized by the Pareto Frontier creation

19