Optimization of Ejector's Performance With a CFD Analysis Amanda Mattos Karolline Ropelato Ricardo Medronho
2 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 Diffuser Mixture Chamber Secondary Fluid Primary Nozzle Primary Fluid Throat Suction Chamber
Entrainment Ratio 3 Basic Operational Principles Typical Performance Ejector s Efficiency Evalutation Choked flow Entrainment Ratio (RM) Unchoked flow Reversed flow Compression Ratio (CR) Expansion Ratio (ER) Choked flow Breakdown Pressure Discharge Pressure Critical Pressure Reversed Flow 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
4 Bibliographic Research Study of Sriveerakul et al. (2007a) Objective: validate a representative model through experimental data Model characteristics: Bidimensional domain with axyssimetric Pressure aproximation experimental data 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
5 Computational Model CFD Objective: validate a representative model Geometry Bidimensional domain Axyssimetric aproximation Axyssimetric
6 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 Axyssimetric Fluido Primário Primary Fluid Discharge Saída Secondary Fluido Secundário
7 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) Secondary Fluid Secondary Fluid 2 2 3 1 Parameter 1 Primary Nozzle Diameter Mixture Chamber Diameter Throat Length Primary Nozzle Diameter Mixture Chamber Diameter 3 Range 6-8 [mm] 19-29 [mm] Throat Length Secondary Fluid Temperature D CM - 6 D CM 278-288 [K]
Pressão [mbar] Velocidade [m/s] 8 Mesh Independency Test Objective: identify variations on pressure and velocity profiles under different levels of mesh refinement Hexaedrical mesh chosen Velocity [m/s] Pressure [mbar] 30 25 20 15 10 5 0 1200 1000 800 600 400 200 0 Pressure Profile on center line (a) Perfil de pressão na linha central 0 50 100 150 200 250 300 350 400 (b) Perfil de velocidade na linha central Velocity Profile on center line 0 50 100 150 200 250 300 350 400 X [mm] Mesh 110 Mesh 40 Mesh 13 Mesh 8
Velocidade [m/s] Pressão [mbar] 9 1 3 2 4 5 CFD model validation 1 2 Pressure Velocity 3 4 Primary Fluid Secondary Fluid Mixture Sonic Velocity 1 3 2 4 5 5 Velocity [m/s] Pressure [mbar] 30 25 20 15 10 5 0 1200 1000 800 600 400 200 0 First series of oblique shocks 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 X [mm] X [mm] Second series of oblique shocks
Pressure [mbar] Pressão [mbar] 10 CFD model valitation Pressure profile analysis 35 30 25 20 15 10 5 0 0 50 100 150 200 250 300 350 400 X [mm] X [mm]
Pressure [mbar] Pressão [mbar] 11 CFD model valitation Pressure profile analysis Entrainment ratio analysis Operation Calculated Experimental Condition Entrainment Ratio Entrainment Ratio Error A 0,54 0,53-1,88% B 0,39 0,40 1,46% C 0,26 0,31 15,27% 35 30 25 20 15 10 5 0 0 50 100 150 200 250 300 350 400 X [mm] X [mm]
12 CFD model valitation Pressure profile analysis Entrainment ratio analysis Calculated profiles Supersonic flow on diverging duct Velocity [m/s] Absolute Pressure [mbar] A p v T ρ c м м> 1 Oblique shock wave formation Density [kg/m 3 ] Lower Pressures Pressões diminuindo Temperature [K] Onda de choque oblíqua Oblique shock wave
13 CFD model valitation Mach Number 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 Lower primary fluid pressure Lower secondary fluid pressure Standard Operation Condition Operation Calculated Experimental Condition Entrainment Ratio Entrainment Ratio Error A 0,54 0,53-1,88% B 0,39 0,40 1,46% C 0,26 0,31 15,27%
Entrainment Ratio 14 Geometry Optimization Total of 150 cases Initial population with 15 cases Negative entrainment ratio Observed in designs of experiment Design of Experiments Optimal Point Simulations Velocity [m/s]
Entrainment Ratio 15 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 Simulations Optimal Point Case D BP [mm] D CM [mm] C G [mm] Entrainment Ratio Original 8,00 24,00 5,00* D CM 0,5400 Optimal 7,14 26,17 4,51* D CM 0,6754 Mach Number 25% efficiency increase
Entrainment Ratio Compression Ratio 16 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 Optimal Point Simulations Optimal Point
Entrainment Ratio 17 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 Optimal Curve Compression Ratio
Effect Size Effect Size 18 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 Parameter Primary Nozzle Diameter Throat Length Entrainment Ratio Significance for RM Compression Ratio Significance for 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 CR High values of significance Mixture Chamber Diameter Secondary Fluid Temperature
19 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