Multi-Objective Optimization of a Kinetics-Based HCCI Model Ali M. - PowerPoint PPT Presentation

Multi-Objective Optimization of a Kinetics-Based HCCI Model Ali M. Aldawood, Sebastian Mosbach, Markus Kraft University of Cambridge Amer A. Amer Saudi Aramco JSAE Paper No. 20119051 SAE Paper No. 2011-01-1783

Outline  Introduction & Motivation  Optimization setup ─ Engine & model ─ Optimization variables ─ Objective functions ─ Search method  Results  Conclusions 2

Introduction  Detailed-kinetics modeling is computationally intensive, and thus reduced kinetics are favored when time and resources are limited 3

Reduced-Mechanism Performance P= 40 bar,  =1.0 Shock tube data from Fieweger et al. 4

Reduced-Mechanism Performance 1200 rpm, PRF40,  =0.19 1200 rpm, PRF40,  =0.26 1200 rpm, PRF60,  =0.26 Cylinder Pressure (bar) Experiment 80 80 80 767-Species 157-Species 33-Species 60 60 60 40 40 40 P in =1.5 bar 20 20 20 T in =75 o C HCCI, PFI 0 0 0 -50 0 50 -50 0 50 -50 0 50 1200 rpm, PRF60,  =0.32 1200 rpm, PRF60,  =0.29 1200 rpm, PRF60,  =0.21 Cylinder Pressure (bar) 80 80 80 60 60 60 40 40 40 20 20 20 0 0 0 -50 0 50 -50 0 50 -50 0 50 CAD (deg) CAD (deg) CAD (deg) 5

Motivation  Kinetic mechanism reduction speeds up computations but could compromise model predictivity of certain responses of interest  Reduced mechanisms are normally optimized to preserve good fit with ignition delay data. How does this affect other responses?  Use multi-objective optimization to examine the interplay among different responses  Understand best ways for optimizing kinetic engine models for better prediction of engine responses 6

Optimization Setup

Optimization Scheme 8

Experimental Setup Number of cylinders 1 Operation cycle 4-stroke Combustion mode HCCI Number of valves 4 Displacement (litres) 0.5 Bore (mm) 84 Stroke (mm) 90 Connecting rod (mm) 159 Crank radius (mm) 45 Compression ratio 12:1 Fuel delivery PFI Intake pressure (bar) 1.5 Intake temperature ( o C) 75 9

Experimental Setup 10

Stochastic HCCI Model • Non-spatial notional particles represent cylinder charge space • Volume, density, and pressure are treated as global variables • Temperature and composition evolve locally in each particle according to a probability density function • Inter-particle mixing is based on temperature proximity • Convective heat transfer with the cylinder wall is calculated by Woschni's coefficient SAE Papers: 2004-01-0561, 2005-01-0161, 2006-01-1362, 2009-01-1134 11

Optimization Variables Arrhenius Equation  Four SRM parameters (wall    E temperature, residual gas   k AT exp    RT  fraction, turbulent mixing time and stochastic heat transfer coefficient)  Arrhenius equation's pre- exponential factor (A) , temperature exponent (  ) and activation Energy (E)  Optimization was constrained and carried out against 12 experiments at each iteration 12

Sensitivity Analysis 13

Objective Function Formulation  Sum of squared differences between experiment and model values  Nine points for ignition delay curve, five on cylinder pressure curve, and single points for CO and HC emissions  SRM parameters optimized for best pressure fit are used as basis for estimating improvement in predictivity 14

Search Method  Search for global minimum within nonlinear constrained search space  Stochastic search using multi- objective genetic algorithm  GA is based on evolution theory, where variable values (chromosomes ) of best solutions from initial population (parents) are used to produce next generation (children)  Randomization (mutation) allows experimenting new regions within the search space, therefore escaping local minima 15

Optimization Results

Cylinder Pressure vs. Ignition Delay 17

Ignition Delay 18

Engine Model Responses 8 x 10 12 Solution points Pareto front 10 HC Objective Function 8 6 Pressure & HC Best Fit 4 2 0 150 CO Best Fit 2.5 2 100 Original Model 1.5 50 1 4 x 10 0.5 0 0 CO Objective Function Pressure Objective Function 19

Cylinder Pressure (1200 rpm) 1200 rpm, PRF80,  =0.35 1200 rpm, PRF40,  =0.21 80 80 r Pressure (bar) 60 60 40 40 20 20 0 0 -50 0 50 -50 0 50 CAD (deg) CAD (deg) 20

Cylinder Pressure (1200 rpm) 1200 rpm, PRF40,  =0.19 1200 rpm, PRF40,  =0.21 1200 rpm, PRF40,  =0.26 1200 rpm, PRF40,  =0.29 Cylinder Pressure (bar) 80 80 80 80 60 60 60 60 40 40 40 40 20 20 20 20 0 0 0 0 -50 0 50 -50 0 50 -50 0 50 -50 0 50 1200 rpm, PRF40,  =0.32 1200 rpm, PRF60,  =0.21 1200 rpm, PRF60,  =0.26 1200 rpm, PRF60,  =0.29 Cylinder Pressure (bar) 80 80 80 80 60 60 60 60 40 40 40 40 20 20 20 20 0 0 0 0 -50 0 50 -50 0 50 -50 0 50 -50 0 50 1200 rpm, PRF60,  =0.32 1200 rpm, PRF80,  =0.29 1200 rpm, PRF80,  =0.32 1200 rpm, PRF80,  =0.35 Cylinder Pressure (bar) 80 80 80 80 60 60 60 60 40 40 40 40 20 20 20 20 0 0 0 0 -50 0 50 -50 0 50 -50 0 50 -50 0 50 CAD (deg) CAD (deg) CAD (deg) CAD (deg) 21

Cylinder Pressure (1500 rpm) 1500 rpm, PRF40,  =0.23 1500 rpm, PRF80,  =0.36 80 80 r Pressure (bar) 60 60 40 40 20 20 0 0 -50 0 50 -50 0 50 CAD (deg) CAD (deg) 22

Cylinder Pressure (1500 rpm) 1500 rpm, PRF40,  =0.20 1500 rpm, PRF40,  =0.23 1500 rpm, PRF40,  =0.26 1500 rpm, PRF40,  =0.29 Cylinder Pressure (bar) 80 80 80 80 60 60 60 60 40 40 40 40 20 20 20 20 0 0 0 0 -50 0 50 -50 0 50 -50 0 50 -50 0 50 1500 rpm, PRF40,  =0.33 1500 rpm, PRF60,  =0.23 1500 rpm, PRF60,  =0.27 1500 rpm, PRF60,  =0.30 Cylinder Pressure (bar) 80 80 80 80 60 60 60 60 40 40 40 40 20 20 20 20 0 0 0 0 -50 0 50 -50 0 50 -50 0 50 -50 0 50 1500 rpm, PRF60,  =0.32 1500 rpm, PRF80,  =0.34 1500 rpm, PRF80,  =0.35 1500 rpm, PRF80,  =0.36 Cylinder Pressure (bar) 80 80 80 80 60 60 60 60 40 40 40 40 20 20 20 20 0 0 0 0 -50 0 50 -50 0 50 -50 0 50 -50 0 50 CAD (deg) CAD (deg) CAD (deg) CAD (deg) 23

Cylinder Peak Pressure 1200 rpm - IAT 75 o C 1200 rpm - IAT 75 o C 1200 rpm - IAT 75 o C 90 90 90 PRF40 PRF60 PRF80 Original Model Original Model Original Model 80 80 80 Best Pressure Fit Best Pressure Fit Best Pressure Fit Peak Pressure (bar) Peak Pressure (bar) Peak Pressure (bar) 70 70 70 60 60 60 50 50 50 40 40 40 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 1500 rpm - IAT 75 o C 1500 rpm - IAT 75 o C 1500 rpm - IAT 75 o C 90 90 90 PRF40 PRF60 PRF80 Original Model Original Model Original Model 80 80 80 Best Pressure Fit Best Pressure Fit Best Pressure Fit Peak Pressure (bar) Peak Pressure (bar) Peak Pressure (bar) 70 70 70 60 60 60 50 50 50 40 40 40 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4    24

CO & HC Emissions 1200 rpm - PRF40 1200 rpm - PRF60 1200 rpm - PRF80 5 5 5 Experimental data Original Model 4 4 4 Best CO Fit 3 3 3 CO (%) CO (%) CO (%) 2 2 2 1 1 1 0 0 0 0.2 0.25 0.3 0.2 0.25 0.3 0.25 0.3 0.35 0.4    1200 rpm - PRF40 1200 rpm - PRF60 1200 rpm - PRF80 5000 7000 14000 Experimental data 6000 12000 Orignal Model 4000 Best HC Fit 5000 10000 3000 HC (ppm) HC (ppm) HC (ppm) 4000 8000 3000 6000 2000 2000 4000 1000 1000 2000 0 0 0 0.2 0.25 0.3 0.2 0.25 0.3 0.25 0.3 0.35 0.4    25

Conclusions  Conflicting trends observed among objectives normally used in mechanism optimization  Reduced mechanisms, normally optimized for ignition delay prediction, may not be as predictive of engine responses  Careful selection of optimization objectives increases the likelihood of better predictivity of reduced mechanisms  Multi-objective optimization could offer great help for guiding mechanism reduction process  Multi-objective optimization offers more freedom for customizing kinetic models based on intended purpose  Useful in practical applications where high degree of predictivity for limited number of responses is needed, but only a reasonable computational expense is afforded 26

Thank You 27