HIERARCHICAL MODELING FOR DESIGN AND OPTIMIZATION OF DIESEL ENGINE CONTROL STRATEGIES

HIERARCHICAL MODELING FOR DESIGN AND OPTIMIZATION OF DIESEL ENGINE CONTROL STRATEGIES Ivan Arsie, Cesare Pianese, Gianfranco Rizzo, Marco Sorrentino Dipartimento di Ingegneria Meccanica Università di Salerno pianese@unisa.it Applicazioni e Prospettive del controllo nei veicoli Dei Politecnico di Milano May 1th, 7

Agenda Context and Objectives Common Rail benefits Modeling approach Multi-Zone Models Description Parameters identification Results Two-Zone Models Description Parameters identification Results Optimization and hierarchical structure Conclusions /6

Context and Objectives Meet stringent emissions standards for NOx and Soot, retain fuel economy benefits of Diesel engines. Improve Electronic Control for Diesel engines, critical due to the large number of control variables. EURO# Need to cut experiments for control strategies development to limit time and costs. ECU 3/6

[beta] [dma_eng] [df] [tauf] [taum] rpm [dma_thr] [pman] [dma_eng] dmf_inj [sprk] [dmf_eng] [afr] [df] [tauf] [taum] [ref_speed] [dma_eng] afr_exh Mu [T_e] [eta_g] [Exh] Context and Objectives Model based structures: Hierarchical modeling Real-time application HIL Virtual/Rapid Prototyping On-board application HIL-VP RP AIR DYNAMICS FUEL DYNAMICS TORQUE EMISSIONS DRIVELINE ACTUATORS ECU CRUISE CONTROL Development of simulation models with satisfactory accuracy. Boost computational speed. Balanced precision among sub-models to be consistent with embedded applications. 4/6

Common Rail Control CONTROL VARIABLES OPEN ISSUES Injection pressure # of strikes SOI Pulse widths Dwell time EGR Control Design Find optimum combination(s) of parameters for given Load, Speed, EGR ratio and Boost Pressure. Large calibration effort. Introducing Model-Based optimization to reduce experiments. 6/6

Models Trade-Off CFD Phenomenological Multi Zone Two Zone Single Zone Experiments Parameters Comp. resources Models Hierarchy Black Box Phenomenological models are based on a simplified description of the physical phenomena vs multi-dimensional (3-D) approach. A set of parameters guarantees the accuracy for different engine operations and geometry. 8/6

Hierarchical Structure ECU <1 Cycles Steady State Strategy Optimization Dynamic Real-Time On-Board Multi-Zone > Cycles Two-Zone >1 Cycles Black Box 9/6

Models Hierarchy SINGLE ZONE TWO ZONES MULTI ZONE Single Zone Mixing Air Jet Air SAE 4-1-1877 SAE 5-1-111 SAE 6-1-1384 Experiments Parameters Comp. resources 1/6

Approaches comparison SINGLE ZONE TWO ZONES MULTI ZONE Single Zone Mixing Air Jet Air SAE 4-1-1877 [#] SAE 5-1-111 SAE 6-1-1384 [s] 18 16 14 15 EXPERIMENTS 16 PARAMETERS 1, 1 14 TIME [s] 1 1 1 8 6 4,1 9 5, - 4 1-3 injs 3-1 injs SINGLE TWO MULTI 1 expected 3 8 6 4 11/6

Multi-zone Model Features and Structure High precision vs. computational time. Easy-to-hand parameters identification. FEATURES MODULES (sub-models) Decoupling of some phenomena. Modularity. Balanced precision. Jet Develop. Turb. Injection Multi-zone Heat Transfer Comb. Evap. Ignition Delay NO/Soot Models 13/6

Multi Zone Model Energy Volume Variables E & V i cyl = Q& = i V W& a + [ ] vb vu p,t,t, i, j i, j Ta i + i j,i j V i a q i, j m& i, j h i, j vu q i, j inj m i, j fv m i, j Liquid Unburned gas Burned gas i = 4 i = 3 i = i = 1 Q W c a a + Q r a A i r ae m i, j Q W ( fv ae i, j i, j) x m + m vu, c vu, r i, j i, j vu i, j + Q Heat / Work Mass Flow Q W vu, c vu, r i, j i, j vu i, j + Q j = 1 j = 3 14/6

Injection Delay ET CURRENT ET ED Energizing Time Energizing Delay ED COD SOLENOID VALVE NEEDLE CCD NEEDLE LIFT COD CCD NOD Control Valve Opening Delay Control Valve Closing Delay Needle Opening delay NOD ISD IED EID NCD ISD NCD IED Injection Start Delay Needle Closing Delay Injection End Delay ISD C 1 = V f,inj f,inj EID = C V ET EID Effective Injection Duration 15/6

Jet Development equal mass and momentum fluxes as the equivalent real spray at the same axial location; uniform velocity profile; constant injection velocity; no velocity slip between the fuel and the entrained air; conical shape. non-dimensional penetration by integrating the non-dimensional velocity (Naber and Siebers, 96) m ae θ The air entrained by each zone is computed from the momentum conservation: m f,inj Uf ds ae 3 m & = -C ds dt dt m ae 16/6

Evaporation After the break-up, the fuel evaporation rate is derived from mass diffusion and heat transfer for a spherical droplet with initial diameter equal to the SMD (Jung & Assanis, 1): q& i, j fv m& i, j t b = 4.351 C d [ ρ ( p p )].5 a ρ d l f n a U a ρ a P T q& i, j ρ l T l fv m& i, j The droplet temperature is assumed homogeneous Energy balance -> dmfv p p = πdlndsh v ln m dt v & RT p - p ( vu ) m q=πdln k T -Tl Nu e z -1 dtl 1 dm = q-λ & dt mlcp,l dt fv z vsurf 17/6

Ignition Delay The ignition delay is computed with an Arrhenius-like model (Heywood, 88; Jung & Assanis, 95). τ id = 3.45 1-3 p 1. exp 1 T To account for pressure and temperature variation the following integral is solved with respect to SOC SOC SOI dt τ id = 1 18/6

Turbulence The turbulence is described assuming isotropic homogeneous turbulence and equilibrium between production and dissipation of turbulent kinetic energy. The combustion does not influence directly the turbulence. k ε model dk k dρ = ε dt 3 ρ dt dε 4 ε dρ ε = dt 3 ρ dt k The initial value of k is proportional to the mean piston speed. The initial value of ε is derived from the equilibrium hypothesis (L I valve lift). 3 ( ) = ( BV ) k IVC ( IVC) ε = 1 mp ( ) ( IVC) k IVC L I 3 19/6

Combustion Model The combustion rate is modeled as function of a characteristictime, which is the weighted sum of the laminar and turbulent combustion time scales. dm m m = dt τ b e b b τ = τ + γτ b b,lam b,turb γ 1.8.6.4...4.6.8 1 x The laminar time scale is derived from an Arrheniuns-like relationship (Kaario et al.,). The turbulent combustion time scale is assumed proportional to the eddy turnover. -.75 1.5 E 3 τ = 4 1 n n exp - RT % b,lam fv O vb τ b, turb =.14 k ε -1 /6

NO and Soot Models The NO model is based on the well known Zeldovich mechanism O + N NO + N N + O NO + O N + OH NO + H Formation rate 1 V b dn dt NO = 1 + R1{ 1 ([ NO]/[ NO] e ) } ([ NO]/[ NO] ) R /( R + R ) e 1 3 The Soot model is based on the Hiroyasu approach Net soot mass rate dm dt dm dt Mass formation rate dm sf n = K f M fv dt Mass oxidation rate dm so = K om sxo dt s dm = dt sf so 1/6

Engine Engine FIAT 1.9 JTD 16v Cycle Diesel Engine FIAT 1.9 JTD 16 valves Strokes Cylinders Valves Bore (mm) Stroke (mm) Displacement (cm 3 ) Compression ratio Connecting rod to stroke ratio 4 4 16 8 9.4 199 18.3177 3/6

Parameters Identification Engine: Fiat 1.9 16 V M-Jet The parameters related to general physical phenomena (e.g. evaporation, combustion, heat transfer) have been taken from the literature. The parameters characterizing the injection system (C 1, C ) and the jet-air-geometry interaction (C 3 ) have been identified in one reference point. bmep Max One injection Two injections Three injections @ 9 EGR 13% inj. IDENTIFIED PARAMETERS C 1 [µs mm3] 3618.4 C [1/mm3] C 3 [/].475 1.8 Min 1 Engine speed (rpm) 45 4/6

Parameters Identification Engine: Fiat 1.9 16 V M-Jet The unknown parameters have been identified by comparing predicted and measured pressure cycle. 1 x 16 Pressure [Pa] predicted measured 8 6 4 8 x 15 6 4 Heat Release Rate [J/s] predicted measured - -15-1 -5 5 1 15 Crank angle [deg] - -5 5 1 Crank angle [deg] pmax, m pmax,c =.6[bar] θ = p max.3[deg] 5/6

Generalization Test The model has been tested versus a wide set of the experimental data composed of 89 engine cycles. CONTROL VARIABLE Injections Injection timing Dwell angle Fuel injected/cycle Fuel injected/strike P rail EGR RANGE 1; 3 47 ; - BTDC 1 ; 3 5; 71 mm 3 1; 7 mm 3 3; 14 bar ; 45 % 5 15 1 5 R =.99 imep predicted [bar] 5 1 15 5 imep measured [bar] Average relative error 1% Max relative error <1% Standard deviation 4% 6/6

Results Engine Cycle 8 x 16 Pressure [Pa] predicted measured 6 4 Heat Transfer Gas, EGR Heat Transfer 5 x 15 4 3 Heat Release Rate [J/s] predicted measured Initial cond. k-ε combustion 1 - -15-1 -5 5 1 15 Crank angle [deg] -1-5 5 1 Crank angle [deg] Engine Speed (rpm) Brake Mean Effective Pressure (bar) EGR Ratio (%) Number of injections 15 5 7 8/6

Results Engine Cycle 7 x 16 Pressure [Pa] predicted 6 measured 5 4 6 x 15 5 4 3 predicted measured Heat Release Rate [J/s] 3 1 - -15-1 -5 5 1 15 Crank angle [deg] 1-1 9 5-5 5 1 Crank angle [deg] Engine Speed (rpm) Brake Mean Effective Pressure (bar) EGR Ratio (%) Number of injections 5 6 9/6

Results Engine Cycle 9 x Heat Release Rate [J/s] 14 x 15 16 Pressure [Pa] predicted 1 measured predicted measured 9 x 15 Heat Release Rate [J/s] predicted measured 1 6 6 8 36 3 4 - -5-15 -1-5 5 5 1 1 15 Crank Crank angle angle [deg] [deg] -5 5 1 Crank angle [deg] Discretization zones Engine Speed (rpm) Brake Mean Effective Pressure (bar) 13 Discretization 1 zones EGR Ratio (%) Number of injections 3/6

Results Engine Cycle 14 x 16 Pressure [Pa] predicted 1 measured 1 x 15 1 Heat Release Rate [J/s] predicted measured 1 8 6 4 Heat Relase In. Cond. 8 6 4 - -15-1 -5 5 1 15 Crank angle [deg] - -5 5 1 Crank angle [deg] Engine Speed (rpm) Brake Mean Effective Pressure (bar) EGR Ratio (%) Number of injections 4 9 1 31/6

Results NO Emissions Comparison between measured and estimated NO Frequency distribution of the NO Relative Error 5 NO predicted [ppm] 45@13 R =.94 1@1 1.8 Cumulative Distribution Frequency 7% 15.6 1.4 5. 5 1 15 5 NO measured [ppm]..4.6.8 1 Absolute Relative Error [/] 3% 3/6

Results NO Emissions predicted measured NO [ppm] Φ 1 15 1 Injections with EGR 3 Injections without EGR 5 EGR Temperature increase 5 1 15 bmep [bar] Engine Speed (rpm) 15 33/6

Results NO Emissions predicted measured NO [ppm] Φ 1 15 Injections with EGR 1 5 EGR Injections without EGR Temperature increase 5 1 15 5 bmep [bar] Engine Speed (rpm) 5 34/6

Results Soot Emissions 4 3 x 1-4 Soot [g] predicted measured Φ 1 1 Injections with EGR EGR Injections without EGR Temperature increase 5 1 15 5 bmep [bar] Engine Speed (rpm) 5 35/6

Two Zone Model Injection Break -up S.O.C E.O.C. Combustion Liquid fuel Fuel Preparation Air 37/6

Thermodynamic Model v a v l v m Energy Equation E& = Q& W& + m& h i w, i i i, j i, j j, i j Volume Equation V = V + V cyl a i, j i j 1 6 5 3 4 i = a, m j = a, l, m i = a,, l m j = 1Kn nh W & p& Liquid fuel & m l, m Mixing-zone & m a, m Air-zone Q & v B La C L A + + Ga Gm = f( p, Ta, Tm, Φ, θ ) = B Fa C F D Ga Gm La Fa p T& + & a = g( p, Ta, Tm, Φ, θ ) = Ga Lm + Fm p& Tm = h( p, Ta, Tm, Φ, θ ) = G m m m m& l Q & Q & 38/6

Thermodynamic model Injection Delay Spray Model t inj, d dsbb CD = dθ ω ds dθ 1.475 ( p p) rail ρ.5 ab prail = SOI p ρa l dn ω. 5 ( θ θ ) Spray velocity t b ρl dn = 4.351 C ρ p D a Break-up Time 39/6

Fuel Preparation and Combustion The time for fuel atomization, vaporization and micromixing with entrained air is described by means of a fuel preparation rate [Whitehouse & Way]: 1 θ 3 θ θ 3 dm f, inj.4 dm f, inj dm f, p f, p( θ) = 1 θ ( ( θ) ) θ θ dθ dθ dθ m& C d p d d The fuel burning rate depends on the amount of available fuel, weighted by an Arrhenius term [Whitehouse & Way]: ( θ ) ( θ ) T A C p θ Tmean ( θ ) dm f, p dm f, b m& f, b( θ ) = e d N' T dθ dθ mean θ 4/6

Parameters Identification Fiat 1.9 16 V M-Jet The parameters related to general physical phenomena (e.g. spray, combustion, heat transfer, NO and Soot) have been taken from the literature. The parameters characterizing the injection system (t inj,d ; C D ) have been identified in 9 reference points. Multiple regressions have been derived to express parameters variation vs. engine operation. t inj, d C C D D [ ms] b b ( q N ) = a = 1 1 a = 1 ( q N ) fuel N 1 3 4 5 6 7 8 9 Engine Speed [rpm] fuel if 45 45 45 45 45 4 4 35 35 if q q fuel fuel bmep [bar].5 3 5 9 1 11 16 9 1 1 a N > a 1 1 a N < a 1 4/6

Generalization Test The model has been tested versus a wide set of the experimental data composed of 81 engine cycles. CONTROL VARIABLE Injections Injection timing Dwell angle Fuel injected/cycle Fuel injected/strike P rail EGR RANGE 1; 3 47 ; - BTDC 1 ; 3 5; 71 mm 3 1; 7 mm 3 3; 14 bar ; 45 % 5 15 1 5 Test Set Identification Set Predicted IMEP [bar] R =.985 5 1 15 5 Measured IMEP [bar] 43/6

8 7 6 5 4 3 1 Validation In-Cylinder Pressure Pressure [bar] Predicted Measured 1 8 6 4 Pressure [bar] Predicted Measured - -15-1 -5 5 1 15 Crank Angle [bar] Engine Speed 15 rpm BMEP 5 bar EGR 7 % Pre and main injection - -15-1 -5 5 1 15 Crank Angle [bar] Engine Speed rpm BMEP 9 bar EGR 1.7 % Pre and main injection 44/6

7 6 5 4 3 1 Validation In-Cylinder Pressure Pressure [bar] Predicted Measured 175 15 15 1 75 5 5 Pressure [bar] Predicted Measured - -15-1 -5 5 1 15 Crank Angle [bar] Engine Speed 3 rpm BMEP 3 bar EGR 16.8 % Pre and main injection - -15-1 -5 5 1 15 Crank Angle [deg] Engine Speed 4 rpm BMEP 15 bar EGR % Main injection 45/6

5 15 1 Predicted Measured 15 rpm Results NO emissions NO [ppm] 15 1 Predicted Measured NO [ppm] 5 5 1 15 BMEP [bar] 14 1 1 8 6 4 Predicted Measured NO [ppm] 3 rpm 5 1 15 BMEP [bar] 5 16 14 1 1 8 6 4 5 rpm 5 1 15 5 BMEP [bar] Predicted Measured NO [ppm] 4 rpm 4 6 8 1 1 14 BMEP [bar] 47/6

8 x 1-5 Soot [g] 7 6 5 4 3 1 Results Soot emissions Predicted Measured 15 rpm 1 x 1-4 Predicted Measured 5 rpm Soot [g] 5 1 15 BMEP [bar] x 1-4 Soot [g] 5 1 15 5 BMEP [bar] 6 x Soot [g] 1-4 Predicted Measured 5 4 Predicted Measured 3 rpm 3 4 rpm 1 1 4 6 8 1 1 14 16 18 BMEP [bar] 5 1 15 BMEP [bar] 48/6

Results Effects of Prail 6 x 1-4 Soot [g/cyle] 5 4 6 bar Prail IMEP=7 bar +/-1.5% IMEP=11.5 bar +/-.1% IMEP=15.3 bar +/-.8% IMEP=17. bar +/-4.% Base condition 3 Load 1 bar 5 rpm 1 5 1 15 NO [ppm] 49/6

Optimization DPF filter enhances significant reduction of soot emissions PM [g/km].5 EURO 3 DPF.5.15 EURO 5 EURO 4 DeNOx..5.5 NOx [g/km] 51/6

Optimization An Optimization analysis has been performed on 6 operating conditions aimed at minimizing NO emissions with constraints on Soot and IMEP. The optimization is effectively done in minutes per point on a IBM Xeon 3. GHz; computational time per cycle varies from less than 1 second (1 inj.) to 3 seconds ( inj.) and to 7 seconds (3 inj.) V inj min NO inj θ, θ,, inj P rail EGR ( V,, P, EGR) inj rail 16 14 1 -.3% NO [ppm] -1.9% Base Optimal 1-6.4% Soot Soot base IMEP < 1% < 5% 8 6 4-8.% -15.3% -3% 15 @ 9 15 @ 17 5 @ 9 5 @ 15 35 @ 9 35 @ 17 5/3

Optimization 3.5 x 1-4 3 Base Optimal Soot [g/cycle] +4.5% Soot.5 1.5 +4.5% 1.5 +4.6% +4.5% +4.9% +4.7% 15 Base Optimal Rail Pressure [bar] -4.4% -3.6% -9.% 15 @ 9 15 @ 17 5 @ 9 5@ 15 35 @ 9 35 @ 17 1-8.5% -.1% -15.5% 5 Rail Pressure 15 @ 9 15 @ 17 5 @ 9 5 @ 15 35 @ 9 35 @ 17 53/3

Hierarchical Structure Application A first attempt has been performed to identify the Two-Zone model via Multi-Zone generated pressure cycles. The hierarchical modeling structure guarantees an accuracy level comparable to direct identification from experiments. 5 Test Set Predicted IMEP [bar] Identification Set 15 1 5 R =.997 Multi-Zone Two-Zone 5 1 15 5 1 cycles Measured IMEP [bar] 54/6

Hierarchical Structure Application 15 Two-zone Measured Multi-zone NO [ppm] 5 Two-zone Measured Multi-zone NO [ppm] 15 1 1 5 5 15 rpm 5 rpm 5 1 15 5 bmep [bar] 5 1 15 bmep [bar] 3.5 x Soot [g/cycle] 1-4 Two-zone 3 Measured Multi-zone.5 1.5 5 rpm 1 Multi-Zone Two-Zone.5 1 cycles 5 1 15 5 bmep [bar] 55/6

Hierarchical Structure Application Vehicle Dynamic Simulation <1 Cycles Multi-Zone >1 Cycles _ u(t) X _ y(t) Y Neural Network 56/6

Mean Value Model for transient simulation of Turbocharged CI engine Actuator PME ECU Injection, EGR ENGINE Exhaust Emission Engine Speed Torque DRIVELINE Mission Drive Controller Vehicle Speed 57/6

Mean Value Model for transient simulation of Turbocharged CI engine Intake Manifold Compressor ENGINE EGR valve EGR cooler Mech. link Exhaust Manifold Turbine 58/6

Results massa di combustibile iniettato [mm 3 /colpo] 9 x 14 regime del turbocompressore [rpm] 8.8 1.5 8.6 1 8.4 8..5 8 7.8 5 1 15 5 tempo [s] 7.6 5 1 15 5 tempo [s] 1.115 pressione collettori [bar] aspirazione scarico 66 65 aspirazione scarico temperatura nei collettori [K] 313 31.5 1.11 1.4 64 31 1.15 1.35 63 311.5 6 311 1.1 5 1 15 5 1.3 tempo [s] 61 31.5 5 1 15 5 tempo [s] 59/6

Results ECE/EUDC Driving Cycle Reference Vehicle: Alfa Romeo 147 1.9 JTDm Fuel consumption ECE/EUDC cycle = 16.84 km/l [provided by Alfa Romeo = 16.95 km/l] Acceleration -1 km/h = 8.3 s [provided by Alfa Romeo = 8.8 s] 15 Vehicle Speed [km/h] 35 Engine Speed [rpm] reference 1 actual 3 5 5 1 3 4 5 6 Time [s] 15 1 3 4 5 6 Time [s] 6/6

Results.8 Air Flow Rate [kg/s] Torque [Nm].7 15.6 1.5.4 5.3 1 3 4 5 6 Time [s] 1 3 4 5 6 Time [s].15 EGR Flow Rate [kg/s] 35 Injected Fuel [mm 3 /cycle] 3.1 5.5 15 1 1 3 4 5 6 Time [s] 5 1 3 4 5 6 Time [s] 61/6

Conclusions A Hierarchical modeling structure has been developed for the design and optimization of Diesel engine control strategies. A satisfactory compromise between accuracy, computational time and experimental effort has been effectively achieved by cascading phenomenological models (Multi/Two-zone). The models accurately simulate pressure cycles and emissions (NOx and Soot) in Common-Rail Multi-Jet Diesel Engine. In the Multi-Zone model three parameters (Ignition delay and air entrainment) have been identified using one engine cycle. In the Two-Zone model two parameters (Ignition delay and discharge coefficient) have been identified using nine experimental cycles or 1 cycles generated via multi-zone model. The Two-Zone model can be used for investigating the effects of control parameters and for optimization analyses aimed at improving fuel efficiency and emissions. A Mean Value Model has been developed for the dynamic simulation of engine /vehicle transients and tested vs. literature data. 6/6

Air Entrainment Momentum conservation S ml dsbb dsab = ( ml + mae) dθ dθ Before Break-up After Break-up m& ae, i Air mass entrainment Air mass flow entrainment m ae = dsbb ml dθ ds d ab θ 1 1 dmae dθ = m l dsbb dθ dsab ab dθ θ d S d 63/6