Modeling for Control of HCCI Engines Gregory M. Shaver J.Christian Gerdes Matthew Roelle P.A. Caton C.F. Edwards Stanford University Dept. of Mechanical Engineering D D L ynamic esign aboratory
Outline What is HCCI? Experimental test-bed at Stanford Motivation for modeling and control Proposed model Conclusion Future work Stanford University Modeling for Control of HCCI Engines - 2 Dynamic Design Lab
What is HCCI? Homogeneous Charge Compression Ignition: combustion due to uniform auto-ignition using compression alone. Main Benefit: Low post-combustion temperature reduced NOx emissions. Requires: A sufficient level of inducted gas internal energy Approaches to increasing inducted gas internal energy: Pre-heating the intake Pre-compressing the intake Throttling exhaust/intake promotes hot exhaust gas re-circulation Stanford University Modeling for Control of HCCI Engines - 3 Dynamic Design Lab
Another Approach: Variable Valve Actuation (VVA) with VVA: Exhaust reinduction achieved using late EVC Load variation achieved by late IVO coupled with late EVC Benefits: No pumping penalty More control over presence of reactant/exhaust products in cylinder at any time Challenges: Currently no VVA systems on production vehicle R&D: ongoing by many cylinder volume valve opeing V BDC V TBC 0 IVO EVC IVC intake exhaust EVO 220 490 220 490 crank angle [deg.] Stanford University Modeling for Control of HCCI Engines - 4 Dynamic Design Lab
Emissions characteristics of HCCI with VVA 2500 50 ηth (HCCI) Nitric Oxide (ppm dry) 2000 1500 1000 ηth (SI) NO (SI) 40 30 20 Indicated Efficiency (%) 500 10 NO (HCCI) 0 0 2 3 4 5 6 net IMEP (bar) Experimental results from Stanford single-cylinder research engine Stanford University Modeling for Control of HCCI Engines - 5 Dynamic Design Lab
Experimental Testbed Single cylinder research engine Fuels: Propane Hydrogen Gasoline Comp. Ratio: 13:1 (adjustable) Engine rpm: 1800 Stanford University Modeling for Control of HCCI Engines - 6 Dynamic Design Lab
Motivation for Modeling and Control Challenge: Combustion Phasing No direct combustion initiator (like spark for SI or fuel injection for Diesel combustion) Combustion phasing depends on: Concentrations of reactants and re-inducted products Initial temperature of reactants and products Initial Concentrations/temperature directly controlled with VVA system Stanford University Modeling for Control of HCCI Engines - 7 Dynamic Design Lab
Modeling Approach Assumptions Homogeneous mixture Uniform combustion Complete combustion to major products States volume, V temperature, T concentrations: [X C3 H 8 ], [X O2 ], [X CO2 ], [X N2 ], [X H2 O], [X CO ] mass of products in exhaust manifold: m e internal energy of products in exhaust manifold: u e Stanford University Modeling for Control of HCCI Engines - 8 Dynamic Design Lab
Modeling Approach Volume Rate Equations Valve Flow Equations Concentration Rate Equations Temperature Rate Equations Exhaust Manifold Modeling: Mass Flows and Internal Energy Combustion Chemistry Modeling Temperature threshold approach Integrated Arrhenius rate threshold approach Stanford University Modeling for Control of HCCI Engines - 9 Dynamic Design Lab
Volume Rate Equations where: V = V c + πb2 4 (l a acosθ l 2 a 2 sin 2 θ) V = π 4 B2 a θsinθ(1 cosθ + a (L 2 a 2 sin 2 θ) ) θ = ω ω - the rotational speed of the crankshaft a - is half of the stroke length L - connecting rod length B - bore diameter V c - clearance volume Stanford University Modeling for Control of HCCI Engines - 10 Dynamic Design Lab
Valve Flow Modeling for un-choked flow (p T /p o > [2/(γ + 1)] γ/(γ 1) ): ṁ = C DA R p o RTo ( pt for choked flow (p T /p o [2/(γ + 1)] γ/(γ 1) ): p o ) [ [ 1/γ 2γ 1 γ 1 ṁ = C DA R p o RTo γ [ 2 γ + 1 ( pt p o ] (γ+1)/2(γ 1) ) (γ 1)/γ ]] where: A R - effective open area for the valve p o - upstream stagnation pressure INTAKE VALVE. m 1. m 2 EXHAUST VALVE INTAKE VALVE. m 3 EXHAUST VALVE T o - downstream stagnation temperature p T - downstream stagnation pressure Stanford University Modeling for Control of HCCI Engines - 11 Dynamic Design Lab
Temperature Rate Equation The first law of thermodynamics for an open system is: d(mu) dt = Q c W + ṁ 1 h 1 + ṁ 2 h 2 ṁ 3 h 3 u - internal energy Q c - heat transfer rate using the definition of enthalpy, h = u + pv: d(mh) dt W = p V - piston work h - enthalpy of species = ṁpv/m + ṗv + m 1 h 1 + m 2 h 2 m 3 h 3 with: Q c = h c A c (T c T wall ) Assuming ideal gas and specific heats as functions of temperature, can re-write equation as a temperature rate expression Stanford University Modeling for Control of HCCI Engines - 12 Dynamic Design Lab
Concentration Rate Equations [X i ] = d ( ) Ni N = i dt V V V N i V 2 w i = w rxn,i + w valves,i = w i V N i V 2 where: w rxn,i - combustion reaction rate for species i w valves,i - volumetric flow rate of species i through the valves N i - number of moles of species i in the cylinder w valves,i = w 1,i + w 2,i + w 3,i = (Y 1,i m 1 + Y 2,i m 2 Y 3,i m 3 )/(V MW i ) where: Y 1,i - mass fraction of species i in the intake (constant) Y 2,i - mass fraction of species i in the exhaust (constant) Y 3,i = [X i]mw i [Xi ]MW i - mass fraction of species i in the cylinder Stanford University Modeling for Control of HCCI Engines - 13 Dynamic Design Lab
Exhaust Manifold Modeling (Mass Flow) Exhaust Manifold Mass Flow Diagram:. m e,residual m ce m e,max (a) (b) (c). m ec m e,evc m e,evc -m e,residual ω EVO-EVC (d) (e) (f) (a) residual mass from previous exhaust cycle, θ = EV O (b) increase in mass due to cylinder exhaust, EV O < θ < 720 (c) maximum amount of exhaust manifold mass, θ = 720 (d) decrease in mass due to reinduction, 0 < θ < EV C (e) post-reinduction mass, θ = EV C (f) decrease in mass to residual value, EV C < θ < EV O Stanford University Modeling for Control of HCCI Engines - 14 Dynamic Design Lab
Exhaust Manifold Modeling (Internal Energy) An internal energy rate equation can be formulated from the first law, as: where: u e = 1 m e γ [ṁce (h c h e ) + ha (T ambient T e ) ] Q e = h e A e (T e T ambient ) So the condition of the product gases in the exhaust manifold is characterized w/ two states: the mass: m e the internal energy: u e Stanford University Modeling for Control of HCCI Engines - 15 Dynamic Design Lab
Combustion Chemistry Modeling: Temperature Threshold Approach The rate of reaction of propane is approximated as a function of crank angle and volume following the crossing of a temperature threshold: w C3 H 8 = [ ] ((θ θinit ) θ) [C 3 H 8 ] i V i θexp 2σ 2 V σ 2π T T th 0 T < T th where: θ init - crank angle when T = T th V i - crank angle when T = T th [C 3 H 8 ] i - propane concentration when T = T th σ - crank angle standard deviation θ - mean crank angle Stanford University Modeling for Control of HCCI Engines - 16 Dynamic Design Lab
Combustion Chemistry Modeling: Temperature Threshold Approach (cont.) The complete combustion of a stoichiometric propane/air mixture to major products is assumed, such that the global reaction equations is: C 3 H 8 + 5O 2 + 18.8N 2 3CO 2 + 4H 2 O + 18.8N 2 By inspection of the global reaction equation: w O2 = 5w C3 H 8 w N2 = 0 w CO2 = 3w C3 H 8 w H2 O = 4w C3 H 8 Stanford University Modeling for Control of HCCI Engines - 17 Dynamic Design Lab
Combustion Chemistry Modeling: Temperature Threshold Approach (cont. 2) Model Results: 70 60 experiment temp. threshold 70 60 experiment temp. threshold 50 50 Pressure (bar) 40 30 Pressure (bar) 40 30 20 20 10 10 0 50 0 50 Crankshaft ATC 0 50 0 50 Crankshaft ATC IVO @ 25deg., EVC @ 165 Combustion phasing not captured REASON: Combustion phasing depends on temperature AND concentrations IVO @ 45deg., EVC @ 185 Stanford University Modeling for Control of HCCI Engines - 18 Dynamic Design Lab
Combustion Chemistry Modeling: Integrated Arrhenius Rate Approach The rate of reaction of propane is approximated as being a function of crank angle and volume following the crossing of an integrated Arrhenius rate: w C3 H 8 = [ ] ((θ θ [C 3 H 8 ] i V i θexp init ) θ) 2σ 2 V σ 2π 0 RR RRth RR < RRth where: RR = θ IV O Aexp(E a /(RT ))[C 3 H 8 ] a [O 2 ] b dθ This equation gives insight into combustion phasing with VVA IVO: residence time for mixing (start of integration) IVO + EVC: initial reactant concentrations, [C 3 H 8 ] init [O 2 ] init, and mixture temperature, T init. Stanford University Modeling for Control of HCCI Engines - 19 Dynamic Design Lab
Combustion Chemistry Modeling: Integrated Arrhenius Rate Approach (cont.) The complete combustion of a stoichiometric propane/air mixture to major products is assumed, such that the global reaction equations is: C 3 H 8 + 5O 2 + 18.8N 2 3CO 2 + 4H 2 O + 18.8N 2 By inspection of the global reaction equation: w O2 = 5w C3 H 8 w N2 = 0 w CO2 = 3w C3 H 8 w H2 O = 4w C3 H 8 Stanford University Modeling for Control of HCCI Engines - 20 Dynamic Design Lab
Combustion Chemistry Modeling: Integrated Arrhenius Rate Approach (cont. 2) Model Results: 70 60 experiment Integrated Arrhenius rate threshold 70 60 experiment Integrated Arrhenius rate threshold 50 50 Pressure (bar) 40 30 Pressure (bar) 40 30 20 20 10 10 0 50 0 50 Crankshaft ATC IVO @ 25deg., EVC @ 165 Combustion phasing captured Pressures well predicted 0 50 0 50 Crankshaft ATC IVO @ 45deg., EVC @ 185 Stanford University Modeling for Control of HCCI Engines - 21 Dynamic Design Lab
Cycle-to-Cycle Coupling Cycle-to-Cycle coupling through the re-inducted exhaust gas is clearly evident: Cylinder Pressure [kpa] 65 55 45 35 25 15 Simulated HCCI Combustion Over a Valve Profile Transition Valve Profiles A B IVO 40 EVC 165 IVO 70 EVC 185 Steady State (A) Cycle 1 Cycle 2 Cycle 3 Cycle 4 5 300 350 400 450 Crank Angle Degrees Model allows prediction of these dynamics Stanford University Modeling for Control of HCCI Engines - 22 Dynamic Design Lab
Conclusion Combustion Model Uniform complete combustion to major products Simplified chemistry models developed Temperature threshold approach propane reaction evolves as fcn. of crank angle following temp. threshold crossing Does not capture combustion phasing Integrated Arrhenius Rate threshold approach propane reaction evolves as fcn. of crank angle following int. threshold crossing Captures combustion phasing Discrepancy along pressure peak Independent control of phasing and load seem feasible: with variation of IVO/EVC, should be able to vary inducted reactant charge (related to load) and phasing (Int. Arr. Model suggests this) Stanford University Modeling for Control of HCCI Engines - 23 Dynamic Design Lab