Tackling the Transition: A Multi-Mode Combustion Model of SI and HCCI for Mode Transition Control

Homogeneous charge compression ignition (HCCI) offers a promising way to improve efficiency and emissions. However, when HCCI is induced by reinducting exhaust gases, less power is produced. A possible solution is to couple HCCI with spark ignition (SI) operation at higher loads. This requires a way to smoothly switch between combustion modes. The authors present a multi-cycle, multi-mode combustion model to aid in understanding and controlling the mode transition. The model captures early ignition and low work after a switch from SI to HCCI. Furthermore, the model reveals a need to coordinate intake and exhaust valve timing to correct the HCCI phase and work. To demonstrate the model, the paper concludes with an example trajectory that maintains constant work and ignition phasing after a switch from SI to HCCI. NOMENCLATURE Ak Arrhenius rate pre-exponential factor Ae Surface area of exhaust manifold Aev Area of exhaust valve Aiv Area of intake valve ak Arrhenius rate propane concentration exponent Ac Exposed cylinder surface area aW Wiebe constant Bc Cylinder bore diameter bk Arrhenius rate oxygen concentration exponent ĉp Molar specific heat CD Coefficient of discharge Ek Arrhenius rate activation energy EVC Exhaust valve closing time EVO Exhaust valve opening time γ Specific heat ratio h Enthalpy ĥ Molar enthalpy h̄ Convection coefficient IVC Intake valve closing time IVO Intake valve opening time M Molecular mass m Mass ṁ Mass flow rate mW Wiebe constant N Number of moles nk Arrhenius rate temperature exponent ω Engine speed of rotation p Pressure φ Equivalence ratio, ( f uel/air) ( f uel/air)stoich Q Heat transfer R Specific gas constant R̂ Molar universal gas constant Ψ Integrated global Arrhenius rate Ψth Integrated global Arrhenius rate threshold T Temperature θ Engine position ∆θ Wiebe function combustion duration u Internal energy 1 Copyright c © 2004 by ASME V Volume v̄p Mean piston velocity W Work [X] Species concentration in terms of moles per unit volume Y Mass fraction a Subscript denoting an ambient parameter i Subscript denoting an intake parameter c Subscript denoting a cylinder parameter e Subscript denoting an exhaust parameter j Subscript denoting a species enumeration ign Subscript denoting an ignition parameter ic Subscript denoting flow from intake to cylinder ce Subscript denoting flow from cylinder to exhaust ec Subscript denoting flow from exhaust to cylinder ea Subscript denoting flow from exhaust to ambient rxn Subscript denoting a reaction parameter INTRODUCTION As automotive engine designers pursue methods of improving engine efficiency, emissions and performance, multiplecombustion-mode engines open a new realm of possibilities. A multi-mode engine coupling spark ignition (SI) with homogeneous charge compression ignition (HCCI) could have the range and startability of SI and the efficiency and low NO x of HCCI. Using multiple combustion modes, however, necessitates a strategy for switching between them. This paper presents a multimode combustion model and a simulation of a desirable transition from SI to HCCI. There are several methods of achieving HCCI in internal combustion engines. For engines that use pre-mixed fuel and modest compression ratios, the pre-compression energy or fuel concentration of the cylinder contents must be raised so that the mixture will auto-ignite. Exhaust gases can be trapped by closing the exhaust valve early [1] or reinducted by closing the exhaust valve late [1,2], the intake can be heated or pre-compressed [3,4] or methods can be combined [5,6]. We achieve HCCI by reinducting hot exhaust gases along with fresh fuel and air (residual-affected HCCI). This form of HCCI eliminates the pumping losses associated with throttled SI [7, 8]. The reinducted exhaust sinks heat during combustion, lowering the peak temperature and reducing NO x. The exhaust also leaves less room for fresh reactants, reducing the work capacity of HCCI. SI can achieve more power and provide hot exhaust to initiate HCCI. It makes sense to include both modes in an engine. In a multi-mode engine, mode transitions are necessary to vary work output smoothly through the space of engine capability. Martinez-Frias et al. suggest using SI with HCCI to reach higher loads [9]. Koopmans et al. have demonstrated mode transitions and have observed low work and advanced ignition phasing following a switch from SI to HCCI [10]. 0 100 200 300 400 500 600 700 800 0 5 10 15 20 25 30 35 40 45 50 Volume [ml] P re ss u re [ b a r] HCCI (steady-state) SI HCCI (first cycle) (a) 300 320 340 360 380 400 420 440 Crank Angle [deg] SI HCCI (first cycle) HCCI (steady-state) (b) Figure 1. (a) P-V DIAGRAM OF AN EXPERIMENTAL SI TO HCCI MODE TRANSITION AND (b) PRESSURE TRACE ACROSS THE SAME TRANSITION Switching from HCCI to SI is simple. SI combustion is predominantly independent of the previous cycle. Cooler cylinder wall temperatures after HCCI may slow the flame speed [10], but the switch to SI does not affect ignition timing. Switching to SI from HCCI is a fairly straightforward matter of choosing the transition points, switching to SI valve timings and turning on the spark. Conversely, the SI to HCCI transition is complicated. When reinducted exhaust is used to induce HCCI, the intake and exhaust valves are open and unthrottled for much of the induction stroke. Hot products exhausted in the last combustion cycle are reinducted along with fresh reactants, raising the sensible energy of the mixture in the cylinder. The energy in the reinducted exhaust gas and quantity of fresh reactants dictate the point of ignition, work produced and exhaust temperature. Thus, the exhaust dynamically links cycles of residual-affected HCCI. The first cycle of HCCI combustion after a transition will depend on the exhaust temperature of SI combustion, complicating the transition. Figure 1 provides evidence of the influence of SI exhaust on HCCI ignition. A transition from steady-state SI to steadystate HCCI valve timing exhibits early ignition on the first cycle following the transition. The total work for that cycle is much lower than steady state HCCI, Fig. 1 (a). Ignition phasing and engine work should be smooth regardless of the direction of the mode transition. To explain the dynamics of the transition, the authors have created a multi-cycle, multi-mode model of SI and HCCI. The model uses several ordinary differential equations of state. Gas exchange, ignition and combustion are modeled to simulate SI and HCCI combustion. The exhaust manifold is modeled in order to capture cycle-to-cycle dynamics. Based on cylinder pressure traces from simulation and experiment, the model correctly predicts premature HCCI phasing following an SI cycle. The model predicts that inducting less hot exhaust can retard the ignition to a nominal point. Simulation shows that closing the exhaust valve early to reduce exhaust reinduction can indeed correct the ignition phasing. However, 2 Copyright c © 2004 by ASME the lack of exhaust in the cylinder increases fresh reactant and work. To achieve the nominal work and ignition phasing, both exhaust and fresh reactant must be limited. Exhaust temperature links HCCI to the previous combustion cycle, whether it be HCCI or SI. Relatively hot SI exhaust causes early, even pre-mature, ignition in the first cycle of HCCI following a mode transition. The multi-mode combustion model presented here captures this behavior. Simulation of the model with adjusted valve timing demonstrates an example trajectory that maintains constant work and ignition phasing. The model provides a tool for choosing valve timing to achieve a smooth transition. MODEL DESCRIPTION The model is composed of several nonlinear ordinary differential equations of state. It is based on the first law of thermodynamics with: • 1-D compressible flow through the intake and exhaust ports; • Single-zone thermodynamic control-volume models of the cylinder and exhaust manifold; • Heat transfer via simple convective models; • Combustion via a Wiebe function; and, • Ignition initiated by spark timing (SI) or an integrated Arrhenius threshold (HCCI). It includes the following seven states: 1. Fuel concentration (kmol/m 3), [ f uel]; 2. Oxygen concentration (kmol/m 3), [O2]; 3. Nitrogen concentration (kmol/m 3), [N2]; 4. Carbon dioxide concentration (kmol/m 3), [CO2]; 5. Water concentration (kmol/m 3), [H2O]; 6. Cylinder gas temperature (K), Tc; and, 7. Exhaust manifold internal energy (kJ/kg), ue. The model presented here is an extension of previous work and some details are left to the earlier treatment [11]. The model will be discussed in the following sections as the cylinder gas exchange, the combustion chamber control volume, and the exhaust manifold control volume. Gas Exchange As in the physical system, valve timing dictates the flow into and out of the cylinder. Fresh products flow into the cylinder, ṁic when the intake valve is open. Similarly, exhaust flows from the cylinder to the exhaust manifold,̇ mce, or vice versa,ṁec, when the exhaust valve is open. The valve strategy investigated here does not have significant flow from the cylinder back to the intake, so, these flows are not included. Figure 2 represents the flows visually. m ce . Intake