Chapter 12. Engine Ignition
This chapter discusses the theory behind the engine ignition models available in ANSYS FLUENT. Information can be found in the following sections.
• Section 12.1: Spark Model
• Section 12.2: Autoignition Models
• Section 12.3: Crevice Model
For information about using these ignition models, see Chapter 20: Modeling Engine Ignition in the separate User’s Guide.
12.1 Spark Model The spark model in ANSYS FLUENT will be described in the context of the premixed tur- bulent combustion model. For information about using this model, see Section 20.1: Spark Model in the separate User’s Guide. Information regarding the theory behind this model is detailed in the following sections:
• Section 12.1.1: Overview and Limitations
• Section 12.1.2: Spark Model Theory
12.1.1 Overview and Limitations Initiation of combustion at a desired time and location in a combustion chamber can be accomplished by sending a high voltage across two narrowly separated wires, creating a spark. The spark event in typical engines happens very quickly relative to the main combustion in the engine. The physical description of this simple event is very involved and complex, making it difficult to accurately model the spark in the context of a multi- dimensional engine simulation. Additionally, the energy from the spark event is several orders of magnitude less than the chemical energy release from the fuel. Despite the amount of research devoted to spark ignition physics and ignition devices, the ignition of a mixture at a point in the domain is more dependent on the local composition than on the spark energy (see Heywood [128]). Thus, for situations in which ANSYS FLUENT is utilized for combustion engine modeling, including internal combustion engines, the
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spark event does not need to be modeled in great detail, but simply as the initiation of combustion over a duration, which you will set. Since spark ignition is inherently transient, the spark model is only available in the transient solver. Additionally, the spark model requires chemical reactions to be solved. The spark model is available for all of the combustion models, however, it may be most applicable to the premixed and partially premixed combustion models. The Spark Model used in ANSYS FLUENT is based on a one-dimensional analysis by Li- patnikov [203]. The model is sensitive to perturbations and can be subject to instabilities when used in multi-dimensional simulations. The instabilities are inherent to the model and can be dependent on the mesh, especially near the beginning of the spark event when the model reduces diffusion to simulate the initial laminar spark kernel growth. The instability is susceptible to numerical errors which are increased when the mesh is not aligned with the flame propagation. As the spark kernel grows and the model allows turbulent mixing to occur, the effect of the instability decreases.
12.1.2 Spark Model Theory The spark model in ANSYS FLUENT is based on the work done by Lipatnikov [203] and extended to other combustion models. The derivation of the model can be done in the context of the Zimont premixed combustion model.
Zimont Premixed Flame Model The transport equation for the mean reaction progress variable, c, is given by Equa- tion 12.1-1
∂ρc + ∇ · (ρ~vc) = ∇ · (D ∇c) + ρ U |∇c| (12.1-1) ∂t t u t
where Dt is the turbulent diffusivity, ρu is the density of the unburned mixture and Ut is the turbulent flame speed. Since the spark is often very small compared to the mesh size of the model and is often laminar in nature, the Zimont model is modified such that
∂ρc + ∇ · (ρ~vc) = ∇ · ((κ + D )∇c) + ρ U |∇c| (12.1-2) ∂t tt u t
where κ is the laminar thermal diffusivity and the effective diffusivity Dtt is given by
( −ttd Dt 1 − exp τ 0 if ttd ≥ 0 Dtt = (12.1-3) Dt if ttd < 0
where is ttd = t−tig and tig denotes the time at which the spark is initiated. Additionally, τ 0 is an effective diffusion time, which you can set.
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Only turbulent scales that are smaller than the spark radius can contribute to turbulent spark diffusion, so the expression for the effective turbulent diffusivity, Dtt, is ramped up as the spark grows. This creates higher temperatures at the location of the spark and can cause convergence difficulties. In addition to convergence difficulties, small changes in the diffusion time can change the result significantly. Because of these issues, the diffusion time can be controlled by the you, and has a default value of 1e-5 seconds.
Other Combustion Models The spark model is compatible with all combustion models in ANSYS FLUENT. However, the premixed and partially premixed models differ in that the progress variable inside the spark region is set equal to 1, a burned state, for the duration of the spark event. Other combustion models have the energy input into the cell. If the temperature exceeds 2500 K or the spark duration is exceeded, no energy from the spark model will be added to the spark cells. The spark model can be used in models other than the premixed and partially premixed combustion models, however, you must balance energy input and diffusivity to produce a high enough temperature to initiate combustion, which can be a nontrivial undertaking. The model’s use has been extended to be compatible with the other models, however, in some cases it simply creates a high temperature region and does not guarantee the initiation of combustion.
12.2 Autoignition Models Autoignition phenomena in engines are due to the effects of chemical kinetics of the reacting flow inside the cylinder. There are two types of autoignition models considered in ANSYS FLUENT:
• knock model in spark-ignited (SI) engines
• ignition delay model in diesel engines
For information regarding using autoignition models, see Section 20.2: Autoignition Models in the separate User’s Guide. The theory behind the autoignition models is described in the following sections:
• Section 12.2.1: Overview and Limitations
• Section 12.2.2: Ignition Model Theory
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12.2.1 Overview and Limitations Overview The concept of knock has been studied extensively in the context of premixed engines, as it defines a limit in terms of efficiency and power production of that type of engine. As the compression ratio increases, the efficiency of the engine as a function of the work extracted from the fuel increases. However, as the compression ratio increases, the temperature and pressure of the air/fuel mixture in the cylinder also increase during the cycle compressions. The temperature and pressure increase can be large enough for the mixture to spontaneously ignite and release its heat before the spark plug fires. The premature release of all of the energy in the air/fuel charge is almost never desirable, as this results in the spark event no longer controlling the combustion. As a result of the premature release of the energy, catastrophic damage to the engine components can occur. The sudden, sharp rise in pressure inside the engine can be heard clearly through the engine block as a knocking sound, hence the term “knock”. For commonly available gasoline pumps, knock usually limits the highest practical compression ratio to less than 11:1 for premium fuels and around 9:1 for less expensive fuels. By comparison, ignition delay in diesel engines has not been as extensively studied as SI engines, mainly because it does not have such a sharply defining impact on engine efficiency. Ignition delay in diesel engines refers to the time between when the fuel is injected into the combustion chamber and when the pressure starts to increase as the fuel releases its energy. The fuel is injected into a gas which is usually air, however, it can have a considerable amount of exhaust gas mixed in (or EGR) to reduce nitrogen oxide emissions (NOx). Ignition delay depends on the composition of the gas in the cylinder, the temperature of the gas, the turbulence level, and other factors. Since ignition delay changes the combustion phasing, which in turn impacts efficiency and emissions, it is important to account for it in a diesel engine simulation.
Model Limitations The main difference between the knock model and the ignition delay model is the manner in which the model is coupled with the chemistry. The knock model always releases energy from the fuel while the ignition delay model prevents energy from being released prematurely. The knock model in ANSYS FLUENT is compatible with the premixed and partially premixed combustion models. The autoignition model is compatible with any volumetric combustion model, with the exception of the purely premixed models. The autoignition models are inherently transient and so are not available with steady simulations.
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The autoignition models in general require adjustment of parameters to reproduce engine data and are likely to require tuning to improve accuracy. Once the model is calibrated to a particular engine configuration, then different engine speeds and loads can be reasonably well represented. Detailed chemical kinetics may be more applicable over a wider range of conditions, though are more expensive to solve. The single equation autoignition models are appropriate for the situation where geometric fidelity or resolution of particular flow details is more important than chemical effects on the simulation.
12.2.2 Ignition Model Theory Both the knock and the ignition delay models are treated similarly in ANSYS FLUENT, in that they share the same infrastructure. These models belong to the family of sin- gle equation autoignition models and use correlations to account for complex chemical kinetics. They differ from the eight step reaction models, such as Halstead’s “Shell” model [121], in that only a single transport equation is solved. The source term in the transport equation is typically not stiff, thus making the equation relatively inexpensive to solve. This approach is appropriate for large simulations where geometric accuracy is more im- portant than fully resolved chemical kinetics. The model can be used on less resolved meshes to explore a range of designs quickly, and to obtain trends before utilizing more expensive and presumably more accurate chemical mechanisms in multidimensional sim- ulations.
Transport of Ignition Species
Autoignition is modeled using the transport equation for an Ignition Species, Yig, which is given by
∂ρYig µt + ∇ · (ρ~vYig) = ∇ · ∇Yig + ρSig (12.2-1) ∂t Sct where Yig is a “mass fraction” of a passive species representing radicals which form when the fuel in the domain breaks down. Sct is the turbulent Schmidt number. The term Sig is the source term for the ignition species which has a form
Z t dt Sig = t=t0 τig where t0 corresponds to the time at which fuel is introduced into the domain. The τig term is a correlation of ignition delay with the units of time. Ignition has occurred when the ignition species reaches a value of 1 in the domain. It is assumed that all the radical species represented by Yig diffuse at the same rate as the mean flow.
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Note that the source term for these radical species is treated differently for knock and ignition delay. Furthermore, the form of the correlation of ignition delay differs between the two models. Details of how the source term is treated are covered in the following sections.
Knock Modeling When modeling knock or ignition delay, chemical energy in the fuel is released when the ignition species reaches a value of 1 in the domain. For the knock model, two correlations are built into ANSYS FLUENT. One is given by Douaud [76], while the other is a generalized model which reproduces several correlations, given by Heywood [128].
Modeling of the Source Term
In order to model knock in a physically realistic manner, the source term is accumu- lated under appropriate conditions in a cell. Consider the one dimensional flame in Figure 12.2.1. Here, the flame is propagating from left to right, and the temperature is relatively low in front of the flame and high behind the flame. In this figure, Tb and Tu represent the temperatures at the burned and unburned states, respectively. The ignition species accumulates only when there is fuel. In the premixed model, the fuel is defined as fuel = 1 − c, where c is the progress variable. If the progress variable has a value of zero, the mixture is considered unburned. If the progress variable is 1, then the mixture is considered burned.
T 6
Tb fuel = 0 ¤ fuel > 0 Sig = 0 Sig > 0
- Tu ¦ - X Figure 12.2.1: Flame Front Showing Accumulation of Source Terms for the Knock Model
When the ignition species reaches a value of 1 in the domain, knock has occurred at that point. The value of the ignition species can exceed unity. In fact, values well above that can be obtained in a short time. The ignition species will continue to accumulate until there is no more fuel present.
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Correlations
An extensively tested correlation for knock in SI engines is given by Douaud and Eyzat [76]:
ON 3.402 3800 τ = 0.01768 p−1.7 exp (12.2-2) 100 T where ON is the octane number of the fuel, p is the absolute pressure in atmospheres and T is the temperature in Kelvin. A generalized expression for τ is also available which can reproduce many existing Ar- rhenius correlations. The form of the correlation is
ON a −E τ = A pbT cRPMdΦd exp a (12.2-3) 100 RT where A is the pre-exponential (with units in seconds), RPM is the engine speed in cycles per minute and Φ is the fuel/air equivalence ratio.
Energy Release
Once ignition has occurred in the domain, the knock event is modeled by releasing the remaining fuel energy with a single-step Arrhenius reaction. An additional source term, which burns the remaining fuel in that cell, is added to the rate term in the premixed model. The reaction rate is given by
−E ω˙ = A exp a (12.2-4) 0 RT
9 where A0 = 8.6 × 10 , and Ea = −15078. These values are chosen to reflect single-step reaction rates appropriate for propane as described in Amsden [4]. The rate at which the fuel is consumed is limited such that a completely unburned cell will burn during three of the current time steps. Limiting the reaction rate is done purely for numerical stability.
Ignition Delay Modeling When modeling ignition delay in diesel engines, chemical reactions are allowed to occur when the ignition species reaches a value of 1 in the domain. For the ignition delay model, two correlations are built into ANSYS FLUENT, one given by Hardenburg and Hase [125] and the other, a generalized model which reproduces several Arrhenius correlations from the literature.
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If the ignition species is less than 1 when using the ignition delay model, the chemical source term is suppressed by not activating the combustion model at that particular time step; thus, the energy release is delayed. This approach is reasonable if you have a good high-temperature chemical model, but does not wish to solve for typically expensive low temperature chemistry.
Modeling of the Source Term
In order to model ignition in a physically realistic manner, the source term is accumulated under appropriate conditions in a cell. Consider the one dimensional spray in Figure 12.2.2. Here, the spray is propagating from left to right and the fuel mass fraction is
6 Yfuel
fuel > 0 ¤ fuel = 0 Sig > 0 Sig = 0
- ¦ - X Figure 12.2.2: Propagating Fuel Cloud Showing Accumulation of Source Terms for the Ignition Delay Model
relatively low in front of the spray and high behind the spray. If there is no fuel in the cell, the model will set the local source term to zero, nevertheless, the value of Yig can be nonzero due to convection and diffusion.
Correlations
If fuel is present in the cell, there are two built-in options in ANSYS FLUENT to calculate the local source term. The first correlation was done by Hardenburg and Hase and was developed at Daimler Chrysler for heavy duty diesel engines. The correlation works over a reasonably wide range of conditions and is given by
C + 0.22S ! " 1 1 ! 21.2 !ep # τ = 1 p exp E − + (12.2-5) id 6N a RT 17, 190 p − 12.4
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where τid is in seconds, C1 is 0.36, N is engine speed in revolutions per minute, Ea is the effective activation energy and ep is the pressure exponent. The expression for the effective activation energy is given by
E E = hh (12.2-6) a CN + 25
where CN is the cetane number. The activation energy, Ehh, pre-exponential, C1, pres- sure exponent, ep, and cetane number, CN, are accessible from the GUI. The default values of these variables are listed in the table below.
Table 12.2.1: Default Values of the Variables in the Hardenburg Correlation
Variable Ehh CN C1 ep Default 618,840 25 0.36 0.63
The second correlation, which is the generalized correlation, is given by Equation 12.2-3 and is available for ignition delay calculations.
Energy Release
If the ignition species is greater than or equal to 1 anywhere in the domain, ignition has occurred and combustion is no longer delayed. The ignition species acts as a switch to turn on the volumetric reactions in the domain. Note that the ignition species “mass fraction” can exceed 1 in the domain, therefore, it is not truly a mass fraction, but rather a passive scalar which represents the integrated correlation as a function of time.
12.3 Crevice Model This section describes the theory behind the crevice model. Information can be found in the following sections:
• Section 12.3.1: Overview
• Section 12.3.2: Limitations
• Section 12.3.3: Crevice Model Theory
For information regarding using the crevice model, see Section 20.3: Crevice Model in the separate User’s Guide.
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12.3.1 Overview The crevice model implemented in ANSYS FLUENT is a zero-dimensional ring-flow model based on the model outlined in Namazian and Heywood [245] and Roberts and Matthews [295]. The model is geared toward in-cylinder specific flows, and more specifically, direct- injection (DI) diesel engines, and thus is available only for time-dependent simulations. The model takes mass, momentum, and energy from cells adjoining two boundaries and accounts for the storage of mass in the volumes of the crevices in the piston. Detailed geometric information regarding the ring and piston—typically a ring pack around the bore of an engine—is necessary to use the crevice model. An example representation is shown in Figures 12.3.1–12.3.3.
Cylinder Land length wall 1 p 0
Ring spacing 2
3
1: Top gap 2: Middle gap Piston to bore 3: Bottom gap clearance p 6
Figure 12.3.1: Crevice Model Geometry (Piston)
Wr Tr
Figure 12.3.2: Crevice Model Geometry (Ring)
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p = cylinder pressure p • 0 Ring 1 1• • p 2 Ring 2 p • 3 • p 4 Ring 3 p • 5 • p = crankcase pressure 6
Figure 12.3.3: Crevice Model “Network” Representation
Model Parameters • The piston to bore clearance is the distance between the piston and the bore. Typ- ical values are 2 to 5 mil (80 to 120 µm) in a spark engine (SI) and 4 to 7 mil (100 to 240 µm) in some diesel engines (DI).
• The ring thickness is the variable Tr in Figure 12.3.2. Typical values range from 1 to 3 mm for SI engines and 2 to 4 mm for DI engines.
• The ring width is the variable Wr in Figure 12.3.2. Typical values range from 3 to 3.5 mm for SI engines and 4 to 6 mm for DI diesel engines.
• The ring spacing is the distance between the bottom of one ring land and the top of the next ring land. Typical values of the ring spacing are 3 to 5 mm for SI engines and 4 to 8 mm for DI diesel engines.
• The land length is the depth of the ring land (i.e., the cutout into the piston); always deeper than the width of the ring by about 1 mm. Typical values are 4 to 4.5 mm for SI engines and 5 to 7 mm for DI diesel engines.
• The top gap is the clearance between the ring land and the top of the ring (40 to 80 µm).
• The middle gap is the distance between the ring and the bore (10 to 40 µm).
• The bottom gap is the clearance between the ring land and the bottom of the ring (40 to 80 µm).
• The shared boundary and leaking wall is the piston (e.g., wall-8) and the cylinder wall (e.g., wall.1) in most in-cylinder simulations. Cells that share a boundary with the top of the piston and the cylinder wall are defined as the crevice cells.
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The ring pack is the set of rings that seal the piston in the cylinder bore. As the piston moves upward in the cylinder when the valves are closed (e.g., during the compression stroke in a four-stroke cycle engine), the pressure in the cylinder rises and flow begins to move past the rings. The pressure distribution in the ring pack is modeled by assuming either fully-developed compressible flow through the spaces between the rings and the piston, or choked compressible flow between the rings and the cylinder wall. Since the temperature in the ring pack is fixed and the geometry is known, once a pressure distribution is calculated, the mass in each volume can be found using the ideal gas equation of state. The overall mass flow out of the ring pack (i.e., the flow past the last ring specified) is also calculated at each discrete step in the ANSYS FLUENT solution.
12.3.2 Limitations The limitations of the crevice model are that it is zero dimensional, transient, and cur- rently limited to two threads that share a boundary. A zero-dimensional approach is used because it is difficult to accurately predict lateral diffusion of species in the crevice. If the lateral diffusion of species is important in the simulation, as in when a spray plume in a DI engine is in close proximity to the boundary and the net mass flow is into the crevice, it is recommended that the full multidimensional crevice geometry be simulated in ANSYS FLUENT using a nonconformal mesh. Additionally, this approach does not specifically track individual species, as any individual species would be instantly distributed over the entire ring pack. The mass flux into the domain from the crevice is assumed to have the same composition as the cell into which mass is flowing. The formulation of the crevice flow equations is inherently transient and is solved using ANSYS FLUENT’s stiff-equation solver. A steady problem with leakage flow can be solved by running the transient problem to steady state. Additional limitations of the crevice model in its current form are that only a single crevice is allowed and only one thread can have leakage. Ring dynamics are not explicitly accounted for, although ring positions can be set during the simulation. In this context, the crevice model solution is a stiff initial boundary-value problem. The stiffness increases as the pressure difference between the ring crevices increases and also as the overall pressure difference across the ring pack increases. Thus, if the initial conditions are very far from the solution during a time step, the ODE solver may not be able to integrate the equations successfully. One solution to this problem is to decrease the flow time step for several iterations. Another solution is to start with initial conditions that are closer to the solution at the end of the time step.
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12.3.3 Crevice Model Theory ANSYS FLUENT solves the equations for mass conservation in the crevice geometry by assuming laminar compressible flow in the region between the piston and the top and bottom faces of the ring, and by assuming an orifice flow between the ring and the cylinder wall. The equation for the mass flow through the ring end gaps is of the form
m˙ ij = CdAijρcηij (12.3-1) where Cd is the discharge coefficient, Aij is the gap area, ρ is the gas density, c is the local speed of sound, and ηij is a compressibility factor given by
" #0.5 2 γ−1 2 pi γ pi γ pi γ−1 p − p p > 0.52 j j j ηij = (12.3-2) γ+1 2(γ−1) 2 pi ≤ 0.52 γ−1 pj where γ is the ratio of specific heats, pi the upstream pressure and pj the downstream pressure. The equation for the mass flow through the top and bottom faces of the ring (i.e., into and out of the volume behind the piston ring) is given by
2 2 2 hij pi − pj Aij m˙ ij = (12.3-3) 24WrµgasRT where hij is the cross-sectional area of the gap, Wr is the width of the ring along which the gas is flowing, µgas is the local gas viscosity, T is the temperature of the gas and R is the universal gas constant. The system of equations for a set of three rings is of the following form:
dp1 p1 = (m ˙ 01 − m˙ 12) (12.3-4) dt m1 dp2 p2 = (m ˙ 02 +m ˙ 12 − m˙ 23 − m˙ 24) (12.3-5) dt m2 dp3 p3 = (m ˙ 23 − m˙ 34) (12.3-6) dt m3 dp4 p4 = (m ˙ 24 +m ˙ 34 − m˙ 45 − m˙ 46) (12.3-7) dt m4 dp5 p5 = (m ˙ 45 − m˙ 56) (12.3-8) dt m5
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where p0 is the average pressure in the crevice cells and p6 is the crankcase pressure input from the text interface. The expressions for the mass flows for numerically adjacent zones (e.g., 0-1, 1-2, 2-3, etc.) are given by Equation 12.3-3 and expressions for the mass flows for zones separated by two integers (e.g., 0-2, 2-4, 4-6) are given by Equations 12.3-1 and 12.3-2. Thus, there are 2nr − 1 equations needed for the solution to the ring-pack equations, where nr is the number of rings in the simulation.
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