chp19

19.1
Spark Model
The spark model in FLUENT will be described in the context of the premixed turbulent combustion model. Information regarding the theory and use of this model is detailed in the following sections: • Section 19.1.1: Overview and Limitations • Section 19.1.2: Spark Model Theory • Section 19.1.3: Using the Spark Model
19-2
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19.1 Spark Model
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 user, and has a default value of 1e-5 seconds.
where κ is the laminar thermal diffusivity and the effective diffusivity Dtt is given by Dt 1 − exp Dt
−ttd τ
Dtt =
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if ttd ≥ 0 if ttd < 0
(19.1-3)
where is ttd = t − tig and tig denotes the time at which the spark is initiated. Additionally, τ is an effective diffusion time, set by the user.
19.1.2
Spark Model Theory
The spark model in FLUENT is based on the work done by Lipatnikov [215] and extended to other combustion models. The derivation of the model can be done in the context of the Zimont premixed combustion model.
Other Combustion Models
The spark model is compatible with all combustion models in 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, the user 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.
19.1.1
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 multidimensional 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 [140]). Thus, for situations in which FLUENT is utilized for combustion engine modeling, including internal combustion engines, the spark event does not need to be modeled in great detail, but simply as the initiation of combustion over a duration set by the user.
Zimont Premixed Flame Model
The transport equation for the mean reaction progress variable, c, is given by Equation 19.1-1 ∂ρc + ∇ · (ρvc) = ∇ · (Dt ∇c) + ρu Ut |∇c| ∂t (19.1-1)
c Fluent Inc. September 29, 2006
19-1
Modeling Engine Ignition
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 FLUENT is based on a one-dimensional analysis by Lipatnikov [215]. 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 grid 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.
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 grid size of the model and is often laminar in nature, the Zimont model is modified such that ∂ρc + ∇ · (ρvc) = ∇ · ((κ + Dtt )∇c) + ρu Ut |∇c| ∂t (19.1-2)
Chapter 19.
Modeling Engine Ignition
This chapter discusses the engine ignition models available in FLUENT in the following sections: • Section 19.1: Spark Model • Section 19.2: Autoignition Models • Section 19.3: Crevice Model