Numerical Modeling of Diesel Spray Formation and Combustion C ...

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1D Euler-Euler Spray Model The 1D quasi steady spray model of Versaevel et al. [21] is an extension of the earlier efforts of Naber et al. [11] and Siebers [15]. Naber and Siebers developed a 1D model for non-vaporizing spray penetration first, and later Siebers added some thermodynamics to distinguish liquid penetration from vapor penetration. But Siebers’ contribution is based on the assumption that only at the steady liquid length position thermodynamic equilibrium exists. This approach implies that no temperature information is available, except at the liquid length position. Also the composition of the spray volume between the nozzle exit and liquid length is unknown. Versaevel et al. overcame this shortcoming by introducing a void fraction m that couples the mass, momentum and energy equations. The model is based on five basic assumptions from which the first four are the same as in the work of Naber et al. [11] and Siebers [15]. ⇒ no velocity slip between gas and liquid phases ⇒ whole system at constant pressure ⇒ uniform velocity, density and temperature profiles ⇒ constant spray angle ⇒ whole system at thermodynamic equilibrium The last assumption is necessary to gain information about the temperature and composition of the spray in the entire 1D domain. The mass, momentum and energy equations are derived by considering a control volume as defined in Figure 1. The spray is described in one direction due to the constant angle and the axisymmetry. The figure shows that from fuel injection ( ˙mfl,0) into the xdirection the spray diverges due to air entrainment ( ˙ma) into the spray volume. Air entrainment is controlled by the prescribed spray angle ( θ 2 ). For this purpose an experimental dispersion relation is chosen. At the liquid length just enough hot air is entrained into the spray to evaporate all liquid fuel, so from that point on the fuel penetrates the surrounding gas as a vapor. The phenomenological spray model is implemented in Matlab. The standard non-linear solver of Matlab is used for this purpose. Material properties, except the liquid fuel . mfl,0 . ma . ma control volume /2 d eff gas and liquid gas only Figure 1: Definition of the control volume used in the derivation of the 1D model [21] df x 2 density, are temperature dependent, and are obtained from the thermophysical database of DIPPR [6]. The calculated spray length compares good with IFP measurements [20] as shown in Figure 2, indicated with the solid en dotted lines, respectively. SL [mm] 50 45 40 35 30 25 20 15 case: IFP heptane 10 5 3D model Fluent DPM 1D model fit through IFP measurements 0 0 0.1 0.2 0.3 0.4 0.5 Time [ms] 0.6 0.7 0.8 0.9 1 Figure 2: Spray length as function of time with the Euler-Euler 3D model, compared to Fluent DPM, Euler-Euler 1D model and IFP measurement 3D Spray Simulation The 1D phenomenological spray model discussed in the previous section is, in contrary to the earlier model of Naber and Siebers, suitable to apply in combination with a 3D CFD code. To accomplish such an interaction, source terms are extracted from the 1D model and are assigned to the corresponding transport equations in Fluent (see [3] for the details). Subsequently the combined model is validated through spray length comparison with experimental data. IFP [20] and Sandia [15][7] measurements are used for validation purposes. These are all for single component fuels that are well documented, so thermophysical data needed for the numerical model is found in literature. The implemented 3D model (circles) predicts the spray length better than Fluent’s DPM model (stars), as is shown in Figure 2. The correctness of the 3D model prediction is best visualized with the contours of fuel mass fraction at the spray cross-section shown in Figure 3. The upper spray is a DPM simulation result and the other one is gained with the 3D model, both at 1 ms. Apart from the obvious spray length difference, the shape/width of the sprays are also dissimilar. DPM gives too wide sprays, since relatively large cells have to be used to meet the requirements of the Lagrangian approach. In the 3D Euler- Euler case one can refine the grid until the spray is resolved sufficiently, without having discrete phase related problems. Summarizing, the better overall performance (spray length and shape) and the proper mesh resolution behavior (higher resolution gives better solutions) of the 3D Euler-Euler model, together with the ability to parallelize is a major advantage compared with Fluent’s DPM model. Since the DPM model uses only one CPU to do all discrete
Figure 3: Case: IFP heptane. Contours of fuel mass fraction gained with Fluent’s DPM model and the implemented 3D spray model. Note the minimum/maximum values between the brackets at the right hand side, the colorbar is scaled for each separately phase calculations no matter how many CPUs are available. The consequence is large computation times despite the relatively small amount of cells. Possible improvements to the 1D/3D spray model for the future may be the following: ⇒ Make 3D spray model pressure dependent in order to simulate spray formation in a variabele volume combustion chamber. ⇒ Sound spray angle prediction. Not really an improvement to the model itself, but spray angle prediction certainly has a large effect on the final results. Therefore the quest for proper and generic angle prediction methods/relations should be promoted. Combustion Modeling In the preceding chapters a 3D Euler-Euler spray model is implemented and validated for evaporating inert fuel sprays. This model is mesh and solver timestep independent, and is suitable for parallel simulations. So, regarding the status of modeling the mixing process, additional modeling features, which may require fine spatial and time resolutions, can be included. In this chapter an attempt is made to add combustion, more specific, the emphasis is on the application of FGMs (Flamelet Generated Manifolds) in modeling of the turbulent combustion of a transient igniting spray. In the following, first the principle of flamelets and its use for modeling combustion with tabulated chemistry is shortly mentioned. Then, the procedure of a FGM generation is shown. Subsequently, its implementation into Fluent is described. FGM Approach Detailed models can be very accurate, but unfortunately also computationally very expensive. To overcome 3 the impractical computing times, while solving the combustion process still with high detail (depends on used reaction scheme), an approach with tabulated chemistry is applied. This so-called FGM approach is developed by van Oijen [19] for laminar premixed flames, and makes use of 1D laminar flamelet data to tabulate composition, density, temperature etc. as function of local control variables. However, the flamelet concept views a turbulent flame as an ensemble of thin, laminar, locally 1D flames, called flamelets, embedded within the turbulent flow field. Furthermore, the concept is based on the assumption that the smallest turbulent time and length scales are much larger than the chemical ones, and there exists a locally undisturbed sheet where chemical reactions occur [16]. So, later Ramaekers [13] extended the application to turbulent partially-premixed combustion by choosing one control variable describing non-premixed (mixture fraction Z) and one describing premixed (reaction progress variable P V ) combustion, and by PDF (Probability Density Function) integration to account for turbulence. In this study non-premixed flamelets for a counterflow setup are solved with CHEM1D [1], which is a specialized one-dimensional laminar flame code developed at the Eindhoven University of Technology. A heptane flamelet database at constant pressure is calculated, making use of a reduced n-heptane mechanism [12]. In non-premixed combustion it is common practice to introduce the mixture fraction Z, here the definition of Bilger [4] is adopted: Z = 2 YC−YC,2 MC 2 YC,1−YC,2 MC 1 + YH −YH,2 (YO−YO,2) 2 − MH MO + 1 YH,1−YH,2 2 − MH YO,1−YO,2 MO , (1) where Y stands for mass fraction, M is the molar mass and the subscripts C, H and O indicate the quantities for the elements carbon, hydrogen and oxygen, respectively. The subscripts 1 and 2 refer to the constant mass fraction in the original fuel and oxidizer streams, respectively. In the fuel stream the mixture fraction is equal to unity and monotonically decreases to zero at the oxidizer stream. An additional control variable, called the reaction progress variable P V , is introduced to parameterize the progress of the irreversible combustion process. In this study a combination of CO2, CO and CH2O mass fractions is chosen as a reaction progress variable: P V = YCO2 MCO2 + YCO + MCO YCH2O . (2) MCH2O The succes of this concept is related to the fact that all occurring compositions tend to have a common, low-dimensional, attractor in composition space, a socalled intrinsic low-dimensional manifold (ILDM) [9]. Hence, the complex chemistry is reduced and completely described by the mixture fraction Z and the reaction progress variable P V . FGM Construction and Implementation FGMs can be generated in many ways. For stationary flames, there is a classical way with steady flamelets only,
Page 1: Numerical Modeling of Diesel Spray
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Numerical Modeling of Diesel Spray Formation and Combustion C ...

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