International Multidimensional Engine Modeling User s Group Meeting April 7, 24, Detroit, Michigan, USA An extended CMC model for the simulation of diesel engines with multiple injections Michele Bolla, Nicolò Frapolli, Yuri M. Wright and Konstantinos Boulouchos Swiss Federal Institute of Technology, ETH Zurich In this study, a model capable of accounting for an arbitrary number of temporally separated multiple-injections in a diesel engine is presented based on the conditional moment closure (CMC) model with a single total mixture fraction (MFT). It consists of a sequential two-feed system and not of a three-feed system. The model is subsequently validated by means of different post-injection strategies in an optically accessible heavy-duty diesel engine. Simulation results have been compared with experimental data by means of apparent heat release rates (AHRR). The model was found to reproduce very well the influence of injection dwells on AHRR. Overall, the proposed model represents a cost-efficient variant demonstrated to achieve very good results for diesel engines operated with multipleinjections. Introduction Modern diesel engines are routinely equipped with common rail injection systems allowing for high pressure and very flexible injection scheduling and it is nowadays common practice to employ multiple injection strategies (pilot, main and post injection). With the application of multiple injections, the interaction between fuel streams augments the pre-existing modeling challenges for single injection diesel engines w.r.t. the understanding of incylinder processes and towards supporting development of modern internal combustion engines. Different combustion models have been proposed for the simulation of multiple injections in engines such as the perfectly stirred reactor (PSR) e.g. [], the characteristic time-scales combustion (CTC) model [2, 3], the partially stirred reactor (PaSR) e.g. [4] and the 2D flamelet model [5]. The PSR, PaSR and CTC models do not require additional modeling for multiple injections and simulation is straightforward. For more elaborate models such as Representative Interactive Flamelets (RIF) or CMC which are based on mixture fraction (MF), the complexity of the model is considerably increased, since two different MF are needed for the description of the two distinct fuel streams. While the first fuel stream exhibits a classical autoignition process, the following fuel streams undergo autoignition but are additionally subject to strong interaction with the preceding streams, which may lead to a forced ignition upon contact in the case of an established flame. This study hence seeks to develop an extension of a well-established CMC model for single injections (cf. e.g. [6]), which is able to account for multiple injections using a single, total mixture fraction as the conditioning scalar. This is supported by findings from [5, 7-9] reporting a rapid transition in 2D flamelet space along the overall stoichiometric mixture leading to a quasi-d structure in the MFT coordinate. Validation of the proposed approach is performed by means of data from a heavy-duty single cylinder engine for several post injection dwell times. 2 Experimental setup Experimental data available from the optically accessible heavy-duty diesel engine installed at Sandia National Laboratories [] has been used for model validation. The measurements were obtained on a single-cylinder, common-rail, direct-injection heavy-duty diesel engine based on a Cummins N-series with 39.7 mm bore and 2.34 liters displacement. The main specifications of the engine and injector are summarized in Table. To minimize thermal loading the engine was operated skip fired where every tenth cycle was fired. The injector has eight equally spaced orifices with a nominal diameter of.96 mm. An ultra-low sulphur diesel fuel was employed. Optical access is provided by an extended piston and a flat piston-crown window for signal collection as well as windows located around the top of the cylinder-wall for laser-based imaging diagnostics. For a detailed description of the engine specifications and diagnostics employed the reader is referred to [] and references therein.
Table : Engine specifications In this study, cases reported in [2] have been considered. The impact of the injection dwell time of the post injection has been studied. The configuration of the main injection was kept unvaried with start of injection (SOI) SOI=-8 crank angle (CA), a duration of injection (DOI) of 6 CA. Different SOI of the post injection have been considered with SOI2 ranging between 8 and 4 CA. Quantities used for model validation are AHRR. All cases were operated at an engine speed of 2RPM, ambient oxygen mole fraction of 2.6% and a nominal ambient temperature and density at top dead center (TDC) of 95K and 4 kg/m 3. 3 Numerical methodology 3. Flow field solver Engine type base Cummins N-4, Diesel Swirl ratio.5 Bore x Stroke [mm] 39.7 x52.4 Bowl width, depth [mm] 97.8, 5.5 Displacement [L] 2.34 Geometric compression ratio.2 Fuel injector type Common rail Fuel Diesel #2 Number of holes 8, equally spaced Spray included angle 52 Nozzle orifice diameter [mm].5 Nozzle orifice L/D 5 Numerical simulations have been carried out with the flow field solver STAR-CD v4.6 [3], a fullycompressible finite-volume code for unstructured grids with time-varying geometries. A PISO based algorithm was employed with a constant time step from SOI of.2 CA corresponding to 2.8x -6 s. An unsteady RANS approach with two-equation k-ε turbulence model was adopted. The liquid phase of the spray was treated with a Lagrangian approach for which details can be found in [6, 3]. The measured injection mass flow rate has been imposed for the simulation. A 45 degrees sector mesh has been considered, as the injector has eight equally spaced orifices. The CFD resolution in the piston bowl is around mm 3 resulting in 5, cells at TDC. In the sweep volume a cell size with.3mm in axial direction is considered resulting in 24, cells at bottom dead center (BDC). Unconditional species mass fractions are returned to the flow field solver by convoluting the conditional quantities with a presumed beta-pdf. The latter is governed by the mean MF and mixture fraction variance (MFV), for which transport equations are solved. The mean scalar dissipation rate is modeled using turbulence 2 quantities, i.e. the turbulent kinetic energy, k, and the eddy dissipation rate, ε, as c, with c χ = 2.. k Figure : Mesh of engine geometry at top dead centre. In black is the CFD grid with the CMC grid overlaid in red. 2
3.2 CMC formulation for single injection In CMC for non-premixed combustion the gas-phase MF is used as conditional quantity. Transport equations are solved for conditionally averaged reactive scalars and temperature. A detailed derivation of the CMC governing equations is given in [4] and is not repeated here. The reader is referred to [6] for details concerning governing equations and sub-models for the various terms. Conditional chemical source terms due to reaction are closed at first order using the reduced n-heptane chemistry from [5] consisting of 22 solved species and 8 chemical reactions. A two-dimensional formulation denoted 2D-CMC is followed here in which cells in azimuthal direction are collapsed. In the piston bowl a x 2 mm CMC resolution is considered (axially x radially), resulting in 35 x 3 CMC nodes at TDC. 3.3 CMC formulation for multiple injections The main idea is to transform the original temperature and composition conditional on MF into representative profiles that are conditional on MFT. The spatial resolution of CMC allows for a detailed determination of the time and location of contact between fuel streams as well as their local conditions. Using this localised information, the model is based on a re-initialization of the conditional temperature and composition in every CMC cell at the time of first MF appearance from the second fuel stream. In order to reconstruct a representative temperature conditioned on MFT two fundamental assumptions are introduced: ) at the time of first MF2 appearance into a CMC cell, MF as well as MFV tends to decrease due to convection-diffusion effects and due to the absence of a MF source. This implies a temporal separation of MF and MF2 sources at a given position. 2) when the second fuel stream enters a cell, the increase in MFT is attributed to MF2 only. For the reconstruction of the re-initialized conditional temperature at a given MF, the left domain of the local MF is retained and a vertical line along MF2 is drawn corresponding to adiabatic mixing of the local MF with T η η, for the new coming MF2 assumed to be the unique MFT source. The new temperature profile,, a pre-existingη can be described by the following expression: Double tot ( ) ( ) ( ) TDouble η, ηtot = Tη η tot H ηtot H ηtot η + TMix ηtot H ηtot η () where ηtot is MFT, η is the local MF, ( ) H η is the Heaviside step function, T η η tot is the original temperature profile before re-initialization and TMix η tot is the mixing temperature obtained following the coordinate for a constant on the double conditioned temperature distribution. The probability to encounter a given MF in a CMC cell is assumed to be the current MF PDF. The new temperature profile conditional on MFT, TNew η tot, is computed considering the marginal PDF for MF, ( ) P ξ ξ η η, to be approximated as ( ) of MF2. It follows: P ξ η due to the instantaneous initialization and the consequently absence T η = T η, η P η dη (2) ( ) New tot Double tot ξ The final solution at the CFD resolution relies on conditional expectations of quantities as typical in the CMC framework, obtained by the convolution of the new profile resulting after re-initialization or its time evolution, and the total MF PDF. The effect of the localized initialization is then transported in physical as well as conserved scalar space, as is the case for the single injection CMC method. Note that the number of subsequent injections is not limited; in fact it is sufficient to re-initialize the profiles every time that fuel coming from a new injection enters into a CMC cell. 3
4 Results and Discussion 4. Spatial distribution of mean quantities Figure 2 illustrates the temporal evolution of mean MFT (left), mean temperature (middle) and mean soot volume fraction (right) in the vertical section across the nominal injector axis for SOI2=2 CA. The effective start and end of the second fuel injection are 5.5 and 9 CA, respectively. The contribution of the second fuel stream to the MFT is clearly visible by the rich region propagating downstream from the injection location; strong evaporation is visible in the temperature distribution in this area. The MF field from the first injection event has undergone significant mixing and exhibits considerably lower values which are located primarily close to the bowl edge and rim. The flow field plays a major role for the ignition of the post injection, which ignites when it interacts with the pre-existent high temperature region from the first fuel stream. As expected, ignition takes place at the tip of the second fuel stream where MF is higher. MF [ ] T [K] FvS [ppmv] 5 7 9 2 23 25.2 9 25 4 Figure 2: Spatial distribution of mean total mixture fraction (left), mean temperature (middle) and mean soot volume fraction (right) in a vertical section through the injector axis at five time instants (top to bottom, times in CA equivalent in brackets on the leftmost images). Black iso-lines denote stoichiometric contour. The new soot is mainly formed at the tip of the post injection due to the high temperature and fuel rich conditions. The decrease of soot originated from the first injection is due to a combination of oxidation and swirl. The latter deviates the peak soot concentration from the nominal vertical plain shown here. 4.2 Comparison of the apparent heat release rate Figure 3 shows AHRR with the main injection only (black) and with post injection at 8, 6, 24, 32 and 4 CA. Experimental and simulation results are drawn with dashed and solid lines, respectively. Injection profiles are shown at the bottom of the figure. The simulation reproduces very well the AHRR for the test case without post injection. The split between premixed and diffusion burn is in excellent agreement, being consistent with previous single injection test cases at the same test facility [6, 6]. This good agreement further confirms that the initial conditions for the second injection are appropriately predicted. The ignition delays as well as the subsequent AHRR evolutions are well reproduced for all five different dwell times investigated. 4
3 AHRR [J/ CA] 25 2 5 5 8 6 24 32 4 5 No post 2 2 4 6 8 Crank angle [ ATDC] Figure 3: Apparent heat release rates with main only (black) and post injection at 8, 6, 24, 32 and 4 CA. Experiment dashed, simulation solid lines. Fuel injection profiles are drawn below. 5 Conclusions In this study, a model capable of accounting for an arbitrary number of temporally separated multiple injections in a diesel engine based on the conditional moment closure (CMC) method has been presented and successfully tested with post injection cases from an optically accessible heavy-duty diesel engine. The problem configuration is described as a sequential two-feed system and not a three-feed system, i.e. species and temperature are conditioned on the total mixture fraction only. It was shown that the model extension is capable of accurately predicting ignition delays of the second injected fuel spray. Ignition of the second fuel stream is triggered through interaction with the first fuel stream and rapid flame propagation along overall stoichiometric mixture is observed, consistent with observations from studies using two-dimensional flamelets. Comparison of apparent heat release rates showed very good agreement for all dwell times. 6 Acknowledgements Financial support from the Swiss Federal Office of Energy (grant SI/588-) and project HERCULES-C (EC FP7-Program) is gratefully acknowledged. The authors thank Dr. M.P.B. Musculus and Dr. M.K. Bobba for helpful discussions and providing data. 7 References [] Y. Sun and R. D. Reitz, "Modeling Diesel Engine NOx and Soot Reduction with Optimized Two-Stage Combustion," SAE 26--27, 26. [2] G. D Errico, et al., "Application of the CTC Model to Predict Combustion and Pollutant Emissions in a Common-Rail Diesel Engine Operating with Multiple Injections and High EGR," SAE 22--54, 22. [3] C. Chryssakis, et al., "Effect of Multiple Injection on Fuel-Air Mixing and Soot Formation in Diesel Combusion Using Flame Visualization and CFD Techniques," Proc. ASME ICES25-6, 25. [4] R. Ehleskog, et al., "Experimental and Numerical Investigation of Split Injection at Low Load in an HDDI Diesel Engine Equipped with a Piezo Injector," SAE 26--3433, 26. [5] C. Hasse and N. Peters, "A two mixture fraction flamelet model applied to split injections in a DI Diesel engine," Proceedings of the Combustion Institute, vol. 3, pp. 2755-2762, 25. [6] M. Bolla, et al., "Modeling of soot formation in a heavy-duty diesel engine with conditional moment closure," Fuel, vol. 7, pp. 39-325, 23. [7] C. Felsch, et al., "An extended flamelet model for multiple injections in DI Diesel engines," Proceedings of the Combustion Institute, vol. 32, pp. 2775-2783, 29. 5
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