PDF-based simulations of turbulent spray combustion in a constant-volume chamber under diesel-engine-like conditions

Transcription

1 International Multidimensional Engine Modeling User s Group Meeting at the SAE Congress Detroit, MI 23 April 2012 PDF-based simulations of turbulent spray combustion in a constant-volume chamber under diesel-engine-like conditions S. Bhattacharjee, J. Jaishree, V. Raj Mohan, H. Zhang and D.C. Haworth Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA Transported probability density function (PDF) methods are used to account for turbulent fluctuations in composition and temperature in simulations of liquid fuel injection (n-heptane), vaporization, mixing, autoignition, combustion and soot formation for a constant-volume combustion chamber. Both stochastic Lagrangian particle and stochastic Eulerian field methods are used to solve the modeled PDF transport equation. Model results are compared with experimental measurements from the Engine Combustion Network for nonreacting vaporizing sprays and for cases with autoignition and combustion. Parametric studies are performed with variations in key physical models and numerical parameters to establish sensitivities. Results obtained using the PDF method are compared with results obtained by neglecting turbulent fluctuations to determine the extent to which turbulence-chemistry interactions (TCI) influence the results. Depending on the choice of chemical mechanism, a model that neglects turbulent fluctuations in composition and temperature can reproduce the measured trends in ignition delay and liftoff length with variations in the thermochemical environment. However, the computed turbulent flame structure is qualitatively incorrect when TCI are ignored, and there are significant differences in computed soot distributions between simulations that consider TCI and simulations that do not. Quantitative differences in computed ignition delays and liftoff lengths between simulations that include TCI and simulations that do not are larger for the less robust combustion environments that are expected to be representative of those in advanced compression-ignition engines (e.g., low temperatures and/or low oxygen levels). 1. Introduction In-cylinder aero-thermal-chemical processes in reciprocating-piston internal combustion engines are rich and complex, and modern engines are already at high levels of refinement. Further increases in performance, reductions in fuel consumption and emissions, and accommodation for nontraditional fuels will require the effective use of high-spatial-and-temporal-resolution optical diagnostics and numerical simulations. In this research, high-fidelity computational fluid dynamics (CFD)-based tools are being developed to simulate autoignition, combustion, and pollutant emissions in compression-ignition engines. The modeling framework is a transported composition probability density function (PDF) method. This approach accommodates arbitrarily detailed models for gas-phase chemistry, soot and radiation heat transfer with minimal further modeling required to account for the influences of turbulent fluctuations in composition and temperature [1]. Here the models are applied to a constant-volume spray combustion chamber where measurements are available for a range of thermochemical conditions representative of modern diesel engines [2]. The fuel is n-heptane. Parametric studies of the influences of key physical and 1

2 numerical parameters are performed to establish sensitivities and best practices to be carried forward into subsequent modeling studies of engines. 2. Configuration The step from atmospheric-pressure laboratory flames where model development and validation traditionally have been performed to practical engines is a big one. For example, there is no reason to expect that a soot model that has been developed for atmospheric-pressure flames should perform satisfactorily for the thermochemical environments that characterize modern direct-injection compression-ignition engines. An important missing link has been the availability of reliable data for well-characterized turbulent spray flames under engine-like thermochemical conditions, but without the geometric and other complexities of a real engine. An effort to fill this gap is the Engine Combustion Network (ECN) [2]. The purpose of the ECN is to provide an open forum for international collaboration among experimental and computational researchers in engine combustion. One target configuration is a constant-volume turbulent spray combustion chamber that can reach thermochemical conditions (composition, temperature, and pressure) that are typical of those in a modern direct-injection compressionignition engine, while allowing a high degree of optical access for advanced diagnostics and well-characterized initial and boundary conditions for simulations, including the fuel-injector characterization. Measurements are available for multiple fuels and operating conditions. Here the ECN nonreacting and reacting n-heptane cases are considered. The initial pressure and temperature for the baseline case are 4.21 MPa and 1000 K, respectively. 3. Physical Models and Numerical Methods Two different CFD codes have been used: OpenFOAM v1.5 [3] and STAR-CD v4 [4]. In both cases, the mean momentum, pressure and turbulence model equations are solved using a segregated, pressure-based, iteratively implicit finite-volume method with second-order spatial discretizations. Stochastic Lagrangian parcel formulations are used for vaporizing liquid fuel sprays. A modeled transport equation for the joint PDF of species mass fractions and mixture specific enthalpy then is solved using either a consistent hybrid Lagrangian particle/eulerian mesh (LPEM) method or a stochastic Eulerian field (SEF) method [1,5]. In all cases, turbulence is modeled using a standard two-equation k- model, gradient transport is assumed for turbulent scalar transport and mixing is modeled using interaction-by-exchange-with-the-mean. Skeletal n- heptane mechanisms (29-, 34- or 40-species) are used for gas-phase chemistry, and either a semiempirical two-equation model or a detailed model based on a method-of-moments with interpolative closure is used for soot. Results obtained using a transported PDF method are compared with those obtained by neglecting turbulent fluctuations in composition and temperature (i.e., a locally well-stirred-reactor model at the finite-volume cell level) to quantify the importance of turbulence-chemistry interactions (TCI). The computational domain is an axisymmetric wedge of hexahedral cells with a single computational cell in the azimuthal direction. The meshes are nonuniform in the axial and radial directions. The nominal number of computational particles per cell in the LPEM method, or the number of stochastic Eulerian fields in the SEF method, ranges from 20 to 40. In some cases, ISAT [6] has been used to accelerate the chemistry calculations. 2

3 4. Results and Discussion The first step is to establish baseline physical and numerical parameters to match the experimentally measured global spray characteristics for nonreacting, vaporizing sprays. A systematic parametric study has been performed to establish the sensitivities of computed liquid and vapor penetration lengths to variations in physical models (e.g., fuel injector and spray models, turbulence model), numerical parameters (e.g., mesh size and distribution, computational time step), initial conditions (e.g., initial turbulence intensity and length scale), and postprocessing parameters (e.g., thresholds used to determine liquid and vapor penetration). Computed results are sensitive to variations in the spray and turbulence models, in particular. From this exercise, a baseline set of physical and numerical parameters has been selected that gives reasonable agreement between experiment and model. Examples of computed and measured liquid penetration, vapor penetration and mean mixture fraction profiles are shown in Fig. 1. Even in the absence of chemical reaction, the influence of turbulence-chemistry interactions can be seen in the computed mean mixture-fraction profiles. Figure 1: Left: Computed (OpenFOAM, without PDF method labeled FV ) and measured liquid and vapor penetration versus time for a nonreacting n-heptane spray with baseline physical and numerical parameters. Right: Computed (STAR-CD) and measured radial profiles of mean mixture fraction for a nonreacting n-heptane spray with baseline physical and numerical parameters, 6 ms after the start of injection and 20 mm from the fuel-injector tip. Two computed profiles are shown: one with a transported PDF method (a LPEM method), and one where local turbulent fluctuations in composition have been ignored (a well-stirred reactor model, labeled FV ). Reacting simulations then were performed using the baseline model settings for a range of ambient oxygen levels, from 8% O 2 to 21% O 2. Examples of computed and measured ignition delays and liftoff lengths for three chemical mechanisms, without consideration of TCI, are shown in Fig. 2. A model that ignores TCI can capture the measured trends reasonably well, depending on the choice of chemical mechanism. However, there are large quantitative differences in computed ignition delays and liftoff lengths between simulations where TCI are considered using the PDF method and simulations where TCI are neglected. These differences increase with decreasing O 2 level and with decreasing ambient temperature (not shown). 3

4 Figure 2: Computed (STAR-CD) and measured ignition delays (left) and liftoff lengths (right) for three different chemical mechanisms, without consideration of TCI. There are also large qualitative differences in computed turbulent flame structure between results with versus without the transported PDF method. Examples of computed mean OH mass fraction contours are provided in Fig. 3. The PDF-based flame structures are more consistent with the broadened mean reaction zones that are observed in the experiments. Examples of computed and measured soot distributions are shown in Fig. 4. There results obtained without consideration of TCI are compared with results obtained with consideration of TCI (using a stochastic Eulerian field PDF method). Here a semi-empirical two-equation soot model has been used. The computed soot levels are comparable to the measured levels. This is noteworthy in itself, given the significant uncertainties in soot modeling and in soot measurements. The computed spatial distribution of soot is broader, and the peak soot level is lower, when TCI are considered. It can be argued which of the computed distributions (with versus without TCI) better matches the experimental measurements, but clearly TCI make a difference. The total computed soot mass is approximately two times higher with consideration of TCI. 5. Concluding Remarks Simulations of nonreacting and reacting n-heptane turbulent sprays and spray flames under diesel-engine-like conditions have been performed using transported PDF methods. Two different CFD codes have been used, and two different approaches have been implemented for solving the modeled PDF transport equation. Baseline sets of physical and numerical parameters have been selected to match experimentally measured liquid and vapor penetration versus time in nonreacting sprays. Simulations using these baseline parameters then have been performed for reacting spray flames. The model generally captures the measured trends in ignition timing and liftoff length with variations in the thermochemical environment. There are large qualitative differences in flame structure and soot distributions, and quantitative differences in ignition delays and liftoff lengths, between results from simulations that consider TCI using the transported PDF method and those from simulations that neglect turbulent fluctuations in composition and temperature. It is expected that quantitative agreement between simulations and experiment for reacting cases can be improved with further tuning of physical and numerical 4

5 parameters, and with better gas-phase chemistry mechanisms. Further analysis is ongoing to establish guidelines for conditions where TCI are expected to be important in compressionignition engines, and conditions where TCI can be neglected. Figure 3: Time sequence of computed mean OH contours for a n-heptane spray flame with 21% O 2. Left to right: 1 ms, 2 ms, 3 ms, and 4 ms after start of injection. Top row: A well-stirred-reactor model. Middle row: A LPEM transported PDF method. Bottom row: A SEF transported PDF method. 5

6 Figure 4: Measured (left) and computed (STAR-CD; center without TCI, right with TCI) soot volume fraction distributions for the baseline n-heptane spray flame with 21% O 2. Acknowledgments This research has been supported by the U.S. Department of Energy, the Pennsylvania Department of Labor and Industry, GE Transportation and the GE Global Research Laboratory, Volvo, and CD-adapco. The last author is a consultant to CD-adapco. References [1] D.C. Haworth (2010) Progress in probability density function methods for turbulent reacting flows. Prog. Energy Combust. Sci. 36: [2] L.M. Pickett (2011) Engine Combustion Network. Combustion Research Facility, Sandia National Laboratories, Livermore, CA. See [3] OpenFOAM (2011) See [4] CD-adapco (2011) See [5] J. Jaishree and D.C. Haworth (2011) Comparisons of Lagrangian and Eulerian PDF methods in simulations of nonpremixed turbulent jet flames with moderate-to-strong turbulencechemistry interactions, Combust. Theory Modell. In press. [6] L. Lu and S.B. Pope (2009) An improved algorithm for in situ adaptive tabulation, J. Comput. Phys. 228: