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Research Papers: Internal Combustion Engines

Modeling Auto-Ignition Transients in Reacting Diesel Jets

[+] Author and Article Information
Layal Hakim

Sandia National Laboratories,
Livermore, CA 94550
e-mail: lhakim@sandia.gov

Guilhem Lacaze

Sandia National Laboratories,
Livermore, CA 94550
e-mail: gnlacaz@sandia.gov

Mohammad Khalil

Sandia National Laboratories,
Livermore, CA 94550
e-mail: mkhalil@sandia.gov

Habib N. Najm

Sandia National Laboratories,
Livermore, CA 94550
e-mail: hnnajm@sandia.gov

Joseph C. Oefelein

Sandia National Laboratories,
Livermore, CA 94550
e-mail: oefelei@sandia.gov

1Corresponding author.

Contributed by the IC Engine Division of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received February 3, 2016; final manuscript received March 9, 2016; published online May 24, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 138(11), 112806 (May 24, 2016) (8 pages) Paper No: GTP-16-1054; doi: 10.1115/1.4033502 History: Received February 03, 2016; Revised March 09, 2016

The objective of the present work is to establish a framework to design simple Arrhenius mechanisms for simulation of diesel engine combustion. The goal is to predict auto-ignition over a selected range of temperature and equivalence ratio, at a significantly reduced computational cost, and to quantify the accuracy of the optimized mechanisms for a selected set of characteristics. The methodology is demonstrated for n-dodecane oxidation by fitting the auto-ignition delay time predicted by a detailed reference mechanism to a two-step model mechanism. The pre-exponential factor and activation energy of the first reaction are modeled as functions of equivalence ratio and temperature and calibrated using Bayesian inference. This provides both the optimal parameter values and the related uncertainties over a defined envelope of temperatures, pressures, and equivalence ratios. Nonintrusive spectral projection (NISP) is then used to propagate the uncertainty through homogeneous auto-ignitions. A benefit of the method is that parametric uncertainties can be propagated in the same way through coupled reacting flow calculations using techniques such as large eddy simulation (LES) to quantify the impact of the chemical parameter uncertainty on simulation results.

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Figures

Grahic Jump Location
Fig. 1

Comparison of the auto-ignition delay time for a stoichiometric mixture of n-dodecane/air at 2 MPa, computed using the detailed mechanism by Sarathy et al. [3], the skeletal mechanism by Narayanaswamy et al. [4], and the skeletal mechanism by Luo et al. [5] against the experimental shock tube data by Vasu et al. [6]. The simulations are performed using a constant volume homogeneous reactor.

Grahic Jump Location
Fig. 2

Comparison of the adiabatic flame temperature provided by equilibrium calculations with the current two-step mechanism (line) and with the reference mechanism by Narayanaswamy et al. [4] (symbols), at an initial temperature of T0 = 850 K and for equivalence ratios ranging from 0.5 to 4. The pressure is 6 MPa.

Grahic Jump Location
Fig. 3

One-dimensional and 2D marginal pdfs of the model parameters

Grahic Jump Location
Fig. 4

Arrhenius rate parameter pdfs at T0 = 700 K, ϕ=1.0: (a) the activation energy, Ea, (b) the pre-exponential factor, In A, and (c) joint pdf

Grahic Jump Location
Fig. 5

Model predictions at 6 MPa with the MAP estimate values—(a) ignition delay times: (colored surface) reference data (gray surface) two-step mechanism predictions. (b) Relative error between the reference data and the model predictions. (c) Ignition delay times at three different equivalence ratios. Symbols: Narayanaswamy et al. [4] and lines: the optimized two-step mechanism (see online figure for color).

Grahic Jump Location
Fig. 6

Model predictions with the MAP estimate values (dashed lines) compared to those of Narayanaswamy et al. [4] (plain lines)—(a) time evolution of temperature at T0 = 950 K and 6 MPa for ϕ=0.5 (light gray), ϕ=1 (medium gray), and ϕ=3 (black). (b) Time evolution of temperature at stoichiometry and 6 MPa for T0 = 750 K (light gray), T0 = 850 K (medium gray), and T0 = 950 K (black).

Grahic Jump Location
Fig. 7

Auto-ignition delay time at 6 MPa and ϕ=1 given by (dotted line) the PCE of In τ (Eq. (13)), (plain line) chemkin homogeneous reactor simulations using the two-step mechanism optimized with the MAP value, and (dashed line) chemkin homogeneous reactor simulations using the skeletal mechanism [4]

Grahic Jump Location
Fig. 8

Auto-ignition delay time at ϕ=1 predicted by the optimized two-step mechanism and the state-of-the-art detailed and skeletal mechanisms [35]

Grahic Jump Location
Fig. 9

PDFs of In τ generated with the PCE evaluated at 106 samples at ϕ=1 and (a) T0 = 750 K, (b) T0 = 850 K, and (c) T0 = 1100 K

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