Research Papers: Internal Combustion Engines

Optimization and Uncertainty Analysis of a Diesel Engine Operating Point Using Computational Fluid Dynamics

[+] Author and Article Information
Daniel M. Probst, Peter K. Senecal

Convergence Science, Inc.,
Madison, WI 53719

Peter Z. Chien, Max X. Xu, Brian P. Leyde

Madison, WI 53705

Contributed by the IC Engine Division of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received February 27, 2017; final manuscript received March 26, 2018; published online June 25, 2018. Editor: David Wisler.

J. Eng. Gas Turbines Power 140(10), 102806 (Jun 25, 2018) (9 pages) Paper No: GTP-17-1080; doi: 10.1115/1.4040006 History: Received February 27, 2017; Revised March 26, 2018

This study describes the use of an analytical model, constructed using sequential design of experiments (DOEs), to optimize and quantify the uncertainty of a diesel engine operating point. A genetic algorithm (GA) was also used to optimize the design. Three engine parameters were varied around a baseline design to minimize indicated specific fuel consumption without exceeding emissions (NOx and soot) or peak cylinder pressure (PCP) constraints. An objective merit function was constructed to quantify the strength of designs. The engine parameters were start of injection (SOI), injection duration, and injector included angle. The engine simulation was completed with a sector mesh in the commercial computational fluid dynamics (CFD) software CONVERGE, which predicted the combustion and emissions using a detailed chemistry solver with a reduced mechanism for n-heptane. The analytical model was constructed using the SmartUQ software using DOE responses to construct kernel emulators of the system. Each emulator was used to direct the placement of the next set of DOE points such that they improve the accuracy of the subsequently generated emulator. This refinement was either across the entire design space or a reduced design space that was likely to contain the optimal design point. After sufficient emulator accuracy was achieved, the optimal design point was predicted. A total of five sequential DOEs were completed, for a total of 232 simulations. A reduced design region was predicted after the second DOE that reduced the volume of the design space by 96.8%. The final predicted optimum was found to exist in this reduced design region. The sequential DOE optimization was compared to an optimization performed using a GA. The GA was completed using a population of nine and was run for 71 generations. This study highlighted the strengths of both methods for optimization. The GA (known to be an efficient and effective method) found a better optimum, while the DOE method found a good optimum with fewer total simulations. The DOE method also ran more simulations concurrently, which is an advantage when sufficient computing resources are available. In the second part of the study, the analytical model developed in the first part was used to assess the sensitivity and robustness of the design. A sensitivity analysis of the design space around the predicted optimum showed that injection duration had the strongest effect on predicted results, while the included angle had the weakest. The uncertainty propagation was studied over the reduced design region found with the sequential DoE in the first part. The uncertainty propagation results demonstrated that for the relatively large variations in the input parameters, the expected variation in the indicated specific fuel consumption and NOx results were significant. Finally, the predictions from the analytical model were validated against CFD results for sweeps of the input parameters. The predictions of the analytical model were found to agree well with the results from the CFD simulation.

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Fig. 1

The cylinder geometry is shown with a cut plane. The fuel injector included half angle as the angle between the injector (shown with a cone) and the vertical axis.

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Fig. 2

Flow chart for the proposed DOE-based optimization

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Fig. 3

The merit achieved with the GA. X markers indicate generations when the population microconverged, which happened a total of 7 times. The diamond marker indicates the merit of the baseline design.

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Fig. 4

Distribution of design parameters for all the GA cases evaluated. The bounding box represents the min and max allowed in the study: (a) cross section showing SOI and duration and (b) cross section showing Included half angle and duration.

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Fig. 5

Distribution of design parameters for the first DOE: (a) cross section showing SOI and duration and (b) cross section showing Included half angle and duration

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Fig. 6

Distribution of design parameters for the second DOE. Note that the DOE evaluated designs beyond the min/max limits of the optimization in order to develop the analytical model: (a) cross section showing SOI and duration and (b) cross section showing Included half angle and duration.

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Fig. 7

Design of experiment 3 and reduced design region; note that this is a two-dimensional representation of a three-dimensional space. A reduced design space was determined as shown with the dashed line.

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Fig. 8

Visualization of the emulator surface corresponding to DOE 5 showing gISFC with respect to two of the design parameters, included half angle and injection duration

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Fig. 9

Best case merit for each of the DOES

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Fig. 10

Duration sweep: emulator results are shown as a solid line, converge simulations as solid square markers with a dashed line and optimal point as single solid triangle

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Fig. 11

Start of injection sweep: emulator results are shown as a solid line, converge simulations as solid square markers with a dashed line and optimal point as single solid triangle

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Fig. 12

Included half angle sweep: emulator results are shown as a solid line, converge simulations as solid square markers with a dashed line and optimal point as single solid triangle

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Fig. 13

Propagation of uncertainty results for gISFC and NOx. The Y-axis shows the predicted probability frequency for the given output range on the X-axis.



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