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Research Papers

Uncertainty Quantification of Large-Eddy Spray Simulations

[+] Author and Article Information
Noah Van Dam

Mechanical Engineering Department,
University of Wisconsin-Madison,
Engineering Research Building, Room 1008,
1500 Engineering Drive,
Madison, WI 53706
e-mails: nvandam@wisc.edu; nvandam@anl.gov

Chris Rutland

Mechanical Engineering Department,
University of Wisconsin-Madison,
Engineering Research Building, Room 1018B,
1500 Engineering Drive,
Madison, WI 53706
e-mail: rutland@engr.wisc.edu

1Corresponding author.

2Present address: Argonne National Laboratory 9700 S. Cass Ave., Lemont, IL 60439.

Manuscript received January 28, 2015; final manuscript received November 15, 2015; published online January 5, 2016. Assoc. Editor: Christopher J. Roy.

J. Verif. Valid. Uncert 1(2), 021006 (Jan 05, 2016) (8 pages) Paper No: VVUQ-15-1006; doi: 10.1115/1.4032196 History: Received January 28, 2015; Revised November 15, 2015

Two uncertainty quantification (UQ) techniques, latin-hypercube sampling (LHS) and polynomial chaos expansion (PCE), have been used in an initial UQ study to calculate the effect of boundary condition uncertainty on Large-eddy spray simulations. Liquid and vapor penetration as well as multidimensional liquid and vapor data were used as response variables. The Morris one-at-a-time (MOAT) screening method was used to identify the most important boundary conditions. The LHS and PCE methods both predict the same level of variability in the response variables, which was much larger than the corresponding experimental uncertainty. Nested grids were used in conjunction with the PCE method to examine the effects of subsets of boundary condition variables. Numerical modeling parameters had a much larger effect on the resulting spray predictions; the uncertainty in spray penetration or multidimensional spray contours from physically derived boundary conditions was close to the uncertainty of the measurements.

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Figures

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Fig. 1

Mean liquid penetration from experiments, LHS, and PCE along with liquid penetration for a single simulation using the mean values of the uncertain input parameters. The results are all consistent with one another; the single simulation results predict the same approximate quasi-steady liquid length, but with greater variability.

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Fig. 2

Standard deviation of liquid penetration for experimental and UQ methods. The UQ methods predict greater variability throughout the injection duration. The variability jumps suddenly around 1.0 ms ASOI as the individual spray events that constitute the averages begin to vaporize at different times.

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Fig. 3

Mean vapor penetration from experiments, LHS, and PCE along with the vapor penetration for a single simulation using the mean values of the uncertain input parameters. The results, including the single injection input mean, are all quite close until very late when the input mean simulation begins to underpredict relative to the experiments while the UQ methods both start to overpredict slightly.

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Fig. 4

Standard deviation of vapor penetration for experiment and UQ methods. The uncertainty in the UQ results is several times that of the experiments and grows at a much faster rate than the experimental uncertainty.

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Fig. 5

Experiment (left), PCE (center), and LHS (right) measured or predicted liquid probability contours 0.7 ms ASOI. The outermost isolines of the PCE and LHS results are similar to the experimental contour, but the total probability bands of the UQ results are wider, with contour lines filling the interior of the spray shapes.

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Fig. 6

Experiment (left), PCE (center), and LHS (right) measured or predicted vapor probability contours 2.0 ms ASOI. The simulation results are very different from the experiment with much larger variability predicted in the vapor contours.

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Fig. 7

Mean liquid penetration of the experiment and subsamples of the PCE data using only either numerical or physical boundary condition uncertainty. Both subsets predict mean liquid penetrations that are very close to the measured data.

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Fig. 8

Liquid penetration standard deviation of the experiment and subsamples of the PCE data using only either numerical or physical boundary uncertainty. Using only numerical parameter uncertainty results in a much higher standard deviation throughout the simulation, while using only physical boundary condition uncertainty results in a standard deviation that is very similar to the measured data.

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Fig. 9

Mean vapor penetration of the experiment and subsamples of the PCE data of either numerical or physical boundary condition uncertainty. The subsamples predict mean vapor penetration curves that diverge only slightly at the end of the spray.

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Fig. 10

Vapor penetration standard deviation of PCE subsamples using only either numerical or physical boundary conditions. The standard deviation from only the numerical parameters is much larger than either the experiment or physical boundary condition variability.

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Fig. 11

Liquid probability contours 0.7 ms ASOI for experiment (left) and either numerical parameter (center) or physical boundary condition (right) uncertainty alone. The outer contours are very similar, but the experimental data have a very narrow probability band, while both simulation subsamples show much wider probability bands.

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Fig. 12

Vapor probability contours 2.0 ms ASOI for experiment (left) and either numerical parameter (center) or physical boundary condition (right) only uncertainty alone. The physical-only results are much closer to the experimental results, while the numerical-only results do not resemble the experimental spray shape.

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