Injector 210677 has been used for these experiments. See SAE 2007-01-0647 and SAE 2011-01-0686 for the experimental methodology.

Images have been processed to consider uncertainties and the effect of spatial filtering via median filtering on the mean, standard deviation (or variance) and overall uncertainty. The table below lists the format of the newly processed images.

pixels/mm | radial/axial pixels | radial values [mm] | axial values [mm] | median filter for mean | median filter for std. dev. |

14.06 | 401 x 475 | -14.4 to 14.1 | 17.8 to 51.6 | 13 x 13 pixels | 9 x 9 pixels |

Instantaneous (individual) images are not shown here due to particle contamination. Only the mean, together with standard deviation and uncertainties are made available. Spatial filtering (median filtering) has been applied on individual images to compute convergent statistics. As shown in the figures below, spatial filtering does not significantly change the mean result (left), but larger filtering regions do decrease the apparent standard deviation (and uncertainty) as expected (right). At the same time, particles or laser artifacts, obviously are erroneous and increase the standard deviation. A suitable compromise is to use two sets of median filters. As shown in the table, a larger median filter (13 x 13 pixels) is applied to safely remove artifacts without changing the mean result. A smaller median filter (9 x 9 pixels) is applied to compute the standard deviation to prevent overfiltering, but particles and noise evidently remain in the standard deviation “image”. To remove these noise effects, while not reducing the standard deviation, a large (17 x 17 pixels) spatial filter is then applied. Note that the standard deviation results show (see figure) that the level is unchanged if a large filter is applied afterwards, but fluctuations are removed. To date, this last spatial filter is the best technique attempted to dynamically remove noise artifacts while not compromising (decreasing) the standard deviation. Also note that image spatial filtering is only one aspect of measurement resolution bias as a finite laser sheet thickness (approaching 0.5 mm with beam steering) also enlarges the spatial resolution.

** Results **

Ensemble-averaged data are stored as ‘png’ image files, but also as zipped text files, in terms of fuel mixture fraction (or fuel mass fraction as the system is inert with 0% ambient oxygen). The 16-bit png images can be converted to mixture fraction Z using Z = png*maxImg/(2^16), where maxImg is the range (maximum) of the images listed in the table below. Scale, axial, and radial dimensions are given above. Column 2 is mean mixture fraction. Column 3 is standard deviation, which is the square root of the variance. Standard deviation is given to ensure consistency in the units (all in terms of mixture fraction). Column 4 is mean mixture fraction uncertainty, computed using bias error uncertainty, the standard deviation and the number of samples. To express a 95% confidence interval in the mean, use mean value ± this uncertainty. Note that uncertainties are relatively high because of the low number of images available at each condition (generally between 20 and 40; see SAE 2011-01-0686). Column 5 is standard deviation uncertainty computed using parameters similar to the mean. Column 6 is ensemble-averaged computed using adiabatic mixing relationships for n-dodecane fuel and ambient conditions (Mixing temperature as a function of mixture fraction for Spray A (900 K – 22.8 kg/m3) and for the 1100 K – 15.2 kg/m3 environment). The 16-bit ‘png’ images can be converted to temperature T in [K] using T = png*Rng/(2^16) + 600; where Rng is 450 for an ambient temperature of 900 K and 600 for an ambient temperature of 1100 K (i.e. the range of the images will either be from 600 to 1050 K or from 600 to 1200 K).

File type | Temp. | Density | Inj. Pres. | Mean | Uncertainty of mean | Standard deviation | Uncertainty of std. dev. | Mean temperature [K] |

Images | 900 K | 22.8 kg/m3 | 150 MPa | mean.png | meanunc.png | rms.png | rmsunc.png | Tmean.png |

maxImg | – | – | – | 0.16 | 0.04 | 0.02 | 0.02 | see above |

Text files | 900 K | 22.8 kg/m3 | 150 MPa | mean.zip | meanunc.zip | rms.zip | rmsunc.zip | Tmean.zip |

Images | 900 K | 22.8 kg/m3 | 100 MPa | mean.png | meanunc.png | rms.png | rmsunc.png | Tmean.png |

maxImg | – | – | – | 0.16 | 0.05 | 0.03 | 0.02 | see above |

Text files | 900 K | 22.8 kg/m3 | 100 MPa | mean.zip | meanunc.zip | rms.zip | rmsunc.zip | Tmean.zip |

Images | 900 K | 22.8 kg/m3 | 50 MPa | mean.png | meanunc.png | rms.png | rmsunc.png | Tmean.png |

maxImg | – | – | – | 0.16 | 0.04 | 0.02 | 0.02 | see above |

Text files | 900 K | 22.8 kg/m3 | 50 MPa | mean.zip | meanunc.zip | rms.zip | rmsunc.zip | Tmean.zip |

Images | 1100 K | 15.2 kg/m3 | 150 MPa | mean.png | meanunc.png | rms.png | rmsunc.png | Tmean.png |

maxImg | – | – | – | 0.19 | 0.05 | 0.03 | 0.02 | see above |

Text files | 1100 K | 15.2 kg/m3 | 150 MPa | mean.zip | meanunc.zip | rms.zip | rmsunc.zip | Tmean.zip |