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Clustering of paraffin-based hybrid rocket fuels combustion data

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Clustering was applied to image data of hybrid rocket combustion tests for a better understanding of the complex flow phenomena. Novel techniques such as hybrid rockets that allow for cost reductions of space transport vehicles are of high importance in space flight. However, the combustion process in hybrid rocket engines is still a matter of ongoing research and not fully understood yet. Recently, combustion tests with different paraffin-based fuels have been performed at the German Aerospace Center (DLR). For a detailed analysis, the combustion process has been captured with a high-speed video camera, which leads to a huge amount of images for each test. In the end, a large data set with a total number of 30,000 images for each combustion test has to be analyzed. To catch the essential flow structures, the combustion data set was clustered with a K-means++ algorithm. Since the algorithm might converge to local optimal solutions, expensive repetitions have been performed to ensure that a global solution is found in the end. Furthermore, a detailed analysis was performed to find an adequate clustering algorithm in the first place and to estimate the number of relevant clusters K in each experiment. As a result, valuable insights into the different combustion phases were obtained and a comparison of the quality of the combustion flame in the different tests could be made. In particular, depending on the fuel formulation and oxidizer mass flow, differences in the transients and flame brightness were found.

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\(C_i\) :

single cluster (−)


grayscale pixel intensity (−)

J :

objective function (squared error) (−)

K :

number of clusters (−)

\(\varvec{x}_j\) :

data point j (a single image) (−)

d :

problem dimension (resolution of \(\varvec{x}_j\)) (−)

n :

number of data points in single test (−)

\(s(\varvec{x}_j)\) :

silhouette value of the data point \(\varvec{x}_j\) (−)

\(\bar{x}, \bar{y}\) :

image barycenter coordinates (−)


evaluation function to determine K (−)

\(\alpha _k\) :

weight factor in f(K) (−)

\(\varvec{\mu }_i\) :

mean of cluster \(C_i\) (centroid) (−)


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This research was carried out under the project Antriebstechnologien und Komponenten für Trägersysteme (ATEK) by the German Aerospace Center (DLR).

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Correspondence to A. Rüttgers.

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Rüttgers, A., Petrarolo, A. & Kobald, M. Clustering of paraffin-based hybrid rocket fuels combustion data. Exp Fluids 61, 4 (2020).

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