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Machine Learning and transcritical sprays: A demonstration study of their potential in ECN Spray-A

Koukouvinis, F. ORCID: 0000-0002-3945-3707, Rodriguez, C., Hwang, J. , Karathanassis, I. K. ORCID: 0000-0001-9025-2866, Gavaises, M. ORCID: 0000-0003-0874-8534 & Pickett, L. (2022). Machine Learning and transcritical sprays: A demonstration study of their potential in ECN Spray-A. International Journal of Engine Research, 23(9), pp. 1556-1572. doi: 10.1177/14680874211020292


The present work investigates the application of Machine Learning and Artificial Neural Networks for tackling the complex issue of transcritical sprays, which are relevant to modern compression-ignition engines. Such conditions imply the departure of the classical thermodynamic perspective of ideal gas or incompressible liquid, necessitating the use of costly and elaborate thermodynamic closures to describe property variation and simulation methods. Machine Learning can assist in several ways in speeding up such calculations, either as a compact, trained thermodynamic model that can be coupled to the flow solver, or as a surrogate predictive tool of spray characteristics. In this work, such applications are demonstrated and their performance is assessed against more traditional approaches. Such applications involve the prediction of macroscopic spray characteristics, for example, the spray penetration over time, or the spray distribution in space and time, and predictions of fluid properties for the thermodynamic states encountered in such applications. Macroscopic characteristics can be adequately predicted by relatively simple network structures, involving just a hidden layer of 3–4 neurons, whereas prediction of thermodynamic states requires several layers of 5–20 neurons each. The results of integrating Artificial Neural Networks in transcritical sprays are rather promising; prediction of thermodynamic properties at pressures greater than 1bar has effectively zero error, yielding simulations indistinguishable from standard tabulated approaches with minimal overhead. When used as a regression method for time-histories either of spray characteristics or spray distributions, the results are within experimental uncertainty of similar experiments, not included in the training dataset.

Publication Type: Article
Additional Information: This article is distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 License ( which permits non-commercial use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (
Publisher Keywords: Fuel injection, real-fluid thermodynamics, transcritical mixing, Machine Learning, regression, Artificial Neural Network, multiphase flows
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
R Medicine > RC Internal medicine > RC0321 Neuroscience. Biological psychiatry. Neuropsychiatry
T Technology > TL Motor vehicles. Aeronautics. Astronautics
Departments: School of Science & Technology > Engineering
SWORD Depositor:
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