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Water jet angle prediction in supersonic crossflows: Euler–Lagrange and machine learning approaches

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Abstract

This study presents a comprehensive investigation into water jet injection dynamics in supersonic crossflows, employing a hybrid approach that integrates machine learning techniques, specifically random forest, with traditional discrete phase methods. The aim is to accurately model water jet structures and understand the underlying dynamics for optimizing flow control strategies. Through extensive numerical analysis, the study examines the influence of key parameters such as pressure levels, Weber number, droplet diameter and water jet velocity on penetration depth. Additionally, machine learning techniques are employed to analyze the impact of momentum, mass flow, pressure, Mach number and injection angle on penetration height. The findings reveal intricate interactions between pressure levels and penetration depth, driven by factors such as momentum transfer, evaporation efficiency and shock wave behavior. A direct correlation is observed between Weber number and penetration depth, emphasizing the role of inertial forces in determining penetration characteristics. Droplet diameter and water jet velocity emerge as critical factors affecting penetration depth, with smaller droplets and higher velocities resulting in deeper penetration into the crossflow. Machine learning analysis highlights the significance of momentum in influencing penetration height, while also indicating comparable effects of pressure, Mach number and injection angle. The random forest model demonstrates robust performance, achieving an accuracy exceeding 86.7% with an average absolute error of 0.00282, underscoring its reliability in predicting infiltration height.

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Data availability statement

The data that support the findings of this study are available upon request. Please contact Seyed Hamed Godasiaei for access to the data.

Abbreviations

d :

Droplet's diameter

d 0 :

The diameter of the injector orifice

h :

Penetration height (spray)

L :

Nozzle passage length

M :

Mach number

q . :

Ratio of jet to freestream momentum flux [\(\rho_{\rm L} w_{\rm j}^{2} /\rho_{\infty } u_{\infty }^{2}\)]

u :

Velocity in the direction of X (m/s)

w :

Velocity in the direction of Z (m/s)

x :

Distance in the freestream direction

SMD:

Sauter mean diameter

C d :

Drag coefficient

h :

Height of fluid jet penetration

n :

Distribution shape parameter

v :

Dynamic viscosity (kg m−1s−1)

ρ :

Fluid density (kg m−3)

θ :

Jet injection angle

Pr:

Prandtl number

Nu:

Nusselt number

p :

Pressure (N/m2)

Re:

Reynolds number

t :

Time (s)

T :

Temperature (K)

Y d :

Density function of droplet size

y :

Distance in the direction of the stream

RF:

Random forest

ML:

Machine learning model

u* :

Velocity component

ω :

Transport of the specific dissipation rate

D :

Characteristic size parameter

j :

Characteristic of liquid at injector exit

L :

Liquid phase characteristic

\(\infty\) :

Belonging to freestream

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Funding

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Authors and Affiliations

  1. School of Chemical Engineering and Technology, Xi’an JiaoTong University, 28 Xianning West Road, Xi’an, Shaanxi, 710049, People’s Republic of China

    Seyed Hamed Godasiaei

  2. Mechanical Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran

    Hosseinali Kamali

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Contributions

Seyed Hamed Godasiaei conceived and designed the study, collected and analyzed the data, contributed to the interpretation of the results and drafted the manuscript. The authors critically revised and approved the final version.

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Correspondence to Seyed Hamed Godasiaei.

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The authors declare that they have no competing interests.

Ethical statement

This study was conducted in accordance with ethical standards and guidelines. The study protocol was followed, and all participants provided informed consent.

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Godasiaei, S.H., Kamali, H. Water jet angle prediction in supersonic crossflows: Euler–Lagrange and machine learning approaches. Eur. Phys. J. Plus 139, 251 (2024). https://doi.org/10.1140/epjp/s13360-024-05047-9

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