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Vortex ring formation process in starting jets with uniform background co- and counter-flow

Published online by Cambridge University Press:  07 August 2023

Jianwei Zhu Open the ORCID record for Jianwei Zhu [Opens in a new window] ,
Guoqing Zhang Open the ORCID record for Guoqing Zhang [Opens in a new window] ,
Lei Gao Open the ORCID record for Lei Gao [Opens in a new window]  and
S.C.M. Yu Open the ORCID record for S.C.M. Yu [Opens in a new window]
Jianwei Zhu
Affiliation:
Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, PR China
Guoqing Zhang*
Affiliation:
Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, PR China
Lei Gao
Affiliation:
School of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, PR China
S.C.M. Yu
Affiliation:
Department of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, PR China
*
†Email address for correspondence: [email protected]
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Abstract

The formation process of the leading vortex ring in starting jets with uniform background co- and counter-flow has been studied numerically for $-0.5\leq R_v\leq 0.5$, where $R_v$ is the ratio of background velocity to jet velocity. For the cases with background counter-flow, the normal formation process of the leading vortex ring would be destroyed when $R_v<-0.4$, i.e. the trailing jet would overtake the leading vortex ring through the centre, a phenomenon reminiscent of vortex leapfrogging. As the velocity ratio $R_v$ increases, the formation number $F_{t^*}$ decreases from $9.6$ at $R_v=-0.4$ to $1.92$ at $R_v=0.5$. An analytical model based on the kinematic criterion has been developed so as to describe the relationship between the formation number $F_{t^*}$ and velocity ratio $R_v$. A linear relationship between the vortex core parameter and stroke ratio of starting jet ($\varepsilon \sim k_1L/D$) for the Norbury vortex ring has been established and used effectively to close the model. For co-flow with $0< R_v\leq 0.5$, the results from this model are consistent with the present numerical simulation and the experiments by Krueger et al. (J. Fluid Mech., vol. 556, 2006, pp. 147–166). For counter-flow, two different equations are proposed for $-0.4\leq R_v\leq -0.2$ and $-0.2< R_v<0$, respectively.

JFM classification

Wakes/Jets: Jets Vortex Flows: Vortex shedding
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 968 , 10 August 2023 , A26
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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