A methodology of Lagrangian integral time scale in cavitating flow based on finite-time Lyapunov exponent

doi:10.1007/s10483-025-3327-6

Abstract

Abstract:

The Lagrangian integral time scale (LITS) is a crucial characteristic for investigating the changes in fluid dynamics induced by the chaotic nature, and the finite-time Lyapunov exponent (FTLE) serves as a key measure in the analysis of chaos. In this study, a new LITS model with an explicit theoretical basis and broad applicability is proposed based on the FTLE, along with a verification and evaluation criterion grounded in the Lagrangian velocity correlation coefficient. The model is used to cavitating the flow around a Clark-Y hydrofoil, and the LITS is investigated. It leads to the determination of model constants applicable to cavitating flow. The model is evaluated by the Lagrangian velocity correlation coefficient in comparison with other solution methods. All the results show that the LITS model can offer a new perspective and a new approach for studying the changes in fluid dynamics from a Lagrangian viewpoint.

Key words: Lagrangian integral time scale (LITS), finite-time Lyapunov exponent (FTLE), cavitating flow, correlation coefficient, fluid dynamics

2010 MSC Number:

Peifeng LIN, Tianyu ZANG, Jinming ZHANG. A methodology of Lagrangian integral time scale in cavitating flow based on finite-time Lyapunov exponent. Applied Mathematics and Mechanics (English Edition), 2025, 46(12): 2407-2426.

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Figures/Tables 27

Fig. 1

Fig. 2

Table 1

Mesh-independent analysis"

Mesh	Node	$C d$	$C l$
Mesh 1	3 904 320	0.12	0.75
Mesh 2	4 411 840	0.12	0.75
Mesh 3	4 974 430	0.12	0.75

Table 1

Fig. 3

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Fig. 5

Fig. 6

Fig. 7

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Fig. 12

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Table 2

LITS results derived from different methods (unit: s)"

Particle	Berlemont model	FTLE method	New model
$B 1$	0.000 419 847 0	0.000 1	0.000 145 501
$C 1$	0.000 076 674 7	0.000 1	0.000 111 179
$B 2$	0.000 211 756 0	0.000 1	0.000 138 492
$C 2$	0.000 088 440 3	0.000 2	0.000 185 086
$B 3$	0.000 082 910 7	0.000 2	0.000 165 730
$C 3$	0.000 111 309 0	0.000 1	0.000 131 161

Table 2

Table 3

Results of RL,U derived from different methods"

Particle	Berlemont model	FTLE method	New model
$B 1$	0.979 870	0.999 409	0.998 821
$C 1$	0.994 288	0.993 632	0.991 963
$B 2$	0.967 309	0.993 645	0.988 344
$C 2$	0.985 182	0.992 924	0.993 697
$B 3$	0.992 751	0.998 737	0.999 111
$C 3$	0.975 325	0.997 816	0.996 334

Table 3

Table 4

1pt Results of RL,V derived from different methods"

Particle	Berlemont model	FTLE method	New model
$B 1$	0.977 254	0.999 603	0.999 123
$C 1$	0.984 935	0.980 115	0.972 441
$B 2$	0.951 383	0.989 305	0.985 153
$C 2$	0.988 061	0.975 398	0.978 168
$B 3$	0.986 081	0.994 932	0.996 485
$C 3$	0.977 460	0.993 160	0.988 032

Table 4

Table 5

Results of RL,W derived from different methods"

Particle	Berlemont model	FTLE method	New model
$B 1$	0.973 202	0.998 412	0.996 920
$C 1$	0.962 809	0.975 862	0.969 563
$B 2$	0.940 683	0.988 975	0.979 073
$C 2$	0.981 311	0.939 722	0.966 545
$B 3$	0.986 683	0.988 059	0.991 612
$C 3$	0.979 294	0.984 909	0.974 075

Table 5

Fig. 21

Table 6

Average Lagrangian velocity correlation coefficient derived from different methods"

Coefficient	Berlemont model	FTLE method	New model
$R ¯ L$	0.980 970	0.988 034	0.987 215

Table 6

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