---

Journal of Environmental Accounting and Management 12(2) (2024) 141--154 | DOI:10.5890/JEAM.2024.06.003

Zhizhe Chen$^{1,2}$, Yong Luo$^{1}$, Shuaibin Han$^{1}$, Jiazhong Zhang$^{2}$, Shuhai Zhang$^{1}$, Shicheng Fan$^{2}$,\\ Yulin Cheng$^3$, Feng Xu$^3$, Wei Ding$^3$

$^1$ State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, 621000 Mianyang, China

$^2$ Xi'an Jiaotong University, Xi'an 710049, China

$^3$ Shaanxi Branch of Huaneng New Energy Co., Ltd., Xi'an 710000 China

Download Full Text PDF

 

Abstract

Finite-time Lyapunov exponent (FTLE) is introduced to study the evolution of streamwise vortices in a cavity flow, which is crucial in the mass exchange and pollutant emission around aircrafts. First, the structures of streamwise vortices are captured using ridges of FTLE, and the evolution of streamwise vortex structures is illustrated in detail. The results show that there exists asymmetry featured by differences in structure and scale between streamwise vortices. Then, the evolution of vortex structures is analyzed and compared. It is found that several critical flow structures inside the cavity could block the forming of certain vortex, causing differences in evolution of vortex structures. Such flow structures are then briefly introduced and studied. Finally, the influences of asymmetry of the flow on streamwise vortex formation are summarized. In conclusion, the differences in flow structures imply that critical flow structures have strong influences on the formation of streamwise vortices, which could serve as a main mean of mass transport across the shear layer. The results provide theoretical support for controlling mass transport and thus reduce pollutant emission through cavity structures.

Acknowledgments

This work is supported by the Projects of the Manned Space Engineering Technology (No. 2020-ZKZX-5011), the National key fundamental research project (No. 2019-JCJQ-ZD-177-01), the National Natural Science Foundation of China (grant No. 11732016), and Sichuan Science and Technology Program (grant No. 2018JZ0076).

References

1. [1]	Thangamani, V., Knowles, K., and Saddington, A.J. (2014), Effects of scaling on high subsonic cavity flow oscillations and control, Journal of Aircraft, 51(2), 424-433.

2. [2]	Casper, K.M., Wagner, J.L., Beresh, S.J., Spillers, R.W., and Henfling, J.F. (2019), Fluid–structure interactions on a tunable store in complex cavity flow, Journal of Aircraft, 56(4), 1501-1512.

3. [3]	Crook, S.D., Lau, T.C., and Kelso, R.M. (2013), Three-dimensional flow within shallow, narrow cavities, Journal of Fluid Mechanics, 735, 587-612.

4. [4]	Rossiter, J.E. (1964), Wind Tunnel Experiments on the Flow Over Rectangular Cavities at Subsonic and Transonic Speeds, Technical Report 64037, Royal Aircraft Establishment, Bedford, UK.

5. [5]	Rowley, C.W., Colonius, T., and Basu, A.J. (2002), On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities, Journal of Fluid Mechanics, 455, 315-346.

6. [6]	El Hassan, M. and Keirsbulck, L. (2017), Passive control of deep cavity shear layer flow at subsonic speed, Canadian Journal of Physics, 95(10), 894-899.

7. [7]	Sipp, D., Marquet, O., Meliga, P., and Barbagallo, A. (2010), Dynamics and control of global instabilities in open-flows: a linearized approach, Applied Mechanics Reviews, 63(3), 030801.

8. [8]	Zhong, T. and Yang, C. (2022), Application of the patch transfer function method for predicting flow-induced cavity oscillations, Journal of Sound and Vibration, 521, 116678.

9. [9]	Besse, N. and Frisch, U. (2017), Geometric formulation of the cauchy invariants for incompressible euler flow in flat and curved spaces, Journal of Fluid Mechanics, 825, 412-478.

10. [10]	Haller, G. (2015), Lagrangian coherent structures, Annual Review of Fluid Mechanics, 47, 137-162.

11. [11]	Haller, G. and Yuan, G. (2000), Lagrangian coherent structures and mixing in two-dimensional turbulence, Physica D, 147(3-4), 352-370.

12. [12]	Wang, L., Cao, S., Li, Y., and Zhang, J. (2019), On synchronization in flow over airfoil with local oscillating flexible surface at high angle of attack using lagrangian coherent structures, European Physical Journal-Special Topics, 228, 1515-1525.

13. [13]	Cao, S., Dang, N., Ren, Z., Zhang, J., and Deguchi, Y. (2020), Lagrangian analysis on routes to lift enhancement of airfoil by synthetic jet and their relationships with jet parameters, Aerospace Science and Technology, 104, 105947.

14. [14]	Venditti, C., Giona, M., and Adrover, A. (2022), Invariant manifold approach for quantifying the dynamics of highly inertial particles in steady and time-periodic incompressible flows, Chaos, 32, 023121.

15. [15]	Han, S., Luo, Y., and Zhang, S. (2019), Lagrangian vortex dynamics in the open cavity flow, Advances in Aeronautical Science and Engineering, 10(5), 691-697+734.

16. [16]	Zheng, X., Chen, Z., Chen, Z., Chai, L., and Zhang, J. (2022), Analysis of pollutant transport around a circular cylinder in subcritical regime using lagrangian coherent structures, Journal of Environmental Accounting and Management, 10(3), 321-333.

17. [17]	Tu, H., Marzanek, M., Green, M.A., and Rival, D.E. (2021), FTLE and surface-pressure signature of dynamic flow reattachment during delta-wing axial acceleration, AIAA Journal, 60(4), 2178-2194.

18. [18]	Haller, G. and Sapsis, T. (2011), Lagrangian coherent structures and the smallest finite-time Lyapunov exponent, Chaos, 21, 023115.

19. [19]	Hunt, J.C., Wray, A.A., and Moin, P. (1988), Eddies, Streams, and Convergence Zones in Turbulent Flows, Center for Turbulence Research Report CTR-S88, 193-208.

20. [20]	Luo, Y., Tian, H., Wu, C., Li, H., and Zhang, S. (2021), Numerical Study of Mode Behavior of Three-Dimensional Cavity with Doors, 2021 4th International Conference on Information Communication and Signal Processing (ICICSP), 239-243.

21. [21]	Shur, M.L., Spalart, P.R., Strelets, M.K., and Travin, A.K. (2008), A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities, International Journal of Heat and Fluid Flow, 29(6), 1638-1649.