09.09.2023

THE INSTITUTE NEEDS YOUR HELP

IHM NASU was damaged by the attack of rashist drones
Read more
01.10.2024

COMPUTER HYDROMECHANICS, 2024 (Program, Abstracts)

IX International Scientific & Practical Conference "Computer Hydromechanics"
Read more

HYDRODYNAMICS AND ACOUSTICS

2018 ◊ Volume 1 (91) ◊ Issue 3 ◊ p. 316-333

N. F. Dimitrieva*

* Institute of Hydromechanics of NAS of Ukraine, Kyiv, Ukraine
**National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"

Flows around a 2D horizontal wedge in a steadily stratified liquid

Gidrodin. akust. 2018, 1(3):316-333

https://doi.org/10.15407/jha2018.03.316

TEXT LANGUAGE: Russian

ABSTRACT

The paper deals with studying of the flows of continuously stratified fluid characterized by a wide range of values of internal scales that are absent in a homogeneous fluid. The problem is solved by numerical methods in a 2D unsteady formulation for a fluid at rest and uniform motion. For the mathematical description of the problem, a system of differential equations of mechanics of inhomogeneous multicomponent fluids was chosen in the Boussinesq approximation with considering the small density variations only in terms describing the gravity force. The problem is solved by the method of finite volumes in a free software package OpenFOAM. The particular attention was paid to creation of a high-quality high-resolution computational grid taking into account the multi-scale diffusion-induced flows. The use of standard and advanced utilities of the OpenFOAM package to implement the complex boundary conditions and develop new numerical models is discussed. The fields of diffusion-induced flows on a fixed wedge being in qualitative agreement with experimental data are used for initial conditions in the problem of external flow of a stratified medium around the wedge. The influence of edge effects and curvature of edge lateral surface on the flow structure is shown. The results of calculation reveal the extended region of pressure deficit at the acute top forming the integral force that is the reason for self-motion of free wedge in apex direction along the neutral buoyancy horizon in stably stratified medium. In stratified fluid, the evolution of flow pattern of the wedge starting the uniform motion from the rest at the velocity of 10-4 m/s is demonstrated. In all regimes, the flow is characterized by complex internal structure with the initially expressed dissipative-gravity waves and further emerging group of attached waves forming in antiphase at wedge's edges. With the increase of external flow velocity vortices dominating in the wake become the main component of the flow.

KEY WORDS

numerical simulation, open computing packages, stratification, fluid flow, diffusion, self-motion

REFERENCES

  1. O. M. Phillips, "On flows induced by diffusion in a stably stratified fluid", Deep Sea Research and Oceanographic Abstracts, vol. 17, no. 3, pp. 435–443, 1970. https://doi.org/10.1016/0011-7471(70)90058-6.
  2. V. S. Maderich, V. I. Nikishov, and A. G. Stecenko, The dynamics of internal mixing in stratified medium. Kyiv: Naukova Dumka, 1988, 238 pp.
  3. V. V. Bulatov and Y. V. Vladimirov, Waves in stratified media. Moscow: Nauka, 2015, 736 pp.
  4. A. E. Gargett, "Differential diffusion: An oceanographic primer", Progress in Oceanography, vol. 56, no. 3-4, pp. 559–570, 2003. https://doi.org/10.1016/S0079-6611(03)00025-9.
  5. C. Brouzet, I. N. Sibgatullin, H. Scolan, E. V. Ermanyuk, and T. Dauxois, "Internal wave attractors examined using laboratory experiments and 3D numerical simulations", Journal of Fluid Mechanics, vol. 793, pp. 109–131, 2016. https://doi.org/10.1017/jfm.2016.119.
  6. A. Shapiro and E. Fedorovich, "A boundary-layer scaling for turbulent katabatic flow", Boundary-Layer Meteorology, vol. 153, no. 1, pp. 1–17, 2014. https://doi.org/10.1007/s10546-014-9933-3.
  7. J. Oerlemans and W. J. J. van Pelt, "A model study of Abrahamsenbreen, a surging glacier in northern Spitsbergen", The Cryosphere, vol. 9, no. 2, pp. 767–779, 2015. https://doi.org/10.5194/tc-9-767-2015.
  8. V. N. Zyryanov and L. E. Lapina, "Slope flows governed by diffusion effects in seas, lakes, and reservoirs", Water Resources, vol. 39, no. 3, pp. 294–304, 2012. https://doi.org/10.1134/S0097807812030128.
  9. P. F. Linden and J. E. Weber, "The formation of layers in a double-diffusive system with a sloping boundary", Journal of Fluid Mechanics, vol. 81, no. 4, pp. 757–773, 1977. https://doi.org/10.1017/S002211207700233X.
  10. C. M. Hocut, D. Liberzon, and H. J. S. Fernando, "Separation of upslope flow over a uniform slope", Journal of Fluid Mechanics, vol. 775, pp. 266–287, 2015. https://doi.org/10.1017/jfm.2015.298.
  11. L. H. Cisneros, R. Cortez, C. Dombrowski, R. E. Goldstein, and J. O. Kessler, "Fluid dynamics of self-propelled microorganisms, from individuals to concentrated populations", Experiments in Fluids, vol. 43, no. 5, pp. 737–753, 2007. https://doi.org/10.1007/s00348-007-0387-y.
  12. M. J. Mercier, F. M. Ardekani, M. R. Allshouse, B. Doyle, and T. Peacock, "Self-propulsion of immersed object via natural convection", Physical Review Letters, vol. 112, no. 20, 204501(1–5), 2014. https://doi.org/10.1103/PhysRevLett.112.204501.
  13. M. R. Allshouse, M. F. Barad, and T. Peacock, "Propulsion generated by diffusion-driven flow", Nature Physics, vol. 6, pp. 516–519, 2010. https://doi.org/10.1038/nphys1686.
  14. M. A. Page, "Propelled by diffusion", Nature Physics, vol. 6, pp. 486–487, 2010. https://doi.org/10.1038/nphys1718.
  15. N. F. Dimitrieva, V. V. Levitskii, and Y. D. Chashechkin, "Shadow visualization of the self-movement of a free wedge in a stratified fluid", in Abstracts of the 7th International Scientific Workshop of Young Researchers "Waves and Vortices in Complex Media", Moscow: Institute of Applied Mechanics, RAS, 2016, pp. 66–68.
  16. N. F. Dymytriieva, "Calculation of stratified flows around a wedge using open software packages", Applied Hydromechanics, vol. 17, no. 2, pp. 26–35, 2015.
  17. Ia. V. Zagumennyi and N. F. Dimitrieva, "Diffusion induced flow on a wedge-shaped obstacle", Physica Scripta, vol. 91, no. 8, 084002(1–8), 2016. https://doi.org/10.1088/0031-8949/91/8/084002.
  18. Y. D. Chashechkin, Y. V. Zagumennyi, and N. F. Dimitrieva, "Dynamics of formation and fine structure of flow pattern around obstacles in laboratory and computational experiment", in Supercomputing. RuSCDays 2016, V. Voevodin and S. Sobolev, Eds., ser. Communications in Computer and Information Science, vol. 687, Cham: Springer, 2016, pp. 41–56. https://doi.org/10.1007/978-3-319-55669-7_4.
  19. V. G. Baidulov and Y. D. Chashechkin, "Invariant properties of systems of equations of the mechanics of inhomogeneous fluids", Journal of Applied Mathematics and Mechanics, vol. 75, no. 4, pp. 390–397, 2011. https://doi.org/10.1016/j.jappmathmech.2011.09.003.
  20. Y. D. Chashechkin and V. V. Mitkin, "A visual study on flow pattern around the strip moving uniformly in a continuously stratified fluid", Journal of Visualization, vol. 7, no. 2, pp. 127–134, 2004. https://doi.org/10.1007/BF03181585.
  21. N. F. Dimitrieva, "The numerical solution of the problem of stratified fluid flow around a wedge using OpenFOAM", Proceedings of the Institute for System Programming of the RAS, vol. 29, no. 1, pp. 7–20, 2017. https://doi.org/10.15514/ISPRAS-2017-29(1)-1.
  22. Y. D. Chashechkin and N. F. Dimitrieva, "The evolution of the stratified flow structure around a wedge with increasing velocity of motion", in Topical Problems of Fluid Mechanics 2017, D. Simurda and T. Bodnar, Eds., Prague, 2017, pp. 79–86. https://doi.org/10.14311/TPFM.2017.011.
  23. N. F. Dimitrieva and Y. D. Chashechkin, "The structure of induced diffusion flows on a wedge with curved edges", Physical Oceanography, no. 3, pp. 77–86, 2016. https://doi.org/10.22449/1573-160X-2016-3-70-78.