HYDRODYNAMICS AND ACOUSTICS

2021 ◊ Volume 2 (92) ◊ Issue 2 ◊ p. 149-175

V. G. Kuzmenko ^*

^* Institute of Hydromechanics of NAS of Ukraine, Kyiv, Ukraine

Simulating the separated turbulent flow. Evolution of the energy of coherent structures end their sizes

Gidrodin. akust. 2021, 2(2):149-175

https://doi.org/10.15407/jha2021.02.149

TEXT LANGUAGE: Russian

ABSTRACT

The paper deals with the numerical study of a non-stationary three-dimensional turbulent flow of an incompressible fluid over a rectangular two-dimensional barrier. For the boundary layer, a hybrid LES/URANS approach is used. A finite-difference method with second-order approximation accuracy was applied for near-wall models. The ratio of the height of the barrier to its length was 4, the Reynolds number for the obstacle was Re=10500, and the Reynolds number for the turbulent boundary layer at the "inlet" Re_δ=10500. The number of grid nodes used was 1601 x 101 x 141 = 22799841. The coherent structures were identified by the Q-criterion with monitoring {Q_si} threshold values for the entire calculation area. Q-isosurfaces, integral energy characteristics, and cross-sectional area of organized vortex formations were studied by numerical modeling. For the computational zone with a longitudinal size of about 80 obstacle heights, coherent structures with different scales and configurations were found. The highest values of the turbulent energy of coherent structures occur in the zone of the separated flow reattachment and its recovery. Significant amounts of turbulent energy are still observed far behind the barrier, and its maxima are close to the local energy maximum above the obstacle. A new technique for processing numerical data for the evolution of random and coherent formations of various scales has been developed. It provides determining of limiting values of the integral turbulent energy characteristics when distinguishing different types of eddies over a long time interval. A complex nonlinear relationship between the coherence parameter Q, turbulent energy, vortex sizes, and their integral characteristics is revealed in various sections along the flow corresponding to the turbulent boundary layer, separation, recirculation zone, reattachment, and recovery.

KEY WORDS

turbulent boundary layer, obstacle, numerical method, coherent structures, identification criterion, evolution

REFERENCES

[1] H. Siller and H. Fernholtz, "Control of separated flow downstream of a two-dimensional fence by lowfrequency forcing," Applied Sciences Research., vol. 57, pp. 309-318, 1997.
https://doi.org/10.1007/BF02506066

[2] M. C. Good and P. N. Joubert, "The form drag of two-dimensional bluff-plates immersed in turbulent boundary layers," Journal of Fluid Mechanics, vol. 31, no. 3, pp. 547-582, 1968.
https://doi.org/10.1017/S0022112068000327

[3] H. A. Siller and H.-H. Fernholz, "Separation behaviour in front of a two-dimensional fence," European Journal of Mechanics - B/Fluids, vol. 20, no. 5, pp. 727-740, 2001.
https://doi.org/10.1016/S0997-7546(01)01153-0

[4] L. M. Hudy, A. Naguib, and W. M. Humphreys, "Stochastic estimation of a separated-flow field using wall-pressure-array measurements," Physics of Fluids, vol. 19, no. 024103, 2007.
https://doi.org/10.1063/1.2472507

[5] J. Zhou, R. J. Adrian, and S. Balachandar, "Autogeneration of near-wall vortical structures in channel flow," Physics of Fluids, vol. 8, no. 1, pp. 288-290, 1996.
https://doi.org/10.1063/1.868838

[6] J. Carlier and M. Stanislas, "Experimental study of eddy structures in a turbulent boundary layer using particle image velocimetry," Journal of Fluid Mechanics, vol. 535, pp. 143-188, 2005.
https://doi.org/10.1017/S0022112005004751

[7] V. K. Natrajan and K. T. Christensen, "The role of coherent structures in subgrid-scale energy transfer within the log layer of wall turbulence," Physics of Fluids, vol. 18, no. 065104, 2006.
https://doi.org/10.1063/1.2206811

[8] M. Lesieur, P. Begou, P. Comte, and O. Metais, "Vortex recognition in numerical simulations," European Research Community On Flow, Turbulence And Combustion Bulletin, no. 46, pp. 25-28, 2000.

[9] V. A. Gushchin and P. V. Matyushin, "Mechanisms of vortices formation in the wake behind the sphere at 200 < < 380," Izvestia RAN Mechanics of Liquid and Gas, no. 5, pp. 135-151, 2006.

[10] S. Zhang and D. Choudhury, "Eigen helicity dencity: A new wortex indentification scheme and its application in accelerated inhomogeneous flows," Physics of Fluids, vol. 18, no. 058104, 2006.
https://doi.org/10.1063/1.2187071

[11] V. Kol'aˇr, "Vortex identification: New requirements and limitations," International Journal of Heat and Fluid Flow, vol. 28, no. 4, pp. 638-652, 2007.
https://doi.org/10.1016/j.ijheatfluidflow.2007.03.004

[12] P. Chakraborty, S. Balachandar, and R. Adrian, "On the relationships between local vortex identification schemes," Journal of Fluid Mechanics, vol. 535, pp. 189-214, 2005.
https://doi.org/10.1017/S0022112005004726

[13] J. Jeong, F. Hussain, W. Schoppa, and J. Kim, "Coherent structures near the wall in a turbulent channel flow," Journal of Fluid Mechanics, vol. 332, pp. 185-214, 1997.
https://doi.org/10.1017/S0022112096003965

[14] C. Meneveau and J. Katz, "Scale-invariance and turbulence models for Large-Eddy Simulation," Annual Review of Fluid Mechanics, vol. 32, pp. 1-32, 2000.
https://doi.org/10.1146/annurev.fluid.32.1.1

[15] A. S. Neto, D. Grand, O. M'etais, and M. Lesieur, "A numerical investigation of the coherent vortices in turbulence behind a backward-facing step," Journal of Fluid Mechanics, vol. 256, pp. 1-25, 1993.
https://doi.org/10.1017/S0022112093002691

[16] V. G. Kuzmenko, "The simulation of turbulent flow with the fence by different external conditions. Part 2. Coherent structures identification," Applied Hydromechanics, vol. 17(89), no. 3, pp. 18-34, 2015.

[17] G. Haller, "Distinguished material surfaces and coherent structures in three-dimensional fluid flows," Physica D: Nonlinear Phenomena, vol. 149, no. 4, pp. 248-277, 2001.
https://doi.org/10.1016/S0167-2789(00)00199-8

[18] V. G. Kuzmenko, "Simulation of turbulent flow with the fence and 3d coherent structures identification," Applied Hydromechanics, vol. 18(90), no. 1, pp. 31-42, 2016.

[19] C. VerHulst and C. Meneveau, "Large Eddy Simulation study of the kinetic energy entrainment by energetic turbulent flow structures in large wind farms," Physics of Fluids, vol. 26, no. 2, p. 025113, 2014.
https://doi.org/10.1063/1.4865755

[20] F. Selimefendigil and W. Polifke, "Nonlinear, proper-orthogonal-decomposition-based model of forced convection heat transfer in pulsating flow," American Institute of Aeronautics and Astronautics Journal, vol. 52, no. 1, pp. 131-145, 2014.
https://doi.org/10.2514/1.J051647

[21] J.-L. Balint, J. M. Wallace, and P. Vukoslavcevic, "The velocity and vorticity vector fields of a turbulent boundary layer. Part 2. Statistical properties," Journal of Fluid Mechanics, vol. 228, pp. 53-86, 1991.
https://doi.org/10.1017/S002211209100263X

[22] A. Orellano and H. Wengle, "Numerical simulation (DNS and LES) of manipulated turbulent boundary layer flow over a surface-mounted fence," European Journal of Mechanics - B/Fluids, vol. 19, no. 5, pp. 765-788, 2000.
https://doi.org/10.1016/S0997-7546(00)00115-1

[23] V. G. Kuzmenko, "The simulation of turbulent wall flow with a fence on the base of hybrid LES/RANS-approach," Applied Hydromechanics, vol. 13(85), no. 3, pp. 48-60, 2011.

[24] M. Germano, U. Piomelli, P. Moin, and W. H. Cabot, "A dynamic subgrid-scale eddy viscosity model," Physics of Fluids A: Fluid Dynamics, vol. 3, no. 7, pp. 1760-1765, 1991.
https://doi.org/10.1063/1.857955

[25] U. Piomelli and E. Balaras, "Wall-layer models for Large-Eddy Simulations," Annual Review of Fluid Mechanics, vol. 34, pp. 349-374, 2002.
https://doi.org/10.1146/annurev.fluid.34.082901.144919

[26] V. G. Kuzmenko, "3D numerical modelling of turbulent boundary layer in the regime of developed roughness on the basis of LES-technique," Applied Hydromechanics, vol. 4(76), no. 3, pp. 31-41, 2002.

[27] V. G. Kuzmenko, "The numerical 3D modelling of turbulent boundary layer in the regime of intermediate roughness," Applied Hydromechanics, vol. 5(77), no. 2, pp. 27-36, 2003.

[28] V. G. Kuzmenko, "Numerical 3-D modelling of turbulent boundary layer on the basis of economical LES-technique," Applied Hydromechanics, vol. 6(78), no. 1, pp. 19-24, 2004.

[29] V. G. Kuzmenko, "Dynamic subgridscale model for LES-technique," Applied Hydromechanics, vol. 6(78), no. 3, pp. 48-53, 2004.

[30] V. G. Kuzmenko, "The simulation of turbulent flow with separation in asymetric channel on the base of hybrid LES/RANS-technique," Applied Hydromechanics, vol. 12(84), no. 3, pp. 24-37, 2010.

[31] V. G. Kuzmenko, "Numerical modelling of nonstationary turbulent flow with seperation over and inside cavity," Applied Hydromechanics, vol. 11(83), no. 3, pp. 28-41, 2009.

[32] M. Breuer, "Wall models for LES of separated flows," European Research Community On Flow, Turbulence And Combustion Bulletin, vol. 72, pp. 13-18, 2007.

[33] V. G. Kuzmenko, "Simulation of turbulent flow with separation beyond backward-facing step," Applied Hydromechanics, vol. 9(81), no. 4, pp. 37-48, 2007.

[34] V. G. Kuzmenko, "The simulation of unsteady turbulent flow with obstacle on the base of hybrid LES/URANS-approach," Applied Hydromechanics, vol. 15(87), no. 2, pp. 22-36, 2013.

[35] V. G. Kuzmenko, "The simulation of turbulent flow with the fence by different external conditions on the base of hybrid LES/URANS-approach. Part 1," Applied Hydromechanics, vol. 17(89), no. 1, pp. 59-71, 2015.

[36] E. T. Spyropoulos and G. A. Blaisdell, "Large-Eddy Simulation of a spatially evolving supersonic turbulent boundary-layer flow," AIAA Journal, vol. 36, no. 11, pp. 1983-1990, 1998.
https://doi.org/10.2514/2.325

[37] K. G. Ranga Raju, J. Loeser, and E. J. Plate, "Velocity profiles and fence drag for a turbulent boundary layer along smooth and rough flat plates," Journal of Fluid Mechanics, vol. 76, no. 2, pp. 383-399, 1976.
https://doi.org/10.1017/S0022112076000682

[38] H. A. Siller and H.-H. Fernholz, "Manipulation of the reverse-flow region downstream of a fence by spanwise vortices," European Journal of Mechanics - B/Fluids, vol. 26, no. 2, pp. 236-257, 2007.
https://doi.org/10.1016/j.euromechflu.2006.05.005

[39] K. Aoki, K. Kanba, and S. Takata, "Numerical analysis of a supersonic rarefied gas flow past a flat plate," Physics of Fluids, vol. 9, no. 4, pp. 1144-1161, 1997.
https://doi.org/10.1063/1.869204

[40] A. E. Perry, S. Henbest, and M. S. Chong, "A theoretical and experimental study of wall turbulence," Journal of Fluid Mechanics, vol. 165, no. 1, pp. 163-199, 1986.
https://doi.org/10.1017/S002211208600304X

[41] A. E. Perry, K. L. Lim, and S. M. Henbest, "An experimental study of the turbulence structure in smooth- and rough-wall boundary layers," Journal of Fluid Mechanics, vol. 177, pp. 437-466, 1987.
https://doi.org/10.1017/S0022112087001034