Numerical Study of Correlation of Fluid Particle Acceleration and Turbulence Intensity in Swirling Flow
Nan Gui
Institute of Nuclear and New Energy Technology of Tsinghua University and the Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education, Beijing 100084, China tsinghua.edu.cn
Department of Thermal Energy Engineering, College of Mechanical and Transportation Engineering, China University of Petroleum, Beijing 102249, China cup.edu.cn
Search for more papers by this authorXingtuan Yang
Institute of Nuclear and New Energy Technology of Tsinghua University and the Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education, Beijing 100084, China tsinghua.edu.cn
Search for more papers by this authorJie Yan
China Academy of Space Technology, Beijing 10094, China cast.cn
Search for more papers by this authorJiyuan Tu
Institute of Nuclear and New Energy Technology of Tsinghua University and the Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education, Beijing 100084, China tsinghua.edu.cn
School of Aerospace, Mechanical & Manufacturing Engineering, RMIT University, Melbourne, VIC 3083, Australia rmit.edu.au
Search for more papers by this authorCorresponding Author
Shengyao Jiang
Institute of Nuclear and New Energy Technology of Tsinghua University and the Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education, Beijing 100084, China tsinghua.edu.cn
Search for more papers by this authorNan Gui
Institute of Nuclear and New Energy Technology of Tsinghua University and the Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education, Beijing 100084, China tsinghua.edu.cn
Department of Thermal Energy Engineering, College of Mechanical and Transportation Engineering, China University of Petroleum, Beijing 102249, China cup.edu.cn
Search for more papers by this authorXingtuan Yang
Institute of Nuclear and New Energy Technology of Tsinghua University and the Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education, Beijing 100084, China tsinghua.edu.cn
Search for more papers by this authorJie Yan
China Academy of Space Technology, Beijing 10094, China cast.cn
Search for more papers by this authorJiyuan Tu
Institute of Nuclear and New Energy Technology of Tsinghua University and the Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education, Beijing 100084, China tsinghua.edu.cn
School of Aerospace, Mechanical & Manufacturing Engineering, RMIT University, Melbourne, VIC 3083, Australia rmit.edu.au
Search for more papers by this authorCorresponding Author
Shengyao Jiang
Institute of Nuclear and New Energy Technology of Tsinghua University and the Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education, Beijing 100084, China tsinghua.edu.cn
Search for more papers by this authorAbstract
Numerical investigation of correlation between the fluid particle acceleration and the intensity of turbulence in swirling flows at a large Reynolds number is carried out via direct numerical simulation. A weak power-law form correlation between the Lagrangian acceleration and the Eulerian turbulence intensity is derived. It is found that the increase of the swirl level leads to the increase of the exponent φ and the trajectory-conditioned correlation coefficient ρ(aL, uE) and results in a weak power-law augmentation of the acceleration intermittency. The trajectory-conditioned convection of turbulence fluctuation in the Eulerian viewpoint is generally linearly proportional to the fluctuation of Lagrangian accelerations, indicating a weak but clear relation between the Lagrangian intermittency and Eulerian intermittency effects. Moreover, except the case with vortex breakdown, the weak linear dependency is maintained when the swirl levels change, only with the coefficient of slope varied.
References
- 1 Baldyga J. and Bourne J. R., Mixing and fast chemical reaction-VIII: initial deformation of material elements in isotropic, homogeneous turbulence, Chemical Engineering Science. (1984) 39, no. 2, 329–334, https://doi.org/10.1016/0009-2509(84)80031-7, 2-s2.0-0001452525.
- 2 Marshall J. S. and Huang Y., Simulation of light-limited algae growth in homogeneous turbulence, Chemical Engineering Science. (2010) 65, no. 12, 3865–3875, https://doi.org/10.1016/j.ces.2010.03.036, 2-s2.0-77951101139.
- 3 Freitag M., Klein M., Gregor M., Geyer D., Schneider C., Dreizler A., and Janicka J., Mixing analysis of a swirling recirculating flow using DNS and experimental data, International Journal of Heat and Fluid Flow. (2006) 27, no. 4, 636–643, https://doi.org/10.1016/j.ijheatfluidflow.2006.02.020, 2-s2.0-33745727917.
- 4 Giannadakis A., Perrakis K., and Panidis T., A swirling jet under the influence of a coaxial flow, Experimental Thermal and Fluid Science. (2008) 32, no. 8, 1548–1563, https://doi.org/10.1016/j.expthermflusci.2008.04.010, 2-s2.0-49649098957.
- 5 Xing T., Direct numerical simulation of Open von Kármán Swirling Flow, Journal of Hydrodynamics. (2014) 26, no. 2, 165–177, https://doi.org/10.1016/S1001-6058(14)60019-6, 2-s2.0-84899874576.
- 6 Hreiz R., Gentric C., and Midoux N., Numerical investigation of swirling flow in cylindrical cyclones, Chemical Engineering Research and Design. (2011) 89, no. 12, 2521–2539, https://doi.org/10.1016/j.cherd.2011.05.001, 2-s2.0-82855165188.
- 7 Siamas G. A., Jiang X., and Wrobel L. C., Numerical investigation of a perturbed swirling annular two-phase jet, International Journal of Heat and Fluid Flow. (2009) 30, no. 3, 481–493, https://doi.org/10.1016/j.ijheatfluidflow.2009.02.020, 2-s2.0-67349092106.
- 8 Tanaka S., Shimura M., Fukushima N., Tanahashi M., and Miyauchi T., DNS of turbulent swirling premixed flame in a micro gas turbine combustor, Proceedings of the Combustion Institute. (2011) 33, no. 2, 3293–3300, https://doi.org/10.1016/j.proci.2010.07.034, 2-s2.0-79251621550.
- 9 La Porta A., Voth G. A., Crawford A. M., Alexander J., and Bodenschatz E., Fluid particle accelerations in fully developed turbulence, Nature. (2001) 409, no. 6823, 1017–1019, https://doi.org/10.1038/35059027, 2-s2.0-0035931880.
- 10 Sun H. G. and Chen W., Fractal derivative multi-scale model of fluid particle transverse accelerations in fully developed turbulence, Science in China, Series E: Technological Sciences. (2009) 52, no. 3, 680–683, https://doi.org/10.1007/s11431-009-0050-3, 2-s2.0-61349121414.
- 11 Pope S. B., Lagrangian PDF methods for turbulent flows, Annual Review of Fluid Mechanics. (1994) 26, 23–63, https://doi.org/10.1146/annurev.fl.26.010194.000323.
- 12 Rammohan A. R., Kemoun A., Al-Dahhan M. H., and Dudukovic M. P., A lagrangian description of flows in stirred tanks via computer-automated radioactive particle tracking (CARPT), Chemical Engineering Science. (2001) 56, no. 8, 2629–2639, https://doi.org/10.1016/S0009-2509(00)00537-6, 2-s2.0-0035938677.
- 13 Falkovich G., Gawędzki K., and Vergassola M., Particles and fields in fluid turbulence, Reviews of Modern Physics. (2001) 73, no. 4, 913–975, https://doi.org/10.1103/RevModPhys.73.913, MR1878800, 2-s2.0-0035470905.
- 14 Voth G. A., Satyanarayan K., and Bodenschatz E., Lagrangian acceleration measurements at large Reynolds numbers, Physics of Fluids. (1998) 10, no. 9, 2268–2280, https://doi.org/10.1063/1.869748, 2-s2.0-11644283416.
- 15 Mordant N., Crawford A. M., and Bodenschatz E., Three-dimensional structure of the lagrangian acceleration in turbulent flows, Physical Review Letters. (2004) 93, 214501, https://doi.org/10.1103/PhysRevLett.93.214501, 2-s2.0-42749100681.
- 16 Crawford A. M., Mordant N., and Bodenschatz E., Joint statistics of the lagrangian acceleration and velocity in fully developed turbulence, Physical Review Letters. (2005) 94, no. 2, 024501, https://doi.org/10.1103/PhysRevLett.94.024501, 2-s2.0-18144400648.
- 17 Mordant N., Metz P., Michel O., and Pinton J.-F., Measurement of lagrangian velocity in fully developed turbulence, Physical Review Letters. (2001) 87, no. 21, 214501, 2-s2.0-0035914752.
- 18 Chevillard L., Roux S. G., Levêque E., Mordant N., Pinton J.-F., and Arneodo A., Lagrangian velocity statistics in turbulent flows: effects of dissipation, Physical Review Letters. (2003) 91, no. 21, 214502, 2-s2.0-0347682136.
- 19 Fu D. X. and Ma Y. W., A high order accurate difference scheme for complex flow fields, Journal of Computational Physics. (1997) 134, no. 1, 1–15, https://doi.org/10.1006/jcph.1996.5492, MR1455253, 2-s2.0-0031161230.
- 20 Lele S. K., Compact finite difference schemes with spectral-like resolution, Journal of Computational Physics. (1992) 103, no. 1, 16–42, https://doi.org/10.1016/0021-9991(92)90324-R, MR1188088, ZBL0759.65006, 2-s2.0-9144220381.
- 21 Jameson A. and Schmidt W., Some recent developments in numerical methods for transonic flows, Computer Methods in Applied Mechanics and Engineering. (1985) 51, no. 1–3, 467–493, https://doi.org/10.1016/0045-7825(85)90043-X, MR822753, 2-s2.0-0000525843.
- 22
Anantha Krishnaiah U.,
Manohar R., and
Stephenson J. W., Fourth-order finite difference methods for three-dimensional general linear elliptic problems with variable coefficients, Numerical Methods for Partial Differential Equations. (1987) 3, no. 3, 229–240, https://doi.org/10.1002/num.1690030307, MR1012916.
10.1002/num.1690030307 Google Scholar
- 23 Gui N., Yan J., Li Z., and Fan J., Direct numerical simulation of confined swirling jets, International Journal of Computational Fluid Dynamics. (2014) 28, no. 1-2, 76–88, https://doi.org/10.1080/10618562.2014.898754, MR3195898, 2-s2.0-84897913775.
- 24 Gui N., Fan J., and Chen S., Numerical study of particle-vortex interaction and turbulence modulation in swirling jets, Physical Review E: Statistical, Nonlinear, and Soft Matter Physics. (2010) 82, no. 5, 056323, https://doi.org/10.1103/PhysRevE.82.056323, 2-s2.0-78651385745.
- 25 Billant P., Chomaz J.-M., and Huerre P., Experimental study of vortex breakdown in swirling jets, Journal of Fluid Mechanics. (1998) 376, 183–219, https://doi.org/10.1017/S0022112098002870, MR1658974, ZBL0941.76522, 2-s2.0-0032299004.
- 26 Gui N., Fan J. R., Cen K. F., and Chen S. A., A direct numerical simulation study of coherent oscillation effects of swirling flows, Fuel. (2010) 89, no. 12, 3926–3933, https://doi.org/10.1016/j.fuel.2010.06.037, 2-s2.0-77956610498.
- 27 Gui N., Fan J. R., and Chen S., Numerical study of particle-particle collision in swirling jets: a DEM-DNS coupling simulation, Chemical Engineering Science. (2010) 65, no. 10, 3268–3278, https://doi.org/10.1016/j.ces.2010.02.026, 2-s2.0-77950581696.
- 28 Orlanski I., A simple boundary condition for unbounded hyperbolic flows, Journal of Computational Physics. (1976) 21, no. 3, 251–269, https://doi.org/10.1016/0021-9991(76)90023-1, ZBL0403.76040, 2-s2.0-0016870918.
- 29 Moin P. and Mahesh K., Direct numercial simulation: a tool in turbulence research, Annual Review of Fluid Mechanics. (1998) 30, 539–578.