Numerical Investigations of Taylor-Couette Flow Using DNS/SVV Method
Tuliszka-Sznitko Ewa *, Kiełczewski Kamil
Institute of Thermal Engineering, Poznań University of Technology
Poznań, ul. Piotrowo3, 60-965 Poznań
*E-mail: ewa.tuliszka-sznitko@put.poznan.pl
Received:
Received: 15 June 2015; revised: 30 September 2015; accepted: 30 September 2015; published online: 03 November 2015
DOI: 10.12921/cmst.2015.21.04.005
Abstract:
In the paper the authors present the results obtained during a numerical investigation (Direct Numerical Simulation/Spectral Vanishing Viscosity method – DNS/SVV) of a Taylor-Couette flow, i.e. the flow between two concentric disks and two concentric cylinders. The Taylor-Couette flow is one of paradigmatical systems in hydrodynamics, widely used for studying the primary instability, pattern formation, transitional flows and fully turbulent flows. Simultaneously, the flows in rotating cavities appear in numerous machines in the field of mechanics and chemistry, e.g., in cooling systems of gas turbines and axial compressors. In the paper, attention is focused on the laminar-turbulent transition region of the Taylor-Couette flow. The main purpose of the computations is to investigate the influence of different parameters (the aspect ratio, the end-wall boundary conditions, temperature gradient) on the flow structure and on flow characteristics.
Key words:
DNS, heat transfer, laminar-turbulent transition, Taylor-Couette flow, turbulence
References:
[1] K.T. Coughlin, P.S. Marcus, Modulated waves in
Taylor-Couette flow Part 1. Analysis. J. Fluid Mech.
234, 1-18 (1992).
[2] D.P. Lathrop, J. Fineberg, H.L. Swinney, Transition
to shear-driven turbulence in Couette-Taylor flow.
Phys. Rev. A 46, 6390-6405 (1992).
[3] Ch. Egbers, G. Pfister, Physics of rotating fluids, Lecture
Notes in Physics. Springer (2000).
[4] O. Czarny, E. Serre, P. Bontoux, R.M. Lueptow, Interaction
of wavy cylindrical Couette flow with endwalls.
Phys. Fluids 16, 1140-1148 (2004).
[5] S. Dong, Direct numerical simulation of turbulent
Taylor-Couette flow. J. Fluid Mech. 587, 373 (2007).
[6] U. Harlander, G. Wright, Ch. Egbers, Reconstruction
of the 3D flow field in a differentially heated
rotating annulus laboratory experiment. Geophysical
Research Abstracts 14 EGU2012-5368 (2012).
[7] H. Brauckmann, B. Eckhardt, Direct numerical simulations
of local and global torque in Taylor-Couette
fow up to Re D 30000. J. Fluid Mech 718, 398 (2013).
[8] W. Serre, J.P. Pulicani, A three dimensional pseudospectral
method for convection in rotating cylinder.
J. Computers & Fluids 30, 491 (2001).
[9] E. Tuliszka-Sznitko, A. Zieli´nski, W. Majchrowski,
LES of the non-isothermal transition flow in rotating
cavity, Int. J. Heat and Fluid Flow 30, 534 (2009).
[10] E. Tuliszka-Sznitko, A. Zieli´nski, W. Majchrowski,
Large eddy simulation of non-isothermal flow in rotor/
stator cavity. Proceedings of Int. Sym. On Heat
Transfer in Gas Turbine Systems, Antalya, CD-ROM,
pp.1-14, (2009).
[11] I.E. Tadmor, Convergence of spectral methods for
nonlinear conservation laws. SIAM, J. Numerical
Analysis, 26, 30 (1989).
[12] E. Severac, E. Serre, A spectral viscosity LES for the
simulation of turbulent flows within rotating cavities.
J. Comp. Phys. 226, 2, 1234 (2007).
[13] K. Kielczewski, E. Tuliszka-Sznitko, Numerical
study of the flow structure and heat transfer in rotating
cavity with and without jet. Arch. Mech. 65, 527
(2013).
[14] S. Sarra, Chebyshev Pseudospectral Methods for
Conservation Laws with Source Terms and Application
to Multiphase Flow. PhD Thesis, Morgantown,
West Virginia (2002).
[15] K. Kiełczewski, E. Tuliszka-Sznitko, P. Bontoux,
Numerical investigation of the Taylor-Couette and
Batchelor flows with heat transfer: physics and numerical
modeling. J. of Physics CS, 530, 1-8 (2014).
[16] K.A. Cliffe, T. Mullin, A numerical and experimental
study of anomalous modes in the Taylor experiment.
J. Fluid Mech. 153, 243-258 (1985).
[17] B. Bansch, Ch. Egbers, O. Meincke, N. Scurtu, Taylor
Couette System with Asymmetric Boundary Conditions.
Universitat Bremen, Zentrum fur Thenomathematik,
Report 0004 (2000).
[18] T. Mullin, C. Blohm, Bifurcation phenomena in a
Taylor-Couette flow with asymmetric boundary conditions.
Phys. Fluids 13, 136 (2001).
[19] J. Jeong, F. Hussain, On the identification of a vortex.
J. Fluid Mech. 285, 69 (1995).
[20] P. Chakraborty, S. Balachandar, R.J. Adrian, On
the relationships between local vortex identification
schemes. J. Fluid Mech. 535, 202 (2005).
In the paper the authors present the results obtained during a numerical investigation (Direct Numerical Simulation/Spectral Vanishing Viscosity method – DNS/SVV) of a Taylor-Couette flow, i.e. the flow between two concentric disks and two concentric cylinders. The Taylor-Couette flow is one of paradigmatical systems in hydrodynamics, widely used for studying the primary instability, pattern formation, transitional flows and fully turbulent flows. Simultaneously, the flows in rotating cavities appear in numerous machines in the field of mechanics and chemistry, e.g., in cooling systems of gas turbines and axial compressors. In the paper, attention is focused on the laminar-turbulent transition region of the Taylor-Couette flow. The main purpose of the computations is to investigate the influence of different parameters (the aspect ratio, the end-wall boundary conditions, temperature gradient) on the flow structure and on flow characteristics.
Key words:
DNS, heat transfer, laminar-turbulent transition, Taylor-Couette flow, turbulence
References:
[1] K.T. Coughlin, P.S. Marcus, Modulated waves in
Taylor-Couette flow Part 1. Analysis. J. Fluid Mech.
234, 1-18 (1992).
[2] D.P. Lathrop, J. Fineberg, H.L. Swinney, Transition
to shear-driven turbulence in Couette-Taylor flow.
Phys. Rev. A 46, 6390-6405 (1992).
[3] Ch. Egbers, G. Pfister, Physics of rotating fluids, Lecture
Notes in Physics. Springer (2000).
[4] O. Czarny, E. Serre, P. Bontoux, R.M. Lueptow, Interaction
of wavy cylindrical Couette flow with endwalls.
Phys. Fluids 16, 1140-1148 (2004).
[5] S. Dong, Direct numerical simulation of turbulent
Taylor-Couette flow. J. Fluid Mech. 587, 373 (2007).
[6] U. Harlander, G. Wright, Ch. Egbers, Reconstruction
of the 3D flow field in a differentially heated
rotating annulus laboratory experiment. Geophysical
Research Abstracts 14 EGU2012-5368 (2012).
[7] H. Brauckmann, B. Eckhardt, Direct numerical simulations
of local and global torque in Taylor-Couette
fow up to Re D 30000. J. Fluid Mech 718, 398 (2013).
[8] W. Serre, J.P. Pulicani, A three dimensional pseudospectral
method for convection in rotating cylinder.
J. Computers & Fluids 30, 491 (2001).
[9] E. Tuliszka-Sznitko, A. Zieli´nski, W. Majchrowski,
LES of the non-isothermal transition flow in rotating
cavity, Int. J. Heat and Fluid Flow 30, 534 (2009).
[10] E. Tuliszka-Sznitko, A. Zieli´nski, W. Majchrowski,
Large eddy simulation of non-isothermal flow in rotor/
stator cavity. Proceedings of Int. Sym. On Heat
Transfer in Gas Turbine Systems, Antalya, CD-ROM,
pp.1-14, (2009).
[11] I.E. Tadmor, Convergence of spectral methods for
nonlinear conservation laws. SIAM, J. Numerical
Analysis, 26, 30 (1989).
[12] E. Severac, E. Serre, A spectral viscosity LES for the
simulation of turbulent flows within rotating cavities.
J. Comp. Phys. 226, 2, 1234 (2007).
[13] K. Kielczewski, E. Tuliszka-Sznitko, Numerical
study of the flow structure and heat transfer in rotating
cavity with and without jet. Arch. Mech. 65, 527
(2013).
[14] S. Sarra, Chebyshev Pseudospectral Methods for
Conservation Laws with Source Terms and Application
to Multiphase Flow. PhD Thesis, Morgantown,
West Virginia (2002).
[15] K. Kiełczewski, E. Tuliszka-Sznitko, P. Bontoux,
Numerical investigation of the Taylor-Couette and
Batchelor flows with heat transfer: physics and numerical
modeling. J. of Physics CS, 530, 1-8 (2014).
[16] K.A. Cliffe, T. Mullin, A numerical and experimental
study of anomalous modes in the Taylor experiment.
J. Fluid Mech. 153, 243-258 (1985).
[17] B. Bansch, Ch. Egbers, O. Meincke, N. Scurtu, Taylor
Couette System with Asymmetric Boundary Conditions.
Universitat Bremen, Zentrum fur Thenomathematik,
Report 0004 (2000).
[18] T. Mullin, C. Blohm, Bifurcation phenomena in a
Taylor-Couette flow with asymmetric boundary conditions.
Phys. Fluids 13, 136 (2001).
[19] J. Jeong, F. Hussain, On the identification of a vortex.
J. Fluid Mech. 285, 69 (1995).
[20] P. Chakraborty, S. Balachandar, R.J. Adrian, On
the relationships between local vortex identification
schemes. J. Fluid Mech. 535, 202 (2005).
