LES and DNS of the Flow with Heat Transfer in Rotating Cavity
Tuliszka-Sznitko Ewa, Majchrowski Wojciech
Institute of Thermal Engineering, Poznań University of Technology
60-965 Poznań, Poland
e-mail: ewa.tuliszka-sznitko@put.poznan.pl
Received:
Received: 1 December 2009; revised: 2 March 2010; accepted 10 March 2010; published online: 20 April 2010
DOI: 10.12921/cmst.2010.16.01.105-114
OAI: oai:lib.psnc.pl:709
Abstract:
In the present paper we summarized our numerical investigations on the flow with heat transfer in rotating cavity performed by DNS (Direct Numerical Simulation) and LES (Large Eddy Simulation). We considered different geometrical configurations and different flow and thermal conditions. All presented computations have been performed in Poznań Supercomputing and Networking Center. The objective of our investigations was to analyze the coherent structures of transitional and turbulent flows and to compute statistical parameters, i.e. turbulent heat fluxes, the Reynolds stress tensor components, the turbulent Prandtl number and others. In the LES we used a version of the dynamic Smagorinsky eddy viscosity model proposed by Meneveau et al. (A Lagrangian dynamic subgrid-scale model of turbulence, J. Fluid Mech., vol. 319, 1996), in which the Smagorinsky coefficient at a given position x depends on the history of the flow along the fluid particle pathline.
Key words:
DNS, flow instability, laminar-turbulent transition, LES, rotating cavity, spectral methods
References:
[1] J.W. Daily, R.E. Nece, Chamber dimension effects on induced flow and friction resistance of enclosed rotating disks. J. Basic Engng. 82, 217-232 (1960).
[2] S.T. McComas, J.P. Hartnett, Temperature profiles and heat transfer associated with a single disk rotating in still air. Proc. 4th Heat Transfer Conf., Versailles, 3, FC7.7 (1970).
[3] C.O. Popiel, L. Boguslawski, Local heat-transfer coefficients on the rotating disk in still air. Int. J. Heat Mass Transfer 18, 167-170 (1975).
[4] H.S. Littell, J.J. Eaton, Turbulence characteristics of the boundary layer on a rotating disk. J. Fluid Mech. 266, 175-207 (1994).
[5] C.J. Elkins, J.K. Eaton, Turbulent heat and momentum transport on a rotating disk. J. Fluid Mech. 402, 225-253 (2000).
[6] N.I. Nikitenko, Experimental investigation of heat exchange of a disk and screen. J. Eng. Phys. 6, 1-11 (1963).
[7] J.M. Owen, J.R. Pincombe, Velocity measurements inside a rotating cylindrical cavity with a radial outflow of fluid. J. Fluid Mech. 99, 111-127 (1980).
[8] V.K. Schukin, V.V. Olimpiev, Heat transfer of disc rotating in a housing with transitional and turbulent boundary layer. Soviet Aeronaut. 18, 77-81 (1975).
[9] J. M. Owen, R. Rogers, Flow and heat transfer in rotatingdisc systems. vol. 1. Research Studies Press Taunton (1989).
[10] J.M. Owen, R.H. Rogers, Flow and heat transfer in rotating- disc systems. vol. 2. Research Studies Press Taunton (1995).
[11] S. Mochizuki, W. Yang, Three mechanisms of convective enhancement in stationary disk systems. Trans. ASME J. Heat Transfer 108, 978-980 (1986).
[12] M. Itoh, Y. Yamada, S. Imao, M. Gonda, Experiments on turbulent flow due to an enclosed rotating disk. In: Ganic, E., Rodi, W. (Eds.), Engineering Turbulence Modeling and Experiments, Elsevier, New York, 659-668 (1990).
[13] M. Djaoui, R. Debuchy, Heat transfer in a rotor-stator system with a radial inflow. C.R. Acad. Sci. Paris II B. 326, 309-314 (1998).
[14] J. Pellé, S. Harmand, Heat transfer measurements in an opened rotor–stator system air-gap. Exp. Therm. Fluid Sci. 31, 165-180 (2007).
[15] A. Morse, Numerical prediction of turbulent flow in rotating cavities. In: Gas Turbine Conf. and Exhibition, Anaheim, CA, ASME Paper 87-GT-74 (1987).
[16] B.E. Launder, B.I. Sharma, Application of the energy dissipation model of turbulence to the calculation of flow near a spinning disc. Letters in Heat and Mass Transfer. 1(2), 131-138 (1974).
[17] J.W. Chew, C.M. Vaughan, Numerical predictions for the flow induced by an enclosed rotating disc. In: 33rd Gas Turbine Conf., Amsterdam, ASME Paper 88-GT-127, (1988).
[18] E. Serre, J.P. Pulicani, A three-dimensional pseudospectral method for rotating flows in a cylinder. Comput. Fluids 30, 491 (2001).
[19] E. Serre, E. Tuliszka-Sznitko, P. Bontoux, Coupled numerical and theoretical study of the transition flow between a rotating and stationary disk, Phys. Fluids 16 (3), 688-707, (2004).
[20] F. Moisy, O. Doaré, T. Pasutto, O. Daube, M. Rabaud, Experimental and numerical study of the shear layer instability between two counter-rotating disks. J. Fluid Mech. 507, 175-202 (2004).
[21] R. Jacques, P. Le Quéré, O. Daube, Axisymmetric numerical simulations of turbulent flow in a rotor stator enclosures. Int. J. Heat Fluid Flow. 23, 381-397 (2002).
[22] A. Randriamampianina, S. Poncet, Turbulence characteristics of Bödewadt layer in a large enclosed rotor-stator system. Phys. Fluids 18, 055104 (2006).
[23] E. Tuliszka-Sznito, E. Serre, P. Bontoux, On the nature of the boundary layers instabilities in a flow between a rotating and a stationary disc. C.R. Acad. Sci. Paris 330, 91-99 (2002).
[24] E. Tuliszka-Sznitko, A. Zieliński, W. Majchrowski, LES and DNS of the non-isothermal transitional flow in rotating cavity. Int. J. Heat and Fluid Flow. 30 (3), 534-548 (2009).
[25] E. Tuliszka-Sznitko, A. Zieliński, W. Majchrowski, LES of the transitional flow in rotor/stator cavity. Archive of Mechanics 61(2), 93-118 (2009).
[26] M. Lygren, H.I. Andersson, Turbulent flow between a rotating and a stationary disk. J. Fluid Mech. 426, 297 (2001).
[27] X. Wu, K.D. Squires, Prediction and investigation of the turbulent flow over a rotating disk. J. Fluid Mech. 418, 231-264 (2000).
[28] H.I. Andersson, M. Lygren, LES of open rotor-stator flow. Int. J. Heat Fluid Flow 27 (4), 551-557 (2006).
[29] E. Séverac, S. Poncet, E. Serre, M.P. Chauve, Large eddy simulations and measurements of turbulent enclosed rotor–stator flows. Phys. Fluids 19, 085113-1-17 (2007).
[30] A. Randriamampianina, P. Bontoux, B. Roux, Ecoulements induits par la force gravifique dans une cavité cylindrique en rotation. Int. J. Heat Mass Transfer 30 (7), 1275-1292 (1987).
[31] C. Meneveau, T.S. Lund, W.H. Cabot, A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319, 353-385 (1996).
[32] E. Serre, E. Crespo del Arco, P. Bontoux, Annular and spiral patterns between a rotating and a stationary disk. J. Fluid Mech. 434, 65-100 (2000).
[33] M. Germano, U. Piomelli, P. Moin, W. Cabot, A dynamic subgrid-scale eddy-viscosity model. Phys. Fluids A, 3 (7), 1760-1765 (1991).
[34] D.K. Lilly, A proposed modification of the Germano subgrid- scale closure method. Phys. Fluids A, 4 (3), 633-635 (1992).
[35] E. Tuliszka-Sznitko, W. Majchrowski, Large eddy simulation of non-isothermal flow in rotor/stator cavity. Proceedings of Int. Symp. on Heat Transfer in Gas Turbine Systems
(2009).
[36] E. Tuliszka-Sznitko, A. Zielinski, W. Majchrowski, LES of the non-isothermal flow in rotating cavity. Springer, Hybrid RANS-LES Methods, ed. by W. Haase (accepted) (2009).
[37] D.E. Wróblewski, P.A. Eibeck, An experimental investigation of turbulent heat transport in a boundary layer with an embedded streamwise vortex. PhD Thesis, University of
California at Berkeley, Mechanical Engineering Department (1990).
[38] M.M. Gibson, C.A. Verriopoulos, Turbulent boundary layer on a middle curved surface. Part 2: Temperature field measurements, Exps. Fluids 2, 73-80 (1984).
[39] C.S. Subramanian, R.A. Antonia, Effect of Reynolds number on a slightly heated turbulent boundary layer. Int. J. Heat Mass Transfer 24, 1833-1846 (1981).
[40] E. Tuliszka-Sznitko, A. Zielinski, DNS/LES of Transitional Flow in Rotating Cavity. Int. J. of Transport Phenomena 10(3), 223-234 (2008).
[41] G. Gauthier, P. Gondret, F. Moisy, M. Rabaud, Instabilities in the flow between co- and counter-rotating disks. J. Fluid Mech. 473, 1-21 (2002).
In the present paper we summarized our numerical investigations on the flow with heat transfer in rotating cavity performed by DNS (Direct Numerical Simulation) and LES (Large Eddy Simulation). We considered different geometrical configurations and different flow and thermal conditions. All presented computations have been performed in Poznań Supercomputing and Networking Center. The objective of our investigations was to analyze the coherent structures of transitional and turbulent flows and to compute statistical parameters, i.e. turbulent heat fluxes, the Reynolds stress tensor components, the turbulent Prandtl number and others. In the LES we used a version of the dynamic Smagorinsky eddy viscosity model proposed by Meneveau et al. (A Lagrangian dynamic subgrid-scale model of turbulence, J. Fluid Mech., vol. 319, 1996), in which the Smagorinsky coefficient at a given position x depends on the history of the flow along the fluid particle pathline.
Key words:
DNS, flow instability, laminar-turbulent transition, LES, rotating cavity, spectral methods
References:
[1] J.W. Daily, R.E. Nece, Chamber dimension effects on induced flow and friction resistance of enclosed rotating disks. J. Basic Engng. 82, 217-232 (1960).
[2] S.T. McComas, J.P. Hartnett, Temperature profiles and heat transfer associated with a single disk rotating in still air. Proc. 4th Heat Transfer Conf., Versailles, 3, FC7.7 (1970).
[3] C.O. Popiel, L. Boguslawski, Local heat-transfer coefficients on the rotating disk in still air. Int. J. Heat Mass Transfer 18, 167-170 (1975).
[4] H.S. Littell, J.J. Eaton, Turbulence characteristics of the boundary layer on a rotating disk. J. Fluid Mech. 266, 175-207 (1994).
[5] C.J. Elkins, J.K. Eaton, Turbulent heat and momentum transport on a rotating disk. J. Fluid Mech. 402, 225-253 (2000).
[6] N.I. Nikitenko, Experimental investigation of heat exchange of a disk and screen. J. Eng. Phys. 6, 1-11 (1963).
[7] J.M. Owen, J.R. Pincombe, Velocity measurements inside a rotating cylindrical cavity with a radial outflow of fluid. J. Fluid Mech. 99, 111-127 (1980).
[8] V.K. Schukin, V.V. Olimpiev, Heat transfer of disc rotating in a housing with transitional and turbulent boundary layer. Soviet Aeronaut. 18, 77-81 (1975).
[9] J. M. Owen, R. Rogers, Flow and heat transfer in rotatingdisc systems. vol. 1. Research Studies Press Taunton (1989).
[10] J.M. Owen, R.H. Rogers, Flow and heat transfer in rotating- disc systems. vol. 2. Research Studies Press Taunton (1995).
[11] S. Mochizuki, W. Yang, Three mechanisms of convective enhancement in stationary disk systems. Trans. ASME J. Heat Transfer 108, 978-980 (1986).
[12] M. Itoh, Y. Yamada, S. Imao, M. Gonda, Experiments on turbulent flow due to an enclosed rotating disk. In: Ganic, E., Rodi, W. (Eds.), Engineering Turbulence Modeling and Experiments, Elsevier, New York, 659-668 (1990).
[13] M. Djaoui, R. Debuchy, Heat transfer in a rotor-stator system with a radial inflow. C.R. Acad. Sci. Paris II B. 326, 309-314 (1998).
[14] J. Pellé, S. Harmand, Heat transfer measurements in an opened rotor–stator system air-gap. Exp. Therm. Fluid Sci. 31, 165-180 (2007).
[15] A. Morse, Numerical prediction of turbulent flow in rotating cavities. In: Gas Turbine Conf. and Exhibition, Anaheim, CA, ASME Paper 87-GT-74 (1987).
[16] B.E. Launder, B.I. Sharma, Application of the energy dissipation model of turbulence to the calculation of flow near a spinning disc. Letters in Heat and Mass Transfer. 1(2), 131-138 (1974).
[17] J.W. Chew, C.M. Vaughan, Numerical predictions for the flow induced by an enclosed rotating disc. In: 33rd Gas Turbine Conf., Amsterdam, ASME Paper 88-GT-127, (1988).
[18] E. Serre, J.P. Pulicani, A three-dimensional pseudospectral method for rotating flows in a cylinder. Comput. Fluids 30, 491 (2001).
[19] E. Serre, E. Tuliszka-Sznitko, P. Bontoux, Coupled numerical and theoretical study of the transition flow between a rotating and stationary disk, Phys. Fluids 16 (3), 688-707, (2004).
[20] F. Moisy, O. Doaré, T. Pasutto, O. Daube, M. Rabaud, Experimental and numerical study of the shear layer instability between two counter-rotating disks. J. Fluid Mech. 507, 175-202 (2004).
[21] R. Jacques, P. Le Quéré, O. Daube, Axisymmetric numerical simulations of turbulent flow in a rotor stator enclosures. Int. J. Heat Fluid Flow. 23, 381-397 (2002).
[22] A. Randriamampianina, S. Poncet, Turbulence characteristics of Bödewadt layer in a large enclosed rotor-stator system. Phys. Fluids 18, 055104 (2006).
[23] E. Tuliszka-Sznito, E. Serre, P. Bontoux, On the nature of the boundary layers instabilities in a flow between a rotating and a stationary disc. C.R. Acad. Sci. Paris 330, 91-99 (2002).
[24] E. Tuliszka-Sznitko, A. Zieliński, W. Majchrowski, LES and DNS of the non-isothermal transitional flow in rotating cavity. Int. J. Heat and Fluid Flow. 30 (3), 534-548 (2009).
[25] E. Tuliszka-Sznitko, A. Zieliński, W. Majchrowski, LES of the transitional flow in rotor/stator cavity. Archive of Mechanics 61(2), 93-118 (2009).
[26] M. Lygren, H.I. Andersson, Turbulent flow between a rotating and a stationary disk. J. Fluid Mech. 426, 297 (2001).
[27] X. Wu, K.D. Squires, Prediction and investigation of the turbulent flow over a rotating disk. J. Fluid Mech. 418, 231-264 (2000).
[28] H.I. Andersson, M. Lygren, LES of open rotor-stator flow. Int. J. Heat Fluid Flow 27 (4), 551-557 (2006).
[29] E. Séverac, S. Poncet, E. Serre, M.P. Chauve, Large eddy simulations and measurements of turbulent enclosed rotor–stator flows. Phys. Fluids 19, 085113-1-17 (2007).
[30] A. Randriamampianina, P. Bontoux, B. Roux, Ecoulements induits par la force gravifique dans une cavité cylindrique en rotation. Int. J. Heat Mass Transfer 30 (7), 1275-1292 (1987).
[31] C. Meneveau, T.S. Lund, W.H. Cabot, A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319, 353-385 (1996).
[32] E. Serre, E. Crespo del Arco, P. Bontoux, Annular and spiral patterns between a rotating and a stationary disk. J. Fluid Mech. 434, 65-100 (2000).
[33] M. Germano, U. Piomelli, P. Moin, W. Cabot, A dynamic subgrid-scale eddy-viscosity model. Phys. Fluids A, 3 (7), 1760-1765 (1991).
[34] D.K. Lilly, A proposed modification of the Germano subgrid- scale closure method. Phys. Fluids A, 4 (3), 633-635 (1992).
[35] E. Tuliszka-Sznitko, W. Majchrowski, Large eddy simulation of non-isothermal flow in rotor/stator cavity. Proceedings of Int. Symp. on Heat Transfer in Gas Turbine Systems
(2009).
[36] E. Tuliszka-Sznitko, A. Zielinski, W. Majchrowski, LES of the non-isothermal flow in rotating cavity. Springer, Hybrid RANS-LES Methods, ed. by W. Haase (accepted) (2009).
[37] D.E. Wróblewski, P.A. Eibeck, An experimental investigation of turbulent heat transport in a boundary layer with an embedded streamwise vortex. PhD Thesis, University of
California at Berkeley, Mechanical Engineering Department (1990).
[38] M.M. Gibson, C.A. Verriopoulos, Turbulent boundary layer on a middle curved surface. Part 2: Temperature field measurements, Exps. Fluids 2, 73-80 (1984).
[39] C.S. Subramanian, R.A. Antonia, Effect of Reynolds number on a slightly heated turbulent boundary layer. Int. J. Heat Mass Transfer 24, 1833-1846 (1981).
[40] E. Tuliszka-Sznitko, A. Zielinski, DNS/LES of Transitional Flow in Rotating Cavity. Int. J. of Transport Phenomena 10(3), 223-234 (2008).
[41] G. Gauthier, P. Gondret, F. Moisy, M. Rabaud, Instabilities in the flow between co- and counter-rotating disks. J. Fluid Mech. 473, 1-21 (2002).
