Modeling and Numerical Simulation of Wings Effect on Turbulent Flow between two contra-rotating cylinders

Author(s)
Maher Raddaoui

ABSTRACT

Many industries in the world take part in the pollution of the environment. This pollution often comes from the reactions of combustion. To optimize these reactions and to minimize pollution, turbulence is a funda- mental tool. Several factors are at the origin of turbulence in the complex flows, among these factors, we can quote the effect of wings in the rotating flows. The interest of this work is to model and to simulate numeri- cally the effect of wings on the level of turbulence in the flow between two contra-rotating cylinders. We have fixed on these two cylinders eight wings uniformly distributed and we have varied the height of the wings to have six values from 2 mm to 20 mm by maintaining the same Reynolds number of rotation. The numerical tool is based on a statistical model in a point using the closing of the second order of the transport equations of the Reynolds stresses (Reynolds Stress Model: RSM). We have modelled wings effect on the flow by a source term added to the equation tangential speed. The results of the numerical simulation showed that all the average and fluctuating variables are affected the value of the kinetic energy of turbulence as those of Reynolds stresses increase with the height of the wings.

Many industries in the world take part in the pollution of the environment. This pollution often comes from the reactions of combustion. To optimize these reactions and to minimize pollution, turbulence is a funda- mental tool. Several factors are at the origin of turbulence in the complex flows, among these factors, we can quote the effect of wings in the rotating flows. The interest of this work is to model and to simulate numeri- cally the effect of wings on the level of turbulence in the flow between two contra-rotating cylinders. We have fixed on these two cylinders eight wings uniformly distributed and we have varied the height of the wings to have six values from 2 mm to 20 mm by maintaining the same Reynolds number of rotation. The numerical tool is based on a statistical model in a point using the closing of the second order of the transport equations of the Reynolds stresses (Reynolds Stress Model: RSM). We have modelled wings effect on the flow by a source term added to the equation tangential speed. The results of the numerical simulation showed that all the average and fluctuating variables are affected the value of the kinetic energy of turbulence as those of Reynolds stresses increase with the height of the wings.

KEYWORDS

Pollution, Turbulence, Combustion, Wing, Modeling, Numerical Simulation, Contra-Rotating Cylinders, Reynolds Stress Model, Source Term

Pollution, Turbulence, Combustion, Wing, Modeling, Numerical Simulation, Contra-Rotating Cylinders, Reynolds Stress Model, Source Term

Cite this paper

nullM. Raddaoui, "Modeling and Numerical Simulation of Wings Effect on Turbulent Flow between two contra-rotating cylinders,"*Journal of Modern Physics*, Vol. 2 No. 5, 2011, pp. 392-397. doi: 10.4236/jmp.2011.25048.

nullM. Raddaoui, "Modeling and Numerical Simulation of Wings Effect on Turbulent Flow between two contra-rotating cylinders,"

References

[1] A. P. Morse, “Numerical Prediction of Turbulent Flow in Rotating Cavities,” ASME Journal of Turbomachinery, Vol. 110, No. 2, 1988, pp. 202-212. doi:10.1115/1.3262181

[2] A. P. Morse, “Application of a Low Reynolds Number k-ε Model to High Speed Rotating Cavity Flows,” ASME Journal of Turbomachinery, Vol. 113, No. 1, 1992, pp. 98-105. doi:10.1115/1.2927743

[3] H. Iacovides and P. Toumpanakis, “Turbulence Modelling of Flow in Axisymmetric Rotor-Stator Systems,” 5th International Symposium on Refined Flow Modelling and Turbulence Measurements, Presses de l’Ecole Nationale des Ponts et Chaussées, Paris, September 1993, pp. 7-10.

[4] R. Schiestel, L. Elena and T. Rezoug, “Numerical Modeling of Turbulent Flow and Heat Transfer in Rotating Cavities,” Numerical Heat Transfer, Part A, Vol. 24, No. 1, 1995, pp. 45-65. doi:10.1080/10407789308902602

[5] L. Elena and R. Schiestel, “Turbulence Modeling of Confined Flow in Rotating Disk Systems,” AIAA Journal, Vol. 33, No. 5, 1995, pp. 812-821. doi:10.2514/3.12800

[6] B. E. Launder and D. P. Tselepidakis, “Application of a New Second-moment Closure to Turbulent Channel Flow Rotating in Orthogonal Mode,” International Journal of Heat and Fluid Flow, Vol. 15, No. 1, 1994, pp. 2-10. doi:10.1016/0142-727X(94)90025-6

[7] K. Hanjalic and B. E. Launder, “Contribution towards a Reynolds-Stress Closure for Low-Reynolds Number Turbulence,” Journal of Fluid Mechanics, Vol. 74, No. 4, 1976, pp. 593-610. doi:10.1017/S0022112076001961

[8] M. Itoh, Y. Yamada, S. Imao and M. Gonda, “Experiments on Turbulent Flow Due to an Enclosed Rotating Disk,” In: W. Rodi and E. N. Ganic, Eds., Engineering Turbulence Modeling and Experiments, Elsevier, New York, 1990, pp. 659-668.

[9] L. Elena and R. Schiestel, “Turbulence Modeling of Rotating Confined Flows,” International Journal of Heat and Fluid Flow, Vol. 17, No. 3, 1996, pp. 283-289. doi:10.1016/0142-727X(96)00032-X

[10] H. Iacovides and I. P. Theofanopoulos, “Turbulence Modeling of Axisymmetric Flow Inside Rotating Cavities,” International Journal of Heat and Fluid Flow, Vol. 12, No. 1, 1991, pp. 2-11. doi:10.1016/0142-727X(91)90002-D

[11] R. Schiestel, “Les Ecoulements Turbulents,” 2nd Edition, Hermès, Paris, 1998.

[12] L. Elena, “Modélisation de la Turbulence Inhomogène en Présence de Rotation,” Ph. D, Université Aix-Marseille I-II, 1994.

[13] S. Poncet, R. Schiestel and R. Monchaux, “Turbulence Modeling off the Von Karman Flow: Viscous and Inertial Stirrings,” International Journal of Heat and Fluid Flow, Vol. 29, No. 1, 2008, pp. 62-74. doi:10.1016/j.ijheatfluidflow.2007.07.005

[14] R. Schiestel and L. Elena., “Modeling of Anisotropic Turbulence in Rapid Rotation,” Aerospace Science and Technology, Vol. 1, No. 7, 1997, pp. 441-451. doi:10.1016/S1270-9638(97)90006-7

[15] S. Poncet, R. Schiestel and M. P. Chauve, “Turbulence Modelling and Measurements in a Rotor-Stator System with Throughflow,” ERCOFTAC International Sympo- sium on Engineering Turbulence Modelling and Measure- ments, Sardinia, Italy, 2005.

[16] P. Boronski, “Méthode des Potentiels Polo?dal-Toro?dal Appliquée à l’écoulement de Von Karman en Cylindre Fini,” Ph. D, Ecole Polytechnique, 2005.

[1] A. P. Morse, “Numerical Prediction of Turbulent Flow in Rotating Cavities,” ASME Journal of Turbomachinery, Vol. 110, No. 2, 1988, pp. 202-212. doi:10.1115/1.3262181

[2] A. P. Morse, “Application of a Low Reynolds Number k-ε Model to High Speed Rotating Cavity Flows,” ASME Journal of Turbomachinery, Vol. 113, No. 1, 1992, pp. 98-105. doi:10.1115/1.2927743

[3] H. Iacovides and P. Toumpanakis, “Turbulence Modelling of Flow in Axisymmetric Rotor-Stator Systems,” 5th International Symposium on Refined Flow Modelling and Turbulence Measurements, Presses de l’Ecole Nationale des Ponts et Chaussées, Paris, September 1993, pp. 7-10.

[4] R. Schiestel, L. Elena and T. Rezoug, “Numerical Modeling of Turbulent Flow and Heat Transfer in Rotating Cavities,” Numerical Heat Transfer, Part A, Vol. 24, No. 1, 1995, pp. 45-65. doi:10.1080/10407789308902602

[5] L. Elena and R. Schiestel, “Turbulence Modeling of Confined Flow in Rotating Disk Systems,” AIAA Journal, Vol. 33, No. 5, 1995, pp. 812-821. doi:10.2514/3.12800

[6] B. E. Launder and D. P. Tselepidakis, “Application of a New Second-moment Closure to Turbulent Channel Flow Rotating in Orthogonal Mode,” International Journal of Heat and Fluid Flow, Vol. 15, No. 1, 1994, pp. 2-10. doi:10.1016/0142-727X(94)90025-6

[7] K. Hanjalic and B. E. Launder, “Contribution towards a Reynolds-Stress Closure for Low-Reynolds Number Turbulence,” Journal of Fluid Mechanics, Vol. 74, No. 4, 1976, pp. 593-610. doi:10.1017/S0022112076001961

[8] M. Itoh, Y. Yamada, S. Imao and M. Gonda, “Experiments on Turbulent Flow Due to an Enclosed Rotating Disk,” In: W. Rodi and E. N. Ganic, Eds., Engineering Turbulence Modeling and Experiments, Elsevier, New York, 1990, pp. 659-668.

[9] L. Elena and R. Schiestel, “Turbulence Modeling of Rotating Confined Flows,” International Journal of Heat and Fluid Flow, Vol. 17, No. 3, 1996, pp. 283-289. doi:10.1016/0142-727X(96)00032-X

[10] H. Iacovides and I. P. Theofanopoulos, “Turbulence Modeling of Axisymmetric Flow Inside Rotating Cavities,” International Journal of Heat and Fluid Flow, Vol. 12, No. 1, 1991, pp. 2-11. doi:10.1016/0142-727X(91)90002-D

[11] R. Schiestel, “Les Ecoulements Turbulents,” 2nd Edition, Hermès, Paris, 1998.

[12] L. Elena, “Modélisation de la Turbulence Inhomogène en Présence de Rotation,” Ph. D, Université Aix-Marseille I-II, 1994.

[13] S. Poncet, R. Schiestel and R. Monchaux, “Turbulence Modeling off the Von Karman Flow: Viscous and Inertial Stirrings,” International Journal of Heat and Fluid Flow, Vol. 29, No. 1, 2008, pp. 62-74. doi:10.1016/j.ijheatfluidflow.2007.07.005

[14] R. Schiestel and L. Elena., “Modeling of Anisotropic Turbulence in Rapid Rotation,” Aerospace Science and Technology, Vol. 1, No. 7, 1997, pp. 441-451. doi:10.1016/S1270-9638(97)90006-7

[15] S. Poncet, R. Schiestel and M. P. Chauve, “Turbulence Modelling and Measurements in a Rotor-Stator System with Throughflow,” ERCOFTAC International Sympo- sium on Engineering Turbulence Modelling and Measure- ments, Sardinia, Italy, 2005.

[16] P. Boronski, “Méthode des Potentiels Polo?dal-Toro?dal Appliquée à l’écoulement de Von Karman en Cylindre Fini,” Ph. D, Ecole Polytechnique, 2005.