An efficient Petrov-Galerkin Chebyshev spectral method coupled with the Taylor-series expansion method of moments for solving the coherent structures effect on particle coagulation in the exhaust pipe

CMES - Computer Modeling in Engineering and Sciences

Volumn 51, Issue 3, 2009, Pages 191-212

  Chan, T L ^a   Xie, M L ^a,b   Cheung, C S ^a  

^a HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^b HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Coagulation; Exhaust pipe; Moment method; Nanoparticles; Spectral

Indexed keywords

ANALYTICITY; CHEBYSHEV SPECTRAL METHODS; COHERENT STRUCTURE; DAMKOHLER NUMBER; EDDY STRUCTURES; EXHAUST PIPE; EXHAUST PIPES; FLUID CONVECTION; GENERAL DYNAMICS EQUATION; GENERATION RATE; GOVERNING EQUATIONS; LARGE-SCALE EDDIES; MOMENT METHOD; NON-DIMENSIONAL PARAMETERS; PARTICLE COAGULATION; PARTICLE VOLUME; PETROV-GALERKIN; POLE CONDITION; QUADRATURE METHOD OF MOMENTS; SCHMIDT NUMBERS; SOLENOIDAL VECTOR FIELDS; TAYLOR SERIES EXPANSIONS; TEMPORAL EVOLUTION; VECTOR FUNCTIONS;

COAGULATION; GALERKIN METHODS; MONTE CARLO METHODS; NANOPARTICLES; PIPE; REYNOLDS NUMBER; SOLENOIDS; SPECTROSCOPY;

METHOD OF MOMENTS;

EID: 77449132897     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (59)

1. Barrret, J. C.; Jheeta, S. J. (1996): Improving the accuracy of the moments method for solving the aerosol general dynamic equation. J. Aerosol Sci., vol.27, pp.1135-1142.
2. Biau, D.; Bottaro, A. (2009): An optimal path to transition in a duct. Philos. Trans. R. Soc. A- Math. Phys. Eng. Sci., vol.367, pp. 529-544.
3. Bierbrauer, F.; Zhu, S. P. (2007): A solenoidal initial condition for the numerical solution of the Navier-Stokes equations for two-phase incompressible flow. CMES: Computer Modeling in Engineering & Sciences, vol.19, pp. 1-22.
4. Chan, T. L.; Lin, J. Z.; Zhou, K.; Chan, C. K. (2006): Simultaneous numerical simulation of nano and fine particle coagulation and dispersion in a round jet. J. Aerosol Sci., vol.37, pp. 1545-1561.
5. Cohen, J.; Philip, J.; Ben-Dov, G. (2009): Aspects of linear and nonlinear instabilities leading to transition in pipe and channel flows, Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., vol.367, pp. 509-527.
6. Davidson, C. I.; Phalen, R. F., Solomon, P. A. (2005): Airborne particulate matter and human health: A review. Aerosol Sci. Technol., vol.39, pp. 737-749.
7. Duggleby, A. K.; Kenneth, B.; Schwaenen, M. (2009): Structure and dynamics of low Reynolds number turbulent pipe flow. Philos. Trans. R. Soc. A- Math. Phys. Eng. Sci., vol.367, pp. 473-488.
8. Duguet, Y.; Willis, A. P.; Kerswell, R. R. (2008): Transition in pipe flow: the saddle structure on the boundary of turbulence. J. Fluid Mech. vol.613, pp. 255- 274.
9. Eckhardt, B. (2008): Turbulence transition in pipe flow: some open questions. Nonlinearity, vol.21, pp. 1-11.
10. Eckhardt, B. (2009): Introduction. Turbulence transition in pipe flow: 125th anniversary of the publication of Reynolds' paper. Philos. Trans. R. Soc. A- Math. Phys. Eng. Sci., vol.367, pp. 449-455.
11. Fornberg, B.; Sloan, D. M. (1994): A review of pseudospectral methods for solving partial differential equation, Acta Numerica, vol.3: 203-267.
12. Fornberg, B. (1995): A pseudospectral approach for polar and spherical geometries. SIAM J. Sci. Comput., vol.16, pp. 1071-1081.
13. Friedlander, S. K. (2000): Smoke, Dust, and Haze: Fundamentals of Aerosol Dynamics, Oxford University Press, 2nd edition.
14. Fox R. O. (2003): Computational Models for Turbulent Reacting Flows, Cambridge University Press.
15. Garrick, S. C.; Lehtinen, K. E. J.; Zachariah, M. R. (2006): Nanoparticle coagulation via a Navier Stokes nodal methodology: Evolution of the particle field. J. Aerosol Sci., vol.37, pp. 555-576.
16. Hof, B.; van Doorne, C. W. H.; Westerveel, J.; Nieuwstadt, F. T. M.; Faisst, H.; Eckhardt, B.; Wedin, H.; Kerswell, R. R.; Waleffe, F. (2004): Experimental observation of nonlinear travelling waves in turbulent pipe flow. Science, vol.305, pp. 1594-1598.
17. Hof, B.; Westerweel, J.; Schneider, T. M.; Eckhardt, B. (2006): Finite lifetime of turbulence in shear flows. Nature, vol.443, pp. 59-62.
18. Jacobson, M. Z.; Kittelson, D. B.;WattsW. F. (2005): Enhanced coagulation due to evaporation and its effect on nanoparticle evolution. Environ. Sci. Tech., vol.39, pp. 9486-9492.
19. Kerswell, R. R.; Tutty, O. R. (2007): Recurrence of travelling waves in transitional pipe flow, J. Fluid Mech., vol.584, pp. 69-102.
20. Kittelson, D. B. (1998): Engines and nanoparticles: A review, J. Aerosol Sci., vol.29, pp. 575-588.
21. Lee, K. W. (1983): Change of particle size distribution during Brownian coagulation. J. Colloid Interf. Sci., vol.92, pp. 315-325.
22. Lin, H.; Atluri, S. N. (2000): Meshless local Petrov-Galerkin (MLPG) method for convection-diffusion problems. CMES: Computer Modeling in Engineering & Sciences, vol.1, pp. 45-60.
23. Lin, H.; Atluri, S. N. (2001): The meshless local Petrov-Galerkin (MLPG) method for solving incompressible Navier-Stokes equations. CMES: Computer Modeling in Engineering & Sciences, vol.2, pp. 117-142.
24. Lin, J. Z.; Chan, T. L.; Liu, S.; Zhou, K.; Zhou, Y.; Lee, S. C. (2007): Effects of coherent structures on nanoparticle coagulation and dispersion in a round jet. Int. J. Nonlinear Sci. Numer. Simul., vol.8, pp. 45-54.
25. Liu, C.S.; Atluri, S. N. (2008): A novel time integration method for solving a large system of non-linear algebraic equations. CMES: Computer Modeling in Engineering & Sciences, vol.31, pp. 71-83.
26. Liu, C.S.; Atluri, S. N. (2009): A highly accurate technique for interpolations using very high-order polynomials, and its applications to some ill-posed linear problems. CMES: Computer Modeling in Engineering & Sciences, vol.43, pp. 253-276.
27. Lopez, J. M.; Shen, J. (1998): An efficient spectral projection method for the Navier-Stokes equations in cylindrical geometries I. Axisymmetric cases. J. Comput Physics, vol.139, pp. 308-326.
28. Mellibovsky, F.; Meseguer, A. (2009): Critical threshold in pipe flow transition. Philos. Trans. R. Soc. A- Math. Phys. Eng. Sci., vol.367, pp. 545-560.
29. Meseguer, A.; Trefethen, L. N. (2003): Linearized pipe flow to Reynolds number 107. J. Comput. Physics, vol.186, pp. 178-197.
30. Miller, S. E.; Garrick, S. C. (2004): Nanoparticle coagulation in a planar jet. Aerosol Sci. Technol., vol.38, 79-89.
31. Mohammadi, M. H. (2008): Stabilized Meshless Local Petrov-Galerkin (MLPG) Method for Incompressible Viscous Fluid Flows. CMES: Computer Modeling in Engineering & Sciences, vol.29, pp. 75-94.
32. Orsini, P.; Power, H.; Morvan, H. (2008): Improving Volume Element Methods by Meshless Radial Basis Function Techniques. CMES: Computer Modeling in Engineering & Sciences, vol.23, pp.187-208.
33. Otto, E.; Fissan, H.; Park, S. H. (1999): The log-normal size distribution theory of Brownian aerosol coagulation for the entire particle size range: Part II. Analytical solution using dahneke's coagulation kernel. J. Aerosol Sci., vol.30, pp. 17-34. (Pubitemid 28488407)
34. Pohjola, M.; Pirjola, L.; Kukkonen, J. ; Kulmala, M. (2003): Modelling of the influence of aerosol processes for the dispersion of vehicular exhaust plumes in street environment. Atmos. Environ., vol.37, pp. 339-351.
35. Pohjola, M.; Pirjola, L.; Kukkonen, J. ; Kulmala, M. (2006): Correction to modelling of the influence of aerosol processes for the dispersion of vehicular exhaust plumes in street environment. Atmos. Environ., vol.40, pp. 311-314.
36. Pope, C. A.; Dockery D.W. (2006): Health effects of fine particulate air pollution: Lines that connect. J. Air Waste Manage. Assoc., vol.56, pp. 709-742.
37. Prakash, A.; Bapat, A. P.; Zachariah, M. R. (2003): A simple numerical algorithm and software for solution of nucleation, surface growth, and coagulation problems. Aerosol Sci. Technol., vol.37, pp. 892-898.
38. Pringle, C.C.T.; Kerswell, R. R. (2007): Asymmetric, helical and mirror-symmetric travelling waves in pipe flow. Phys. Rev. Lett., vol.99, 074502.
39. Pratsinis, S. E. (1988): Simultaneous nucleation, condensation, and coagulation in aerosol reactor. J. Colloid Interf. Sci., vol.124, pp. 416-427.
40. Pratsinis, S. E.; Kim, K. S. (1989): Particle coagulation, diffusion and thermophoresis in laminar tube flows. J. Aerosol Sci., vol.20, pp. 101-111.
41. Schneider, T. M.; Eckhardt, B.; Yorke, J. A. (2007): Turbulence transition and the edge of chaos in pipe flow. Phys. Rev. Lett., vol.99, 034502.
42. Sellountos, E. J.; Sequeira, A. (2008): A hybrid multi-region BEM/LBIE RBF velocity-vorticity scheme for the two-dimensional Navier-Stokes equations. CMES: Computer Modeling in Engineering & Sciences, vol.23, pp. 127-148.
43. Sellountos, E. J.; Sequeira, A.; Polyzos, D. (2009): Elastic transient analysis with MLPG (LBIE) method and local RBFs. CMES: Computer Modeling in Engineering & Sciences, vol.41, pp. 215-242.
44. Settumba, N.; Garrick, S. C. (2003): Direct numerical simulation of nanoparticle coagulation in a temporal mixing layer via a moment method. J. Aerosol Sci., vol.34, pp. 149-167.
45. Stone, V.; Donaldson, K. (1998): Small particles-big problem. The Aerosol Society Newsletter, vol.33, pp. 12-14.
46. Sioutas, C., Delfino, R.J.; Singh, M. (2005): Review on exposure assessment for atmospheric ultrafine particles (UFPs) and implications in epidemiologic research. Environ. Health Perspect., vol.113, pp. 947-955.
47. Trefethen, L. N.; Trefethen, A. E.; Reddy, S.C.; Driscoll, T. A. (1993): Hydrodynamic stability without eigenvalues. Science, vol.261, pp. 578-584
48. Upadhyay, R. R.; Ezekoye, O. A. (2003): Evaluation of the 1-point quadrature approximation in QMOM for combined aerosol growth laws. J. Aerosol Sci., vol.34, pp. 1665-1683.
49. van Doorne, C. W.; Westerweel J. (2009): The flow structure of a puff. Philos. Trans. R. Soc. A- Math. Phys. Eng. Sci., vol.367, pp. 489-507.
50. Xie, M. L.; Lin, J. Z.; Xing, F. T. (2007): On the hydrodynamic stability of a particle laden flow in growing flat plate boundary layer, J. Zhejiang University- Sciences A, vol.8, pp. 275-284.
51. Xie, M. L.; Chan, T. L.; Zhang Y. D.; Zhou, H. C. (2008): Numerical analysis of nonlinear stability of two-phase flow in the Blasius boundary layer. Int. J. Nonlinear Sci. Numer. Simul., vol.9, pp. 423-434
52. Xie, M. L.; Lin, J. Z.; Zhou H. C. (2009a): Temporal stability of a particle-laden Blasius boundary layer. Mod. Phys. Lett. B, vol.23, pp. 203-216.
53. Xie, M. L.; Lin, J. Z.; Zhou, H. C. (2009b): The effect of non-linear interaction between gas and particle velocities on the hydrodynamic stability in the Blasius boundary layer. Int. J. Non-linear Mech., vol.44, pp. 106-114.
54. Xie, M. L.; Zhou H. C.; Zhang Y. D. (2009c): Hydrodynamics stability of Bickley jet with particle laden flow. J. Hydrodynamics, Ser. B, vol.21, pp. 608-613.
55. Xie, M. L.; Zhou, H. C.; Chan, T. L. (2009d): An improved Petrov-Galerkin spectral collocation solution for linear stability of circular jet. CMES: Computer Modeling in Engineering & Sciences, vol.46, pp. 271-289.
56. Xie, M. L.; Lin J. Z. (2009e): An efficient numerical solution for linear stability of circular jet: A combination of Petrov-Galerkin spectral method and exponential coordinate transformation based on Fornberg's treatment. Int. J. Numer. Meth. Fluids, vol.61, pp. 780-795.
57. Yu, M. Z.; Lin, J. Z.; Chan, T. L. (2008a): A new moment method for solving the coagulation equation for particles in Brownian motion. Aerosol Sci. Technol., vol.42: 705-713
58. Yu, M. Z.; Lin, J. Z.; Chan, T. (2008b): Numerical simulation of nanoparticle synthesis in diffusion flame reactor. Powder Tech., vol.181, pp. 9-20.
59. 2 nanoparticle synthesis in a diffusion flame reactor. Chem. Eng. Sci., vol.63, pp. 2317-2329.