Unified Gas-Kinetic Scheme for Gas-Particle Flow in Shock-Induced Fluidization of Particles Bed
In this paper, a unified-gas kinetic scheme (UGKS)
for the gas-particle flow is constructed. UGKS is a direct modeling
method for both continuum and rarefied flow computations. The
dynamics of particle and gas are described as rarefied and continuum
flow, respectively. Therefore, we use the Bhatnagar-Gross-Krook
(BGK) equation for the particle distribution function. For the gas
phase, the gas kinetic scheme for Navier-Stokes equation is solved.
The momentum transfer between gas and particle is achieved by the
acceleration term added to the BGK equation. The new scheme is
tested by a 2cm-in-thickness dense bed comprised of glass particles
with 1.5mm in diameter, and reasonable agreement is achieved.
[1] X. Rogue, G. Rodriguez, J. Haas, and R. Saurel, “Experimental and
numerical investigation of the shock-induced fluidization of a particles
bed,” Shock Waves, vol. 8, no. 1, pp. 29–45, 1998.
[2] M. Baer and J. Nunziato, “A two-phase mixture theory for the
deflagration-to-detonation transition (ddt) in reactive granular materials,”
International journal of multiphase flow, vol. 12, no. 6, pp. 861–889,
1986.
[3] R. Saurel and R. Abgrall, “A multiphase godunov method
for compressible multifluid and multiphase flows,” Journal of
Computational Physics, vol. 150, no. 2, pp. 425–467, 1999.
[4] R. Saurel, A. Chinnayya, and Q. Carmouze, “Modelling compressible
dense and dilute two-phase flows,” Physics of Fluids, vol. 29, no. 6, p.
063301, 2017.
[5] M. Andrews and P. O’rourke, “The multiphase particle-in-cell (mp-pic)
method for dense particulate flows,” International Journal of Multiphase
Flow, vol. 22, no. 2, pp. 379–402, 1996.
[6] P. J. ORourke, P. P. Zhao, and D. Snider, “A model for collisional
exchange in gas/liquid/solid fluidized beds,” Chemical Engineering
Science, vol. 64, no. 8, pp. 1784–1797, 2009. [7] P. J. ORourke and D. M. Snider, “An improved collision damping time
for mp-pic calculations of dense particle flows with applications to
polydisperse sedimenting beds and colliding particle jets,” Chemical
Engineering Science, vol. 65, no. 22, pp. 6014–6028, 2010.
[8] P. J. O’Rourke and D. M. Snider, “Inclusion of collisional
return-to-isotropy in the mp-pic method,” Chemical engineering science,
vol. 80, pp. 39–54, 2012.
[9] J. Dahal and J. A. McFarland, “A numerical method for shock driven
multiphase flow with evaporating particles,” Journal of Computational
Physics, vol. 344, pp. 210–233, 2017.
[10] A. Chertock, S. Cui, and A. Kurganov, “Hybrid finite-volume-particle
method for dusty gas flows,” D´etail, vol. 3, pp. 139–180, 2017.
[11] K. Xu and J.-C. Huang, “A unified gas-kinetic scheme for continuum
and rarefied flows,” Journal of Computational Physics, vol. 229, no. 20,
pp. 7747–7764, 2010.
[12] Z. Wang, H. Yan, Q. Li, and K. Xu, “Unified gas-kinetic scheme for
diatomic molecular flow with translational, rotational, and vibrational
modes,” Journal of Computational Physics, vol. 350, pp. 237–259, 2017.
[13] T. Xiao, Q. Cai, and K. Xu, “A well-balanced unified gas-kinetic
scheme for multiscale flow transport under gravitational field,” Journal
of Computational Physics, vol. 332, pp. 475–491, 2017.
[14] C. Liu and K. Xu, “A unified gas kinetic scheme for continuum and
rarefied flows v: Multiscale and multi-component plasma transport,”
Communications in Computational Physics, vol. 22, no. 5, pp.
1175–1223, 2017.
[15] K. Xu, “A gas-kinetic bgk scheme for the navier–stokes equations and
its connection with artificial dissipation and godunov method,” Journal
of Computational Physics, vol. 171, no. 1, pp. 289–335, 2001.
[16] P. L. Bhatnagar, E. P. Gross, and M. Krook, “A model for collision
processes in gases. i. small amplitude processes in charged and neutral
one-component systems,” Physical review, vol. 94, no. 3, p. 511, 1954.
[17] C. Chu, “Kinetic-theoretic description of the formation of a shock wave,”
The Physics of Fluids, vol. 8, no. 1, pp. 12–22, 1965.
[18] E. F. Toro, Riemann solvers and numerical methods for fluid dynamics:
a practical introduction. Springer Science & Business Media, pp.
535–536, 2013.
[1] X. Rogue, G. Rodriguez, J. Haas, and R. Saurel, “Experimental and
numerical investigation of the shock-induced fluidization of a particles
bed,” Shock Waves, vol. 8, no. 1, pp. 29–45, 1998.
[2] M. Baer and J. Nunziato, “A two-phase mixture theory for the
deflagration-to-detonation transition (ddt) in reactive granular materials,”
International journal of multiphase flow, vol. 12, no. 6, pp. 861–889,
1986.
[3] R. Saurel and R. Abgrall, “A multiphase godunov method
for compressible multifluid and multiphase flows,” Journal of
Computational Physics, vol. 150, no. 2, pp. 425–467, 1999.
[4] R. Saurel, A. Chinnayya, and Q. Carmouze, “Modelling compressible
dense and dilute two-phase flows,” Physics of Fluids, vol. 29, no. 6, p.
063301, 2017.
[5] M. Andrews and P. O’rourke, “The multiphase particle-in-cell (mp-pic)
method for dense particulate flows,” International Journal of Multiphase
Flow, vol. 22, no. 2, pp. 379–402, 1996.
[6] P. J. ORourke, P. P. Zhao, and D. Snider, “A model for collisional
exchange in gas/liquid/solid fluidized beds,” Chemical Engineering
Science, vol. 64, no. 8, pp. 1784–1797, 2009. [7] P. J. ORourke and D. M. Snider, “An improved collision damping time
for mp-pic calculations of dense particle flows with applications to
polydisperse sedimenting beds and colliding particle jets,” Chemical
Engineering Science, vol. 65, no. 22, pp. 6014–6028, 2010.
[8] P. J. O’Rourke and D. M. Snider, “Inclusion of collisional
return-to-isotropy in the mp-pic method,” Chemical engineering science,
vol. 80, pp. 39–54, 2012.
[9] J. Dahal and J. A. McFarland, “A numerical method for shock driven
multiphase flow with evaporating particles,” Journal of Computational
Physics, vol. 344, pp. 210–233, 2017.
[10] A. Chertock, S. Cui, and A. Kurganov, “Hybrid finite-volume-particle
method for dusty gas flows,” D´etail, vol. 3, pp. 139–180, 2017.
[11] K. Xu and J.-C. Huang, “A unified gas-kinetic scheme for continuum
and rarefied flows,” Journal of Computational Physics, vol. 229, no. 20,
pp. 7747–7764, 2010.
[12] Z. Wang, H. Yan, Q. Li, and K. Xu, “Unified gas-kinetic scheme for
diatomic molecular flow with translational, rotational, and vibrational
modes,” Journal of Computational Physics, vol. 350, pp. 237–259, 2017.
[13] T. Xiao, Q. Cai, and K. Xu, “A well-balanced unified gas-kinetic
scheme for multiscale flow transport under gravitational field,” Journal
of Computational Physics, vol. 332, pp. 475–491, 2017.
[14] C. Liu and K. Xu, “A unified gas kinetic scheme for continuum and
rarefied flows v: Multiscale and multi-component plasma transport,”
Communications in Computational Physics, vol. 22, no. 5, pp.
1175–1223, 2017.
[15] K. Xu, “A gas-kinetic bgk scheme for the navier–stokes equations and
its connection with artificial dissipation and godunov method,” Journal
of Computational Physics, vol. 171, no. 1, pp. 289–335, 2001.
[16] P. L. Bhatnagar, E. P. Gross, and M. Krook, “A model for collision
processes in gases. i. small amplitude processes in charged and neutral
one-component systems,” Physical review, vol. 94, no. 3, p. 511, 1954.
[17] C. Chu, “Kinetic-theoretic description of the formation of a shock wave,”
The Physics of Fluids, vol. 8, no. 1, pp. 12–22, 1965.
[18] E. F. Toro, Riemann solvers and numerical methods for fluid dynamics:
a practical introduction. Springer Science & Business Media, pp.
535–536, 2013.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:77835", author = "Zhao Wang and Hong Yan", title = "Unified Gas-Kinetic Scheme for Gas-Particle Flow in Shock-Induced Fluidization of Particles Bed", abstract = "In this paper, a unified-gas kinetic scheme (UGKS)
for the gas-particle flow is constructed. UGKS is a direct modeling
method for both continuum and rarefied flow computations. The
dynamics of particle and gas are described as rarefied and continuum
flow, respectively. Therefore, we use the Bhatnagar-Gross-Krook
(BGK) equation for the particle distribution function. For the gas
phase, the gas kinetic scheme for Navier-Stokes equation is solved.
The momentum transfer between gas and particle is achieved by the
acceleration term added to the BGK equation. The new scheme is
tested by a 2cm-in-thickness dense bed comprised of glass particles
with 1.5mm in diameter, and reasonable agreement is achieved.", keywords = "Gas-particle flow, unified gas-kinetic scheme,
momentum transfer, shock-induced fluidization.", volume = "12", number = "8", pages = "828-6", }
