Publication Cover
Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 72, 2017 - Issue 5
194
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

Artificial compressibility method on half-staggered grid for laminar radiative diffusion flames in axisymmetric coordinates

, &
Pages 392-407 | Received 04 Aug 2017, Accepted 26 Oct 2017, Published online: 27 Nov 2017

References

  • E. Turkel, “Preconditioned methods for solving the incompressible and low speed compressible equations,” J. Comput. Phys., vol. 72, pp. 277–298, 1987. DOI: 10.1016/0021-9991(87)90084-2.
  • S. Venkateswaran and L. Merkle, “Analysis of preconditioning methods for the Euler and Navier–Stokes equations,” Lect. Ser. - Von Karman Inst. Fluid Dyn., vol. 3, pp. B1–B155, 1999.
  • B. Lessani, J. Ramboer, and C. Lacor, “Efficient large-eddy simulations of low Mach number flows using preconditioning and multigrid,” Int. J. Comput. Fluid Dyn., vol. 18, pp. 221–233, 2004. DOI: 10.1080/10618560310001654319.
  • B. Lessani and M. V. Papalexandris, “Time-accurate calculation of variable density flows with strong temperature gradients and combustion,” J. Comput. Phys., vol. 212, pp. 218–246, 2006. DOI: 10.1016/j.jcp.2005.07.001.
  • A. Majda and J. Sethian, “The derivation and numerical solution of the equations for zero Mach number combustion,” Combust. Sci. Technol., vol. 42, pp. 185–205, 1985. DOI: 10.1080/00102208508960376.
  • E. Motheau and J. Abraham, “A high-order numerical algorithm for Dns of low-Mach-number reactive flows with detailed chemistry and quasi-spectral accuracy,” J. Comput. Phys., vol. 313, pp. 430–454, 2016. DOI: 10.1016/j.jcp.2016.02.059.
  • P. Rauwoens, J. Vierendeels, and B. Merci, “A stable pressure-correction scheme for variable density flows involving non-premixed combustion,” Int. J. Numer. Methods Fluids, vol. 56, pp. 1465–1471, 2008. DOI: 10.1002/fld.1717.
  • H. N. Najm, P. S. Wyckoff, and O. M. Knio, “A semi-implicit numerical scheme for reacting flow,” J. Comput. Phys., vol. 143, pp. 381–402, 1998. DOI: 10.1006/jcph.1999.6322.
  • M. Kooshkbaghi, B. Lessani, and A Collocated Grid, “Projection method for time-accurate calculation of low-Mach number variable density flows in general curvilinear coordinates,” Int. J. Numer. Methods Fluids, vol. 72, pp. 301–319, 2013. DOI: 10.1002/fld.3734.
  • A. J. Chorin, “A numerical method for solving incompressible viscous flow problems,” J. Comput. Phys., vol. 135, pp. 118–125, 1997. DOI: 10.1006/jcph.1997.5716.
  • P. Nithiarasu and C. B. Liu, “Steady and unsteady incompressible flow in a double driven cavity using the artificial compressibility (AC)-based characteristic-based split (CBS) scheme,” Int. J. Numer. Methods Eng., vol. 63, pp. 380–397, 2005. DOI: 10.1002/nme.1280.
  • T. Ohwada and P. Asinari, “Artificial compressibility method revisited: asymptotic numerical method for incompressible Navier–Stokes equations,” J. Comput. Phys., vol. 229, pp. 1698–1723, 2010. DOI: 10.1016/j.jcp.2009.11.003.
  • M. M. Rahman and T. Siikonen, “An artificial compressibility method for viscous incompressible and low Mach number flows,” Int. J. Numer. Methods Eng., vol. 75, pp. 1320–1340, 2008. DOI: 10.1002/nme.2302.
  • C. Corvellec, P. Bruel, and V. A. Sabel’nikov, “A time-accurate scheme for the calculations of unsteady reactive flows at low Mach number,” Int. J. Numer. Methods Fluids, vol. 29, pp. 207–227, 1999. DOI: 10.1002/(SICI)1097-0363(19990130)29:2<207::AID-FLD785>3.0.CO;2-5.
  • P. Bruel, D. Karmed, and M. Champion, “A pseudo-compressibility method for reactive flows at zero Mach number,” Int. J. Comput. Fluid Dyn., vol. 7, pp. 291–310, 1996. DOI: 10.1080/10618569608940767.
  • W. M. C. Dourado, P. Bruel, and J. L. F. Azevedo, “A time-accurate pseudo-compressibility approach based on an unstructured hybrid finite volume technique applied to unsteady turbulent premixed flame propagation,” Int. J. Numer. Methods Fluids, vol. 44, pp. 1063–1091, 2004. DOI: 10.1002/fld.668.
  • L.-C. Huang and L.-C. Huang, “Numerical solution of the unsteady incompressible Navier–Stokes equations on the curvilinear half-staggered mesh,” J. Comput. Math., vol. 18, pp. 521–540, 2000. DOI: 10.1137/s1064827598337099.
  • A. Tyliszczak, “A high-order compact difference algorithm for half-staggered grids for laminar and turbulent incompressible flows,” J. Comput. Phys., vol. 276, pp. 438–467, 2014. DOI: 10.1016/j.jcp.2014.07.043.
  • A. Tyliszczak, “High-order compact difference algorithm on half-staggered meshes for low Mach number flows,” Comput. Fluids, vol. 127, pp. 131–145, 2016. DOI: 10.1016/j.compfluid.2015.12.014.
  • M. R. Schumack, W. W. Schultz, and J. P. Boyd, “Spectral method solution of the stokes equations on nonstaggered grids,” J. Comput. Phys., vol. 94, pp. 30–58, 1991. DOI: 10.1016/0021-9991(90)90161-s.
  • H. Babaee and S. Acharya, “A hybrid staggered/semistaggered finite-difference algorithm for solving time-dependent incompressible Navier–Stokes equations on curvilinear grids,” Numer. Heat Transfer, Part B, vol. 65, pp. 1–26, 2014. DOI: 10.1080/10407790.2013.827012.
  • P. Rauwoens, J. Vierendeels, and B. Merci, “A solution for the odd–even decoupling problem in pressure-correction algorithms for variable density flows,” J. Comput. Phys., vol. 227, pp. 79–99, 2007. DOI: 10.1016/j.jcp.2007.07.010.
  • Y. R. Sivathanu and G. M. Faeth, “Generalized state relationships for scalar properties in nonpremixed hydrocarbon/air flames,” Combust. Flame, vol. 82, pp. 211–230, 1990. DOI: 10.1016/0010-2180(90)90099-d.
  • G. H. Yeoh and K. K. Yuen, Computational Fluid Dynamics in Fire Engineering: Theory, Modelling and Practice, 1st ed., Burlington: Butterworth-Heinemann, 2009, pp. 187–193.
  • S. Turns and D. Kraige, Properties Tables Booklet for Thermal Fluids Engineering, 1st ed., Appendix B, New York: Cambridge University Press, 2007.
  • M. R. J. Charest and C. Groth, “A high-order accurate unstructured finite-volume algorithm for turbulent flames,” Los Alamos National Lab. (L.nl), Los Alamos, New Mexico, Rept. LA-UR-14–25851, 2014.
  • F. Muldoon and S. Acharya, “A modification of the artificial compressibility algorithm with improved convergence characteristics,” Int. J. Numer. Methods Fluids, vol. 55, pp. 307–345, 2007. DOI: 10.1002/fld.1435.
  • R. H. Pletcher, J. C. Tannehill, and D. Anderson, Computational Fluid Mechanics and Heat Transfer, 3rd ed., New York: CRC Press, 2012, pp. 632–637.
  • A. B. Uygur, N. Selçuk, and I. Hakki Tuncer, “A non-iterative pressure based scheme for the computation of reacting radiating flows,” Int. J. Therm. Sci., vol. 47, pp. 209–220, 2008. DOI: 10.1016/j.ijthermalsci.2007.02.009.
  • A. Wray, “Minimal storage time advancement schemes for spectral methods,” NASA Ames Research Center, California, Report No. MS, vol. 202, 1990.
  • R. E. Mitchell, “Nitrogen oxide formation in laminar methane-air diffusion flames,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1975.
  • Y. Xu, M. D. Smooke, P. Lin, and M. B. Long, “Primitive variable modeling of multidimensional laminar flames,” Combust. Sci. Technol., vol. 90, pp. 289–313, 1993. DOI: 10.1080/00102209308907619.
  • M. Fathi Azarkhavarani, R. Hosseini Abardeh, and M. Rahmani, “Calculations of non-gray gas radiative heat transfer by coupling the discrete ordinates method with the Leckner model in 3D rectangular enclosures,” Heat Mass Transfer, vol. 52, pp. 2317–2325, 2016. DOI: 10.1007/s00231-015-1748-3.
  • T. Tarhan and N. Selçuk, “Numerical simulation of a confined methane/air laminar diffusion flame by the method of lines,” Turk. J. Eng. Environ. Sci., vol. 27, pp. 275–290, 2003. DOI: 10.1080/00102200600805926.
  • A. K. Chowdhuri, S. Chakrabarti, and B. K. Mandal, “Numerical study of radiation and airpreheating effect on the velocity, temperature, and species distribution in a confined laminar coflow diffusion flame,” Comput. Thermal Sci. Int. J., vol. 5, pp. 425–440, 2013. DOI: 10.1615/computthermalscien.2013006896.
  • R. E. Mitchell, A. F. Sarofim, and L. A. Clomburg, “Experimental and numerical investigation of confined laminar diffusion flames,” Combust. Flame, vol. 37, pp. 227–244, 1980. DOI: 10.1016/0010-2180(80)90092-9.
  • S. B. Dworkin, Q. Zhang, M. J. Thomson, N. A. Slavinskaya, and U. Riedel, “Application of an enhanced PAH growth model to soot formation in a laminar coflow ethylene/air diffusion flame,” Combust. Flame, vol. 158, pp. 1682–1695, 2011. DOI: 10.1016/j.combustflame.2011.01.013.
  • F. Liu, H. Guo, and G. J. Smallwood, “Effects of radiation model on the modeling of a laminar coflow methane/air diffusion flame,” Combust. Flame, vol. 138, pp. 136–154, 2004. DOI: 10.1016/j.combustflame.2004.04.007.
  • F. Liu, H. Guo, G. J. Smallwood, and Ö. L. Gülder, “Numerical modelling of soot formation and oxidation in laminar coflow non-smoking and smoking ethylene diffusion flames,” Combust. Theory Modell., vol. 7, pp. 301–315, 2003. DOI: 10.1088/1364-7830/7/2/305.
  • R. J. Santoro, T. T. Yeh, J. J. Horvath, and H. G. Semerjian, “The transport and growth of soot particles in laminar diffusion flames,” Combust. Sci. Technol., vol. 53, pp. 89–115, 1987. DOI: 10.1080/00102208708947022.
  • A. K. Dasgupta, “Numerical simulation of axisymmetric laminar diffusion flames with soot,” Ph.D. thesis, The Pennsylvania State University, University Park, Pennsylvania, 2015.
  • C. K. Law, “Comprehensive description of chemistry in combustion modeling,” Combust. Sci. Technol., vol. 177, pp. 845–870, 2005. DOI: 10.1080/00102200590926905.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.