Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-28T13:58:55.324Z Has data issue: false hasContentIssue false
  • English
  • Français

Mixing and combustion in a laminar shear layer with imposed counterflow

Published online by Cambridge University Press:  11 December 2020

William A. Sirignano Open the ORCID record for William A. Sirignano [Opens in a new window]
William A. Sirignano*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA92697, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Three-dimensional, steady laminar flow structures with mixing, chemical reaction, normal strain and shear strain representative of turbulent combustion are analysed. A mixing layer is subjected to counterflow in the transverse $y$- and $z$-directions providing the important practical interaction of shear-strain rate with normal-strain rate. Larger consequences for mixing rates and burning rates occur than would appear with shear strain or normal strain alone. The three characteristic times for chemical reaction, normal strain and shear strain are cast through two ratios: a Damköhler number based on rate of shear strain and a ratio of rate of normal strain to rate of shear strain. Reduction to a one-dimensional similar form is obtained with density and property variations. A generalization is found extending the Crocco integral for non-unitary Prandtl number and for imposed normal strain. A diffusion flamelet model with combined shear and normal strains is developed. Another similar solution is obtained for a configuration with a dominant diffusion flame and a weaker fuel-rich premixed flame. A conserved scalar is cast as the independent variable giving an alternative description. The imposed normal strain decreases mixing-layer thickness and increases scalar gradients and transport rates. Diffusion control is possible for partially premixed flames in the multi-branched flame situation. The imposition of shear strain and thereby vorticity on the counterflow can have a substantial consequence, indicating the need for flamelet models with both shear strain and normal strain.

JFM classification

Reacting Flows: Combustion Boundary Layers: Free shear layers Aerodynamics: High-speed flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , A35
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bilger, R. W. 1976 The structure of diffusion flames. Combust. Sci. Technol. 13, 155–170.CrossRefGoogle Scholar
Boratav, O. N., Elghobashi, S. E. & Zhong, R. 1996 On the alignment of the a-strain and vorticity in turbulent nonpremixed flames. Phys. Fluids 8, 2251–2253.CrossRefGoogle Scholar
Boratav, O. N., Elghobashi, S. E. & Zhong, R. 1998 On the alignment of strain, vorticity and scalar gradient in turbulent, buoyant, nonpremixed flames. Phys. Fluids 10, 2260–2267.CrossRefGoogle Scholar
Cetegen, B. M. & Sirignano, W. A. 1988 Study of molecular mixing and a finite rate chemical reaction in a mixing layer. In Proceedings of Twenty-Second Symposium (International) on Combustion, pp. 489–494. Combustion Institute.CrossRefGoogle Scholar
Cetegen, B. M. & Sirignano, W. A. 1990 Study of mixing and reaction in the field of a vortex. Combust. Sci. Technol. 72, 157–181.CrossRefGoogle Scholar
Crocco, L. 1932 Transmission of heat from a flat plate to a fluid flowing at high velocity. NACA Technical Memorandum 690.Google Scholar
Dorodnitsyn, A. A. 1942 Boundary layer in a compressible gas. J. Appl. Maths Mech. 6 (6), 449–486.Google Scholar
Hamins, A., Thridandam, H. & Seshadri, K. 1985 Structure and extinction of a counterflow partially premixed, diffusion flame. Chem. Engng Sci. 40, 2027–2038.CrossRefGoogle Scholar
Howarth, L. 1948 Concerning the effect of compressibility on laminar boundary layers and their separation. Proc. R. Soc. Lond. A 194, 16–42.Google Scholar
Illingworth, C. R. 1949 Steady flow in the laminar boundary layer of a gas. Proc. R. Soc. Lond. A 199, 533.Google Scholar
Jordà Juanós, A. & Sirignano, W. A. 2014 Triple flame: inherent asymmetries and pentasectional character. Combust. Theor. Model. 18, 454–473.CrossRefGoogle Scholar
Karagozian, A. R. & Marble, F. E. 1986 Study of a diffusion flame in a stretched vortex. Combust. Sci. Technol. 45, 65–84.CrossRefGoogle Scholar
Kennedy, C. A. & Gatski, T. 1994 Self-similar supersonic variable-density shear layers in binary systems. Phys. Fluids 6, 662.CrossRefGoogle Scholar
Kevorkian, J. K. & Cole, J. 1996 Multiple Scale and Singular Perturbation Methods. Springer.CrossRefGoogle Scholar
Lees, L. 1956 Laminar heat transfer over blunt-nosed bodies at hypersonic flight speeds. Jet Propul. 26, 259.CrossRefGoogle Scholar
Libby, P. A. & Liu, T. M. 1968 Some similar laminar flows obtained by quasilinearization. AIAA J. 6, 1541.CrossRefGoogle Scholar
Liñán, A. 1974 The asymptotic structure of counterflow diffusion flames for large activation energies. Acta Astonautica 1, 1007–1039.CrossRefGoogle Scholar
Liñán, A. & Williams, F. A. 1993 Ignition in an unsteady mixing layer subject to strain and variable pressure. Combust. Flame 95, 31–46.CrossRefGoogle Scholar
López-Cámara, C.-F., Jordà Juanós, A. & Sirignano, W. A. 2019 Normal strain rate and pressure effects using detailed and global chemistry models in a ${\rm CH}_4$-air counterflow flame. In Western States/Combustion Institute Meeting. Albuquerque, NM. Combustion Institute.Google Scholar
López-Cámara, C.-F., Jordà Juanós, A. & Sirignano, W. A. 2020 Strain rate and pressure effects on multi-branched counterflow flames. Combust. Flame. (in press), arXiv:2005.14516.CrossRefGoogle Scholar
Marble, F. E. 1985 Growth of a diffusion flame in the field of a vortex. In Recent Advances in the Aerospace Sciences (ed. Casci, C.), pp. 395–413. Plenum Press.CrossRefGoogle Scholar
Nguyen, T., Popov, P. & Sirignano, W. A. 2018 Longitudinal combustion instability in a rocket motor with a single coaxial injector. J. Propul. Power 34 (2), 354–373.CrossRefGoogle Scholar
Nguyen, T. & Sirignano, W. A. 2018 The impacts of three flamelet burning regimes in nonlinear combustion dynamics, invited paper. Combust. Flame 195, 170–182.CrossRefGoogle Scholar
Nomura, K. K. & Elghobashi, S. E. 1992 Mixing characteristics of an inhomogeneous scalar in isotropic and homogeneous sheared turbulence. Phys. Fluids A 4, 606–625.CrossRefGoogle Scholar
Nomura, K. K. & Elghobashi, S. E. 1993 The structure of inhomogeneous turbulence scalar in variable density nonpremixed flames. Theor. Comput. Fluid Dyn. 5, 153–175.CrossRefGoogle Scholar
Peters, N. 2000 Turbulent Combustion, 1st edn. Cambridge University Press.CrossRefGoogle Scholar
Pierce, C. & Moin, P. 2004 Progress-variable approach for large-eddy simulation of non-premixed turbulent combustion. J. Fluid Mech. 504, 73–97.CrossRefGoogle Scholar
Poblador-Ibanez, J., Davis, B. & Sirignano, W. A. 2020 Self-similar solution of a supercritical two-phase laminar mixing layer. arXiv:2004.00564.CrossRefGoogle Scholar
Pruett, C. D. 1993 On the accurate prediction of the wall-normal velocity in compressible boundary-layer flow. Intl J. Numer. Meth. Fluids 16, 133–152.CrossRefGoogle Scholar
Rajamanickam, P., Coenen, W., Sanchez, A. L. & Williams, F. A. 2019 Influences of stoichiometry on steadily propagating triple flames in counterflows. Proc. Combust. Inst. 37, 1971–1977.CrossRefGoogle Scholar
Shvab, V. A. 1948 Relation between the Temperature and Velocity Fields of the Flame of a Gas Burner. Gos. Energ. Izd.Google Scholar
Sirignano, W. A. 2019 a Combustion with multiple flames under high strain rates. Combust. Sci. Technol. 192, 1–30.CrossRefGoogle Scholar
Sirignano, W. A. 2019 b Counterflow and wall stagnation flow with three-dimensional strain. Phys. Fluids 31, 053605.CrossRefGoogle Scholar
Stewartson, K. 1949 Correlated incompressible and compressible boundary layers. Proc. R. Soc. Lond. A 200, 1060.Google Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic Press.Google Scholar
Westbrook, C. K. & Dryer, F. L. 1984 Chemical kinetic modeling of hydrocarbon combustion. Prog. Energy Combust. Sci. 10, 1–57.CrossRefGoogle Scholar
Williams, F. A. 1985 Combustion Theory, 2nd edn. The Benjamin/Cummings Publishing Company.Google Scholar
Zel'dovich, Y. B. 1949 On the theory of combustion of initially unmixed gases (in English). Zhur. Tekhn. Fiz., NACA Tech. Memo. 1296 (1950).Google Scholar