Abu-Hijleh, B. A. K. 2003 Numerical simulation of forced convection heat transfer from a cylinder with high conductivity radial fins in cross-flow. Intl J. Therm. Sci. 42 (8), 741–748.
Anderson, J. D. 2001 Computational Fluid Dynamics: The Basics with Applications, 8th edn. McGraw-Hill.
Andres, J. M. & Ingard, U. 1953 Acoustic streaming at low Reynolds numbers. J. Acoust. Soc. Am. 25, 932–938.
Apelt, C. J. & Ledwich, M. A. 1979 Heat transfer in transient and unsteady flows past a heated circular cylinder in the range 1 ≤ Re ≤ 40. J. Fluid Mech. 95 (4), 761–777.
Balasubramanian, K. & Sujith, R. I. 2008 Thermoacoustic instability in a Rijke tube: Non-normality and nonlinearity. Phy. Fluids 20, 044103.
Bittanti, S., Marco, A. D., Poncia, G. & Prandoni, W. 2002 Identification of a model for thermoacoustic instabilities in a Rijke tube. IEEE Trans. Control Syst. Technol. 10, 490–502.
Candel, S. 2002 Combustion dynamics and control: Progress and challenges. Proc. Combust. Inst. 29 (1), 1–28.
Carvalho, J. A., Ferreira, M. A., Bressan, C. & Ferreira, L. G. 1989 Definition of heater location to drive maximum amplitude acoustic oscillations in a Rijke tube. Combust. Flame 76, 17–27.
Collis, D. C. & Williams, M. J. 1959 Two-dimensional convection from heated wires at low Reynolds numbers. J. Fluid Mech. 6 (3), 357–384.
Coutanceau, M. & Bouard, R. 1977 Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Part 1. Steady flow. J. Fluid Mech. 79 (2), 231–256.
Culick, F. E. C. 2006 Unsteady motions in combustion chambers for propulsion systems. Tech. Rep. AG-AVT-039. RTO AGARDograph.
Fu, W. S. & Tong, B. H. 2002 Numerical investigation of heat transfer from a heated oscillating cylinder in a cross flow. Intl J. Heat Mass Transfer 45 (14), 3033–3043.
Hantschk, C. C. & Vortmeyer, D. 1999 Numerical simulation of self-excited thermoacoustic instabilities in a Rijke tube. J. Sound Vib. 227, 511–522.
Heckl, M. A. 1990 Nonlinear acoustic effects in the Rijke tube. Acustica 72, 63–71.
Heckl, M. A. & Howe, M. S. 2007 Stability analysis of the Rijke tube with a Green's function approach. J. Sound Vib. 305, 672–688.
Kaufmann, A., Nicoud, F. & Poinsot, T. 2002 Flow forcing techniques for numerical simulation of combustion instabilities. Combust. Flame 131 (4), 371–385.
Klein, R. 1995 Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics. Part I. One-dimensional flow. J. Comput. Phys. 121, 213–237.
Klein, R., Botta, N., Schneider, T., Munz, C. D., Roller, S., Meister, A., Hoffmann, L. & Sonar, T. 2001 Asymptotic adaptive methods for multi-scale problems in fluid mechanics. J. Engng Math. 39, 261–343.
Kopitz, J. & Polifke, W. 2008 CFD based application of the Nyquist criterion to thermoacoustic instabilities. J. Comput. Phys. 227, 6754–6778.
Kwon, Y. P. & Lee, B. H. 1985 Stability of the Rijke thermoacoustic oscillation. J. Acoust. Soc. Am. 78, 1414–1420.
Matveev, K. I. & Culick, F. E. C. 2003 a A model for combustion instability involving vortex shedding. Combust. Sci. Technol. 175 (6), 1059–1083.
Matveev, K. I. & Culick, F. E. C. 2003 b A study of the transition to instability in a Rijke tube with axial temperature gradient. J. Sound Vib. 264 (3), 689–706.
McManus, K., Poinsot, T. & Candel, S. 1993 A review of active control of combustion instabilities. Prog. Energy Combust. Sci. 19, 1–29.
Moeck, J. P., Oevermann, M., Klein, R., Paschereit, C. O. & Schmidt, H. 2009 A two-way coupling for modeling thermoacoustic instabilities in a flat flame Rijke tube. Proc. Combust. Inst. 32 (1), 1199–1207.
Moeck, J. P., Schmidt, H., Oevermann, M., Paschereit, C. O. & Klein, R. 2007 An asymptotically motivated hydrodynamic-acoustic two-way coupling for modeling thermoacoustic instabilities in a Rijke tube. In ICSV14, Cairns, Australia.
Padmanabhan, M. S. 1975 The effect of nozzle nonlinearities on the nonlinear stability of liquid rocket motors. PhD thesis, Georgia Institute of Technology, Atlanta, USA.
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. Hemisphere.
Poinsot, T. & Veynante, D. 2005 Theoretical and Numerical Combustion, 2nd edn. Edwards.
Preetham, , Santosh, H. & Liewen, T. 2008 Dynamics of laminar premixed flames forced by harmonic velocity disturbances. J. Propul. Power 24 (6), 1390–1402.
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 2007 Numerical Recipes: The Art of Scientific Computing, 3rd edn. Cambridge University Press.
Rayleigh, Lord. 1878 The explanation of certain acoustical phenomena. Nature 18, 319–321.
Rienstra, S. W. & Hirschberg, A. 2004 An Introduction to Acoustics, IWDE 92-06 edn. Technische Universiteit Eindhoven.
Rijke, P. L. 1859 The vibration of the air in a tube open at both ends. Phil. Mag. 17, 419–422.
Riley, K. F., Hobson, M. P. & Bence, S. J. 2006 Mathematical Methods for Physics and Engineering, 3rd edn. Cambridge University Press.
Sarpkaya, T. 1986 Force on a circular cylinder in viscous oscillatory flow at low Keulegan–Carpenter numbers. J. Fluid Mech. 165, 61–71.
Selimefendigil, F., Föller, S. & Polifke, W. 2008 Nonlinear identification of the unsteady heat transfer of a cylinder in pulsating crossflow. In Intl Conf. on Jets, Wakes and Separated Flows. Technical University Berlin, Berlin, Germany.
Song, W. S., Lee, S., Shin, D. S. & Na, Y. 2006 Thermo-acoustic instability in the horizontal Rijke tube. J. Mech. Sci. Technol. 20, 905–913.
Telionis, D. P. 1981 Unsteady Viscous Flows. Springer.
Ting, L., Klein, R. & Knio, O. M. 2007 Vortex Dominated Flows: Analysis and Computation for Multiple Scales, Series in Applied Mathematical Sciences. Springer.
Wu, X. & Moin, P. 2010 Large-activation-energy theory for premixed combustion under the influence of enthalpy fluctuations. J. Fluid Mech. 655, 3–37.
Wu, X., Wang, M., Moin, P. & Peters, N. 2003 Combustion instability due to the nonlinear interaction between sound and flame. J. Fluid Mech. 497, 23–53.
Zeytounian, K. H. 2002 Asymptotic Modelling of Fluid Flow Phenomena. Kluwer.
Zinn, B. T. & Lieuwen, T. C. 2006 Combustion Instabilities: Basic Concepts – Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms, and Modeling. AIAA.
Zinn, B. T. & Lores, M. E. 1971 Application of the Galerkin method in the solution of non-linear axial combustion instability problems in liquid rockets. Combust. Sci. Technol. 4, 269–278.