T Combustion Instability

If the combustion products of a propellant attain a state of thermal equilibrium, the combustion temperature may be determined theoretically, as described in Chapter 2. However, the combustion in a rocket motor is incomplete and so the flame temperature remains below the adiabatic flame temperature.bl If one assumes that the flame temperature, T, varies with pressure, p, in a rocket motor, T is expressed byl5] 

Equation (13.29) is derived in Section 14.1.3. Using the burning rate of a propellant given by Eqs. (3.68) and (13.29), the criterion for stable burning isl l 

This criterion is the so-called T combustion instability. The stability criterion expressed by 1 is not sufficient to obtain stable combustion when the flame temperature is dependent on pressure.lO In general, m is approximately zero in the high-pressure region for most propellants. However, l/of nitropolymer propellants such as single-base and double-base propellants decreases with decreasing pressure below about 5 MPa. Since direct determination of m is difficult, the heat of explosion, is evaluated as a function of 

Combustion tests carried out for a rocket motor demonstrate a typical T combustion instability. Double-base propellants composed of NC-NG propellants with and without a catalyst (1 % nickel powder) were burned. Detailed chemical compositions of both propellants are given in Section 6.4.6 and the burning rate characteristics are shown in Fig. 6.29. The addition of nickel is seen to have no effect on burning rate and the pressure exponent is n = 0.70 for both propellants. 

The heat of explosion of the uncatalyzed NC-NG propellant decreases rapidly when the pressure is decreased below about 4 MPa, as shown in Fig. 13.12. However, the heat of explosion of the catalyzed NC-NG propellant remains relatively unchanged, even below 2 MPa. 

This criterion is the so-called T combustion instability. The stable criterion expressed by Eq. (9.10) is not enough to obtain stable combustion when the flame temperature is dependent on pressure. 

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The combustion tests conducted for a rocket motor show that the combustion becomes unstable below 1.7 MPa and that the burning acquires a chuffing mode in the case of the uncatalyzed propellant. However, as expected, the combustion is stable even below 0.5 MPa for the nickel-catalyzed NC-NG propellant, as shown in Fig. 13.13. Propellants for which the flame temperature decreases with decreasing pressure tend to exhibit T combustion instability. 

Fig.13.13 T combustion instability evaluated on the basis of the m + n stability criterion.

D.T. Harrje and F.H. Reardon. Liquid propellant rocket combustion instability. Technical Report SP-194, NASA, Washington, DC, 1972. 

T. Poinsot, A. Trouve, D. Veynante, S. Candel, and E. Esposito. Vortex driven acoustically coupled combustion instabilities. Journal of Fluid Mechanics, 177 265-292, 1987. 

T.C. Lieuwen, Y. Neumeier, and B.T. Zinn. The role of unmixedness and chemical kinetics in driving combustion instabilities in lean premixed combustors. Combustion Science and Technology, 135 193-211,1998. 

ICF flame motion during cyclic modulation of the flow <3> = 0.8, v = 1.87 = m/s,/= 150Hz, and v = 0.15m/s. (Adapted from Candel, S., Durox, D., and Schuller, T., Flame interactions as a source of noise and combustion instabilities, AIAA paper 2004—2928,10th AlAAl CEAS Aeroacoustics Conference, Manchester, U.K., May 2004. With permission.)... 

T.C. Lieuwen and V. Yang, eds. Combustion Instabilities in Gas Turbine Engines Operational Experience, Fundamental Mechanisms, and Modeling. Progress in Astronautics and Aeronautics, Vol. 210, AlAA, 2005. 

K. McManus, T. Poinsot, and S. Candel. A review of active control of combustion instabilities. Prog. Energ. Combust. Sci., 19 1-29,1993. 

N. Noiray, D. Durox, T. Schuller, and S. Candel. A unified framework for nonlinear combustion instability analysis based on the flame describing function. /. Fluid Mech., 2008 (In press). 

S. Gandel, D. Durox, and T. Schuller. Elame interactions as a source of noise and combustion instabilities. AIAA Raper 2004-2928, 2004. 

In Chapter 5.2, S. Candel, D. Durox, and T. Schuller consider certain aspects of perturbed flame dynamics. The relation between combustion instability and noise generation is described by reference to systematic experiments. The data indicate that acoustic emission is determined by flame dynamics. On this basis, combustion noise can be linked with combustion instability. 

Neumeir, Y., and B. T. Zinn. 1996. Experimental demonstration of active control of combustion instabilities using real time modes observation and secondary fuel injection. 26th Symposium (International) on Combustion Proceedings. Pittsburgh, PA The Combustion Institute. 2811-18. 

Zinn, B.T., and Y. Neumeier. 1997. Active control of combustion instabilities. AIAA Paper No. 97-0461. 

Yang, V., A. Sinha, and Y-T. Eung. 1992. State-feedback control of longitudinal combustion instabilities. J. Propulsion Power 8(l) 66-73. 

Koshigoe, S., T. Komatsuzaki, and V. Yang. 1999. Active control of combustion instability with on-line system identification. J. Propulsion Power 15 383-89. 

Sirignano L. Crocco, "A Shock Wave Model of Unstable Rocket Combustors , AIAA 2, 1285(1964) I) B.T. Zinn, "A Theoretical Study of Nonlinear Transverse Combustion Instability in Liquid Propellant Rocket Motors (PhD Thesis)> Princeton Univ, May 1966 J) C.E. Mitchell, "Axial Mode Shock Wave Combustion Instability in Liquid Propellant Rocket Engines (PhD Thesis), Princeton Univ, NASA CR 72229(1967) K) E.L. 

N) E.W. Price, "Recent Advances in Solid Propellant Combustion Instability , Ibid, pp 101-113 O) G.A. Marxman C.E. Wooldridge, "Finite-Amplitude Axial Instability in Solid-Rocket Combustion , Ibid, pp 115-27 P) W.A. Sirignano, "A Theory of Axial-Mode Shock-Wave Oscillations in a Solid-Rocket Combustor ,Ibid, pp 129-37 Q) B.T.Zinn C.T. Saveli, "A Theoretical Study of Three-Dimensional Combustion Instability in Liquid-Propellant Rocket Engines , Ibid, pp 139-47 R) R.J. Priem E.J. Rice, "Combustion Instability with Finite Mach Number Flow and Acoustic Liners , Ibid, pp 149-59 S) M.W. Thring, "Combustion Oscillations in Industrial Combustion Chambers , Ibid, pp 163-68... 

T) M. Barrere F.A. Williams, Comparison of Combustion Instabilities Found in Various Types of Combustion Chambers , Ibid, pp 169-81 U) M.W. Beckstead et al, "Combustion Instability of Solid Propellants , Ibid, pp 203-11... 

D.W. Rice, CombstnFlame 8(1), 21-8 (1964) CA 60, 14325 (1964) (Effect of compositional variables upon oscillatory combustion of solid rocket propellants) N ) R.W. Hart F.T. McClure, "Theory of Acoustic Instability in Solid Propellant Rocket Combustion , lOthSympCombstn (1965), pp 1047-65 N2) E.W. Price, "Experimental Solid Rocket Combustion Instability , Ibid, pp 1067-82 Qi) R.S. Levine, "Experimental Status of High Frequency Liquid Rocket Combustion Instability , Ibid, pp 1083-99 O2) L. Crocco,... 

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