Burning surface temperature

A schematic representation of the combustion wave structure of a typical energetic material is shown in Fig. 3.9 and the heat transfer process as a function of the burning distance and temperature is shown in Fig. 3.10. In zone I (solid-phase zone or condensed-phase zone), no chemical reactions occur and the temperature increases from the initial temperature (Tq) to the decomposition temperature (T ). In zone II (condensed-phase reaction zone), in which there is a phase change from solid to liquid and/or to gas and reactive gaseous species are formed in endothermic or exothermic reactions, the temperature increases from T to the burning surface temperature (Tf In zone III (gas-phase reaction zone), in which exothermic gas-phase reactions occur, the temperature increases rapidly from Tj to the flame temperature (Tg). 

Equation (3.54) is the simplified burning rate equation. If the reaction rates in the gas phase are known, the burning rate is given in terms of gas density (pressure), burning surface temperature, initial propellant temperature, and physical properties of the energetic material. 

The burning surface temperature is related to the burning rate by an Arrhenius equation, which assumes a first-order decomposition reaction for each reaction species at the burning surface. 

In order to understand the fundamental concept of the cause of temperature sensitivity, in the analysis described in this section it is assumed that the combustion wave is homogeneous and that it consists of steady-state, one-dimensionally successive reaction zones. The gas-phase reaction occurs with a one-step temperature rise from the burning surface temperature to the maximum flame temperature. 

The combustion wave of HMX is divided into three zones crystallized solid phase (zone 1), solid and/or liquid condensed phase (zone 11), and gas phase (zone 111). A schematic representation of the heat transfer process in the combustion wave is shown in Fig. 5.5. In zone 1, the temperature increases from the initial value Tq to the decomposition temperature T without reaction. In zone 11, the temperature increases from T to the burning surface temperature Tj (interface of the condensed phase and the gas phase). In zone 111, the temperature increases rapidly from to the luminous flame temperature (that of the flame sheet shown in Fig. 5.4). Since the condensed-phase reaction zone is very thin (-0.1 mm), is approximately equal to T . 

The heat transfer process in the combustion wave of TAGN consists of three zones, similar to what was illustrated for HMX in Fig. 5.5. Zone I is the solid phase, the temperature of which increases exponentially from the initial temperature, Tg, to the decomposition temperature, without chemical reaction. Zone II is the condensed phase, the temperature of which increases from T to the burning surface temperature, T, in an exothermic reaction. Zone III is the gas phase, the temperature of which increases rapidly from to the final combustion temperature, Tg, in an exothermic reaction. 

II) Solid-phase reaction zone Nitrogen dioxide and aldehydes are produced in the thermal degradation process. This reaction process occurs endothermically in the solid phase and/or at the burning surface. The interface between the solid phase and the burning surface is composed of a solid/gas and/or soUd/Uquid/gas thin layer. The nitrogen dioxide fraction exothermically oxidizes the aldehydes at the interface layer. Thus, the overall reaction in the solid-phase reaction zone appears to be exothermic. The thickness of the solid-phase reaction zone is very small, and so the temperature is approximately equal to the burning surface temperature, T. ... 

The thermal structure of the combustion wave of a double-base propellant is revealed by its temperature profile trace. In the solid-phase reaction zone, the temperature increases rapidly from the initial temperature in the heat conduction zone, Tq, to the onset temperature of the solid-phase reaction, T , which is just below the burning surface temperature, T. The temperature continues to increase rapidly from T to the temperature at the end of the fizz zone, T, which is equal to the temperature at the beginning of the dark zone. In the dark zone, the temperature increases relatively slowly and the thickness of the dark zone is much greater than that of the solid-phase reaction zone or the fizz zone. Between the dark zone and the flame zone, the temperature increases rapidly once more and reaches the maximum flame temperature in the flame zone, i. e., the adiabatic flame temperature, Tg. 

Since the burning surface temperature, T, is dependent on the regression rate of the propellant, it should be determined by the decomposition mechanism of the double-base propellant. An Arrhenius-type pyrolysis law represented by Eq. (3.61) is used to determine the relationship between the burning rate and the burning surface temperature. 

The temperature profile in the combustion wave of a double-base propellant is altered when the initial propellant temperature Tq is increased to Tq -i- ATq, as shown in Fig. 6.15. The burning surface temperature is increased to -i- AT, and the temperatures of the succeeding gas-phase zones are likewise increased, that of the dark zone from Tgto Tg-t- ATg, and the final flame temperature from 7 to Tf-t- ATf If the burning pressure is low, below about 1 MPa, no luminous flame is formed above the dark zone. The final flame temperature is Tg at low pressures. The burning rate is determined by the heat flux transferred back from the fizz zone to the burning surface and the heat flux produced at the burning surface. The analysis of the temperature sensihvity of double-base propellants described in Section 3.5.4 applies here. 

Fig. 6.17 Dark zone temperature, burning surface temperature, surface heat release, and temperature gradient in the fizz zone for high- and low-energy double-base propellants as a function of initial propellant temperature.

The temperature in the condensed phase increases from the initial propellant temperature, Tq, to the burning surface temperature, Tj, through conductive heat feedback from the burning surface. Then, the temperature increases in the gas phase because of the exothermic reaction above the burning surface and reaches the final combustion temperature, Tg. Since the physical structure of AP composite propellants is highly heterogeneous, the temperature fluctuates from time to time and also from location to location. The temperature profile shown in Fig. 7.2 thus illustrates a time-averaged profile. This is in a clear contrast to the combustion wave... 

Fig. 7.10 Burning surface temperature (7s) and the temperature of the A/PA flame (T as a function of pressure below 0.09 MPa.

The results of the calculations are shown in Fig. 8.4. The assumed values for the physical constants and reaction kinetics are listed in Ref [1]. The burning rate increases with increasing pressure, and also increases with increasing concentration and decreasing particle size of the AP particles. These calculated results compare favorably with the experimental results shown in Fig. 8.4. The calculated burning surface temperature of the DB matrix varies from 621 K at 1 MPa to 673 K at 8 MPa. The temperature sensitivity decreases with increasing pressure (a = 0.0056 K at 8 MPa).[i]... 

The burning-surface temperature data and Qj, datal l are substituted into Eq. (3.73) to determine the condensed-phase parameter, r() . The heat flux feedback from the gas phase, qg, is given by... 

As shown in Fig. 11.13, the temperature in the gas phase increases rapidly when boron particles are added. This is due to the higher burning rate of the boron py-rolant compared with that of the pyrolant without boron. Though the burning surface temperature is approximately 700 K for both pyrolants, the temperature in the gas phase just above the burning surface increases more rapidly when boron is added. The observed results indicate that the boron is oxidized just above the burning surface, within a distance of 0.1 mm. The heat flux transferred back from the gas phase to the burning surface is increased by the increased temperature in the gas phase. 

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