Basic Requirements Heat Flux and Pressure
The energy release system shall provide the heat flux to the motor propellant and the pressure in the motor chamber necessary to ignite the propellant and produce sustained combustion within the required time limit.
Because pyrogen and pelleted pyrotechnic igniters comprise the bulk of igniters currently used in operational motors, the major portion of this section on recommended practices is devoted to these types. References are provided for other systems considered of potential value for specialized applications. Before determining energy release requirements, the designer should ascertain, to the extent the information is available, values for the following variables and design requirements:
(1) Propellant ignition energy requirements, including effects of pressure, temperature, surface condition, and aging.
(2) Location of igniter with respect to the propellant surface to be ignited.
(3) Free volume of the motor.
(4) Nozzle closure effects.
(5) Primary mode of heat transfer.
(6) Initial and total burning surface to be ignited.
(7) Motor port area.
(8) Motor nozzle throat area.
(9) Function time requirements. (10) Time delays.
Methods for the design of igniters involve a mixture of empirical and theoretical treatments. The following sections describe the methods most commonly used by designers. It should be noted that the methods presented in sections 3.2.1.1.1 through 3.2.1.1.5 give energy requirements on the basis of motor characteristics without consideration of performance requirements, e.g., time to ignition, method of heat transfer, and ignition shock. Since propellant ignition time is an inverse exponential function of both heat flux and pressure (as discussed in sec. 2.0.2.3) compliance with complex or critical ignition requirements can be accomplished most effectively when the exact nature of these relationships is known. Thus the designer is able to determine whether changes in heat flux, pressure, or duration will most effectively accomplish ignition objectives. The methods provided in section 3.2.1.1.6 utilize these data in determining energy release system requirements. The selection of a method for a given situation usually is dictated by the designer's experience, complexity of the model, precision required in the motor, and relative expense of trial-and-error testing as opposed to more comprehensive theoretical treatments.
A reasonable correlation exists between the weight of a given pyrotechnic ignition material required to ignite a motor and the free volume of that motor. This relationship is described in reference 124, in which a plot on logarithmic coordinates of the weight of Alclo (sec. 3.2.3.2) versus motor free volume yields a straight line having a slope of 0.7 as shown in figure 10. Thus, the following empirical equation results:
where
Wj = weight of Alclo igniter pellets, gms V = motor free volume, in.3 K = empirically derived constant
102 80 60
Wj = weight of Alclo igniter pellets, gms V = motor free volume, in.3 K = empirically derived constant
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Skybolt ■ 2nd stage
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106 105 104 103 102
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Skybolt ■ 2nd stage
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108 107
106 105 104 103 102
Motor free volume, cu in. Figure 10.—Igniter charge weight vs motor free volume.
This correlation obviously makes the assumption that all pertinent motor variables vary in accordance with the free volume, and thus is a "broad-brush" approach to igniter design.
3.2.1.1.2 Surface Area
Another highly simplified equation for estimating ignition energy requirements has been derived empirically on the basis of total area exposed to igniter products and propellant ignitability (refs. 25 and 125). The equation is
where
Q = total energy required for propellant ignition, cal A = area exposed to products of igniter combustion, cm2 E100 = threshold ignition energy of the propellant at 100 psig, cal/cm2 C = constant that depends on type of ignition material used
Experimentally determined values of C for typical ignition materials are reported in reference 25.
Variations in the constant C apparently are caused by differences in the gas content of combustion products and the effect of the resulting pressure on propellant ignitability. Weight of ignition material required is calculated from the energy requirements Q in calories and the heat of explosion AH in cal/gm as follows:
Grams of ignition material W =--(30)
3.2.1.1.3 Critical Pressure
As previously discussed, at low pressures propellant ignition energy requirements are strongly dependent on pressure. This dependence decreases exponentially, reaching an essentially pressure-independent regime that for many propellants occurs in the range 50 to 100 psia. Consequently, one of the methods used for sizing igniters has been based on attaining a given pressure in the motor port. The desired pressure is based on the "calculated critical pressure" required for sustained burning (ref. 126); or on the pressure-heat flux relationship obtained from arc-image data; or on an established pressure (e.g., 50 to 100 psia) based on experience.
There are various methods for determining the charge size and characteristics necessary to attain the desired pressure. When the nozzle closure burst pressure is sufficiently high or the nozzle is small, pressure obtained from a given charge should be calculated based on the free volume of the motor acting as a closed vessel. Methods for calculating pressurization in a vented chamber are described in references 127 and 128. When motor ignition times on initial tests are critical or the consequences of failure are severe, igniter pressure and heat flux output should be evaluated, prior to motor firings, in a test chamber that simulates motor volume and throat conditions.
3.2.1.1.4 Mass Discharge Coefficients
The mass discharge coefficient CMD often is used in the design of pyrogen igniters. CMD is simply the ratio of the igniter mass discharge rate m, to the motor nozzle throat area At, or
This discharge coefficient is assigned a desired value based on experience and the configuration of the igniter and motor. The nominal value is 0.20 lb/sec-in.2; but may be as low as 0.10 for ideal forward end ignition conditions or greater than 0.30 when the propellant surface is relatively inaccessible to the igniter efflux. The use of proper CMD ensures that a certain pressure level in the motor is produced by the igniter; this aids the ignition of most propellants.
This method is used also for pyrotechnic igniters; it is not as simple to apply, however, because the m4 is usually highly regressive and equilibrium conditions are not maintained.
3.2.1.1.5 Bryan-Lawrence Equation
An empirical relationship between certain rocket motor parameters and the energy required to obtain satisfactory ignition (developed by the U. S. Naval Ordnance Laboratory (ref. 129)) is
Lg — length of grain, cm Ap = port area, cm2 qc = ignitability of propellant, cal/cm2
To simplify computations the variables may be grouped, and the equation reduces to the following (calories are converted to British thermal units, and centimeters to inches):
where
If qc is considered an inherent characteristic of a specific propellant, then 116.5 qc106 = K, a constant for that propellant. The plot of the grouped terms A0-435 L„0-625 Ap0-313 versus Q yields a straight line for each propellant as shown in figure 11. For a frequently used pyrotechnic formulation with a given heat of explosion, the graph also includes a direct conversion to the weight of ignition material, as shown.
350 280
105 52.5
- 2400 n-
1600
2400
3200
1600
2400
3200
Figure 11.—Chart for estimating ignition energy requirements.
The most accurate method for designing igniters is based on flux produced at the propellant surface by the igniter. This practice relates the design to the basic objective of raising the propellant surface temperature to that required to establish equilibrium combustion. However, a completely comprehensive relationship requires knowledge of several parameters that are difficult to define: the desired propellant surface temperature; the film coefficient for convective heating; the igniter efflux temperature at the film; and the contribution of radiative heating. Theoretical treatments of these areas have been discussed individually in sections 2.0.2.1, 2.0.2.2, and 2.0.2.3. The complexity of the relationships prevents the formation of a comprehensive analytical expression including all potential variables. However, by making simplifying assumptions and approximations, tractable relationships can be derived that generally are more precise than the empirical correlations. Two of these approaches are discussed in 3.2.1.1.6.1 and 3.2.1.1.6.2.
As explained in section 2.0.2.3, the time required for a propellant surface to reach ignition temperature when exposed to a constant flux q may be approximated as follows (cf. eq. (14)):
where
Thus tt, a thermal induction time for the solid, is a function of heat flux. The equation for flux, assumed to be a combination of convective and radiative heating, is of the following form:
where
Ci (m,)'n — convective heat flux term, Btu/ft2-sec (35a)
m = 0.8 (per the Reynolds number exponent) Nu = local Nusselt number Num = Nusselt number for established turbulent flow in a pipe Dp = motor port diameter, ft
C2 = radiative flux = ae (Tg* - Ts4), Btu/ft2-sec (35c)
k — gas thermal conductivity, Btu/ft-°F-sec Cp — specific heat of gas, Btu/lbm-°F /u = gas viscosity, lbm/ft-sec Tg = gas temperature, °R Ts = propellant surface temperature, °R
Therefore, when the ignition delay is specified, the required flux q is calculated; then the mass discharge from the igniter m; required to give this flux is determined. The solution to this equation requires that the ignition temperature of the propellant be known. Satisfactory results have been obtained by this method, using arc-image data on a 1:1 basis, if first decomposition is used as the criterion of ignition and if the radiation effects are not significant (ref. 130). In establishing ignition temperatures and ignition requirements, the propellant surface conditions in the test samples must be representative of actual motor conditions. The effects of release agents, fuel-rich surfaces, and aging on ignitability can be highly significant (ref. 17).
In this approach (refs. 18 and 90) convective heating is assumed to be strongly dominant and the induced flux follows the relationship q = h(Tg-Ts) xhTg (36)
The film heat-transfer coefficient h is reduced to terms of the mass flow rate of the igniter and the port area of the motor as follows:
where x is the distance downstream from the igniter impingement point. Equations (36) and (36a) may be simplified to
Thus the induced heat flux q is calculated as a function of the igniter mass flow rate mi; the motor port area A„, and the available energy of the igniter charge Qlgn. Pressure induced in the motor port by the igniter is calculated from conventional mass balance equations used in motor ballistics, assuming an inert free volume with no motor propel-lant burning.
To determine the flux required to obtain propellant ignition, knowledge of the pressure— heat flux—ignition time relationship for the propellant involved is required. Again, arc-image data providing curves of ignition time versus pressure at various flux levels have been used satisfactorily. When these curves are plotted with igniter-induced motor pres-surization curves on a common graph, the intercept provides the ignition time, as illustrated in figure 12.
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