P_sun is the power emitted at the Sun’s surface (in Watts) as determined by Stefan–Boltzmann’s blackbody equation;

σ is the Stefan–Boltzmann constant = 5.670400 × 10^–8 Js^–1m^–2K^–4

T is 6000 degrees Kelvin

R_sun is the radius of the Sun in meters (6.9599 × 10⁸ m)

and the solar radiation intensity at a given distance, D, in meters is given by:

Historical development of SNPS

A good source is Angelo (1985), covering:

Threat environment

A very important aspect of the propellants used is their ability to impart energy to other parts of the launch vehicle during uncontrolled burning or explosive events, particularly hazardous systems such as RTGs, which could in turn be demolished causing release of harmful radioactive material. The section on “Containment Design” describes the vulnerabilities of the nuclear source material such as clad melting temperatures, overpressure limits, and effects of vaporization. Predicting the environment that this material must potentially survive is the objective of the rest of this section.

Liquid propellant fireballs

A conceptual model of a fireball is shown in Figure 6.17. Combusting propellants embedded within the fireball are the source of the combustion products (Dobranich, 1997). The physics of fireball formation is thoroughly described in Sandia Report SAND97-1585 (Dobranich, 1997), which explains their Fireball Integrated Code Package simulating responses of physical and chemical processes occurring in a fireball and is presented here:

Fireball temperature

Based on a single control volume, the time-dependent temperature of the fireball is determined by solving the following energy balance equation (assuming a constant-pressure combustion process):

(3)

where n_f is the quantity of combustion products and entrained air that comprise the fireball (mol), h_f is the molar enthalpy of the fireball (J/mol), t is time (sec), R is the reactant enthalpy inflow (W), L is the fireball energy loss rate (W), and E is the enthalpy inflow from air entrainment (W). Note that both n_f and h_f are dependent variables. The molar gas quantity in the fireball is:

(4)

where n_p is the quantity of combustion products (mol), and n_a is the quantity of entrained air (mol). The reactant enthalpy inflow term, R, is given by:

(5)

where is the molar combustion rate of propellant reactants (mols/s), which is assumed known, and h_r is the specified enthalpy of the reactants (J/mol). Likewise, the air entrainment enthalpy inflow term is given by:

(6)

where is the molar rate of air entrainment (mol/s), and is the enthalpy of the ambient air (J/mol). Equation (6) can be expanded using the chain rule and rearranged to provide

(7)

where is the molar product production rate (mol/s).

The product production rate, , is expressed in terms of the reactant combustion rate using:

(8)

where y is the molar quantity of combustion products produced per mole of reactant, and is the specified reactant combustion rate (mol/s). This equation is required for the solution of eq. (8). Based on equilibrium chemistry, the fraction y is determined using:

(9)

where n_p is the quantity of products (mol), n_r is the quantity of reactants (mol), and W_r and W_p are the mean molecular weights of the reactants and products, respectively (g/mol). The mean molecular weights are given by:

(10)

and

(11)

where N_r is the number of reactant species, N_p is the number of product species, and are the mole fractions of reactant species j and product species I, respectively, and and are the molecular weights of the reactant and product species, respectively (g/mol).

Equation (7) can now be rearranged to provide:

(12)

This equation is based on the following definition of enthalpy:

(13)

where h_F is the enthalpy of formation (also known as the heat of formation) at the standard state (298.15 K, 1 atm), and Δh is the change in enthalpy from the standard state to some other state, including sensible heat and heats of transition when appropriate.

The loss term in eq. (7), L, is given by:

(14)

where ε is the effective emissivity of the fireball, σ is the Stefan–Boltzmann constant (5.67 × 10^–12 W/cm²⋅K⁴), A is the surface area of the spherical fireball (cm²), T is the temperature of the fireball (K), T_a is the ambient environment temperature (K), ε_Al is the surface emissivity of the aluminum structures within the fireball, T_Al is the surface temperature of the aluminum structures (K), h_Al is the heat transfer coefficient for convective heat transfer between the aluminum structures and the fireball (W/cm²⋅K), and q_Al is the heat added to the fireball from aluminum combustion (W). Calculation of the aluminum surface temperature and the combustion source term are not described in this chapter.

Qualitatively, eq. (3) indicates that the time rate of change of the fireball energy equals the rate of energy inflow from reactants and air entrainment minus the rate of fireball energy loss. The loss term in eq. (14) includes four contributions: (1) thermal radiation from the fireball to the ambient environment; (2) thermal radiation from the fireball interior (treated as gray semitransparent participating medium) to the aluminum structures (the rocket) within the fireball; (3) convective heat transfer from the fireball interior to the aluminum structures, and (4) heat added to the fireball from combustion of aluminum structures. Following liftoff, only the first loss term contribution is included because the structures are assumed to no longer be immersed in the rising fireball.

Using the calculated fireball enthalpy and product mole fractions, the fireball temperature is determined using:

(15)

where y_a is the molar air fraction defined as the molar quantity of entrained air in the fireball divided by the molar quantity of air and all combustion products in the fireball, is the mole fraction of product species i, is the enthalpy of product species i (J/mol), and h_a is the enthalpy of the air entrained into the fireball (J/mol). The molar air fraction is defined as:

(16)

Because and are functions of fireball temperature T, eq. (15) must be solved iteratively for temperature. This is accomplished using Newton iteration, recognizing that the derivative of enthalpy with respect to temperature at constant pressure is equal to c_p, the constant-pressure specific heat (J/mol⋅K). Enthalpies are provided as fifth-order polynomials in temperature and account for heat of formation, sensible heat, phase transitions, and corrections for non-ideal gas behavior. Specific heats are provided as fourth-order polynomials in temperature.

Empirical formulae

Roberts (1982) used the empirical data of Hasegawa and Sato (1977) to correlate the measured radiation flux q received by a detector at a distance L (m) from the center of a fireball with a hydrocarbon fuel mass (AICE, 1994), m_f (kg):

(17)

Heat flux density thermochemical model predictions are shown along with upper bound experimental data, plotted versus dimensionless time, t/t_b, in Figure 6.18. Temperature within the fireball can be estimated from the heat flux data by assuming that radiation effects dominate and the emissivity is 1.0 (blackbody). Consider the initial radiant flux of 2000 kW/m². This corresponds to a temperature of 2433 K via the Stefan–Boltzmann relation:

(18)

where E_b is the blackbody emissive power, or heat flux (kW/m²), σ is the Stefan–Boltzman constant, and T is the fireball temperature (K). The maximum fireball temperatures are higher than this value, but rapidly drop down within milliseconds.

Fireball rise time

Failure of the propellant containment system can lead to a subsequent explosion that can be located near the ground, during early flight, or in the air, during later flight. In surface fireballs associated with propellant explosions, as the pressure of the detonation products decreases to ambient, the density of the gas is considerably below ambient density and the resultant buoyant force causes the gases to begin to rise. The bulk of the propellant is then entrained in the fireball and rapidly burned (High, 2006). A hemispherical shape is maintained during most of this period until the fireball growth rate is exceeded by the buoyancy and a spherical shape develops. After the spherical shape is completely formed, the fireball lifts from the ground, and surrounding air is drawn into the fireball by a combination of convective forces and a vortex motion to continue mass addition. A stem is created with propellant spilled on the ground to produce a mushroom-type cloud. The hot fireball continues to change into an oblate spheroid and finally a torus, as seen in Figure 6.19. Combustion between the fuel-rich gases and entrained air dilutes and cools the gases. The radiative losses also contribute to a rapid cooling process. The dynamic behavior of the fireball can be described as a spherical thermal composed of hot fireball gases on top and entrained air below. The development and rise of this thermal are controlled by thermal radiation, addition and combustion of propellant, and air entrainment.

Following completion of the combustion stage, the fireball lifts from the ground, rapidly entraining air. The molar rate of air entrainment, based on an assumed entrainment coefficient, is determined using:

(19)

where α is an entrainment coefficient, u is the rise velocity of the fireball (cm/s), A is the surface area of the fireball (cm²), p is the pressure of the fireball (atm), which is assumed to equal the ambient pressure, is the universal gas constant (82 cm³⋅atm/mol⋅K), and T is the fireball temperature (K). The quantity of entrained air is added to the existing product species in the calculation of fireball temperature via eq. (15). Also, during the entrainment stage, the reactant enthalpy inflow term is zero.

The air entrainment model is based on the “macro-scale” process of a bubble (the fireball) rising through a medium (air), which is applicable after fireball liftoff. Such a model is common in bubble flow and atmospheric simulations. However, the model is also used before fireball liftoff, when air entrainment is a “micro-scale” process in which turbulent eddies near the boundaries of the fireball bring in ambient air. Because these turbulent eddies are not captured in the fireball model, there is no reasonable way to predict this entrainment. The micro-scale entrainment is expected to be much smaller than the macro-scale entrainment. Different entrainment coefficients may be used during the combustion and entrainment stages to reflect the different processes (e.g., α = 0.025 during the combustion stage and 0.25 during the entrainment stage). It is also possible to introduce entrained air by specifying it as a reactant; thus micro-scale entrainment calculated by some other means (such as a computational fluid dynamics code) can be incorporated in the fireball simulation if desired.

The rise velocity of the fireball is determined from solution of the following momentum balance:

(20)

where ρ is the density of the fireball (g/cm³), V is the volume of the fireball (cm³), g is the acceleration due to gravity (981 cm/s²), C_d is the drag coefficient, is the density of the ambient air (g/cm³), and A_P is the projected area of the fireball (cm²). The first term to the right of the equal sign is the buoyant force due to the density difference of the ambient air and the fireball, and the second term is the drag force. Application of the chain rule and rearrangement yields the following equation for numerical solution:

(21)

with

(22)

(23)

and

(24)

where b is a constant that depends on the Reynold’s number, n_f is the quantity of all fireball constituents (mol), which includes combustion products and entrained air, W_f is the mean molecular weight of the fireball mixture (g/mol), the superscript k indicates the time step number, Δt is the selected time step (sec), ρ is the fireball density (g/cm³), a is another constant that depends on the Reynold’s number, is the density of the ambient air (g/cm³), is the dynamic viscosity of the ambient air (g/cm-sec), and r is the fireball radius (cm). The product n_fW_f, which is the fireball mass, is calculated as:

(25)

where W_a is the molecular weight of air (28.97 g/mol).

The drag coefficient, C_d, is expressed as:

(26)

where Re is the Reynold’s number of the rising fireball given as

(27)

where u is the rise velocity (cm/s) and r is the fireball radius (cm). The constants a and b are both functions of the Reynold’s number, and for flow around a sphere are provided in Table 6.6, based on simple curve fits to graphical data. Although the fireball will deviate from a spherical shape, the errors introduced are considered insignificant for our purposes.

The height of the center of the fireball is determined by integrating the rise velocity over time with z equal to as the initial condition. Thus:

(28)

A hemispherical fireball is formed initially. The fireball grows in the shape of a truncated sphere as it rises, attaining a full spherical shape when it lifts from the ground. This growth is depicted schematically in Figure 6.20.

The volume and surface area of the fireball before liftoff are given by:

(29)

and

(30)

with

(31)

and

(32)

where V is the volume (cm³), r is the radius of the fireball (cm), r_c is the radius of the circle formed by the intersection of the fireball truncated sphere and the ground (cm), and z is the height of the fireball center (cm). Equations (29)–(32) are solved to determine r and A given V and z. Following liftoff, the volume and surface area of a full sphere are used.

The volume of the fireball is based on the ideal gas law:

(33)

The quantity of all fireball constituents, n_f, is found by integrating the rate of fireball growth, , over time. Thus:

(34)

where the fraction y (eq. (9)) is defined as the molar ratio of combustion products to reactants (determined by the equilibrium combustion solution), and is the molar rate of air entrainment (mol/s).

The effective emissivity of the fireball, accounting for all particles within the fireball and assuming non-absorbing fireball gases and diffuse particle surfaces, is given by:

(35)

where L_b is an effective thickness of the fireball (cm), N_s is the number of particle sizes, is the emissivity of particle size i, Cⁱ is the number concentration of particles of size i (cm^–3), and is the effective projected area of particle size i (cm^–3), which is given by

(36)

where χⁱ is the dynamic shape factor for particles of size i, and is the diameter of the volume-equivalent sphere for particles of size i (cm). The effective fireball thickness, L_b, is usually referred to as the mean beam length, which for a sphere is given as:

(37)

where r is the fireball radius (cm). Before the fireball attains a full spherical shape, the mean beam length is approximated as:

(38)

Equation (35) is easily modified to approximately account for absorbing gases (CO₂ and water vapor) within the fireball. Thus:

(39)

where ε_g is the effective gas emissivity based on the temperature, pressure, and mean beam length of the fireball product gases. The calculation of the gas emissivity is based on an engineering approach assuming that water vapor and carbon dioxide are the dominant contributors to emissivity. Thus:

(40)

where the H₂O and CO₂ subscripts refer to water vapor and carbon dioxide gas, respectively, and f and Δε are correction factors. The emissivities for the two dominant gases along with the correction factors are based on approximate curve fits to experimental data and are given as:

(41)

(42)

(43)

(44)

(45)

(46)

where T^∗ is equal to T divided by 1000; T is the fireball temperature (K), L_b is the mean beam length (cm), y is the mole fraction, and p is the fireball pressure (atm). The data points for the curve fits were selected to emphasize the high temperatures expected in a fireball.

Equation (39) for fireball emissivity couples the aerosol physics-governing equations, which are used to determine the agglomerated particle concentrations, to the fireball temperature and size equations, and to the structure and particle heat transfer equations.

Both the fireball energy equation and the fireball rise velocity equation are solved using a Runge–Kutta–Fehlberg approach. An adaptive time step algorithm is incorporated to ensure both equations are solved accurately. This algorithm uses the difference between a fourth- and fifth-order solution to control the truncation error as the solutions are advanced in time. Thus different combustion scenarios can be simulated without concern for time step selection.

It is necessary to define gas mixture properties for viscosity and conductivity in terms of the fireball constituent properties. The mixing model of Wilke as modified by Herning and Zipperer is used for this averaging process:

(47)

where μ is the dynamic viscosity (g/cm⋅sec), N_p is the number of gaseous product species in the fireball at the current time, y_k is the mole fraction for species k, and W_k, is the molecular weight for species k. As suggested in a prior report (Reid, Prausnitz and Poling, 1987), the same equation is used for conductivity with μ replaced with k (W/cm⋅K).

The final equations presented here for fireball physics describe the calculation of the turbulent dissipation term, which follows the work of Turner. This term is required in the aerosol physics solution of agglomeration due to turbulent diffusion. Although particle agglomeration due to Brownian motion is expected to dominate, the enhancement of agglomeration due to turbulence within the fireball should not be neglected.

The local turbulent energy dissipation rate is approximated as the product of kinematic viscosity and the square of the vorticity:

(48)

where ε_T is the turbulent energy dissipation rate (cm²/s³), μ is the dynamic viscosity of the fireball gas mixture (g/cm⋅sec), ρ is the fireball density (g/cm³), and is the gas velocity vector (cm/sec). The flow field within the fireball is assumed to be approximated by a spherical vortex, for which the stream function is:

(49)

where u is the vortex (fireball) rise velocity, r is the radial position within the vortex, θ is the angle describing the azimuthal position within the fireball, and is the radius of the vortex. The radial and angular components of the velocity vector, and are given by:

(50)

and

(51)

Now the vorticity cross product can be evaluated as:

(52)

The turbulent dissipation rate, assuming isotropic turbulence, can be expressed as:

(53)

Because the fireball is modeled as a single uniform control volume, the spatial dependence of turbulent dissipation must be removed. A volumetrically averaged dissipation can be derived as:

(54)

where

(55)

Now the average turbulent dissipation rate is:

(56)

where the radius of the vortex is taken as the radius of the fireball. This quantity is evaluated based on the current state of the fireball and used for calculation of agglomeration due to turbulent diffusion.

To determine the products of combustion and their relative amount, a calculation of the combustion thermodynamics is required. The thermodynamic properties of the fireball are necessary to determine the temperature and size of the fireball, and to assess the vaporization and agglomeration of the plutonium-bearing particles. To simplify the combustion thermodynamics, two assumptions are made in the Fireball Code Package:

Chemical equilibrium is based on the minimization of either Gibb’s free energy or Helmholtz free energy. The Fireball Code Package utilizes the minimization of Gibb’s free energy, which is a function of pressure, temperature, and chemical composition. For a mixture of N_p product species, the chemical contribution to the Gibb’s free energy for the mixture is given by:

(57)

where μ_j is the chemical potential for species j. If pressure and temperature are constant then:

(58)

The condition for equilibrium is the minimization of free energy and is applied to this equation subject to mass balance and non-negativity constraints.

Of principal interest for fireball simulations is the behavior of plutonium-bearing particles. The discipline of aerosol physics deals primarily with the agglomeration (or forming into round masses) of aerosol particles, of the same or different size, in a gaseous suspension. Generally, particles of diameter less than 0.01 cm (100 μm) are considered to behave as aerosols. Larger particles, often referred to as “rocks”, are assumed not to agglomerate. The objective of aerosol physics is to determine how the fireball environment modifies the size distribution of plutonium-bearing aerosol articles.

Empirical formulae

Previous studies (Mansfield, 1969), (Willoughby, Wilton & Mansfield, 1968), (Gayle & Bransford, 1965) have shown that the size, duration, and temperature of fireballs of various propellant mixtures have nearly the same quantitative behavior. Also, the empirical models used to characterize fireballs are generally well established and accepted. These estimates are based on experimental data from tests with up to 25,000 lb of liquid propellant and summarized in (Reinhart, 1999). In the studies, the fireball size and duration relationships were estimated from accumulated test and incident data, and analyzed empirically to obtain the following relationships:

The maximum diameter of the fireball is given by:

(59)

where D is the diameter of the fireball (ft), and W is the combined (fuel and oxidizer) propellant weight (lb). The standard error in D (i.e., the standard deviation of the data from the fitted equation), is about 30%.

The fireball liftoff time is given by:

(60)

where t_b (secs) is the point in the fireball development when buoyancy and entrainment become dominant.

The duration of visible radiation (in seconds) is given by:

(61)

with a standard error estimated to be 84%.

The stem liftoff time defines the point when the heat flux drops abruptly, ceasing to be a measurable threat, is given by:

(62)

Solid propellant composition

The thermal environment exhibited by burning solid propellant is determined in large part by its chemical makeup. Other factors affecting variability in the thermal environment include the geometrical configuration/size of the burning fragments, the amount of fracturing due to mechanical damage, and ambient conditions. Solid propellant stores the fuel and oxidizer together in solid form. The fuel is typically powdered aluminum, and the oxidizer is ammonium perchlorate (Wertz & Larson, 1991). A synthetic rubber such as polybutadiene holds the fuel and oxidizer powders together. Table 6.7 shows the typical type and quantity of some solid propellants used on launch vehicles and also lists the ingredients of several popular propellants.

Burn rate

The surface recession rate r, called the burning rate, is an empirically determined function of the propellant composition and certain conditions within the combustion chamber. These conditions include propellant initial temperature, combustion pressure, and the velocity of the gaseous combustion products over the surface of the solid (Hill and Peterson, 1970). This function is approximated by:

(63)

where a and n are constants for a particular propellant mix and p is the pressure within the combustion chamber. Values of the constants for several propellants are also shown in Table 6.7.

Combustion process

The qualitative description of the combustion process which a solid propellant chunk will exhibit during ambient-atmosphere burning on the ground is presented here from Price et al. (1979):

Because of slow aluminum combustion, the combustion zone has the macroscopic structure shown in Figure 6.21. In a thin region (roughly one centimeter thick) adjoining the propellant surface, the oxidizer and polymeric binder decompose and interact. This is followed by an extended Region A in which the aluminum droplets are burning, and the gaseous products are near equilibrium composition (i.e., equilibrium for the amount of aluminum burned at that point). Region B corresponds to a distance from the burning surface great enough so that all of the aluminum has burned (observed to be about 1 meter). Along the sides of the combustion plume there are regions where the environmental air has mixed with propellant products. Because the propellant products are highly fuel rich, air admixture leads to further reaction and heat release, concurrent with dilution and cooling with atmospheric nitrogen.

The important aspect of this macroscopic description of the combustion zone is the recognition of the difference in reaction rate-controlling processes in the different regions. Near the propellant surface, the dominant rates involve binder and oxidizer decomposition and mixing. In Region A, the rate is limited by the aluminum droplet combustion. In Region B, combustion is constant. In Regions C and D, the rate is limited by air mixing. The principal scale effect in going to large propellant samples is the decreasing importance of edge effects (Regions C and D). Region A remains the same thickness for all sample sizes that are large enough for complete aluminum combustion before appreciable air admixture.

The macroscopic structure of the combustion zone is substantially determined by microscopic details, as is the nature of the two-phase flow seen by an object immersed in the fire. Looking at the combustion sequence on a more microscopic scale, the oxidizer and binder on the propellant surface decompose to gases, while the aluminum particles (10 to 30 microns) accumulate and adhere to form larger agglomerate droplets up to 299 microns in diameter. The oxidizer and binder gases mix and react near the burning surface. The aluminum agglomerate droplets ignite and burn on the surface, then move out into the gas flow. There they burn so slowly that they produce an extended combustion zone roughly 1 meter in thickness. The final product flow is roughly 30% aluminum oxide, which is in liquid droplet form.

Starting with aluminum agglomerate droplets in the 20 to 200 micron diameter range, the droplets burn by two paths that produce distinctive product oxide droplets. Fine (<2 micron) smoke droplets are formed in a flame envelope around each aluminum droplet. Oxide also forms and accumulates on the aluminum. This in turn forms a distinctive oxide lobe that eventually becomes a residual droplet when the aluminum is consumed. Thus an increasingly dense oxide cloud develops as the burning aluminum droplets and smoke move away from the propellant droplets, and larger ones being formed later as the larger aluminum droplets burn out.

A series of chemical equilibrium calculations were made for UTP 3001 propellant at 1 atm at the Air Force Weapons Laboratory, with percent aluminum reacted as a parameter. The results are shown in Figures 6.22 and 6.23. In these calculations, the temperature of the unburned aluminum was assumed as shown in the figure. Of the three temperatures referred to, 2533 K is most plausible for Region A, while lower values are appropriate near the burning surface, which corresponds to near 0% aluminum reacted.

From these figures it can be seen that the aluminum combustion brings the temperature in Region A up from 2350 K at about a centimeter above the burning surface, to 2990 K at the start of Region B where aluminum combustion is complete. In the process, H₂O and CO₂ are reduced to H₂ and CO. The equilibrium properties shown at 100% aluminum burned are applicable to Region B of the combustion zone. This is a major part of the fire environment of a large piece of propellant, encompassing that region more than 1 meter or so from the burning surface, out to those regions where air admixture has become important. For a large propellant sample (e.g., 1 meter across the burning surface), the temperature calculated by this means is probably more accurate than can be measured directly. The calculation for less than 100% aluminum burned tells nothing about the droplet size distribution at each point in the combustion zone or the spatial variation of temperature within the combustion zone. Table 6.8 provides a summary of the reaction zone characteristics for UTP 3001 propellant.

The extended region of the combustion zone of the propellant in which aluminum droplets burn is a region where chemical heat release continues locally around the aluminum droplets and flows to the surrounding media, with corresponding temperature gradients. The most intense heat release is in the high temperature zone, which is a detached flame envelope around each aluminum droplet. In this flame envelope, the most energetic step is the formation of Al₂O₃ in liquid form, primarily on the surface of existing smoke droplets in that envelope. It is the resulting energy of that reaction, and the corresponding high temperature of those smoke droplets, that makes the combustion so luminous. At 1 atm the Al₂O₃ temperature is about 3800 K. In a convective environment the flame envelope may be drawn out into a tail. From a practical viewpoint, it should be stressed that the high temperature around the burning agglomerates, while the source of a large part of the radiant energy and heat, contains very little mass, and only small droplets that are not expected to be deposited extensively on objects in the flow.

Inside the flame zone, the aluminum droplet is necessarily at a temperature below the aluminum boiling point (2740 K) and above the Al₂O₃ melting point (2318 K). The reason is that the flame cannot support the high vaporization rate of the boiling point, while the combustion would be arrested, or drastically reduced, if the oxide were frozen (because it would encapsulate the agglomerate). The aluminum droplet, at a temperature that lies between 2318 and 2740 K, with 2500 K taken as a best estimate, and, in aggregate, representing a substantial mass, readily impinges on immersed objects, reacting exothermally after being retained on the object. This effect (impingement and retention on an immersed object) would be more pronounced near the burning surface of the propellant where the aluminum concentration is high.

The third temperature zone of the aluminum combustion is all that volume outside the droplet flame envelope, where the temperature is something like the flame temperature of the propellant (with due regard for the percent aluminum consumed at the particular location). This temperature ranges from 2350 K near the propellant surface to 2990 K further out where the aluminum is 100% consumed.

In summary, most of the fire environment consists of the following:

Spatial distribution of temperature is as follows: Near the propellant burning surface (lower Region A) there is a heavy flow of burning aluminum (droplet temperature about 2500 K), with a correspondingly large flame envelope radiation (temperature about 3800 K); and with a correspondingly low smoke density in the rest of the volume (temperature range of 2400 to 2500 K). As the material flows further from the surface (outer Region A), the aluminum droplets decrease in size and total mass while remaining at about 2500 K; the total volume and radiation of the flame envelope (temperature of 3800 K) decreases; the population of both smoke and residual oxide droplets increases and the temperature rises towards 3000 K if the air admixture does not intervene unduly. Beyond about 1 meter (Region B), the aluminum droplets and their flame envelopes disappear, leaving only a homogenous flow of gas, oxide smoke, and residual oxide droplets at about 3000 K.

The radiation field in the combustion zone showed spectral lines of several gaseous species and a higher level of thermal radiation from the Al₂O₃ smoke cloud. Measurements of the smoke cloud 15 cm from the burning surface indicated a temperature of about 2800 K, an emissivity of 0.03, and an absorption coefficient of about 0.1/cm. Intensity-emissivity measurements are wavelength-dependent, apparently due to the presence of a small amount of smoke that is in the agglomerate flame envelope, which is much hotter than the bulk volume.

Experimental measurement

Immersion heat probes, including bare thermocouples, immersion calorimeters and water-cooled calorimeter tubes, were used to investigate the fire environment. The environment experienced by these types of devices would be similar to a test object in the fire such as an RTG. Bare thermocouples experienced direct impingement with droplets in the flow, gave very erratic readings, and survived only briefly. Some measurements made in the wake of deflectors survived longer and gave better records; however, it was not clear how the temperature there could be related to the free stream temperature, even if the thermocouple survived. In high-temperature flows where immersion probes deteriorate, measurements of the heat-up rate of the probe can be used to estimate the plume temperature when an equation for the heat transfer between the probe and the flow can be written. When only convection and radiation were considered, an inordinately high plume temperature was inferred. This demonstrated that the heat transfer from deposition and reaction of condensed material on the probe was a major component of the heat transferred to the probe.

In tests at Los Alamos National Laboratory to determine the response of Light Weight Radioisotope Heater Units (LWRHUs) when exposed to solid propellant fires (Tate & Land, 1985), thermocouples measured temperatures of 2333 K out to distances of at least 1.8 meters for UTP 3001 propellant.

In tests at Lawrence Livermore National Laboratory to characterize the thermal environment of burning Minuteman III Stage 3 propellant (ANB-3066) (Diaz, 1993, 1994), spectral radiometry and pyrometry methods were used to determine plume temperatures. Temperatures along the centerline of the plume were observed by using graphite sight tubes, with the inboard end cut at an angle. The sight tube was inserted into the plume with the slant cut facing in the direction of flow of the plume. The sensor (for spectrometry or pyrometry methods) and sight tube were mounted, one on each end, to an alignment tube. Heat fluxes to objects engulfed in the plume were estimated by imbedding thermocouples in solid metal objects and placing them in the plume. Inverse modeling calculations were then completed using a heat transfer model to duplicate the observed temperature history of the calorimeters. Two devices were used. One consisted of a 2.5 cm diameter by 15.25 cm long molybdenum rod with two tungsten–rhenium thermocouples embedded on the centerline at 3.18 cm and 8.25 cm from the exposed end of the rod. An additional thermocouple was placed on the wall at 8.25 cm from the exposed end. The rod was wrapped with an insulating ceramic blanket and placed in a holder that exposed only one end of the rod. The second calorimeter was a 5 cm diameter by 5 cm long stainless-steel cylinder, with one end machined into a hemisphere. The other end was drilled to the center point of the hemisphere and a tungsten–rhenium thermocouple was placed in the center. The temperature, emissivity, and heat flux profiles obtained from these experiments are shown in Figure 6.24. The temperature is seen to vary from 2273 K at the burning surface to a peak at 2573 K about 32 cm off the initial surface. The heat flux of about 20 cal/cm²·sec was measured at a standoff of 25 cm. There was a high level of confidence in the experimental methods; however, the temperatures were observed to vary by ± 10% due to the turbulence and thermal characteristics of the propellant fire. ANB-3066 has an adiabatic flame temperature of 3003 K.

In tests at Sandia National Laboratories to characterize the thermal environment from an unpressurized burning bed of an AP, Al, and HTPB composite solid propellant Gill et al. (1994), measurements were made with arrays of slug calorimeters located adjacent to the plume and with cylindrical calorimeters inserted into the plume. The locations of the slug calorimeters were chosen so the plume was viewed from several vantage points. The analytic model viewed the plume as a well-stirred reactor, which could be characterized by a thermal loss that is a fixed percentage of the total heat released in the reactor volume, and by the reactor temperature. From this the plume was found to have an effective temperature near 2073 K and to radiate 34% of the total heat released. To simulate a body immersed within the plume, cylindrical calorimeters were positioned horizontally above the propellant burning surface at two elevations, at 5 cm and 20 cm standoffs. A thin-walled (0.64 cm) and thick-walled (3.2 cm) version, both with a 10.2 cm outside diameter, were positioned 11 cm apart at each standoff. The calorimeters were divided into thermally isolated quadrants to provide a measure of circumferential variation of the heat flux. Each quadrant of the thick-walled unit and the top and side quadrants of the thin-walled unit had one thermocouple. The bottom of the thin-walled calorimeter had three thermocouples. They were oriented so that each quadrant preferentially viewed the top, bottom, and lateral heat fluxes. The heat flux versus time from each segment indicated a slow increase in flux to a maximum level. The thin calorimeters then melted while the thick calorimeters remained intact. The maximum heat flux levels are shown in Figure 6.25.

The average heat flux into a calorimeter is 84.7 W/cm², with a range of ± 8%. The average incident heat flux (W/cm²) to a specific quadrant of these calorimeters is given by:

(64)

The Chemical Propulsion Information Agency (CPIA) estimated the adiabatic temperature for Titan IV SRMU propellant burning at ambient pressure at 3097 K using the NASA Lewis – Chemical Equilibrium and Transport Properties of Chemical Systems Program (Gordon, McBride & Coveny, 1990).

Pre-launch to early flight phase explosions

Even before the launch vehicle begins its escape from the gravity well there are scenarios in which onboard nuclear source materials can be damaged. The final preparations for integration of the nuclear source system and the launch vehicle/spacecraft involve hazardous operations which, in failure situations, can lead to adverse environments similar to launch failure scenarios. Drops during crane lifts, electrical connection failures causing fires, electrostatic discharge to solid propellants, and other processing failures can lead to the destruction of the entire launch pad or vehicle processing facility. This was woefully exemplified on August 22, 2003, during final processing of Brazil’s Veículo Lançador de Satélites (Satellite Launch Vehicle) (VLS) at Alcântara (Figure 6.26). Twenty-one people working at the launch site were killed when one of the rocket’s four first stage solid rocket motors ignited accidentally.

Probably the most hazardous threat to nuclear material onboard the payload occurs in a scenario in which the vehicle launches nominally, then shortly after liftoff executes an immediate rotation impacting the ground nose first. In this position, large amounts of unburned solid propellant can be placed either on top of or beside the nuclear source. Impact velocities sufficient to cause secondary explosions and subsequent burning of solid propellant sets up an environment conducive to potential removal of the nuclear material’s protective shielding followed by vaporization of the material. This scenario was played out (sans nuclear payload) on February 15, 1996, when the Chinese Long March 3B rocket veered off-course immediately after launch, crashing in the nearby village only 22 seconds later, killing an estimated 100 people and destroying 80 houses in Xichang (Figure 6.27).

Ascent phase explosions

During later flight, as the vehicle increases velocity, an explosion below the payload would tend to throw the nuclear material forward of the flight path and since this segment would have different aerodynamic characteristics its ballistic trajectory should keep its impact point clear of the returning solid fragments. Figure 6.28 shows the ballistic instantaneous impact points for two times.

The early breakup of the vehicle at T+20 seconds shows that debris tends to impact in one area as the flight is nearly straight up and the programmed turn down-range has not yet been initiated. Later flight is depicted in the second figure at T+40 seconds revealing the debris field has elongated as more impacts occur over a range of points due to varying ballistic coefficients of pieces. Intact impact of the spacecraft itself with the smaller quantities of liquid propellants minimizes the possibilities of overpressures that would harm the nuclear source. There is some concern that solid “kick” motors attached to the spacecraft could impact with sufficient velocity to damage the nuclear material or impose a thermal environment upon burning on the ground to vaporize the source.

Fallback secondary explosions

Figure 6.29 depicts the bombardment of Launch Complex 17 as debris and solid propellant fragments fall during the Delta II explosion on January 16, 1997. These fragments can impact onto hard surfaces (e.g., concrete or steel, Figure 6.30), soft surfaces (e.g., sand or grassy soil), or water. Included in the falling debris, as well as the solid propellant, are any nuclear sources either maintained in their original configuration or freed by the explosive events. These can impact prior to or following a propellant fragment.

The response of solid propellant to ground impact may range from possible ignition and burning to explosive burning or even a detonation. It can be characterized knowing the size of the fragment, its impact velocity, and the type of surface that it impacts. The consequence of this response can then be defined knowing the spatial relationship between the propellant fragment impact point and the nuclear material during the short time interval immediately following the solid propellant ground impact.

For a solid motor fragment to sustain detonation it must be of supercritical size and it must be subjected to a shock stimulus sufficient to initiate detonation. Determining this critical diameter, at which detonation could occur, was one of the objectives of solid propellant testing.

Detonation response

The mechanisms of propellant detonation are dependent upon the variables of size and impact velocity. Detonation is a process in which an explosive reacts to products very close behind a steady, high-pressure shock wave that is supported by the explosive reaction. Detonation is characterized by high rates of propagation (4–9 km/s), extremely high pressures (10–40 GPa), and a short time to the start of reaction (typically 1 μs) (Lee & Green, 1988). In a detonation, 10 cm of material is consumed fully in slightly more than 10 μs. Conversely, deflagration refers to a range of reaction rates involving burning. The term burning is usually applied to a slow deflagration reaction that does not generate significant overpressure and whose time scale to consume 10 cm of material is greater than 1 second. If the material has a relatively large surface area, then a high-velocity deflagration can involve measurable or damaging overpressure and a time scale of 100 μs to 10 ms to consume the material. In this case, the reaction is propagated by conduction, convection, and radiation, and not by a shock wave. The term “explosive burn” is used for high-rate deflagration with significant overpressure to distinguish it from a high yield event like detonation.

There are several responses that the propellant can exhibit given these varying parameters. The shock-to-detonation (SDT) response is a process in which a shock wave entering an explosive material develops into a detonation (Figure 6.31).

Each type of explosive has a characteristic distance of travel for the transition of a shock wave of given amplitude into a detonation. The deflagration-to-detonation transition (DDT) is a process in which a deflagration reaction evolves into a detonation. The term is somewhat misleading in that gas pressure created by the deflagration compresses unburned, porous explosive material to cause a reaction that eventually leads to an SDT process. The initial deflagration does not simply burn faster and faster until a charge detonates; rather, its role is to drive the compaction wave.

Figure 6.32 shows a porous bed of explosive that is ignited. The burning explosive compresses unburned material to form a compaction wave and a reaction within the wave by the intensity of compaction. The intensity of the compaction wave finally grows to that of a shock wave, and a detonation develops. XDT is an initiation process that originally referred to an “unknown” (i.e., X) detonation transition. XDT now commonly means a delayed detonation in which impact damages and creates high porosity in an explosive and then causes a subsequent compaction wave that ultimately leads to a detonation (Figure 6.33). XDT is closely related to DDT in that a compaction wave is the route to detonation. However, the compaction wave in XDT is mechanically, rather than combustion, driven.

Detonation hazard

The hazards associated with ground impact induced solid propellant detonation, whether arising from SDT, DDT, or XDT, can be very severe if appropriate conditions exist to facilitate the detonation transition. Because of the severe blast overpressure and fragment environments potentially generated by solid propellant detonation, the special conditions necessary to cause SDT, DDT, or XDT should be examined in detail. Detonations typically produce:

The capability of the propellant segment or fragment to achieve sufficient impact velocity to undergo detonation must also be examined. In the case of the Cassini payload launched on a Titan IV, the flight profile made conditions necessary to achieve SRMU propellant detonation very unlikely. The launch profile limited maximum SRMU segment and propellant fragment impact velocities to less than about 600 ft/sec, with impacts most likely to occur on soft sandy soil. For mission elapsed times greater than approximately 23 seconds, fragments would impact in the Atlantic Ocean. These velocity limitations bound the upper limit of ground impact pressures to the 2–3 kbar range for soft sandy soil impact and 7–9 kbar for hard surface impact (e.g., steel or concrete). As shown in Figure 6.34, this threshold is well below the rather conservative impact velocity of 1000 ft/sec (and nominal pressure of 20–30 kbar) required for SRMU propellant detonation.

The probability that solid propellant segments or fragments will explode on impact depends on their amount and impact velocity. For Class 1.3 solid propellant in general, Figure 6.35 shows these probabilities given propellant weight and impact speed.

Critical diameter

In order to sustain the detonation shock wave, the propellant geometry must be such that the segment or fragment is supercritical. Below this critical size, the shock wave will lose strength and diminish below supersonic speed which will likely result in deflagration only. Burning propellant does have its hazards however, especially in providing a high thermal environment to exposed RHUs. Above critical size, chemical and physical interactions will “feed” the shock wave, maintaining state dynamics for continuation of the shock’s travel leading to detonation.

There is a unique and explicit relationship between the critical diameter of a material and the critical dimensions of a charge of any shape with uniform cross-section cast from that material (Elwell, Irwin & Vail, 1967). This relationship is the critical geometry, σ_c, which is defined by:

(65)

where A is the area of the cross section, P is its total perimeter, and the subscript c refers to the critical conditions. For a right circular cylinder, eq. (65) becomes:

(66)

where d_c is the critical diameter. If the critical diameter is known, eqs. (65) and (66) define the critical ratio of cross-sectional area to perimeter for any shape. Since area and perimeter can be expressed in terms of the dimensions of the cross section, the critical value of the dimensions (i.e., the critical size) of any shape is thereby defined. Testing of various propellant sample shapes were used to verify and refine eq. (66) through statistical analysis of data. The empirical form of the equation is:

(67)

Solid propellant experimental testing

Most of the knowledge concerning the explosive behavior of hydrocarbon rubber binder–aluminum fuel–ammonium perchlorate oxidizer (HC/Al/AP) propellant was gained in the 1960s from the results of Project SOPHY (Elwell, Irwin & Vail, 1967) conducted at Edwards Air Force Base, CA (Merril, Nichols & Lee, 1999). The SOPHY program looked at only 84% total solids (i.e., ingredients besides binder) propellant. More modern propellants have higher total solids loadings (86–90%) that produce higher thrust performance. Little is known about the explosive behavior of these propellants. Solid rocket motors for the Titan IV (SRMU) have 88% total solids and the Space Shuttle SRBs have 86% total solids (Table 6.7).

The rocket propulsion industry had seemed to assume that explosive potential and impact velocity thresholds for violent propellant response would be similar to that found in the SOPHY program. Table 6.9 shows the range of critical diameters derived from experimentation. These data, and incidents like the 1986 Titan 34D-9 explosion at Vandenberg Air Force Base, CA, indicated that large booster propellants may be more explosive than previously thought and highlighted the need to improve our understanding of booster propellant explosive behavior.

Technology now enables us to study this behavior more economically. Polyvinyl difluoride (PVF2) piezoelectric gauges and advanced recording instrumentation now more accurately measure and record times of arrival coupled with shock magnitude measurements and shock magnitude time histories. During the 1960s, impact experiments were carried out by rocket sled impact. Hardware and range maintenance and refurbishment costs involved high capital outlays and use of substantial manpower. Experimental methods for substantially sized propellant impacts have evolved from ramming a rocket motor or propellant sample on a rocket sled into a barrier, to putting impact barrier material on a rocket sled so that a static, highly instrumented test sample could more easily provide high speed data than in the moving sample impact process, to explosively driven steel plate impactors into instrumented propellant samples resting on relatively inexpensive, replaceable wooden stands. Advanced techniques in combination with computer code simulation could make very large propellant sample testing unnecessary. The Lawrence Livermore National Laboratory (LLNL) has developed a reactive response hydrodynamics computer code called CALE/PERMS (C-language based Arbitrary Lagrangian-Eulerian/Propellant Energetic Response to Mechanical Stimuli), which is moving in that direction.

In 1996 the Propellant Impact Risk Assessment Team (PIRAT) was assembled to specifically investigate the explosive risk posed by a Titan IV-SRMU launch. Selecting propellant sample sizes based on critical diameters reported by the French (Brunet & Salvetat, 1988), and the Super HIPPO experiments in 1992 (Merrill, 1992), a test program was developed with the intent to have impact samples in excess of critical diameter or at least close to critical diameter so that substantial energetic response to impacts could be observed. With support of CALE/PERMS it was projected that even data from samples smaller than critical diameter could provide useful inputs for computer code modification. Cylindrical diameters of 203 mm (8 in), 254 mm (10 in), 305 mm (12 in) and 559 mm (22 in) were selected. Using PVF2 gauges, detonation velocity probes, foil gauges, crystal pins, high speed data recorders, overpressure sensors, and high speed film and video recorders, test articles were initiated using the setup shown in Figure 6.36 with some variations for each diameter tested. After getting encouragement that critical diameters for 88% solid HTPB propellants might be in the range of 200 to 250 mm, it was found that the first booster propellant formulation tested has a critical diameter larger than 559 mm and, perhaps, twice as large as 559 mm. Although the propellant sizes are large in normal testing of explosive materials, they are definitely subscale compared with solid propellant booster motors that can contain more than 500 metric tons of propellant. Larger size samples might be employed in the future since investigation of characteristics above critical diameter is desired. Solid rocket booster propellant in explosive events seems to provide high atmospheric overpressure yields without being involved in true detonations. If detonations are steady state supersonic events in the energetic material and deflagrations are explosive events characterized by subsonic shock in the energetic materials, perhaps a new definition for an explosive process may need to be developed (Merril, Nichols & Lee, 1999).

Additional computer modeling

It appears that detonations in Class 1.3 composite propellants are unconfirmed (some physicists have stated that such detonations are impossible) rapid deflagration is entirely possible and has been observed experimentally. Class 1.3 presents less of an explosive hazard than its more volatile counterpart graded Class 1.1 (e.g., Trident missile propellant). There is data from flyer plate experiments at Lawrence Livermore National Laboratory (LLNL) that show that “violent” explosions were induced in 1.3 propellant from high speed impacts. The test data indicates these explosions were not from shock induced detonation (i.e., there was no SDT); instead the explosion was a rapid conflagration induced in test samples (Williams, 1987). The Solid Rocket Motor Ground Impact (SRMGI) model is an analytical/engineering code developed by RDA Nance, Crawford et al. (1990) to provide estimates of the effects of solid motor impacts. Previous work for the Air Force and NASA in analyzing the Titan 34D-9 failure, particularly ground impact explosions and blowout fragment ranges, led to the development of this code. It was subsequently expanded to include the aft segment of the Shuttle boosters, and Delta II Graphite Epoxy Motors (GEMs). Major subroutines determine the theoretical Sandia penetration depth (Sandia Labs developed penetration scale), gas generating rate void pressure, fragment accelerations and motion, venting, and final fragment velocities. Key assumptions involve percent increase in burn area and, for the stage impact, the cavity formation time, initial cavity size, and blowout fraction. Maximum fuel burn rates, soil burn area characteristics, and blowout fraction can be parametrically varied. The summary of critical velocities versus soil number and burn rate, as predicted by the modified SRMGI code, are presented in the semi-log plot in Figure 6.37.

This figure shows the smaller GEMs require the highest speed (> 400 ft/sec) and hardest surfaces (S < 1.2) to produce runaway explosive. The Titan upper segments could go critical on somewhat softer surfaces at 300–400 ft/sec but require 500–600 ft/sec for soil numbers up to 2.4. Above S = 2.4 the SRMGI code indicates that impacts of the Titan segments should not produce explosive deflagration even if burn rates are as high as 500 in/sec. Both the GEM and the Titan will not go critical if burn rates are less than 8–15 in/sec.

The STS aft segments appear to present the greatest hazard. As indicated in the figure, the STS’s large size produced runaway condition for soil impacts from S ≈ 1.4 up to S ≈ 15 to 20 and for maximum fuel burn rates which are only 5–6 in/sec. For hard surfaces (S < 1.4) when the aft stage does not penetrate more than 6 ft (half the stage diameter, the minimum depth assumed in the code for this segment, impacting end on, to create a cavity) then it is assumed conditions would not be created for a runaway deflagration. The code, with all of its engineering approximations and assumptions, only indicates that conditions for runaway deflagration have been created.

Blast scaling

The upper half of Figure 6.39 represents how a spherical explosive charge of diameter d, produces a blast wave of side-on peak overpressure P, and positive-phase duration t⁺, at a distance R from the charge center. Experimental observations show that an explosive charge of diameter Kd, produces a blast wave of identical side-on peak overpressure p, and positive-phase duration Kt⁺, at a distance KR from the charge center (lower half of Figure 6.40). Consequently, charge size can be used as a scaling parameter for blast. Charge size, however, is not a customary unit for expressing the power of an explosive charge; charge weight is more appropriate. Therefore, the cube root of the charge weight, which is proportional to the charge size, is used as a scaling parameter. If the distance to the charge and the duration of the wave are scaled with the cube root of the charge weight, the distribution of the blast parameters in a field can be graphically represented, independent of charge weight. This technique, which is common practice for high-explosive blast data, is called the Hopkinson scaling law (Hopkinson, 1915).

The compilation of experimental data for TNT surface bursts are presented in Figures 6.40 and 6.41. Early tests of liquid oxygen and RP-1 fuel (kerosene) were conducted under project PYRO in the 1960s to substantiate this curve.

Project PYRO, conducted in the late 1960s, consisted of a comprehensive program to determine the blast and thermal characteristics of the three liquid propellant combinations in most common use at the time in military missiles and space vehicles: liquid oxygen with RP-1, liquid oxygen with liquid hydrogen, and nitrogen tetroxide with Aerozine 50 (50% UDMH/50% N₂H₄) (Willoughby, Wilton & Mansfield, 1968). During the course of the program some 270 tests were conducted with these propellant combinations on weight scales ranging from 200 to 100,000 lb. This basic explosive test program was supplemented by analytical and statistical studies, laboratory-scale experimental studies, simulation tests with inert propellant combinations, and a series of high-explosive tests for calibration and evaluation purposes. Several test configurations were used. The Confinement by Ground Surface (CBGS) condition best simulated the sequential ground impact of separate fuel and oxidizer propellant tanks. This condition could occur by over pressurization of tanks or by the fallback or topple-over of the entire launch vehicle. Mixing interaction between the two propellants involved consideration of two configurations for the CBGS. Examination of the various length-to-diameter (L/D, or L-over-D) ratios and propellant flow velocity combinations revealed that the two propellant masses could have led to two cases of study: when both propellants were vertical, and when both propellants were horizontal.

Figure 6.42 represents the Confinement by the Missile (CBM) configuration in which case an internal failure is assumed to occur, and one propellant falls down into the other. Cause of this type of failure could be the rupture of a common bulkhead between fuel and oxidizer tanks due to over pressurization or fragments from a primary explosion (e.g., engine blowup) penetrating the bulkhead. To simulate this failure, a test setup as shown in Figure 6.42 was used with a small C-4 charge used to propel the breaker ram through the tempered glass diaphragm separating the oxidizer from the fuel. Duration of the CBM case was limited to the time that the propellants remained confined by the walls of the vehicle. This time was determined by the strength of the tankage, the rate of vaporization of the cryogenic material, the initial pressure in the tanks, and the initial ullage space.

The mixing mode in this case is determined by the interaction of the upper propellant and lower propellant at the time of opening. The position and velocity distributions of the lower propellant at the moment of first contact are fairly well specified, since it was assumed to be in its original configuration and to have zero velocity. Those of the upper propellant, however, may have a large range of values, depending on how full the tanks are and how large an opening is created between them. If a relatively small opening is produced, the L/D ratio of the top propellant will be effectively very much greater than that of the bottom one, and its total weight (entering into the mixing at an early enough stage to be a matter of concern) will be much smaller than that for the bottom one. In addition, the top propellant will have an initial velocity given by the fluid head in the top tank and the pressure differential between the two tanks. As the opening between the tanks becomes larger, the L/D ratio and effective weight of the upper propellant more nearly approaches the values they originally had in the missile. In addition, at the time the opening between the tanks is the full cross section of the original tank, the velocity would reach the value given by the acceleration of gravity through the distance of the ullage space in the lower tank, provided there was no pressure difference between the two tanks. Where the opening between the tanks is significantly less than the full cross section of the vehicle, the different initial L/D values for each propellant can be treated by assuming that the L/D ratio refers to the overall vehicle geometry and by defining a D_o/D_t ratio, where D_o is the opening diameter and D_t the vehicle diameter.

The CBGS scenario produces a hemispherical blast while the CBM case generates a spherical shape. When using these graphs, a scaled distance must be determined, equal to

(69)

where R is the distance of interest in feet and W is the combined liquid propellant weight in pounds. Adjustment factors are applied to W to reflect the fraction of terminal yield and the geometry of the explosion wave (i.e., spherical or hemispherical). Empirical data on TNT equivalency of liquid propellant combinations were used to develop Table 6.10 from Air Force Manual 91-201 (AFSC, 2011). The net explosive weight of liquid propellant is the total quantity of fuel (e.g., liquid hydrogen, kerosene (RP-1)) and oxidizer (e.g., liquid oxygen, nitrogen tetroxide) that would mix and explode.

Assume a prelaunch explosion of a Delta II first stage occurs at a distance of 69.3 ft from the nuclear power source installed in the spacecraft. Predict the overpressure environment at this distance assuming the propellants leak to the flame trench of the launch pad forming a pool that is subsequently ignited in a hemispherical explosion.

The Delta II first stage propellant load of LO₂ and RP-1 equals 212,574 lb from Table 6.5.

Using a TNT equivalence rating of 20% for the LO₂ and RP-1 combination from Table 6.10, a scaled distance can be calculated using equation (6) as follows:

(70)

Looking at Figure 6.40 for the hemispherical case (CBGS) the overpressure at a scaled distance of 2.0 ft is approximately 300 psi. If the destruct system had inadvertently activated, opening the LO₂ and RP-1 tanks to afford mixing and ignition at the tanks’ interface, a spherical explosion could be assumed and a factor of 0.5 would need to be applied to the total propellant weight, W in calculating the scaled distance.

(71)

which relates to an overpressure of approximately 240 psi from Figure 6.40.

Experimental data for more recent testing done with nitrogen tetroxide (N₂O₄) and monomethyl hydrazine (MMH) are shown along with PYRO deep hole results in Figure 6.43.

Impulse pressure

The impulse, I, is the area under the positive portion of the overpressure–time response curve (Figure 6.39). This is the more damaging portion of the blast wave, therefore the impulse predicted will be used along with peak overpressure to characterize potential adverse effects of explosive commodities.

Solid propellant yield models

Over the years, great effort has been expended on debris risk model input parameters to improve, understand, clarify, or justify the values used for assessing launch hazards. One of the most controversial issues remaining is the estimation of solid propellant impact yield. There are many models and methods available to estimate the explosive yield produced upon impact of the solid propellant at variable velocities and configurations, many of which have been used for Titan SRMUs, Atlas SRBs, and Delta II GEMs. Solid Rocket Motors have consistently driven explosive debris risks to the general public and personnel for launch area and downrange overflight accident scenarios. Solid propellant also tends to drive risks to payloads requiring SNPSs (e.g., Cassini, MERs, PNH, MSL).

The Space Shuttle SRB in particular provides the highest launch area explosive debris risk value of all the other launch vehicles for one reason: the aft segment does not include a linear shaped charge (LSC) to split the case as is done for the forward segments. This leaves a contained mass of approximately 260,000 lb of 1.3 HTPB propellant descending to impact should destruct action be necessary during ascent. The short lived Ares replacement vehicle of NASA’s Constellation Program provided for extension of the standard LSC to incorporate the aft segment. However, how do I know my yield model is accurate?

Considerable effort has been expended culling available historical data to validate our models, but the truth remains: there is very little controlled testing data. The only true test I know of was the 1964 Titan IIIC segment (~82K lb_m 1.3 HTPB) strapped to a sled and slapped end-on into a concrete wall at 667 ft/sec. Models tend to over-predict the yield calculated from that resultant test data. Other yield “data” tends to come from investigations of real incidents when crater dimensions are used to back-calculate appropriate yield. Some small scale data exists from critical diameter testing but it is questionable if that data adequately relates to fallback yield. Nonetheless, all available data has been previously scrutinized, weighed, and factored into the methods of yield prediction.

Why not get more data? Since 1964, when the sled test was accomplished, constraints to large scale high explosive testing have increased considerably (environmental limitations, high cost). A STAR-48 full scale destruct test, accomplished at WSMC for the MER nuclear risk assessment was an excellent demonstration of the difficulties and the rewards of this type of challenging data acquisition program (Figure 6.44).

Solid propellant computer modeling

Special computer models have been developed to predict the blast environment provided when a solid propellant chunk impacts the ground. The PISCES-2DELK continuum mechanics model, developed by FOILS Engineering, is a hydrodynamics code which was used to envision the impact of a General Purpose Heat Source (GPHS) on sand or concrete followed by a direct impact or near-field impact of a large propellant chunk (Mukunka, 1996). It encompasses the cratering process, the response of the propellant to it, the subsequent fracturing and burning of the propellant, and finally derivation of the flow conditions (pressure, density, etc.) radially away from the impact point. Figures 6.45–6.48 depict predictions of the response and deformation of the GPHS to these events.

RTG/MMRTG structure

Containment is at the GPHS level, but is not as necessary at the RTG level. This is actually a benefit since in most accident cases the RTG can be broken apart leaving the individual GPHS modules to fall back to land with impact. Since they are designed for the re-entry heating, as individual “boxes” they are lighter and their areal density can decrease the impact speed (Figure 6.51).

1. Treaty on Principles Governing the Activities of States in the Exploration and Use of Outer Space, Including the Moon and Other Celestial Bodies (known as the Outer Space Treaty), adopted October 10, 1967;

2. Agreement on the Rescue and Return of Astronauts and the Return of Objects Launched into Outer Space (known as the Rescue Agreement), adopted December 3, 1968;

3. Convention on International Liability for Damage Caused by Space Objects (known as the Liability Convention), adopted October 9, 1973;

4. Convention on Registration of Objects Launched into Outer Space (known as the Registration Convention), adopted September 15, 1976; and

5. Agreement Governing the Activities of States on the Moon and Other Celestial Bodies (known as the Moon Treaty), which was not signed by the U.S., adopted July 11, 1984.

1. Convention on Early Notification of a Nuclear Accident, adopted October 27, 1987; and

2. Convention on Assistance in the Case of a Nuclear Accident or Radiological Emergency, adopted February 26, 1987.

Preamble

The Preamble recognizes that for some missions nuclear power systems are essential and affirms that the Principles only apply to nuclear power systems “… devoted to generation of electric power onboard space objects for non-propulsive purposes, which have characteristics generally comparable to those of systems used and missions performed at the time of the adoption of the Principles …” In other words, the Principles do not apply to nuclear propulsion systems or to new space nuclear systems. The Preamble also recognizes “… that this set of Principles will require future revision in view of emerging nuclear-power applications and of evolving international recommendations on radiological protection”.

Principle 1

Applicability of international law – basically states that the use of nuclear power systems will be carried out in accordance with international law.

Principle 2

Use of terms – defines a number of terms, in particular “… the terms ‘foreseeable’ and ‘all possible’ describe a class of events or circumstances whose overall probability of occurrence is such that it is considered to encompass only credible possibilities for purposes of safety analysis.” In addition, the definition of the term “general concept of defense-in-depth” allows flexibility in achieving this goal by allowing consideration of “… the use of design features and mission operations in place of or in addition to active systems, to prevent or mitigate the consequences of system malfunctions. Redundant safety systems are not necessarily required for each individual component to achieve this purpose. Given the special requirements of space use and of varied missions, no particular set of systems or features can be specified as essential to achieve this objective”.

Principle 3

Guidelines and criteria for safe use – this principle sets forth general goals for radiation protection and nuclear safety followed by specific design safety criteria for nuclear reactors and for radioisotope generators.

Principle 4

Safety assessment – requires a “thorough and comprehensive” safety assessment which is to be made publicly available prior to each launch.

Principle 5

Notification of re-entry – requires a timely notification of the re-entry of radioactive materials into the Earth’s atmosphere and provides a format for such notification.

Principle 6

Consultations – requires States providing information under Principle 5 to respond promptly to requests for further information or consultations sought by other States.

Principle 7

Assistance to States – requires States with tracking capabilities to provide information to the Secretary-General of the United Nations and to any concerned State, and requires the launching State to promptly offer assistance. After re-entry, other States and international organizations with relevant technical capabilities should also provide assistance to the extent possible when requested by an affected State.

Principle 8

Responsibility – States shall bear international responsibility for their use of space nuclear power systems.

Principle 9

Liability and compensation – holds the launching State and the State procuring such a launch internationally liable for any damage, including restoration “… to the condition which would have existed if the damage had not occurred”. Compensation includes “… reimbursement of the duly substantiated expenses for search, recovery and clean-up operations, including expenses for assistance received from third parties.”

Principle 10

Settlement of disputes – disputes “… shall be resolved through negotiations or other established procedures for the peaceful settlement of disputes, in accordance with the Charter of the United Nations.”

Principle 11

Review and revision – requires that “These Principles shall be reopened for revision by the Committee on the Peaceful Uses of Outer Space no later than two years after their adoption.”

Principle 3 is perhaps the most important and most controversial of these Principles. During the adoption of the Principles, the U.S. delegation formally expressed reservations about the technical validity of these Principles to the United Nations. For example, in Section 1.3 of Principle 3, dose limits were established for accidents. Although the dose limits did not apply to “low probability accidents with potentially serious consequences” the U.S. delegation pointed out that Principle 3 should address risk (probability of an adverse consequence) rather than numerical dose limits (Lange, 1991a). In particular, the U.S. delegation made the point that “… this modification, by taking into account the probabilistic concept of risk, which is a central feature of a thorough safety assessment, relates the recommendation directly to the well-proven [space nuclear power system] practices of the United States” (Lange, 1991b). “In November 1990 the International Commission on Radiological Protection published new recommendations in the form of ICRP-60, which supersede the approach taken in Principle 3 when it was developed earlier that year” (Smith, 1992). The International Atomic Energy Agency (IAEA) independently supported the U.S. position by stating that “The sole use of the individual-related dose limits, rather than the complete ICRP system of radiation protection (including source-related constraint), is, in the Agency’s view, inappropriate and does not conform with the aims of the ICRP recommendations. Secondly, as the ICRP has recently issued new recommendations on dose limitation … It might, therefore, be problematic to issue guidelines and criteria of safe use of [nuclear power systems] in outer space that would be outdated from their inception” (IAEA, 1991).

The United States also proposed clarifying language in 1991 with the statement that “We believe that this clarification removes any doubts as to the intent behind the application of the term ‘defense-in-depth’. As was clear at the time that the Legal Subcommittee reached consensus on this principle, the Subcommittee did not intend to apply the terrestrial standards as such to space systems.” In 1991 the U.S. delegation proposed changes to the wording of Section 3.2 (relating to re-entry of radioisotope sources) “… to take into account the fact that the probability of accidental re-entry from a hyperbolic or highly elliptical orbit can be reduced to a very low value by mission design and operations” and to recognize “… the fact that the practical design objective for RTG containment systems is localization rather than zero release under all circumstances, and that there are practical limits from a cost-versus-risk standpoint on ‘complete’ clearing of radioactivity by a recovery operation” (Lange, 1991b).

At a meeting of the Special Political Committee on October 28, 1992, the U.S. representative stated “The United States did not block the consensus recommendation of the Committee to forward the principles to the General Assembly, nor will the United States oppose their adoption here. On some points, however, it remains our view that the principles related to safe use of nuclear power sources in outer space do not yet contain the clarity and technical validity appropriate to guide safe use of nuclear power sources in outer space. The United States has an approach on these points which it considers to be technically clearer and more valid and has a history of demonstrated safe and successful application of nuclear power sources. We will continue to apply that approach” (Hodgkins, 1992).

Although the UN Principles are non-binding, the United States and other nations are working together to establish generally acceptable international safety and environmental guidance relating to space nuclear power. International cooperation in space enterprises and the voice of the international community is expected to increase during the twenty-first century (Sholtis, Marshall, Bennett, Brown, Usov and Dawson, 2008).

Potential detrimental effects of destruct

The normal design of Range Safety Systems (RSSs) are driven by the need to (a) halt thrusting rocket engines (solid or liquid) in order to control a failing vehicle’s terminal impact point; and (b) disperse propellants as necessary to minimize explosive yield events upon impact with the ground. Since the main idea is to destroy the pressurization capability of a thrusting vehicle, there is very little concern for the consequences to other, mission-necessary subsystems (e.g., telemetry, solar power, command computers) since once a need arises that warrants activation of the destruct systems, their utility becomes rapidly less important in the ensuing explosive consequence. It is a very different story for payloads that maintain a radioisotope component. One can argue that any final data that can be capture via telemetry downlink is invaluable to resolve the “What happened” investigation that will follow a launch anomaly.

Conversely, the vulnerability of an onboard SNPS must be considered so that an action meant to mitigate risks to the public, personnel, and critical resources from falling debris, toxic effluent exposure, and distant focusing overpressure hazards does not consequently expose the radioisotope containments systems to extreme environments. Range safety destruct system ordnance components provide penetration energy to defeat tankage and break motor casings. However, what occurs at the “non-business end” of a conical shaped charge (CSC) can be hazardous to spacecraft mounted RTGs. Very small metallic casing pieces of the CSC can translate from the back plane of the device at near-rifle velocity and the proximity of spacecraft systems leave them vulnerable to impacts. Heavier mounting bosses and brackets can also be expelled at slower velocities but the higher “beta” value makes them also very lethal.

The additional concern for evaluation of side effects from flight termination activation is very similar in the world of human spaceflight. Much has been learned about the chaotic nature of vehicle breakup and explosion effects to space vehicle crew which translates well to the nuclear payload sensitivity issue. Difficulties in understanding the near-field effects of liquid and solid propellant explosions can greatly increase uncertainties in modeling these abort scenarios to calculate overall risks.