Essential Physics in CAD/PAD and ECS

Generally, a CAD/PAD has the following major sub-components:

1) hot gas generator where high pressure/high temperature gases are produced by burning of propellants or cold gas reservoir where an inert gas is pressurized and stored;

2) mechanical work device which pushes or pulls by using the energy from either hot gas generator or the cold gas bottle;

3) flow path: sometimes the gas generator/reservoir is connected to the mechanical work device section via a flow path such as tubing or duct.

 

Propellant Burning

The burning rates of many solid propellants follow the empirical pressure-burning law where the burning rate is a strong function of the pressure in which the propellants are burning.  The rate at which the combustion product gases are produced is not only related to the propellants’ intrinsic burning rates, but also to the propellants’ geometry.  The geometry may be designed to yield regressive, neutral, or progressive burning profiles.  In a regressive burn, the total burning surface decreases in time while in a progressive burn, the burning surface increases in time. In a neutral burn, the burning surface remains the same throughout.  The figure below shows the pressure rise in a closed chamber of a fixed volume (or a closed bomb), that is produced by burning of a propellant with a progressive geometry.  The overall pressure-time profile exhibits the “concave” characteristics due to the fact that the total burning surface is increasing in time.  The red curve is the actual test data; and the blue dashed curve is the predicted result.

An Example of Progressive Burning in a Closed Bomb

Thermodynamics

Pressure is an important thermodynamic property because it affects the propellant’s burning rate, and also because it directly produces force.  Pressure, however, is dependent on other thermodynamic properties such as temperature, and density.  These properties are inter-related; and the inter-relatedness may be expressed through an equation of state, and the energy equation.   In addition, another important process, heat transfer, must be accounted for.  Propellant burning rapidly increases the internal pressure to a high level not only by producing low density gases, but also by releasing heat from the chemical reactions.  However, the heat released is quickly transferred to the surrounding; and the pressure quickly decreases.  A good heat transfer model along with a good set of data on the combustion product gases is essential for accurate estimation of CAD/PAD and ECS performances.  The figures below illustrate the significance of heat-loss in a pyrotechnic event.  The plots compare the actual performance data of a relatively large pyrotechnic retractor and the calculated results with assuming no heat-loss, i.e. an adiabatic process.  It is seen that the adiabatic assumption noticeably over-predicts both the pressure output as well as the velocity: the total energy output is over-predicted by 47 percent.  The solid blue curves represent the actual test data while the dashed blue curves represent the adiabatic calculation results.

Pressure and Velocity Results of a Relatively Large Pyrotechnic Retractor

An Illustration of the Significance of Heat Loss

Fluid Mechanics - High Speed Gas Flows

In many applications, the chamber in which the moving piston is located is connected to the gas-generating chamber via a flow passage.  The flow passage may be a simple nozzle, orifice, or a long duct or tubing.  Understanding the flow characteristics is important because the flow directly affects the thermodynamics both in the gas-generating chamber and in the piston chamber, thus affecting the output energy.  When the flow passage is short enough, the transient aspect of the flow can be ignored and a quasi-steady nozzle flow equations can be adapted to obtain good approximations.  However, if the flow passage length is long, the transient pressure waves become non-negligible and must be accounted for.  This is the case for a “gun-barrel” type of pyrotechnic application where a projectile is accelerated through a long duct or a “barrel” due to the pressure increase behind it produced by the propellant burning.  Transient pressure waves generated in such a pyrotechnic event become more noticeable longer the barrel length; and become increasingly significant, influencing the device’s overall performance.  The figures below are the firing test results of a gun-barrel type application and the analytically predicted results that show a good resolution of the fluctuating pressure behind the accelerating projectile.

Performance Predictions for a Highly Transient "Gun-Barrel" Type Pyrotechnic Event

 

Fluid Mechanics - Hydraulics

In some applications, hydraulic fluid is used to aid damping of the actuation process.  For instance, if a pyrotechnic actuator is used to rotate a wing or a door against a high opposing force, but also ensure that the end-of-stroke velocity is low enough to impart no structural damage to the wing or the door, hydraulic damping mechanism is one of the best approaches.  Hydraulics provides the damping that is proportional to the square of the velocity, and is effective in quickly damping out high velocity movements.  For instance, a deployment linkage system may be desired to rotate a pair of wings or panels under various aerodynamic loading possibilities.  The wings or the panels may experience loads that either assist or resist their deployment; but must complete their deployment at a low velocity in order to impart minimum impact to the linkage and the structures.  For such applications, a hydraulically damped pyrotechnic (or pneumatic) actuator may be the best solution.  The Figures below illustrate such effectiveness.

Illustration of Hydraulically-Damped Pyrotechnic Actuator's Performance

Under Extreme External Aerodynamic Load Range

Rigid Body Dynamics

Often the pyrotechnic devices are used to translate a mass from one place to another.  For example, the CED designed BRU-44 B/A, the bomb rack unit for the rotary launcher used in B-2 Bomber, imparts energy to eject the stores away from the aircraft.  Another example is the stage separations that occur during the flight of a launch vehicle.  The trajectories of the moving bodies along with their linear/angular velocities and accelerations are obtained by assuming that the bodies can be approximated as rigid and follow the rigid body equations of motion that are derived from Newton’s second law.  The following figures show the predicted trajectory of the Crew Module and its Cover when separated by a system of three pyrotechnic actuators.

3-Dimensional Trajectories of Cover and Crew Module for

Three Pyrotechnic Actuator Seperation System:

Worst Case Trajectory for Non-simultaneous Actuator Operation

Non-Rigid Body Solid Mechanics

For some applications, local dynamic responses of the solid body are important to the device’s performance.  For example if a pyrotechnic device is used to fail a rod in tension at a pre-set stress threshold, it is essential to understand the dynamic responses of the rod to the tension force applied by the pyrotechnic motion.  Or, if one needs to approximate the permanent deformation of a structure due to a pyrotechnic output, such as the linear shape charge, the local shock responses in the structure must be accounted for.  Accurate predictions of deformations and failures in such transient pyrotechnic events are difficult, but good efforts can be made by utilizing hydro-codes or high velocity physics shock codes such as CTH, developed by Sandia National Laboratory.  The Figure below is the axis-symmetric pressure contour of a rod that is under tension – a CTH output. It shows the break at the notch after 0.13 milliseconds from the start of actuation.

Pressure Contours of a Pyrotechnic Bolt at the incident of Designed Fracture

 

Back to top