Blast Mitigation

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When a solid grain rocket first kicks on there is a huge one-time boom that propagates spherically outward like an explosion. This blast wave can damage expensive launch pad equipment or, even worse, disrupt the launch. This is what the pressure field looks like over a few milliseconds:

Snapshot of pressure 1 millisecond after ignition. Exhaust travels to the right from the nozzle at Mach 3.5. The front of the blast wave has a spherical shape.
Snapshot of pressure 5 milliseconds after ignition. The blast wave has expanded.
Snapshot of pressure 10 milliseconds after ignition. The blast wave impacts the launch pad with an almost 7:1 pressure ratio and the rocket body with a 2:1 pressure ratio.

This phenomena is called Ignition Over-Pressure (IOP). What launch providers do to suppress the IOP’s strength is to dump a bunch of water in the surrounding area. Water absorbs the energy of the shock in several ways, the most significant of which is through vaporization. What the following papers do is to quantify and optimize the process of using the vaporization of water droplets to optimally suppress the IOP’s strength.

Physical picture of blast attenuation with water droplets. The optimal distribution of water droplets in the domain will be the one which most greatly reduces the pressure jump of the transmitted shock.

The first paper simplifies the problem to a single-phase flow with a distributed energy sink. This was useful for demonstrating the requisite novel algorithm and gaining intuition on the flow control.

Time and space plot of the blast wave’s 1D pressure profile.
Time and space plot of a blast wave’s 1D pressure profile under control action. The final amplitude of the shock front has been greatly reduced.
Time and space plot of the control action representing the required amount of energy extraction.

The single-phase problem formulation was published in the AIAA Journal:

Method for Optimally Controlling Unsteady Shock Strength in One Dimension

The second paper has the full two-phase droplet-shock interaction model and the results are the optimal spatial distribution of the water volume fraction for varying degrees of IOP attenuation.

Optimal water volume fraction distribution for increasing levels of blast wave attenuation.
Optimal pressure profiles under control action for increasing levels of blast attenuation.

The two-phase formulation was published in the International Journal of Flow Control:

Optimal Control of Shock Wave Attenuation using Liquid Water Droplets with Application to Ignition Overpressure in Launch Vehicles

A very thorough presentation of the problem is presented in this PhD Dissertation:

Optimal Control of Shock Wave Attenuation in Single- and Two-Phase Flow with Application to Ignition Overpressure in Launch Vehicles