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:
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.
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.
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.
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