The Brilliant Science behind Starship's Mega Shock Diamonds

The Science behind Mach Diamonds is super awesome and here is why..

Hey Explorers,

From ISRO's Chandrayaan 3 landing on the Moon's south pole to Starship's 2nd launch, 2023 was a great year filled with a lot of space activities. 

SpaceX is targeting March 14th 2024 for Starship's 3rd Orbital Test Flight. 

Starship is currently world's biggest rocket with 17.0855 Million pounds of thrust, this 120m tall rocket powered by 33 Raptor engines is no doubt an engineering pinnacle. 

18th November when Starship launched from the SpaceX's Starbase in Boca Chica, few seconds into the flight after successful lift of, the world witness something super cool. 

Welcome to the fascinating world of Mega Shock diamonds, where the intersection of physics and aerodynamics gives rise to this stunning phenomena. 

The Mega *Super* Mach Diamonds

Before Staring, I really want to thank my classmates who interned at SpaceX during Summer 2023, and worked with Starship's Raptor Integration Team; for collaborating to this blog and USC Viterbi School of Engg.'s AME department's Professor Dr. Ivan Bermejo-Moreno for elucidating the concepts of mega Mach Diamonds. 

Mach diamonds, also known as Shock diamonds or Mach disks, are captivating patterns that manifest in the exhaust plumes.

These mesmerizing diamond-shaped formations, resembling a string of radiant jewels, unveil the complex interplay between shockwaves, pressure differentials, and the speed of sound. 

This blog, will embark on a journey to unravel the secrets behind these Mega Mach diamonds, exploring the underlying principles that govern their appearance and delving into the technological marvels that give rise to these dazzling displays in the skies. 

Get ready to delve into the physics of supersonic flows and discover the beauty hidden within the Mach diamonds.

First lets Understand Shock Diamonds!

Shock diamonds are often visible at the exit of nozzle not only in rockets but also in supersonic jets.

F15 Jets

SpaceX's Raptor Engine

Lets break down the science that goes into creating this marvelous phenomena.

Consider a rocket engine, with a Converging and Diverging Nozzle.

The Pressure Ratio (PR) is ratio of outside pressure (PA) to the pressure inside the chamber (PI). And its always (PR) < 1; this results into a flow from inside the engine to outside; as pressure inside is more.

As the flow moves towards the converging section, pressure decreases; subsequently the velocity increases. 

And as the flow moves from the throat to the diverging section, pressure decreases and subsequently the velocity increases.

Now, there comes a point when the velocity of flow will be at Mach = 1 (Speed of particles/ Speed of Sound) in the throat; This is called Choked Flow Condition.

Note :  There is a spell error in "Choked" conditions in the dia below.

Choked Flow Condition

This will result in formation of a Normal Shock; as the pressure beforehand will be supersonic while the pressure after is subsonic.

As the shock moves forward it's strength increases; this happens to maintain the pressure equilibrium.

Near the end of Nozzle the shock will be experiences a lot of pressure.

A condition in most engines is overexpanded (rockets with a fixed-geometry nozzle inevitably operates in different conditions as they traverse the atmosphere at different altitude of flight), as the shock detaches before the end of nozzle which results in optimal conditions during the later flight while experiencing underexpanded conditions in upper atmosphere. 

This is the reason why a huge spray cone of exit plumes emerges during later phase of launch.

This is Underexpansion conditions

Further the Pressure Ratio will decrease to an extent that the Normal shock will break into oblique shocks. 

Oblique shocks are titled shock waves which forms to allow flow to decelerate and to reach pressure equilibrium. 

These oblique shocks will experience reflection at the point of symmetry, along the axis line.

This will result into the beautiful pattern that is visible during supersonic flows from an engine. 

Shocks gets weaker and the Mach number (Speed of particles/ Speed of Sound) decreases downstream the flow.

These shock diamonds disappears when the Pressure Ratio decreases significantly, and this is called Optimally Expanded Condition; which is the most efficient flight condition,

And this is how these super amazing Mach Diamonds forms.

But What's Mega Mach Diamonds?

This phenomena has been only visible when the rocket have multiple engines powering its 1st stage.

Like StaurnV and Starship!

NASA's SaturnV

SpaceX Starship

This occurs as multiple smaller Mach diamonds and there surrounding flow behaves as a single flow.

A clear visuals of multiple shock diamonds can be observed in this awesome picture of Relativity's 3D printed Rocket Terrain 1. Pic Credit: John K

 

Relativity's Terrain 1 (T+2 sec from liftoff)

As the rocket lift-off and within few seconds in flight the flow will adjust to behave as a single flow, while the smaller Mach diamonds are still visible.

Pic Credits: NSF

This is simply awesome.

But, why can't rocket have a huge engine instead of several smaller engines, like Sea Dragon Rocket (the biggest rocket in conceptual design)

Here is a small scale prototype of Sea Dragon the largest rocket ever idealized, standing at 150m and with a 23m dia nozzle.

This rocket was designed to lift off from middle of ocean, literally from inside the ocean, as no launch pad can withstand the 350 Million Newton Thrust produce by its Mega engine. 

Question is, why SpaceX's Starship SuperHeavy doesn't have one single huge engine instead of 33 small raptor engines.

Here, the Nozzle Expansion Ratio (NER) comes into picture, which is Exit Area / Throat Area.

Ideally, using multiple engines results into smaller expansion ratio. A single gigantic engine will have a huge nozzle expansion ratio.

But why not increase Chamber Pressure? 

This can be done to a certain extent; (Raptors already have the highest chamber pressure ever recorded);

While increasing Chamber Pressure will results into damaging the inner call of engine which can cause fatal accidents.

SpaceX's Starship'1 1st stage - Super Heavy 

Thus, having multiple engines not only results in a efficient flight but also forms the stunning Mega Mach Diamonds.

And that brings me to the end of this blog!

Recently I visited NASA's JPL and got chance to closely engage with JPL's upcoming mission to Jupiter's moon Europa: Europa Clipper. 

Head on to : Europa Clipper from JPL for exciting details on this mission as seen inside JPL!

Note: All diagrams in this blog are created by me for better understanding of the concept.

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Starship's Mega Shock Diamond