Pressure gain combustion
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Pressure gain combustion (PGC) is the unsteady state process used in gas turbines in which gas expansion caused by heat release is constrained. First developed in the early 20th century as one of the earliest gas turbine designs, the concept was mostly abandoned following the advent of isobaric jet engines in WWII.[1]
As an alternative to conventional gas turbines, pressure gain combustion prevents the expansion of gas by holding it at constant volume during the reaction, causing an increase in stagnation pressure. The subsequent combustion produces a detonation, rather than the deflagration used in most turbines. Doing so allows for extra work extraction rather than a loss of energy due to pressure loss across the turbine.
Several different variations of turbines use this process, the most prominent being the pulse detonation engine and the rotating detonation engine. In recent years, pressure gain combustion has once again gained relevance and is currently being researched for use in propulsion systems and power generation due to its potential for improved efficiency and performance over conventional turbines.[2][3][4]
Early history
Gas-powered turbines have been researched since the late 18th century, starting with John Barber's 1791 patent. Over a century later, Ægidius Elling built a turbine in 1903 which generated 11 bhp (8.2 kW), the first gas turbine to produce net positive work. In 1909, the first pressure gain combustion turbine was built by Hans Holzwarth. Initially operating at 200 bhp (147 kW), subsequent improvements to the engine increased its power output to 5000 bhp (3728 kW) by 1939. However, the aptly named Explosion Turbine would lose popularity among engineers and inventors as continuous combustion designs gained traction due to their use in jet engine prototypes.[5][1]
Renewed interest
The concept of pulsed propulsion is neither new, nor exclusive to pressure gain combustion. In fact, the German V1 missile utilized a pulse jet operating at 45 Hz. During the space race, NASA's Project Orion concept utilized force from nuclear explosions ignited behind the spacecraft to generate thrust. This process is known as nuclear pulse propulsion and is stylistically similar to the pulse detonation engine.[6]

In the mid-20th century, US aeronautical scientists and engineers were trying to study the properties of detonation waves. To do this, a primitive rotating detonation chamber was created. This development became the basis for the rotating detonation engine, one of the leading PGC engine concepts, although it was largely ignored at the time due to its instability.[7]
However, as gas turbines are becoming more and more optimized, PGC research is now gaining traction in aircraft propulsion, power generation, and even rocket propulsion. In January 2008, a pulse detonation-powered plane completed its first flight as a cooperative project between the Air Force Research Laboratory and Innovative Scientific Solutions, a research and product development company. Currently, various organizations have developed working PGC engines (mostly RDEs), but none have been put to commercial use due to developmental challenges.[7][8][9]
Concept and comparison to conventional turbines
Overview of conventional turbines

The majority of gas turbines consist of an intake through which atmospheric air enters the turbine. The air is then pressurized through a compressor before mixing with fuel. The air-fuel mixture, also known as the working fluid, is combusted in a deflagration (a combustion reaction propagating at subsonic speed), which causes the mixture to expand in volume while maintaining constant pressure. Finally, the combustion product is ejected out of the exhaust to produce thrust. This process is known as the Brayton cycle and has been used as the standard method of jet propulsion and turbine design for about a century.[10][11]
Humphrey cycle

Contrasting with the Brayton cycle used in most turbines, pressure gain combustion is based on the Humphrey cycle. Instead of an isobaric system in which gas volume expands as heat is added to the combustion chamber, the volume of working fluid stays constant as its pressure increases during combustion.[12] While the Brayton cycle describes a subsonic deflagration, the Humphrey cycle occurs in a detonation (a combustion reaction propagating at supersonic speed).[13] The reaction occurs so quickly that the mixture doesn't have time to expand, causing a pressure gain, before being ejected through the exhaust to produce thrust. The whole process occurs rapidly, and turbines will produce anywhere from 20 to 200 detonations per second.[14][15]
Because the working fluid is combusting at a constant volume, there is no pressure loss across the turbine, which increases the net work generated by each cycle. However, since work is done by a series of detonations, rather than a constant reaction generating thrust, the process is naturally more unsteady compared to a conventional turbine.[3][16]
Designs and variations
Pulse detonation engine
The simplest modern PGC turbine is the Pulse detonation engine. Consisting of almost no moving parts, the PDE is externally similar to a ramjet, a type of jet engine without compressor fans that is viable only at supersonic speeds. First, air enters the intake nozzle and travels directly to the combustion chamber to be mixed with injected fuel. There, the mixture is ignited while the front of the chamber closes, producing a detonation wave which both compresses and combusts the mixture, before the working fluid is ejected at supersonic speeds through the exhaust.[17][6]
Because of the engine's simplicity and anatomical similarity to ramjets and scramjets, pulse detonation engines can be implemented as a combined-cycle engine, which can improve the performance and reliability of ramjets. Conventional combined-cycle engines have complex moving parts that are essentially rendered useless at high speeds, an issue that PDE/ramjet drives will not have.[17][6]
Rotating detonation engine

Apart from PDEs, there exist multiple other PGC engine concepts, including resonant pulse combustors and internal combustion wave rotors. However, the majority of modern PGC research is concentrated around the rotating detonation engine (RDE), which aims to solve many of the issues encountered by PDEs.[3]
The main drawback of pulse detonation is the intermittent nature of the combustions. Not only is the reaction hard to control, but the intermittent combustion also loses power due to the time it takes to refuel the combustion chamber after purging, during which no thrust is produced.[17][6] The rotating detonation engine aims to address both these problems. While PDEs involve a series of detonations to ignite batches of air that enter the combustion chamber, RDEs can circumvent this by utilizing a single detonation wave that rotates around the space in between concentric cylinders. A continuous air intake flows through the cylinders, which compresses and combusts as it passes through the rotating detonation wave. This eliminates the need to constantly produce detonations since it only uses a single cyclic detonation, and it allows for a steadier constant flow, instead of the pulsing thrust produced by PDEs.[18][19]