Why does fuel burn at nearly constant pressure in the Brayton cycle?

In the Brayton cycle, fuel is burned at essentially constant pressure because the process occurs within an open-flow combustion chamber where the gas is free to expand as it is heated.1

Thermodynamically, the Brayton cycle is defined by two adiabatic processes and two isobaric (constant pressure) changes. In a gas-turbine engine, air from the compressor enters the combustion chamber, where fuel is injected and burned. Because the combustion chamber is open to the turbine inlet, the heated gases can expand in volume as their temperature rises, which prevents a significant pressure buildup during the combustion phase. This allows the engine to maintain a steady, continuous flow of high-energy gas to drive the turbine.2134