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How do engineers make sure the pressure doesn't rise, but velocity does. I have no idea how that can work, please help!

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I have a feeling The term "Constant Pressure" for a gas turbine engine, And the Term "Burner" used in your question, is slightly confusing to be able to clearly understand your query. Can you please specify if You Mean to ask about the Combustion Chamber where fuel and air is mixed and ignited, or the engine exhaust nozzle where there is a provision for "After Burners" in older jet engines. Know that the Jet Engine is termed as "Constant pressure" machine in comparison with the Piston Engine Combustion, where the pressure changes with every stroke, leading to a power stroke post combustion where the actual force is generated. When compared with Jet engine, the pressure in the Combustion Section of Jet Engine is almost constant, But before reaching Combustion Section (Through Compressor Air delivery) the pressure is made to increase with every stage of the compressors and the reason for this is to obtain high energy post combustion to generate enough force to move the turbines and to enable the Jet velocity Leaving the engine to be as high possible to be able to generate enough thrust (Newton's Third Law), and this is achieved by constructing the Engine Exhaust duct in the Convergent-Divergent shape, The reason best explained by the following paragraph from notes taken from one of the best books i have ever read, The following is as it is from the text book, all credits to the moderators.

"In the convergent exhaust duct, the shape of the duct accelerates the gas. In a turbo-jet, the gas flows at sub-sonic speed at low thrust levels only, at almost all levels above idle power the exhaust velocity reaches the speed of sound in relation to the exhaust gas temperature, at this point the nozzle is said to be ‘choked’. This means that no further increase in velocity can be obtained unless the temperature is increased. When the gas enters the convergent section of the convergent-divergent nozzle its velocity increases with a corresponding fall in static pressure. The gas velocity at this point now reaches the local speed of sound (Mach 1). As the gas flows into the divergent section it progressively accelerates towards the open exit, the reaction to this increase in momentum is a pressure force acting on the inside wall of the nozzle. A component of this force which acts parallel to the longitudinal axis of the nozzle produces the further increase in thrust."

Pressure is kept Constant In the combustion chamber by not allowing the gases to escape from anywhere but to allow them to move forward only, remember there is a slight decrease in pressure during this but then the drop is considered to be negligible, and it is also made sure that the pressure at compressor delivery is high all the time thus facilitating the High to Low flow of pressure.

There are times when the air mass and pressure supposed to be in the combustion chamber returns to the compressor thus resulting into a probable surge and or a stall. But this only happen when the compressor has problems with its blades or rotation or contamination.

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