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Why does combustion happen at constant pressure in gas turbines but at constant volume in pulsejets? I need to ensure my design adds heat at constant volume. Is it because combustion starts from essentialy the escape point in pulsejets with the flame front acting like a wall?

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A Brayton-cycle gas turbine compressor presents a large mass flow of air to the combustors at a pressure that varies with the speed of the blades and their pitch. For the moment we assume that both of these are constant. Heat is added to the compressed air by burning fuel with it in the combustors and the resulting hot gas is free to expand out towards and then through the power turbine. This means that as the combustion process is occurring, the volume of a parcel of gas getting heated in a combustor is expanding and since the direction of that expansion is toward the exhaust nozzle, flow continuity requires that each parcel of gas traversing the combustors must accelerate.

In this way, the gas turbine's heat addition process occurs at variable volume but more or less constant pressure. (Since the gas flowing through the engine is being accelerated, a force is being exerted on it. The resulting reaction force is the thrust output of the engine.)

In a pulsejet, the heat addition process is not a constant: it occurs at separated intervals, and the explosion of a discrete charge of fuel & air happens so fast that the heat addition is modeled as an almost instantaneous event, with no time for the gases to begin expanding while the combustion occurs. With no time for expansion, the heat addition therefore occurs at more or less constant volume.

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