I tried to relate intake pressure recovery in terms which do not involve efficiency of an inlet and capture area, i was able to formulate pressure recovery without intake efficiency but now i need to find a way to formulate capture area of inlet without without use of intake efficiency and pressure recovery is it possible ? if yes please share.
1 Answer
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It is not so hard, actually.
You need to know the speeds ahead and inside the intake. You can deduce their ratio from the pressure recovery factor, and normally the Mach number inside the intake is between 0.4 and 0.5, so this, combined with your design flight speed, is a good starting point.
In supersonic flow the air is rammed into the intake face, producing a shock. This will be a straight shock in case of a pitot intake or an oblique shock in case of an intake ramp. Use the appropriate shock tables to find the corresponding speed and density ratios.
For subsonic flow you can use a Gedankenexperiment: Your intake is flying through a densely packed array of stream tubes. Some of them will end up inside the intake, others will be pushed aside as they come close to the intake lip and will flow around it. The speeds in those tubes varies between flight speed well ahead of the intake and your eventual intake speed inside the intake. In between, things change continuously in subsonic flow or via shocks in supersonic flow. Now assume that all the air which passes through the intake will have to pass through their corresponding stream tubes, both ahead and inside the intake. No air is allowed to cross between tubes. If the air inside the intake flows faster than flight speed, the flow in the tubes will be accelerated as they approach the engine face, so the intake has to ingest a lot of tubes to keep mass flow the same. Conversely, if flight speed is higher than intake speed, some of the tubes will be pushed aside to get a match between the mass flows ahead and inside the intake. Don't forget to adjust stream tube area for density changes: The change in stream tube cross section has to be inversely proportional to the change in air density as the air inside the steam tube changes speed, like this: $$\frac{\delta\rho}{\rho}=-Ma^2\cdot\frac{\delta v}{v}$$
answered Nov 24, 2020 at 17:20
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$\begingroup$ i appreciate your effort in answering the question.thank you. But you told me to deduce the ratio of the speeds using the pressure recovery factor right? but i wont be knowing the pressure recovery factor . the whole effort is to roughly calculate the pressure recovery Pi which do does not have efficiency. is it possible to calculate the capture area using continuity equation? $\endgroup$– vbksNov 25, 2020 at 9:03
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$\begingroup$ @vbks Yes, the continuity equation is the mathematical expression of the thought experiment outlined above. For the pressure recovery you start with lossless compression and then apply an appropriate reduction. Well-designed intakes have efficiencies of 97-98%, so the loss is small. And you need to know either the speeds or the pressures, or there is no basis for a calculation. $\endgroup$ Nov 25, 2020 at 11:20