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Could someone help me to understand how can a wall generate differents streamwise pressure gradients just by its curvature? I can understand how it works in cross-flow (perpendicular to the streamline) but i don't have the intuition neither the math approach to the streamwise direction.

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Federico
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Josue
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  • Do you mean a flat wall/plate or a curved one like the one in the picture? You don't understand the "decreasing" and "increasing pressure" part of the story, correct? But you do understand the variation in y, right? – sophit Feb 09 '23 at 19:10
  • A curved one. Correct, i can't relate how there is variation in the pressure gradient streamwise oriented due to curvature, what leads to acceleration / deccelaration and separation. Yes, if i understood right it happens in y due to the resultant centrifugal force, so pressure "outside" a curved streamline is higher than the pressure applied from the "inner side". – Josue Feb 09 '23 at 19:30
  • Regarding the pressure and velocity variation along x I'd suggest you to read this very good answer, especially the part "Flow over the upper side of the wing". Regarding the variation in y, this is going to help. And no, it has nothing to do with centrifugal forces – sophit Feb 09 '23 at 20:00
  • About 'y' direction: i wasnt talking about velocity gradient in the normal direction and close to the wall, but how a pressure field vary in the normal direction when the streamline is curved, like in this paper: /https://www3.eng.cam.ac.uk/outreach/Project-resources/Wind-turbine/howwingswork.pdf With this we can realize how the normal gradient of pressure is given for a flow over an curved shape. – Josue Feb 09 '23 at 23:19
  • 'x' direction: I don't know if i understood it right but, to maintain the flow aligned with the curved shape, the pressure acting on the flow direction must adjust the velocity to not create 'vacuums'? – Josue Feb 09 '23 at 23:26
  • Wow, that's a really good paper, I'm going to note that down . And now I understand what you meant with pressure variation in y and centrifugal forces. Yes, you're understanding is correct, included the vacuum story (but not in the boundary layer as depicted in your picture where friction among the different layers of fluid makes the physics a bit more complicated). The math in the appendix should also be easy to follow and gives a good background to the text in the paper. – sophit Feb 10 '23 at 07:20

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