. As a simple model of turbine blade cooling flow in a gas turbine engine, a uni

Question

. As a simple model of turbine blade cooling flow in a gas turbine engine, a uniform freestream flows past one side of a flat plate with a small bleed flow hole (that can be modeled as a 2D source flow with strength q at the origin shown). Note: This is NOT a method ofimages problem. a) Find the stream function for this flow b) Find the velocity field for this flow c Find the distance from the origin Rsp of any stagnation point that exists on the flat plate. Is the stagnation point upstream or downstream of the bleed hole (source) at the origin? d) Using your result from part c) find the equation for the dividing streamline which separates the region containing flow from the bleed flow (source) from the rest of the flow Using your results from parts c) and d) and physical intuition, carefully sketch the streamline pattern for this flow, showing several streamlines. e) ) To begin to model an array of turbine blade bleed holes, add a 2d bleed hole (2nd source of strength q) located downstream of the origin at (r,?) (L 0) where L RSP, will the stagnation point on the plate now move upstream or downstream? No need to determine a new equation for stagnation point distance, just use your physical intuition. Also, roughly sketch the streamline pattern for this flow with two bleed holes. Source

Explanation / Answer

As a simple model of turbine blade cooling flow in a gas turbine engine, a uniform freestream flows past one side of a flat plate with a small bleed flow hole (that can be modeled as a 2D source flow with strength q at the origin shown). Note: This is NOT a method ofimages problem. a) Find the stream function for this flow b) Find the velocity field for this flow c Find the distance from the origin Rsp of any stagnation point that exists on the flat plate. Is the stagnation point upstream or downstream of the bleed hole (source) at the origin? d) Using your result from part c) find the equation for the dividing streamline which separates the region containing flow from the bleed flow (source) from the rest of the flow Using your results from parts c) and d) and physical intuition, carefully sketch the streamline pattern for this flow, showing several streamlines. e) ) To begin to model an array of turbine blade bleed holes, add a 2d bleed hole (2nd source of strength q) located downstream of the origin at (r,?) (L 0) where L RSP, will the stagnation point on the plate now move upstream or downstream? No need to determine a new equation for stagnation point distance, just use your physical intuition. Also, roughly sketch the streamline pattern for this flow with two bleed holes. Source

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