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Sheila September 21, 2005 05:28

Flat plate with pressure gradient
Hi everyone,

I want to know what are the pros and cons of modelling effect of blade shape (suction surface) using flat plate with pressure gradient imposed. If the imposed pressure gradient mimics that on the actual blade surface and the freestream conditions are the same, whould'nt the results be the same...?

Thanks. Sheila

Mani September 21, 2005 15:29

Re: Flat plate with pressure gradient
That's an interesting question. It really depends on what kind of flow you are looking at and what the effect of curvature is. The flow that you will get over the flat plate may be quite different from the real situation: You will essentially neglect pressure gradients and other gradients in normal direction and obtain some boundary layer flow, when the real flow could be more complex. Just one example: Think of the centrifugal force acting on a fluid particle that travels along a curved surface. You will not get that normal force on a flat plate.

If it's just a relatively thin airfoil you may be able to prescribe the pressure distribution although there's always going to be trouble near a round leading edge where curvature effects are not negligible (and the boundary layer assumptions are not valid). But even if it does work I see a couple of new questions that this approach opens up:

1) What are you trying to obtain? In most airfoil applications it is the pressure distribution which is of interest because it determines the dominant force, which is lift. In your case, you would actually have to know that pressure distribution in advance, which leads me to the second question:

2) From where do you get the pressure distribution? Is this going to be an inverse design problem, where you arbitrarily specify the pressure distribution (not knowing if any airfoil can actually give you that distribution)? If so, what is it that you are trying to obtain from your flat plate analysis? Surely not the shape of your airfoil...

Sheila September 21, 2005 16:40

Re: Flat plate with pressure gradient
Hello Mani, thank you for your reply. In response to your questions, I am considering the effect of pressure distribution and free strem turbulence conditions resembling those found in small turbines. So, I would be looking at similarity studies, to better understand the flow physics in small turbines.

Thanks again.


Mani September 24, 2005 13:58

Re: Flat plate with pressure gradient

turbines usually impose a lot of "turning" on the flow, with highly staggered or cambered blades, sometimes quite thick, with a large negative pressure gradient. The flow between two turbine blades is influenced by the streamwise varying cross section of the stream tube, due to airfoil thickness.

For similarity solutions and more fundamental studies it makes sense to look a flat plates first, but eventually you may have to look for a way to include the effect of airfoil thickness and camber.

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