Film cooling effectiveness

[borjame]

I'm looking for an equation to calculate the film cooling effectiveness for a flat plate in turbulent flow. The plate has a series of film holes from its leading edge to midspan, the last midspan has no holes (one inch long, .050 inch height, depth irrevelant). The array of film holes are three staggered rows of .015 in diameter holes, approximately .150 apart, each direction. I'm trying to figure how varying flow through the holes, varying dia, and pressure across the holes effects the film downstream. Also I would like (I just want the world, don't I) to know how the film effectiveness drops off vs. length. I hope I have encompassed the problem, if there are variables I left off, just add the variable in. THANKS IN ADVANCE!!!!!

 

[poetix99]

I'm not clear about some of the geometric details you've described, and I'm certain in any case that a good bit of information is missing:


What velocities?
What is the fluid?
Is the bulk flow parallel to the plate, or impinging upon the plate at some "angle of attack"?
What is the orientation of the plate with respect to gravity(i.e. could buoyancy effects be involved)?
What are the different temperatures in your problem (plate, bulk flow, film flow)?
Do you want local heat transfer coefficients (if so, why?), or do you want some sort of average for the entire plate?

Consult a good graduate level heat & mass transfer text (Rohsenow & Choi - "Heat, Mass, and Momentum Transfer" is one that I own) to at least better understand the phenomena involved.

There is not likely to be a single equation to provide your answers. The boundary layer associated with the bulk flow has a normal "development" from laminar/transitional/fully-turbulent as the flow moves downstream from the plate leading edge. The local h.t. coefficient varies as the boundary layer develops, so the effects near the leading edge of the plate can be sensitive to the flow details at the leading edge.

Injection of other fluid in a direction transverse to the plate and the bulk flow (your film holes) would have the effect of retarding and "piling up" the boundary layer flow, and in that way most directly affecting the h.t. coefficient. If there is a difference in the bulk and film fluid temperatures, that will be another complication.

Calculation of the flat plate without injected flow will be well-described in most h.t. texts. That will provide you with a baseline for your actual case.

Your geometry and application might be similar to another situation in: aeronautics, industrial cooling/heating, HVAC, boilers,... It would be a real time saver for you if you were somehow able to find a similar problem and borrow from somebody else's hard work.

Good luck.