Heat transfer in wing by anti-ice system using hot air in piccolo tube

[ApostoF]

TL;DR Summary

Question about reasonable simplifications for heat transfer in hot air piccolo tube anti-ice systems

Hi, I'm doing a project on heat transfer using hot air piccolo tubes as an anti-ice system on the inside of an airplane wing. I've been reading as much info as possible using research papers from modern times and all the way back to when NASA was still NACA haha. I am planning to do a 3D analysis on this, but I also want to simplify the problem and see if a simplified 1D, 2D analysis or 3D analysis using finite difference methods in MATLAB would produce decent approximations of what the 3D fluid flow software would obtain.

My question is, how would you simplify this problem so that a simple program like MATLAB could produce anything reasonable? I have some ideas, and am just looking for feedback or other ideas if you have any.

Here is my thinking so far: For simplifying, first of all, I am considering only using the system as an "anti-ice" and not "de-ice" - i.e., I want to keep the temperatures above freezing, instead of having to calculate the latent heats and whatnot needed to melt ice already there. I am only an undergrad so for the purposes of this project, it is definitely sufficient for what I want to do. I am only doing analysis on the leading edge of the wing, not the entire chord width. I am considering only the flows after the hot air jet leaves the piccolo tube for the 2D model. I am not considering pressure drop through the distance lengthwise of the tube, and am assuming this will be taken care of by the decreasing diameter of the piccolo tube.
For the geometry, I am a little confused about what is reasonable to simplify. If it were accurate, obviously the easiest answer would be to model as a plane wall with convection internally from the hot air streams and external convection from the air around the outside. Not sure if I should instead model as flow over a pipe to somewhat simulate an airfoil shape on the leading edge of the wing instead. If I did, I am unsure how I would model the internal convection, since I am only looking at after the hot air jet leaves the tube, really it would be an odd crossflow situation where the hot air jets would be pointed normal to the internal semi-circular shape (inside of the wing). Additionally, I am wondering if the radiation losses on the outside of the wing are actually non-negligible, because my intuition says maybe not.

So far what I've done is try to model this as a 2D planar wall, but simulating the hot impinging air jets by having a localized higher convection coefficient where the jets are directly pointed towards, then exponentially decreasing the convection coefficient away from the jet streams so that my model shows much higher temps where they are pointed directly - which agrees with the research papers I've read that have done the 3D analysis. In your opinion, is this reasonable? Is there a better geometry to use here? I have attached an output figure I got from MATLAB (I used the wing thickness as 1m just to see if my code was actually calculating the conduction through the wing, obviously it will be a lot thinner).

Any advice or opinions or criticism (or just telling me I'm in way over my head) is welcome! I know it's a lot to ask, but I really appreciate this forum and figured I might as well try to get some outside opinions from people. Thank you.

 

[Flyboy]

First off, welcome to PF!

Yes, there’s definitely some complications to the design, as many heated leading edges(HLE) will have a second inner sheet of metal that matches the internal contour of the HLE, usually about 3-5mm of gap, to help contain the flow and direct it where it’s needed. This will be attached to the ribs that help hold the HLE in place and to retain their shape. The ribs and the inner sheet should provide a fairly well contained structure for your modeling when you switch to 3D. This bay is typically about half a meter to a meter long but I suspect that you can use a smaller span. Attachment of the HLE is usually stainless steel screws, but I think that can be ignored for the sake of the project.

Most HLEs have compound geometry that changes across their length, but you should be able to get a pretty close approximation by keeping the geometry the same across the span. I would argue for a parabolic geometry, though, as that’s more reflective of a real leading edge geometry.

The choice of anti-ice versus de-ice is actually a good one, as it’s typically what’s used on these kinds of systems, and it allows a degree of steady-state operation for your modeling.

That said, I think your biggest unknown could be not radiation losses, but losses to the air flowing past the HLE. Is that something that you are accounting for? What speed, altitude, etc and ambient temperature will you be using?

 

[Baluncore]

There are books on the subject of: "Numerical Simulation of Hot-Air Piccolo Tubes for Icing Protection Systems"
https://link.springer.com/referenceworkentry/10.1007/978-3-031-33845-8_42

 

[ApostoF]

First off, welcome to PF!

Yes, there’s definitely some complications to the design, as many heated leading edges(HLE) will have a second inner sheet of metal that matches the internal contour of the HLE, usually about 3-5mm of gap, to help contain the flow and direct it where it’s needed. This will be attached to the ribs that help hold the HLE in place and to retain their shape. The ribs and the inner sheet should provide a fairly well contained structure for your modeling when you switch to 3D. This bay is typically about half a meter to a meter long but I suspect that you can use a smaller span. Attachment of the HLE is usually stainless steel screws, but I think that can be ignored for the sake of the project.

Most HLEs have compound geometry that changes across their length, but you should be able to get a pretty close approximation by keeping the geometry the same across the span. I would argue for a parabolic geometry, though, as that’s more reflective of a real leading edge geometry.

The choice of anti-ice versus de-ice is actually a good one, as it’s typically what’s used on these kinds of systems, and it allows a degree of steady-state operation for your modeling.

That said, I think your biggest unknown could be not radiation losses, but losses to the air flowing past the HLE. Is that something that you are accounting for? What speed, altitude, etc and ambient temperature will you be using?

Thanks so much for the thoughtful response - I'll definitely try to make the 3d model as accurate as I can geometry wise with the leading edge of the wing, I've found the geometry of many airfoils are posted online luckily. However I'm finding it difficult to get dimensions for the actual piccolo tube system - a lot of the research just says the model was "provided by so-and-so company as a proprietary design", but I'm trying to piece together some reasonable model.

As for the airflow properties, that is something I'm still in the process of getting decent info on for sure. I saw a study similar to what I want to do using a speed of 132 mph and using a NACA 23014. For my initial results I've been using a hot air temp of 120 to 180 deg. Celsius, and an outside ambient temp of -5 to -10 deg C. I haven't considered the altitude effects other than the temp but that is a good idea for sure. By losses from air flowing past the HLE, do you mean as in the "hot air outlets" as the attached image calls them? If so, I was wondering how to account for that too not sure if I have a good answer there yet.

 

[ApostoF]

There are books on the subject of: "Numerical Simulation of Hot-Air Piccolo Tubes for Icing Protection Systems"
https://link.springer.com/referenceworkentry/10.1007/978-3-031-33845-8_42

Thanks, that looks like a great reference !

 

[Flyboy]

Thanks so much for the thoughtful response - I'll definitely try to make the 3d model as accurate as I can geometry wise with the leading edge of the wing, I've found the geometry of many airfoils are posted online luckily. However I'm finding it difficult to get dimensions for the actual piccolo tube system - a lot of the research just says the model was "provided by so-and-so company as a proprietary design", but I'm trying to piece together some reasonable model.

As for the airflow properties, that is something I'm still in the process of getting decent info on for sure. I saw a study similar to what I want to do using a speed of 132 mph and using a NACA 23014. For my initial results I've been using a hot air temp of 120 to 180 deg. Celsius, and an outside ambient temp of -5 to -10 deg C. I haven't considered the altitude effects other than the temp but that is a good idea for sure. By losses from air flowing past the HLE, do you mean as in the "hot air outlets" as the attached image calls them? If so, I was wondering how to account for that too not sure if I have a good answer there yet.

Piccolo tubes are indeed custom/proprietary parts that are not going to be on publicly available drawings. The ones I worked with on a midsize bizjet was about 3cm diameter at the inboard segment where it left the fuselage, dropping down to about half that at the wingtip. Outlet holes were ~1-1.5mm.

Air flowing past the HLE in this case is the ambient air outside flowing over the outer surface of the HLE. You will lose some heat to that. Could be an interesting question to investigate if time and resources permit.

The schematic you found is actually an excellent data source, now that I look at it. It’s calling out several dimensions, and you can probably gather the rest using the known dimensions for scale.

 

[ApostoF]

Piccolo tubes are indeed custom/proprietary parts that are not going to be on publicly available drawings. The ones I worked with on a midsize bizjet was about 3cm diameter at the inboard segment where it left the fuselage, dropping down to about half that at the wingtip. Outlet holes were ~1-1.5mm.

Air flowing past the HLE in this case is the ambient air outside flowing over the outer surface of the HLE. You will lose some heat to that. Could be an interesting question to investigate if time and resources permit.

The schematic you found is actually an excellent data source, now that I look at it. It’s calling out several dimensions, and you can probably gather the rest using the known dimensions for scale.

Ohhh I see what you mean, yes I'm attempting to find some data for Reynolds and Nusselt #'s to calculate a convection coefficient for the heat loss outside due to the outside air flowing over the wing - that's definitely an important point.

That's awesome to hear that those dimensions are reasonable, thanks so much for looking at that piccolo tube reference and providing some more measurements, that is extremely helpful.

Also, that's so cool that you get to work on this stuff in real life!!