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Jonas Larsson September 8, 1999 08:11

Solid-Solid Heat Transfer with Contact Discontinuity
I'm doing a coupled CFD - solids simulation. The case includes a few cavities and disks inside a jet engine. I'm solving RANS in the fluid domains and heat-conduction in the solids.

The problem is that two solids, typically two disks (one supporting the rotor blades and one supporting a seal configuration) sometimes are bolted together, and this contact discontinuity is important for the final temperature field in the solid - representing the bolted area as a continious solid gives incorrect results. I talked to a few "solids guys" here and they say that what they do is that they only "couple a few of the heat transfer elements across the discontinuity", whatever that means. I guess that it means that they reduce the effective heat-conducting area in some way.

I could simulate this in my CFD code by representing the contact area with a thin wall of thickness dw and heat transfer coef. Lw. The question is how to choose dw and Lw.

Has anyone got any ideas about how to choose dw and Lw? It sounds like a simple problem but I haven't been able to figure it out. Noone here seems to know what this "coupling only a few heat transfer nodes" means exactly. Lets say that I want an reduction of "effective heat-conducting area" with 50%. How should I choose dw and Lw?

Achuth Rao September 8, 1999 09:17

Re: Solid-Solid Heat Transfer with Contact Discontinuity
In commercial codes on can define contact elements between such surfaces and define a finite(small) value of conductivity between such elements. I think one can also make conductivity a function stress (pressure) so that one can achive normal conductivity above a certain value. You should be able to get the values for conductivity from literature.

I am guessing this is what the "solid guys" meant when they said couple a few heat transfer elements.

Jonas Larsson September 8, 1999 09:23

Re: Solid-Solid Heat Transfer with Contact Discontinuity
Yes, you can define a conductivity, Lw, but you also need to define a thickness, dw, of the "insulating gap". Any advice about which books I should check?

Achuth Rao September 8, 1999 09:36

Re: Solid-Solid Heat Transfer with Contact Discontinuity
I think this is a springer verlag pub.

C.V. Madhusudana, University of New South Wales, Sidney,Australia

Thermal Contact Conductance (Mechanical Engineering Series. Ed.: F.F. Ling) 1995. Hardcover $64.00 ISBN 0-387-94534-2

Hongjun Li September 8, 1999 09:43

Re: Solid-Solid Heat Transfer with Contact Discontinuity
I think you are in the right approach. I had similar problem a few years ago. I came out with two methods (a) at the S-S interface, apply adiabatic BC (-0-) and coupled BC (-c-) at alternative grid points. This can be easily done in a self-developed program and it can have many patterns (-0-c-0-, -000-c-000-c-, -0-cc-0-cc- etc.) for different contact discontinuity. That may be similar to your "coupling only a few nodes'. (b) insert a thin layer of artifitial material at the interface, just like what you did. Using fixed thickness and controlled heat conductivity kw to model the heat flux reduction due to contact discontinuity (CD).

In either way, the most difficut part is how to determine the pattern in (a) and how to choose kw in (b). We found that the CD is somehow related to the surface roughness and the 'tightness' between the solids. It changes from material to material. So we took two pieces of the material, made 'perfect tight' and tested its CD effects. From there we determined the effective kw and then used it in the model. Sounds ad hoc, but it came out with reasonable good results.


Robin Bornoff September 8, 1999 09:48

Re: Solid-Solid Heat Transfer with Contact Discontinuity

Short of taking a slice through the intersection and determining the average thickness of the interfacial 'material' (using SEM??!!) the only other viable option is calibrate the total interfacial thermal resistance using physical prototyping. For electronic thermal applications this is similar to the interfacial thermal resistance between a bonded heatsink tine and the heatsink base. For the above application interfacial resisitances are of the order of 0.001 (degC m^2/W).

The interfacial resistance (in Flotherm at least) can be imposed implicitly as a numeric value assigned to a solid surface or explicitly as a 'plate' type cuboid with the appropriate thermal conductivity and thickness, sandwiched between the 2 solids.

This is a big issue for heatsink manufacturers, maybe ask a technical authority there for further information. Contact pressure will obviously play a dominant role as will the surface condition of the 2 solids.

Look at the ratio of thermal resistance between the conductive resistance of the solids compared to the interfacial resisitance of the interface layer. This should give you guidance as to the sensitivity of the resistive contact layer.


John C. Chien September 8, 1999 14:12

Re: Solid-Solid Heat Transfer with Contact Discontinuity
(1). This area of contact resistance problem is commonly handled by structure people in the FEM. (2). It is a strong function of the stress, deformation, contact area,etc... It is also a reliability issue. Material fatigue will also affect the condition later in the operation. (3). It is a design side problem. But detailed analysis (FEM) sure will provide a better data base for design. I think, it is a current research problem.

clifford bradford September 8, 1999 14:37

Re: Solid-Solid Heat Transfer with Contact Discontinuity
i think the fem approach is correct. solids guys tend to be inarticulate. as Achuth said the interface can be modelled with contact elements. often the conductivity can then be a function of contact pressure (which it is) that you can specify. this means though that you'll have to solve for the thermo-structuralfield since you need the contact pressure. the problem is iterative as the contact and therefore the heat transfer is structurally dependent (those contact pressures)and the structure is contact dependent. but if you're using a big time FEA code this capability should be available to you. indeed the manual might give you tips about the conductivity-contact pressure relationship (which is dependent on initial surface roughness) or you could call their help desk. if you're using your own (non-commercial) code you'll have to code this yourself. as john said the contact-conductivity relationship is derived experimentally (or perhaps semianalytically)

T.J. Wanat September 8, 1999 22:49

Re: Solid-Solid Heat Transfer with Contact Discontinuity
The book "Handbook of Heat Transfer" by Hartnett & Rosenow has a section on contact thermal resistance. I recall an equation which involves pressure plus the other major influences. I'd expect it to be in any major university library. Look for the 1972 or 1985 edition. You should be able to turn the resistance into a conduction element.

Stephane September 10, 1999 15:46

Re: Solid-Solid Heat Transfer with Contact Discontinuity

a reference from AIAA:

Madhusudana, C.V., and L. S. Fletcher " Contact heat transfer - the last decade " AIAA Journal, Vol. 24, p510 , 1986

may be of help ?

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