Real-time engine simulation - oil temperature

[GMVitus]

Hi folks!

A while ago, we discussed a real-time simulation of an oil cycle within a combustion engine. Back then I was focusing on volume flow and pressure and you were incredibly helpful in coming up with the required formulas, so thank you again for your help!

I'm now moving to the next stage and that is modeling the heat exchange between different parts of the engine. I am looking for a set of formulas that describe by how much a part heats up, or cools down over time.

I'm having a hard time finding the relevant formulas, and the fact that lots of the terms in the field are so similar to each other doesn't really help.

Let's simplify the simulation by substituting the engine as a solid block of steel with a contact area A to the oil. Both mediums have their respective properties like density, mass, various heat parameters etc. I need a formula that tells me the temperature of each of the two components after each simulation step Δt.

What I found so far is that the problem is two-folded, where I first have to work out the rate of heat flow between the two parts and then apply this power to each component individually, based on their respective properties.

My questions is whether my thinking so far is correct or not. Furthermore I'd appreciate any suggestions as to what set of formulas to use for this problem.

Cheers,
Vitus

 

[jrmichler]

Your thinking is good so far. The next step is listing sources of heat and heat loss:
1) Cold oil against hot metal surfaces. Heat transfer is function of temperature difference, area, and heat transfer coefficient.
2) Cold oil in bearings. Heat transfer is function of oil viscosity, area, gap, and relative velocity. This just might be the largest source of heat.
3) Oil pump work. Heat transfer is pressure times flow rate.
4) Hot oil against cold metal (oil pan). Heat transfer is function of temperature difference, area, and heat transfer coefficient.

 

[anorlunda]

In addition to what @jrmichler said, some engines have a separate oil cooler.

It will be difficult to make your simulation accurate. For each of those heat flows, you must estimate the heat transfer coefficients. The steady state temperature distribution will depend on every one of those estimates.

It would be much easier if you had a baseline operating point to calibrate your model. If you know the oil temperature at each critical point in the cycle at the baseline, you can use that to estimate the heat transfer coefficients. Then holding the coefficients constant, your simulation could make predictions about operating points that are not exactly the same as the baseline point.

 

[Ranger Mike]

engine oil does a lot of important things besides lubricating. It is a major requirement to cool the rotating and reciprocating components as well as clean any material debris. The oil squirting out of the connecting rod bearings slings all over the cylinder and soils the piston wrist pin. Its must carry away 500 degree F heat from the bottom of the piston. It must carry away heat from the cylinder walls. Once the engine reaches full operating temperature the oil temperature in the oil pan will be relatively stable.

 

[GMVitus]

Thanks for your replies! I'm glad to hear that you agree with my approach. To make this all a bit more concrete: I want to develop an modular algorithm that I can stick to various parts of the engine to that will simulate the heat exchange for that particular part. For the moment I want to focus on the oil circulation, but I want to later extend that to air-cooling as well.

Some of the aspects mentioned by you I already took care of in my previous simulations. I.e. the oil viscosity (as a function of the oil's temperature), pressure and volume flow are already been taken care of and are completely dynamic. Also, I do take the different parts into consideration - in my simulation I split the oil flow up to lubricate and cool the various components of the engine mentioned. However for the benefit of this discussion, I'd like to keep it simple - I can always add more features as I go. For the moment, I am only looking at the heat exchanged between the cylinders/pistons and the oil.

So for the first step in the calculation I need determine the power transferred from one component to the other. Wikipedia gives me this:
∆Q/∆t = −K A ∆T/x,

where K is the thermal conductivity factor, A the surface area, ∆T the temperature difference and x the thickness of the material. I have some trouble in understanding this calculation.
1. How do I evaluate the thermal conductivity factor? The way I understand it is that it is not the property of either one of the components in question (i.e. the engine block and the oil), but rather the factor at which energy can pass from one to the other. So what would be a formula to determine that?
2. What thickness are we talking about here? Would it be the thickness of both components combined (simplified: the diameter of the cylinder + the diameter of the oil pipe)?
3. What then is the mechanism/formula to calculate the resulting average temperature of each component?

 

[BvU]

1. $k$ or $\lambda$ is a material property. You have to look it up in a table, ahttp://www2.eng.cam.ac.uk/~mpfs/papers/articles/WTC2005/pdfs/t-3/WTC2005-64316.pdf or estimate it using expressions.
If heat is being tranferred through several layers of material, you have a series of resistances; each layer has its own k. Often we only look at the highest resistance and ignore the others (e.g. copper pipe with thermal insulation).
2. Thickness is per layer (Fig. 2 here) Of course the oil film is very thin, so you probably can't use this 'ignoring'.
3. You can average, but I wonder of that is appropriate in an engine model.

 

[jrmichler]

With a viscous liquid such as engine oil, the majority of the heat transfer resistance will be in the oil boundary layer. Procedures to calculate the heat transfer coefficient for that layer fill an entire chapter in an undergraduate heat transfer book, plus you need the earlier chapters to understand that chapter. You can look for generic heat transfer coefficients using Google, but be advised that you will be lucky if get them correct within a factor of ten that way.

Some searching on engine oil temperatures finds mentions of oil temperatures as high as 300 deg F, and oil temperatures 20 to 30 deg C higher than coolant temperature. This implies that, in a fully warmed up engine, much of the engine is cooling the oil. The sources of heat to the oil are then oil jets against piston crowns and the main and rod bearings.

 

[Ranger Mike]

just a note on oil temps - typically the oil sender (sensor) is located in the oil sump or oil gallery of the engine block down stream from the maximum temperature condition of the engine. The oil temperature gage gives a reading of the oil temperature at the sensors location. It is by no means giving you the maximum temperature of the hottest component of the engine. As you will note in my previous post the underside of the piston has temperature of 450 to 500 degree F. The engine oil must be able to splash on the temperature without flaming.
it gets worse!
With the automaker trend today of smaller 4 cylinder engines for economy and turbocharging for performance, the hottest spot now is the exhaust vane connecting the shaft to the intake impeller. Could be as hot a 1600 degree F.

 

[GMVitus]

Gosh, why does it have to be so complicated?
I don't need a super-sophisticated in-depth analysis, but rather a responsive model that incorporates basic mechanisms of heat exchange. No, I won't need complex FFT simulations, I need a formula with a set of material properties that roughly estimate by how much oil heats up in different parts of a running engine. I understand that you can dive deep into the guts of science with a question like this, but that's out of my scope of what I need to achieve.

On a side note, one idea that I had was to do a simple look at the energy. I can calculate how much energy is bound in a given volume of fuel. I know that an engine converts X% of that energy into mechanical energy while the rest is dissipated into heat. Since we roughly know how hot oil gets you can guesstimate how much of the engine's heat is transported off by the oil. This is a veeeery crude way and I want my simulation to be a bit more realistic, but on the other hand I can't go overboard with it (like a FFT) since the calculations need to be very responsive in real-time.

@BvU I read the document on "steady heat conduction", that one really helped my understanding, so thank you for that. I try to find more information on the various heat transfer coefficients/resistances however most data I find is used in civil engineering. Which makes me wonder if that method is useful in my application?

So sticking with my previous example I'd propose the following approach:
1. Find the thermal resistance for oil and steel (taking the geometry into account) and use them to calculate the total resistance of the group: Rt=Roil+Rengine
2. The resistance is used to calculate the rate of heat exchange as an expression of power: ∆Q/∆t = (Toil - Tengine) / Rt
3. Calculate the temperature of oil and engine (considering mass and heat coefficient): T1 = (∆Q/∆t) * ∆t / (c * m) + T0

Does this sound feasible to you?