Hi Anders,
Lovely to see all the internal bits looking so good. I think that your test with a straight pipe will fix many of your current issues. The one big change since your earlier straight nozzle test with lower temps is the 90 degree exhaust pipe.
When a flow is turned in a passage, secondary flows are set up...you see this in turbine blades, exhaust pipes, water pipes, etc...it is due to the pressure differential required to "turn" the flow. There must be a "pressure" side and a "suction" side. These secondary flows cause pressure losses that could easily render your exhaust setup more restrictive than the straight nozzle setup. It is likely that your exhaust also includes a swirl component to the flow which makes things more complicated, but my guess would be that the presence of swirl would increase the passage losses since there would be more boundary layer losses due to the added flow path length.
So I set off trying to quantify this. I did a simplified version that doesn't capture compressible flow effects, heat transfer out through the walls or the effect of swirl in the 90 degree pipe. Using a generalized energy equation (similar to the Bernoulli's equation, but capable of handling additional flow losses), I solved it for the pressure drop due to the losses in an additional component assuming constant flow speed. Then using my Chemical Engineers Handbook (Perry and Chilton, 1963), I got the loss coefficient for a "long radius 90 degree elbow", which is K=0.45. The equation is,
Pressure loss = K*((V^2)/(2*gc))*density
Checking all the units and solving for flows up to 2000 ft/s and with two inlet temperatures, we get...
The pressure drop values aren't the main takeaway here, since we are assuming temperatures, ratios of specific heats, etc,...they give us a sense of the scale of the pressure loss, but the insight from the calculation is the big take away. As you can see, as the gas temperature is reduced, the density increases and the magnitude of the pressure loss increases for a given flow speed. The second big takeaway is the shape of the curve...since it is a function of velocity squared, the losses don't just increase linearly with flow speed, they climb much faster. So without a diffuser upstream of the exhaust bend, you are getting a much larger flow loss downstream of the turbine than could be achieved with a more optimal setup.
This is what I was getting at back when you had issues with the power turbine section on. Flows don't like to turn 90 degrees and we usually pay for that with high pressure losses. I still think that the exhaust out of your power turbine section may be an issue. It would be relatively simple to check with the addition of a few static pressure taps to see if there was exhaust back pressure at the exit plane of the turbine.
The hot spot could easily be the local stagnation pressure (and thus local heat transfer coefficient) being higher due to the presence of the downstream bend. I tried to find anything on a swirling flow in a 90 degree bend with no luck, but I did find a plot of cross-sectional stagnation pressures in a bent circular pipe and it does show that early on in the turn, the flow sets up strong local regions of stagnation pressure that could easily match your setup if the flow swirl cause the high pressure region to rotate in the passage. Unfortunately, I wasn't able to find it free online, but if anyone can get this book from the library,
www.amazon.com/Internal-Flow-Applications-Cambridge-Technology/dp/0521036720it is shown on page 469.
The next item that I feel needs to be discussed is the ability of immersion thermocouples to resolve the temperatures in higher speed flows. As in anything we do with these engines, there is a lot going on, even with the simple thermocouple.
First, we need to know what we are trying to measure...do we need the static gas temperature or the total gas temperature? It depends on your calculations. If we know either of them and the flow speed, we can get the other temperature, but most of the time we don't know the gas temperature.
I think for our purposes, that the calculated flow speeds would not introduce too much error...IF...we know mass flow rates through the engine or something else that really anchors our calculations. Ash's idea of using a auto mass flow meter is really nice for this! This is relatively easy of we are using the stock compressor housing, but once we have made our own, the manufacturers compressor map is nothing more than a suggestion (and probably a bad one at that).
Back to the thermocouples...in high speed flows, there is an additional element to the gas temperature due to the kinetic energy of the gas flow, termed the dynamic temperature...the temperature of the gas that would be felt if we were moving along with it at zero relative speed is termed the static temperature so that finally the total temperature or stagnation temperature is the static temperature plus the dynamic temperature. It is very important to use the correct temperature in the calculations in order to not introduce errors.
So what are we measuring when we stick a thermocouple into the gas flow? It turns out that we are measuring somewhere in between the total temperature and the static temperature, assuming that there is not heating due to radiation from some glowing hot piece of metal. Well, that is not a good assumption for a gas turbine at all! There are glowing hot chunks of stuff everywhere! Heat transfer due to radiation is a big deal...it scales as the temperature to the 4th power!!!!
Let's neglect the radiational heating of the TC for now. The TC comes to an equilibrium temperature if the gas flow conditions are constant long enough and let's assume it is for now. So, we have the TC junction at some temperature and as we move out to the gas flow we see that temp changes due to conduction in the TC sheath to the cooler outside region. Then, the gas closest to the TC is not moving at the same speed as the free stream region due to the boundary layer formed. This can shield the TC or it can cause additional heating due to the viscous shearing in the boundary layer.
So, to account for this, there are often recovery factors and correction factors applied to TCs in high temp high shear flows. You can read about this in here:
www.dtic.mil/dtic/tr/fulltext/u2/a285423.pdfI will try to find some additional resources to supplement this document.
So I ran a simple plot of the temperature change due to speed assuming a correction factor of 0.75 and an initial temperature of 70 F (= 70 + 459.67 = 529.67 R). Note that the temperature units are in degrees Rankine. So, here are the equations...
Here is the resultant plot of the static and total temperatures for a TC that was showing 529.67 R,
So you can see that as the flow speed increases, the temperature error due to flow speed increases.
A plot of the error is shown below,
You can see that if we were to get out to 1000 ft/s we could expect an under/over error of 20% depending on which temp we were trying to measure.
Remember, this is only due to the flow errors, with an assumed correction factor, radiation is a whole other issue that I am trying to work on. I'll get back to you with that...unless you want to build a shielded TC arrangement? I would suggest, a cylinder closed off at the bottom with two holes, one in and one out, at different radial distances...the TC is then stuck into this internal volume (blue cylinder) this is a very common arrangement...see below, the yellow is the hot gas flow and the blue region above is a the cool air outside of the duct.
This allows the gas to enter, "meet" the TC head on (for best temperature recovery) and then exit, while shielding the TC from any external heat radiation sources (like the turbine wheel or hot spot on exhaust duct). Remember, thermal radiation is a line of sight sort of thing...that's why your car frosts first on the roof on a cloudless night. It's "line of sight" is into space, so the temperature it is radiating to is very cold! With the trees and other stuff around the car at nearly the same temperature, there is not much driving the radiant heat transfer in these directions.
Finally, the point of all of this.
Temperature, pressure and other measurements made on higher speed flows with substantial temperatures must be taken with care and it requires some work to get accurate numbers...if you are just using them in a comparative manner, it is not as much of a big deal.
You can calibrate a TC at static conditions, but the flow error is not something that people will be to calibrate for you...we are going to have to work this out.
We need to take into account radiation effects if we use unshielded TCs.
I have a nice book from the MIT press, "Aerodynamic Measurements - Robert C. Dean Jr" that I am trying to go through now to build a spreadsheet to help out with this...more to come.
Chris