Post by finiteparts on May 12, 2017 23:50:21 GMT -5
Hi John,
There is likely some error in my calculations. I did my best to estimate you liner holes sizes and numbers from the photos. I ran a cycle model at what I thought was your design point for your engine, 3.6 lbm/s at 3.5 PR and I assumed a T4 limit of 1600F. With my estimate of dynamic pressure in the outer annulus, and a 5% dP/p it correlated to a Cd ~ 0.8 in the plunged holes and the other chamfered holes I estimated to have Cds around 0.65. I used your 9.5mm throat diameter on your vaporizer tubes with a Cd down near 0.6 due to the rather "rough" flow path and large discharge "dump" ratio.
I estimated that your liner has a total effective area of the holes around 8.85 in^2...with the Lefebvre's equations suggesting the effective area to get 5% dP/p to be 8.1 in^2. Now I would expect that if my numbers were close, you would actually be running lower than the 5% pressure drop because of the leakages at the interfaces to the turbine and also the leakages through the gaps around the liner at the dome and vaporizer end to outer sheet. I haven't attempted to calculate their impact.
My equivalence ratio = 1.8 was based on estimated liner hole sizes from the photos you posted...there's likely some error there...also, the fact that I was assuming that the liner hole area impacts the mass flows through the liner in a linear fashion, which isn't real, but good enough for estimates. In reality as the flow comes around the liner, portions of the total mass flow turn and go through the liner. This reduces the momentum and modifies the local dynamic pressure field, manifesting its impact to each set of holes as a sensitivity to the other holes upstream and downstream of it. Sort of like a network of series and parallel orifices...
The number I quoted is the equivalence ratio, not the AFR...the AFR that I calculated for the tubes was 7.853. If your estimated AFR of 2.6 is correct, that would mean the vaporizer tube equivalence ratio is 5.64, which is well above the rich flammability limit of 3...good for keeping the vaporizer tubes alive...but I would have expected much more coking on the dome for that rich of a vaporizer flow.
I agree with you on the use of tangential flow to make the effective path through the liner longer...I was just saying that it is good to think how those jets move the internal flow.
We want to have some mechanism to recirculate some of the hot, reacting products back upstream to interact with the incoming fresh reactants. This is the primary combustion stabilization mechanism...the incoming reactants are cold and need to be heated up in order to get the reaction times fast enough to allow the combustion to complete within the short time the airflow is in the combustor. Usually this is done by setting up a vortex flow pattern of some kind...and that is why I suggested the axial jets. When you have two jets fairly close, moving in completely opposite directions, you set up a recirculation flow between them.
I hear that "combustion is a black art" comment a lot, but the people that say that don't work in combustion. Back in the 70's and 80's it may have been true, but nowadays it may be common to have to trim a combustor to meet profile or modify some cooling features to meet some durability issue, but not restructure the flowpath. Where I used to work, we made ultra-low combustion systems. We had to run really lean to keep the NOx down and that means that they were on the edge of lean blowout all the time...a much tougher combustion design problem than standard combustors. I can't think of a time when any of the combustors failed to start, anchored the flame differently than design intent, operated at grossly lower efficiencies, etc. We had pretty radically different combustors that fired off the first time and operated close to intent. The only real problem we had was combustion acoustics due to the flame instabilities at lean conditions (think of how a candle flame makes noise when you nearly blow it out). Now I agree at the homebuilder level, it may be an unknown...but I would hate for readers to think that the large gas turbine manufacturers still have such design issues. With modern design and testing tools, the problems have been reduced and the knowledge of the flow fields and the reaction kinetics are much more complete.
Good luck,
Chris
There is likely some error in my calculations. I did my best to estimate you liner holes sizes and numbers from the photos. I ran a cycle model at what I thought was your design point for your engine, 3.6 lbm/s at 3.5 PR and I assumed a T4 limit of 1600F. With my estimate of dynamic pressure in the outer annulus, and a 5% dP/p it correlated to a Cd ~ 0.8 in the plunged holes and the other chamfered holes I estimated to have Cds around 0.65. I used your 9.5mm throat diameter on your vaporizer tubes with a Cd down near 0.6 due to the rather "rough" flow path and large discharge "dump" ratio.
I estimated that your liner has a total effective area of the holes around 8.85 in^2...with the Lefebvre's equations suggesting the effective area to get 5% dP/p to be 8.1 in^2. Now I would expect that if my numbers were close, you would actually be running lower than the 5% pressure drop because of the leakages at the interfaces to the turbine and also the leakages through the gaps around the liner at the dome and vaporizer end to outer sheet. I haven't attempted to calculate their impact.
My equivalence ratio = 1.8 was based on estimated liner hole sizes from the photos you posted...there's likely some error there...also, the fact that I was assuming that the liner hole area impacts the mass flows through the liner in a linear fashion, which isn't real, but good enough for estimates. In reality as the flow comes around the liner, portions of the total mass flow turn and go through the liner. This reduces the momentum and modifies the local dynamic pressure field, manifesting its impact to each set of holes as a sensitivity to the other holes upstream and downstream of it. Sort of like a network of series and parallel orifices...
The number I quoted is the equivalence ratio, not the AFR...the AFR that I calculated for the tubes was 7.853. If your estimated AFR of 2.6 is correct, that would mean the vaporizer tube equivalence ratio is 5.64, which is well above the rich flammability limit of 3...good for keeping the vaporizer tubes alive...but I would have expected much more coking on the dome for that rich of a vaporizer flow.
I agree with you on the use of tangential flow to make the effective path through the liner longer...I was just saying that it is good to think how those jets move the internal flow.
We want to have some mechanism to recirculate some of the hot, reacting products back upstream to interact with the incoming fresh reactants. This is the primary combustion stabilization mechanism...the incoming reactants are cold and need to be heated up in order to get the reaction times fast enough to allow the combustion to complete within the short time the airflow is in the combustor. Usually this is done by setting up a vortex flow pattern of some kind...and that is why I suggested the axial jets. When you have two jets fairly close, moving in completely opposite directions, you set up a recirculation flow between them.
I hear that "combustion is a black art" comment a lot, but the people that say that don't work in combustion. Back in the 70's and 80's it may have been true, but nowadays it may be common to have to trim a combustor to meet profile or modify some cooling features to meet some durability issue, but not restructure the flowpath. Where I used to work, we made ultra-low combustion systems. We had to run really lean to keep the NOx down and that means that they were on the edge of lean blowout all the time...a much tougher combustion design problem than standard combustors. I can't think of a time when any of the combustors failed to start, anchored the flame differently than design intent, operated at grossly lower efficiencies, etc. We had pretty radically different combustors that fired off the first time and operated close to intent. The only real problem we had was combustion acoustics due to the flame instabilities at lean conditions (think of how a candle flame makes noise when you nearly blow it out). Now I agree at the homebuilder level, it may be an unknown...but I would hate for readers to think that the large gas turbine manufacturers still have such design issues. With modern design and testing tools, the problems have been reduced and the knowledge of the flow fields and the reaction kinetics are much more complete.
Good luck,
Chris
