Hi Thomas,
Awesome video(s) Thomas!.
You certainly dont have any screech in that video.
I must have confused your engine with some other jet engine video.
Anyways, while listening to your video a whistling sound is heard at about the 5 second mark. It's probably normal turbine engine operation but if it was a mild combustion instability what kind would it be?
If the whistling is generated within the after burner what is it? The recorded whistle sounds like its in the 2KHz -3KHz range. So to get a better idea of the actual whistle frequency, I pulled out my cell phone and started my function generator / tone generator app. The app has a continuously variable frequency output to the phones speaker. The frequency slider was moved up and down until the tone could be matched to the whistle sound in the video. The whistle frequency and the tone generators matched up at ~2,800 Hz.
So if the AB chamber has an internal acoustic mode whistling, we can look at a frequency of ~2800Hz.
By knowing the whistle frequency and seeing the engine was at full afterburn, we can calculate the whistle wavelength inside the hot gasses of the AB combustion chamber.
With a wave length we may be able to get an indication of type of resonant mode, its location and orientation.
2800 Hz in a combustion chamber, burning fuel near equivalence (stoichiometricly balanced) the combustion gas temperature will be about 2000'K.
The combustion gases ratio of specific heats (gamma) will be about 1.26.
The combustion gases will have an average molecular weight close to air so it will have a Gas Constant R of about 287 J/kg/K.
So, the speed of sound C in your combustion chamber can be calculated as
C = (K R T)^1/2
where
C = Sonic velocity or speed of sound in meters/second.
K = Ratio of specific heats (gamma) of the fuel air combustion gas is about 1.26.
R = the individual gas constant for air or combustion gas is 287 (J/kg K)
T = absolute temperature of about 2000'K
The speed of sound in the chamber is (1.26*287*2000)^1/2 or 850 Meters/second.
The wave length L of 2800 Hz at a sonic velocity C of 850 M/sec = (850 M/sec) / (2800 cycles/sec) = 0.303 meters or 30 centimeters.
30 centimeters is one full wave length at 2800 Hz inside the AB combustion chamber.
If the the whistle sound is an internal resonance, what kind of resonance is it?
To find out, we need to see if there is a connection of the 30cm wavelength to any part of the AB chambers internal geometry.
There can be a large number of possible acoustic modes but lets look at the common/simple modes.
Longitudinal mode
Radial mode
and
Tangential mode.
What part of the after burner internal geometry is equal to 30 centimeters or an integer of 30cm? Length? Width? Diameter? Circumference? etc.. If you find a match, that dimension could be associated with the whistling sound. If there is no geometric commonality, there may be no association to the whistle sound.
For a suspected or proposed mode of resonance to be valid, the modes directional orientation of wave motion needs to fit the application. For example, a radial mode doesn't fit in a longitudinal direction. And vice versa. The orientation of a modes direction of motion defines the mode type.
30cm is the full wave length of 2800Hz. A resonance mode can fit within a 1/2 wave length, a 1/3rd or a 1/4 wave length.
So what part(s) of your chambers internal geometry coincides to 7.5cm, 10cm, 15cm or an integer of 30cm?
Length? Diameter? Circumference? Perhaps the outer circumferential distance between flame holder gutters?
If nothing about the chamber geometry relates to 30cm or its harmonics, that specific acoustic modes may not exist. If you find the chamber internal geometry has a commonality with a 2800Hz wave length, 1/4 wave, 1/2 wave or a full wave, it may be a resonance source.
The Radial Mode:Is your AB chambers "Inner Diameter" equal to 30cm or an integer of 30 cm? If yes, the whistling could be the result of a mild "radial mode".
A radial mode is a wave that moves from the chamber axis, outwardly to the chamber walls where it is reflected back inwardly to the axis again and keeps repeating. In a rocket engine a radial mode can disrupt the injectors fuel and oxidizer mixing process. As the radial modes wave of motion moves inwardly and outwardly from the axis to the combustion chamber wall, this inward and outward motion physically shakes the injected fuel and oxidizer propellant streams. The radial shaking disrupts the smooth injection streams, making them erratic, bushy and causing misalignment of the impinging fuel/oxidizer streams. This reduces propellant mixing efficiency and engine performance. Sometimes the shaking motion can so violent that it can increase the propellant mixing efficiency but does so in an erratic way that still ends up reducing engine performance and life. Radial modes are rough on liquid bipropellant rocket engines because of its interaction with the liquid phase propellants. In a turbo jet engine, a radial mode will likely induce instability to the flame holders recirculation zone and increase heat transfer to the combustion liner. Either way, moderate to heavy radial modes can be a problem.
Looking at your drawing, I can't see 30cm fitting any radial dimension.
The Longitudinal Mode:Is your AB chambers "Length" from end to end including the convergent nozzle (with or without the dump tube length) an integer of 30cm? If yes, the whistle could be a "longitudinal mode".
Longitudinal modes are waves that travel the length of the combustion chamber from end to end. They can induce propellant feed rate problems, buzzing, whistling, rasping, schreeching or other noises. They are the least consequential of acoustic modes in a rocket engine but could pose more difficulty in an after burn chamber. They arent particulary harmful to a rocket engine because the injectors are located at the very end of a standing wave. There is no wave motion at the injector face so it has much less of an effect on the propellant injection/combustion process.
In a jet engine after burner, a longitudinal mode could be more of a problem. If a longitudinal mode is violent enough it could ignite fuel upstream of the flame holder creating a feedback mechanism... and that would get ugly fast. Unless you are designing whistling pyrotechnics, a pulse jet engine or some device specifically designed to resonate, no engineer wants a longitudinal mode in their engine. Looking at your drawing, I don't see 30cm fitting any of the longitudinal dimensions.
Then there is
The Tangential Mode: And this mode gets really interesting.
Does your AB chambers "Inner Circumference" have any connection to an integer of 30 cm? 60cm, 90cm, 120cm, etc?
If there is a close match, the whistle could be caused by a weak Tangential Mode.
A tangential mode is a circular traveling acoustic wave that spins around inside the combustion chamber. It can spin slowly or spin as fast as a tornado. Sometimes tangential modes can spin really fast at transonic or supersonic speeds. In a rocket engine a tangential mode can transition into a spinning detonation wave energized by alternately detonating propellant injector fans.
A tangential modes highest energy intensity is centrifuged up against the combustion chamber wall. In rocket engines, tangential modes can be destructive because the spinning wave can turbulate and scrub the chamber walls protective boundary layer off, dramatically increasing the heat transfer into the wall. Even if streams of liquid fuel are sprayed against the combustion chamber wall to cool it with a protective Boundary Layer Coolant (BLC), if a tangential mode starts spinning up, it will scrub the liquid coolant clean off, atomizing the coolant and sweep it away leaving the chamber wall dry, naked and exposed to extreme heat transfer. Tangential modes can end the life of a rocket engine very quickly. Once a tangential mode starts it can build itself up with self perpetuating, positive reinforcement mechanisms. As a tangential wave spins around the chamber (very near the injector face) the tangential wave slams into one of the many injected streams of fuel and oxidizer flowing from the injector face. Normally, the liquid fuel and oxidizer streams are impinged against each other in a precise way to create a liquid spray fan that mixes and burns the propellants in a smooth deflagration.
But if tangential mode starts up and sends a spinning wave into the side of one or more of the impinging propellant fans, the liquid fan is shattered by the impact. The fans fuel and oxidizer are instantly mixed, atomized and reacted. The reaction energy is released instantly as a small, brissant, detonation. This detonation sends shockwaves into down wind injector propellant fans. Shattering and detonating them, propagating the shockwave in a runaway chain reaction of detonating dominoes. After the detonation wave passes, the detonating dominoes are automatically set back up by the incoming propellant flow and the cycle of spinning detonation waves keeps spinning. Tangential modes of this kind can spin deep into hypersonic velocity, loudly singing inside the combustion chamber at 20+KHz. The turbulence, thermal, acoustic and mechanical effects are extreme. If the engine is not shut down immediately, the engine will shut itself down, ending the engines life in a Rapid Unscheduled Disassembly (RUD).
A tangential mode of this kind is very unlikely to happen in a jet engines combustion liner. Unlike a rocket engine combustion chamber which is smooth and rigid, a jet engines combustion liner is flimsy and full of holes. A flimsy combustion liner full of holes will damp much of its own natural resonance modes. A liner doesn't direct or reflect waves well and being so full of holes the liner will leak and diffuse acoustic energy much more effectively than a rocket engines hard combustion chamber.
In a AB dump combustion chamber such as yours, there is no combustion liner to damp out resonances but its still OK. A tangential mode in a AB dump combustor doesn't have the same positive feed back mechanisms and will never have the destructive potential seen in a rocket engine because there are no liquid fuel/oxidizer propellant fans to shatter and detonate.
Looking at your drawing, integers of 30cm dont fit the AB chamber circumference either. So the 2800Hz whistle sound doesn't appear to be connected to the geometry of the AB chamber.
The engine seems to be running well so the whistling sound is probably just normal turbine engine noise.
There are many other potential instability modes and some may have no connection to the combustion gas speed of sound.
Laminar to turbulent instabilities. Diffuser flow detachment. Vortex shedding, unstable chemical reaction rates, fuel mixing rate instabilities, pneumatic coupling between upstream/downstream chambers separated by the pressure drop of a flame holder, Helmholtz resonances and many others. Fortunately the simplest modes Longitudinal, Radial and Tangential are the most common. They are easier to identify and sometimes easier to fix.
When taking measurements for resonances, pressure sensors, force sensors, accelerometers, condensers transducers or piezo transducers can be used for cheap and easy measurement. With the sensor properly oriented, it may be possible to identify a resonance orientation of motion (which can be helpful).
Tony