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We were encouraged by the limited number of frequencies that we would be working with - we could create a resonator to cancel out the loudest sources of noise! The resonator would be 1/4 of the wavelength of the loudest tone so that the peaks would enter the resonator, and take 1/4 of a period of the wave to move up the resonator, the same amount of time to move back down to the opening, where the flow in the main chamber had also moved the same amount (half of a wavelength in half of a period of time). This means that the peak of pressure in the resonator would be moving back into the main flow where the minimum pressure (half of a wavelength had passed, meaning the wave is now at a minimum). The maximum and the minimum portions of the waves from the resonator and main flow respectively would cancel each other out and destroy the sound wave for that particular frequency.
Our sponsor requested that we orient the exhaust sound damping around the frequencies experienced at full throttle. This would be much easier than trying to attenuate the changing frequencies that the turbine creates as the speed of the engine varies. Just as in a car engine, the higher the engine speed, the higher the frequency it produces.
Initial Design Idea - Resonator Chamber
A previous MAE project was postponed dramatically after one of the fuel lines burst and fuel destroyed the electronics. In an effort to prevent this, we used safety wire to attach all of the lines to the fittings, and we also created boxes to house the fuel and the electronics separately. We chose polycarbonate for its ductile properties and resistance to fracture. In the event of an explosion, we wanted the boxes to absorb as much of the energy as possible. These polycarbonate boxes were bolted down to the cart through their base.
First and foremost, we needed an area for testing. UCSD allowed us to test the Turbojet engine on site, and we modified a cart for our specific use (pictured right). Initially we were interested in an area to bolt down the Turbojet engine by itself, but we realized that a movable cart with all of our supplies at hand was ideal. This cart housed our fuel, electronics, safety gear, and of course the engine itself.
We bolted aluminum sheet under the Turbojet mounts in order to help shield the wooden cart from the hot exhaust. We also created steel mounts for the engine to raise the engine off of the table. This mount was attached by bolts that ran through the table, and the engine was attached to the mounts via shoulder bolts in order to isolate the vibrations.
Test Rig!
As we conducted more research, we discovered that one of the major sources of noise is created outside of the exhaust chamber. This is known as aeroacoustic noise and it is contrasted with mechanical and combustion noise. Essentially the transition between internal turbulent flow and external turbulent flow creates noise. This noise is generated by the eddies, or turbulent vortices caused by the mixing velocities. In addition to this, the large amount of shearing between the exhaust and the ambient air amplifies the noise caused by the eddies.
At this point, we realized that our design could not touch a major source of noise generation. Reduction of noise inside the exhaust chamber cannot control noise that is generated outside (and aimed away from) the noise chamber. A serious redesign was in order. According to our research, the best use of our efforts was to control the velocity profile at the exit. If we could induce a more uniform mixing between the exhaust and surrounding air using chevrons at the exhaust exit, as well as create a smoother velocity gradient at the exit (reduce the maximum slope of the change in velocity as we move from one side of the exhaust to the other), then the noise would be reduced more effectively.
Additionally, we discovered the V8 law, which claims that the noise produced by the difference in velocity from the exhaust to the surrounding air is proportional to velocity raised to the eighth power. This means that slowing down the average velocity at the exit is also a high priority in our next design.
Runner Up Design - Chevrons, Lobes, and Diffuser
More Research - Noise is created and amplified after exiting the engine
We would accomplish this design by welding tubes to the outside of the main flow duct and extending them either a certain distance out from the main flow or in a spiral, depending on the difference in length required (based on the wavelength of the offending frequencies).
After discussing the first plan with experts on Jet engines, we quickly discovered that a half wavelength bypass was a much more effective route. This method uses essentially the same idea, but a portion of the flow is diverted and takes a longer path toward the exit rather than allowing the pressure waves to propagate in the stagnant air in the resonator. This design would also be tuned to the loudest frequencies in order to make the most out of the frequency specific attenuation.
Second Proposal - Half Wavelength Bypass
The Runner Up Design of our noise suppression system tackles the main areas of aeroacoustic noise generation and amplification, namely:
The mean velocity of the flow
Shear due to the velocity gradient between ambient air and jet flow
Generation of coherent turbulent eddies
It was demonstrated by Lighthill (1952) that aeroacoustic noise, that noise which is generated at the outlet of jet flow (as opposed to noise due to mechanical components or combustion) follows the V8 Law. This law states that the noise power is proportional to the eighth power of the mean velocity of the flow at the outlet. This is somewhat intuitive, as it implies that one of the best ways to reduce the jet noise is to simply reduce the velocity. The primary mechanism for this noise is through the generation of coherent turbulent eddies. Jet flow close to the outlet creates fine-scale eddies which generate high frequency noise. Further down from the outlet (approximately 10 outlet diameters away) large eddies generate low frequency noise. The consequence is that aeroacoustic noise has a broad spectral density and cannot be easily attenuated through the use of resonators and the like, which target tonal frequency noise. Lighthill (1954) further showed that the shear layer at the jet orifice acts to amplify the noise generated by the coherent turbulent eddies. This shearing layer instability is caused by the large velocity gradient between the essentially stagnant ambient air and the bulk jet flow. The following image illustrates the shearing instability as well as the formation of fine-scale and large-scale coherent turbulent eddies at a jet orifice:
It is worth noting that the fine-scale eddies are closer to the outlet, thus the mean velocity and hence the mean noise power is higher there. These small vorticies are also close to the shear layer instability causing further amplification. This is why the majority of jet noise is of high frequency.
The Runner Up Design of our noise suppression system consists of three primary components, each of which addresses one or more of the aforementioned aeroacoustic noise sources:
Bulk flow pipe with lobes
Diffuser
Chevrons
The bulk flow pipe carries the majority of the high velocity flow from the jet turbine to the outlet (ambient air). Lobes penetrate the central pipe, transferring a portion of the central flow to the diffuser section, thereby lowering the mean velocity flow without significant reduction of the mass flow. One can think of this as moving a high speed flow from a narrow pipe to a wider pipe to lower the speed. The diffuser section lowers the velocity of the by-pass (transferred) air flow, aiding in velocity profile shaping and reducing the mean velocity. Furthermore, the diffuser is offset from the jet, with an inlet allowing for ambient air to become entrained and mix with the by-pass flow. The amount of entrained air may be adjusted by altering the inlet, making the velocity profile of the by-pass flow adjustable. Finally, the bulk flow pipe is capped with conical chevrons. These chevrons induce mixing at the outlet and help to break up the formation of coherent turbulent eddies.
Three Machined Chevron Caps with 6, 8, and 10 Teeth
Here is a 3-D flow analysis to help visualize how the exhaust chamber operates. The balls represent individual particles of air, and they change color based on their speed (blue is slow, red it fast). The important thing to notice is the secondary flow around the main flow duct and the connection between the two flows.
Flow analysis of the Final Design from Brian Shaw on Vimeo.
Here is another view of the Runner Up Design. This view focuses on the lobes which force air from the main exhaust flow into a secondary flow around it. This is a 3-D simulation, so it is important to note that the blue dots entering from the left side arrive from the atmosphere, and the flow diverted from the main flow enters the secondary flow very quickly (The orange dots inside the lobes).
Close up of flow around Lobes in Jet Exhaust from Brian Shaw on Vimeo.
Current Design - Diffuser
The final design incorporates a full length diffuser. Testing between the Runner Up Design (incorporating a main flow, secondary flow, and chevrons) and the full length diffuser (designed to decrease the flow velocity at the exit) revealed that the most effective way to decrease jet engine noise is to simply slow down the velocity of the exhaust.
For a closer look at the Final Design, click Here
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