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Natural Science Forum / Physics / Acoustics / May 2006length of exhaust pipe should be 1/4 wavelength?
I want to 'tune' the exhaust of a generator to peak the effciency at 3600 rpm.Thats 30 bangs per sec, and if the bang travels 1120 ft/sec down the pipe, a 1/2 wavelength pipe would be about 15 ft long! If the cylinder had 6 in^3 volume, and the piston comes up in 8ms, and the diam of the pipe was about 3/8", the pressure wavefront would travel down the pipe about mach 1.This pulse of exhaust would be half way down the pipe when the exhaust valve closed. I heard that the idea was for the 'momentum' of this pulse to create a lo pressure at the exhaust valve to help scavenge the cylinder when it opens again in 24ms. Does that mean the pipe has to be a full wavelength long? 30 feet?!? I thought you could get a couple concentric tubes and try to tune it like a trombone slide... look for a dip in the fuel consumption at the resonant point. Would it crack like an airplane prop if the pulse exited at mach 1? Thats good news and bad news. The generator uses less fuel, but it gets louder. > I want to 'tune' the exhaust of a generator to peak the effciency at > 3600 rpm.Thats 30 bangs per sec, and if the bang travels 1120 ft/sec [quoted text clipped - 11 lines] > prop if the pulse exited at mach 1? Thats good news and bad news. The > generator uses less fuel, but it gets louder. The pressure pulse will travel at M1 anyway. The way to think about it that probably helps is that the pressure pulse reflects and inverts at the outlet to atmosphere, so you want 2L/c to equal the interval between the relevant exhaust valve events. 4L/c would do as well, but will be less effective.. If the volumetric flow rate achieves M1 (and this is quite common) it will make a noise like a raspberry. There are several solutions, given the option the simplest way is to increase the size of the pipe. Your trombone idea is excellent, we often use that for air intake tuning. Cheers Greg Locock > I want to 'tune' the exhaust of a generator to peak the effciency at > 3600 rpm.Thats 30 bangs per sec, and if the bang travels 1120 ft/sec First of all, 1120 ft/sec belongs to room temperature, which exhaust gas is not. Figure 49*SQRT(459+F) ft/sec where F is the Fahrenheit degree temperature of the exhaust gas... maybe 1000F or so (check it out). > thought you could get a couple concentric tubes and try to tune it like > a trombone slide... Trombone slide (Use Bob Burns' "Bazooka" as a design guide) > look for a dip in the fuel consumption at the > resonant point. That would take a long time and a lot of fuel. Better to disable the speed regulator, and look for a maximum of RPM. > Would it crack like an airplane prop if the pulse > exited at mach 1? Often yes. Long tubes will do that. The 'blatting' or staccato cracking sound heard when cars with no muffler (just a single straight pipe from the headers to the tail pipe end) make that very sound on acceleration (a boutique car aesthetic in some warped minds). These are traditional one dimensional shock waves that form as soon as the impulsive sound pressure level approaches one atmosphere. The longer the tube, the lower the pressure needed. (A garden hose about 10' long , fed by a trombone mouthpiece, blown like a trombone easily makes the same shock wave sounds. > Thats good news and bad news. The generator uses less > fuel, but it gets louder. A little of both; surely more noise; maybe less fuel consumption. Angelo Campanella Very interesting Angelo... I agree that the speed is temperature dependent... 1000 to 1120 ft/sec variation could be dialed in with the tuning.... Is the pressure wave + and - 14.7 psi? Ahead of the pulse its 29.4 and behind it its zero? What SPL is that in dB? 140? Where does air compressibility come into play? Trying to tie together some audio and aerodynamic terms and concepts.... get the big picture..... >Very interesting Angelo... I agree that the speed is temperature >dependent... 1000 to 1120 ft/sec variation could be dialed in with the [quoted text clipped - 3 lines] >compressibility come into play? Trying to tie together some audio and >aerodynamic terms and concepts.... get the big picture..... Compressibility definitely enters into it. The pressure pulse is nonlinear. It steepens as it goes down the tube. The reflection is an expansion, which spreads out as it propagates back toward the engine. The idea is that the expansion will reach the exhaust valve at the right time to help empty the cylinder. It may also propagate through the cylinder (during the overlap period) and help draw the fresh charge in. Really more of a gasdynamic problem than an acoustics problem. It's also a thermodynamics problem. With the elevated temperatures, and the cooling in the expansion, some of the exhaust energy is recovered. Ken Plotkin > I agree that the speed is temperature > dependent... 1000 to 1120 ft/sec variation could be dialed in with the > tuning.... 70 degrees F = about 1100 ft/sec. Exhaust gasses will vary up to 1000F or more,, increasing the speed to 1800 ft/sec and the wavelength accordingly > Is the pressure wave + and - 14.7 psi? It depends on the minor explosion that is let into the exhaust pipe. > Ahead of the pulse its 29.4 and > behind it its zero? The way that negative pressures (really values less than 14.7; it can't go below zero absolute). > What SPL is that in dB? One atmosphere is 196 dB simplistically. If one had a peak-to-peak pressure of 0-14.7 psi, it would be 1/3 that (10 dB less) or 186 dB ("RMS". If one presumed that it would be two atmospheres 0-to-peak (0-29.4 psi), it would be 6 dB more or 192 dB )("RMS"). > 140? Where does air > compressibility come into play? Trying to tie together some audio and > aerodynamic terms and concepts.... get the big picture..... Especially on the negative side, if the volume is doubled, the pressure does not become zero, it becomes only halved, pursuing a "hyperbola" shaped curve, this is the nonlinear nature, with the harmonics therefor. That is the beginning of nonlinearity. More and new phenomena arise as this pressure wave travels down a long pipe. Since the compressions (and rarefactions) occur adiabatically (no time for the pipe metal to cool or heat the exhaust gas), the local sound velocity inside the wave is faster or slower. This makes the pressure peaks travel faster than the pressure valleys. The traveling positive pressure region has no alternative but to become a genuine shock wave, while the trailing negative region merely stretches out thinner (lower density). (Unlike ocean waves, the air cannot form a spillover and white cap... the air must pile up against a shock front where the density is greater behind the shock front, and less before the shock front within the lesser pressure wake of the shock one wavelength ahead of it. These shock fronts, when emitted from the tailpipe of a car without a muffler, sound like a blatting trumpet or trombone. Angelo Campanella |
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