Fig. 1. - The appearance of a 4-step thermo-acoustic motor with a traveling wave
In previous articles, I wrote about how to build a Stirling engine without pistons, that is, about how to build a ring thermo-acoustic engine with a traveling wave 1 article
, 2 article
, Article 3
Fig. 2. - Scheme of the engine
The engine consists of 4 identical blocks. Each of the blocks consists of a heat exchanger consisting of a hot heat exchanger, a cold heat exchanger and a regenerator between them. The heat exchanger is sometimes called the engine core. The entire heat exchanger in the housing is called the engine step.
When the engine is operating inside the entire ring body, an acoustic wave of extremely high intensity is present. What is the typical distribution of pressure fluctuations, oscillatory velocity and acoustic power inside? In order to find out, I modeled the processes occurring in the engine using a special program developed in the Los Alamos National Laboratory (that is, in the same place as the atomic bomb) called DeltaEC. Next come the graphics for the engine under load. That is, for the following case:
Fig. 3. - Engine under load
The case where the engine has a load, even four loads, which are located close to the hot heat exchangers.
The graph of the distribution of the amplitude of pressure fluctuations in one of the four engine blocks looks like this:
Fig. 4. - Distribution of the amplitude of pressure fluctuations along the length of one of the blocks
Here is shown one fourth of the engine. You can see that the graph goes to the length of the body at about 1.5 m - this is the length of one block. It turns out that the length of the entire annular motor case is about 6 meters. In all blocks, all parameters are the same, so it suffices to consider only one of them.
The heat exchanger on the graph is to the left, starting from zero on the horizontal axis. It is seen that in the regenerator, due to viscous losses and the reflection of a part of the wave from it, the amplitude of pressure oscillations decreases. Next comes the load, where the pressure is still much more reduced. Further, the pressure increases to the initial value in the resonator, due to a decrease in the oscillatory gas velocity in the resonator.
Fig. 5. - Distribution of the amplitude of fluctuations of the volume flow along the length of the block
In thermoacoustics, it is customary to use in calculations not the oscillatory velocity of the gas, but the oscillations of the volume flow, that is, the oscillatory velocity multiplied by the cross-sectional area of the body. Fluctuations in volumetric flow rates are proportional to velocity fluctuations with a constant cross-sectional area of the hull.
In fig. 5 it can be seen that a sharp increase, an abrupt increase in the amplitude of oscillations of the volume flow occurs in the regenerator (near zero along the horizontal axis).It is this sharp increase in volume flow oscillations or gas velocity oscillations (which is more convenient for someone) that is the thermo-acoustic effect of amplification of an acoustic wave. The volume flow then decreases slightly as it passes through the load, and then finally decreases to its original value, passing through the resonator. Due to this decrease in volume flow oscillations in the resonator, an increase in pressure oscillations in the resonator occurs, as was described in the description of the previous graph.
What do these two graphics say? They say that the whole engine, which is called a traveling-wave engine, has never been and never will be a purely traveling wave. The traveling wave in this engine is observed only in the zone of the heat exchanger. That is, in the regenerator zone, the phase difference between pressure and gas velocity fluctuations is near zero. In all other parts of the engine, the wave is far from traveling, but is a mixture of traveling and standing waves.
Another interesting thing here is that the thermoacoustic effect does not increase the amplitude of pressure oscillations, but only increases the amplitude of oscillations of the gas volume flow rate.
Now let's see how the power of the acoustic wave changes.
Fig. 6. - Distribution of wave power along the length of the block
It can be seen that the power in the regenerator increases abruptly due to the thermoacoustic effect, then some power is lost when the wave passes to the load, then there is a sharp jump in power down due to the loss of energy on the load and further attenuation of the wave continues in the remaining part of the resonator to the original value.
Let's now think about how to determine the efficiency of the process.
In general, how to calculate the efficiency? It is necessary to divide the useful power by the expenditure. Everything is clear with the power expended here - this is the input thermal power, the heating power of the engine. But what is considered useful acoustic power?
In fig. 6 acoustic power reaches a maximum immediately behind the regenerator and reaches a value of 82 watts. It is this power that should be considered useful here? Not really. The useful acoustic power here is an increase in acoustic power in the regenerator, and a value of about 46 watts relative to which the increase begins can be called the reference level. Rather, even I would call the wave with a power of 46 W here - the reference wave, since it is precisely it that is amplified by the engine regenerator. Then, this power increase in the regenerator goes partially to the load, and partially dissipates, passing through the resonator. When designing the engine to achieve maximum system efficiency, you should try to make the power that is dissipated in the resonator much less than the power that is dissipated on the load, so that as much of the power gain in the regenerator as possible gets to the load and not just dissipated.
It follows from the above that the acoustic efficiency of the engine will always be greater than the efficiency of the entire system with a load, since the power dissipated on the load is part of the increase in power in the regenerator.
So how do you convert sound energy into electricity?
The Stirling engine's power generation is clear. If there is a crankshaft, then a rotating electric generator can be attached to it. If the Stirling engine is resonant, then you can attach a magnet to the working piston and place it in the stator of the linear generator. But what to do in the case of a thermo-acoustic engine? How to get electricity in the engine, where there is no crankshaft or pistons? How to convert high intensity acoustic energy into electrical energy? Today, two ways have been devised to do this.
is to use linear transducers.
Watch a video on my channel where I experiment with a linear transducer:
Fig. 7. - Subwoofer
An ordinary speaker is an example of a linear transducer. Usually, when working, he converts the electrical energy that enters him at the entrance to the sound, that is, into acoustic energy. But it can also work in the opposite direction and convert acoustic oscillations into electricity. Conventional speakers are not designed for extremely high sound intensity as in thermoacoustic devices (160–180 dB.), Therefore, they have large energy losses, which are associated with the low quality of the oscillatory system, high absorption coefficient of the membrane wave due to its insufficient rigidity, and also insufficient the magnitude of the free run of the membrane does not allow to use all the available power. Therefore, special speakers are made - linear alternators, which, by the principle of operation, are no different from the dynamics, but have either a membrane adapted for high sound intensity or replace the membrane with a piston in general.
Fig. 8. - Q-Drive Linear Alternator
The efficiency of conversion of acoustic energy into electrical energy using such a converter can reach up to 80%.
The second method
of conversion is to use a turbo generator with a bidirectional turbine.
Sounds found in the everyday life of most people, such as speech, sounds of passing cars, dogs barking, have a small intensity by the standards of thermoacoustics. Gas displacements from the equilibrium position in the acoustic wave of colloquial speech are fractions of a millimeter, so no one usually perceives a sound wave as the wind, which changes its direction thousands of times per second, that is, changes direction with a frequency equal to the frequency of the wave oscillations. In thermoacoustics, when the intensity of oscillations reaches 180 decibels, the sound is no longer even the wind, which changes direction with great frequency, but rather a hurricane with a peak speed reaching 100 km/h. Therefore, you can use a turbine to convert this sound energy into electricity. In this video, I conducted interesting experiments on this topic in order to visually show what a high-intensity sound wave looks like.
It is immediately clear that the direction of rotation of the turbine rotor for thermoacoustics should not depend on the direction of flow entering and leaving the turbine, otherwise the flow will accelerate the rotor half of the oscillation period, and the second half of the period will slow down. There are two types of bidirectional turbines, the direction of rotation of which does not depend on the direction of flow. This is the turbine of Wales, the rotor blades of which are aerodynamic profiles located across the free stream.
Fig. 9. - Blades of Wales turbine
Aerodynamic profile rejects a large mass of incoming air in the same direction, regardless of the direction of movement of incoming air. The air impulse is constantly deflected, in fig. 9 to the right, then, according to Newton's laws, the force acting on the blades should be directed to the left side. The laws of Newton in this case are working properly, and if such blades are fixed around the circumference, and the circle is fixed on the shaft, the shaft will begin to rotate.
Fig. 10.– Scheme of the Wales turbine
You can improve the design and add guide vanes that will increase the effect.
The second type of bi-directional turbine is the so-called pulsed turbine. This video shows how this turbine works:
Fig. 11.– Diagram of the bidirectional pulsed turbine
The impulse turbine works more efficiently than the Wales turbine due to the more perfect shape of the rotor blades.
For the first experiments on the generation of electricity on my engine, I chose the simplest method and at the same time the most inefficient - using an ordinary low-frequency speaker.
Fig. 12. - Linear converter from speaker
Here in this video I talk about how I created and tried to configure the resulting homemade linear alternator:
I attached the speaker to the resonator of the engine through the adapter, which I printed on a 3D printer.
Fig. 13. - Connecting the speaker
Attached to the resonator from the side of the cold heat exchanger in order not to melt the plastic adapter with high temperature and not to damage the speaker itself. Earlier, I measured the acoustic power of the engine. Power was about 10 watts. Naturally, only part of this power can be converted into electricity. Recalling Figure 6 - the distribution of acoustic power, as a linear alternator, I chose a YDN-78-1 speaker with a maximum power 2 times less than the maximum power, namely 5 W.
The most difficult thing when using a linear alternator is to set up a system consisting of a speaker and an adapter to the resonant frequency of the engine itself. The difficulty is that the oscillation frequency of the engine varies at different heating temperatures of hot heat exchangers, that is, at different levels of thermal power supplied.And all because the more heat output you fail, the greater the average gas temperature inside and with increasing gas temperature the speed of sound in the gas increases, and accordingly the frequency of oscillations. At the same time, measurements made by Aster Thermoacoustics show that the output power of the linear converter strongly depends on the coincidence of its resonant frequency with the resonant frequency of the engine.
Fig. 14. Dependence of the relative output power on the resonant frequency of the engine
Experiments with my engine showed that increasing the temperature of hot heat exchangers from 120 degrees Celsius to 220 degrees, the oscillation frequency increases from 61 Hz to 64 Hz, that is, it changes to 3 Hz. In fig. 14 - Aster Thermoacoustics graph shows the motor frequency on the horizontal axis, and the vertical electrical output power of the linear converter divided by the maximum power of the converter in the entire frequency range (the maximum value on the graph is one). In fig. 14 that when the motor resonant frequency deviates from the resonant frequency of the converter by 5 Hz, the output power drops by 2 times. This means that a thermo-acoustic generator with a linear alternator can work effectively only at a certain level of supplied thermal energy. If you deviate from this optimal point, the output characteristics will fall sharply.
So, the resonant frequency of my engine is 61 - 63 Hz. I did not find speakers with such a low resonant frequency (it is possible that they do not exist at all for such a small power). The resonant frequency of my speaker was originally 147 Hz. How did I measure it?
Fig. 15. - Scheme for determining the resonant frequency of the speaker
I used the scheme from the magazine "Radio" issue №4 1967, 45 page. This is a circuit of a self-oscillating electric circuit, in which there are neither inductances, nor capacitances, therefore, according to the idea, the oscillation frequency of such a circuit is determined by the oscillation frequency of the mechanical oscillatory system - the diaphragm of the dynamics.
Then I reduced the speaker frequency to 61 Hz, sticking clay onto the diaphragm. This increased the mass of the diaphragm and thus reduced the frequency.
After that, I inserted the tuned speaker into the orange adapter. What was my surprise when, instead of the oscillation frequency of 63 Hz, I found the oscillation frequency of 187 Hz, that is, three times more than expected. The 3rd harmonic is excited. Three wavelengths began to fit in the engine body, but not one. In fact, in the engine there are always no main harmonics, just usually thermo-acoustic devices operate at the first harmonic, that is, at the fundamental frequency, and the contribution of the other harmonics is negligible. I was very surprised by the effect of the excitation of the 3rd harmonic in this experiment with the speaker and I began to think how it happened. I came to the conclusion that this effect occurs due to the fact that the speaker is built into the resonator of the engine through an adapter and you need to consider the resonant frequency not of the speaker separately, but of the speaker together with the adapter. The adapter greatly increases the resonant frequency of the entire bundle. Therefore, in order to achieve work at a fundamental frequency of 63 Hz, it is necessary to lower the resonant frequency of the speaker even more.
Fig. 16. - Speaker, encrusted with nuts on the diaphragm. (object of contemporary art)
And indeed it worked, as expected. It was possible to change the mode of operation of the engine to work with the main frequency.There were even very interesting transients, when, at a certain mass, stuck on the diaphragm, the engine then worked at the main frequency, then as the hot heat exchangers cooled, it began to work at tripled frequency. Interestingly, the engine cannot operate at twice the frequency. Either on the main, or on tripled. Apparently the wave parameters at double frequency are not suitable for maintaining the operation of this device.
When using the dynamics and the engine with air at atmospheric pressure as a working fluid, the energy conversion efficiency turned out to be negligible.
In order to achieve efficiency levels of 20–40% of the Carnot cycle, it is necessary to increase the pressure in the engine, replace the working gas with helium or argon, and use other methods of generating electricity than a conventional speaker.