Thermoacoustics
Thermoacoustics is the interaction between temperature, density and pressure variations of acoustic waves.
A similar effect is observed if one side of a stainless steel tube is at room temperature (293 K) and the other side is in contact with liquid helium at 4.2 K. In this case, spontaneous oscillations are observed which are named "Taconis oscillations".
Technologically thermoacoustic devices have the advantage that they have no moving parts, which makes them attractive for applications where reliability is of key importance.
Glass blowers produced heat-generated sound when blowing a hot bulb at the end of a cold narrow tube.
This phenomenon also has been observed in cryogenic storage vessels, where oscillations are induced by the insertion of a hollow tube open at the bottom end in liquid helium, called Taconis oscillations,[7] but the lack of heat removal system causes the temperature gradient to diminish and acoustic wave to weaken and then to stop completely.
Byron Higgins made the first scientific observation of heat energy conversion into acoustical oscillations.
Feldman mentioned in his related review that a convective air current through the pipe is the main inducer of this phenomenon.
Sondhauss observed that sound frequency and intensity depends on the length and volume of the bulb.
Lord Rayleigh gave a qualitative explanation of the Sondhauss thermoacoustic oscillations phenomena, where he stated that producing any type of thermoacoustic oscillations needs to meet a criterion: "If heat be given to the air at the moment of greatest condensation or taken from it at the moment of greatest rarefaction, the vibration is encouraged".
[9] This shows that he related thermoacoustics to the interplay of density variations and heat injection.
Rott made a breakthrough in the study and modeling of thermodynamic phenomena by developing a successful linear theory.
[5] Usually sound is understood in terms of pressure variations accompanied by an oscillating motion of a medium (gas, liquid or solid).
However, at sound levels of 180 dB, which are normal in thermoacoustic systems, the pressure variations are 30 kPa, the displacements more than 10 cm, and the temperature variations 24 K. A full theory of thermoacoustics[2] should account for the propagation of heat in the fluid as it makes compression cycles during the propagation of the sound wave.
In monochromatic plane waves, with angular frequency ω and with ω=kc, the solution is The pressure variations are given by The deviation δx of a gas-particle with equilibrium position x is given by and the temperature variations are The last two equations form a parametric representation of a tilted ellipse in the δT – δx plane with t as the parameter.
The ellipse of the δT – δx plane is reduced to a straight line as shown in Fig.
It can be shown that the power, transported by sound, is given by where γ is the ratio of the gas specific heat at fixed pressure to the specific heat at fixed volume and A is the area of the cross section of the sound duct.
The thermal penetration depth δκ is the thickness of the layer of the gas where heat can diffuse through during half a cycle of oscillations.
Acoustic oscillations in a medium are a set of time depending properties, which may transfer energy along its path.
Along the path of an acoustic wave, pressure and density are not the only time dependent property, but also entropy and temperature.
Temperature changes along the wave can be invested[clarification needed] to play the intended role in the thermoacoustic effect.
The effect can be used to produce acoustic oscillations by supplying heat to the hot side of a stack, and sound oscillations can be used to induce a refrigeration effect by supplying a pressure wave inside a resonator where a stack is located.
In a thermoacoustic prime mover, a high temperature gradient along a tube where a gas media is contained induces density variations.
The cycle of thermoacoustic oscillation is a combination of heat transfer and pressure changes in a sinusoidal pattern.
Self-induced oscillations can be encouraged, according to Lord Rayleigh, by the appropriate phasing of heat transfer and pressure changes.
Thermal penetration depth is defined as the distance that heat can diffuse though the gas during a time 1/ω.
If the temperature at the left side is high enough, the system starts to produces a loud sound.
Just like in the case of the standing-wave system, the machine "spontaneously" produces sound if the temperature TH is high enough.
The resulting pressure oscillations can be used in a variety of ways, such as in producing electricity, cooling, and heat pumping.
