A thermoacoustic device takes advantages of the fact that in a sound wave parcels of gas alternatively compress and expand
adiabatically, and pressure and temperature change simultaneously; when pressure reaches a maximum or minimum, so does the temperature. The device basically consists of
heat exchangers, a
resonator and a stack (on standing wave devices) or
regenerator (on travelling wave devices). Depending on the type of engine, a
driver or
loudspeaker might be used to generate sound waves. In a tube closed at both ends, interference can occur between two waves traveling in opposite directions at certain frequencies. The interference causes
resonance and creates a standing wave. The stack consists of small parallel channels. When the stack is placed at a certain location in the resonator having a standing wave, a temperature differential develops across the stack. By placing heat exchangers at each side of the stack, heat can be moved. The opposite is possible as well: a temperature difference across the stack produces a sound wave. The first example is a heat pump, while the second is a prime mover.
Heat pump Creating or moving heat from a cold to a warm reservoir requires work. Acoustic power provides this work. The stack creates a pressure drop. Interference between the incoming and reflected acoustic waves is now imperfect. The difference in amplitude causes the standing wave to travel, giving the wave acoustic power. Heat pumping along a stack in a standing wave device follows the
Brayton cycle. A counter-clockwise Brayton cycle for a
refrigerator consists of four processes that affect a parcel of gas between two plates of a stack. •
Adiabatic compression of the gas. When a parcel of gas is displaced from its rightmost position to its leftmost position, the parcel is adiabatically compressed, increasing its temperature. At the leftmost position the parcel now has a higher temperature than the warm plate. •
Isobaric heat transfer. The parcel's higher temperature causes it to transfer heat to the plate at constant pressure, cooling the gas. •
Adiabatic expansion of the gas. The gas is displaced back from the leftmost position to the rightmost position. Due to adiabatic expansion the gas cools to a temperature lower than that of the cold plate. •
Isobaric heat transfer. The parcel's lower temperature causes heat to be transferred from the cold plate to the gas at a constant pressure, returning the parcel's temperature to its original value. Travelling wave devices can be described using the
Stirling cycle.
Temperature gradient Engines and heat pumps both typically use stacks and heat exchangers. The boundary between a prime mover and heat pump is given by the temperature gradient operator, which is the mean temperature gradient divided by the critical temperature gradient. :\Iota = \frac{\nabla T_{m}}{\nabla T_{crit}} The mean temperature gradient is the temperature difference across the stack divided by the length of the stack. :\nabla T_{m} = \frac{\Delta T_{m}}{\Delta x_{stack}} The critical temperature gradient is a value that depends on characteristics of the device such as frequency, cross-sectional area and gas properties. If the temperature gradient operator exceeds one, the mean temperature gradient is larger than the critical temperature gradient and the stack operates as a prime mover. If the temperature gradient operator is less than one, the mean temperature gradient is smaller than the critical gradient and the stack operates as a heat pump.
Theoretical efficiency In thermodynamics the highest achievable efficiency is the
Carnot efficiency. The efficiency of thermoacoustic engines can be compared to Carnot efficiency using the temperature gradient operator. The efficiency of a thermoacoustic engine is given by :\eta = \frac{\eta_{c}}{\Iota} The
coefficient of performance of a thermoacoustic heat pump is given by :COP = \Iota \cdot COP_{c} == Practical efficiency ==