Thermo-acoustic Modeling and Computational Analysis for Carbon Nanotube Thin Film in Viscous Flow Fields


Student thesis: Doctoral Thesis

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Awarding Institution
  • Tianyun Li (External person) (External Supervisor)
  • C W LIM (Supervisor)
Award date31 Aug 2021


In this thesis, the theoretical modeling and analysis of carbon nanotube thin film thermo-acoustic conversion device are carried out by fully coupled and semi-coupled models in viscous fluids. Differently from the traditional thin film acoustic structures, the thermo-acoustic conversion of carbon nanotube films transfers the harmonic thermal fluctuation to the fluidic medium through heat transfer, which leads to the expansion and contraction of the fluidic medium and directly converts heat energy into acoustic one. With the development of low specific heat capacity materials, the efficiency of thermo-acoustic emission has been greatly improved. Compared with the traditional thin film vibration and piezoelectric materials, the carbon nanotube thin film thermo-acoustic conversion device is able to produce smooth flat frequency response in high frequency band.

Firstly, this thesis introduces the development of thermo-acoustic conversion, including the development of thermo-acoustic materials as well as the experimental and theoretical progress of thermo-acoustics. The theoretical model of thermo-acoustics in viscous fluid is then studied. A fully coupled thermo-acoustic model is deduced from the conservation equation of mass (equation of continuity), momentum (Newton's second law) and energy conservation equation with the consideration of the fluidic viscosity. In order to aviod the complex solution procedure of the fully coupled model, a thermo-acoustic semi-coupled model is further established by reasonable simplification from the thermo-acoustic coupling equations. The coupling condition on acoustic-solid interface is simultaneously studied in viscous fluid, which lays a foundation for further researches on seeking solution of linear and nonlinear thermo-acoustic equations.

Two classical one-dimensional models are discussed by the fully coupled thermo-acoustic model: the planar wave model and the spherical wave model. Afterwards, the generalized thermo-acoustic one-dimensional model and its general solution are given. The planar wave model can be used to evaluate the near-field acoustic response of planar carbon nanotube thermo-acoustic films, whose size can be regarded as infinite. It is worth noting that for the far-field response beyond Rayleigh distance, the far-field response of sound pressure can be approximately predicted by corresponding processing of planar wave model. Nevertheless, the spherical wave model can be used to predict the acoustic response from spherical carbon nanotube thermo-acoustic film or point thermo-acoustic source. In this thesis, the thermo-acoustic wave number is solved by series expansion and parabola approximation. Combined with the corresponding thermo-acoustic-solid boundary conditions, the sound pressure levels of planar and point thermo-acoustic sources can be solved and verified with comparation.

The thermo-acoustic fully coupled model is able to describe a relatively accurate physical field, but it is difficult to get an analytical solution; the traditional thermo-acoustic semi-coupled one can be relatively easy to solve, but it is not accurate to describe the thermal and viscous attenuation in fluids. With the perturbation method, the wave number and the first order approximation of the two thermo-acoustic propagating modes are derived. By means of wave number reconstruction, an improved thermo-acoustic semi-coupled model can be further proposed. An improved thermo-acoustic nonlinear semi-coupled model is constructed by introducing heat conduction nonlinearity, thermal expansion nonlinearity and acoustic nonlinearity. Then, the improved thermo-acoustic semi-coupled model with simple harmonic boundary can be solved by parabolic approximation and traveling wave coordinate transformation with Holf-Cole transformation.

Three-dimensional thermo-acoustic effect of planar films is further discussed. As it is difficult to obtain the analytical solution for the fully coupled thermo-acoustic model, the semi-coupled one is merely discussed, and the integral solution of the three-dimensional response can be obtained. The thermo-acoustic equivalent velocity is additionally derived. By comparing the integral solution with the boundary element one, the validity of the method in this thesis is proved.

Finally, on the basis of thermo-acoustic studies, the magneto-thermo-acoustic effect of planar thin films is further explored. A thermo-acoustic film is placed in a static magnetic field to increase the total sound pressure response significantly, and further explore its characteristics and influencing factors. Subsequently, the thermo-acoustic film is placed in the alternating steady-state magnetic field. The condition of unidirectional emission of acoustic wave is further studied at specific frequency and phase with power function fitting method applied and physical field nondimensionalized.

In this thesis, mathematical models for the thermo-acoustic energy transfer and emission of carbon nanotube films are established. For different working conditions, solutions to one-dimensional and three-dimensional problems, linear and non-linear problems, thermo-acoustic and magneto-thermo-acoustic problems, and their acoustic response predictions are given from simple to complex. The factors affecting the thermo-acoustic response are analyzed from various aspects, which provides references for the design of the thermo-acoustic transducers of carbon nanotube film.

    Research areas

  • Carbon nanotube film, Thermo-acoustic effect, Viscous flow field, Magnetic field, Fully coupled model, Semi-coupled model