Study On The Microscopic Model Of The Aerodynamic Sound Field Based On The Path Integral

Theoretical analysis and numerical methods were mainly used to study the soundpropagation and acoustic properties in the aerodynamic sound field at present. It’s not outof the two framework..This paper attempts to use the quantum mechanical methods toestablish the micro-model of sound propagation in themacro-gas sound field, and studythe molecular and quantum properties of which.The partition function plays a role of connecting link between macro-phenomenaand micro-phenomena in statistical thermodynamics. The partition function of the air andits calculation method are studied in this paper. Statistical method and the quantum methodwhich is based on the Gaussian computer program are used to calculate the partitionfunctions of the oxygen molecule and nitrogen molecule. The linear expressions of the totalinternal partition functions of the oxygen and nitrogen molecules were obtained. Theresults showed that the calculation results of these two methods were very consistent. Theresults of the simplified linear expressions were compared with the HITRAN database andexisting results at home and abroad, the value of error was about1%. Finally thecalculation result of the partition function of1mol air at298K was given.Path integral theory well contacted with the classical physics and quantum mechanics.A microscopic model of sound propagation was established in this paper, A small group ofair (body element) of10-6m was regarded as a harmonic oscillators. This seriesof harmonic oscillator were quantized into the harmonic oscillator field by Feynman’s pathintegral method. And the energy equation and the wave function of the system wereobtained. The probability amplitude (transition rate) of the system was associated with thepartition function by the density matrix, The path integral was used to calculate thevibrational partition functions of oxygen and nitrogen molecular, we found that comparedto external translation, the internal vibrations of molecules can be neglected, and soundpropagation phenomena is the results of overall movement of the molecules.This paper considered the harmonic oscillator interacting with the macro-sound field,discussed the sound pressure as an external driving force on the role of the harmonic oscillator, and when the air itself can be a sound source, the simple harmonic oscillator asthe source effected with the sound field. In the jet occasions, the air flow rate is high,the oscillator source only works near the jet exit, which was helpful to us to understand themechanism of the jet sound. Finally, as the calculation example, a sound pressure data wasused to calculate the energy of acoustic field and the ground state energy of the soundpressure-driven harmonic oscillator. It can be seen, they had the same magnitude, whichshowed that the selected harmonic oscillator model was appropriate.