Numerical Study of Viscous Effects on Acoustic Waves

Abstract

Simulasi kaedah berangka 2-dimensi telah dilakukan terhadap gelombang akustik di dalam kebuk akustik tertutup segi empat tepat. Penyelesaian dilakukan terhadap persamaan sistem tak lelurus Navier-Stokes 2-dimensi, aliran tak mantap dengan kelikatan yang berbeza. Kaedah perbezaan tak terhingga digunakan dengan kejituan tertib dua terhadap masa dan ruang. Sempadan halaju ialah tanpa gelincir dan tanpa telus aliran, dengan fluks haba sifar pada dinding kebuk. Gelombang akustik dihasilkan oleh pemacu akustik selaput atau omboh yang terletak pada salah satu dinding menegak. Suhu hasil kajian didapati sama dengan penyelesaian teori dan ujikaji untuk gelombang akustik di dalam suatu kebuk tertutup. Nod suhu (minimum) dan antinod suhu (maksimum) masing-masing wujud pada dinding dan di tengah kebuk. Kata kunci: Kajian berangka; gelombang akustik; selaput; omboh A two-dimensional numerical simulation of acoustic waves in a closed rectangular acoustic chamber is completed. Numerical computations are performed by solving the two-dimensional, unsteady, viscous, non-linear Navier-Stokes system of equations. Finite difference methodology was used accurate to second order both in time and space. No-slip, no through flow and zero heat flux are set boundary conditions. Acoustic waves are generated by a vibrating membrane or piston on one wall. Computations are completed for variation in viscosity of the fluid. Results of the temperature profiles seem to agree with analytical solutions for a standing wave in an enclosure and those obtained experimentally with low perturbation to mean pressure ratio. Temperature nodes and anti-nodes each was found to occur near walls and midway through the chamber respectively, results associated with a half wavelength standing wave. Key words: numerical study; acoustic waves; membrane; piston