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Translational motion as well as expansion and contraction of a fluid parcel are numerically simulated using Rott equations inside a narrow tube of a stack in a thermoacoustic engine. Nonlinear effect is partially taken into account by numerically calculating the nonlinear advective derivative of particle velocity. Due to the nonlinear effect, numerical simulations result in gradual shift of mean position of a fluid parcel to higher temperature side of a stack, which is the Stokes drift. The velocity of actual acoustic streaming is the sum of the Stokes drift velocity and the mean Eulerian velocity at a fixed point estimated by experimentally or numerically. The refined numerical simulations of evaporation and condensation of water vapor in a wet stack using the model developed by the authors [J. Acoust. Soc. Am. 141, 4398-4407 (2017)] have indicated that pV work done by a fluid parcel increases by evaporation and condensation due mainly to more increase in mean volume of a fluid parcel by evaporation.

Numerical nonlinear formulation of Rott equations for a thermoacoustic engine: Acoustic streaming and phase change