Linear acoustic characteristics of supercritical droplet vaporization

Our previously developed numerical model of supercritical droplet vaporization is applied to examine the linear acoustic characteristics of liquid-fuel droplets vaporizing in various supercritical environments. The model assumes the hold of phase equilibrium at the droplet surface and incorporates the property of vanishing diffusion coefficient at the critical mixing surface so that the transition to continuous phase change might be simulated. The rate of work conducted by a vaporizing droplet on its surrounding gas provides a fundamental quantity (volume source strength) to examine the way of acoustic interaction between droplet vaporization and ambient gas state fluctuations. In a dilute spray confined in a chamber, the natural pressure oscillation may be excited or attenuated when the amplification rate, which is derived by differentiating the volume source strength with respect to pressure, takes positive or negative values, respectively. The computed amplification rate exhibits distinct behavior in the three regimes of supercritical droplet gasifications, namely: (1) subcritical gasification regime in which the droplet has the surface throughout its lifetime, (2) transitional gasification regime in which the transition to continuous phase change takes place at a finite radius of droplet surface and (3) supercritical gasification regime in which continuous phase change occurs from the beginning. In the subcritical gasification regime, the value of amplification rate changes from positive to negative in a period of time comparable to the droplet temperature relaxation time, and its magnitude is relatively small. The transition to continuous phase change causes the amplification rate to increase abruptly, whereas in the supercritical regime, the amplification rate takes a vanishingly small value. Thus, unusual pressure oscillations may occur for a spray in the transitional gasification regime. The underlying physics are also explained.