Evaluation of commonly used assumptions for isolated and cluster heptane drops in nitrogen at all pressures

Abstract

A study is performed to assess commonly used assumptions in the modeling of drop behavior in moderate to high temperature surroundings and at all pressures. The model employed for this evaluation has been previously validated for isolated drops by using microgravity data, and is very general: it contains Soret and Dufour effects, does not assume mass transfer quasi-steadiness at the drop boundary, or necessarily the existence of a drop surface (i.e., phase discontinuity). Moreover, the numerical simulations are performed with accurate equations of state and transport properties over a wide range of thermodynamic variables. Consistent with low pressure conditions, the drop boundary is identified a posteriori of the calculations with the location of the largest density change. Simulations are here performed for isolated drops, and for monodisperse as well as binary size drop clusters. The results show that at locations arbitrarily near the boundary, the drop does not reach the mixture critical point within the wide range of conditions investigated (far-field temperatures of 470–1000 K and pressures ranging from 0.1 to 5 MPa). However, the state arbitrarily near the boundary is closer to the critical condition for smaller drops in a cluster than for the larger drops. Evaluations of the effect of the relaxation time at the drop boundary show that quasi-steadiness of the mass transfer prevails for drops of radius as small as 2 × 10^(−3) cm. Finally, the diameter squared exhibits a linear time variation only at atmospheric pressure. At all other pressures investigated (1–5 MPa), the diameter squared displays a negative curvature with time which never becomes linear. In agreement with existing experimental data, the drop lifetime increases monotonically with pressure at low far field temperatures (470 K), but exhibits a maximum as a function of pressure at high temperatures (1000 K). On an appropriate scale, the slope of the diameter squared versus time is shown to be independent of the drop size at all pressures.

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