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Velocity histories of vaporizing fuel drops moving through stagnant gas

Publication Date
DOI: 10.1016/0016-2361(75)90003-4
  • Mathematics


Abstract Newton's second law of motion has been applied here to a vaporizing drop being depleted according to the ‘d 2-relation’ in order to determine the velocity histories of drops injected vertically into stagnant gas. In the evaluation of the drag forces, three possible values of drag coefficient, namely Stokes value based on instantaneous velocity and diameter, Stokes value based on average velocity and initial diameter, and a constant value of 1.0 independent of Reynolds number (for which there is experimental justification at Reynolds numbers not too small), have been employed. The second and third cases result in non-linear differential equations for the velocity histories, and have been solved using the Runge-Kutta-Nyström method. The effects on the histories of the initial velocity with which the drops are injected into the ambient gas, either vertically down or up, have been investigated for all three drag values. The results have been plotted in terms of normalized coordinates which (unlike others in the literature) are shown to have physical significance. The concept of a terminal velocity does not apply for a particle whose size is decreasing with time. The velocity histories for the two Stokes drag coefficients are quite similar, despite the considerably different manner in which the Reynolds number is defined in the two cases; this vindicates the common practice of calculating and correlating experimental values of ( Re) and C D on the basis of initial diameter and average velocity for the sake of convenience and practicality. For large downward injection velocities, the gravitational and buoyancy forces can be neglected, especially for the two cases of Stokes C D ; but the errors for all three cases of upward injection are too significant to be neglected.

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