Analyses of spray break-up mechanisms using the integral form of the conservation equations

Quadratic formula for determining the drop size in pressure-atomized sprays with and without swirl

“…[20][21][22] We present the equations here for the purpose of placing this work in context. We consider a control volume that envelops the spray including all its complex break-up and atomization mechanisms, as shown in Figure 1.…”

“…K is the only adjustable constant in this formulation, as the exact relationship between the viscous dissipation terms and the spray volume is approximated. The dissipation term in our previous work [20][21][22] was only dimensionally correct and ad hoc. It led to some reasonable results, but also caused some numerical difficulties when the liquid velocity was large or close to the injection velocity.…”

“…The liquid-and gas-phase momentum equations can be included in iterative numerical solutions, [20][21][22] which would involve the drop drag coefficient and effects of density of both gas (in the drag term) and liquid (in the momentum term). Such momentum effects have been discussed in length in one of our previous works.…”

“…This is a departure from existing methods, where conservation laws are applied in an integral form between "asymptotic" states, therefore bypassing the need for detailed modeling nor complex set of assumptions. Validations of the solutions have been provided in our previous works, [20][21][22] and this method is viable in solving for the drop size and velocities. Both the mean drop and size distributions, obtained using the current method, agree well with experimental data.…”

“…[20][21][22] In this approach, the conservation equations for spray flows, after some algebraic work, render themselves solvable through iterative methods. The key is to use the integral form of the conservation equations so that the input injection parameters are related to the output spray parameters, without having to resolve the details of the atomization physics.…”