This study describes a lumped-element model for a pneumatically actuated, diaphragm-driven pump. The pump was developed to dispense molten metal for automotive electronic circuit manufacturing. In place of a CFD analysis, which proved to involve excessively long computations because of a large range of length scales, we created a lumped-element representation of the physics. The pump has five main region volumes: an air filling chamber, a solder reservoir, an adjustable throttle valve, a main pumping chamber, and a dispensing nozzle or set of nozzles. The pumping process employs a compressed gas pulse, which fills the air chamber and deforms a diaphragm, which then displaces molten solder in the main pumping chamber. The description of the dispensing process requires the coupling of three physical domains: pneumatic, mechanical, and hydraulic. The fluid motion in the pump is modeled by creating lumped fluid elements from control volumes, some with deformable surfaces. The equations for the fluid elements are derived from Bernoulli's equation, when viscous effects are not important, or from the general integral momentum balance, when viscous effects are important. A parametric study describing the relationships between variables is presented, and experimental data is used to confirm the validity of the model. © 2006.
Jairazbhoy, V., & Stevenson, R. C. (2008). Mathematical modeling of molten metal dispensing: A study of a pneumatically actuated diaphragm-driven pump. Applied Mathematical Modelling, 32(2), 141–169. https://doi.org/10.1016/j.apm.2006.11.005