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In this paper we define the extruder analysis in the Eulerian frame. Then, we convert the analysis to the Lagrangian frame to avoid the difficult moving boundary problem. Finally, unlike the classical analysis we convert the solution back to the Eulerian fame before calculation of velocities and flow rates. The single screw pump or extruder has classically been evaluated by leaving the analysis in the Lagrangian reference frame and the flow in the pump is described as due only to down channel drag flow. Since velocity is not frame indifferent, we complete the analysis by transforming the Lagrangian analysis back to the Eulerian solution. The pumping mechanism is quite different when the velocities are properly converted back to the Eulerian frame of reference. This new analysis demonstrates that, if the problem is approached using superposition, the pumping mechanism in a screw pump is due to the “piston like” action of the helix x-component velocity, and that the down channel z-component velocity, drag flow, from the helix and screw core reduce the maximum pump efficiency of the helix by about 50 %.

Frame Indifference: Fluid Flow in Single Screw Pumps and Extruders