Direct ink writing (DIW) is an extrusion-based additive manufacturing (AM) technique. One of the required factors for printing quality in DIW is to extrude continuous and tubular freeform extruded filaments (FEF) with diameters close to the nozzle inner diameter. This paper established a simulation model of FEF with volume of fluid (VOF) method and then evaluated the FEF based on the simulation results. First, ink properties including density, surface tension coefficient and rheological properties were determined by properties tests. Then, the model of FEF was established using VOF simulation method with the software Open FOAM and two evaluation indicators, mean diameter and stability, were proposed to evaluate the FEF. Two inks, a cellulose ink and a Nivea Crème, were used under three levels of piston velocity to verify the method universality for different inks and variable process parameters. The prediction accuracy of the established simulation model was verified as the relative error between simulation and experimental results of diameter was less than 10.22%. In this work, it was found that: (1) piston velocity needed to be set higher than a minimum value to overcome yield stress and surface tension to successfully extrude filaments; (2) mean diameter of FEF decreased while stability of FEF decreased firstly and then increased as piston velocity increased. The proposed model and evaluation indicators gave an accurate and effective framework to analyze effect of the piston velocity on FEF, characterize the ink printability and find suitable printable windows for process parameters in DIW.