The accurate estimation of the entry length required for a flow in a tube to transition from a uniform velocity profile to a fully developed state is crucial in many industrial processes. Although viscoelastic fluids are widely utilized in industrial processes, most studies have concentrated on inelastic fluids. This study employed computational fluid dynamics (CFD) to analyze the developing flow of viscoelastic fluids in a circular tube. An axisymmetric computational domain was employed along with the Giesekus model to represent the viscoelastic fluid flow. The Log Conformation Technique (LCT) was adopted to ensure numerical stability and accuracy at high Weissenberg numbers. The CFD model was first validated against published data for planar contraction flow. After validation and mesh sensitivity analysis for tube geometry, we systematically studied the influence of the Reynolds and Weissenberg numbers, solvent viscosity ratio, and mobility parameter on the entry length. Our results highlight the significant influence of fluid elasticity on flow development. For a constant Wi value, reducing inertia enhances the elastic effects, whereas at a fixed Re number, increasing Wi strongly impacts the developing flow region. Increased elasticity extends the entry length for both velocity and stress fields, with stress typically requiring a longer region to develop fully.

In this work, we present a series of experimental and computational modeling procedures related to precision controls of intermittent dispensing systems for complex fluids. With reductionist approaches, we have modeled key components of dispensing systems with different boundary conditions. With system approaches, we have also connected the pressure differential with the volume flow rate, as well as the characterization of the material properties. Finally, confirmed with a series of experiments and simulations, we demonstrate that traditional reductionist approaches and system modeling tools can be effectively and efficiently employed hand-in-hand with the help of the so-called inversed optimization approaches to derive useful information of relevance for industrial applications.