Effect of a 3-Dimensional Inlet on the Flow Characteristics in a Symmetric Bifurcation Model of Human Pulmonary System
Authors: Farag Ashraf , Olson Dan E. , Hammersley Jeffery , Ng Terry 
Published: January 2022

Abstract
Steady inspiratory flow is studied within a symmetric bifurcation with 35° bend at the inlet to the model for two different flow rates which are typical to middle and small human airways. The angle of the bend is chosen to yield with the bifurcation model a geometrical correct two generation model as observed in different casts of human airways.
Measurements of the primary and secondary velocity profiles are taken at different axial locations in the model using Laser Doppler in the horizontal and vertical planes. These locations are chosen to follow the expected velocity alterations in the model. The bend is placed in the same plane as the model and at 90° to the plane of the model.
Results obtained indicate that the increased degree of mixing involved with the inlet flow due to the secondary current eliminates any potential for flow separation in the parent tube of the model where the area increase occurs. The centrifugal forces at the onset of the daughter branches overwhelm the various entrance conditions to cause similar flow organization within each branch. The resultant flow field typifies that seen in tight bends under similar Reynolds and Dean conditions. The development of circulations within the core and boundary layer of the flow are compared for a series of biological expected entrance conditions. The wall shear distributions are compared and speculations of the stability and biological effects are considered.
Figures 1 to 3 show the axial velocity profiles in the model at Re = 1600. In these figures the curvature of the entrance flow, or the bend, is placed in the same plane as the model, case A. Figure 1 shows the axial velocity profiles in the parent tube of the model in the plane of bifurcation. It should be noted that the profile at the end of the parent tube (before bifurcation) is similar to what we observed at the exit of the daughter branches with flat velocity entrance profile. This infers that the simple bend gives similar effect as having a two generation branching model. The flow enters the parent tube of the model with the fast moving fluid particle shifted towards one side (left side) and the slow moving fluid particles towards the other (right side). The inflection point observed on the right side develops to a second peak as the flow proceeds downstream. This second peak picks up speed as it moves downstream and finally the flow bifurcates in an asymmetrical fashion with the faster moving flow entering the left daughter branch and the slower flow entering the right branch. The development of a second velocity peak on the slow moving side of the velocity field eliminates any potential for flow separation towards that side (as might be expected).
Figure 4 shows the axial velocity profiles in the plane of the bifurcation at different axial locations l/d = −0.23, −0.60, −0.85, −1.35, and −2.65 upstream the flow divider. In this case, when the bend is placed 90° to the plane of the model, since the fluid with higher velocity is pushed towards the lower wall and is replaced at the upper wall by the slower moving fluid from the vicinity of the outer and inner walls; the M-shaped profile becomes more pronounced as the flow proceeds downstream.
The secondary flow in the model showed complex patterns. This complexity is due to the secondary flow carried on from the bend.
We believe that this work will improve our understanding to the three-dimensional convective organization of air flow in the human airways. The main objective is to understand the effects of the highly vortex flow at the entrance to a bifurcation.