NUMERICAL SIMULATION OF STEADY FLOW IN A COMPLIANT TUBE OR CHANNEL WITH TAPERED WALL THICKNESS

Flow through compliant tubes with linear taper in wall thickness is numerically simulated by finite element analysis. Two models are examined: a compliant channel and an axisymmetric tube. For verification of the numerical method, flow through a compliant stenotic vessel is simulated and compared to existing experimental data. Steady two-dimensional flow in a collapsible channel with initial tension is also simulated and the results are compared with numerical solutions from the literature. Computational results for an axisymmetric tube show that as cross-sectional area falls with a reduction in downstream pressure, flow rate increases and reaches a maximum when the speed index (mean velocity divided by wave speed) is near unity at the point of minimum cross-sectional area, indicative of wave-speed flow limitation or “choking” (flow speed equals wave speed) in previous one-dimensional studies. For further reductions in downstream pressure, the flow rate decreases. Cross-sectional narrowing is significant but localized. For the particular wall and fluid properties used in these simulations, the area throat is located near the downstream end when the ratio of downstream-to-upstream wall thickness is 2; as wall taper is increased to 3, the constriction moves to the upstream end of the tube. In the planar two-dimensional channel, area reduction and flow limitation are also observed when outlet pressure is decreased. In contrast to the axisymmetric case, however, the elastic wall in the two-dimensional channel forms a smooth concave surface with the area throat located near the mid-point of the elastic wall. Though flow rate reaches a maximum and then falls, the flow does not appear to be choked.