Three dimensional laminar flow in distorting, axisymmetric, axially varying vessels

Area of Science:

• Fluid dynamics
• Rheology
• Biomechanical engineering

Background:

• Accurate characterization of fluid flow is crucial in many scientific and engineering fields.
• Existing models often require complex measurements or simplifications for three-dimensional (3D) flows.
• Understanding Newtonian fluid behavior in complex geometries is essential for applications like blood flow modeling.

Purpose of the Study:

• To develop a method for determining absolute velocity fields and stresses in 3D laminar, viscid flow of Newtonian fluids.
• To provide a framework applicable when vessel dimensions are known and specific velocity measurements are available.
• To demonstrate the method's utility for complex geometries, such as those found in biological systems.

Main Methods:

• Development of a set of equations for three-dimensional laminar, viscid flow.
• Utilizing known vessel dimensions and measuring two simultaneous axial velocities and the central axis velocity gradient.
• Ensuring the equations satisfy geometric constraints and no-slip boundary conditions.

Main Results:

• Absolute values for axial, radial, and tangential velocity fields are determinable everywhere within the vessel.
• Normal and shear stresses can be calculated from the flow field.
• The developed equations are compatible with general dynamic flow expressions and can be used independently for specific problems.

Conclusions:

• The proposed method offers a comprehensive approach to analyzing 3D laminar Newtonian fluid flow.
• It provides a robust tool for determining detailed flow characteristics, including stresses.
• The methodology is applicable to various scenarios, including those with secondary flows and complex vessel geometries like the pulmonary trunk.