Persistence of Asymmetry in Nonaxisymmetric Entry Flow in a Circular Cylindrical Tube and Its Relevance to Arterial Pulse Wave Diagnosis

Abstract

In an experiment motivated by the study of arterial blood flow along the lines suggested by the traditional Chinese medicine, the flow in a pipe whose lumen was blocked by a semi-circular plug two tube-diameters long was visualized by suspended particles, recorded by cinematography, and analyzed digitally. The Reynolds number was in the range of 100 to 450 based on the pipe diameter, similar to that of blood flow in the radial artery in the arms of man. The blockage was found to have a profound effect on the velocity profile of the flow in the wake, but it had little influence on the symmetry of the velocity profile upstream of the block, except in its immediate neighborhood. When the end conditions far away from the block were steady, the flow in the wake was steady. The asymmetry of the flow in the wake can be judged by the deviation of the location of the maximum axial velocity from the center line of the pipe as seen in the plane of symmetry of the blockage. Our results show that the deviation can be described as the sum of two components. The first is a strong one which decays exponentially in an entry length which is about twice as long as the classical Boussinesq entry length of axisymmetric flow. The second is a weaker component which is wavy spatially and persists far downstream (many times the entry length). The separated flow and vortex system behind the blockage are sensitive to the flow rate. The relevance of these findings to the arterial pulse wave diagnosis methods used in the traditional Chinese medicine is discussed. We show that the human arteries are shorter than the entry length, hence nonaxisymmetric disturbances can be propagated throughout the circulation system. We propose that the propagation of the persistent, small, wavy asymmetric wave is relevant to the “localization” of the spheres of influence of internal and external organs in a two-inch region of the radial artery. We propose further that the method of pressing hard on the artery to “feel” the pulse is to amplify the signal by creating a wake that is very sensitive to velocity of flow.