# Numerical simulation of flows in a circular pipe transversely subjected to a localized impulsive body force with applications to blunt traumatic aortic rupture

## TL;DR

This study numerically explores how localized impulsive transverse forces affect pulsatile blood flow in a circular pipe, revealing complex secondary flows and their dependence on flow phase, with implications for understanding traumatic aortic rupture.

## Contribution

It introduces a novel numerical analysis of impulsive transverse forces on pulsatile flow, highlighting phase-dependent secondary flow development and proposing a new dimensionless influence parameter.

## Key findings

- Counter-rotating vortices form at the forced boundary
- Secondary flow development varies with flow phase
- Proper orthogonal decomposition reveals flow restoration mechanisms

## Abstract

Much debate surrounds the mechanisms responsible for the occurrence of blunt traumatic aortic rupture in car accidents, particularly on the role of the inertial body force experienced by the blood due to the abrupt deceleration. The isolated influence of such body forces acting on even simple fluid flows is a fundamental problem in fluid dynamics that has not been thoroughly investigated. This study numerically investigates the fundamental physical problem, where the pulsatile flow in a straight circular pipe is subjected to a transverse body force on a localized volume of fluid. The body force is applied as a brief rectangular impulse in three distinct cases, namely during the accelerating, peak, and decelerating phases of the pulsatile flow. A dimensionless number, termed the degree of influence of the body force ({\Psi}), is devised to quantify the relative strength of the body force over the flow inertia. The impact induces counter-rotating cross-stream vortices at the boundaries of the forced section accompanied by complex secondary flow structures. This secondary flow is found to develop slowest for an impact occurring during an accelerating flow and fastest during a decelerating flow. The peak skewness of the velocity field, however, occurred at successively later times for the three respective cases. After the impact, these secondary flows act to restore the unforced state and such dominant spatial structures are revealed by proper orthogonal decomposition of the velocity field. This work presents a new class of problems that requires further theoretical and experimental investigation.