Numerical investigation of a concentration divider for ultrasound calibration using constructal design.

Abstract

This study applies the Constructal Design method to the geometric optimization of a branched symmetric concentration divider for calibrating ultrasound devices used to monitor tumor response with dynamic contrast. Accurate calibration ensures image quality and diagnostic reliability. The geometry consists of a three-dimensional, tree-shaped flow network with two inlets and three outlets, where inlet 1 carries water containing contrast particles, while inlet 2 carries only water. Laminar flow simulations are performed using Computational Fluid Dynamics (CFD) with Ansys Fluent, assuming no-slip wall conditions and zero-pressure outlets. The analysis investigates the effects of the inlet velocity ratio, the diameter ratio, and the vertical positions of the central outlet and inlet tubes, while keeping the total volume and inlet diameter constant. Additionally, velocity, pressure, particle distributions, flow partition ratio, and hydraulic resistance are evaluated. Results show nearly linear concentration responses among the outlets (100%, 50%, and 0%) when the device approaches geometric symmetry with equal inlet velocities, demonstrating efficient control of flow splitting. Although the diameter ratio imposes a trade-off with hydraulic resistance, geometric symmetry combined with Constructal Design promotes improved flow uniformity and enhanced performance, with potential applications in microfluidic mixers that require precise intermediate concentrations.