Simulating pulsatile flows through a pipe orifice by an immersed-boundary method

A pulsatile laminar flow of a viscous, incompressible fluid through a pipe with a sudden constriction (an orifice) was simulated by an immersed-boundary method. A fluid is forced to move by an imposed sinusoidally varying pressure difference, Δp (t). For a pulsatile flow through a pipe orifice, an oscillating recirculation bubble develops behind the orifice. The induced flow rate, Q(t), the recirculation bubble length, L_b(t), as well as their phase shift (φ_Q, φ_L) with respect to the imposed pressure difference were computed for different constriction ratios and the Womersley (Ws) number.