*2.1. Numerical Method*

Ansys CFX commercial software based on finite volume method was used to run pulsatile flow simulations in this study. According to previous experimental results, especially in the studies of velocity and pressure distribution, blood flow was assumed incompressible, turbulent, and Newtonian [2,4].

The continuity equation and the Reynolds-averaged Navier–Stokes (RANS) equation can be written as follows:

$$\frac{\partial u\_l}{\partial \mathbf{x}\_l} = 0 \tag{1}$$

$$\frac{\partial \mu\_i}{\partial t} + \frac{\partial u\_i u\_j}{\partial \mathbf{x}\_j} = -\frac{1}{\rho} \frac{\partial P}{\partial \mathbf{x}\_j} + \frac{1}{\rho} \frac{\partial}{\partial \mathbf{x}\_j} (\mu(\frac{\partial u\_i}{\partial \mathbf{x}\_j} + \frac{\partial u\_j}{\partial \mathbf{x}\_i}) - \rho \overline{u\_i' u\_j'}) \tag{2}$$

where ρ is the blood density, *u* is the velocity, *P* is the pressure, and μ is the dynamic viscosity. These governing equations are numerically solved for the pressure and velocity profiles in the flow field.

$$p(\mathbf{x}, y, z, t) = p\_{\mathbf{m}}(\mathbf{x}, y, z, t) + p'(\mathbf{x}, y, z, t) \tag{3}$$

$$v(\mathbf{x}, y, z, t) = v\_{\mathbf{m}}(\mathbf{x}, y, z, t) + v'(\mathbf{x}, y, z, t) \tag{4}$$

As shown in Equations (3) and (4), all of the spontaneous variables are decomposed into average values and fluctuating components [14]. For example, where *p* is the transient pressure at some point in the flow field, *p*<sup>m</sup> and *p* represent the time-average pressure and time-average pulsating pressure, respectively.

In this study, the pressure pulsation of the BMHV internal flow field under different flow rate and opening angle conditions was analyzed by the non-dimensional coefficient of pressure pulsation.

$$\pi = p'(x, y, z, t) / (\rho u^2 / 2) \tag{5}$$

where τ is the coefficient of pressure pulsation (it was proposed to evaluate the impact on pressure pulsation induced by unsteady blood flow).
