# Influence of Baffle Location on the Diodicity of Tesla Valves
## 2 Problem Setup
### Simulation Methods  
Figure 4 presents the meshing details of the single-stage TV, delineating the comprehensive meshing of its fluid domain. In this investigation, water at a temperature of approximately 20 \({}^{\circ}\)C serves as the working fluid. Referring to the standard thermophysical properties, the density of water is recorded as 998.2 kg/m\({}^{3}\), and its dynamic viscosity is 0.001 Pa-s. An inlet boundary condition specifying velocity is imposed at the inlet, while an outlet boundary condition specifying pressure is applied at the outlet. The outlet gauge pressure is prescribed as 0 Pa, reflecting this study's focus on the flow characteristics of the TV under normal operating conditions, excluding cavitation effects. The locations of the inlet and outlet are ascertained in accordance with the flow direction as depicted in Figure 1. The remaining boundaries of the model are designated as smooth, no-slip wall boundaries.  
Figure 1: Geometric parameters of the single-stage Tesla valve (unit: mm).  
Figure 2: Optimization cases for Tesla valve. Cases 1-4 with the baffle at different positions are shown in (**a**), (**b**), (**c**), and (**d**), respectively.  
The continuity and incompressible Navier-Stokes equations are used in the following form:  
\[\rho(\mathbf{u}\cdot\
abla)\mathbf{u}=-\
abla p+\mu\
abla^{2}\mathbf{u} \tag{2}\]  
\[\
abla\cdot\mathbf{u}=0 \tag{3}\]  
where \(\rho,\mathbf{u},p,\text{and }\mu\) denote the density, velocity, pressure, and dynamic viscosity of the fluid. The simulations detailed in this paper were performed utilizing the pressure-based steady solver within Ansys Fluent. Given that the Reynolds number is within the range from 1 to 300, a laminar flow model was employed for this analysis. The steady-state flow field solution was achieved using the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm for pressure-velocity coupling. Both convective and diffusive terms were discretized employing a second-order upwind scheme. The convergence criteria were established to ensure computational convergence when the residuals for the continuity equation and the momentum conservation equation fell below \(1\times 10^{-6}\).  
Grid partitioning is a critical component of numerical flow field simulations. Ensuring an adequate number and high-quality grid is essential for obtaining reliable numerical computation results, achieving good convergence, and maintaining high computational  
Figure 4: Meshing of the single-stage Tesla valve.  
Figure 3: Optimization cases for Tesla valves with two baffles. Cases 5-8 with the baffle at different positions are shown in (**a**), (**b**), (**c**), and (**d**), respectively.  
efficiency. While sparse grids may compromise numerical accuracy, overly dense grids can lead to prolonged computational times and excessive resource utilization. As illustrated in Figure 5, by balancing computational accuracy with laboratory server capabilities, this study opted for a grid count of 500,000 for the single-stage TV. The linear relationship between the Di and the Reynolds number, as illustrated in Figure 6, is consistent with the findings reported by [PERSON] et al. and [PERSON]. The grid quality of the fluid domain for the single-stage TV exceeds 0.8, signifying that the grid resolution is adequate to ensure the simulation's accuracy.