*2.2. Boundary Conditions and Simulation Settings*

As shown in Figure 1b, there are three boundary conditions in the two-dimensional model of the flow channel, inlet, outlet, and wall. Among them, the inlet boundary is where the oil enters, Since the intensity of the change of oil flow field at the nozzle is most directly affected by the flow velocity, the inlet oil flow velocity is set as the inlet boundary condition. The outlet oil tank is set as the pressure outlet. The other surface is set as the wall. As shown in Figure 1b, *Vin* represents the velocity inlet, *pout* represents the pressure outlet, and the unspecified surfaces are all wall surfaces.

Fluent 19.0 (ANSYS 19.0, ANSYS, Inc., Canonsburg, PA, USA, 2018) is used for present numerical solution. Since there are vertical pipes in the channel model, the gravity factor should be taken into account and the gravity acceleration is 9.81 m/s2. As mentioned above, flow oscillation is a wave–vorticity coupled flow phenomenon. Therefore, when setting the fluid as a turbulent flow, compressibility must be considered, fluid state as a transient state, and the LES model is suitable for solving model. The pressure–velocity coupling term is selected as the Semi-Implicit Method for Pressure-Linked Equations Consistent (SIMPLEC) algorithm, which is improved by the SIMPLE algorithm. The correction term in the velocity equation is not neglected in each iteration. Therefore, the pressure correction value obtained is generally appropriate, and an under-relaxation coefficient less than 1 can be selected according to the situation to accelerate the convergence of the solution in the iteration process [18]. When factors such as cavitation are not considered, the oil is a single-phase flow. Since the LES model belongs to direct numerical simulation to some extent, the discrete scheme of momentum and size terms are chosen as the second-order upwind scheme with second-order accuracy. Since most of the flow field grids are quadrilateral grids and mainly focus on wave–eddy coupling, it is necessary to observe the eddy effect in turbulence, so in order to avoid errors in the difference value and the eddy effect in turbulence, the discrete scheme is adopted as the second-order upwind scheme with second-order accuracy. The pressure gradient hypothesis on the boundary is advantageous to the flexible calculation, and the pressure term is chosen as PRESTO. In order to ensure continuity, the convergence condition is defined as the third-order residuals of each parameter, and the transient equation is a second-order implicit equation. The time step is 0.0001 s, as shown in Table 2.


**Table 2.** Solution strategy.
