# Performance Study of a Fluidic Hammer Controlled by an Output-Fed Bistable Fluidic Oscillator
## 3 Numerical Procedure
### Methodology of Simulation and Computational Domains  
The flow fields of fluidic oscillators are similar to that of the fluidic devices which have been numerically andexperimentally investigated.Tesar and [PERSON] [26] performed a study, by means of CFD computations and PIV (Particle Image Velocimetry) measurements, aimed at clarifying the behavior of a typical fluidic valve at low Reynolds numbers. By using simplified 2D computation CFD models, [PERSON] et al. [27] investigated the effect of varying structural parameters on the flow characteristics of the fluidic flowmeter, and they found that the numerical results were consistent with the experimental results. In order to investigate the flow behavior in monostable mini- and micro-oscillators, [PERSON] et al. [28] proposed a hybrid simulation approach, which consists both of the 2D CFD simulation and analytical modeling method. Presumably due to the traditional planar design of the fluidic devices, the challenges existing in the difficulty of convergence, and huge demand on computer resources, there have been fewer CFD studies based on the 3D computational models on fluidic oscillators than other numerical studies, namely, the use of 2D simulation models or the analytical modeling. Considering that the relaxation bistable oscillator is a 2D analogue of the Tesar-Zimmerman oscillator [29] (3D feedback loops), the output-fed bistable fluidic oscillator studied here can certainly loop around the vents in 2D topologically. However, for an output-fed bistable fluidic oscillator in the fluidic hammer, the movement of the impact body is influential to the oscillating behavior of the oscillator. There exists acomplex coupling relationship between the fluid flow in the output-fed fluidic oscillator and the movement of the impact body. Simulations on an isolated output-fed bistable fluidic oscillator are deficient and unreasonable. In the fluidic hammer, because of the nonplanar cylinder and the impact body, the fluid flows in the working chambers and the passages connecting them are not planar or axisymmetric, thus the use of 2D computational models are apparently not suitable. Besides, in order to retain a high level of predictive accuracy, analytical modeling method depending heavily on experimental data is not desirable.  
The above review points out the need to use more elaborated models to simulate the fluid flow inside an output-fed bistable fluidic oscillator coupling with the movement of the impact body. The dynamic mesh modeling technique using 3D computational models has provided a promising approach to clarify the flow behavior in the fluidic hammer, as the computational domains can be updated automatically at each time step based on the moving positions of the impact body. Therefore, CFD simulation method with the technique of dynamic mesh was used in this study.  
The computational flow domain of a typical fluidic hammer includes the flow field of a fluidic oscillator, the front and rear chambers of the cylinder, the connecting passages between the fluidic oscillator and the cylinder, the outer flow field of the impact body, and the side passages connecting with the vents and the outer flow field of the impact body. Three different mesh densities with mesh sizes varying from 180,000 to 750,000 for the fluidic hammer were calculated. After performing the grid independence analysis from the geometry spatial discretization and considering the reasonable computational time and the satisfactory model accuracy, medium grids were used in this study. One of the computational domains is showed in Figure 4. In this grid there are total 368,522 cells, of which 9752 cells are pentahedrons, and the others are hexahedrons.  
Figure 4: A typical 3D grid model of flow domain and the boundary condition types.