# Numerical and Experimental Analysis of Pressure Pulsation Attenuator Based on Helmholtz Resonator
## 4 Fluent-Based Pressure Pulsation Dynamic Characteristics Simulation Analysis  
In this paper, the simulation analysis is performed in Ansys Workbench using the Fluent module, and the simulation process is divided into two parts: steady-state analysis and transient analysis, where the results of steady-state analysis are used as the initial state of transient analysis to improve the computational convergence. Prior to the simulation, the following assumptions were made about the fluid state: the pulsation attenuator is ideal and fits precisely with the hydraulic system piping with no radial clearance and no leakage. The fluid domain model is a loss-free model with constant dynamic viscosity \(\mu\). It is assumed that there is no heat transfer within the system, and the energy exchange with the outside world is ignored. Standard k-epsilon is selected for the model, standard wall functions are set for the incoming wall treatment and the rest of the settings are default. The turbulence intensity is set to 6%, and the turbulence length scale is 0.016 m. Set gravitational acceleration g = 9.81 m/s\({}^{2}\). The specific control equations are as follows:  
Continuity equation:  
\[\frac{\partial\rho}{\partial t}+\frac{\partial(\rho u)}{\partial x}+\frac{ \partial(\rho v)}{\partial y}+\frac{\partial(\rho w)}{\partial z}=0 \tag{22}\]  
Momentum equation of incompressible viscose fluid:  
\[\rho\frac{\mathrm{d}u}{\partial t}=\rho f-\mathrm{grad}p+\frac{\mu}{3}\mathrm{ grad}(\
abla u)+\mu\
abla^{2}u \tag{23}\]  
The turbulence model employs a standard k \(-\)\(\varepsilon\) double equation model:  
\[\frac{\partial}{\mathrm{d}t}(\rho k)+\frac{\partial}{\mathrm{d}x_{i}}\big{(} \rho uj\big{)}=\frac{\partial}{\partial x_{i}}\Bigg{[}\bigg{(}\mu+\frac{\mu_{ i}}{\sigma_{k}}\bigg{)}\frac{\partial k}{\mathrm{d}x_{j}}\Bigg{]}+G_{K}+G_{b}- \rho\varepsilon-Y_{M}+S_{K} \tag{24}\]  
\[\frac{\partial}{\mathrm{d}t}(\rho\varepsilon)+\frac{\partial}{\mathrm{d}x_{i} }\big{(}\rho uj\varepsilon\big{)}=\frac{\partial}{\partial x_{i}}\Bigg{[} \bigg{(}\mu+\frac{\mu_{i}}{\sigma_{k}}\bigg{)}\frac{\partial\varepsilon}{ \mathrm{d}x_{j}}\Bigg{]}+C_{1\varepsilon}\frac{\varepsilon}{k}(G_{K}+C_{3 \varepsilon}G_{b})-\rho C_{2\varepsilon}\frac{\varepsilon^{2}}{k}+S_{\varepsilon} \tag{25}\]  
In the above laws, \(\rho\) is the fluid density; \(u\), \(v\), \(w\) are the velocity component of the velocity vector in the directions \(x\), \(y\) and \(z\); \(\mu\) is the dynamic viscosity of fluid; \(\mu_{t}\) is the turbulent viscosity; \(G_{k}\), \(G_{b}\) are turbulent energy terms; \(C_{1\varepsilon}\), \(C_{2\varepsilon}\),\(C_{3\varepsilon}\) are empirical constants, which are 1.44, 1.92, and 0.99, respectively; \(\sigma_{k}\), \(\sigma_{\varepsilon}\) are Prandtl numbers of turbulence, which are 1.0 and 1.3, respectively. 1. Using the structural parameters in Table 1, build a geometric model of the HTPA (as shown in Figure 7). Extract the fluid domain in the Fluent module and complete the meshing of the fluid domain. The maximum number of layers was set to 5. In order to better capture the vortices at the duct-neck joint sections, the mesh size was set to 1 mm and the number of cells to 1,500,074 [34]. 2. Definition of material properties: the internal fluid was selected as No. 46 anti-wear hydraulic oil, and each parameter of the fluid is shown in Table 2.
3. Boundary condition setting: the inlet boundary condition is set to mass flow inlet. The average mass flow rate is 0.53416 kg/s: \[\Phi=\Phi_{0}+\Phi_{1}sin(2\pi f_{1}t)+\Phi_{2}(2\pi f_{2}t)+\Phi_{3}(2\pi f_ {3}t)\] (26) where \(\phi_{1}=0.0284\) kg/s, \(\phi_{2}=0.0128\) kg/s, \(\phi_{3}=0.0078\) kg/s; \(f_{1}=225\) Hz, \(f_{2}=450\) Hz, \(f_{3}=675\) Hz. The outlet boundary condition is a pressure outlet, and the pressure is set to 21 Mpa. The wall boundary condition is a rigid stationary wall with no slip without considering wall absorption.