## 4 Analysis of Experimental Results  
### Comparative Analysis of Experimental Phenomena and Numerical Simulation Results  
Based on the geometric parameters of the spiral-vortex in situ separator in Chapter 2, a numerical simulation model of the flow field inside the separator is established. The particle trajectory in the spiral-vortex flow channel is verified through discrete element method (DEM) numerical simulation analysis. Assuming that the liquid phase inside the separator can be considered as a viscous incompressible fluid, the continuity and momentum equations are as follows [20]. The continuity equation:  
\[\rho\frac{\partial u_{i}}{\partial x_{i}}=0 \tag{2}\]  
where \(\rho\) is the fluid density, \(u_{i}\) is the velocity in the \(i\) direction, and \(x_{i}\) is the position in the \(i\) direction. The momentum conservation equation:  
\[\left\{ \begin{array}{l}v\frac{\partial w}{\partial r}+w\frac{\partial w}{ \partial z}=-\frac{1}{\rho}\frac{\partial p}{\partial z}+\frac{\mu}{\rho} \Big{[}\frac{1}{r}\frac{\partial}{\partial r}\Big{(}r\frac{\partial w}{ \partial r}\Big{)}+\frac{\partial^{2}w}{\partial z^{2}}\Big{]}\\ v\frac{\partial w}{\partial r}+w\frac{\partial w}{\partial z}-\frac{u^{2}}{r} =-\frac{1}{\rho}\frac{\partial}{\partial r}+\frac{\mu}{\rho}\Big{[}\frac{1}{ r}\frac{\partial}{\partial r}\Big{(}r\frac{\partial w}{\partial r}\Big{)}+\frac{ \partial^{2}v}{\partial z^{2}}-\frac{v}{r^{2}}\Big{]}\\ v\frac{\partial w}{\partial r}+w\frac{\partial w}{\partial z}+\frac{wu}{r}= \frac{\mu}{\rho}\Big{[}\frac{1}{r}\frac{\partial}{\partial r}\Big{(}r\frac{ \partial w}{\partial r}\Big{)}+\frac{\partial^{2}u}{\partial z^{2}}-\frac{u}{ r^{2}}\Big{]}\end{array} \right. \tag{3}\]  
where \(u\), \(v\), and \(\omega\) represent the axial, radial, and tangential velocities, respectively \(\mu\) is the fluid viscosity, and \(p\) is the pressure. A screw-cyclone coupling in situ separator usually works in a turbulent state when the centrifugal separation of the multi-phase flow is carried out. There are many turbulence models to choose when flow field simulation is carried out. The Euler-Euler method is mainly used in cases where the volume fraction of the dispersed phase is less than 10% [21]. The model is suitable for the simulation of a fully turbulent flow process [22]. Large eddy simulation can provide a good prediction of multi-phase flow turbulence, but compared with other methods, it requires higher computing resources. The Reynolds stress model has a good prediction ability for the turbulent flow field of a hydrocyclone [23]. RSM can predict anisotropic turbulence and capture the high swirl fluctuation of a curved boundary [24]. Since the real flow in the spiral-cyclone separator for natural gas hydrate is an unsteady and complex three-dimensional turbulent motion, the numerical simulation analysis of the separator in this paper adopts the Reynolds stress model. The hexahedral mesh was chosen to reduce computational errors, as it better captures the parameter gradient changes inside the separator. To improve computational accuracy, local mesh refinement is applied to the model, as shown in Figure 5.  
The inlet of the separator was modeled with a velocity inlet boundary condition, where the inlet velocity was calculated based on the flow rate and area, and a vertical inlet boundary was used for fluid inflow. The outlet applied a pressure outlet boundary condition. After mud/sand separation, the discharge was directed to the sand jet discharge module, with the relative pressure set at 0.1 MPa. The geometric parameters and operating conditions for the numerical simulation are provided in Table 2.  
The simulated fluid was a mixture of seawater, natural gas hydrates, and mud/sand, using the Mixture model for multiphase flow and the DPM model for discrete phases. The pressure-velocity coupling was handled with the SIMPLE algorithm, with a time step of 0.001 and 5000 simulation steps.