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Describing Multi-Phase Fluid Flow Using Smoothed Particle Hydrodynamics

Key Takeaways

  • The solution for eliminating mesh-related problems associated with multi-phase flow simulation is to use a mesh-free method. 

  • Smoothed particle hydrodynamics is a mesh-free method used to study multi-phase fluid flow behavior.

  • Smoothed particle hydrodynamics features the harmonic combination of particle approximation and Langrangian formulation.

 Fluid flow

In engineering applications, multi-phase fluid flow is a typical phenomenon

In engineering applications, multi-phase fluid flow is a typical phenomenon. Studying multi-phase flow in flow channels and fluidized beds is essential for devising better engineering solutions. CFD methods are commonly employed for investigating multi-phase flow in engineering systems. These CFD methods can be mesh-based or particle-based.

Most grid or semi-grid-based numerical methods are not effective at simulating multi-phase flow. Grid-based numerical methods fail to define and track interfaces, so mesh-free methods are required to simulate multi-phase flow. One such method is smoothed particle hydrodynamics, which we will explore in this article.

CFD Methods and Multi-Phase Fluid Flow  

CFD simulations are used to transform the mathematical definitions of the physics related to fluid flow into a set of instructions that can reproduce fluid motion using a computer. Since computers are incapable of reproducing the continuum, the precision of describing fluid differs at all points. In CFD methods, discretization is included to break down the application domain into smaller sections. There are two types of CFD methods based on the spatial discretization adopted: mesh-based methods and particle-based methods.

Most mesh-based methods encounter problems while addressing multi-phase flow in engineering systems. We will explore the reason for opting out of mesh-based methods for multi-phase flows next. 

Methods for Modeling Multi-Phase Fluid Flow  

Multi-phase fluid flow is common in engineering applications such as gas-liquid flow in flow channels and fluid-particle flow in fluidized beds. To investigate multi-phase fluid flow, there are a few methods that can be used. 

Numerical Methods

Due to developments in computing systems, numerical methods gained importance in investigating multi-phase flow. The advantage offered by numerical methods, such as safety, high efficiency, and low cost, make them popular. However, numerical methods fail to model interface tracking accurately. In numerical methods, defining interface behavior involves moving surfaces, large surface deformation, and solid walls.

Typical numerical methods employed for multi-phase flow modeling are the particle in cell (PIC), level set (LSM), volume of fluid (VOF), and marker and cell (MAC) methods. All these numerical methods are grid-based or semi-grid-based methods, and the presence of mesh or grid is a hindrance to tracking and describing interfaces accurately. While tracking the interfaces in these numerical methods, other problems such as mesh distortions, overlay, twisting, or deformation may intervene in the simulation. 

Mesh-Free Methods

To eliminate mesh-related problems in multi-phase flow simulation, designers should use a mesh-free method. Smoothed particle hydrodynamics is a well-known mesh-free method used to solve problems in mechanics. This method is often used in hydrodynamics. 

Smoothed Particle Hydrodynamics

Smoothed particle hydrodynamics is a mesh-free method used to study multi-phase fluid flow behavior. The fundamental idea of smoothed particle hydrodynamics is the discretization of the continuum domain into a finite number of particles. These particles determine the physical quantities of interest from weighted interpolations of the quantities in the neighboring particles.

This method was developed by Lucy, Gingold, and Monaghan as a pure Lnagragian particle method. It uses a series of particles to represent the fluid. The particles carry physical properties, and each particle's information is independent of others. The change of motion and physical information of all the particles follow the governing conservation equations. Once the locations and physical information of the particles are determined, simulations are carried out. Numerical solutions are obtained from the particles using particle approximations and kernel approximations. 

Advantages of Smoothed Particle Hydrodynamics

Although smoothed particle hydrodynamics is relatively new compared to traditional grid-based methods, due to its mesh-free nature, it finds extensive application in modeling multi-phase fluid flows and dynamic fluid flows with large deformations.

A few of the merits of smoothed particle hydrodynamics are:

  • Self-adaptability
  • Free distribution of particles
  • Easy interface tracking
  • Mesh distortions don’t limit the numerical accuracy in simulations of large deformations
  • Free of numerical diffusion
  • Natural concurrent computations

Given these merits, smoothed particle hydrodynamics is a powerful mesh-free method for solving CFD problems governed by the Navier-Stokes equations. If you are working on modeling the multi-phase flow of fluids, Cadence’s suite of CFD tools can help. The complete set of CFD simulation features in Fidelity from Cadence can be utilized for CFD analysis of fluids in motion.

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About the Author

With an industry-leading meshing approach and a robust host of solver and post-processing capabilities, Cadence Fidelity provides a comprehensive Computational Fluid Dynamics (CFD) workflow for applications including propulsion, aerodynamics, hydrodynamics, and combustion.

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