Particle Simulation Solidification Rigid Body Motion
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Solution Overview
Problem
Current numerical calculation methods, such as those using the finite difference or finite volume methods, face challenges in handling moving boundary problems and fluid-structure interaction analysis, particularly in casting and forging simulations, where the Cleary method requires small time steps due to increased viscosity coefficients, leading to long calculation times and reduced accuracy in solidification processes.
Innovation Solution
A simulation method that represents a continuum with particles and determines the state of particles using the equation of motion of a rigid body for solid particles, grouping particles into the same solid based on proximity, allowing for accurate calculation of solidification and deformation processes without increasing the time step or calculation operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If the Cleary method is used to simulate solidification by increasing viscosity coefficient, then solidification process can be represented, but calculation time increases due to small time steps
Solution Approach 1:
The patent changes the fundamental parameter used to represent solidification from viscosity coefficient to density. By using density changes (liquid density to solid density) instead of viscosity changes, the method avoids the need for small time steps that result from high viscosity values, thereby reducing calculation time while maintaining solidification simulation accuracy
Solution Approach 2:
The patent substitutes the mechanical approach of using viscosity-based fluid dynamics with a density-based approach. Instead of relying on the Navier-Stokes equations with high viscosity to represent solidified material, the method uses density as the primary indicator of solidification state, fundamentally changing the mechanical model used for solidification simulation
2Manufacturing precision
If particles are treated as individual solids during solidification, then solid-liquid interaction can be calculated, but calculation operations increase and accuracy decreases
Solution Approach 1:
The patent merges multiple solid particles into a single solid body when they are in close proximity. By detecting when solid particles are within a predetermined distance of each other and combining them into one solid, the method reduces the number of individual solid-liquid interaction calculations needed, thereby improving calculation efficiency while maintaining accuracy in representing the solidified structure
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enables accurate simulation of solidification and deformation processes with reduced calculation time and increased efficiency by using the equation of motion of a rigid body for solid particles, improving the accuracy of solid-liquid interactions and reducing the number of calculation operations.
Implementation Method 1
calculating the state of each particle belonging to the same solid using an equation of motion of a rigid body
Implementation Method 2
The particle method analyzes the motion of a continuum as the motion of a finite number of particles
Implementation Method 3
The Cleary method calculates the time evolution of the internal energy of each liquid particle using the SPH method which is one of the particle methods and calculates the temperature, density, and viscosity coefficient of the liquid particle as a function of internal energy
Data Source
AI summary
A state of a particle which was in a liquid state at a first time is calculated at a second time after the first time when a continuum including a liquid and a solid is represented by the plurality of particles. It is determined whether the particle has become a first solid particle at the second time. The first solid particle and all particles belonging to a solid which includes a second solid particle arranged in a predetermined range from the first solid particle are defined as particles belonging to the same solid when it is determined that the particle which was in the liquid state at the first time has become the first solid particle at the second time. The state of each of the particles belonging to the same solid is calculated using an equation of motion of a rigid body.