Particle Motion Simulation With Coarse-Grained Drag Correction
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Solution Overview
Problem
Existing methods for simulating particles motion, such as the Distinct Element Method (DEM) and Simpler Coarse-Grain Model (SCG), have limitations that restrict their applicability to specific conditions, particularly in handling non-spherical particles and a wide range of Reynolds numbers.
Innovation Solution
A program and method that corrects mass, density, or force applied to particles to maintain acceleration equality during coarse-graining, using a drag coefficient equation \( C_D = a \cdot Re + b \cdot Re^c \) to simulate particles motion in fluids, applicable to non-spherical particles and a broader range of Reynolds numbers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the Simpler Coarse-Grain Model (SCG) is used to reduce computational load, then productivity is improved, but the model can only be employed under limited conditions (worsening adaptability)
Solution Approach 1:
The patent changes the drag coefficient calculation from Stokes' law (valid only for Re<2) to a general formula valid for Re<1000, and modifies the coarse-graining correction factors to maintain acceleration equivalence under the new drag regime. This allows the SCG model to be applied across a much broader range of Reynolds numbers while preserving computational efficiency
Solution Approach 2:
The patent creates a universal coarse-graining model that works across different Reynolds number regimes (from creeping flow to transitional flow) by using a unified drag coefficient formula and acceleration-equivalence correction approach, making the model applicable to diverse particle systems rather than being restricted to specific conditions
2Device complexity
If conventional drag coefficient formulas (Stokes' law) are used, then calculation simplicity is improved, but the formula is only valid for Re<2 (worsening adaptability)
Solution Approach 1:
The patent replaces Stokes' law with a general drag coefficient formula C_D = 24/Re + 6/(1+0.5Re) that remains computationally simple while extending validity from Re<2 to Re<1000, capturing both low-Reynolds-number viscous effects and higher-Reynolds-number inertial effects
3Productivity
If coarse-graining is applied to reduce particle count, then productivity is improved, but acceleration accuracy deteriorates without proper correction
Solution Approach 1:
The patent introduces correction factors (k_m, k_ρ, k_F) that modify the mass, density, or force parameters of coarse-grained particles to compensate for the altered drag characteristics, ensuring that the acceleration of coarse-grained particles matches that of the original fine particles across different Reynolds number regimes
Solution Approach 2:
The patent establishes a feedback mechanism where the drag coefficient calculation informs the correction factor determination, which in turn adjusts the coarse-grained particle properties to maintain physical accuracy, creating a self-correcting system that preserves acceleration equivalence
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
Enables accurate simulation of particles motion for non-spherical particles and across a wider range of Reynolds numbers, improving computational efficiency and accuracy.
Implementation Method 1
calculating the particles motion includes calculating the particles motion at least based on a drag coefficient of the fluid, and wherein the drag coefficient is expressed by the following equation: C_D = a/Re + b/Re^c
Implementation Method 2
wherein Re is the Reynolds number of the fluid and a, b, and c are respectively constants that can be determined in dependence on sphericity of the first particles
Data Source
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AI summary
The object of the present disclosure is to provide a means of simulating particles that eliminates at least some of the certain limitations. In one aspect, the following invention is provided: a program, a medium, a method using the program and/or the medium, and a device in which the program is installed, for simulating particles motion wherein they are capable of executing steps including: reading a fluid data; reading a first particle data; coarse-graining particles at least based on the first particle data to generate a second particle data; and calculating particles motion at least based on the fluid data and the second particle data; wherein calculating the particles motion includes calculating the particles motion at least based on a drag coefficient of the fluid, and wherein the drag coefficient is expressed by the following equation: CD=aRe+bRe+c (Wherein Re is the Reynolds number of the fluid, and a, b, and c are respectively constants that can be determined in dependence on sphericity of the first particles.