An Improved Multi-Relaxation Time Lattice Boltzmann Method for the Non-Newtonian Influence of the Yielding Fluid Flow in Cement-3D Printing
Abstract
:1. Introduction
2. Improved MRT-LBM for Yielding Fluids
2.1. Rheological Equation of Yielding Fluids
2.2. Improved MRT-LBM
- (1)
- Conduct the physical transformation according to the dimension theory. The Reynolds number is taken as the key criteria, and then the other parameters used in simulation can be obtained.
- (2)
- Set the simulation domain and initial conditions, especially the initial value of the factor s8.
- (3)
- Calculate the equilibrium distribution function according to Equation (5).
- (4)
- Conduct the collision step, where the specific function is shown as:
- (5)
- Calculate the strain rate tensor and shearing rate by using Equations (11)–(13), then the kinetic viscosity can be obtained using Equation (3) and the relaxation factor s8 will be updated.
- (6)
- Conduct the streaming step, where the streaming function is shown as:
- (7)
- Process the boundary condition, where the non-equilibrium bounce-back scheme is taken as the boundary method.
- (8)
- Conduct the next calculation from Step (3).
- (9)
- Calculate the density and velocity, where the corresponding equations are:
3. Flow Analysis for the Mixture Fluids in Cement-3D Printing
3.1. Rheological Equation of Fluids
3.2. Structure of Extruding Head
3.3. Flow Simulation using Improved MRT-LBM
4. Validation and Discussion
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Factor | Meaning | Value |
---|---|---|
W | the width of the channel | 30 mm |
h | the depth of the channel | 10 mm |
θ | angle of lead | 20° |
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Huang, T.; Gu, H.; Zhang, J.; Li, B.; Sun, J.; Wu, W. An Improved Multi-Relaxation Time Lattice Boltzmann Method for the Non-Newtonian Influence of the Yielding Fluid Flow in Cement-3D Printing. Materials 2018, 11, 2342. https://doi.org/10.3390/ma11112342
Huang T, Gu H, Zhang J, Li B, Sun J, Wu W. An Improved Multi-Relaxation Time Lattice Boltzmann Method for the Non-Newtonian Influence of the Yielding Fluid Flow in Cement-3D Printing. Materials. 2018; 11(11):2342. https://doi.org/10.3390/ma11112342
Chicago/Turabian StyleHuang, Tiancheng, Hai Gu, Jie Zhang, Bin Li, Jianhua Sun, and Weiwei Wu. 2018. "An Improved Multi-Relaxation Time Lattice Boltzmann Method for the Non-Newtonian Influence of the Yielding Fluid Flow in Cement-3D Printing" Materials 11, no. 11: 2342. https://doi.org/10.3390/ma11112342