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ABSTRACT
We proposed a truncated multiple-relaxation-time lattice Boltzmann method (MRT-LBM) for the Herschel–Bulkley flow with high Reynolds number. The effectiveness of the proposed model was verified by Poiseuille flow. We analyzed the effect of the initial yield stress and the relative errors with diverse lattice nodes in case of different power-law indexes. Finally, the improved MRT-LBM was used to simulate the lid-driven flow of high Reynolds numbers. The streamlines prove not only the effectiveness of MRT-LBM in simulating the flow with high Reynolds number, but also the feasibility of the method in dealing with the yielding behavior of Herschel–Bulkley fluids.
Nomenclature
| Symbols | = | Meaning |
| c | = | lattice speed |
| cs | = | sound speed |
| ei | = | discrete velocities |
| f | = | distribution function |
| h | = | width of the channel |
| H | = | distance between two plates |
| K | = | viscosity coefficient |
| L | = | pitch of the single screw |
| m | = | related to the increase in the stress |
| M | = | transformation matrix |
| n | = | power-law index |
| N | = | lattice nodes |
| Ns | = | rotation speed |
| r | = | displacement vector |
| = | main diagonal matrix related to the relaxation process | |
| Sαβ | = | strain-rate tensor |
| t | = | Time |
| u | = | velocity vector |
| v vx vz | = | Velocities |
| W | = | depth of the channel |
| yl yh yτ | = | critical values |
| α1 α2 α3 | = | constant terms |
| = | shearing rate | |
| δx | = | lattice spacing |
| δt | = | time spacing |
| θ | = | lead angle |
| μ | = | dynamic viscosity |
| μB | = | viscosity coefficient of Bingham fluids |
| νap ν νmin νmax | = | related kinematic viscosity |
| ρ | = | Density |
| τ | = | relaxation time |
| τa | = | τ0 stress |
| ωi | = | weight coefficient |
| ∇P | = | pressure gradient |
Nomenclature
| Symbols | = | Meaning |
| c | = | lattice speed |
| cs | = | sound speed |
| ei | = | discrete velocities |
| f | = | distribution function |
| h | = | width of the channel |
| H | = | distance between two plates |
| K | = | viscosity coefficient |
| L | = | pitch of the single screw |
| m | = | related to the increase in the stress |
| M | = | transformation matrix |
| n | = | power-law index |
| N | = | lattice nodes |
| Ns | = | rotation speed |
| r | = | displacement vector |
| = | main diagonal matrix related to the relaxation process | |
| Sαβ | = | strain-rate tensor |
| t | = | Time |
| u | = | velocity vector |
| v vx vz | = | Velocities |
| W | = | depth of the channel |
| yl yh yτ | = | critical values |
| α1 α2 α3 | = | constant terms |
| = | shearing rate | |
| δx | = | lattice spacing |
| δt | = | time spacing |
| θ | = | lead angle |
| μ | = | dynamic viscosity |
| μB | = | viscosity coefficient of Bingham fluids |
| νap ν νmin νmax | = | related kinematic viscosity |
| ρ | = | Density |
| τ | = | relaxation time |
| τa | = | τ0 stress |
| ωi | = | weight coefficient |
| ∇P | = | pressure gradient |