We conduct a comparative study to evaluate several lattice Boltzmann (LB) models for solving the near incompressible Navier-Stokes equations, including the lattice Boltzmann equation with the multiple-relaxation-time (MRT), the two-relaxation-time (TRT), the single-relaxation-time (SRT) collision models, and the entropic lattice Boltzmann equation (ELBE). The lid-driven square cavity flow in two dimensions is used as a benchmark test. Our results demonstrate that the ELBE does not improve the numerical stability of the SRT or the lattice Bhatnagar-Gross-Krook (LBGK) model. Our results also show that the MRT and TRT LB models are superior to the ELBE and LBGK models in terms of accuracy, stability, and computational efficiency and that the ELBE scheme is the most inferior among the LB models tested in this study, thus is unfit for carrying out numerical simulations in practice. Our study suggests that, to optimize the accuracy, stability, and efficiency in the MRT model, it requires at least three independently adjustable relaxation rates: one for the shear viscosity ν (or the Reynolds number Re), one for the bulk viscosity ζ, and one to satisfy the criterion imposed by the Dirichlet boundary conditions which are realized by the bounce-back-type boundary conditions.
A non-sinusoidal trajectory profile is proposed for the oscillating hydrofoil in the energy generators instead of conventional sinusoidal plunging/pitching motions to seek better energy extraction performance. The novel profile is achieved by combining a specially designed trapezoidal-like pitching motion with a sinusoidal plunging motion and investigated numerically on its output energy coefficient and total output efficiency. Through an adjustable parameter b, the pitching profile can be altered from a sinusoidal (b ¼ 1.0) to a square wave (b / N). In this work, a series of b ranging from 1.0 to 4.0 are investigated to examine the effect of combined motion trajectory on the energy extraction performance. The study encompasses the Strouhal numbers (St) from 0.05 to 0.5, nominal effective angle of attacks a0 of 10 and 20 and plunging amplitude h0/c of 0.5 and 1.0. Numerical results show that, for different b pitching motions, a larger a0 always results in a higher extraction power Cop and total efficiency hT. Compared with the sinusoidal motion (b ¼ 1), significant increment of Cop and hT can be observed for b > 1 over a certain range of St. The investigation also shows that there exists an optimal pitching profile which may increase the output power coefficient and total output efficiency as high as 63% and 50%, respectively, over a wide range of St. Detailed examination on the computed results reveal that, the energy extraction performance is determined by the relative ratio of the positive and negative contributions from the different combination of lift force, momentum and corresponding plunging velocity and pitching angular velocity, all of which are considerably affected by b
SUMMARYThe ow ÿelds in the neighbourhoods of series vascular stenoses are studied numerically for the Reynolds numbers from 100 to 4000, diameter constriction ratios of 0.2-0.6 and spacing ratios of 1, 2, 3, 4 and ∞. In this study, it has been further veriÿed that in the laminar ow region, the numerical predictions by k-! turbulence model matched those by the laminar-ow modelling very well. This suggests that the k-! turbulence model is capable of the prediction of the laminar ow as well as the prediction of the turbulent stenotic ow with good accuracy. The extent of the spreading of the recirculation region from the ÿrst stenosis and its e ects on the ow ÿeld downstream of the second stenosis depend on the stenosis spacing ratio, constriction ratio and the Reynolds number. For c 1 = 0:5 with c 2 6c 1 , the peak value of wall vorticity generated by the second stenosis is always less than that generated by the ÿrst stenosis. However, the maximum centreline velocity and turbulence intensity at the second stenosis are higher than those at the ÿrst stenosis. In contrast, for c 1 = 0:5 with c 2 = 0:6, the maximum values at the second stenosis are much higher than those at the ÿrst stenosis whether for centreline velocity and turbulence intensity or for wall vorticity. The peak values of the wall vorticity and the centreline disturbance intensity both grow up with the Reynolds number increasing. The present study shows that the more stenoses can result in a lower critical Reynolds number that means an earlier occurrence of turbulence for the stenotic ows.
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