A Comparative Study Of Turbulence Models For The Simulation Of Subaqueous Gravity Flows

With the development of computer technology and computational science, numerical simulation becomes an important method for the study of underwater gravity flows. Gravity currents form turbulent flows due to strong shearing in free shear zone and boundary layer. In order to choose the best turbulence model for simulating gravity flows among existing turbulence models, this study applies six different turbulence models to simulate gravity flows and compares simulated results with experimental data. These turbulence models are:k-ε model, Mellor-Yamada model, K-L model, Spalart-Allmaras model, k-ω model and Reynolds stress model. The experimental data are from experiments of Garcia(1993) and Islam&Imran (2010). For convenience, we divided these models into two groups, group A and group B. Group A includes k-ε model, Mellor-Yamada model and K-L model. Group B includes Spalart-Allmaras model, k-ω model, Reynolds stress model and the best model from group A.First of all, compares model results of A group models with experimental data, we found that the standard deviations of velocity of k-ε model, K-L model and M-Y model are0.01,0.023and0.021respectively; standard deviations of concentrations are0.013,0.304and0.26respectively; standard deviations of turbulence kinetic energies are0.016,0.02and0.667respectively. The data shows that k-ε model performs best in predictingsubaqueous gravity flows. Futher observation shows that K-L model and M-Y models present an excess diffusion in vertical direction. The reason for these may be that k-ε model’s fundamental assumption of the equilibrium of generation and dissipation of turbulence kinetic energy applies equally well in both bottom boundary layer and upper interface shear flow regions while the wall boundary based length scale in K-L model and M-Y models may not applicable in the free shear region.Secondly, compares the model results of B group models with experimental data, we found that:(1) the standard deviations of velocities of RSM and k-ε models are0.012and0.013, the difference between them is very small; the standard deviations of velocities of S-A and k-ω model are0.11and0.12respectively, is an order of magnitude larger than that of both RSM or k-ε models;(2), the concentration standard deviations of k-ε, RSM, k-ω and S-A models are0.01,0.015,0.51and0.55 respectively;(3) current thickness standard deviations of RSM, k-ε, k-ω and S-A models are0.018,0.012,0.61and0.62respectively;(4) for turbulence kinetic energyof k-ε and RSM models, on ramp the deviations are0.016and0.018; on horizontal bed, the deviations are0.013and0.034respectively.RSM model was not observed better than k-ε model in modeling gravity currents, perhaps the closure assumption of RSM is not sutable for gravity flows.We compared the modelling results of three dimensional simulation to those of two dimensional simulation with k-ε model. The standard deviations of3D and2D simulations compared with experimental data:(1) For velocity, are0.012and0.013respectively;(2) for current thickness, are0.012and0.01respectively;(3)for concentrations, tare0.02and0.014.respectively;(4) for turbulent kinetic energy, are0.0101and0.0102respectively. As those data show, there is no significant difference between2D and3D simulations for gravity flows.