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To fully reflect the effect of the flow characteristics, sidewall conditions and sediment concentrations on the bed roughness of sand-bed rivers, this study established a new flow resistance equation by introducing a comprehensive influence coefficient presented via a combination of power-function forms of the relative flow velocity, von Karman constant of sediment-laden flows and the ratio of particle size to viscous sublayer thickness. The comprehensive influence coefficient accordingly acts as a synthesized factor representing the combined effects of the flow intensity, bed material movement, energy consumption condition, and relative friction condition in the near-wall region of sediment-laden flows. Based on the field data from sediment-laden flows under scenarios of both high and low sediment concentrations, the performance of the proposed equation was validated to achieve the best accuracy in the calculation of Manning’s roughness coefficient compared with that of several previously presented flow resistance equations. Furthermore, the proposed flow resistance equation was adopted to quantify the stable channel width of the Lower Yellow River (LYR), i.e., the optimum main channel width for sediment transportation in the typical wandering reach of the LYR. The calculated stable channel width is consistent with the current river training width of the LYR, indicating that the proposed equation has great potential as a theoretical tool that can be used to support the determination of the river training strategy for the LYR.

A combined numerical model is proposed in order to solve ablation and denudation under high temperature and high pressure. Vortex method is used for simulating vorticity field and pressure distribution; a three-equation model is used for resolving the ablation mass loss; and a trajectory model is adopted for solving the motion of denudated particles. Compared with the flow past an ablating cylinder with the same Re number and ablation condition, the ablation effect on the sphere-conic is more significant and the vorticity contour turned to an asymmetric structure earlier; the particle traces are no longer symmetric, and the particles distribution become unorganized; the linear momentum of the ablating sphere-conic become larger than the non-ablating one; This simulation may offer numerical references to ablation experiments on thermal protection materials.

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