Study on the Best Water Cushion Depth of Stilling

The water cushion depth of stilling basin with shallow-water cushion is a key factor that 13 affects the flow regime of hydraulic jump in the basin. However, the specific depth at which the 14 water cushion is considered as “shallow” has not be stated clearly for now, and only conceptual 15 description is provided. This paper attempts to specify the best water cushion depth based on the 16 flow regime of hydraulic jump and underflow speed; namely, in case of critical hydraulic jump in 17 the basin, the best water cushion depth is located where the minimum distance to the bottom plate 18 of the stilling basin is 1/5~1/4 of the water cushion depth. The theoretical analysis indicates, at 19 different inclinations of discharge chute (θ) and depth ratios of inlet (m), instead of monotonic 20 change, the Froude number (Fr) at inlet of the stilling basin with shallow-water cushion firstly 21 reduces and then increases as the flow velocity at discharge chute inlet (V) increases; the parameters 22 of inflection point (critical flow velocity and critical Fr) increase as the inclinations of discharge chute 23 (θ) and depth ratios of inlet (m) increase. Such regularity is the theoretical basis for selecting 24 representative study cases. The reliability of the large eddy simulation calculation results are 25 verified by a model test; in the paper, 30 cases including five different Froude numbers and six 26 shallow-water cushion depths are selected, for calculating the hydraulic factors such as flow profile, 27 flow regime and flow velocity in the stilling basin with shallow-water cushion; and the varying 28 pattern between the best depth of stilling basin with shallow-water cushion (depth-to-length ratio) 29 and the inflow Froude number is obtained which indicates that the best depth of stilling basin with 30 shallow-water cushion varies little as the change of the Froude number before reaching the critical 31 Froude number; however, the best depth-to-length ratio of stilling basin with shallow-water cushion 32 increases as the Froude number increases after the critical Froude number is reached. The study 33 results in this paper are of reference significance to design and calculation of the stilling basin with 34 shallow-water cushion. 35