山区航道机动船消滩水力指标的无因次表达及计算

消滩水力指标一般是指某船舶在额定载重、额定主机功率条件下能够自航上滩的最大航线流速和比降的组合，是判定船舶能否自航上滩的临界水流条件，是急滩整治效果分析的参照依据。分析现有确定急滩消滩水力指标的方法存在的缺陷，指出了现有综合消滩水力指标表达式存在的关键参数选择不合理、影响因子与主变量的关系不明确等不足。基于水流阻力与流速、坡降阻力与比降的基本关系，依据船舶推力与航行阻力平衡的基本原理，从克服现有消滩水力指标计算和表达等不足的角度出发，导出了无因次消滩水力指标的简要表达式和预估公式。应用澜沧江500 t级船舶静水航速实船试验成果，获得了螺旋桨实际转速与额定转速之比随进速系数的变化规律，计算消滩水力指标时，螺旋桨转速不宜取额定转速。分析结果表明，兹万科夫公式计算的水流阻力与船舶推力存在较为明显的偏差，并绘制了阻力修正系数随船舶佛汝德数的修正曲线，指明兹万科夫水流阻力计算公式需根据实船试验成果进行适当修正。分析计算了澜沧江多种机动船型的消滩水力指标，检验了无因次消滩水力指标简要表达式的合理性，采用无因次项的抛物线曲线描述消滩水力指标中流速、比降的关系甚为恰当。基于因次分析原理，通过澜沧江多种机动船消滩水力指标的数值回归分析，建立了无因次综合消滩水力指标与船舶基本参数无因次功载比、方形系数之间的关系式，明显提高了消滩水力指标的计算效率，可在缺乏船型详细资料的情况下预估消滩水力指标。

Dimensionless Expression and Calculation of Rapids Abating Hydraulic Index for Motor Ship in Mountainous Waterway

The rapids abating hydraulic index generally refers to the combination of the maximum route flow velocity and gradient of a ship which can sail through the rapids by itself under the condition of rated load and rated main engine power, it is the critical flow condition to determine whether the ship can sail through the rapids by itself, and it is the reference basis for analyzing the effect of rapids regulation. This paper analyzes the defects of the existing methods to determine the rapids abating hydraulic index, and points out the shortcomings of the existing expressions of comprehensive rapids abating hydraulic index, such as unreasonable selection of key parameters, unclear relationship between influencing factors and main variables, etc. Based on the basic relationship between flow resistance and flow velocity, gradient resistance and gradient, and according to the basic principle of the balance between ship thrust and navigation resistance, from the perspective of overcoming the existing shortcomings of the calculation and expression of the rapids abating hydraulic index, a brief expression and pre-estimation formula of dimensionless rapids abating hydraulic index were derived. Applying the test results of 500-ton ship at hydrostatic speed in Lancang River, the variation law between the ratio of actual propeller speed to the rated propeller speed with the advancing coefficient was obtained. When calculating the rapids abating hydraulic index, the propeller speed should not be taken as the rated speed. The analysis results show that there is an obvious deviation between the flow resistance calculated by the Zvankov formula and the ship thrust. The correction curve of the resistance correction coefficient with the ship Froude number was plotted. It is pointed out that the calculation formula of Zvankov flow resistance needs to be properly modified according to the results of full-scale ship test. The rapids abating hydraulic indexes of various types of motor ships in Lancang River were analyzed and calculated, and the rationality of the brief expression of dimensionless rapids abating hydraulic index were verified. It is more reasonable to describe the relationship between flow velocity and gradient in the rapids abating hydraulic index by using dimensionless parabolic curve. Based on the principle of dimensional analysis and through the numerical regression analysis of the rapids abating hydraulic indexes of various motor ships in Lancang River, the relational expression between the dimensionless comprehensive index, the basic ship parameters dimensionless power-load ratio and the block coefficient were established, which can significantly improve the calculation efficiency of the rapids abating hydraulic index. It can be used to predict the rapids abating hydraulic index in the absence of detailed information of the ship types.