基于速度矩守恒的离心泵节能蜗壳断面几何参数求解

螺旋形蜗壳是离心泵的基本压水室形式,降低蜗壳中的流动损失是提高泵效率的重要措施。分析表明,蜗壳各轴面断面的周长是决定蜗壳中水力损失的重要因素。在传统的蜗壳设计方法中,并未重视蜗壳湿周与蜗壳水力损失的关系,也未将改善蜗壳断面几何特征作为产生节能产品的设计目标。该文以速度矩守恒原理为依据,在保证蜗壳断面入口无显著扩散的条件下,提出了实现蜗壳断面最小湿周的理念与实现方法。利用等面积图形中圆具有最小周长的几何特征,该文给出了与现行蜗壳断面有区别的断面确定原则,并根据断面要求通过的不同流量形成了2种减小断面湿周的断面新结构。由于这种断面几何参数没有解析解,该文给出了它们详尽的数值求解方法与过程。事实证明,该文提出的方法对改善泵效率有积极效果,在设计点附近的提高幅度均达到1.6%。该文设计的断面蜗壳有望成为实现改善泵效率这一预期目标的可行结构。

Geometric parameters numerical calculation for energy saving volute cross sections of centrifugal pumps based on conservation of angular momentum

Abstract: Volute casings are extensively used in centrifugal pumps. Minimizing hydraulic losses generated in casings is an effective approach to improve pump efficiency. After water from impellers enters volute casings, as no external forces do work on the water, mechanical energy of water can''t be increased. On the contrary, energy dissipation is inevitable due to the friction in casings. Based on previous research, it is found that hydraulic losses in volute can account for half of the total losses in the pump. Analysis revealed that, as the flow in the volute is fully rough flow of high Reynolds number, the friction loss is independent of Reynolds number, but is only determined by the relative roughness of casing wall and is proportional to the length of wetted perimeters of volute cross sections. However, in 2 leading conventional designs, i.e. the calculation based on statistical data and the theorem of conservation of angular momentum, the relationship between perimeters of casing cross sections and friction losses is always neglected and no effort has been made to shorten the perimeters as a measure to increase pump efficiency. In this paper, we proposed a novel method to minimize the cross sectional perimeters and the friction losses in the volute. In all figures with identical area, circle has the shortest perimeter. The new design method provided in this paper takes the geometrical advantages of circles and forms new volute cross section shapes, which is different from the commonly used traditional trapezoidal section. In meridional sections, as streamlines of flow from the impeller can not change their directions abruptly, 2 eddies may appear at volute entrance if the volute section is constructed using circles. That is why full circles are not applicable for pump volute design. In order to make use of circle advantages and avoid its side effect, this paper suggested 2 types of volute sections, which are neither circular nor trapezoidal. The flow rates passing different volute sections are not identical and are related to the section positions in the volute. For high flow rate sections, the new sections involve a trapezoid located at lower portion and a single arc located at upper portion, while for low flow rate sections, the sections are formed by quadrangles with curved sides. It is evident that the perimeters of both types of new cross sections are shorter than the corresponding perimeters of conventional trapezoidal sections. The volute section outlines are controlled by its geometrical parameters. The first step in the volute design process is calculating all these parameters. As the theorem of conservation of angular momentum is widely used for volute design, the sectional parameters in this paper are obtained based on this theorem. Due to the complexity of both types of volute cross sections, it is impossible to gain analytical solutions of the section parameters. Therefore, numerical calculations are employed for parameter establishment. The flow circulation at impeller exit at design point is determined, as well as the entrance width of the volute cross sections, the angle between 2 volute sides in the meridional section and the vertical plane, and the radius of the base circle; and among all geometrical parameters to be decided, only one parameter is dominant and others can be obtained by this crucial parameter. In the calculation process for a particular section of any type, the first step is to assume the dominant parameter and divide the section into finite small elements. The second step is to calculate the flow rates passing all individual elemental areas based on the theorem of conservation of angular momentum. The sum of all flow rates is the total discharge passing the section considered. The last step, in terms of the comparison between the calculated total flow rate and the specified flow rate for the particular section, is to adjust the previously assumed parameter properly and repeat the computing process until 2 flow rates become identical. As a result, the last assumed value for the parameter is the final solution. The principles and the detailed numerically calculating procedures for 2 types of cross sections are presented in this paper. Tests indicated that expected results can be achieved by using the new approach described in the paper, and the new method is applicable in volute designs.