Effects of an Impeller Rim and Radial Clearance on Energy Characteristics of an Axial Pump

The results of numerical and experimental research conducted in the Laboratory for Hydraulic Machinery Construction of Peter the Great St. Petersburg Polytechnic University are presented. The research is aimed at studying the effects of an impeller radial clearance and rim on the energy characteristic of low-pressure axial pumps of the specific speed ns≈600. It is shown that these design features of a flow duct have significant effects on stage parameters, and they have to be accounted for when verifying design and experimental characteristics of axial pumps.


Introduction
The flow energy in an axial pump is gained only on account of the force of the response from the lift acting on the fluid on the part of the blades upon rotation of the impeller and the transformation of the kinetic energy in a diffuser flow of the flow part [1]. Therefore, dynamic pumps of this type are unable to ensure high pressure gains, and the design features of the flow part can have significant effects on their energy and cavitation characteristics. A radial clearance between the pump impeller and casing wall is one of such design factors. An axial pump impeller can also have such element as a rim connecting the blades along the external contour. A rim enhances structural rigidity, increases natural oscillation frequency, prevents leakages of the fluid from the pressure side to the vacuum side of the blade. It is obvious that radial clearance, length of the rim, volume of leakage amounts, surface roughness can have effects on energy characteristics of an axial pump. The degree of these effects will be different for pumps with different specific speeds. This fact calls for research to determine optimal parameters of these design features, and also their accounting in verifying design and experimental characteristics of axial pumps. Certain works note also significant effects of radial clearance and rim on parameters of axial pumps with low specific speed [2,3] and other machines [4,5].

Setting an objective and the goal of research
The effects of these design parameters for axial pumps with specific speed ns ≈ 600 have been investigated.  For an impeller with a rim the actual relative radial clearance determined on a bench along the impeller circumference using measuring probes was δrel = δ/Dimp = 0.0025-0.003. For an impeller without a rim δrel = 0.0025-0.005.

Numerical research of energy characteristics of computational models
Numerical research using 3D CFD methods [6,7,8]  To evaluate the effects of the impeller rim and the radial clearance numerical computations of several models were conducted:  For an impeller with a rim. Relative radial clearances δrel = 0.001 and δrel = 0.005 were simulated. In the impeller region on the exterior flow boundary ("shroud" surface) a boundary condition "rotation" was assigned equal to the rotational frequency of the impeller.
 For an impeller without a rim. Relative radial clearances δrel = 0.001 and δrel = 0.005 were simulated. In the impeller region on the exterior flow boundary a boundary condition "counter-rotation" was assigned. Therefore, in the absolute coordinate system the rotational speed of the chamber wall was assumed to be zero.
Also, the following boundary conditions were assigned: at the inlet to the computational region -complete pressure 0 bars, at the outlet -mass flow rate corresponding to the operating conditions. The flow state was turbulent. A conventional two-equation k-ε turbulence model [9,10]  The computed speeds and pressures in the flow being studied were visualized to analyze and evaluate the obtained results. Figures 5-6 presents profiles for a model with a rim and relative radial clearance δrel = 0.005 under the nominal operation conditions of a pump.
From figure 5 it follows that static pressure drop Δpst is formed in the clearance, the value of which is ~5.2 m.  Under part load conditions the static pressure drop increases, which leads to considerable increases in leakage flows. Under the conditions Q = 0.2Qnominal it is already 20 % of the entire consumption that flows through the radial clearance (figure 7).

Fig. 7. Relative leakage flow
Thus, in the radial clearance there is constant circulation of the fluid volume ΔQ that does not participate in the energy gain and the creation of the pump power output and, in essence, increase volume losses. This leads to the fact that the optimum of the energy characteristics of the axial pump is shifted to the area of low flows, by the value of the volume of these leakages.

Conclusions
According to the results of the conducted research, the following conclusions can be drawn:  Computational and experimental characteristics of the model of the axial pump being studied have a high degree of correlation, which confirms the appropriateness of the selected mathematical model.  For a model without a rim an increase in relative radial clearance from 0.001 to 0.005 results in reduced efficiency of the pump under the rated conditions by 6 %.  For a model with a rim an increase in relative radial clearance from 0.001 to 0.005 results in reduced efficiency of the pump under the rated conditions by 2.5 %.
 The presence of the impeller rim significantly increases losses of "disk" friction, which results in considerable reduction of the pump efficiency. Compared to a model without a rim the reduced pump efficiency under the rated conditions was 17 % with relative radial clearance 0.001. The efficiency was reduced by 13.5 % with relative radial clearance 0.005.  For a model without a rim and with minimum clearance δrel = 0.001 the design optimal conditions coincide with rated conditions.  For a model without a rim an increase in relative radial clearance from δrel = 0.001 to δrel = 0.005 results in the optimal conditions shifting toward less flow.  For a model with a rim even with the minimum clearance δrel = 0.001 the optimum is shifted toward less flow.

5
E3S Web of Conferences 320, 04006 (2021) ESEI 2021 https://doi.org/10.1051/e3sconf/202132004006  The required pump pressure under the rated conditions is ensured only for a model without a rim and with minimum clearance δrel = 0.001.
 For axial pumps with specific speed ns ≈ 600 it is recommended to maintain the relative clearance δrel = 0.001.