Performance improvement of an axial flow pump model

3.1 Design of new axial-flow pump model

The design parameters of both pump models are shown in Table 1. The new model is designed to supply flow to a propeller hydro-turbine model located downstream of the axial pump. Hence, the design operating condition of the new model is changed appropriately according to the design specification of the propeller hydro-turbine model by changing the specific speed of the pump slightly. The hub diameter of the new impeller was increased to maintain a constant specific speed, which is expressed as Equation (1). The two pump models are designed for a similar operating condition, which is described by the head coefficient (Equation (2)), flow coefficient (Equation (3)), and rotational speed. A flow chart of the design procedure of the new pump model is presented in Figure 2. A closed design loop of the pump model including the CFD analysis is repeated continuously until the design targets are met.

Table 1:

Design parameters of the pump models

Figure 2:

Design process of the new axial-pump model

The preliminary design of an impeller blade considers the velocity triangles at the impeller inlet and outlet, which are presented in Figure 3. The entrance flow assumes no pre-rotation at the impeller blade inlet. Hence, the tangential velocity at the entrance (V_u1) should not exist. With a design assumption that same amount of flow rate is transported from the leading to the trailing edge, the meridional velocity (V_m) is determined considering the flow rate in the flow passages.

Figure 3:

(a) Entrance velocity triangle and (b) Exit velocity triangle of a blade section

The impeller blade angles (β) at the inlet and outlet can be obtained from Equation (4) and Equation (5), respectively, where indicators “1” and “2” represent the entrance and exit angles of the impeller, respectively; and U is the peripheral velocity; U₁ = U₂ at the same span of impeller blade. The tangential velocity at the impeller blade outlet is calculated from the Euler equation considering hydraulic efficiency (η) as $$ V_{u2}=\frac{\eta gH}{U_2}$$. A rough estimation of the meridional velocity can be determined by $$ V_m=\frac{4Q}{\pi \left(D^2-d^2\right)}$$,where D, and d are the impeller diameter and hub diameter, respectively. The same hydrofoil shape from the previous study [9] is adopted for the impeller blade. A comparison of the three-dimensional impeller blade models is illustrated in Figure 4.

Figure 4:

Old and new impeller models

3.2 Numerical method

Owing to the improved accuracy and reliability nowadays, computational fluid dynamics (CFD) analysis is used to predict the performance of fluid machinery as a pre-manufacturing stage. This study uses a commercial code of ANSYS CFX version 18.1 [10] to investigate the performance of both pump models. The experimental results are compared to validate the CFD analysis results.

Numerical fluid domains of the models are built using a three-dimensional software. As seen in Figure 5, the fluid domains of the new pump model have five domains. To calculate the pump performance, the tip clearance gap is included in the impeller domain.

Figure 5:

Numerical fluid domains of the new pump model

To reuse the existing apparatus system, the only changes to the new pump model are the changed impeller shape and the addition of a diffuser. Moreover, as the pump size is small and to improve the convenience of the assembly process of the pump parts, a relatively long spacing is included between the impeller and diffuser domains.

The boundary conditions of whole flow passages are introduced in Table 2. This boundary condition is adopted for all steady state calculations of both pump models. To reduce the calculation time and obtain reliable CFD analysis results, a grid sensitivity test was conducted. All meshes of fluid domains were generated using ANSYS ICEM [10]. Figure 6 shows the results of the grid test in terms of the efficiency of the new pump and different grid sizes of all fluid domains. From the comparison of the pump efficiency with the mesh number, a mesh of three million nodes was selected for CFD analysis. The averaged near-wall treatment y+ value of the main fluid domains of the selected grid are shown in Table 3. Meshes of one pitch of impeller blade and diffuser vane of the selected grid are illustrated in Figure 7.

Table 2:

Boundary conditions for whole flow passages

Figure 6:

Comparison of the new model performance decay calculation for all tested grids

Table 3:

Averaged y+ value of main fluid domains

Figure 7:

Structured meshes of one pitch of diffuser vane and impeller blade (new model) of the chosen grid

4.1 Performance curves

The performance curves of both pump models presents at various flow coefficients in Figure 8. The best efficiency points (BEP) of each pump model matched with the design points. The old pump model was chosen as a reference model with which to evaluate the performance of the new pump model and to validate the CFD results. The CFD results matched well with the experimental results for both models. In the experimental results, the efficiency of new model reached 73.4%, which is 8.2% higher than the efficiency of the old model at the design point. Moreover, under the all-flow conditions, the efficiency of the new model was higher than that of the old model.

Figure 8:

Comparison of performance curves of pump models

4.2 Hydraulic loss analysis

Using hydraulic loss analysis for the pump models is a helpful way to understand the reason for the varying performances of the different designs of pump model. Hydraulic losses of all fluid domains were calculated using Equation (6) and Equation (7).

where Δp is the change of total pressure in the analyzed domain, Q is flow rate pumped of the pump model, T is the torque provided to the impeller through the shaft of the motor, and ω is the angular velocity of the impeller. The subscript “Imp.” means the impeller domain. A comparison of the hydraulic losses of the old and new models at the design point is shown in Figure 9. The hydraulic losses of the new model declined significantly compared with those of the old model in most of the fluid domains. The loss of impeller domain decreased from 17.2% in the old model to 14.4% in the new model. The losses of the diffuser and outlet domains reduced drastically from 14.9% in the old model to 8.5% in the new model. The loss of impeller domain showed the highest loss in both pump models. Thus, the internal flows of the impeller fluid domain need to be investigated in further detail.

Figure 9:

Comparison of hydraulic losses of fluid domains between the old and new pump models by CFD analysis at the design point

4.3 Pressure contours in impeller domain

Figure 10 shows the static pressure contours of flow passages in both impeller models on a plane perpendicular to the flow direction at the middle of the impeller blades, at the BEP. The figure indicates a gradual increase in static pressure contours from the suction side (SS) to the pressure side (PS) of both pump model blades. The pressures that developed inside the flow passages of the new impeller were more uniform than those of the old model. Figure 11 presents the static pressure contours at the mid-span of the impeller models at the BEP. The static pressure in the flow passage around the blades increased owing to the effect of the blade lift force in both pump models. The lowest pressure is indicated at the suction side of the old impeller model. This is position at which where cavitation usually occurs in axial pumps.

Figure 10:

Static pressure contours of the impeller models on a plane perpendicular to flow direction (from view of entrance flow) at the BEP

Figure 11:

Static pressure contours at the mid-span of the impeller models under the BEP condition

4.4 Streamlines in the impeller domain

The streamlines of the old and new models are compared in Figure 12. Non-uniform flows were found in the vicinity of the hub area in the old model. Relatively large circulation areas occurred inside the old impeller passages, which is regarded to decrease the flow rate, and consequently the hydraulic power. Moreover, the loss in the impeller domain increased, and the pump efficiency decreased, as seen in the performance curves of the old pump model. In the new pump model, smooth streamlines are shown in the blade passages. Thus, the percentage loss in the impeller domain of the new pump model is lower than that of the old pump model; this demonstrates the higher efficiency of the new pump model.

Figure 12:

Streamlines of both impeller models on a plane perpendicular to flow direction (from view of entrance flow) under the BEP condition

4.5 Cavitation performance

The results of the internal flow analysis indicate that the lowest pressure areas of both models were in the leading edge. Therefore, the cavitation was analyzed to examine the areas that could start cavitation on the impeller blade. Both pump models were simulated under the BEP condition without changing the static pressure at the inlet of the pump. Thus, the efficiencies of neither pump model changed.

The Rayleigh–Plesset model was adopted as a cavitation model in the calculation analysis. The Rayleigh-Plesset equation [11] describes the growth of a vapor bubble in a liquid. The homogeneous model was selected with a pair of fluids; water refers to a value of “0” and water vapor (air) refers to a value of “1”. The values were used to evaluate the possibility of cavitation occurrence, as well as the areas on impeller surface in which cavitation could appear. The derivation and the parameters in the cavitation model are discussed extensively in F. Bakir et al. [12]. The standard parameters were used for the presented calculations.

Figure 13 and Figure 14 illustrate the water-air volume fraction (AVF) contours and values on the impeller blade surfaces of both pump models at the BEP. A small area on the leading edge of the impeller blade of the old model indicates a maximum AVF value of 0.13. An AVF value of zero was found in all spans of the new impeller model. This means that both impeller models had a very low possibility of cavitation occurrence at the BEP condition.

Figure 13:

Water-air volume fraction contours on the impeller surfaces of (a) old model and (b) new model at the BEP

Figure 14:

Air volume fraction distributions on the blade surfaces of the pump models at the BEP

Author Contributions

Conceptualization, V. L. Vu; Methodology, V. L. Vu; Software, Y. D. Choi; Validation, V. L. Vu; Formal analysis, V. L. Vu; Investigation, V. L. Vu ; Resources, V. L. Vu; Data Curation, V. L. Vu; Writing-original draft preparation, V. L. Vu; Writing-review and editing, V. L. Vu; Supervision, Y. D. Choi, Funding acquisition, Y. D. Choi.