Bellmouth Shape Optimization for the Suppression of Flow Instability in a Pump Sump Model

1. Introduction

The pump sump is widely used in the industrial and agricultural sectors because it is an integral component of the pumping system. The performance of the pumping system is directly related to the flow behavior in the pump sump. Hence, the stable flow should be maintained in the pump sump to reduce efficiency drop, cavitation, swirl flow, vorticity, noise, and vibration.^(1,2) The proper design of the pump sump is a necessity for the stable operation of the pumping system. The poor intake design of the pump sump causes swirl flow in the pumping system.⁽³⁾

The pump sump design consists of a suction pipe and a sump.⁽⁴⁾ The standards and guidelines for pump sump design are published by American National Standards Institution (ANSI),⁽⁵⁾ the British Standards Institution (BSI),⁽⁶⁾ the Japan Society of Mechanical Engineers (JMSE).⁽⁷⁾ Generally, BM is the most common intake structure for the pump sump.⁽⁸⁾ BMs are used to reduce the flow instabilities before entering into the pumping system.⁽⁹⁾ However, many vortices exist in the pump sump, which causes swirl flow, cavitation, noise, and vibration.⁽¹⁰⁾ The uneven flow distribution and large-scale turbulence are occurred in the pump sump.⁽¹¹⁾ The air-entraining vortices occur at the intake of the pump sump.⁽¹²⁾

Rajendran et al.⁽¹³⁾ made a 3D turbulent flow analysis in the pump sump and compared it with the experimental results. Li et al.⁽¹⁴⁾ observed velocity streamlines in the pump sump intake using Reynolds-Averaged Navier Stokes (RANS) equation. They concluded that the steady-state is unable to elaborate the flow in the pump intake. Nagahara conducted a PIV experiment and CFD analysis to visualize flow streamlines in the pump sump intake.⁽¹⁵⁾ Tokyay and Constantinesu compared the flow structure in the pump sump by large eddy simulation (LES) and RANS models with PIV measurement.⁽¹⁶⁾ They concluded that the LES model provides better predictions of the velocity, vorticity, streamline than the Shear Stress Transport model.⁽¹⁶⁾ The LES approach is suitable for the unsteady flow prediction in the pump sump.⁽¹⁷⁾ Bayeul et al.⁽¹⁸⁾ also used a CFD commercial code to predict the flow behavior in the pump sump and study the flow characteristic of air entertainment by comparing multi-phase numerical study results with experimental investigations.

The proper intake design provides uniform swirl-free flow to the pumping system.⁽¹⁹⁾ The anti-vortex device (AVD) is used to suppress vortex instability in the pump sump.²⁰⁾ Kim et al.⁽²¹⁾ showed the effectiveness of AVD for the suppression of vorticity and turbulence kinetic energy. In this study, various design approaches were adopted for the proper parametric design of BM. The basic design process is incorporated with optimization to generate an optimized BM shape. Therefore, this study is aimed to suppress the flow instabilities like vorticities and swirl flow at the intake.

2. Design and Numerical Methodology

2.1 Design of bellmouth shape

The BM shape is essential for the proper operation of the pump sump. The BM shape can be designed by using various techniques. This study adopted three design methods: a) radius method,⁽²²⁾ b) elliptical method,⁽²²⁾ and c) spline method.⁽²³⁾ Fig. 1 shows the design methods of BM using radius, elliptical, and spline methods. D₁ and D₂ are 50 mm and 100 mm, respectively.

Fig. 1

Design methods for BM a) radius method b) elliptical method and c) spline method

In the radius method, the circular arc is used to make the BM shape. The BM shape is prepared by an ellipse in the elliptical. In the spline method, a spline curve is used to design the BM shape.

In the radius method, the radius of curvature is considered as the design parameter. Fig. 1 a) indicates the arc radius r is used to embody the BM shape. Similarly, in the elliptical design method, an ellipse is used to make the BM shape, whose design parameters are major and minor radii. Fig. 1 b) indicates that a and b are major and minor radii of the ellipse, respectively. In the spline method, the three spline points are used to make the BM shape. Thus, the horizontal and vertical coordinates are considered as the design parameters. Fig. 1 c) shows that points P₁, P₂ and P₃ are used to create the spline curve. The coordinate of these spline points was used as design parameters for BM from the spline method.

The initial design of BM was adopted from the previous studies.^(24-26) The initial BM shape design is based on the radius method. Fig. 2 indicates the 2D view of the pump sump model and measurement location. The same BM position and diameters are used for the optimization.

Fig. 2

a) Cross section view and b) top view of BM in pump sump

The initial BM shape is prone to the vortex core and swirl flow. In this study, the BM shape optimization was performed to suppress the vortex core.

2.2 Numerical Methodology

CFD analysis is used to investigate the flow behavior in the pump sump. ANSYS CFX 19.2⁽²⁷⁾ was used to conduct CFD analysis. The structured grids were generated using ANSYS ICEM 19.2⁽²⁷⁾ and shown in Fig. 3. Fig. 4 illustrates the boundary conditions for pump sump analysis. The red and blue colors represent the water and air, respectively. The upper section of the pump sump is subject to atmospheric pressure. The unsteady internal flow in the pump sump is changing according to the CFD methods. The various models were selected to illustrate the internal flow behavior in the pump sump. The average y+ value for the BM is less than 5. Therefore, the numerical grids are suitable for the CFD analysis. Boundary conditions were adopted from previous studies,^(23,26) which is illustrated in Table 1. The instantaneous results at 10 sec were used to observe the vortex at the BM inlet.

Fig. 3

Numerical grid of pump sump with initial BM shape

Fig. 4

Boundary conditions for BM CFD analysis

Table 1

Boundary conditions for the CFD analysis of pump sump

The vorticity illustrates the flow field in the BM inlet. It is defined as the curl of the flow velocity (u), and the definition can be expressed as in Eq. (1).

$\[ {\omega }^n=\nabla \times \overrightarrow{u} \]$

(1)

The mesh dependency test was conducted as shown in Fig. 5, and 1 million nodes are suitable for DES, LES, and SAS-SST analysis method Fig. 6 shows vorticity distribution in the BM at line AA. The maximum vorticity in the BM inlet is 400 s.^-1 The swirling strength (λ) is the excellent vortex indicator in the wall turbulence.⁽²⁸⁾

Fig. 5

Mesh dependency test

Fig. 6

Vorticity with various methods in initial BM shape

Fig. 7 shows the swirling strength comparison among various methods. Finally, LES was selected to optimize and visualize the internal flow in BM.

Fig. 7

Swirling strength contours with various turbulence model in initial BM shape

3. Optimization Methodology

Fig. 8 shows the flow chart for the BM shape optimization process. The optimization flow chart explains the process required to perform optimization. The parametric design of the BM shape was achieved by various design methods. The surrogate model was prepared, which predicts the objective functions with a change in design variables. The precise surrogate model was selected based on the goodness of fit.⁽²⁹⁾ The multi-objective genetic algorithm⁽²⁹⁾ was used to obtain the optimal shape for the BM. Finally, the optimal solution was verified by CFD analysis. Hence, the optimal BM shape will be achieved.

Fig. 8

Optimization methodology for BM shape optimization

3.2 Surrogate modeling

Surrogate modeling is an essential part of the optimization process. The surrogate model is the approximation model used to predict the objective function with a change in design parameter values. The preparation of the surrogate model is highly dependent on the design of experiments (DOE). Therefore, the optimal space-filling method⁽²⁹⁾ was selected to generate DOE within the design space. The bound values for design parameters are shown in Table 2. The design space is considered to satisfy the limitation of BM shape and pump sump design.

Table 2

Bound values for the BM shape design

Recently, numerous techniques are available for the generation of the surrogate model. The methods like genetic aggregation (GA),⁽³⁰⁾ Kriging (KG),⁽³¹⁾ radial basis function (RBF),⁽³²⁾ non-parametric regression (NPR),⁽³³⁾ neural network (NN)⁽³⁴⁾ are available to prepare the surrogate model. Among these methods, GA was selected to formulate the explicit surrogate model.⁽²⁹⁾ The surrogate model reduces the computational cost and time. It can interpolate numerous design points for the optimization process. Hence, an accurate surrogate model will provide a precise approximation between design variables and objective functions.

3.3 Optimization Algorithm

The optimization formulation for the BM shape optimization is shown in Eq. (5).

$\[ \begin{array}{l}maximize S_u\left(d_i\right)\\ minimize {\omega }^n\left(d_i\right)\\ subject to d_i^L\le d_i\le d_i^U\end{array} \]$

(5)

where S_u is the flow uniformity, ωⁿ is the vorticity, d_i is the design parameter varying according to the design method, superscript L and U are lower and upper bound of design parameters.

Flow uniformity is defined as the deviation between local and average flow velocity in the specified cross-section area. It is calculated by using Eq. (6).

$\[ S_u=\left[1-\oint \frac{\sqrt{\left(u-\stackrel{-}{u}\right)}}{2A\stackrel{-}{u}}\right]\times 100\% \]$

(6)

where u is the local velocity, u is the average flow velocity, A is the cross-sectional area.

The flow uniformity and vorticity are measured at the BM inlet. The multi-objective genetic algorithm (MOGA) was used to optimize the BM shape. The setting criteria for MOGA were adopted from the previous study,⁽²⁹⁾ which is indicated in Table 3.

Table 3

Setting criteria for Optimization

4. Results and Discussion

4.1 Optimal BM shape

The Pareto front is used to obtain the optimal design based on design criteria. The vorticity and flow uniformity were chosen to prepare the Pareto front. The vorticity and flow uniformity were measured on the line AA. The Pareto front indicates the trade-off between vorticity and flow uniformity in the BM. Pareto fronts from various design methods are compared in Fig. 9. The optimal BM shape from the radius method is preferable for the vortex suppression in the BM. Fig. 10 indicates optimal BM shape comparison generated by radius, elliptical, and spline design methods.

Fig. 9

Pareto front for the BM shape optimization

Fig. 10

Comparison between initial and optimal BM shapes

The optimal BMs were selected from various design methods. Fig. 11 shows a vorticity comparison between initial and optimal BM shapes from various design methods. The change of vorticity from negative to positive value indicates the direction change of vortex in the initial BM shape. Moreover, the magnitude of vorticity in the BMs with radius, elliptical, and spline methods are 315 s^-1, 610 s^-1, and 560 s^-1, respectively. The optimal BM shape from the radius method has minimum vorticity compared to other design methods.

Fig. 11

Vorticity comparison between initial and optimal BM shapes with a) radius b) elliptical and c) spline methods

Fig. 12 shows the circumferential velocity contours in the initial and optimal BM shape. The eccentric and negative velocity movement is visible in the initial BM shape. The negative circumferential velocity is the cause of negative vorticity in the initial BM, as shown in Fig. 11. The BM shape optimization successfully suppressed the negative velocity distribution at the BM inlet. The BM designed by the elliptical and spline method showed a larger negative velocity zone compare to the radius method. The difference in positive and negative velocity zone is the cause for the swirl flow and vortex formation in the BM. The circumferential velocity distribution is more uniform in the optimal BM by radius method than other BM shapes, which reduces the vorticity strength. The proper BM designed is required to suppress swirl flow and vortex instability in the pumping system. Therefore, the optimal BM shape from the radius method was selected.

Fig. 12

Circumferential velocity contour comparison in a) initial and optimal BM shapes by b) radius c) elliptical d) spline methods

4.2 Comparison between initial and optimal BM shapes

The optimal BM shape was prepared by the radius method. A detailed flow behavior comparison between initial and optimal BM shapes was accomplished. Fig. 11 shows the possibility of the vortex in the BM. The optimal BM reduces the vorticity from 423 s^-1 to 315 s^-1. Therefore, the optimization of BM suppresses the vortex strength in the pump sump. Fig. 13 shows the comparison between circumferential velocity in the BM shape. The sharp circumferential velocity drop indicates the strong vortex in the proximity of the BM center. The magnitude of negative circumferential velocity is decreased from 1.51 m/s to 0.55 m/s with the optimal BM shape. Moreover, the optimal BM shape helps to recover the steep fall in the circumferential velocity. Eventually, the vortex strength is suppressed by the optimal BM shape installation.

Fig. 13

Circumferential velocity comparison between initial and optimal BM shape

Furthermore, qualitative analyses were used to visualize the swirl flow and vortex instability in the BM. Fig. 14 illustrates the pressure contours comparison in the initial and optimal BM shape. The pressure contours indicate a large negative static pressure zone in the initial BM shape, which leads to cavitation, noise, and vibration. The optimal BM shape recovers the negative pressure in the BM inlet. Fig. 15 represents the swirling strength in the BM. At the vortex center, the swirling strength is comparatively higher than in other locations. It implies that the suppression of swirling strength will reduce the vortex strength in the BM. Fig. 15 shows that the optimal BM shape reduces the swirling strength at the vortex core and in the inner edge of the optimal BM shape.

Fig. 14

Static pressure contour comparison between a) initial and b) optimal BM shapes

Fig. 15

Swirling strength comparison between a) initial and b) optimal BM shapes

The comparison between initial and optimal BM shapes is shown in Table 4. The flow uniformity is increased from 62.85 % to 96.28 % in the optimal BM inlet. The installation of optimal BM reduced the swirling strength from 431 s^-1 to 104 s^-1. The average static pressure changed to a positive value in optimal BM shape, compared to the initial BM shape. The higher flow uniformity indicates that the difference in the average and local flow velocity is minimum.

Table 4

Comparison between initial and optimal BM shape

The optimal BM shape improved the flow uniformity and suppressed the swirling strength significantly at the BM inlet. Hence, the optimal BM is effective in the suppression of the vortex instability in the pump sump.

5. Conclusions

The vortex instability in the pump sump intake is dependent on the BM shape. The radius, elliptical, and spline design techniques were selected to design the BM shape. The radius, elliptical, and spline design methods are one design variable, two design variables, and six design variables optimization problems, respectively. The BM shape design with the spline method is a high-dimensional problem compare to other design methods. The design of BM is highly complicated with the spline method.

The flow uniformity and vorticity were selected as the performance measures for the BM shape optimization. The optimal BM shape is obtained from each design approach. The Pareto front and CFD analyses showed that the radius method is suitable for the BM shape design. Therefore, the optimal BM shape was selected from the radius design method.

The comparison between initial and optimal BM shapes was carried out. The flow uniformity was increased from 62.85% to 96.28% with the installation of optimal BM shape. The vorticity was decreased from 4340 s^-1 to 730 s^-1. The optimization of the BM shape reduced the vortex instability at the BM inlet. The static pressure was increased drastically in optimal BM shape compare to the initial one. Hence, the cavitation possibility was minimized with the installation of an optimal BM shape. Therefore, the effective suppression of cavitation, swirl flow, and vorticity is possible from the optimal BM shape installation.

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