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This work provides a detailed description of the fluid dynamic design of a low specific-speed industrial pump centrifugal impeller. The main goal is to guarantee a certain value of the specific-speed number at the design flow rate, while satisfying geometrical constraints and industrial feasibility. The design procedure relies on a modern optimization technique such as an Artificial-Neural-Network-based approach (ANN). The impeller geometry is parameterized in order to allow geometrical variations over a large design space. The computational framework suitable for pump optimization is based on a fully viscous three-dimensional numerical solver, used for the impeller analysis. The performance prediction of the pump has been obtained by coupling the CFD analysis with a 1D correlation tool, which accounts for the losses due to the other components not included in the CFD domain. Due to both manufacturing and geometrical constraints, two different optimized impellers with 3 and 5 blades have been developed, with the performance required in terms of efficiency and suction capability. The predicted performance of both configurations were compared with the measured head and efficiency characteristics.

The optimum configuration of a centrifugal pump is a compromise between reliability, low-cost manufacturing and high aerodynamic efficiency (Gopalakrishnan [

In this context, Termomeccanica Pompe S.p.A. and the “Sergio Stecco” Department of Energy Engineering at the University of Florence started a joint research project for the design of pump stages, mainly based on the use of CFD techniques coupled with modern optimization tools.

The work described in this paper deals with the fluid dynamic design and optimization of the centrifugal impeller of a low specific-speed pump. The optimization campaign aimed at matching the design point and the best efficiency point with a prescribed specific-speed number, together with an overall minimum value of the pump efficiency and a good suction capability.

The design of the impeller was carried out using an in-house parameterization tool (e.g., Bonaiuti et al. [

In order to obtain a prediction of the pump performance, the impeller was coupled with all the static components. These ones, especially the volute, are key factors for the performance of a low specific-speed centrifugal pump. Their flow environment is very complex, and the performance prediction is a challenging task for CFD. Moreover, a CFD simulation of the whole pump is an extremely time-consuming task. For these reasons, a simple 1D model based on correlations was used to account for their influence on the pump. The proposed approach was validated against the experimental data available for an existing pump with a specific-speed number

Two different optimizations were performed aiming at obtaining a 3-blade and a 5-blade impeller, while satisfying geometrical constraints and industrial feasibility. A multistep approach was considered for the first one, while a global approach was used for the second one. After the optimization, both impellers were manufactured, and the predicted performance was verified against the experimental data in terms of head and efficiency characteristics.

The three-dimensional impeller geometry is handled in a parametric way. In a direct design procedure, it is essential to parameterize the component using as few geometrical parameters as possible. To this end, the geometrical properties of integral B-spline curves are exploited, for which the shape of the curve can be controlled using a few control points. A three-dimensional cylindrical coordinate system (

Cylindrical coordinate system.

The input of the parameterization tool are the following geometrical data.

Meridional channel.

The impeller computational domain was discretized with a structured elliptic single-block H-grid with

3D view of the impeller grid.

2D view of the meridional channel grid.

The multirow, multiblock, incompressible single-phase version of the TRAFMS code (Arnone [

The spatial discretization of the equations is based on a finite-volume cell-centered scheme. A blended second- and fourth-order artificial dissipation model, together with an eigenvalue scaling, is used in order to minimize the amount of artificial diffusion inside the shear layers. The equations are advanced in time using an explicit four-stage Runge-Kutta scheme, until the steady state solution is reached. In order to reduce the computational cost and speed up convergence to the steady solution, four computational techniques are employed: local time stepping, implicit residual smoothing, multigrid full-approximation storage (FAS), and grid refinement. Several turbulent closures are available, namely, the algebraic Baldwin-Lomax model [

The code has recently been used for the design and optimization of centrifugal and mixed-flow pump components (Arnone et al. [

Stage performance is evaluated considering fluid dynamic area-averaged quantities at two sections, the first one just upstream of the impeller leading edge and the second one downstream of the impeller trailing edge. In Figure

In order to evaluate the pump specific speed, it is necessary to model all the pump components. Two approaches can be followed: the first one is to include all the pump components in the CFD domain, and the second one consists of the CFD analysis of the impeller alone and uses a correlative approach to account for the losses of the other components. The first method has a high computational cost, and thus it is not suitable for optimization purposes. The second one is much less time consuming and more appropriate for use in an optimization procedure. For this reason, the latter approach was selected in this work for calculating the pump performance. Additional losses related to the static components, at a given flow rate, were estimated by means of a 1D code:

leakages (Stepanoff [

ducts: inlet and outlet conical diffusers, discharge bent duct (Idel'cik [

circular volute (Van den Braembussche [

The optimization method is based on the use of Artificial Neural Networks (ANNs). ANNs are used for the construction of metamodels of each constraint or objective function within an optimization. They are chosen mainly for one reason: the use of metamodel allows performing calculations in parallel, with a consequent reduction of the overall timescale of the activity [

Experimental data are available for a pump with

The

Comparison between predicted and measured pump characteristics (

The agreement is fairly good with the exception of the higher flow rates where a steep degradation is visible in the measured pump performance due to cavitation. Going towards the low flow rates, unsteady flow phenomena tend to arise, and it is not possible to calculate the impeller with a steady-state approach.

The objectives of the design of the new pump were

specific-speed number of

overall minimum value of total-to-total efficiency of the pump (

good suction capability (

The imposed constraints follow the industrial requirements of feasibility. In the low specific speed range, the impeller passage height at the outlet (

The chosen degrees of freedom are 11 geometrical parameters of the impeller. This choice has been carried out based on the specified target to be reached (see Table

Degrees of freedom and their influence on pump's performance.

BEP at DP | |||||||||||

Since the industrial requirement is to design a 2D blade in the

Blade sections, stacked at the TE, have a constant thickness over the whole camber line, the leading edge is shaped with a prescribed curve, and the trailing edge is cut at a constant radius.

In the present application, the number of blades is not a degree of freedom and only two configurations have been investigated for industrial needs: a 3-blade impeller and a 5-blade impeller. A 5-blade impeller configuration, with the same constraints on the minimum value of

Hence, starting from the same set of parameters, two optimizations were carried out at the design point (DP), and two different strategies were chosen. For the 3-blade impeller, the optimized geometry was obtained by means of a multistep analysis. During each step, a limited number of parameters were varied, and the range of variation was progressively refined. For the 5-blade impeller, a one-step global method was adopted, and all the parameters were involved in the optimization procedure with a large range of variation. Generally speaking, the computational cost of the first method is lower, but the results can be affected by the designer's choice of the various subset of parameters considered in each single step. On the contrary, the main advantage of the global method is that the only critical choice is related to the initial selection of the parameters. The influence of all the parameters is then investigated at the same time. The higher the number of parameters, the higher the number of computations needed for an appropriate training of the neural network. As a result, the second method would require a much higher number of calculations with respect to the first one. Despite this fact, the two optimization procedures were applied by using about the same amount of computational resources, for testing them against a tight industrial design scheduling. Each computed geometry required about 1.5 hours on a Xeon CPU X5650 at 2.67 GHz, so that a single optimization was obtained in 3 days on a 40-core cluster.

A three-step method was chosen to perform this optimization. Since the specific-speed number (

Parameters varied in 3-blade impeller optimization's steps.

OPT STEP | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

1st | |||||||||||

2nd | |||||||||||

3rd |

Once the

The final step of the optimization involved the 6 parameters, yet investigated in the first step, with a refined range of variation. In fact, this subset of parameters is the most effective for obtaining the target specific speed. Results of the computations performed in the various steps are summarized in Figure

Sample and validation set sizes for the two metamodels.

sample set size | validation set size | |
---|---|---|

OPT3 | 676/594/150 | 20/30/30 |

OPT5 | 1757 | 30 |

The optimization clouds: (a) 3-blade impeller, (b) 5-blade impeller.

In this case, the optimization was carried out in a single step, and the eleven parameters were allowed to vary at the same time, covering a range of values as wide as possible. The

Two-response surfaces were generated for the 3-blade and 5-blade impeller, respectively. Hence, two different Artificial Neural Networks were trained since the goal was to obtain two optimized impellers with a different number of blades. The two optimization clouds are shown in Figures

Comparison between pump performance predicted by ANN and calculated with CFD.

ANN | CFD | ANN | CFD | |

OPT3 | 9.59 | 9.65 | +0.67% | +0.60% |

OPT5 | 9.56 | 9.43 | +0.24% | +0.27% |

The predicted operating characteristics of the two optimized geometries are compared with experimental data in Figure

Comparison between computed 3-blade and 5-blade pump characteristics (

Figure

Spanwise distributions at DP in the outlet region.

The relative velocity magnitude contours in a blade-to-blade section at midspan are shown in Figure

3D view of the impeller flow field at DP (

OPT3

OPT5

Pressure distributions at BEP for three different spans,

In this paper, the aerodynamic design of the impeller of a low specific-speed pump was presented and described in detail. The design targets were to match the design point and the best efficiency point with a prescribed specific-speed number (

Such a process started with the CFD analysis of the

The aerodynamic design of the impeller was carried out using a parameterization tool which allowed a direct control on manufacturing and structural constraints and made it possible to identify the effect of single parameters on impeller aerodynamic performance. The overall design procedure exploited a Neural-Network-based approach which was a fast and powerful tool for the optimization of the pump performance. Two configurations with a 3-blade (OPT3) and a 5-blade (OPT5) impellers were selected and optimized with the additional target of obtaining a good suction capability (

Both configurations satisfied the desired targets of specific speed and efficiency, with an increase of about 0.6%, for OPT3, and 0.3%, for OPT5, with respect to the minimum required value at DP. The 5-blade impeller configuration was able to mitigate the flow recirculation inside the impeller passages which instead tended to persist with the 3-blade solution, due to the constraints on the impeller exit width and on the blade angular development. Results obtained with the proposed optimization method were assessed against experimental data for the pumps with the 3-blade and the 5-blade impellers. A very good agreement was found between the predicted and measured operating characteristics demonstrating how the proposed approach offers an economical and reliable design tool for industrial needs.

Impeller width (m)

Absolute velocity magnitude (m/s)

Gravity acceleration (m/s^{2})

Head (m)

Meridional abscissa (m)

Impeller rotational speed (rpm)

Specific-speed number,

Pressure (Pa)

Inlet total pressure for cavitation criterion (Pa)

Volume flow rate (m3/s)

Cylindrical coordinates.

Flow angle, tan^{−1}(

Metal angle (°)

Efficiency,

Slope angle in the meridional plane (°)

Density (kg/m^{3})

Azimuthal angle (°).

Inlet section

Outlet section

Circumferential

Blade

Hub

Intermediate, meridional

Maximum value

Radial

Reference value

Tip

Total

Vapor

Axial.

Artificial Neural Networks

Best efficiency point

Computational fluid dynamics

Design point

Leading edge

Net positive suction head,

Optimized 3-blade impeller

Optimized 5-blade impeller

Trailing edge.

The authors would like to express their appreciation for the financial support from the Italian Ministero dell'Istruzione, Universitá e Ricerca (MIUR), under the Research Project PACOMAR no. DM29847. They would also like to express their gratitude to Ing. Andrea Schneider of the University of Florence for the numerous and fruitful discussions on the use of artificial neural networks.