Journal of Physics: Conference Series You may also like PAPER • OPEN ACCESS Decoupled CFD-based optimization of efficiency and cavitation performance of a double-suction pump - Interaction of impeller and guide vane in a series-designed axial-flow pump S Kim, Y S Choi, K Y Lee et al. To cite this article: A Škerlavaj et al 2017 J. Phys.: Conf. Ser. 813 012048 - Characterizing flows with an instrumented particle measuring Lagrangian accelerations Robert Zimmermann, Lionel Fiabane, Yoann Gasteuil et al. - A novel energy harvesting device for selfmonitoring wireless sensor node in fluid dampers Si Qi Wang, Miao Yu, Jie Fu et al. View the article online for updates and enhancements. This content was downloaded from IP address 18.209.175.170 on 16/01/2023 at 07:30 Hyperbole IOP Conf. Series: Journal of Physics: Conf. Series 813 (2017) 012048 IOP Publishing doi:10.1088/1742-6596/813/1/012048 Decoupled CFD-based optimization of efficiency and cavitation performance of a double-suction pump A Škerlavaj1,2, M Morgut2, D Jošt1 and E Nobile2 Kolektor Turboinštitut, Rovšnikova 7, 1210 Ljubljana, Slovenia University of Trieste, Department of Engineering and Architecture, Piazzale Europa 1, 34127 Trieste, Italy 1 2 E-mail: aljaz.skerlavaj@kolektor.com Abstract. In this study the impeller geometry of a double-suction pump ensuring the best performances in terms of hydraulic efficiency and reluctance of cavitation is determined using an optimization strategy, which was driven by means of the modeFRONTIER optimization platform. The different impeller shapes (designs) are modified according to the optimization parameters and tested with a computational fluid dynamics (CFD) software, namely ANSYS CFX. The simulations are performed using a decoupled approach, where only the impeller domain region is numerically investigated for computational convenience. The flow losses in the volute are estimated on the base of the velocity distribution at the impeller outlet. The best designs are then validated considering the computationally more expensive full geometry CFD model. The overall results show that the proposed approach is suitable for quick impeller shape optimization. 1. Introduction Centrifugal pumps are widely used in industrial applications. Double-suction (also called: doubleentry) centrifugal pumps allow transportation of greater flow rates than single-entry pumps [1] because they are less prone to cavitation problems (smaller NPSHR, required net positive suction head). Another advantage is counter-balancing of axial hydraulic forces due to double-entry design [1]. The optimization techniques bring many benefits over the traditional "trial-and-error" design process, including less hard-to-spot human-based errors. In turbomachines in general, usually multiple objectives are to be optimized. One of the first multi-objective optimization study was performed by Lipej and Poloni [2]. Due to importance of centrifugal pumps in industrial applications, as well as of pump-turbines, many recent studies aim to optimize their geometry to improve their performance. Shingai et al. [3] performed a multi-objective optimization of pump-turbine, where the objectives were efficiency of turbine, pump efficiency, cavitation characteristics for both types of operation, torque to hold runner blades and total pump head. Xuhe et al. [4] optimized pump turbine for efficiency in both modes of operation whereas Zhang et al. [5] performed optimization of a centrifugal pump for vibration, using fluid-structure interaction (FSI). The purpose of this work is to propose and validate an economical decoupled simulation method for the optimization of a pump. In the presented decoupled optimization case, only the impeller geometry was allowed to be modified, while the rest of the geometry was fixed. Therefore, initially, Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd 1 Hyperbole IOP Conf. Series: Journal of Physics: Conf. Series 813 (2017) 012048 IOP Publishing doi:10.1088/1742-6596/813/1/012048 flow losses in the volute were estimated from CFD simulations as a function of the velocity distribution at the inlet of the volute. During the optimization only the flow in the impeller passage was simulated, whereas the flow losses in the volute were assessed from impeller outflow velocity distribution. The validation of the method was performed, for the most promising design candidates, by using a full geometry coupled method, considering the suction chambers, full impeller geometry and the double volute. However, given the interest in comparing the two methods, the non-uniformity of the flow at the impeller inlet due to the suction chambers was deliberately disregarded in case of the coupled method, by using the so-called stage (mixing plane) condition at the rotor-stator interface. Besides the maximization of pump's hydraulic efficiency, also the minimization of the cavitation extent was set as the objective of the optimization. For the latter objective, a simple method for estimation of reluctance to cavitation was used and validated. In this study, the specific speed nq of a pump was equal to 62 (specified per impeller side). 2. Numerical procedure The geometry of the double-suction centrifugal pump is presented in figure 1. Instead of using the fullgeometry (in this paper also called coupled) model (figure 1a), the optimization was performed for a decoupled model (figure 1c). The coupled model was used during the validation process, to compare the decoupled model to the coupled one. Figure 1. Double-suction centrifugal pump. (a) Geometry. In yellow: inlet pipe with suction chambers. In blue: impeller. In green: double volute with outlet pipe. (b) Double sided impeller. (c) Mesh of the impeller passage. Arrows represent inlet and outlet boundary conditions for the coupled (a) and the decoupled (c) simulation case. It is well known that the suction chamber delivers a non-uniform flow to the pump impeller, which for instance results in length of the blade-attached cavities, varying upon the theta (circumferential) position of the impeller blade. In [6] it was shown that the growth and reduction of the cavities strongly depend upon the location, strength and rotation direction of the vortices formed in the suction chamber, close to the rib. In [7] the non-uniformity was quantified with the angle 𝛾 = arctg(𝑣𝑐𝑖𝑟𝑐 ⁄𝑣𝑎𝑥𝑖𝑎𝑙 ). Before performing the decoupled optimization, the coupled CFD simulation was performed, to obtain the velocity distribution at the impeller inlet. The angle γ and the velocity distribution at the grid interface between the suction chamber and the impeller is presented in figure 2. 2 Hyperbole IOP Conf. Series: Journal of Physics: Conf. Series 813 (2017) 012048 IOP Publishing doi:10.1088/1742-6596/813/1/012048 In the optimization phase, which was performed with the decoupled CFD model (figure 1c), the velocity components at the inlet boundary condition were prescribed as a function of radius around the rotation axis (figure 2b). At the outlet, the average pressure boundary condition was set. Periodic boundary conditions (in grey in figure 1c) were used to take into account the periodicity of the impeller passage. For the impeller, the shape of the meridional channel was based on past experience and was not modified during the optimization procedure. On the other hand, the blade passage geometry was generated from a set of 14 input parameters provided by an in-house code that uses an inverse-singularity method. The data was exported to ANSYS DesignModeler commercial tool, where a 3-D geometry of an impeller was automatically created. For each geometry, a tetrahedral-based, unstructured mesh of the impeller was automatically created in ANSYS ICEM, which also provided the generation of 15 prism layers on the walls. Figure 2. Flow conditions at the impeller entrance. (a) Contour plot of angle γ at the outlet from the asymmetric suction chamber. Blue dashed lines represent flow directions from the suction chamber. (b) Distribution of axial, circumferential and radial velocities at the entrance to the impeller. Velocities are relative to the average axial velocity at the entrance to the impeller. Radial velocity values in graph are multiplied by the factor of 10. The optimization process was driven by modeFRONTIER 2014 [8] optimization platform. The objectives of the optimization were overall pump efficiency and reluctance to cavitation. The latter was assessed from the pressure difference between the impeller domain inlet boundary surface and the surface on the impeller blade, consisting of the leading edge and a part of the blade suction side. To obtain the overall pump efficiency, the flow losses of the volute ΔHvolute were assessed as a function of the angle α2 between circumferential and absolute velocity at the impeller outlet, at regions near hub, at midspan and near shroud: 𝛥𝐻𝑣𝑜𝑙𝑢𝑡𝑒 = 𝑓(𝛼2,ℎ𝑢𝑏 )+𝑓(𝛼2,𝑚𝑖𝑑𝑠𝑝𝑎𝑛 )+𝑓(𝛼2,𝑠ℎ𝑟𝑜𝑢𝑑 ) 3 , (1) where the function f, a relationship between the flow losses and the α2, was obtained prior to optimization from CFD simulations of the volute alone. Besides the two objectives, two constraints were used: the overall pump head (as an interval), as it also influences the direction of the optimizer towards large heads [9, 10], and the allowed Δα2mid-sh, the difference of α2 angle between the midspan and shroud intervals. Based on the volute simulations, the cases with the value of Δα2mid-sh smaller than two degrees were considered as unfeasible. Design of experiments (DOE), which fills the design space with the initial set of design variables, was based on the Latin Hypercube [11] samplings, but consisted also of some known high-efficiency designs, obtained in previous optimization cases. The Latin Hypercube sampling guarantees uniform random distribution of points over the variable range. The initial generation thus represented 48 sets of variables. Afterwards, the Multi Objective Genetic Algorithm (MOGA-II) [12], based on generational 3 Hyperbole IOP Conf. Series: Journal of Physics: Conf. Series 813 (2017) 012048 IOP Publishing doi:10.1088/1742-6596/813/1/012048 evolution, was used for 10 generations. Probability of directional cross-over, probability of selection and probability of mutation were set to 0.5, 0.05 and 0.1, respectively. The validation of the decoupled-simulation-based method was performed for the most promising design candidates, by using a full geometry coupled method. Namely, after performing CFD simulations on 480 cases, each one taking less than six minutes of clock-time to complete, the simulations were ordered by the predicted efficiency. The ones with the largest efficiency value were then validated using the full geometry model (figure 1a), using modeFRONTIER platform as a convenient way to drive the CFD simulations and performing the postprocessing. Both, coupled and decoupled CFD simulations, were performed with the ANSYS CFX software. These were performed only for the design point, as steady-state single-phase simulations with ShearStress-Transport turbulence model [13] with a curvature correction [14] (SST-CC). The 'highresolution' advection scheme was used, which is an upwind adaptive scheme, based on the Barth and Jespersen's limiter [15]. A local time-scale factor equal to 10 was used. For the decoupled case, simulations lasted for up to 550 iterations, or stopped when RMS residuals were smaller or equal to 1.10-5. The result data (head, torque and efficiency) were averaged over the last 20 iterations to produce meaningful result. It was checked that even for simulations with shorter number of iterations the averaging sample size choice did not influence the value of the output variables. For the validation with the coupled case, the simulations were performed using the stage condition [16] as a general grid interface between the impeller and the suction chamber on one side, and the volute on the other side. In this case the CFD simulations lasted for 600 iterations. All other settings remained the same. The process of case generation, case simulation and its postprocessing lasted for about 2:45 hours, on 128 computer cores. 3. Results and discussion Figure 3a presents predicted efficiency by using decoupled and full geometry numerical approach. Results are presented in relative form, ordered by the decreasing value of the efficiency of the decoupled simulations. Case 0 is the case with highest efficiency (relative efficiency of 100%). It can be noticed that the inclination of the trendline of the full geometry model prediction is similar to the inclination of the results of the decoupled approach, which means that in general such method can be used for the optimization. However, the line of predicted efficiency with full geometry approach is jagged, with values oscillating for approximately ±0.5%, so it is worth investigating the reasons for such behaviour. 100 99.5 99 Decoupled CFD Full geom. CFD Trendline - Full Geom. CFD 98.5 98 0 a) Relative flow losses in volute [%] Relative efficiency [%] 100.5 10 20 30 40 Ordered simulation number [-] 150 140 130 120 110 100 90 80 70 60 50 Decoupled CFD Full geom. CFD 0 50 b) 10 20 30 40 Ordered simulation number [-] 50 Figure 3. Comparison of (a) efficiency and (b) flow losses in the volute for decoupled and fullgeometry steady-state simulations. Cases are ordered by efficiency, obtained by the decoupled numerical model. Efficiency and flow losses are relative to the values obtained in case 0. 4 Hyperbole IOP Conf. Series: Journal of Physics: Conf. Series 813 (2017) 012048 IOP Publishing doi:10.1088/1742-6596/813/1/012048 Since for the decoupled approach the prediction of the flow losses in the volute is based on the α2 parameter, it is worth comparing predicted values of α2 at hub, midspan and shroud intervals for the two numerical approaches. In our case, for the decoupled approach, the α2 at hub was overpredicted by approximately 1.3°, whereas the α2 at shroud was underpredicted by approximately 1.3° (figure 4). At midspan, the underprediction was negligible, 0.2°. The systematic deviations at hub and at shroud, due to the volute interaction with the impeller, can be taken into account in future optimization processes, to improve the results. When the systematic deviations in figure 4 are eliminated, the discrepancy between the two curves in each graph is small, usually smaller than 1°. Nevertheless, flow losses, predicted by equation (1), do not change much when the corrected value of α2 is used. 23 21 21 Decoupled CFD, shroud Full geom. CFD, shroud Angle α2 [°] Angle α2 [°] 23 19 19 17 17 15 0 Decoupled CFD, hub Full geom. CFD, hub 10 20 30 40 Ordered simulation number [-] 15 50 0 10 20 30 40 Ordered simulation number [-] 50 Relative flow losses in volute [%] Figure 4. Angle α2 at hub and shroud, predicted by decoupled and full-geometry steady-state simulations. The order of the cases is the same as in figure 3. Angle α2 [°] 150 140 130 120 110 100 90 80 70 60 50 Losses - full geom. CFD Losses, predicted from alpha2 25 Alpha2 average - full geom. CFD Alpha2, hub - full geom. CFD24 23 22 21 20 19 18 17 16 10 20 30 40 Ordered simulation number [-] 0 Figure 5. Primary axis: relative (to case 0 baseline, as predicted by the CFD) flow losses in volute for the full geometry model - comparison of CFD and prediction by equation (1). Secondary axis: angle α2 - average value and value at hub. Order of cases is the same as in figure 3. For the reason presented above it is necessary to consider a modification of equation (1), to address other reasons influencing the volute flow losses. In figure 5 only the full geometry (coupled) CFD model is considered. For the full model, the flow losses predicted by equation (1), where angles α2 are obtained from the coupled simulations, are compared to the "real" losses (blue curves). It can be noticed that the approach presented by equation (1) is acceptable for designs from case 10 onwards. However, large discrepancy can be noticed for cases 0, 3, 4, 6, 7, 8, 9 and 33. These cases seem to be the cases where the value of α2,hub is smaller than the average value of α2 (figure 5). Small value of 5 Hyperbole IOP Conf. Series: Journal of Physics: Conf. Series 813 (2017) 012048 IOP Publishing doi:10.1088/1742-6596/813/1/012048 α2,hub seems to act beneficially on reducing the flow losses in the volute, so the equation (1) could be modified by using a weight factor, accounting for the low value of α2,hub. Apart from the efficiency, another objective of the optimization was reluctance to cavitation. A very simple variable was considered as indicative of this risk: minimal value of pressure difference Δp between the impeller domain inlet boundary surface and the surface on the impeller blade, consisting of the leading edge and a part of the blade suction side. In figure 6 it is possible to observe that the decoupled and the full geometry CFD approach predicted similar values of Δp. In figure 7 the values of Δp can be observed for cases 14 and 33. Although only the minimal value of such pressure difference is presented in figure 6, it can be observed in figure 7 that low-pressure values are attributed to a part of a surface, rather than just one point. This means that the result is not just a pure coincidence, based on a location of a node of the surface mesh. The proposed variable is therefore a good simple candidate for assessment of reluctance to cavitation. 0 0 10 20 30 40 50 -50000 Delta pressure [Pa] -100000 -150000 -200000 -250000 -300000 Decoupled CFD, shroud -350000 Full geom. CFD, shroud -400000 Ordered simulation number [-] Figure 6. Pressure difference between pressure at inlet to impeller domain and pressure at blade surface (leading edge and suction side). Comparison of decoupled and full-geometry steady-state CFD simulations. Order of cases is the same as in figure 3. Figure 7. Pressure difference, predicted by decoupled approach: (a) case 14; (b) case 33. 4. Conclusions A decoupled numerical model for the optimization of a double suction pump's impeller was presented. Results for the most promising candidates for high pump efficiency were validated with the full geometry CFD numerical models. The following conclusions were drawn:  The presented method with estimation of flow losses in the volute represents a good approach for quick optimization; 6 Hyperbole IOP Conf. Series: Journal of Physics: Conf. Series 813 (2017) 012048     IOP Publishing doi:10.1088/1742-6596/813/1/012048 Values of angle α2 at hub and at shroud predicted with the decoupled approach need small adjustments; Low value of angle α2, when compared to the average α2 value, acts beneficially on reducing the volute flow losses. The value α2 at hub should be included in the equation for determination of the volute flow losses; The presented Δp variable is a good simple candidate for the assessment of reluctance to cavitation. Acknowledgements The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme FP7/2007-2013/ under REA grant agreement n°612279 and from the Slovenian Research Agency ARRS - Contract No. 1000-15-0263. References [1] Gülich JF 2008 Centrifugal Pumps (Berlin: Springer-Verlag) p 926 [2] Lipej A and Poloni C 2000 Design of Kaplan runner using multiobjective genetic algorithm optimization J. Hydraul. Res. 38(4) pp 73–9 [3] Shingai K, Omura Y, Tani K, Tominaga H and Ito S 2008 Multi-objective optimization of diagonal flow type reversible pump-turbines Proc. of 24th Symp. on Hydraulic Machinery and Systems October 27-31 Foz do Iguassu (Madrid: IAHR) [4] Xuhe W, Baoshan Z, Lei T, Jie Z and Shuliang C 2014 Development of a pump-turbine runner based on multiobjective optimization IOP Conf. Ser.: Earth Environ. Sci. 22 012028 [5] Zhang Y, Hu S, Zhang Y, Chen L 2014 Optimization and analysis of centrifugal pump considering fluid-structure interaction Scientific World J. 2014 131802 [6] Škerlavaj A and Pavlin R 2014 Effect of vortical structures on cavitation on impeller blades in pumps with suction chambers IOP Conf. Ser.: Earth Environ. Sci. 22 052002 [7] Muntean, S., Škerlavaj, A., Drăghici, I. and Anton, L.E., 2015. Numerical analysis of the flow non-uniformity generated by symmetrical suction elbows of the large storage pumps Proceedings of 6th IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, Ljubljana, Slovenia. [8] ESTECO 1999-2016 modeFRONTIER User Manual (ESTECO: Trieste)p 504 [9] Kim JH, Oh KT, Pyun KB, Kim CK, Choi YS and Yoon JY 2012 Design optimization of a centrifugal pump impeller and volute using computational fluid dynamics IOP Conf. Ser.: Earth Environ. Sci. 15 032025 [10] Škerlavaj A, Morgut M, Jošt D and Nobile E 2016 Optimization of a single-stage doublesuction centrifugal pump To appear in proc. of 34th UIT Heat Transfer Conference July 4-6 Ferrara [11] McKay MD, Conover WJ and Beckman RJ 1979 Latin hypercube sampling: a comparison of three methods for selecting values of input variables in the analysis of output from a computer code Technometrics 21 239–45 [12] Poles S 2003 MOGA-II An improved Multi-Objective Genetic Algorithm (Trieste: ESTECO) [13] Menter FR, Kuntz M and Langtry R 2003 Ten years of industrial experience with the SST turbulence model Turbulence, Heat and Mass Transfer 4 ed K Hanjalić, Y Nagano et al (New York: Begell House) pp 625-32 [14] Smirnov PE and Menter F 2009 Sensitization of the SST turbulence model to rotation and curvature by applying the Spalart-Shur correction term J. Turbomach. 131 041010 [15] Barth TJ and Jespersen DC 1989 The design and application of upwind schemes on unstructured meshes Proc. of 27th Aerosp. Sci. Meet. (Reno: AIAA) 0366 (12pp) [16] ANSYS 2016 ANSYS CFX-Solver Theory Guide (ANSYS: Canonsburg) p 362 7 

Journal of Physics: Conference Series You may also like PAPER • OPEN ACCESS Decoupled CFD-based optimization of efficiency and cavitation performance of a double-suction pump - Interaction of impeller and guide vane in a series-designed axial-flow pump S Kim, Y S Choi, K Y Lee et al. To cite this article: A Škerlavaj et al 2017 J. Phys.: Conf. Ser. 813 012048 - Characterizing flows with an instrumented particle measuring Lagrangian accelerations Robert Zimmermann, Lionel Fiabane, Yoann Gasteuil et al. - A novel energy harvesting device for selfmonitoring wireless sensor node in fluid dampers Si Qi Wang, Miao Yu, Jie Fu et al. View the article online for updates and enhancements. This content was downloaded from IP address 35.172.111.127 on 16/01/2023 at 07:30 Hyperbole IOP Conf. Series: Journal of Physics: Conf. Series 813 (2017) 012048 IOP Publishing doi:10.1088/1742-6596/813/1/012048 Decoupled CFD-based optimization of efficiency and cavitation performance of a double-suction pump A Škerlavaj1,2, M Morgut2, D Jošt1 and E Nobile2 Kolektor Turboinštitut, Rovšnikova 7, 1210 Ljubljana, Slovenia University of Trieste, Department of Engineering and Architecture, Piazzale Europa 1, 34127 Trieste, Italy 1 2 E-mail: aljaz.skerlavaj@kolektor.com Abstract. In this study the impeller geometry of a double-suction pump ensuring the best performances in terms of hydraulic efficiency and reluctance of cavitation is determined using an optimization strategy, which was driven by means of the modeFRONTIER optimization platform. The different impeller shapes (designs) are modified according to the optimization parameters and tested with a computational fluid dynamics (CFD) software, namely ANSYS CFX. The simulations are performed using a decoupled approach, where only the impeller domain region is numerically investigated for computational convenience. The flow losses in the volute are estimated on the base of the velocity distribution at the impeller outlet. The best designs are then validated considering the computationally more expensive full geometry CFD model. The overall results show that the proposed approach is suitable for quick impeller shape optimization. 1. Introduction Centrifugal pumps are widely used in industrial applications. Double-suction (also called: doubleentry) centrifugal pumps allow transportation of greater flow rates than single-entry pumps [1] because they are less prone to cavitation problems (smaller NPSHR, required net positive suction head). Another advantage is counter-balancing of axial hydraulic forces due to double-entry design [1]. The optimization techniques bring many benefits over the traditional "trial-and-error" design process, including less hard-to-spot human-based errors. In turbomachines in general, usually multiple objectives are to be optimized. One of the first multi-objective optimization study was performed by Lipej and Poloni [2]. Due to importance of centrifugal pumps in industrial applications, as well as of pump-turbines, many recent studies aim to optimize their geometry to improve their performance. Shingai et al. [3] performed a multi-objective optimization of pump-turbine, where the objectives were efficiency of turbine, pump efficiency, cavitation characteristics for both types of operation, torque to hold runner blades and total pump head. Xuhe et al. [4] optimized pump turbine for efficiency in both modes of operation whereas Zhang et al. [5] performed optimization of a centrifugal pump for vibration, using fluid-structure interaction (FSI). The purpose of this work is to propose and validate an economical decoupled simulation method for the optimization of a pump. In the presented decoupled optimization case, only the impeller geometry was allowed to be modified, while the rest of the geometry was fixed. Therefore, initially, Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd 1 Hyperbole IOP Conf. Series: Journal of Physics: Conf. Series 813 (2017) 012048 IOP Publishing doi:10.1088/1742-6596/813/1/012048 flow losses in the volute were estimated from CFD simulations as a function of the velocity distribution at the inlet of the volute. During the optimization only the flow in the impeller passage was simulated, whereas the flow losses in the volute were assessed from impeller outflow velocity distribution. The validation of the method was performed, for the most promising design candidates, by using a full geometry coupled method, considering the suction chambers, full impeller geometry and the double volute. However, given the interest in comparing the two methods, the non-uniformity of the flow at the impeller inlet due to the suction chambers was deliberately disregarded in case of the coupled method, by using the so-called stage (mixing plane) condition at the rotor-stator interface. Besides the maximization of pump's hydraulic efficiency, also the minimization of the cavitation extent was set as the objective of the optimization. For the latter objective, a simple method for estimation of reluctance to cavitation was used and validated. In this study, the specific speed nq of a pump was equal to 62 (specified per impeller side). 2. Numerical procedure The geometry of the double-suction centrifugal pump is presented in figure 1. Instead of using the fullgeometry (in this paper also called coupled) model (figure 1a), the optimization was performed for a decoupled model (figure 1c). The coupled model was used during the validation process, to compare the decoupled model to the coupled one. Figure 1. Double-suction centrifugal pump. (a) Geometry. In yellow: inlet pipe with suction chambers. In blue: impeller. In green: double volute with outlet pipe. (b) Double sided impeller. (c) Mesh of the impeller passage. Arrows represent inlet and outlet boundary conditions for the coupled (a) and the decoupled (c) simulation case. It is well known that the suction chamber delivers a non-uniform flow to the pump impeller, which for instance results in length of the blade-attached cavities, varying upon the theta (circumferential) position of the impeller blade. In [6] it was shown that the growth and reduction of the cavities strongly depend upon the location, strength and rotation direction of the vortices formed in the suction chamber, close to the rib. In [7] the non-uniformity was quantified with the angle 𝛾 = arctg(𝑣𝑐𝑖𝑟𝑐 ⁄𝑣𝑎𝑥𝑖𝑎𝑙 ). Before performing the decoupled optimization, the coupled CFD simulation was performed, to obtain the velocity distribution at the impeller inlet. The angle γ and the velocity distribution at the grid interface between the suction chamber and the impeller is presented in figure 2. 2 Hyperbole IOP Conf. Series: Journal of Physics: Conf. Series 813 (2017) 012048 IOP Publishing doi:10.1088/1742-6596/813/1/012048 In the optimization phase, which was performed with the decoupled CFD model (figure 1c), the velocity components at the inlet boundary condition were prescribed as a function of radius around the rotation axis (figure 2b). At the outlet, the average pressure boundary condition was set. Periodic boundary conditions (in grey in figure 1c) were used to take into account the periodicity of the impeller passage. For the impeller, the shape of the meridional channel was based on past experience and was not modified during the optimization procedure. On the other hand, the blade passage geometry was generated from a set of 14 input parameters provided by an in-house code that uses an inverse-singularity method. The data was exported to ANSYS DesignModeler commercial tool, where a 3-D geometry of an impeller was automatically created. For each geometry, a tetrahedral-based, unstructured mesh of the impeller was automatically created in ANSYS ICEM, which also provided the generation of 15 prism layers on the walls. Figure 2. Flow conditions at the impeller entrance. (a) Contour plot of angle γ at the outlet from the asymmetric suction chamber. Blue dashed lines represent flow directions from the suction chamber. (b) Distribution of axial, circumferential and radial velocities at the entrance to the impeller. Velocities are relative to the average axial velocity at the entrance to the impeller. Radial velocity values in graph are multiplied by the factor of 10. The optimization process was driven by modeFRONTIER 2014 [8] optimization platform. The objectives of the optimization were overall pump efficiency and reluctance to cavitation. The latter was assessed from the pressure difference between the impeller domain inlet boundary surface and the surface on the impeller blade, consisting of the leading edge and a part of the blade suction side. To obtain the overall pump efficiency, the flow losses of the volute ΔHvolute were assessed as a function of the angle α2 between circumferential and absolute velocity at the impeller outlet, at regions near hub, at midspan and near shroud: 𝛥𝐻𝑣𝑜𝑙𝑢𝑡𝑒 = 𝑓(𝛼2,ℎ𝑢𝑏 )+𝑓(𝛼2,𝑚𝑖𝑑𝑠𝑝𝑎𝑛 )+𝑓(𝛼2,𝑠ℎ𝑟𝑜𝑢𝑑 ) 3 , (1) where the function f, a relationship between the flow losses and the α2, was obtained prior to optimization from CFD simulations of the volute alone. Besides the two objectives, two constraints were used: the overall pump head (as an interval), as it also influences the direction of the optimizer towards large heads [9, 10], and the allowed Δα2mid-sh, the difference of α2 angle between the midspan and shroud intervals. Based on the volute simulations, the cases with the value of Δα2mid-sh smaller than two degrees were considered as unfeasible. Design of experiments (DOE), which fills the design space with the initial set of design variables, was based on the Latin Hypercube [11] samplings, but consisted also of some known high-efficiency designs, obtained in previous optimization cases. The Latin Hypercube sampling guarantees uniform random distribution of points over the variable range. The initial generation thus represented 48 sets of variables. Afterwards, the Multi Objective Genetic Algorithm (MOGA-II) [12], based on generational 3 Hyperbole IOP Conf. Series: Journal of Physics: Conf. Series 813 (2017) 012048 IOP Publishing doi:10.1088/1742-6596/813/1/012048 evolution, was used for 10 generations. Probability of directional cross-over, probability of selection and probability of mutation were set to 0.5, 0.05 and 0.1, respectively. The validation of the decoupled-simulation-based method was performed for the most promising design candidates, by using a full geometry coupled method. Namely, after performing CFD simulations on 480 cases, each one taking less than six minutes of clock-time to complete, the simulations were ordered by the predicted efficiency. The ones with the largest efficiency value were then validated using the full geometry model (figure 1a), using modeFRONTIER platform as a convenient way to drive the CFD simulations and performing the postprocessing. Both, coupled and decoupled CFD simulations, were performed with the ANSYS CFX software. These were performed only for the design point, as steady-state single-phase simulations with ShearStress-Transport turbulence model [13] with a curvature correction [14] (SST-CC). The 'highresolution' advection scheme was used, which is an upwind adaptive scheme, based on the Barth and Jespersen's limiter [15]. A local time-scale factor equal to 10 was used. For the decoupled case, simulations lasted for up to 550 iterations, or stopped when RMS residuals were smaller or equal to 1.10-5. The result data (head, torque and efficiency) were averaged over the last 20 iterations to produce meaningful result. It was checked that even for simulations with shorter number of iterations the averaging sample size choice did not influence the value of the output variables. For the validation with the coupled case, the simulations were performed using the stage condition [16] as a general grid interface between the impeller and the suction chamber on one side, and the volute on the other side. In this case the CFD simulations lasted for 600 iterations. All other settings remained the same. The process of case generation, case simulation and its postprocessing lasted for about 2:45 hours, on 128 computer cores. 3. Results and discussion Figure 3a presents predicted efficiency by using decoupled and full geometry numerical approach. Results are presented in relative form, ordered by the decreasing value of the efficiency of the decoupled simulations. Case 0 is the case with highest efficiency (relative efficiency of 100%). It can be noticed that the inclination of the trendline of the full geometry model prediction is similar to the inclination of the results of the decoupled approach, which means that in general such method can be used for the optimization. However, the line of predicted efficiency with full geometry approach is jagged, with values oscillating for approximately ±0.5%, so it is worth investigating the reasons for such behaviour. 100 99.5 99 Decoupled CFD Full geom. CFD Trendline - Full Geom. CFD 98.5 98 0 a) Relative flow losses in volute [%] Relative efficiency [%] 100.5 10 20 30 40 Ordered simulation number [-] 150 140 130 120 110 100 90 80 70 60 50 Decoupled CFD Full geom. CFD 0 50 b) 10 20 30 40 Ordered simulation number [-] 50 Figure 3. Comparison of (a) efficiency and (b) flow losses in the volute for decoupled and fullgeometry steady-state simulations. Cases are ordered by efficiency, obtained by the decoupled numerical model. Efficiency and flow losses are relative to the values obtained in case 0. 4 Hyperbole IOP Conf. Series: Journal of Physics: Conf. Series 813 (2017) 012048 IOP Publishing doi:10.1088/1742-6596/813/1/012048 Since for the decoupled approach the prediction of the flow losses in the volute is based on the α2 parameter, it is worth comparing predicted values of α2 at hub, midspan and shroud intervals for the two numerical approaches. In our case, for the decoupled approach, the α2 at hub was overpredicted by approximately 1.3°, whereas the α2 at shroud was underpredicted by approximately 1.3° (figure 4). At midspan, the underprediction was negligible, 0.2°. The systematic deviations at hub and at shroud, due to the volute interaction with the impeller, can be taken into account in future optimization processes, to improve the results. When the systematic deviations in figure 4 are eliminated, the discrepancy between the two curves in each graph is small, usually smaller than 1°. Nevertheless, flow losses, predicted by equation (1), do not change much when the corrected value of α2 is used. 23 21 21 Decoupled CFD, shroud Full geom. CFD, shroud Angle α2 [°] Angle α2 [°] 23 19 19 17 17 15 0 Decoupled CFD, hub Full geom. CFD, hub 10 20 30 40 Ordered simulation number [-] 15 50 0 10 20 30 40 Ordered simulation number [-] 50 Relative flow losses in volute [%] Figure 4. Angle α2 at hub and shroud, predicted by decoupled and full-geometry steady-state simulations. The order of the cases is the same as in figure 3. Angle α2 [°] 150 140 130 120 110 100 90 80 70 60 50 Losses - full geom. CFD Losses, predicted from alpha2 25 Alpha2 average - full geom. CFD Alpha2, hub - full geom. CFD24 23 22 21 20 19 18 17 16 10 20 30 40 Ordered simulation number [-] 0 Figure 5. Primary axis: relative (to case 0 baseline, as predicted by the CFD) flow losses in volute for the full geometry model - comparison of CFD and prediction by equation (1). Secondary axis: angle α2 - average value and value at hub. Order of cases is the same as in figure 3. For the reason presented above it is necessary to consider a modification of equation (1), to address other reasons influencing the volute flow losses. In figure 5 only the full geometry (coupled) CFD model is considered. For the full model, the flow losses predicted by equation (1), where angles α2 are obtained from the coupled simulations, are compared to the "real" losses (blue curves). It can be noticed that the approach presented by equation (1) is acceptable for designs from case 10 onwards. However, large discrepancy can be noticed for cases 0, 3, 4, 6, 7, 8, 9 and 33. These cases seem to be the cases where the value of α2,hub is smaller than the average value of α2 (figure 5). Small value of 5 Hyperbole IOP Conf. Series: Journal of Physics: Conf. Series 813 (2017) 012048 IOP Publishing doi:10.1088/1742-6596/813/1/012048 α2,hub seems to act beneficially on reducing the flow losses in the volute, so the equation (1) could be modified by using a weight factor, accounting for the low value of α2,hub. Apart from the efficiency, another objective of the optimization was reluctance to cavitation. A very simple variable was considered as indicative of this risk: minimal value of pressure difference Δp between the impeller domain inlet boundary surface and the surface on the impeller blade, consisting of the leading edge and a part of the blade suction side. In figure 6 it is possible to observe that the decoupled and the full geometry CFD approach predicted similar values of Δp. In figure 7 the values of Δp can be observed for cases 14 and 33. Although only the minimal value of such pressure difference is presented in figure 6, it can be observed in figure 7 that low-pressure values are attributed to a part of a surface, rather than just one point. This means that the result is not just a pure coincidence, based on a location of a node of the surface mesh. The proposed variable is therefore a good simple candidate for assessment of reluctance to cavitation. 0 0 10 20 30 40 50 -50000 Delta pressure [Pa] -100000 -150000 -200000 -250000 -300000 Decoupled CFD, shroud -350000 Full geom. CFD, shroud -400000 Ordered simulation number [-] Figure 6. Pressure difference between pressure at inlet to impeller domain and pressure at blade surface (leading edge and suction side). Comparison of decoupled and full-geometry steady-state CFD simulations. Order of cases is the same as in figure 3. Figure 7. Pressure difference, predicted by decoupled approach: (a) case 14; (b) case 33. 4. Conclusions A decoupled numerical model for the optimization of a double suction pump's impeller was presented. Results for the most promising candidates for high pump efficiency were validated with the full geometry CFD numerical models. The following conclusions were drawn:  The presented method with estimation of flow losses in the volute represents a good approach for quick optimization; 6 Hyperbole IOP Conf. Series: Journal of Physics: Conf. Series 813 (2017) 012048     IOP Publishing doi:10.1088/1742-6596/813/1/012048 Values of angle α2 at hub and at shroud predicted with the decoupled approach need small adjustments; Low value of angle α2, when compared to the average α2 value, acts beneficially on reducing the volute flow losses. The value α2 at hub should be included in the equation for determination of the volute flow losses; The presented Δp variable is a good simple candidate for the assessment of reluctance to cavitation. Acknowledgements The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme FP7/2007-2013/ under REA grant agreement n°612279 and from the Slovenian Research Agency ARRS - Contract No. 1000-15-0263. References [1] Gülich JF 2008 Centrifugal Pumps (Berlin: Springer-Verlag) p 926 [2] Lipej A and Poloni C 2000 Design of Kaplan runner using multiobjective genetic algorithm optimization J. Hydraul. 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