Effect of Splitter Blades on Performances of a Very Low Specific Speed Pump

energies Article Effect of Splitter Blades on Performances of a Very Low Specific Speed Pump Lilian Chabannes *, David Štefan and Pavel Rudolf   Citation: Chabannes, L.; Štefan, D.; Rudolf, P. Effect of Splitter Blades on Performances of a Very Low Specific Speed Pump. Energies 2021,14, 3785. https://doi.org/10.3390/en14133785 Academic Editor: Ricardo J. Bessa Received: 28 May 2021 Accepted: 21 June 2021 Published: 24 June 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: c 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Victor Kaplan Department of Fluid Engineering, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2896/2, 616 69 Brno, Czech Republic; [email protected].cz (D.Š.); [email protected].cz (P.R.) *Correspondence: [email protected] Abstract: The usage of splitter blades to enhance the performances of low specific speed pumps is common practice. Based on experimental and numerical studies, the influence of the addition of one and two splitter blades is investigated on a very low specific speed pump to assess their impact not only on the performance characteristics but also on the losses in all pump domains. First, the main characteristic curves are discussed and it is shown that the usage of splitter blades enhances the head of the pump while not impairing its efficiency. Secondly, a detailed analysis of the losses in the pump reveals that splitter blades improve the flow in all parts of the pumps, but the volute. The flow at the impeller outlet shows that splitter blades largely benefit the slip factor and discharges a more blade-congruent flow in the volute. However, higher absolute velocity at the outlet of the impeller with splitter blades increases friction at the volute wall, as confirmed by the average wall shear stress in the different tested cases. Keywords: low specific speed; numerical simulation; splitter blades; volute; centrifugal pump 1. Introduction Pumps with a specific speed nq< 20 are called low specific speed (LSS) pumps. Their design presents many challenges. The most important is certainly related to their low efficiency, which is inherent to their design. At low specific speed, pumps provide high pressure at low flow rate. To achieve these performances, impellers have large diameters, causing an important part of the shaft power to be dissipated in the sidewall gaps of the pump due to disk friction [ 1 , 2 ]. These pumps are also prone to low-flow head instability, where a positive head slope at low-flow can be observed ( dH/dQ > 0). These phenomena are accentuated with lower specific speeds and commonly present at very low specific speed where nq<10. Despite the certain constraints that LSS pumps suffer from, they have a wide range of applications, especially in the oil, gas, hydrocarbon [ 3 , 4 ] and even aerospace industry [ 5 ] and preferred to positive displacement pumps due to a simpler design, high speed operation and lower failure probability. The general performance and physical limitations of LSS pumps have been investigated by Kurokawa [ 6 ] and Olimstad [ 7 ]. Special design has also been proposed by Klas [ 8 , 9 ] where thick trailing edge replaced classic blading, or more recently by Wei [ 10 ] and Yang [ 11 ] who tested slit impeller blades on a pump with a specific speed nq= 5.7. Nonetheless, the most common solutions for LSS pumps is the addition of splitter blades to the impeller, to raise the pressure developed by the impeller as extensively studied in references [ 12 – 17 ], where generally variations of a splitter blade position in the impeller passage is studied for pump optimization. Cui et al. [ 18 ] investigated experimentally and numerically a high-speed multiblade impeller with a specific speed of nq= 7.7. The initial impeller has four blades, and different splitter blades were added to have a total of 8, 16 and 24 blades. As the number of blades raises, the recirculation regions in the impeller are reduced, leading to a more uniform outlet flow. The efficiency Energies 2021,14, 3785. https://doi.org/10.3390/en14133785 https://www.mdpi.com/journal/energies Energies 2021,14, 3785 2 of 13 improved with increased number of blades and the head becomes extremely flat, but stable, for the 24-bladed impeller. The head is higher for the 24-bladed impeller at partload, but at overload the 16-bladed impeller has a higher head. Based on the summarized problematic of LSS pump operation, one of the best solutions is to consider the design of impeller with splitter blades. Therefore the motivation of this study is the detailed analysis of the influence of splitter blades on the performances of a very low specific speed pump. A 4-bladed impeller is used as a reference and the effect of the addition of one and two splitter blades per passage is investigated both numerically and experimentally. Thanks to a detailed CFD analysis, the study focuses on the influence of splitter blades on the power losses in each domain of the pump, on the flow at the outlet of the impeller and in the volute. 2. Geometry and Numerical Methods 2.1. Pump Model The pump investigated in this paper is a water pump, and has a specific speed nq= 8.9 at the design point and an impeller diameter of 200 mm. The pump is scaled down from the original model, which is described and investigated by Klas in [ 8 , 9 ]. The geometry of the pump studied here differs from the referenced studies, as both the impeller and volute have been redesigned with an in-house code based on quasi-potential flow theory, presented in references [19,20]. The main pump parameters can be seen in Table 1. Table 1. Pump parameters. Designation Symbol Value Units Rotor speed N1450 RPM Design head Hd12.5 m Design flow rate Qd0.00168 m3·s−1 Specific speed nq=NQ0.5 d H0.75 d 8.9 - Impeller outlet diameter d2200 mm Impeller outlet width b23.75 mm Impeller outlet blade angle β2B25 deg Main Blade number Z4 - The volute design is unconventional, as it does not respect the classic design rule of the conservation of angular momentum, or constant cross-sectional velocity. The area of the volute rapidly increases close to the throat area, and has a throat area too large for the design specific speed. This design choice has been made to ensure high performance of the pump at high-flow, and avoid a rapid head drop due to the choked flow at the volute throat. The consequence of this volute design over a classic design is a displacement of the Best Efficiency Point (BEP) to higher flow rates. Three impellers are designed. The first impeller has 4 main blades. The second impeller has 8 total blades (4 main blades and 4 long splitters) and the third impeller has 12 total blades (4 main blades, 4 long splitters and 4 short splitters), see Figure 1for the splitter leading edge position and Figure 2for a visualization of the splitters in the impeller. The splitter blades follow the definition of the main blades (i.e., blade centerlines follow the same blade angle). The placement of the splitter blades follows design rules established by Yuan [ 13 ], which fixes the position of the leading edge of the splitter and its circumferential position in the passage. The long splitter is not located in the middle of the passage but displaced towards the suction side of the main blade. The short splitter is placed between the pressure side of the main blade and the suction side of the long splitter blade. Because the influence of splitter blades is of interest in this study, the three cases are labelled Case 0sp, Case 1sp and Case 2sp, respectively, for the case with zero, one and two additional splitter blades per impeller passage. The sidewall gaps have a constant thickness of 2 mm for the gap on the hub side and 3.125 mm for the gap on the shroud side. Energies 2021,14, 3785 3 of 13 Impeller Volute Sidewall gap hub (SGhub) Sidewall gap shroud (SGshroud) Flow path Sealing Gap (Seal.) Leading Edge (main blade) Leading Edge (long splitter) Leading Edge (short splitter) Figure 1. Meridional section of the numerical domain. Main blade Long splitter Short splitter Figure 2. Splitter blades position for the 3 studied cases. 2.2. Mesh and CFD Specification The numerical simulation of low specific speed pumps can be problematic as thoroughly presented by Juckelandt [ 21 ] when using eddy-viscosity turbulence models. He showed that modeling the flow using the wall functions method may result in inaccurate Energies 2021,14, 3785 4 of 13 performance predictions of these pumps at high flow rates. The reason lies in a detachment zone downstream the volute tongue responsible for large losses, which is not captured by the wall-functions. Resolving the boundary layer by using the Low–Reynolds number method allows to capture the physics of this phenomenon, but leads to a fine mesh near the wall as the criterion on the non-dimensional wall distance y+< 1 must be respected with an appropriate expansion ratio. These guidelines have been applied in this study and the average value of y+ at all walls is 1.3. This criteria is not respected at the trailing edge of the impeller where flow separation is evident. The meshes of the different fluid domains are created using the pre-processor ICEMHEXA 19.1. The cell count per domain and mesh quality metrics can be seen in Table 2, according to ICEM criteria. Table 2. Mesh metrics per computational domain. Domain Elements (106) Max Ortho Max Aspect Ratio Min Quality Suction pipe 0.7 38 741 0.79 Impeller (0 splitter) 3.4 67 2153 0.40 Impeller (1 splitter) 4.6 68 2826 0.38 Impeller (2 splitters) 5.3 68 1773 0.38 Volute 4.3 65 4206 0.42 SG (hub) 2.7 1.4 1506 0.96 SG (shroud) 4.3 33 1401 0.84 The total cell count of each case is 15.4, 16.6 and 17.2 million cells for Case 0sp, Case 1sp and Case 2sp, respectively. A grid convergence analysis is performed for the case Case 0sp to ensure that numerical results are independent of the grid. The torque τ , head H and and hydraulic efficiency η are numerically evaluated. The results are shown in Figure 3and the chosen grid in Figure 4. Each parameter is scaled by its final value (subscript f ) obtained for the finer tested mesh. 0 5 10 15 20 25 Cells[106] −3 −2 −1 0 1 2 3 rel. error [%] Chosen Mesh +1 % error −1 % error τ/τf H/Hf η/ηf Figure 3. Grid convergence analysis results for Case 0sp. Energies 2021,14, 3785 5 of 13 Figure 4. View of the grid for Case 0sp. ANSYS-CFX 19.1 is used to perform the computation. The turbulence model used is k−ωSST by Menter [ 22 ] with automatic wall-treatment. The curvature-correction option is set. Steady state simulations are used as initial conditions for transient simulations where the time step is fixed to 1.5 ◦ of impeller rotation per time step, or 1.72 × 10 −4 s. The RMS residuals target is set to 10 −5 . The connection between the impeller and its neighbour is ensured with the Transient Rotor Stator interface. Stationary domains are connected with the General Grid Interface (GGI) boundary. The steady state behaviour of the pumps is of interest, thus all results and flow fields have been time-averaged over the last 5 impeller rotations, after a periodic behaviour is observed. Six flow rates are computed for each case, from 10% to 160% of the design flow rate. The boundary conditions were set to mass flow rate at the inlet and average static pressure at the outlet. The inlet surface is placed at a distance L/D= 6 from the impeller inlet relative to the suction pipe diameter and the outlet is placed at a distance L/D= 13 from the volute outlet relative to the discharge pipe diameter. 3. Validation The validation of the numerical results is done for the three impellers. The impellers are 3D printed using the Fused Deposition Modeling (FDM) technology with Nylon 12. This method and material were used for a pump with comparable specific speed with higher performances by Olimstad [ 7 ]. The volute casing is CNC-milled from 2 blocks to ensure smooth hydraulic surfaces. The material used is Aluminium 5754, that has good corrosion resistance. A schematic diagram of the test rig can be seen in Figure 5and a partial view of the physical test bench in operation in Figure 6. The inductive flow meter, torque transducer and pressure transducers, respectively, have errors of ± 0.3%, ± 0.2% and ±0.35% of the measured value. The steady state condition of the system was observed before recording a point of the characteristic curve. Each point is the result of averaging over 30 seconds with sampling frequency 2000 Hz. Energies 2021,14, 3785 6 of 13 T p p p Main Throttle Valve Flowmeter Motor Torque Speed Water Pipe Pump Shaft F Pressure Control System Figure 5. Schematic diagram of the test rig. Figure 6. Partial view of the test rig. The results for the head and the hydraulic efficiency are seen in Figures 7–9for Case 0sp, Case 1sp and Case 2sp, respectively. The standard deviation for each measurement is shown in the grey band. The results of the CFD computations are also presented on these figures. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Q(l/s) 0 2 4 6 8 10 12 14 16 H(m) HEXP ηEXP HCF D ηCF D 0.0 0.2 0.4 0.6 0.8 1.0 η Figure 7. Head and efficiency as a function of the flow rate for Case 0sp. Energies 2021,14, 3785 7 of 13 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Q(l/s) 0 2 4 6 8 10 12 14 16 H(m) HEXP ηEXP HCF D ηCF D 0.0 0.2 0.4 0.6 0.8 1.0 η Figure 8. Head and efficiency as a function of the flow rate for Case 1sp. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Q(l/s) 0 2 4 6 8 10 12 14 16 H(m) HEXP ηEXP HCF D ηCF D 0.0 0.2 0.4 0.6 0.8 1.0 η Figure 9. Head and efficiency as a function of the flow rate for Case 2sp. The experimental and numerical results are in good agreement for the head especially. For the hydraulic efficiency, a discrepancy is observed for all cases. The efficiency for all cases is similar and averages to 56% for the CFD and 50% for the experiment at the design point. The discrepancies in efficiencies may have several causes but the main one certainly resides in the fact that the impellers are 3D printed, and so their surface roughness influences the torque produced. It should also be noted that the hydraulic efficiency has been calculated by subtracting the static torque of the pump. The static torque has been measured by flooding the hydraulic circuit without impeller and by rotating the shaft at the rated speed. This way, the presented hydraulic efficiency does not include losses in the shaft seal and bearings. Another interesting point is the standard deviation amplitude of the measured pressure, which is considerably reduced by the presence of splitter blades, indicating that the pressure and flow rate fluctuations decrease, providing a more stable flow delivery with lower pulsations. 4. Results and Discussion Comments on the integral results (head, hydraulic efficiency) are based directly on the experimental values. Comments on flow features and loss analysis are based on CFD results. All results are time-averaged. The integral results are plotted in Figure 10. They show that the head increases with the addition of splitters. At Qd , the head coefficients relative to Case 0sp are 8.2% and 11.3% higher for Case 1sp and Case 2sp, respectively. The maximum hydraulic efficiency for each case is similar at 52%, but is always located at higher flow rates than the design Energies 2021,14, 3785 8 of 13 point. The BEP is located at values Q/Qd of 1.24, 1.30 and 1.34 for Case 0sp, Case 1sp and Case 2sp, respectively, showing that the introduction of splitters displaces the BEP to higher flow rates. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Q(l/s) 0 2 4 6 8 10 12 14 16 H(m) Hdesign HEXP Case 0sp HEXP Case 1sp HEXP Case 2sp ηEXP Case 0sp ηEXP Case 1sp ηEXP Case 2sp 0.0 0.2 0.4 0.6 0.8 1.0 η Figure 10. Experimental results for the 3 tested impellers. It is clear that the introduction of splitters in impeller passages has a negative impact on the stability of the head curve at low flow. The head is stable for Case 0sp, strictly flat for Case 1sp and raises slowly from the shut-off point for Case 2sp until Q/Qd= 0.37. It should be noted that the numerical simulations were able to capture the slight head instability for the Case 2sp. To better understand the influence of splitter blades on the pump performance, a power loss analysis is performed in each numerical domain. For a domain i , the formula to calculate the power loss PL,iis given by Equation (1). PL,i=∑Pτ,i+Pin/out,i(1) Pτ=ωτ isthepowertransferredtothefluidmeasuredatrotatingwallsand Pin/out =RpT ρd˙ m measures the power entering and leaving a domain. Essentially, this formula is related to the total pressure loss in each numerical domain. All losses are scaled by the shaft power at the design point for each respective case, to allow for a comparison of relative losses. The numerical domain investigated are the impeller, the volute and the sidewall gaps (shroud and hub side separately). The losses in the suction pipe are not considered. First, the total relative losses are plotted as a function of the flow rate in Figure 11. At low flow, the relative losses are slightly higher for Case 0sp but very similar at design point and higher flow rates. This is expected as the hydraulic efficiency is similar for all cases. The detail of relative losses per domain can be seen in Figure 12. The impeller relative losses are similar over the whole range of flow rates. Despite the addition of splitter blades and absolute increase of power losses (skin friction of additional blades and shock loss at the leading edges), the impeller relative losses are not impacted. Gülich [ 23 ] suggests that the introduction of disruptive elements in the flow passages of low specific speed impellers implies virtually no loss due to the transfer of energy which is mostly centrifugal. The relative losses in the sidewall gaps (both hub and shroud side) are higher for Case 0sp. The losses in the gaps are mainly a function of the impeller diameter and the rotor speed, so the absolute losses for all cases are similar. Because Case 0sp develops less power (due to lower blade number), the relative power dissipation in the gaps is higher. The volute is the domain where Case 1sp and Case 2sp have significantly higher relative losses than Case 0sp. At the design point, the relative losses are 21% and 17% higher for Case 2sp and Case 1sp, respectively, compared to Case 0sp. Energies 2021,14, 3785 9 of 13 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Q(l/s) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Relative P ower Loss Case 0sp Case 1sp Case 2sp Figure 11. Relative total losses. Volute SG (hub side) Impeller SG (shroud side) Figure 12. Scaled relative losses per domain. The reason for the increased volute losses is not straightforward, as the splitter blades’ role is also to provide a better flow guidance and output a more uniform flow into the volute. In fact, the main known effect of splitter blades on the impeller flow is the suppression of the jet-wake flow pattern. The reason for this pattern is a local eddy located on the pressure