Maximum Efficiency Despite Lowest Specific Speed—Simulation

International Journal of Turbomachinery Propulsion and Power

Article Maximum Efﬁciency Despite Lowest Speciﬁc Speed—Simulation and Optimisation of a Side Channel Pump †

Markus Mosshammer 1,*, Helmut Benigni 1,*, Helmut Jaberg 1,* and Juergen Konrad 2

1 Institute of Hydraulic Fluidmachinery, Faculty of Mechanical Engineering, Graz University of Technology. Kopernikusgasse 24/IV, 8010 Graz, Austria 2 Dickow Pumpen GmbH & Co. KG, Siemensstraße 22, 84478 Waldkraiburg, Germany; [email protected] * Correspondence: [email protected] (M.M.); [email protected] (H.B.); [email protected] (H.J.); Tel.: +43-316-873-8074 (M.M.) † This paper is an extended version of our paper published in the Proceedings of the Conference on Modelling Fluid Flow (CMFF) 2018, Paper No. 31.

Received: 15 December 2018; Accepted: 19 March 2019; Published: 27 March 2019

Abstract: Side channel pumps provide high pressure at relatively low flow rates. This comes along with a quite low specific speed and thus with the known disadvantage of a quite poor maximum efficiency. This paper describes the detailed analysis and optimisation of a typical 1-stage side channel pump with an additional radial suction impeller by means of computational fluid dynamics (CFD) simulations. In a first step, the model was successively generated and it was obvious that it has to contain all details including suction impeller and main stage (both 360◦ models) as well as the pressure housing and all narrow gaps to provide useful simulation results. Numerical simulations were carried out in a stationary and transient way with scale resolving turbulence models to analyse the components in detail. Finally the CFD-simulations were validated with model tests. For the optimisation process it was necessary to generate a reduced numerical model to analyse the effects of more than 300 geometry variations. The findings were then combined to establish the desired objectives. Finally the best combinations were validated again with the full numerical model. Those simulations predict a relative efficiency increase at best efficiency point (BEP) and part load >30% with respect to all given limitations like identical head curve, suction behavior, and dimensions.

Keywords: CFD; low speciﬁc speed; optimisation; side channel pump; simulation; (U)RANS

1. Introduction Providing high pressure at relatively low flow rates, side channel pumps are often used when choosing between a displacement pump and a centrifugal pump like Grabow [1,2] has shown in Figure1. In this paper, the efficiency is plotted versus specific speed nq (defined according to Equation (1) instead of the specific speed σ (defined according to Equation (2)) used by Grabow as the specific speed nq is more common in the pump industry. For side channel pumps, the specific speed is 3 3 approximately between nq = 1 [rpm, m /s, m] and nq = 10 [rpm, m /s, m] as marked in Figure1.

Q1/2 nq = n· (1) H3/4

1/2 φ nq σ = ≈ (2) ψ3/4 157

Int. J. Turbomach. Propuls. Power 2019, 4, 6; doi:10.3390/ijtpp4020006 www.mdpi.com/journal/ijtpp Int. J. Turbomach. Propuls. Power 2019, 4, 6 2 of 19

Q A φ = SC (3) ra·ω 2·∆p = ψ 2 (4) ρ·(ra·ω) Beside the main advantages of an outstanding suction performance and the capability of pumping fluids with high gas loads, the drawback of side channel and peripheral pumps is a quite poor hydraulic efficiency of <50% as shown in Figure1. It is remarkable that both for large specific speeds and small specific speeds a very good efficiency can be reached with centrifugal and displacement Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 2 of 20 pumps, whereas in-between no machine type exists reaching a very good efficiency.

In the past, when efficiency was often negligible,1/ 2 this fact was simply accepted. Nowadays, ϕ nq σ = ≈ (2) companies are pushed by law to increase the efficiencyψ 3/ 4 157 of their products, e.g., by the Energy Efficiency Directive of the European Union [3] or the Paris Agreement. As pumps almost require 20% of the world electric power consumption [4], they offer aQ huge potential for saving energy. Though many A manufacturers have recognized this trend andϕ improved= SC their main models, some exotics(3) like side r ⋅ω channel pumps were neglected in the past. a Due to the fact that side channel pumps neither2 ⋅ belongΔp to displacement pumps nor to centrifugal ψ = pumps, the technological progress in both fieldsρ is⋅ () not⋅ω applicable.2 Actually, the design of(4) most side ra channel pumps available on the market today is quite old (>30 years) as are the few available design guidelines. AlsoBeside modern the main design advantages techniques of an likeoutstanding numerical suction simulations performance have and therefore the capability not been of applied pumping fluids with high gas loads, the drawback of side channel and peripheral pumps is a quite often. Even in cases when simulation results were experimentally validated [5,6], the deviations in poor hydraulic efficiency of <50% as shown in Figure 1. It is remarkable that both for large specific head andspeeds efficiency and small are often specific not speeds satisfying. a very good efficiency can be reached with centrifugal and Thisdisplacement paper describes pumps, whereas the detailed in-between analysis no machin ofe a type typical exists 1-stagereaching sidea verychannel good efficiency. pump with an additional radialIn the suctionpast, when impeller efficiency by was means often negligible, of computational this fact was fluid simply dynamics accepted.(CFD) Nowadays, simulations and showscompanies the required are pushed numerical by law to effort increase to the generate efficiency reliable of their results.products, For e.g., that by the purpose Energy Efficiency it is necessary to Directive of the European Union [3] or the Paris Agreement. As pumps almost require 20% of the analyse theworld occurring electric power losses consumption between inlet[4], they and offer outlet a huge to understandpotential for saving the loss energy. mechanisms Though many in all parts. Thereforemanufacturers it was necessary have recognized to increase this the trend numerical and improved model their successively—ending main models, some exotics with like a quite side complex model tochannel get an pumps accurate were loss neglected analysis in the for past. each part.

100 Reciprocating pumps radial semi-axial axial

90 >2500m³/h Gear pumps 250m³/h 80 100m³/h 2500m³/h Rotary screw 70 50m³/h pumps 25m³/h

60 Displacement Centrifugal

[%] pumps pumps

50 250m³/h 100m³/h Efficiency 40 50m³/h 25m³/h 30 10m³/h Jet pumps 20 Side channel pumps 10

- 1.E-021·10 1·10 1.E-01 1.E+001·10 1.E+011·10 1·10 1.E+02 1.E+031·10 Specific speed nq [rpm] FigureFigure 1. Maximum 1. Maximum efficiency efficiency depending depending on on specific specific speed speed and andflowrate flowrate [2]. [2].

Due to the fact that side channel pumps neither belong to displacement pumps nor to centrifugal pumps, the technological progress in both fields is not applicable. Actually, the design of most side channel pumps available on the market today is quite old (>30 years) as are the few available design

Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 3 of 20 guidelines. Also modern design techniques like numerical simulations have therefore not been applied often. Even in cases when simulation results were experimentally validated [5,6], the deviations in head and efficiency are often not satisfying. This paper describes the detailed analysis of a typical 1-stage side channel pump with an additional radial suction impeller by means of computational fluid dynamics (CFD) simulations and shows the required numerical effort to generate reliable results. For that purpose it is necessary to analyse the occurring losses between inlet and outlet to understand the loss mechanisms in all parts. Therefore it was necessary to increase the numerical model successively—ending with a quite complex model to get an accurate loss analysis for each part. Int. J. Turbomach. Propuls. Power 2019, 4, 6 3 of 19 2. Theoretical Flow in a Side Channel Pump 2. TheoreticalSide channel Flow pumps in a Side are rather Channel to be Pump regarded rotating displacement pumps according to their functioning although they can easily be mistaken as centrifugal pumps because of the design Side channel pumps are rather to be regarded rotating displacement pumps according to their principle. Their functioning is related to a multistage radial pump as the liquid is entrained in the functioning although they can easily be mistaken as centrifugal pumps because of the design principle. circumferential direction by the rotation of the impeller and is sucked in through the suction opening Their functioning is related to a multistage radial pump as the liquid is entrained in the circumferential (Figure 2). Inside the impeller (in the rotating system) energy is applied to the medium by this direction by the rotation of the impeller and is sucked in through the suction opening (Figure2). acceleration and at the same time the fluid moves outwards as it undergoes a centrifugal force and Inside the impeller (in the rotating system) energy is applied to the medium by this acceleration and moves into the side channel (stationary system). In this stationary system the medium is decelerated at the same time the ﬂuid moves outwards as it undergoes a centrifugal force and moves into the and moves towards the machinery axis. In the stationary system, the kinetic energy is changed into side channel (stationary system). In this stationary system the medium is decelerated and moves pressure by deceleration. Closer to the impeller center the flow is directed backwards into the towards the machinery axis. In the stationary system, the kinetic energy is changed into pressure by impeller, is again dragged away and kinetic energy is anew transferred into the liquid, which moves deceleration. Closer to the impeller center the ﬂow is directed backwards into the impeller, is again outward and back into the side channel, where again the kinetic energy is changed into pressure, and dragged away and kinetic energy is anew transferred into the liquid, which moves outward and back so on. This is the so called “internal multistage” effect which is the main characteristic of the side into the side channel, where again the kinetic energy is changed into pressure, and so on. This is the so channel pump. called “internal multistage” effect which is the main characteristic of the side channel pump.

Pressure port Suction port

Interrupter Suction opening

Gas outlet Suction opening

Pressure opening Side channel

Impeller

Gas outlet at gas extraction

Pressure opening

Figure 2. Transport principle of a side channel pump. Figure 2. Transport principle of a side channel pump. In the meridional view the ﬂuid moves in a circle (see Figure2 right) and in the cross sectional view (FigureIn 2the left) meridional in a form view of wiggly the fluid line untilmoves it leavesin a circle through (see theFigure pressure 2 right) side and which in the is separatedcross sectional from viewthe suction (Figure side 2 left) by in the a form so called of wiggly interrupter. line until This it multipleleaves through addition the of pressure energy inside the which impeller is separated channels fromand thethetransfer suction ofside kinetic by the energy so called into interrupter. pressure in theThis side multiple channels addition allow of the energy side channel in the impeller pump to channelsreach large and pressure the transfer heads of for kinetic very lowenergy ﬂow into rates, pre andssure its in characteristic the side channels is comparatively allow the side steep. channel pumpThe to reach principal large design pressure of a sideheads channel for very pump low thereforeflow rates, consists and its of characteristic is comparatively steep. • TheImpeller principal (commonly design of open a side design) channel pump therefore consists of • Side channel • Impeller (commonly open design) • Interrupter (separating low and high pressure side) • Suction and pressure port (axial/axial, axial/radial, radial/axial, radial/radial)

Until now, two theories, “theory of flow filament” and “theory of shear stress” are still used to describe the flow inside a side channel pump:

(a) The theory of shear stress, also called theory of turbulence and/or mixing theory is based on the induced shear stress of the impeller on the fluid in the side channel—the fluid is dragged against the existing pressure gradient. Whether the centrifugal forces are included (Pfleiderer [7], Senoo [8–10]) or not (Iverson [11]), the main functional principle is based on displacement. Fluid Int. J. Turbomach. Propuls. Power 2019, 4, 6 4 of 19

with high velocity exits the impeller to the side channel and is there decelerated. In parallel, fluid enters the impeller from the side channel and gets accelerated. This mixing procedure of high turbulence fluid from the impeller and low turbulence fluid from the side channel is repeated multiple times along the side channel and the physical background of this theory. (b) The theory of flow filament is based on the helical flow between side channel and impeller. The reason behind the helical flow is based on one hand on the different velocities of the fluid in the impeller and the side channel and on the other hand on the difference between the centrifugal forces of the rotating and the stationary parts. It is assumed, that the impeller induces an angular momentum racua (in the rotating system) which returns near the hub with an angular momentum of ricui (in the stationary system). The difference of the induced angular momentum on the participating fluid volume of the side channel ASC is the theoretical head of of a single “stage” of the side channel pump.

Though they are based on the different physical principles, “common design guidelines” for side channel pumps like from Grabow [12] or Surek [13] use both theories. The most inﬂuential dimensions of both theories are the side channel area ASC and the diameter/radius of the impeller. The main dimensions of a side channel pump are described in Section 5.1. A good overview of geometrical inﬂuence on side channel pumps is given in [14].

3. Methodology of Numerical Simulations In this chapter the methodology used to simulate a side channel pump is described, starting with the generation of a 3D-model, meshing, and preparation of a suitable numerical setup up to the used post-processing.

3.1. Preparation of the Geometry and Mesh Generation In a ﬁrst step, the real pump had to be transferred in a 3D-computer-aided design (CAD) model. For that, drawings and dimensions of the pump were used in addition to a 3D-Laserscan of the impeller. Based on the 3D-CAD model, the geometry was prepared for meshing. As an example, the impeller is mentioned as it consists of 24 identical blades (1 blade equals to a section of 15◦), where only one was used for meshing. To generate a suitable, structured mesh, it was necessary to split the geometry (we call it blocking) as shown in Figure3 on top right. Those blocks were meshed separately in ANSYS Meshing (Canonsburg, PA, USA), but each of them with a conformal interface to maximize the resulting mesh quality and to overcome the need of an arbitrary interface. The same procedure was used at the suction impeller, where 1 out of 6 blades was used to generate a structured mesh in ANSYS TURBOGrid. Besides a correct modelling of the impellers, it is vital to mention, that the resulting head and efﬁciency of a pump, and especially of a side channel pump, relies heavily on the existing gaps. In Figure4 the radial gap of 0.3 mm at the suction impeller (left) and the even more narrow axial gap of 0.1 mm at the impeller (right) are shown. To get an impression of the size of the gaps, it is vital to mention that they equal 0.25%, respectively 0.08% of the impeller diameter. Those gaps in addition to the hub and shroud cavities and the side channel itself are of essential importance for reliable simulation results. The full CFD-model of the side channel pump as shown in Figure5, including amongst others all narrow gaps and 360◦ models of suction runner and impeller, consists of 15 mio. nodes. As already mentioned, mainly structured grids for the impellers, side channel, suction piece, and gaps were used. Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 5 of 20

Int. J. Turbomach. Propuls. Power 2019, 4, 6 5 of 19 Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 5 of 20

Figure 3. Preparation of the geometry and mesh generation of the impeller.

Besides a correct modelling of the impellers, it is vital to mention, that the resulting head and efficiency of a pump, and especially of a side channel pump, relies heavily on the existing gaps. In Figure 4 the radial gap of 0.3 mm at the suction impeller (left) and the even more narrow axial gap of 0.1 mm at the impeller (right) are shown. To get an impression of the size of the gaps, it is vital to mention that they equal 0.25%, respectively 0.08% of the impeller diameter. Those gaps in addition to the hub and shroud cavities and the side channel itself are of essential importance for reliable simulation results.Figure 3. Preparation of the geometry and meshmesh generation of the impeller.

FigureFigure 4. 4. NarrowNarrow gaps gaps at at impellers. impellers.

Figure 4. Narrow gaps at impellers.

Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 6 of 20

The full CFD-model of the side channel pump as shown in Figure 5, including amongst others all narrow gaps and 360° models of suction runner and impeller, consists of 15 mio. nodes. As already mentioned, mainly structured grids for the impellers, side channel, suction piece, and gaps were Int. J. Turbomach. Propuls. Power 2019, 4, 6 6 of 19 used.

Figure 5. Full computational fluid dynamics (CFD) model of the analysed original side channel pump Figure 5. Full computational fluid dynamics (CFD) model of the analysed original side channel pump with radial suction runner (left) and impeller (right). with radial suction runner (left) and impeller (right). 3.2. Numerical Model of the Side Channel Pump 3.2. Numerical Model of the Side Channel Pump Based on numerous successfully performed projects in the field of hydraulic fluid machinery at the instituteBased within on numerous the last decade successfully [15–18 performed], a wealth ofprojects experience in the was field gained. of hydraulic The simulations fluid machinery of the at investigatedthe institute pump within are the primary last decade based [15–18], on this a knowledge, wealth of experience especially was the definitionsgained. The of simulations the numerical of the modelinvestigated and the solverpump are (turbulence primary modelling,based on this boundary knowledge, conditions, especially interfaces, the definitions iterations of the... numerical), and approachesmodel and of modellingthe solver hub(turbulence and shroud modelling, cavities. boundary conditions, interfaces, iterations…), and approachesAs stationary of modelling simulations hub and mostly shroud give cavities. a good first impression on the flow situation it is vitalAs stationary for getting simulations the most mostly accurate give a good results, first toimpression also perform on the flow transient situation simulations. it is vital for Thegetting turbulence the most model accurate used for results, stationary to also simulations perform (Reynolds-Averagedtransient simulations. Navier–Stokes, The turbulence RANS) model was used k-ωfor-SST-turbulence stationary simulations model (Shear (Reynolds-Averaged Stress Transport turbulence Navier–Stokes, model) fromRANS) Menter was [19 k-],ω combining-SST-turbulence the 2-equations-turbulence-modelsmodel (Shear Stress Transport k-ε -turbulence and k-ω. Thismodel turbulence-model) from Menter [19], requires combining an adequate the 2-equations- mesh for modellingturbulence-models near wall (k- k-ωε)- andand wallk-ω. distantThis turbulence-model (k-ε) flow regimes. requires an adequate mesh for modelling nearThough wall (k- theω) and SST-turbulence wall distant (k- modelε) flow could regimes. be used for transient simulations (Unsteady Reynolds-AveragedThough the SST-turbulence Navier–Stokes, model URANS), could experience be used for has transient shownthat simulations it does not (Unsteady always provideReynolds- satisfyingAveraged results, Navier–Stokes, even if the gridURANS), and time experience step resolution has shown would that be it sufficient does notfor always that purpose.provide satisfying That is whyresults, the scale even resolving if the grid turbulence and time modelstep resolution SAS-SST(Scale-Adaptive would be sufficient Simulation for that Shearpurpose. Stress That Transport is why the turbulencescale resolving model) fromturbulence Menter model [20] was SAS-SST(Scale utilized. It combines-Adaptive the Simulation advantages Shear of the Stress SST-model Transport in steadyturbulence zones but model) enables from to switchMenter to [20] SRS was (Scale-Resolving utilized. It combines Simulation) the advantages mode in flows of the with SST-model large and in unstablesteady separation zones but enables zones which to switch are likely to SRS to (Scale-R be presentesolving between Simulation) impeller mode and side in flows channel. with large and unstableIn stationary separation simulations, zones which the interfaces are likely betweento be present suction between piece andimpeller impeller and asside well channel. as impeller and sideIn channel stationary were simulations, modelled with the theinterfaces Frozen between Rotor approach suction as piece simulations and impeller with theas well mixing as impeller plane approachand side were channel highly were unstable modelled due to with the averagingthe Frozen which Rotor is approach just not applicable as simulations for the with investigated the mixing zones.plane As approach the Frozen were Rotor highly modelling unstable assumes due to a fixedthe averaging Rotor-Stator-position, which is just five not simulations applicable withfor the clockedinvestigated positions—each zones. As with the an Frozen impeller Rotor moved modellin 3◦ further—wereg assumes made a fixed and theRotor-Stator-position, final result represents five thesimulations arithmetical with average clocked of all positions—each five simulations. with During an impeller stationary moved simulations, 3° further—were between 600 made and and 2000 the iterationsfinal result were represents required the depending arithmetical on the average convergence of all five of simulations. each operating During point. stationary The evaluation simulations, of thebetween convergence 600 and was 2000 based iterations on two factors.were required First on thedepending RMS-weighted on the convergence residuals and of second each operating on the behavior of the defined monitor points (e.g., different defined pump heads). When residual were sufficiently small and the fluctuations of the monitor points negligible, the simulations were stopped. Int. J. Turbomach. Propuls. Power 2019, 4, 6 7 of 19

For the calculation of the results, the arithmetic average of the last 100 iterations was used. (For information, one stationary simulation took 20 h on a High-Performance Workstation with 16 cores) For transient simulations, which used the corresponding stationary result for initial values, the Transient-Rotor-Stator approach with an adaptive timestep was used. The ﬁrst two revolutions used a timestep which equals for 2◦ as shown in Equation (5).

2·π 2 t ◦ = · (5) trans,0–720 1450 360 Those two revolutions were used as settling time for the simulation. Afterwards the timestep was reduced to get a resolution of 1◦ for the next two revolutions, whereas only the last one was used for calculating the results. This timestep allows for a RMS Courant Number of around 5 but as CFX uses an implicit solver it therefore does not have a numerical stability limit based on Courant Number.

2·π 1 t ◦ = · (6) trans,720–1440 1450 360

3.3. Post-Processing A major advantage of simulations compared to measurements is the inﬁnite possibilities of the analysis of the results. Beside conventional measurement data like head curve, efﬁciency and shaft power it is possible to calculate quantities and data such as

• Pump head from inlet to outlet • Velocity components (cm, cu, . . . ) of the suction impeller • Flow interaction between impeller and side channel • Flow situation of all components to detect possible flow separation and backflow zones • Leakage flow in narrow gaps

Given that kind of information, it is possible to get deeper insights into the functionality and behaviour of the pump and its components. The whole post-processing was carried out with ANSYS CFX Post 17.1 and some quantities are described in detail below. Head-curve was calculated according to EN ISO 9906 as described in Equation (7).

p − p u2 − u2 H = z − z + 2 1 + 2 1 (7) 9906 2 1 ρ·g 2·g

Whereas the data in the defined positions, each two diameter before the inlet respectively after the outlet, were calculated at corresponding planes (PlaneInlet and PlaneOutlet). The definition of the head with the so called CFX expression language (CEL) uses the area averaged pressure and velocities (pump discharge divided by plane areas) at those planes. Efficiency is defined as the ratio of the hydraulic power (pump head and discharge) by shaft power as described in Equation (8): ρ·g·Q·H η = (8) Psha f t The required shaft power is calculated on all wetted, rotating surfaces of the pump including hub and shroud cavities and gaps. Pump head from inlet to outlet: needs defined positions to get an overview of the behaviour and the occurring losses inside. Those positions are

• Pump inlet • Outlet suction impeller • Inlet suction piece • Impeller—0–360◦ Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 8 of 20

• Int. J. Turbomach.Outlet suction Propuls. impeller Power 2019 , 4, 6 8 of 19 • Inlet suction piece • Impeller—0–360° • Pump outlet

On all mentioned positions except the impeller, th thee total pressure on the stationary part of the interface was used to calculate the existing head. In In the the impeller, impeller, the following positions as shown in Figure6 6 were were deﬁneddefined andand usedused forfor aa deeperdeeper analysisanalysis ofof thethe headhead riserise andand interactioninteraction ofof impellerimpeller andand side channel.

Figure 6. PlanesPlanes ( (leftleft)) and and radii radii ( (rightright)) for for calculation calculation of of total total energy energy inside the impeller.

First, four different planes were placedplaced acrossacross thethe impellerimpeller andand sideside channelchannel (Figure(Figure6 6 left): left): • Plane 1: 1 mm distance in axial direction from suction side • Plane 2: in the middle of the impeller • • Plane 3: 1 mm distance in axial direction from pressure sideside • • Plane 4: in the middle of the side channel Additionally the pressure/pump head was calculated on four different radii (Figure 6 right): Additionally the pressure/pump head was calculated on four different radii (Figure6 right): • Radius 1: r = 40 mm • Radius 1: r = 40 mm • Radius 2: r = 50 mm • Radius 2: r = 50 mm • Radius 3: r = 60 mm • Radius 3:4: r = 70 60 mm mm (only for planes 3 & 4) • Radius 4: r = 70 mm (only for planes 3 & 4) Given the data on all mentioned circles, it is possible to evaluate the pressure rise from inlet— whichGiven is defined the data as 0° onposition—to all mentioned outlet—defined circles, it isas possible345° position. to evaluate The missing the pressure15° account rise for from the ◦ ◦ ◦ interrupterinlet—which which is defined is required as 0 position—tofor the function outlet—defined of the pump itself, as 345 butposition. is not of Theinterest missing for the 15 resultingaccount pumpfor the head. interrupter which is required for the function of the pump itself, but is not of interest for the resulting pump head. 4. Results 4. Results The results of the pump head and efficiency are shown in Figure 7 for stationary and transient simulations.The results Though of the the pump pump head head and and efficiency efficiency are near shown BEP in show Figure a satisfying7 for stationary correlation and transient with the measurementsimulations. data Though (measurements the pump ac headcording and to efficiency EN ISO 9906 near Class BEP 1) showprovided a satisfying by the manufacturer correlation with[21], it the can measurement be seen that the data transient (measurements results give according a more accurate to EN ISO prediction 9906 Class of the 1) real provided BEP position. by the Additionally,manufacturer the [21 ],transient it can be head seen curv thate the in part transient load resultsis more give reliable. a more accurate prediction of the real BEP position. Additionally, the transient head curve in part load is more reliable.

Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 9 of 20 Int.Int. J. Turbomach. Propuls.Propuls. PowerPower 20192019,, 44,, 6x FOR PEER REVIEW 99 of 19 20

50 50% 50 50%

45 45% 45 45%

40 40% 40 40%

35 35% 35 35%

30 30% 30 30%

25 25% 25 25%

Pump Head [m] Head Pump 20 20% PumpEfficiency [%] Pump Head [m] Head Pump 20 20% PumpEfficiency [%]

15 15% 15 15% Head [m] - Measurement data 10 Head_CFD_statHead [m] - Measurement [m] data 10% 10 Head_CFD_transHead_CFD_stat [m] [m] 10% eff_hydrHead_CFD_trans [%] - Measurement [m] data 5 5% eff_hydr [%] - Measurement data 5 eff_hydr_CFD_stat [%] 5% eff_hydr_CFD_transeff_hydr_CFD_stat [%] [%] 0 eff_hydr_CFD_trans [%] 0% 0 01234567890% 0123456789Flowrate [m³/h] Flowrate [m³/h] FigureFigure 7.7. ComparisonComparison ofof measurementmeasurement and computational fluid fluid dynamics dynamics (CFD) (CFD) results results (stationary (stationary Figure 7. Comparison of measurement and computational fluid dynamics (CFD) results (stationary and transient). and transient). and transient). In overloadoverload conditionsconditions it it is is surprising surprising to to see see that that stationary stationary simulations simulations are superior,are superior, in both in headboth In overload conditions it is surprising to see that stationary simulations are superior, in both headand efficiency. and efficiency. A possible A possible explanation explanation may be may the occurringbe the occurring convergence convergence behavior behavior and the and chosen, the head and efficiency. A possible explanation may be the occurring convergence behavior and the chosen,already describedalready described calculation calculation which uses which the uses average the valueaverage of thevalue last of 100 the iterations. last 100 iterations. As shown As in chosen, already described calculation which uses the average value of the last 100 iterations. As shownFigure8 in, the Figure pump 8, headthe pump heavily head fluctuates heavily influctuat stationaryes in stationary mode—even mode—even in BEP. In transientin BEP. In mode transient the shown in Figure 8, the pump head heavily fluctuates in stationary mode—even in BEP. In transient modefluctuations the fluctuations can clearly can be assignedclearly be to assigned the impeller to the blades impeller as shown blades in as Figure shown8, although in Figure the 8, although timestep mode the fluctuations can clearly be assigned to the impeller blades as shown in Figure 8, although theneeds timestep to be sufficiently needs to be small sufficiently to describe small the to realdescribe behavior. the real behavior. the timestep needs to be sufficiently small to describe the real behavior. 35.0 70% 35.0 70%

30.0 60% 30.0 60%

25.0 50% 25.0 50%

stationary results transient 0°-720° transient 720°-1080° ] %

° ° ] stationary results transient 0°-720° transient 720 -1080 [

20.0 40% % [

20.0 40% rad g s rad g g s 15.0 30% g

Förderhöhe[m] 15.0 30% Wirkun Förderhöhe[m] Wirkun Pump head Pump efficiency

10.0Pump head 20% Pump efficiency 10.0 20% Monitorpoint - Pump head Monitorpoint - Efficiency Monitorpoint - Pump head Monitorpoint - Efficiency 5.0 10% 5.0 10%

0.0 0% 0.0500 700 900 1100 1300 1500 1700 0% 500 700 900Anzahl 1100 Iterationen [-] 1300 1500 1700 Anzahl# of iterationsIterationen [-] # of iterations Figure 8. Monitor of head and efficiency at best efficiency point (BEP) for stationary and transient simulation. Figure 8. Monitor of head and efficiency at best efficiency point (BEP) for stationary and transient Figure 8. Monitor of head and efficiency at best efficiency point (BEP) for stationary and transient simulation. simulation.

Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 10 of 20

In Figure 9, the total energy, calculated as an average value of all three planes at the four mentionedInt. J. Turbomach. radii, Propuls. is shown Power 2019 for, 4BEP., 6 Starting at the suction piece, the pressure only slightly increases10 of 19 withinInt. J. Turbomach. the first Propuls. 60° (which Power 2019 represents, 4, x FOR PEERfour REVIEWblade passages). In region 2, the significant energy 10rise of of 20 the pump is gained. Starting with a lower gradient at the beginning, a nearly linear behavior as In FigureFigure9 ,9, the the total total energy, energy, calculated calculated as an as average an average value of value all three of planesall three at theplanes four at mentioned the four theoretically predicted can be shown. When the transition from impeller to outlet begins (marked as radii,mentioned is shown radii, for is BEP.shown Starting for BEP. at theStarting suction at the piece, suction the pressure piece, the only pressure slightly only increases slightly within increases the zone 3 in◦ Figure 9), the energy stays nearly constant until the interrupter. ﬁrstwithin 60 the(which first 60° represents (which represents four blade four passages). blade passages). In region 2,In the region signiﬁcant 2, the significant energy rise energy of the rise pump of isthe gained. pump Startingis gained. with Starting a lower with gradient a lower at thegradient beginning, at the abeginning, nearly linear a nearly behavior linear as theoreticallybehavior as predictedtheoretically can predicted be shown. can When be shown. the transition When the from transi impellertion from to impeller outlet begins to outlet (marked begins as (marked zone 3 as in Figurezone 39 in), theFigure energy 9), the stays energy nearly stays constant nearly until constant the interrupter. until the interrupter.

Figure 9. Total energy from impeller inlet to outlet at BEP.

A more detailed view of zone 2 at the linear characteristic is shown in Figure 10. At a constant radius, the total energy atFigure all four 9. Total planes energy is shown from impeller for six inletblade to passages outlet at BEP. (each covers 15°). It can be seen that the highest pressureFigure 9.is Totalreached energy near from the impeller small gap inlet between to outlet impellerat BEP. and suction side and then decreasesA more detailed towards view the ofside zone channel. 2 at the Inside linear the characteristic side channel, is the shown pressure in Figure along 10 a .blade At a constantpassage A more detailed view of zone 2 at the linear characteristic is shown in Figure 10. At a constant staysradius, nearly the total constant energy and at then all four increases planes across is shown the passing for six blade blade. passages (each covers 15◦). It can be radius, the total energy at all four planes is shown for six blade passages (each covers 15°). It can be seenAnother that the highestoutcome pressure is the expected is reached pressure near the decreas smalle gap in the between wake impellerbehind a and passing suction blade. side This and seen that the highest pressure is reached near the small gap between impeller and suction side and phenomenonthen decreases seems towards to thebe more side channel.distinct Insidenear the the side side channel channel, as the there pressure is an along additional a blade pressure passage then decreases towards the side channel. Inside the side channel, the pressure along a blade passage decreasestays nearly due constant to significant and then inflow. increases across the passing blade. stays nearly constant and then increases across the passing blade. Another outcome is the expected pressure decrease in the wake behind a passing blade. This phenomenon seems to be more distinct near the side channel as there is an additional pressure decrease due to significant inflow.

FigureFigure 10.10. Distribution ofof totaltotal pressurepressure atat differentdifferent planes—rplanes—r == 6060 mm—Qmm—Q == 5 m3/h.

Figure 10. Distribution of total pressure at different planes—r = 60 mm—Q = 5 m3/h.

Int. J. Turbomach. Propuls. Power 2019, 4, 6 11 of 19

Another outcome is the expected pressure decrease in the wake behind a passing blade. This Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 11 of 20 phenomenon seems to be more distinct near the side channel as there is an additional pressure decrease due toIn significant Figure 11, inflow. the total pressure from pump inlet to outlet is shown for six operating points, with the Inpressure Figure at11 inlet, the is total defined pressure at zero from for pump all points. inlet to outlet is shown for six operating points, with the pressure at inlet is defined at zero for all points.

Q=1.25m³/h Q=2.50m³/h Q=3.75m³/h Q=5.00m³/h Q=6.25m³/h Q=7.5m³/h Total pressure

Figure 11. Total pressure from pump inlet to outlet at certain positions—stationary results. Figure 11. Total pressure from pump inlet to outlet at certain positions—stationary results. At the inlet of the suction piece it gets more interesting. Though the suction stage delivers the 3 highestAt head the inlet in deep of the part suction load ofpiece 1.25 it mgets/h, more the resultinginteresting. head Though at the the inlet suction of the stage suction delivers piece the is lowest.highest This head yields in deep from part the energyload of dissipation 1.25 m3/h, inside the resulting the connecting head at passage the inlet between of the thesuction outlet piece of the is suctionlowest. impeller This yields and from inlet the of the energy suction dissipation piece as itin consistsside the ofconnecting a quite big passage volume between which is the obviously outlet of notthe suitable suction for impeller small flowrates. and inlet of the suction piece as it consists of a quite big volume which is obviouslyFollowing not suitable the flow for through small flowrates. the pump, the suction piece is the next part to be investigated. As shownFollowing in Figure the 12flow, it canthrough be shown the pump, that especially the suction in partpiece load is the a relativelynext part largeto be backflowinvestigated. exists As (markedshown in in Figure blue color). 12, it can Even be aroundshown that BEP especially a significant in part backflow load a occurs relatively as shown large backflow in Figure exists12b. Although(marked in this blue phenomenon color). Even cannot around be BEP eliminated a significant entirely backflow it should occurs be as minimized shown in duringFigure the12b. optimizationAlthough this process. phenomenon cannot be eliminated entirely it should be minimized during the ◦ ◦ optimizationAt the inlet process. region of the impeller between 0 and 60 the total pressure for all investigated operatingAt the points inlet are region almost of identical. the impeller With between increasing 0° wrap and angle60° the the total pressure pressure rise showsfor all the investigated expected linearoperating trend points whereas are the almost gradient identical. gets steeper With at incr decreasingeasing wrap flowrates. angle the pressure rise shows the expectedNear thelinear outlet trend of thewhereas impeller, the thegradient pressure gets rise steeper declines at decreasing and stays almost flowrates. constant until the outlet of theNear pump. the outlet of the impeller, the pressure rise declines and stays almost constant until the outletThis of analysisthe pump. gives a good insight in the optimization potential of the investigated pump which identifiesThis the analysis connecting gives passagea good insight between in outletthe optimization of the suction potential impeller of andthe investigated inlet of the suction pump piecewhich identifies the connecting passage between outlet of the suction impeller and inlet of the suction piece as a main cause of losses. Additionally, the outlet of the impeller could be improved to get more head out of the last three blade passages.

Int. J. Turbomach. Propuls. Power 2019, 4, 6 12 of 19 as a main cause of losses. Additionally, the outlet of the impeller could be improved to get more head out of the last three blade passages. Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 12 of 20

Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 12 of 20 100%

100%80%

60%80%

40%60% Qin [%] Qout [%] 20%40% Qin [%] Qout [%] 20%0%

-20%0% Relative discharge suction area[%] -40%-20%

Relative discharge suction area[%] 0.00 1.25 2.50 3.75 5.00 6.25 7.50 8.75 -40% 0.00 1.25 2.50 3.75Q [m³/h] 5.00 6.25 7.50 8.75 Q [m³/h] (a) (b) (a) FigureFigure 12. 12.(a) ( Relativea) Relative discharge discharge at atsuction suction area; ( (bb) )Inflow Inflow (red) (red) and and outflo outfloww (blue)(b) (blue) areas areas at BEP. at BEP. Figure 12. (a) Relative discharge at suction area; (b) Inflow (red) and outflow (blue) areas at BEP. 5. Optimisation5. Optimisation Besides5. OptimisationBesides optimising optimising the the connecting connecting passagepassage between between outlet outlet of ofthe the suction suction impeller impeller and inlet and inletof of the suctionthe suctionBesides piece piece optimising and and the the transitionthe transition connecting from from passage impellerimpeller between to to outlet, outlet, outlet it itis of isvital the vital tosuction tounderstand understand impeller the and behaviour the inlet behaviour of and interactionandthe suctioninteraction piece of impellerof andimpeller the and transition and side side channel. channel. from impeller Due to to to the the outlet, high high numericalit numericalis vital to effort understand effort of the of presented the the presented behaviour “full” “full” numerical model of the side channel pump; this may not be suitable for optimization tasks. Therefore numericaland interaction model of of the impeller side channel and side pump; channel. this Due may to the not high be suitablenumerical for effort optimization of the presented tasks. “full” Therefore a simplified model is presented to analyse various geometrical variations of impeller and side channel a simplifiednumerical model model is of presented the side channel to analyse pump; various this may geometrical not be suitable variations for optimization of impeller tasks. and Therefore side channel whicha simplified are then model validated is presented in the tofull analyse model various again. geometrical variations of impeller and side channel which are then validated in the full model again. which are then validated in the full model again. 5.1. Numerical Model for Optimisation 5.1. Numerical Model for Optimisation 5.1. NumericalAccording Model to investigations for Optimisation from Fleder [3], a simplified numerical model was generated as shownAccordingAccording in Figure to investigations to13. investigations This model, fromwhich from FlederisFleder completely [[3],3], a simplifiedparametric, simplified numerical consists numerical of model a modelstraight was was inflowgenerated generated region as as shownwithshown in a Figure cross-section in Figure 13. 13. This areaThis model, followingmodel, which which the isoriginal is completely completely one. The parametric, parametric, impeller consistsand consists side of channel a of straight a straight were inflow completely inflow region region withparametricwith a cross-section a cross-section and only area area the following followinggap between the the original originalimpeller one.one. and The Thesuction impeller impeller side andremained and side side channel unchanged. channel were were completelyThe completelyoutlet parametricregionparametric was and andmodelled only only the the gapas gapa betweenstraight between circular impeller impeller pipe. andan dGiven suction those side side simplifications remained remained unchanged. unchanged. it was possible The Theoutlet to outlet regiongenerateregion was modelledwas a reliable modelled asmodel a straightas (asa straightproven circular withcircular pipe. a mesh pipe. Given study) Given those with those simplifications only simplifications two mio. nodes. it was it was possible possible to generate to a reliablegenerate model a reliable (as proven model with(as proven a mesh with study) a mesh with study) only with two only mio. two nodes. mio. nodes.

Figure 13. Simple model of side channel pump for optimisation. Figure 13. Simple model of side channel pump for optimisation. Figure 13. Simple model of side channel pump for optimisation.

Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 13 of 20

The main parametrised components of the pump model are (in streamwise direction)

•Int. J.Suction Turbomach. area: Propuls. cross-section Power 2019, 4 ,with 6 four parameters as shown in Figure 14 right 13 of 19 • Impeller (simple): fixed diameters with five parameters as shown in Figure 14 left •Int. J. SideTurbomach. channel: Propuls. two Power different 2019, 4, sidex FOR channel PEER REVIEW geometries with three resp. Six parameters as shown 13 of in 20 FigureThe main 15. parametrised components of the pump model are (in streamwise direction) The main parametrised components of the pump model are (in streamwise direction) • Suction area: cross-section with four parameters as shown in Figure 14 right • Suction area: cross-section with four parameters as shown in Figure 14 right • Impeller (simple): ﬁxed diameters with ﬁve parameters as shown in Figure 14 left • Impeller (simple): fixed diameters with five parameters as shown in Figure 14 left • Side channel: two different side channel geometries with three resp. Six parameters as shown in • Side channel: two different side channel geometries with three resp. Six parameters as shown in Figure 15. Figure 15.

Figure 14. Parameters of impeller and suction area for optimisation.

With the given parameters, more than 300 models were generated. For each model, at least three flow rates (BEP, 75% BEP, 125% BEP) were simulated. After an analysis of all Q/H/η characteristics, for the 20 most interesting models the full characteristics with seven operating points were simulated. Figure 14. Parameters of impeller and suction area for optimisation. Figure 14. Parameters of impeller and suction area for optimisation.

Figure 15. Parameters of side channel geometry for optimisation. Figure 15. Parameters of side channel geometry for optimisation. With the given parameters, more than 300 models were generated. For each model, at least three 5.2. Results of the Optimisation Model flow rates (BEP, 75% BEP, 125% BEP) were simulated. After an analysis of all Q/H/η characteristics, for theAs 20presenting most interesting all relevant models results the fullwould characteristics go beyond withthe scope seven of operating this paper, points only were some simulated. selected examples are shown. In Figure 16, the effect of the impeller inclination angle is shown. As all other parameters5.2. Results ofwere the Optimisationidentical,Figure the15. Model Parametersinfluence isof impresside channelsive. geometryThough thefor optimisation.difference between the pictured anglesAs is presentinghuge (±25°) all investigations relevant results of inclination would go beyondangles in the between scope offit this perfectly paper, in only the someshown selected trend. 5.2. Results of the Optimisation Model Forexamples the given are side shown. channel In Figure and suction 16, the area, effect it seems of the impellerthat a straight inclination impeller angle blade is shown.yields the As optimum all other parametersAs presenting were identical, all relevant the influenceresults would is impressive. go beyond Though the scope the of difference this paper, between only some the picturedselected examplesangles is huge are shown. (±25◦) In investigations Figure 16, the of effect inclination of the angles impeller in betweeninclination fit perfectlyangle is shown. in the shown As all trend.other parameters were identical, the influence is impressive. Though the difference between the pictured angles is huge (±25°) investigations of inclination angles in between fit perfectly in the shown trend. For the given side channel and suction area, it seems that a straight impeller blade yields the optimum

Int. J. Turbomach. Propuls. Power 2019, 4, 6 14 of 19

Int.Int. J. Turbomach. J. Turbomach. Propuls. Propuls. Power Power 2019 2019, 4, ,x 4 FOR, x FOR PEER PEER REVIEW REVIEW 14 14 of 20of 20 For the given side channel and suction area, it seems that a straight impeller blade yields the optimum efﬁciencyefficiencyefficiency and and highest and highest highest head. head. head. However However However not not not only only only headhead head and and efficiency efﬁciency efficiency depend dependdepend on on onthe the theinclination inclination inclination angle, angle, angle, but alsobutbut thealso also position the the position position of the of ofthe BEP. the BEP. BEP.

50 50 50%50%

45 45 45%45%

40 40 40%40%

35 35 35%35% InclinationInclination angle angle 0° - 0°Head - Head Inclination angle +25° - Head 30 30 30%30% Inclination angle +25° - Head InclinationInclination angle angle -25° -25° - Head - Head 25 25 25%25% InclinationInclination angle angle 0° - 0°eff - eff 20 20%

Pump Head [m] Head Pump 20 20% Inclination angle+25° - eff

Pump Head [m] Head Pump Inclination angle+25° - eff PumpEfficiency [%] PumpEfficiency [%] Inclination angle -25° - eff 15 15 15%15% Inclination angle -25° - eff

10 10 10%10%

5 5 5% 5%

0 0 0% 0% 0246802468 FlowrateFlowrate [m] [m] FigureFigureFigure 16. 16.Effect 16. Effect Effect of of impeller impellerof impeller inclination inclination inclination angle angle on on onpump pump pump head head head and andand efficiency. efficiency. efﬁciency.

ThisThis isThis interesting, is interesting,is interesting, because because because when when when varying varying varying thethe the impellerimpeller impeller depth depth depth and and and leaving leavingleaving all all allother other other parameters parameters parameters identicalidenticalidentical as shown as asshown shown in Figure in inFigure Figure 17 ,17, the 17, the position the position position of of theofthe the BEPBEP BEP remains remains remains unchanged unchanged unchanged although although head head head curve curve curve and and and maximummaximummaximum efﬁciency efficiency efficiency vary. vary. vary.

50 50 50%50%

45 45 45%45%

40 40 40%40%

35 35 35%35% d=10mmd=10mm - Head - Head 30 30 30%30% d=11mmd=11mm - Head - Head 25 25 25%25% d=13mmd=13mm - Head - Head d=10mm - eff 20 20% d=10mm - eff

Pump Head [m] Head Pump 20 20% Pump Head [m] Head Pump

Pump Efficiency [%] d=11mm - eff

Pump Efficiency [%] d=11mm - eff 15 15 15%15% d=13mmd=13mm - eff - eff 10 10 10%10%

5 5 5% 5%

0 0 0% 0% 0246802468 FlowrateFlowrate [m³/h] [m³/h] FigureFigureFigure 17. 17.Effect 17. Effect Effect of of impeller impellerof impeller depthdepth depth on onpump pump pump head head head and and and efficiency. efﬁciency.efficiency.

AnotherAnotherAnother interesting interesting interesting fact fact isfact theis theis identicalthe identical identical efficiencyefficiency efficiency up up to to toBEP BEP BEP for for for all allall impeller impellerimpeller variations variations variations though though though head curvesheadhead curves differcurves differ significantly. differ significantl significantl Thisy. wasy.This This already was was already observedalready observed observed in Figure in in 16Figure Figurewhich 16 leads16which which to leads the leads presumption to tothe the presumption that the impeller only has limited influence on efficiency (up to BEP) but strong effect that thepresumption impeller only that has the limited impeller influence only has onlimited efficiency influence (up on to efficiency BEP) but (up strong to BEP) effect but on strong head effect curve. on head curve. Theon dimensions head curve. of the side channel have a major influence on head and efficiency as shown TheThe dimensions dimensions of ofthe the side side channel channel have have a major a major influence influence on on head head and and efficiency efficiency as asshown shown in in in Figure 18. Although the side channel area was only changed by ±10% a smaller one yields a FigureFigure 18. 18. Although Although the the side side channel channel area area was was on only lychanged changed by by ±10% ±10% a smallera smaller one one yields yields a highera higher highermaximum maximummaximum efficiency efficiency efficiency at ata at lowera alower lower flowrate fl flowrateowrate respectively respectively respectively a largera larger a larger one one a one lowera lower a lowermaximum maximum maximum efficiency efficiency efficiency at at at overloadoverloadoverload conditions. conditions. conditions. AA smallerAsmaller smaller side side channel channel channel also alsoalso shows showsshows a asteepa steepsteep efficiency efficiencyefficiency decrease decrease decrease at atoverloadat overload overload conditions.conditions.conditions. Despite Despite Despite a similar a similar a similar head head head characteristic, characteristic, characteristic, thethe the head head around around around BEP BEP BEP heavily heavilyheavily varies. varies. As describedAsAs described described in chapter in inchapter chapter 2, up to2, 2, nowup up to there tonow now are there stillthere ar two ear stille theories still two two theories trying theories to tryingdescribe trying to todescribe the describe functionality the the of a sidefunctionalityfunctionality channel pump.of ofa side a side If channel theory channel pump. of pump. angular If theoryIf theory momentum of ofangular angular would momentum momentum be appropriate, would would be beappropriate, pump appropriate, head pump should pump be head should be depending on blade (tipping) angle as shown in Figure 19. A positive tipping angle— dependinghead on should blade be (tipping)depending angle on blade as shown(tipping) in angle Figure as shown 19. A in positive Figure 19. tipping A positive angle—the tipping angle— so-called forward curved blade—would yield a higher head than a backward curved one. Though this is not Int.Int. J.J. Turbomach.Turbomach. Propuls.Propuls. PowerPower 20192019,, 44,, xx FORFOR PEERPEER REVIEWREVIEW 15 15 of of 20 20 Int. J. Turbomach. Propuls. Power 2019, 4, 6 15 of 19 thethe so-calledso-called forwardforward curvedcurved blade—wouldblade—would yieldyield aa higherhigher headhead thanthan aa backwardbackward curvedcurved one.one. ThoughThough thisthis isis notnot commoncommon forfor radialradial pumpspumps asas bladeblade loadingloading increasesincreases andand flowflow hardlyhardly followsfollows thethe bladeblade commonchannel,channel, for itsits radial influenceinfluence pumps waswas as investigatedinvestigated blade loading duringduring increases thethe opoptimisationtimisation and flow processprocess hardly asas somesome follows literatureliterature the bladesuggestssuggests channel, itit its influence[2,12,13].[2,12,13]. was investigated during the optimisation process as some literature suggests it [2,12,13].

5050 50%50%

4545 45%45%

4040 40%40% dSC=9.5mm;dSC=9.5mm; ASC271mm²ASC271mm² -- HeadHead 3535 35%35% dSC=10mm;dSC=10mm; ASC286mm²ASC286mm² -- HeadHead 3030 30%30% dSC=11mm;dSC=11mm; ASC316mm²ASC316mm² -- HeadHead dSC=11.5mm;dSC=11.5mm; ASC331mm²ASC331mm² -- HeadHead 2525 25%25% dSC=9.5mm;dSC=9.5mm; ASC271mm²ASC271mm² -- effeff 2020 20%20% dSC=10mm;dSC=10mm; ASC286mm²ASC286mm² -- effeff Pump Head [m] Head Pump Pump Head [m] Head Pump Pump Efficiency [%] Efficiency Pump Pump Efficiency [%] Efficiency Pump dSC=11mm;dSC=11mm; ASC316mm²ASC316mm² -- effeff 1515 15%15% dSC=11.5mm;dSC=11.5mm; ASC331mm²ASC331mm² -- effeff 1010 10%10%

55 5%5%

00 0%0% 0246802468 FlowrateFlowrate [m³/h] [m³/h] FigureFigureFigure 18. 18.18.Effect EffectEffect of ofof side sideside channel channelchannel depth depthdepth and and arar areaeaea onon on pumppump pump headhead head andand and efficiency.efficiency. efﬁciency.

BackwardBackward curved curved blade blade ForwardForward curvedcurved blade blade RückwärtsRückwärts gekrümmte gekrümmte Schaufeln Schaufeln VorwärtsVorwärts gekrümmte gekrümmte Schaufeln Schaufeln

FlowFlow

FigureFigureFigure 19. Theoretical19.19. Theoretical pump pump head head depending depending on bl bladeadeade tippingtipping tipping angleangle angle forfor for aa radialradial a radial impeller.impeller. impeller.

It isIt shownIt isis shownshown in Figure inin FigureFigure 20 2020that thatthat for forfor a aa certain certaincertain configurationcoconfiguration pump pump head head stays stays almost almost constant constant for for significantlysignificantlysignificantly varying varyingvarying blade bladeblade tipping tippingtipping angles. angles.angles. ThisThisThis lead leadsleadss toto to thethe the assumptionassumption assumption thatthat that thethe the theorytheory theory ofof angularangular of angular momentummomentum is not is not entirely entirely applicable applicable for for side side channelchannel pumps. pumps. Interestingly Interestingly the the pump pump efficiency efficiency and and the location of the best efficiency point is clearly influenced by the blade tipping angle. A lower the locationthe location of the of best the efficiencybest efficiency point point is clearly is clea influencedrly influenced by the by bladethe blade tipping tipping angle. angle. A lower A lower tipping tippingtipping angleangle yieldsyields aa higherhigher thethe efficiencyefficiency atat lowerlower flowrates.flowrates. ThisThis maymay bebe usefuluseful whenwhen tryingtrying toto shiftshift angle yields a higher the efficiency at lower flowrates. This may be useful when trying to shift the Int.thethe J. locationlocation Turbomach. ofof Propuls. thethe BEP.BEP. Power 2019, 4, x FOR PEER REVIEW 16 of 20 location of the BEP.

45% 30 44% 25 43% 42% 20 Tipping Angle = 3° 41% Tipping Angle = 0° 40% 15 39% Tipping Angle = -3°

PumpHead[m] 10 38% Tipping Angle = -6° PumpEfficiency [%] 37% 5 Tipping Angle = -10° 36% 35% 0 3456734567 Flowrate [m³/h] Flowrate [m³/h] Figure 20. Effect of blade tipping angle on pump head. Figure 20. Effect of blade tipping angle on pump head.

As the pump may operate at different rotational speeds it is of major interest if there are certain phenomena or if pump head and efficiency can be estimated according to similarity laws for discharge as described in Equation (9) or head as described in Equation (10) like radial or axial pumps. n = 2 ⋅ Qanalytic,n2 Qn1 (9) n1

2  n  =  2  ⋅ Hanalytic,n2   Hn1 (10)  n1 

A comparison of numerical and analytical calculation of pump head and efficiency for 1750 rpm, based on a rotational speed of 1450 rpm, is shown in Figure 21. It can be shown that at least for relatively small variations (+20%) of the rotational speed, the application of similarity laws is acceptable and reliable.

80 50%

72 45%

64 40%

56 35%

48 30% 1450 - H 1750 - H 40 25% 1750 - H (analytical) 32 20% 1450 - eff Pump Head [m] Head Pump

Pump Efficiency [%] Efficiency Pump 1750 - eff 24 15% 1750 - eff (analytical) 16 10%

8 5%

0 0% 024681012 Flowrate [m³/h]

Figure 21. Pump head and efficiency for different rotational speed—numerical vs. analytical.

Finally a comparison of the results for the used simplified optimization model with the full model was carried out. As for the optimization only three operating points around BEP were investigated; it can be noted that those are quite in good accordance with the results of the full model as shown in Figure 22. In particular, the pump head in this region is predicted quite well. Due to the

Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 16 of 20

45% 30 44% 25 43% 42% 20 Tipping Angle = 3° 41% Tipping Angle = 0° 40% 15 39% Tipping Angle = -3°

PumpHead[m] 10 38% Tipping Angle = -6° PumpEfficiency [%] 37% 5 Tipping Angle = -10° 36% 35% 0 3456734567 Int. J. Turbomach. Propuls. Power 2019, 4, 6 16 of 19 Flowrate [m³/h] Flowrate [m³/h]

Figure 20. Effect of blade tipping angle on pump head. As the pump may operate at different rotational speeds it is of major interest if there are certain phenomena orAs if the pump pump head may operate and efﬁciency at different can rotational be estimated speeds it according is of major tointerest similarity if there lawsare certain for discharge phenomena or if pump head and efficiency can be estimated according to similarity laws for as described in Equation (9) or head as described in Equation (10) like radial or axial pumps. discharge as described in Equation (9) or head as described in Equation (10) like radial or axial pumps. n = 22⋅ QanalyticQanalytic,n2,n2= ·QQn1n1 (9) (9) n11

2 2  n 2 H H ==  2  ⋅ H·H (10) analyticanalytic,n2 ,n2  n  n1 n1 (10)  n11

A comparisonA comparison of numerical of numerical and and analyticalanalytical calculation calculation of pump of pumphead and head efficiency and for efﬁciency 1750 rpm, for 1750 rpm, basedbased on on a rotationala rotational speed of of 145 14500 rpm, rpm, is shown is shown in Figure in Figure21. It can 21 be. Itshown can bethat shown at least thatfor at least for relativelyrelatively small small variations variations (+20%) (+20%) of the the rotational rotational speed, speed, the theapplication application of similarity of similarity laws is laws is acceptableacceptable and reliable. and reliable.

80 50%

72 45%

64 40%

56 35%

48 30% 1450 - H 1750 - H 40 25% 1750 - H (analytical) 32 20% 1450 - eff Pump Head [m] Head Pump

Pump Efficiency [%] Efficiency Pump 1750 - eff 24 15% 1750 - eff (analytical) 16 10%

8 5%

0 0% 024681012 Flowrate [m³/h]

Figure 21.FigurePump 21. Pump head head and and efﬁciency efficiency for for different different ro rotationaltational speed—numeric speed—numericalal vs. analytical. vs. analytical.

Finally aFinally comparison a comparison of the of the results results for for the the usedused simplified simplified optimization optimization model modelwith the with full the full model wasmodel carried was carried out. out. As forAs for the the optimization optimization only only three three operating operating points points around around BEP were BEP were investigated; it can be noted that those are quite in good accordance with the results of the full model investigated;as shown it can in Figure be noted 22. In particular, that those the arepump quite head inin this good region accordance is predicted with quite thewell. resultsDue to the of the full model asInt. shown J. Turbomach. in Figure Propuls. Power 22. 2019 In particular,, 4, x FOR PEER theREVIEW pump head in this region is predicted quite 17 of 20 well. Due to the simplifications a quantitative match cannot be expected although the qualitative match—defined simplifications a quantitative match cannot be expected although the qualitative match—defined as as the correctthe correct prediction prediction of theof the location location ofof BEP—is accomplished, accomplished, which which is of major is of importance major importance for a for a reliable optimization.reliable optimization.

50 50%

45 45%

40 40%

35 35%

30 30% Full Model - H 25 25% Simple Model - H 20 20% Full Model - eff Pump Head [m] Head Pump

PumpEfficiency [%] Simple Model - eff 15 15%

10 10%

5 5%

0 0% 012345678 Flowrate [m³/h]

FigureFigure 22. Resulting 22. Resulting pump pump head head and and efﬁciencyefficiency depending depending on model on model complexity. complexity.

5.3. Optimisation Results of the Full Model and Comparison with Original The optimum geometry for achieving the identical head curve of the original pump and increasing the efficiency significantly was found in the simple model. Although the results of the simple model are quite reliable, it was vital to prove the performance in the full model, as the suction impeller and inflow and outflow conditions presumably influence the behavior of the pump. As not only the suction area, impeller, and side channel were changed but also the connecting passage between outlet of the suction impeller and inlet of the suction piece, simulations in the full model were necessary anyhow. Figure 23 shows the impressive efficiency increase of the optimised pump whilst ensuring a nearly identical head characteristic at the same time. Besides increasing efficiency more than 30% (relatively) between deep part load and BEP, it is important to notice that the position of BEP was also shifted to slightly lower flowrates, as required from the manufacturer. It can also be seen that numerical simulations, both for the original and the optimised pump, predict the position of BEP at lower flowrates. The measurements also show a bit lower absolute value of the hydraulic efficiency which is probably due to neglected wall roughness of the rotating parts in the CFD-simulations.

Int. J. Turbomach. Propuls. Power 2019, 4, 6 17 of 19

5.3. Optimisation Results of the Full Model and Comparison with Original The optimum geometry for achieving the identical head curve of the original pump and increasing the efficiency significantly was found in the simple model. Although the results of the simple model are quite reliable, it was vital to prove the performance in the full model, as the suction impeller and inflow and outflow conditions presumably influence the behavior of the pump. As not only the suction area, impeller, and side channel were changed but also the connecting passage between outlet of the suction impeller and inlet of the suction piece, simulations in the full model were necessary anyhow. Figure 23 shows the impressive efficiency increase of the optimised pump whilst ensuring a nearly identical head characteristic at the same time. Besides increasing efficiency more than 30% (relatively) between deep part load and BEP, it is important to notice that the position of BEP was also shifted to slightly lower flowrates, as required from the manufacturer. It can also be seen that numerical simulations, both for the original and the optimised pump, predict the position of BEP at lowerInt. flowrates. J. Turbomach. ThePropuls. measurements Power 2019, 4, x FOR also PEER show REVIEW a bit lower absolute value of the hydraulic 18 efficiency of 20 which is probably due to neglected wall roughness of the rotating parts in the CFD-simulations.

50 50%

45 45%

40 40%

35 35%

30 30%

25 25%

20 20% Pump Head [m] Head Pump 15 15% [%] Efficiency Pump

10 10%

5 5%

0 0% 02468 Flowrate [m³/h]

OPT trans. - Head OPT - measurement - Head ORIGINAL trans. - Head ORIGINAL - measurement - Head OPT trans. - eff OPT - measurement - eff ORIGINAL trans. -eff ORIGINAL - measurement - eff

Figure 23. Comparison of original and optimised pump. Figure 23. Comparison of original and optimised pump. 6. Conclusions 6. Conclusions Though side channel pumps are rather known more as a mandatory powerful workhorse in industrialThough facilities side than channel an efficiency pumps talent,are rather the presentedknown more paper as a showsmandatory how powerful to get the workhorse most out ofin them. By usingindustrial a large facilities numerical than modelan efficiency to cover talent, all effectsthe presented inside, paper it is possible shows how to identify to get the the most reasons out of for the them. By using a large numerical model to cover all effects inside, it is possible to identify the reasons losses and eliminate them. As soon as the behaviour and the interaction of impeller and side channel for the losses and eliminate them. As soon as the behaviour and the interaction of impeller and side are known, it is possible to adapt head curve, position of BEP, and improve the maximum efficiency. In channel are known, it is possible to adapt head curve, position of BEP, and improve the maximum parallel,efficiency. all required In parallel, gaps all for required safe operation gaps for safe and operation to comply and with to comply standards with are standards already are included. already Inincluded. addition of optimising the presented pump, the paper also shows the strong influence of less known butIn importantaddition of parametersoptimising the like presented side channel pump,depth, the paper or lessalso shows important the strong assessed influence parameters of less like impellerknown depth, but important on head andparameters efficiency. like side channel depth, or less important assessed parameters like impeller depth, on head and efficiency. Author Contributions: Conceptualization, M.M. and H.B.; Data curation, J.K.; Formal analysis, M.M.; Funding acquisition,Author H.B.;Contributions: Investigation, Conceptualization, M.M.; Methodology, M.M. and H.B.; M.M.; Data Project curation, administration, J.K.; Formal analysis, H.B.; M.M.; Resources, Funding M.M.; Supervision,acquisition, H.B. H.B.; and H.J.;Investigation, Validation, M.M.; J.K.; Methodology, Visualization, M.M.; M.M.; Project Writing—original administration, draft, H.B.; M.M.; Resources, Writing—review M.M.; & editing,Supervision, H.B. and H.B. H.J. and H.J.; Validation, J.K.; Visualization, M.M.; Writing—original draft, M.M.; Writing—review & editing, H.B. and H.J.

Funding: This research received no external funding

Acknowledgments: We gratefully acknowledge the cooperation with Dickow Pumpen GmbH & Co. KG, who provided the pump, measurement data and many other information.

Conflicts of Interest: The authors declare no conflict of interest.

Appendix A—Nomenclature

A [m2] area H [m] pump head Q [m3/s] pump discharge P [W] power

Int. J. Turbomach. Propuls. Power 2019, 4, 6 18 of 19

Funding: This research received no external funding Acknowledgments: We gratefully acknowledge the cooperation with Dickow Pumpen GmbH & Co. KG, who provided the pump, measurement data and many other information. Conﬂicts of Interest: The authors declare no conﬂict of interest.

Nomenclature

A [m2] area H [m] pump head Q [m3/s] pump discharge P [W] power c [m/s] absolute velocity cm [m/s] meridional velocity cu [m/s] tangential part of absolute velocity g [m/s2] gravitational constant n [rpm] rotational speed nq [rpm] specific speed p [Pa] pressure r [m] radius t [s] timestep for transient simulations u [m/s] velocity z [m] geodetic head δ [-] specific diameter η [-] efficiency ρ [kg/m3] density σ [-] specific speed ϕ [-] flow number ψ [-] pressure number ω [1/s] angular velocity Subscripts and Superscripts 1 pump inlet 2 pump outlet 9906 referring to DIN EN ISO 9906:2013-03 o at the outer radius of the impeller i at the inner radius of the impeller SC side channel shaft properties at pump shaft trans transient

References

1. Grabow, G. Das erweiterte Diagramm für Fluidenergiemaschinen und Verbrennungs-motoren. Freiberger Forschungshefte A 830, Maschinen- und Energietechnik; Deutscher Verlag für Kunststoffindustrie: Leipzig, Germany, 1993. 2. Grabow, G. Optimalbereiche von Fluidenergiemaschinen—Pumpen und Verdichter. Forsch. Ing. 2002, 67, 100–106. [CrossRef] 3. Almeida, A.T.; Ferreira, F.J.T.E.; Fong, J.; Fonseca, P. EuP Lot 11 Motors Final Report; University of Coimbra: Coimbra, Portugal2008. 4. Richtlinie 96/61/EG des Rates vom 24. September 1996 über die Integrierte Vermeidung und Verminderung der Umweltverschmutzung; EU-Richtlinie 96/61/EG; European Union: Brussels, Belgium, 1996. 5. Fleder, A.; Böhle, M. Numerical and Experimental Investigations on the Influence of the Blade Shape on Industrial Side Channel Pumps. In Proceedings of the International Rotating Equipment Conference, Düsseldorf, Germany, 27–28 September 2012. 6. Meakhail, T.; Seung, O.P.; Lee, D.A.; Mikhail, S. A study of circulating flow in regenerative pump. In Proceedings of the KSAS 1st International Session, Gyeongju, Korea, 14–15 November 2003; pp. 19–26. Int. J. Turbomach. Propuls. Power 2019, 4, 6 19 of 19

7. Pfleiderer, C. Die Kreiselpumpen für Flüssigkeiten und Gase; Band 3; Springer: Berlin, Germany, 1949. 8. Senoo, Y. Theoretical Research on Friction Pum; Research Institute for Fluid Engineering, Kyushu University: Fukuoka, Japan, 1948. 9. Senoo, Y. Researches on Peripheral Pumps. Rep. Res. Inst. Appl. Mech. 1954, 3, 53–113. 10. Senoo, Y. A Comparison of Regenerative-Pump Theories Supported by New Performance Data. Trans. ASME 1956, 78, 1091–1102. 11. Iverson, H.W. Performance of the Periphery Pump. Trans. ASME 1955, 77, 19–22. 12. Grabow, G. Ermittlung der Hauptabmessungen für Seitenkanalmaschinen. Forsch. Ing. 1999, 65, 41–47. [CrossRef] 13. Surek, D. Geometrische Dimensionierung von Seitenkanalmaschinen. Forsch. Ing. 1996, 62, 229–238. [CrossRef] 14. Appiah, D.; Zhang, F.; Yuan, S.; Osman, M.K. Effects of the geometrical conditions on the performance of a side channel pump: A review. Int. J. Energy Res. 2017, 42, 416–428. [CrossRef] 15. Mosshammer, M. Untersuchung und Optimierung einer mehrstufigen Spaltrohrmotorpumpe. Ph.D. Thesis, Graz University of Technology, Graz, Austria, 2018. 16. Höller, S.; Jaberg, H.; Benigni, H.; Kim, J.J. Cavitation optimization of a variable pitch mixed flow pump for cooling water by numerical methods and test rig verification. In Proceedings of the International Rotating Equipment Conference, Düsseldorf, Germany, 14–15 September 2016. 17. Benigni, H.; Jaberg, H.; Yeung, H.; Salisbury, T.; Berry, O.; Collins, T. Numerical Simulation of Low Specific Speed American Petroleum Institute Pumps in Part-Load Operation and Comparison with Test Rig Results. J. Fluid. Eng. 2012, 134, 024501. [CrossRef] 18. Schiffer-Rosenberger, J.; Benigni, H.; Jaberg, H. Numerical Simulation of a Francis Turbine Including the Runner Seals on Crown and Band Side. Technical Report; Institute of Hydraulic Fluidmachinery: Graz, Austria, 2016. 19. Menter, F.R. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 1994, 32, 1598–1605. [CrossRef] 20. Menter, F.R.; Egorov, Y. Scale-Adaptive Simulation Method for Unsteady Flow Predictions. Part 1: Theory and Model Description. J. Flow Turbul. Combust. 2010, 85, 113–138. [CrossRef] 21. Konrad, J. Prüfprotokoll SCM 3561. Waldkraiburg, Germany, Unpublished measurement report. 2014.

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