Successes and failures in CFD liquid flow modeling in multistage centrifugal pumps with low specific speed

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1 MECHANIK No. 3/ Successes and failures in CFD liquid flow modeling in multistage centrifugal pumps with low specific speed Sukcesy i niepowodzenia w modelowaniu przepływu cieczy w pompach wielostopniowych o małym wyróżniku szybkobieżności WITOLD LORENZ * MARCIN JANCZAK Original article in Polish language: DOI: /mechanik Article awarded at the conference Simulation 2016 It has been presented the application of numerical calculations in the designing process of multistage centrifugal pump with low specific speed. The obtained work results were presented and validated by means of two computational codes: ANSYS Fluent and ANSYS CFX. Numerical simulations were held with respect to both Steady Flow and Variable Flow conditions. The results clearly indicate the direction and way of conducting CFD simulations for this type of pumps. KEYWORDS: fluid-flow hydraulic machinery, multistage centrifugal pumps, CFD simulations, validation of CFD results. Zaprezentowano zastosowanie obliczeń numerycznych w procesie projektowania wielostopniowej pompy wirowej o niskim wyróżniku szybkobieżności. Przedstawiono i zwalidowano wyniki uzyskane za pomocą dwóch kodów obliczeniowych: ANSYS Fluent i ANSYS CFX. Obliczenia prowadzono dla przepływu w stanie ustalonym i nieustalonym. Uzyskane wyniki jednoznacznie wskazują kierunek i sposób prowadzenia badań CFD dla tego rodzaju pomp. SŁOWA KLUCZOWE: hydrauliczne maszyny przepływowe, wielostopniowe pompy wirowe, obliczenia CFD, walidacja wyników CFD In the process of global technological development much attention is paid to high efficient energy production and processing. It is caused by economic factors and growing requirements of reducing machines energy consumption. Nearly 30% of total energy in industrial processes is consumed by centrifugal pumps and due to this fact designing new pumps is directed to maximizing efficiency while minimizing the dimensions. Project titled Model multistage pumps with higher suction properties (implemented under the Operational Programme Innovative Economy, Activities 1.4.POIG Support of targeted projects) included of designing new type series of centrifugal pumps WH type with modular design designated for pumping liquid fuels and clean water with maximum temperature up to 140 o C. Under these works the type series of high-flow system pumps with using Control Flow Design were engineered. The main purpose of analysis (real and CFD) was developing methodology of numerical simulation for multistage pump with low kinematic specific speed n q (specific speed) which provides high predictability of real pumps` parameters at the stage of their design and modelling. The subject of the research was pump WHA.3.14 (14-stage) [5] which was installed at the pump testing station (fig. 1). The shape of the impeller of centrifugal pump is closely linked to the hydraulic parameters which the pump is supposed to achieve. Characteristic dimensions rather narrowly specify its tangential section. Unified mathematical description of the impeller type resulting from the similarity of flow of centrifugal pumps is described by specific speed n q [3] called also specific shape and is defined as follows n q = n Q 4, H 3 where: n rotational speed, Q pump s capacity, H-total head This factor means the rotational speed n q of the geometrically similar pump with set up impeller diameter achieving capacity Q=1 m 3 /s at total head H=1 m. In pump engineering n q is assumed as a dimensionless value. Tangential shape of the impeller for the adequate value n q was shown schematically on the fig. 2. Fig. 1. WHA.3.14 Pump on the test rig (pump s capacity Q=50 m 3 /h total head: H 14 stages = 600 m, H 1st stage = 42 m) * Dr inż. Witold Lorenz, dr inż. Marcin Janczak Research & Development Department of Hydro-Vacuum S.A. Grudziądz Fig. 2. Impeller s tangential shape depending on the value of specific speed [4]

2 Validation of the CFD simulations for centrifugal pump at n q=40 Comparison of numerical results with real results it s a key issue related with forecasting of parameters of modernized and new centrifugal pumps. Due to this reason all presented results were confirmed by experimental research. For n q = CFD calculations quite well match with actual results. This is due to the liquid flow in the impeller, characterized by: slight change in the direction of the flow, relatively short multi-vane channel and thus relatively increased distance between cascade of blades. On the fig. 3 energy performances one of the tested deep-well pump GBC type was presented. Solid lines marked characteristics obtained by measuring the actual pump made on pump testing rig in the closed circuit. Measurements were carried out in accordance with the guidelines of ISO 9906: 2012, Class 2. The accuracy of measuring instruments in relation to the measuring range were as follows: barometric pressure δpb = ± 0,1%, capacity δq =± 0,2%, manometric pressure δpm = ± 0,2 %, power δpw = ± 0,2 %, temperature δt = ± 0,5 C. With dotted lines it has been applied characteristics obtained on the basis of CFD numerical simulations. Results were shown for one stage pump. At the optimal point (Q opt =40 m 3 /h), in which pump has maximal efficiency, the difference between actual and numerical values of the hydraulic parameters is smaller than 1% (tab. I). Due to the fact that pumps are selected to work in terms of capacity ensuring achieving high efficiency, the case was analysed Q/Q n = 0,8 1,2. Dispersion of the numerical results in the whole tested range was higher, but still at the good level. The fig. 4 shows trajectories of the liquid particles for pump GBC with n q = 40. Table I. CFD validation for n q=40 Discrepancy of the actual results and CFD simulations Q opt Q/Q opt = ( ) H rz/h CFD ~ 0.8% ~ 1.5% Pw rz/pw CFD ~ 0.3% ~ 5% eta rz/eta CFD ~ 0.15% ~ 1.5% Indications: H total head, Pw pump s power consumption, eta - efficiency, Q pump s capacity; indexes: rz and CFD respectively relate to actual tests and CFD simulations Fig. 4. Streamlines in the stage of the deep-well pump, n q=40 [6] Fig. 5. Comparison of discriminant of theoretical delivery head ψth calculated by CFD method and tested marked relatively: ψth(cfd) and ψth (Test) for the different specific speed n q [1]; with red colour it is marked the range of n q=(12 20). Conducting numerical simulations for pumps with low specific speed i.e. n q <20 is quite difficult and not very accurate. The literature shows that the spread between the actual and numerical results may be in this case about 5 8% [1] (fig. 5), wherein the cited results do not include multistage pumps, which modelling is much more complicated in comparison with single stage pumps. It is connected with several features such as: high share of disc friction losses, big angle of flow change (from axial at the inlet to radial at the outlet from the impeller). Short distance between impeller s inlet and the edge of the spiral for single stage centrifugal pumps, or vanes of the centrifugal diffuser with vanes for multistage centrifugal pumps Validation of the CFD simulations for centrifugal pumps with n q=18 Fig. 3. CFD validation for n q=40 In order to design the shape of high efficiency impeller and centrifugal guide-ring for multistage pump it is necessary to know the nature of the flow in both cooperating parts. The designer must therefore check not only the physical parameters such as: total head and power consumption but also identify the potential places of stagnation and formation of return currents, which can be a consequence of improperly formed palisades. Due to mutual, two-way interaction of impeller and diffuser with vanes it is necessary to carry out the calculations for the whole stage of multistage pump i.e. impeller (fig.6 blue parts) with centrifugal guidering (fig 6. parts in metallic colour).

3 The study covered the whole range of WH type series while the search for a meaningful calculation algorithm was limited only to pump WH.3 based on which they developed the methodology of CFD simulations. The parameters of the considered pumps were as follows: Nominal capacity Q n=50 m 3 /h, nominal delivery head H n= 42 m at nominal rotation speed n n=2950 min -1. CAD models of the tested parts were discretized with the use of tetragonal elements and prismatic elements near the wall, without the option of adaptation the mesh and marking gradients of mesh size (increasing the mesh size for Δx 1,2). The size of the meshes on the surfaces connecting each volumes was constant. The connections were made by using models GG and MFR (fig.6 orange filed). First the calculations of flow in Steady State (RANS) were carried out (Steady State, MRF) and next in Transient (RSI, SMM). Dimensionless ratio of the distance from the Y+ wall as within the range 30 <Y +< ~ 100 with maintaining the model of standard wall function. On the inlet they give the mass flow rate condition (fig.6 green field) while on the outlet side static pressure (fig 6 red field). The wall rotating in the model (fig.6 blue fields) were given rotational speed corresponding to the rotational speed of impeller of the real pump. Preliminary calculations were made for several turbulence models (standard k-ԑ, Renormalization Group Method k- ԑ, Realizable k- ԑ) - it turned out that the choice of the model does not significantly affect ton the obtained results. Based on the literature [2] and the authors own experience for further analysis assumed only model Realizable k-ԑ and intensity of turbulence on the inlet 5%. Calculations were stopped after stabilization of the pressure on inlet and outlet within interactions and obtaining value of finished reminders from the equations of Navier-Stokes on the level below Numerical calculations were carried out on several stages with using two calculation codes. ANSYS CFX and ANSYS Fluent. All further presented results for pump stage relate to the same geometry of the impeller and centrifugal guide-ring. The actual characteristics of the tested stage were calculated in this way so they not include mechanical losses, friction of spinning disks and leakages in the impeller`s internal sealing of the working pump. On the charts there were marked with steady lines energy performance received by measuring the real pump, dotted lines characteristics received from numerical simulations (with distinction on flow in Steady State and Transient). differ significantly from the actual values (differences are respectively ~ 11% and 16%) what excludes the possibility of approval these results. Additionally not all channels of centrifugal diffuser with vanes cooperating with impeller are evenly filled with liquid such flow in real pump is unrealistic which confirms low creditability of achieved results. This case was presented on fig.8 showing the trajectory of the liquid particles moving with relative speed in relation to local coordinate system of relative calculation area. Arrows indicate these fields of centrifugal diffuser`s channel which do not work correctly and in which occurs unnatural flow. Fig. 7. CFD validation (ANSYS CFX, Steady State, n q=18) Fig. 8. Trajectories of the liquid particles in the pump`s stage (ANSYS CFX, Steady State simulations, n q=18) Solver: ANSYS Fluent, flow at Steady State simulations Fig. 6. The type of the considered stage of the pump and initial conditions Solver: ANSYS CFX, flow at Steady State simulations The obtained energy performance of the pump stage is presented on fig.7. For optimal pump efficiency Q opt =50 m 3 /h calculated hydraulic efficiency of the stage substantially coincides with real state (accuracy ~1%), but calculated delivery head and power consumption In order to find more reliable calculation system for flow in a Steady State further simulations in the software ANSYS Fluent were carried out. The difference of total head for Q opt is high is ~ 11% (fig.9). In case of numerical model the power consumption was much smaller over 20% - in comparison with actual pump. Understated values of total head and power consumption cause that the difference between the actual and numerical efficiency is higher than 6%. Similarly as in previous analysis carried out in ANSYS CFX not all channels of centrifugal diffuser with vanes were correctly filled (fig.10). Due to the repeated error the numerical mesh of the model was checked again. At considered stage of the pump there were not detected incorrectly working elements of the mesh which could increase the calculation error.

4 In the analysis of the flow in the Steady State the torque was only given to the rotating parts, therefore the solid of the impeller and its mesh actually do not change their position in relation to the local coordinate system and other flow parts (centrifugal guide-ring) - it is only taken into account in the calculation code. So the suspicion existed that, irrespective of solver applied for calculation of flow in a Steady State - in the area of improperly working channels occurred adverse mutual positioning flow edge of the vane of impeller and the edge of inlet vane of diffuser with vanes. It is decided to carry out the calculations of flow in Transient, wherein boundary and initial conditions were determined on the basis of the flow analysis in a Steady State simulations. Fig. 11. CFD validation (ANSYS CFX, Transient, n q=18) Fig. 9. CFD validation (ANSYS Fluent, Steady State, n q=18) Fig. 12. Trajectories of the liquid particles in the pump`s stage (ANSYS, Fluent, Transient, n q=18) Fig.10. Trajectories of the liquid particles in the pump`s stage (ANSYS, Fluent, Steady State, n q=18) Solver: ANSYS CFX, flow at Transient simulations Calculations related to the flow in non-steady state were carried out with the time step meeting the condition CFL i.e. not exceeding the limit value and ensuring the stability of numerical solution. The characteristics obtained during numerical calculations still continued to significantly deviate from the real characteristics. (fig.11). Numerical total head was higher than real one ~ 8%. Differences of the power value were acceptable were ~ 3% whereas in the case of efficiency discrepancies were significant ~ 7%. Such big error is the result of improper quality of the flow. (fig.12). The flow of the impeller is correct with even distribution of the total pressure, however the channels of diffuser with vanes do not keep the character of the flow in the impeller. Disturbances of the flow, unnatural trajectories of the liquid particles, failure to maintain the pressure value are clearly visible. These turbulences suggested incorrect connection of impeller volume and diffuser with vanes. It should be noted that for analyses was taken the same discrete model as previously so discussed irregularities should be evident in calculation of flow in Steady State, namely it should appear the increased values of speed in the areas of transferring the calculating values together with appearance of significant gradients and dead flow zones in non-cooperating areas. Solver: ANSYS Fluent, flow at Transient simulations Due to unsatisfactory results of simulation of flow in Transient obtained by ANSYS CFX calculations were repeated with using ANSYS Fluent and as previously boundary and initial conditions determined on the basis of calculations of flow in Steady State. At the optimal point the difference between real and numerical values was: for delivery head ~ 4,5%, power consumption: ~ 1,7% an efficiency less than 4% (tab. II). Within the recommended pump selection Q/Q n = bigger mistake concerned only delivery head did not exceed 7%.

5 In case of power consumption and efficiency the error stayed at the similar level. In the considered range numerical and actual energy performance quite well overlap and had similar shape fig.13. At the fig.14 it has been compared the distribution of relative speed in the impeller and diffuser with vanes obtained with using ANSYS Fluent (Q opt) respectively for flow in Steady State (fig.14a) and Transient after a certain rotation of impeller (fig.14b). The results of flow calculation in Steady State flow indicate at whirl of return current in blade of impeller outlet area in close proximity to improperly working channel of the diffuser (black arrows). By turning the whole volume of the impeller in Transient simulation of flow improperly working zone has been extinguished and considered diffusers with vane have been completely filled (red arrows). This is the correct image of the flow in centrifugal multistage pumps. Fig. 13. CFD results validation (ANSYS Fluent, Transient, n q=18) a) Summary Numerical calculations allow for quick evaluation of the design solution. It is necessary to keep in mind that their outcome is always approximate. In the case of the pump discusses in this article this result is a function of: the shape of the flow system of the pump, the quality of a discrete model (including implemented simplifications), initial and boundary conditions and used turbulence models which were closing equations. On the basis carried our studies it has been stated that for designed multistage pumps with low specific speed the most satisfactory result of simulation was obtained in ANSYS Fluent for flow in Transient simulations. This article was elaborated based on the results of the project : Model multistage pumps with increased suction abilities which is funded by European Union from European Regional Development Fund. References b) 1. Gϋlich J.F. Centrifugal pump. Berlin: Springer-Verlag Berlin Heidelberg, ANSYS documentation for Relase 15.0.Canonsburg: ANSYS Inc., Jędral W. Pompy wirowe. Warszawa: Oficyna Wydawnicza Politechniki Warszawskiej, User manual for CFturbo 9.2 software. Drezno: CFturbo Software & Engineering GmbH, Modelowe pompy wielostopniowe o podwyższonych zdolnościach ssania. Sprawozdanie merytoryczne z realizacji Zadania 1 (BP) pt. Opracowanie, wykonanie i badania modelowego układu mechanicznego i przepływowego modelowej pompy wielostopniowej serii WH o wielkości DN50, nr POIG /12, dokument wewnętrzny Hydro-Vacuum S.A., Grudziądz, Raport obliczeń numerycznych pompy głębinowej GBC.4. Raport wewnętrzny Hydro-Vacuum S.A., Grudziądz, Fig. 14. Trajectories of the liquid particles in the pump`s stage achieved thanks to ANSYS Fluent: a) flow in Steady State, b) flow in Transient Table. II. CFD results validation (ANSYS Fluent, Transient, n q=18) Analyzed hydraulic parameters Percentage differences between the actual and CFD results for: Q opt Q/Qrz = 0,8 1.2 H rz/h Fluent, transient ~ 4.5% ~ 7% Pw rz/pw Fluent, transient ~ 1.7% ~ 1.8% eta rz/eta Fluent, transient ~ 3.7% ~ 3.7%