Numerical and Experimental Investigation of the Flow in a Centrifugal Pump Stage

Transcription

1 Numerical and Experimental Investigation of the Flow in a Centrifugal Pump Stage FRIEDRICH-KARL BENRA, HANS JOSEF DOHMEN Faculty of Engineering Sciences Department of Mechanical Engineering, Turbomachinery University of Duisburg-Essen Lotharstr. 1, Duisburg, Germany hans-josef.dohmen@uni-due.de Abstract: - In the first part of this paper, a steady state numerical simulation of the first stage of a multistage centrifugal pump, consisting of an impeller, a diffuser and a return channel, is performed by the commercial software Ansys-CFX. The obtained simulation results are compared with experiments that are designed and conducted by Laser Doppler Velocimetry (LDV) in the diffuser region for the same part load point. The experiments are done in a test facility which has been especially prepared for optical flow measurements. To reduce the numerical effort for this calculation a stage interface between rotating and stationary frames and a periodic boundary condition (only one blade of each blade row is simulated) is used for this calculation. For the stage interface, the flow behind the impeller is averaged circumferentially to be the inflow conditions of the diffuser blades. The experimental investigations support the simulation results. In the second part of this contribution the transient flow in this pump stage, which has an impeller with seven blades, a radial diffuser with ten vanes and a return channel with also ten separate vanes, has been simulated transient with the same software. Because of the unfavorable ratio of blade numbers a complete meshing of all flow channels was necessary. In consequence the cumulative amount of grid nodes reached a number of nearly 6 million nodes for this calculation. As a result of the numerical investigation of the time dependent flow accomplished for this part, the influence of the rotating impeller on the flow in the stationary parts of the pump is presented in detail. For this operation point all flow parameters are shown as a function of time and are discussed with respect to the position of the impeller relative to the stator vanes. 1 Introduction Multistage centrifugal pumps are used to realize high pressures in liquids. This is the case for example in the conveyance of ground water from a great depth. Also for drainage of mines high elevation differences have to be overcome. In the considered pressure and temperature range liquids can be treated as fluid with a constant density. This means the volume flow doesn t change with increasing pressure. This fact makes it possible to use a series connection of identical pump stages to realize the desired delivery head. Fig. 1 shows exemplarily a three stage double flow submersible motor pump. For extreme applications this type of pump can be build with ten ore even more stages. The number of stages is only limited by the rotor dynamic characteristics, which are mainly influenced by the length of the pump rotor. This makes it important to realize a high efficiency for a small overall Figure 1: Three stage double-flow submersible motor pump (Ritz Pumpen, Schwaebisch Gmuend [1]) length of each stage. So the design is very complex and demands considerable knowledge of the flow behavior in all components of the stage. As shown by [2-4] the interaction between the relative flow of the impeller and the stationary stator blades of the radial diffuser has a strong impact to the efficiency of the stage. The knowledge of the time dependent flow behavior in all parts of a pump stage is of outstanding importance. Analytical investigations of the flow field are not available for such complex flow geometries. Also measurements of the time dependent flow field in such geometries are very complicated. Fig. 2 shows the CAD model of a test pump at the University of Duisburg-Essen to investigate the flow field in one single stage of the commercial multistage pump shown in Fig.1. The flow field in this stage has been investigated first by Laser Doppler Velocimetry (LDV). At this time the available measurement equipment allows only the determination of time averaged flow fields in parts of the stationary blade channels. In addition the test stand allows only reduced pressure levels so for the measurement the rotational speed of the impeller was reduced. The measured results are compared to numerical results obtained by a steady state calculation in only one blade channel of each blade row. To get an impression of the time behavior e.g. the rotor/stator interaction, a time dependent calculation of ISSN: Page 71 ISBN:

2 the complete flow field in this stage has been calculated for design conditions of the pump. This calculation should be the basis of future experimental investigations on the transient flow field in this stage. reference frame, it is better to create the grid together in order to reduce the number of grid interfaces. Because of the complexity of the combined geometry, the grid generation tool Ansys-ICEM-CFD is utilized to generate the hexahedral structured grid which includes 333,285 nodes (310,944 hexahedral elements) for one blade passage. The total number of nodes for the here calculated problem with one blade passage is 583,045 (543,010 hexahedral elements). After meshing the flow region, the setup for the numerical simulation has been accomplished. The numerical code Ansys-CFX is used to solve the fully three dimensional incompressible Reynolds Averaged Navier-Stokes (RANS) equations. The simulation is performed for one impeller passage and one combined stator passage (diffuser and return channel) to a steady state solution by applying the periodic boundary conditions to the surfaces of passages in order to reduce the computational requirements. The turbulence is simulated with a k-ω turbulence model and a SST near wall treatment [6]. Interface 2 Figure 2: CAD model of test pump 1 : Windows for optical access 2 : Bearing block 3 : Impeller 4 : Stator 5 : Return vane 6 : Outlet holes Important design data of this stage are: - H = 45 [m] - Q = 225 [m 3 /s] - n = 2950 [min -1 ] - n q = 42.4 [min -1 ] 2 Numerical Investigation Fig. 3 shows the cross-sectional view of the test pump. The flow enters the pump by a straight pipe and has therefore no swirl. The flow behind the return channel vanes should also be swirl free to provide the same flow conditions for the second pump stage as it has been used for the first stage. The three dimensional volume models of all pump blade passages which are shown in Fig. 2 are created in the 3D-CAD system Pro/Engineer. These data are used as the basis for grid generation. The grid for the impeller is generated with the commercial software package Ansys-CFX-TurboGRID with a multi-block grid template in which an O-Grid is created around the blade and a H-Grid is used in the blade passage. The grid includes 249,760 nodes (232,066 hexahedral elements) for one blade passage. The diffuser and return channel are both in the stationary frame. As they share the same Stator Rotor Inlet Return vane Outlet Interface 1 Figure 3: Cross-sectional view of the test pump and Computational domains The discretization in space used is of second order accuracy. Boundary conditions have to be specified to the surfaces exposed to the fluid to solve the RANS equations. At the inlet of the pump stage, the total pressure, the direction of the velocity vector and a turbulence intensity of T u =5% are given. At the outlet of the flow regime, the mass flow rate is given. Two pairs of periodic boundary conditions have been applied. In addition, a no slip condition is given in the appropriate frame of reference for the flow at the wall boundaries of the hubs, the shrouds and the blades. An interface has to be used to connect the grids of different components of the pump. As the impeller is rotating and the combined stator part is stationary, a change in the frames of reference at the interface between these two components is necessary. In addition, due to the different blade numbers of the impeller and the stator parts (pitch ratio 1), a stage interface should be used to get a steady state solution, because by this interface the flow parameters are averaged in circumferential direction ISSN: Page 72 ISBN:

3 behind the impeller to be the inflow conditions for the diffuser. The stage interface makes it possible to analyze only one passage of each component even though the pitch ratio is different from 1. It is recommended to get a convergent result first by the interface of frozen rotor in which the position of the impeller is fixed relative to the diffuser during the calculation process. After that, a change of the interface from frozen rotor to stage is to be accomplished to recalculate the flow field. The convergence criteria for all the non-dimensional residuals are below 1x10-4 and the global imbalances of the conservation equations are lower than 0.001%. For the transient calculation the model has to be changed because the blade numbers in the rotating and stationary frame of reference have no common factor. This needs a complete calculation of all impeller blade passages and all stator blade passages. So the meshes of the first calculation are rearranged to give a model of all blade passages. In addition a new grid segment containing a part of the inlet pipe is introduced in front of the impeller. The grid size for this transient calculation reaches nearly 6 million nodes. The mesh of the inflow region and the rotor mesh are connected by a transient rotor-stator interface. The rotor is in the rotating frame of reference and the inflow is in the stationary frame of reference. The stator grid is also in the stationary frame of reference. It is connected to the flow domain of the rotor with another transient rotor-stator interface. The discretization in space was also of second order accuracy and the time discretization was second order backward. The convergence criteria for the transient simulation was a maximum RMS value lower than 10-3 in each time step for all residuals in all domains. The time step for the calculation was chosen to 48.4 e -6 s to encounter the periodic positions for the rotor and the stator during the revolution of the impeller. This gives an impeller rotation of deg for each time step. 3 Experimental Investigation In order to validate the numerical simulation results, experiments have been accomplished. The development of optical measurement methods and data acquisition systems makes it possible to identify the velocities in pump components without reaction on the flow. For the investigations performed for this paper, Laser Doppler Velocimetry (LDV) is used to measure the velocity field in a part of the diffuser region. LDV has been widely used to measure the velocities in pumps [7-9] and has therefore been proven to be an adequate method to provide a realistic velocity field. The LDV-system which has been utilized for the internal flow investigations is one dimensional, but by changing the angle of the axis of the optical system the velocity components in two directions (x- and y-direction) can be measured one after the other. The velocity component in the third direction (z-direction) is not measured and assumed to be negligible. The laser used for the investigations here is a Helium-Neon laser which has a wave length of 633 nm and an output power of 22 mw. For the diffuser, LDV-measurements of the velocity components in an axis normal plane at the middle span surface have been accomplished. 11X15 points are measured, 11 points in each radial direction and 15 points in each circumferential direction, respectively. The point by point measurements of the flow field inside one diffuser blade passage consist of 5000 separate measurements at arbitrary impeller positions for each point. An ensemble averaging method has been used to get one velocity value at each point. 4 Results In the first part of this chapter, the flow conditions in all components of the pump are discussed for an operating point with a rotating speed n = 2190 min -1 and a volumetric flow rate of Q = 225 m 3 /h. These operating conditions present an overload point for the chosen speed of rotation with a lower pressure increase of the stage than in the design point. This was necessary due to problems in the leak tightness of the transparent windows of the test pump at higher pressure levels. The computed relative velocities in the middle section of the impeller are shown in Fig. 4. A region of small velocities appears at the pressure side of the blades, but no flow separation can be asserted. The flow seems to be regular without any distortions. Figure 4: Computed velocity contours in the middle section of the impeller In order to verify whether the used CFD code is able to predict the flow behavior, a comparison of the velocities between numerical and experimental results should be done. The vectors of the measured mean flow velocity field [5] at half blade height are shown in Fig. 5. For a more precise comparison, the magnitude of velocities at two selected radius curves, at the starting measuring radius and at the middle radius of the measuring region respectively (see Fig. 5), are quantitatively shown in Fig. 6 and Fig. 7, in which a ISSN: Page 73 ISBN:

4 negative value means that the vector direction is in the reverse direction of the main flow. Re-circulation zone Figure 5: Measured velocity vectors at mid section of diffusor For the starting measuring radius (Fig. 6) the differences in magnitude of the velocities between the numerical and experimental results are greater than that at the middle radius. The biggest discrepancy appears at about 70 percent of the relative length from the starting point which is located near the suction side of the diffuser blade. The reason is that the CFD code predicts the onset of the flow separation earlier than that obtained by the experiments. So the magnitude of the velocities obtained by numerical simulation decrease sharply, when the relative length of the measuring position reaches the amount of 0.5. At the radius in the middle of the measurement region (Fig. 7), the agreement between the numerical and the experimental results is much better. For more than 90% of the relative length the measured and the computed velocities are nearly the same. In the second part of this chapter the results of the transient calculation are described. To investigate the time evolution of pressure and velocity in the blade channels three monitor points were defined. All of them are at half blade height. In Fig. 8 the location of the monitor points for the impeller, the diffuser vanes and the return channel vanes are shown. Figure 6: Comparison of velocities between numerical and experimental results at starting radius. Figure 8: Monitor points in all blade channels In Fig. 9 the static pressure and the absolute velocity at the observation points are shown for a complete impeller revolution. The pressure increases from impeller exit to Figure 7: Comparison of velocities between numerical and experimental results at middle radius. Figure 9: Static pressure and absolute velocity at monitor points return blade inlet and the associated decrease in the velocity can also be seen. The fluctuations of pressure and velocity are more distinct in the impeller and the stator channels than in the return channels. The shape of the curves for the pressure and the velocity is affected by a time periodic behavior. The shift in the phases of the ISSN: Page 74 ISBN:

5 curves is a result of the different blade numbers in the impeller and the stator. The frequency spectra of these curves, which were obtained by a FFT analysis, are shown in Fig. 10. They are dominated by the rotor and stator frequency and multiples of it. These frequencies can be calculated from: ω fim = zst = 491,6[Hz] 2π ω fst = zim = 344,16[Hz] 2π These frequencies can be found in Fig. 10 for the pressure and the velocity and in the frequency spectra of all other quantities of this pump stage. Figure 10: Frequency spectra of static pressure and velocity In Fig. 11 the definition of the investigated positions in stream wise (sw) direction is given. in a blade to blade view. Here also the rotating and the stationary frames of reference are indicated. Figure 12: Time distribution of mass flow in blade channels the impeller and stator channel than in the return blade channel. No periodic behavior after 42, 60 time steps is available for the transient mass flow in all blade rows. In the impeller channel the mass flow is lowest when the impeller blade passes the stator blade. The lowest mass flow in the stator channel is reached a little earlier. In Fig. 13 the area averaged static pressure is shown in planes of constant stream wise location. The distributions in the impeller show a periodic behavior with a period of 42 time steps. The averaged static pressure is strongly influenced by the impeller blade, when passing the stator blade. During the passing of the blades a decrease of the pressure appears (time steps 25-30). The highest pressure is found in the case of a complete overlap of the stator channel by the impeller blade. Going downstream through the stator (higher stream wise position numbers) the influence of the impeller blade decreases and vanishes in the return channel blade passage. Figure 13: Time distribution of static pressure in blade channels Figure 11: Definition of investigated positions In Fig.12 the variation of the area averaged mass flow in one blade channel of each blade row is shown as function of time. The fluctuations of the mass flow are higher in Figure 14: Time distribution of velocity in blade channels The influence at the velocity distributions is smaller than at the pressure but anyway noticeable at the impeller blade channel exit and at the stator blade channel inlet, as ISSN: Page 75 ISBN:

6 shown in Fig. 14. Unlike to the pressure curves (Fig. 13) the velocity curves for the impeller and the stator channels are not in phase. They show a nearly opposite behavior in the impeller distribution compared to the distribution of the first locations of the stator. 5 Conclusions One stage of a multistage centrifugal pump including impeller, diffuser and return channel vane is simulated by the commercial RANS code Ansys-CFX. Experiments are also conducted by Laser Doppler Velocimetry (LDV) in part of the diffuser region to measure the mean flow velocity at the middle span plane in order to validate the numerical computations. The comparisons between computation and experimental investigation show that the simulation is able to predict the measured recirculation zone at the pressure side of the diffuser blade, even when the flow in only one blade channel is simulated by steady state method. The computed recirculation is somewhat bigger than that found by the experiments. More measurement points at different blade heights are required to get more accurate results in experiments. To be fairly compared with the transient calculations, the measurements have to be related to the impeller turning angle and averaged for several impeller positions. The investigation of the transient flow field has also been presented in this contribution. Here the focus was mainly addressed to the interaction of the rotor and stator flow field. At certain points in one impeller, stator and return channel vane passage the change in time of the static pressure is shown. The periodic behavior of the flow field can be seen clearly. In the frequency spectra of the pressure distributions the blade passing frequencies depending on the rotational speed and the blade numbers are identified. Here the investigations are limited to the flow field in one blade channel. The interaction of all channels should be investigated at the same time steps. Also the flow in the impeller side chambers should be taken into account for future investigations. The results have to be validated by experimental methods. To do this, additional optical measurements of the transient flow field (PIV, LDV) in this pump stage and measurements of the transient pressure at the blades of all components are planned..nomenclature Arabic letters g m/s 2 gravity constant H m delivery head n min -1 number of revolutions n q min -1 specific speed p bar pressure Q m 3 /s volume flow rate t s time T u - Turbulence degree u m/s circumferential velocity v m/s velocity Greek letters Δ - difference φ deg angle of rotation ρ kg/m 3 density ω s -1 angular velocity Θ deg pitch angle Subscripts abs absolute in inlet out outlet im impeller st stator re return channel t total References: [1] Ritz Pumpenfabrik GmbH & Co. KG, 2004: URL [2] Arndt, N., Acosta, A. J., Brennen, C. E., Caughey, T. K., 1990: Experimental Investigation of Rotor-Stator Interaction in a Centrifugal Pump with Several Vaned Diffusers, Transactions of the ASME Vol. 112 [3] Shi, F., Tsukamoto, H., 2001: Numerical Study of Pressure Fluctuations Caused by Impeller-Diffuser Pump Stage, Journal of Fluids Engineering, Vol. 123 [4] Aysheshim, W., Stoffel, B., 2002: Rotor-Stator- Interaction and Turbulence in a Centrifugal Pump Stage, Proceedings of the XXI st IAHR Symposium on Hydraulic Machinery and Systems, Lausanne, Switzerland [5] Benra, F.-K., Dohmen, H., Nowack, O., 2004: PIV- und LDV-Messungen im beschaufelten Diffusor einer radialen Kreiselpumpenstufe, GALA-Fachtagung, Karlsruhe [6] Menter, F. R., 1994: Two-equation eddy viscosity turbulence models for engineering applications, AIAA 32(8) [7] Pedersen, N., Larsen, P. S., Jacobsen, C. B.. Flow in a Centrifugal Pump Impeller at Design and Off- Design Conditions-Part I: Particle Image Velocity (PIV) and Laser Doppler Velocimetry(LDV)Measurements, Journal of Fluids Engineering, Vol. 125, pp , [8] Combes, J. F., Rieutord, E.. Numerical and Experimental Analysis of the Flow in a Centrifugal Pump at Nominal and Partial Flow Rate, ASME 92-GT- 284, Cologne, Germany, [9] Miner, S. M.; Beaudoin, R. J., Flack, R. D.. Laser Velocimeter Measurements in a Centrifugal Flow Pump, Journal of Turbomachinery, Vol. 111, ISSN: Page 76 ISBN: