Rotating stall in the vaneless diffuser of a radial flow pump. A. Dazin 1, O. Coutier-Delgosha 1, P. Dupont 2, S. Coudert 3, G. Caignaert 1, G.

Transcription

1 Proceedings of the 8 th International Symposium on Experimental and Computational Aerothermodynamics of Internal Flows Lyon, July 27 Paper reference : ISAIF8-12 Rotating stall in the vaneless diffuser of a radial flow pump. A. Dazin 1, O. Coutier-Delgosha 1, P. Dupont 2, S. Coudert 3, G. Caignaert 1, G. Bois 1 1 Laboratoire de Mécanique de Lille (UMR CNRS 817), ENSAM, 8 Bd Louis XIV, 5934 Lille Cedex, France. antoine.dazin@lille.ensam.fr 2Laboratoire de Mécanique de Lille, Ecole Centrale de Lille. 3Laboratoire de Mécanique de Lille, CNRS. The paper refers to the behavior of a vaneless diffuser of a radial flow pump in partial flow operating conditions. Some experimental data have been obtained using 2D/2C PIV and unsteady pressure measurements within the diffuser, in various operating conditions. The experimental results at the lower flow rate are compared with two-dimensionnal numerical calculations. Keywords: Vaneless diffuser, Radial flow pump, Instability, Particle Image Velocimetry, Pressure measurements, 2D calculations. Nomenclature b Height (m) Greek letters β Blade angle f frequency (Hz) ρ density (kg/m 3 ) N speed of rotation (rpm) ω Angular velocity (rad/s) Q flow rate (m 3 /s) Γ Circulation (m 2 /s). Q d design flow rate Subscripts R Radius (m) 1 impeller inlet Re Reynolds number at the impeller outlet diameter. 2 impeller outlet r Radial coordinate in a frame centered in a vortex. 3 diffuser inlet r Vortex radius 4 diffuser outlet Z Number of blades b blade Imp impeller rs Rotating stall Introduction Rotating stall in the vaneless diffuser of a centrifugal pump or compressor is a low frequency and high amplitude phenomenon which can cause damage and noise. It also affects the performance of the pump or the compressor. The behavior of vaneless diffusers of radial flow pumps, fans and compressors has been widely studied theoretically, experimentally and numerically [1-5]. Tsujimoto et al [6] have used a two-dimensional inviscid and incompressible flow analysis to study the rotating stall of vaneless diffuser. They suggest the existence of a two-dimensional core flow instability at the onset of rotating stall in vaneless diffusers. But, there is still a need for a better knowledge of the complex flow fields that

2 2 Proceedings of the 8 th International Symposium on Experimental and Computational Aerothermodynamics of Internal Flows can be encountered during the development of instabilities such as rotating stall. The development of PIV allows for such a better understanding [7]. Levjar et al [8] have conducted numerical calculations using a two dimensional viscous incompressible flow model to decide if 2D instabilities in the diffuser can contribute to rotating stall. They have compared [9] their results to already published [1-11] PIV measurements performed in the vaneless diffuser of a centrifugal pump. In order to make better comparison between experiments and calculations and to improve the knowledge of the flow, experiments, associating PIV and unsteady pressure measurements, have been conducted on the same test-rig. Some preliminary analyses of these experiments [12] have allowed identifying zones of well established rotating stall. It has also been established that these zones are separated with transition zones for which several modes exist intermittently. The experimental set-up, as well as some pressure measurements results are reminded here. For the lower flow rate, PIV measurements are analyzed to characterize more accurately the instability phenomenon. The experimental results at this flow rate are also compared with two-dimensional numerical simulations. Experimental results Experimental set-up The tests refer to the so-called SHF impeller matched with a vaneless diffuser. They have been made in air, on a test rig (Fig. 1) well adapted for studies on interactions between impeller and diffuser, as there is no volute downstream of the diffuser. The test rig is also well adapted for the use of optical method and especially Particle Image Velocimetry (PIV). It has been used for several studies with the same impeller: - Studies with a short vaneless diffuser [1-11] - Studies with two different vaned diffusers [13] 1 Suction (air + particles) CCD Caméras Impeller shroud Vaneless diffuser YAG Laser microphones Free air Acquisition system DIFA-SCADAS Fig. 1 : Experimental test-rig. Table 1 Pump characteristics Impeller characteristics Outlet radius R mm Tip inlet radiusr R mm Number of blades Z 7 Exit blade height b mm Outlet blade angle measured β from the peripheral direction Nominal speed of rotation N 25 rpm speed Design flow rate Q d mm Reynolds number Re Diffuser characteristics Inlet Radius R mm Oultet Radius R 4 39 mm Constant height b 4 mm The present study refers to new experiments combining pressure measurements and 2D/2C PIV at partial

3 Antoine DAZIN et al. Rotating stall in the vaneless diffuser of a radial flow 3 flow rates within a new vaneless diffuser with a larger outlet radius, in order to obtain conditions with well established rotating stall. The main characteristics of the so called SHF pump impeller used for tests in air are presented in table 1: A first measurement campaign has been made using pressure transducers on the shroud diffuser wall, for 15 flow rates between.26 Q d and.95 Q d and for two impeller speeds of rotation (12 and 18 rpm). A second campaign associating pressure and PIV measurements has been performed for six flow rates (.26,.46,.55,.65,.74,.9Q d ) at 171 rpm. a Free air c Four Brüel & Kjaer condenser microphones (Type 4135) are used for the unsteady pressure measurements. They are flush mounted at two different radii (R = 27 mm and 37 mm) and two different angular positions (angular difference of 75 between the transducers) on the shroud side of the diffuser wall. The data are acquired by a LMS Difa-Scadas system. During the first campaign, average crosspower and autopower spectra have been directly measured. During the second campaign, time acquisitions of the unsteady pressure signals were realized. In both cases the sampling frequency was 248 Hz. 16 free air b Y (mm) 1 8 diffuser impeller 5 1 X (mm) Fig. 2 : particle images from the two cameras and a reconstructed velocity map. During PIV experiments, the laser sheet is generated by a Quantel CFR2 ND:YAG Laser (1 mj/pulse) at mid-height of the vaneless diffuser. P.I.V. snapshots have been simultaneously recorded by two identical cameras (Kodak Flowmaster x 124 pxl2) positioned side by side (two simultaneous snapshots can be seen in Fig 2a and b.). A home made software developed by the Laboratoire de Mécanique de Lille has been used for the images treatment (cross-correlation was used with a correlation window size of 32 * 32 pixels2 and an overlapping of 5%. Correlation peaks were fitted with a three points Gaussian model). Then the data obtained with the

4 4 Proceedings of the 8 th International Symposium on Experimental and Computational Aerothermodynamics of Internal Flows two cameras have been elaborated with a dedicated post processing technique in order to build a single domain (an example of reconstructed velocity map is presented in Fig 2c). The results consist in fields of 113 x 177 mm2 and 74 x 121 velocity vectors with a temporal resolution of 4 velocity maps per second and one velocity map every 7 impeller rotations. For each flow rate, thirteen acquisitions of 8 velocity maps have been realised. The PIV system sends a signal to the LMS Difa-Scadas acquisition system in order to synchronize the pressure measurements with the velocity maps. Pressure measurements The analysis of the crosspower spectra of two pressure transducers located at the same radius but at two different angular positions enables the detection of the rotating stall phenomenon [14-15] and gives its characteristics (number of cells and velocity). Fig. 3 summarizes the results of the first experimental campaign. The results are presented for the two speeds of rotation. The static pressure coefficient ψ ( P ψ = ρr2ω 2 imp ) of the whole pump is plotted as a function of the flow rate to design flow rate ratio. If rotating stall occurs, its number of cells and the stall speed of rotation to impeller speed of rotation ratio are also indicated on the figure. black : 2 Hz gray : 3 Hz.6 solid : pressure coefficient dashed : rotating stall speed ψ.3.2 s / imp ω ω.2 3cells 2cells 4cells.1 transition transition no rotating stall Q/Q d Fig. 3 :Pump performance and rotating stall zones for the two rotation speed : 2 Hz = 12 rpm and 3 Hz = 18 rpm. Depending on the flow rate, several behaviors of the flow in the diffuser can be identified: - For Q/Q d >.78, there is no rotating stall. - For Q/Q d <.78 various rotating stall conditions occur: For.26 < Q/Q d <.36, there are three cells and a rotation speed of the phenomenon about.28 ω imp. For.54 < Q/Q d <.58, there are two cells and a rotation speed of the phenomenon about.27 ω imp.

5 Antoine DAZIN et al. Rotating stall in the vaneless diffuser of a radial flow 5 For.68 < Q/Q d <.78, there are four cells and a rotation speed of the phenomenon about.18 ω imp. Between the zones where rotating stall occurs, there are transition zones. In these zones, several types of rotating stall exist intermittently, as shown in [12]. Two amplitude spectra are presented in Fig 4. Amplitudes of the crosspower spectra of two pressure transducers located at the same radius, scaled by ρr2ω imp are drawn as a function of the frequencies scaled by the impeller rotation 2 frequency. a Non dimensionnal crosspower spectrum Q/Q d =.26:2and3Hz f rs 2f rs 2f rs -f 1 AMPLITUDE f b 2Hz 3Hz 1-5 f rs -f 1 f rs +f 1 f b -f rs f b +f rs f ψ f/f imp b Non dimensionnal crosspower spectrum Q/Q d =.9:2and3Hz AMPLITUDE 2Hz 3Hz ψ f/ f imp Fig. 4 : Average crosspower spectra for 3 flow rates and two rotation speed (2 Hz = 12 rpm and 3 Hz = 18 rpm). (a).26 Q d : rotating stall zone. (b).9 Q d : no rotating stall zone. When no rotating stall occurs (Fig. 4b), the spectrum is dominated by a single peak at the non-dimensional frequency f/fimp = 7, that is the impeller blade passing frequency. On the contrary, at flow rates where rotating stall occurs (Fig. 4a), the dominant peak is at a low frequency frs (f/fimp =.83 in Fig. 4a) whose value corresponds to the product of the rotating stall speed by its number of cells. Other peaks are combination of this low frequency and the impeller blade passing frequency. Results presented in Fig. 3 and 4 are also very similar for the two speeds of rotation and it can be said that the phenomena follows a Reynolds similarity law. PIV measurements The low frequency, high amplitude pressure fluctuations shown in the previous paragraph are associated with the passage of rotating cells in front of the pressure

6 6 Proceedings of the 8 th International Symposium on Experimental and Computational Aerothermodynamics of Internal Flows transducers. The PIV results are used to characterize these cells at the lower flow rate (.26 Q d ). In order to evidence the rotating structures at this flow rate on the PIV results, an average map, coming from 24 instantaneous flow fields has been constructed and subtracted a Y 18 b Y 18 from these flow fields. Two velocity maps obtained with this method are presented Fig. 5. Fig 5a show the flow observed in a rotating cell, and Fig 5b outside a rotating cell Free air Vortex rotation direction Impeller rotation direction 5 1 X Impeller 5 1 Fig. 5: Velocity maps at.26 Q d. (a) in a rotating cell. (b) outside a rotating cell. X The rotating cells are clearly characterized (Fig 5a.), as already shown by Ljevar [16] by a vortex whose vorticity is of opposite sign with the impeller rotation direction. Numerical simulations Numerical model The simulations are based on the Reynolds Averaged Navier-Stokes (RANS) equations. The flow is considered as two-dimensional, so no influence of the diffuser height is taken into account in the present calculations. The finite volume method is applied for the space discretization, while an unconditionally stable, second order implicit scheme is applied for time discretization. The numerical resolution is based on the pressure-correction method proposed by Patankar [17]. The computational domain is based on a curvilinear orthogonal grid, composed of cells. So, velocity components u and v in the simulations denote the tangential velocity and the radial velocity, respectively. No contraction or stretching of the grid is applied, since no wall is considered in the simulations. The classical boundary conditions for incompressible flows are applied: imposed inlet velocity, and fixed outlet pressure. The inlet velocity distribution is based on the results of the PIV measurements at the diffuser inlet. The side by side position of the two cameras in the experiments enables to calculate the time-averaged velocity profile for a distance in the azimuthal direction equal to nearly one blade to blade passage. Then the profile is interpolated to obtain the profile in a complete blade-to blade passage, and repeated seven times to get the boundary condition in the whole diffuser inlet (figure 6). Calculations are based on non-dimensional variables, so velocity components u/u ref and v/u ref are considered in the simulations, with U ref the runner outlet velocity. The inlet velocity profile applied for the present simulation corresponds to the mass flow rate Q/Qd =.26.

7 Antoine DAZIN et al. Rotating stall in the vaneless diffuser of a radial flow 7 However, the integration of the time-averaged radial inlet velocity component over the diffuser inlet surface leads to a significant over-estimation of this mass flow rate. This is mainly due to the fact that the mid-height experimental profile has been selected to apply the boundary conditions, in order to avoid the effects of the diffuser walls. Consequently, low speed areas of the boundary layers are not taken into account, which explains the flow rate over-estimation. Thus, two calculations have been performed: in calculation 1, the velocity component v has been corrected so that the mass flow rate Q/Qd is respected. Conversely in calculation 2 no correction has been applied, so the mass flow rate is notably over-estimated, but the velocity angle at the diffuser inlet is consistent with the experiments. To simulate the rotation of the runner in the diffuser frame, the inlet boundary conditions rotate at speed N. This condition is applied by shifting the position of the inlet velocity profile at each time step: the advance is equal in the present simulations to 1 cell per time-step. It implies that the time step Δt is adjusted so that 812 Δt corresponds to the rotation duration of the runner. A non-dimensional time Δt/T ref is used in the calculations, with T ref = L ref /U ref where L ref denotes the diffuser diameter. The simulations are performed during 75 T ref, i.e. about 24 runner rotations, which is sufficient in the present case to characterize the rotating stall and calculate its frequency. The Reynolds number based on L ref and U ref is equal to 1576, so the k-epsilon RNG turbulence model [18] is applied in the simulations. (figure 7). However, this periodical flow pattern progressively destabilises, and it finally leads to a rotating stall phenomenon characterized by three nearly identical cells (figures 8, 9). Fig. 7: distribution of V / U ref before the flow destabilizes (calculation 1, t/ T ref = 3) u/uref 1 v/uref theta (deg) Fig. 6: Time-averaged velocity profile at the diffuser inlet (boundary condition for the simulation) Results During about half the calculation, the flow in the diffuser remains nearly periodical, with period 2π/7 corresponding to the number of runner blades. Only the seven identical wakes of the blades can be seen in the results Fig. 8: distribution of V / U ref in the case of a rotating stall (calculation 1, t/ T ref = 75) Both calculations 1 and 2 lead to this result, which is consistent with the experiments, as can be seen in figure

8 8 Proceedings of the 8 th International Symposium on Experimental and Computational Aerothermodynamics of Internal Flows 3. Conversely, the rotation speed of the cells depends on the simulation: in calculation 1, ω rs /ω imp =.285, which is very close to the experimental value (ω rs /ω imp =.28, see figure 3), whereas in calculation 2, a slightly lower value ω rs /ω imp =.26 is obtained. This result matches the experimental tendency, which exhibits a progressive decrease of the rotating stall frequency when the mass flow rate is increased. The evolution of the rotating stall at frequency ω rs is investigated in more details in figure 1. The distribution of the non-dimensional vorticity is drawn at height successive times, in order to show the evolution of the three rotating cells. The time interval between sequence (a) and sequence (h) is close to the period of the runner. Although the wakes of the blades is still observable close to the diffuser inlet, most of the flow is governed by the evolution of the three periodical vortices. Each vortex is created close to the diffuser inlet, and then it rotates in the diffuser, while it is convected downstream. As it reaches the diffuser outlet, a second vortex is created, which replaces the previous one calculation 1 calculation 2.15 v / U ref t / T ref Fig. 9: Time evolution of v/uref at the diffuser outlet (a) (b) (c) (d) (e) (f) (g) (h) Fig. 1: Evolution of the non-dimensional vorticity for 65.7< t/t ref < 68.5 (About one rotation of the runner)

9 Antoine DAZIN et al. Rotating stall in the vaneless diffuser of a radial flow 9 In order to characterize these vortices and compare them to the ones observed in the experimental results, their tangential velocity distribution is fitted, in both experimental and numerical results, with an Oseen vortex profile. For this kind of vortices, the tangential velocity profiles, in a cylindrical frame centered on the vortex centre, is given by [19] v Γ = 1 e 2πr 2 r 1 r θ. The values of the vortex circulation Γ and radius r are adjusted by the least square method. The average non-dimensional value (r /L ref ) of the vortex radius is very similar in calculation 1 (r /L ref =.9) and in the PIV results (r /L ref =.95). On the other side, the vortices observed in the experimental results are stronger (Γ /(L ref.u ref ) =.38) than the ones observed in the calculation (Γ /(L ref.u ref ) =.112). This difference is attributed : - First, to the 2D hypothesis which ignore some phenomena, (like the boundary layer separation on the walls) which could give energy to the vortices created by the instability. - Second, to the damping effect of the turbulence model. Conclusion. Some experiments and numerical calculations on the rotating stall of the vaneless diffuser of a radial flow pump have been presented. The experiments have associated unsteady pressure measurements to 2D/2C PIV measurements. 2D numerical simulations have also been conducted. The analysis of the pressure fluctuations at several partial flow rates has evidenced several zones of rotating stall with different number of cells and rotation speeds. The pressure fluctuations are induced by vortical cells which are observed in both PIV and numerical results for the lower flow rate. The characteristics of these cells (rotation speed, number of cells and vortex radius) are comparable in experimental and numerical results, especially when the radial velocity v is corrected to respect the mass flow rate. On the other side, the simulation underestimates the circulation of the rotating cells, that is the intensity of the phenomenon. This means that the 2D hypothesis is right to study the onset of rotating stall but not to describe completely the phenomenon. The analysis presented in this paper have to be carried on, and especially extended to the other flow rates for which PIV results are available. Besides, as the low sampling rate of standard PIV is not satisfying to study such an unsteady phenomenon, and as at the lower flow rates, the flow is strongly three-dimensional new experiments using time resolved (1 KHz) stereo-piv are planned on this test-rig. Acknowledgements The numerical model IZ was initially developed for the CNES (French Space Agency) in the LEGI laboratory (Grenoble, France) with successive contributions of Y. Delannoy, J-L. Reboud, and co-workers. References. [1] Jansen. W., Rotating stall in a radial vaneless diffuser, ASME Journal of Basic Engineering, (1946) [2] Senoo Y., Kinoshita Y., Ishida M., Asymmetric flow in vaneless diffusers of centrifugal blowers. ASME Journal of Fluids Enginnering 99 (1) : (1977) [3] Nishida H., Kobayashi. H., Takagi T., and Fukoshima Y. A study on the rotating stall of centrifugal compressors (1st Report, Effect of vaneless diffuser width on rotating stall). Transactions of the Japan Society of Mechanical Engineers (B Edition) 54(499): (1988) [4] Kobayashi H., Nishida H., Takagi T., and Fukoshima Y. A study on the rotating stall of centrifugal compressors (2nd Report, Effect of vaneless diffuser inlet shape on rotating stall). Transactions of the Japan Society of Mechanical Engineers (B Edition) 56(529): (199) [5] Ferrara G., Ferrari L. Baldassarre L. Rotating Stall in Centrifugal Compressor Vaneless Diffuser: Experimental Analysis of Geometrical Parameters Influence on Phenomenon Evolution International Journal of Rotating Machinery, 1(6): , (24) [6] Tsujimoto Y, Yoshida Y., Mori Y., Study of vaneless diffuser rotating stall based on two dimensionnal inviscid flow analysis. ASME Journal of Fluids engineering, 118 : (1996). [7] Hayashi N., Koyama M., Ariga I, Study of Flow Patterns in Vaneless Diffusers of a Centrifugal Compressors using PIV. 11th International Symposium - Application of Laser Techniques to Fluid Mechanics. Lisbon. Portugal (2)

10 1 Proceedings of the 8 th International Symposium on Experimental and Computational Aerothermodynamics of Internal Flows [8] Ljevar S., de Lange H. C., and van Steenhoven A. A., Two-Dimensional Rotating Stall Analysis in a Wide Vaneless Diffuser, International Journal of Rotating Machinery, vol. 26, Article ID 5642, 11 pages, 26. [9] Llevar S., de Lange H.C., van Steenhoven A.A, Dupont P, Caignaert G., Bois G., Core flow instability in wide vaneless diffusers on behalf of rotating stall investigation. The 13th international Conference on Fluid Flow technologies. Budapest, Hungary, September 26 [1] Wuibaut G., Dupont P., Bois G., Caignaert. G., Stanislas M., Analysis of flow velocities within the impeller and the vaneless diffuser of a radial flow pump, ImechE Journal of Power and Energy, part A, 215, p (21) [11] Wuibaut G., Dupont P., Bois G., Caignaert. G., Stanislas M., PIV Measurements in the impeller and the vaneless diffuser of a radial flow pump in design and off design operating conditions. ASME Journal of Fluids Engineering,, vol 124, p (22) [12] Dazin A., Coudert S, Dupont P., Caignaert G., Bois G., Ljevar S, de Lange H.C. Rotating stall in the vaneless diffuser of a radial flow pump, 7 th European Conference on Turbomachinery, Athens, March 27. [13] Wuibaut G., Bois G, Dupont P., Caignaert. G., «Rotor stator interactions in a vaned diffuser of a radial flow pump for different flow rates using PIV measurement technique», 9th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, ISROMAC 9, 1-14 Février 22, Hawaii, USA, paper FD-ABS-18. [14] Suzuki, Ugai, Harada, Noise Characteristics in partial discharge of a centrifugal fan. Bull. JSME, vol , (1978) [15] G. Caignaert, B. Desmet, D. Stevenaert, Experimental investigations on the flow in the impeller of a centrifugal fan. ASME Paper B2-GT-37. (1982) [16] Ljevar S. Rotating stall in wide vaneless diffusers. Ph D. Thesis. Eindhoven University of Technology. (27) [17] S.V. Patankar Numerical heat transfer and fluid flow. Hemisphere Publishing Corporation (1981). [18] S.A. Orszag, Renormalization Group Modelling and Turbulence Simulations, Near Wall Turbulent flows. Elsevier Science Publishers B.V., Amsterdam, The Netherlands (1993). [19] P.G. Saffman. Vortex Dynamics.Cambridge University Press (1992).