Numerical Predictions of Pressure Fluctuations in a Model Pump Turbine with Small Guide Vane Opening based on Partial Averaged Navier Stokes Approach

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1 Jornal of Applied Flid Mechanics Vol. 9 No. 6 pp Available online at ISSN EISSN Nmerical Predictions of Pressre Flctations in a Model Pmp Trbine with Small Gide Vane Opening based on Partial Averaged Navier Stoes Approach J. T. Li 1 Y. L. W and Y. Li 1 Beiing Institte of ontrol Engineering Beiing hina Department of Thermal Engineeering Tsingha University Beiing hina orresponding Athor liintao86@hotmail.com (Received December 0 015; accepted March ) ABSTRAT omparing with conventional hydralic trbine (e.g. Francis trbine) pmp trbine shows significant nstable characteristics becase its design is a compromise between a pmp and a trbine. In present paper nsteady flow and pressre flctations within a model pmp trbine are nmerically stdied throgh Partial Averaged Navier Stoes (PANS) approach. The PANS approach is flfilled throgh modification of RNG -ε trblence model in a commercial FD code. Pmp trbine operating at different conditions with gide vanes opening angle 6 is simlated. Reslts revealed that the predictions of performance and relative pea-to-pea amplitde by PANS approach agree well with the experimental data. Velocity vortex and trblent inetic energy at the inlet of rnner are very large near the pressre srface and the blade leading edge leading to high pressre flctations within the vaneless area otablef pmp trbine. The maximm amplitde of pressre flctation occrs when the pmp trbines rn at rnaway point. The primary dominant freqency of pressre flctation is the rnner blade passing freqency in the vaneless space. The above high pressre flctations shold be avoided dring the design of pmp trbines especially those operating at high-head condition. Keywords: Pmp trbine; Pressre flctation; Partial-Averaged Navier-Stoes; Unsteady flow. NOMENLATURE D1 f fz Hd n n11 p P Q11 Qd t T i U U υ V rnner inlet diameter in pmp mode nresolved-to-total ratios of inetic energy nresolved-to-total ratios of dissipations rated head trblent inetic energy of RANS approach trblent inetic energy of PANS approach rotational speed of the rnner nit speed of the model pmp trbine pressre prodction terms of trblence inetic energy nit discharge of the model pmp trbine rated discharge time trblence time scale nresolved part of instantaneos velocity partially averaged velocity of instantaneos velocity mean component of velocity trblence velocity scale instantaneos velocity x ZS ZG Z coordinates nmber of stay vanes nmber of gide vanes nmber of rnner blades inematic viscosity ε trblent dissipation of RANS approach ε trblent dissipation of PANS approach ρ density μ dynamic viscosity γ relative opening of gide vanes of the pmp trbine LES Large Eddy Simlation PANS Partially-Averaged Navier- Stoes URANS Unsteady Reynolds Averaged Navier-Stoes FFT Fast Forier Transform

2 J. T. Li et al. / JAFM Vol. 9 No. 6 pp INTRODUTION Pmped-storage power plant is one of essential components for the development of renewable energy and the enhancement of electricity spply secrity. Among all the elements of the pmpedstorage power plant pmp trbine is the most important one. Since design of the pmp trbine is a compromise between a pmp and a trbine the performance of pmp trbine always shows significant and nstable characteristics comparing with conventional hydrotrbines (e.g. Francis trbine) with the same specific speed as shown in Fig. 1. If a pmp trbine is operated within the S region (e.g. conditions dring transient process of start-p rnaway and load reection) oscillations nder this operating conditions may case the shift of pmp trbine from trbine mode to the trbine braing mode or even force the nit frther into reverse pmp mode affecting its operational stability (Yamagchi et al. 1984). Fig. 1. haracteristics crves dring operations of pmp trbines. One of the main reasons for the instability of trbine mode of pmp trbine is that the optimm speed of trbine mode is not the same as one of pmp mode. Since the speed of pmp trbine is mainly governed by the pmp mode performance pmp trbine will be operated at off-design conditions in its whole operational domain dring the trbine mode. Therefore a strong instability within pmp trbine will be indced dring operating at off-design conditions. Moreover some nwished phenomena (e.g. strctral vibrations noises and cavitation) also occr at those off-design conditions. Stabli et al. (008) predicted the characteristic of pmp trbine near rnaway and the flow phenomena leading to the instability at small flow rates. Hasmatchi et al. ( ) experimentally and nmerically investigated the hydrodynamics of a model pmp trbine operated at off-design conditions (i.e. 5 and 10 gide vane openings).yan et al. (010 01) nmerically stdied the characteristic crve and the pressre flctation of a model pmp-trbine with 10 gide vane opening. In pmp trbines rotor-stator interaction is sally considered as the sorce of nsteady phenomena and dynamic flctations especially at operation condition with high head (Jng et al. 01 W et al. 013). For example the interaction between impeller blades and gide vanes is one of the main cases of vibrations in pmp trbines. Nicolet et al. (006) modeled the one-dimensional rotor-stator interaction in pmp-trbine. Zobeiri et al. (006) nmerically investigated the rotor-stator interactions of a model pmp trbine in trbine mode for the maximm discharge operating conditions. The rotor-stator interaction can be considered as an interaction between potential and viscos flow and waes. Those phenomena are of interest to improve the design trbine toward better efficiency at off-pea conditions (W et al. 013). For predictions of pressre flctations in hydralic machinery a three-dimensional flow simlation based on the Unsteady Reynolds Averaged Navier- Stoes (URANS) eqations have been well discssed in the literatre (Qian et al. 010 W et al. 011). Specifically for URANS approach in pmp trbines the nstable characteristics and pressre flctations in a pmp trbine have been analyzed throgh sing URANS (Hang et al. 013 Wang et al. 011). Yin et al. (011 01) frther stdied the compressibility of water on the pressre flctations of pmp trbine based on URANS approach. Li et al. (01 013) stdied three-dimensional nsteady and incompressible flows in a pmp trbine dring a transient process of load reection sing URANS approach with the nonlinear trblence model to incorporate the nearwall trblence anisotropy to improve the simlation accracy. Unfortnately the aforementioned URANS approach coldn t captre the flow with all inds of scales. Large Eddy Simlation (LES) cold improve predictions bt is not comptationally economical de to the considerable high cost for engineering problems (e.g. simlations of whole passage of pmp trbine). As an alternative varios hybrid RANS/LES approaches have been proposed. For example a Partially-Averaged Navier-Stoes (PANS) approach which changes seamlessly from RANS to the direct nmerical soltion of the Navier-Stoes eqations was proposed by Girimai et al. ( ). Two variants of the PANS model are derived based on the -ε formlation (Mirzaei et al. 015 Shi et al. 015) and the -ω formlation (Srinivasan et al. 014) respectively. Predictions of PANS have been fond to be better than those of LES in the flow regions sffering from poor near-wall resoltion dring simlations (Lashmipathy et al. 004). Recently Ji et al. (013) stdied the nsteady cavitating trblence flow arond a highly sewed model marine propeller based on the PANS approach. In present paper PANS approach based on the RNG -ε formlation will be employed to simlate the nsteady flow throgh a model pmp trbine operating at conditions with small gide vane opening. Experimental data of the model trbine are employed to validate the predictions (e.g. performance and relative pea-to-pea amplitde) by PANS approach. Unsteady phenomena (e.g. pressre flctations) are also stdied to improve the design of pmp trbine. 66

3 J. T. Li et al. / JAFM Vol. 9 No. 6 pp GOVERNING EQUATIONS For incompressible flow the continity eqation and Reynolds averaged Navier-Stoes eqations are (Germano et al. 199) V i V p U U U U t x x x x x i i i i i p U U Vi V i xi xi x xi xi x (1) () Here V is the instantaneos velocity (sbscript i and indicating components in different directions); U is the partially averaged velocity; t is the time; p is the pressre; < > denotes a constant-preserving arbitrary (implicit or explicit) filter commting with spatial and temporal differentiation; x denotes the coordinates; v is the inematic viscosity. Here Vi is partitioned into two parts: partially averaged velocity (U) nresolved part (i) V U i i i U V. i i (3) (4) In Eqs. (1) and () the additional non-linear term τ(vi V) (i.e. the generalized central second moment) is defined as V V V V V V. i i i (5) In RNG -ε trblence mode the eqations for trblent inetic energy () and trblent dissipation (ε) can be given as follows (Yahot et al. 199) U t x x x U t P (6) t t x x x 1P (7) where t 1 U U i Si x x i with (1 / ) ( S S ) i 1/ i In Eqs. (6) and (7) ρ is the density; U is the mean component of velocity; μ is the dynamic viscosity; P denotes the prodction terms of trblence inetic energy. As shown in Girimai et al. (006) the extent of PANS averaging relative to RANS can be qantified sing the nresolved-to-total ratios of inetic energy (f) and dissipations (f) f f The relationship between P in RNG -ε trblence mode and P in PANS model can obtained throgh eqating the sorce terms sch as 1 ( ) P P f f (9) Then we can obtain PANS model by the modification of RNG -ε trblence model with the following eqations U t x x P x U * 1 (10) t x x x P (11) with f f f * f 1 1 f where f 1.39 (1) (13) (14) onsidering the nonlinear trblence flow in the pmp trbine the shear stress was solved by nonlinear trblence model which was proposed by Ehrhard et al. (1999) U P U iu x UU i i P TSi P T SiS SlSli 3 T S S e i i 1 3 P T i lli 3 3 T S S S 4 e i l li l T S S S T S and P i l l 6 P i l l (15) (16) 663

4 J. T. Li et al. / JAFM Vol. 9 No. 6 pp P min S ; 1 U U i i x x S S i i S i ; ; i i e where exps P P P. In Eq. (16) T is the trblence time scale and is the trblence velocity scale. variants are prescribed. () At the otlet the gradients of all physical variants normal to the bondaries are given. (3) On solid walls of the domain the non-slip flow condition is adopted and near the solid walls the enhanced wall treatment is employed. (4) Zero pressre gradient normal to the srface is employed for all bondaries of the domain except a point corresponding to the reference pressre. 3. GEOMETRY OF PUMP TURBINE In present paper a model pmp trbine with the parameters shown in Table 1 will be investigated. In Table 1. The strctre of pmp trbine is shown in Fig. a. In present paper the relative opening (γ) of gide vanes of the pmp trbine is 6. Fig. b shows the meridian line of the rnner obtained from the hydralic design. The srface formed by the meridian line of the rnner rotating on Z axial is termed as S1 srface. The simlated reslts on the S1 srface will be shown in the following sections. (a) Table 1 Parameters of the model pmp trbine simlated Rated head Hd (m) 60.6 Rated floe rate Qd (m 3 /s ) 0.5 Rotational speed n (rpm) 100 Rnner otlet diameter D1 (m) 0.4 Nmber of rnner blade Z 9 Nmber of stay vanes ZS 0 Nmber of gide vanes ZG 0 The experimental data shown in present paper were acqired throgh the model tests. The pressre flctations at the inlet of case and the otlet of draft tbe were obtained by pressre sensors dring the tests. The head can be calclated based on the pressre difference between the inlet of case and the otlet of draft tbe. The rotation speed of the rnner and the flow rate of the pmp trbine were measred by revoltion speed transdcer and flow measrement device respectively. 3.1 Bondary onditions In present paper the following bondary conditions are employed to investigate the trblent flow in the pmp trbine (1) At the inlet of the flow domain definite vales of all physical (b) Fig.. Geometry profile of the simlated pmp trbine. To satisfy the continity condition correction of velocity magnitde to the otlet distribtion is made based on the difference between the inflow and the otflow dring the simlation (W et al. 011). 3. Simlation of Unsteady Flow at Trbine Mode In this section trblent flow throgh the model pmp trbine at trbine model will be simlated. Fig. shows the whole flow passage of pmp trbine (inclding spiral case stay vanes gide vanes rnner and draft tbe) to be simlated. The SIMPLE algorithm was sed to enforce mass conservation. For the qad/hex grids and complex flows in trbine mode a second-order center difference was employed for the pressre interpolation and a second-order pwind difference was employed for the terms of momentm eqations and terms of two new sets of scalar eqations to improve accracy. The flow was assmed to be converged when the residal error is less than In the PANS Soltion we assmed f=0. and f =1 (Hang et al. 013).The relaxation factor settings 664

5 J. T. Li et al. / JAFM Vol. 9 No. 6 pp were as follows: momentm and pressre term is 0.3; density term is 1; trblent viscos term is 0.8; and a new two scalar relaxation factor is 1. For nsteady simlation the orant nmber was controlled to be below 10. Time step for the rnner rotation were controlled to be 1 rotation of rnner in each time step. The nmber of iterative simlations in each time step is set to be 100. Mesh independency has been investigated and mesh with abot 9 million cells in total was chosen for the simlations. 4. RESULTS AND DISUSSIONS 4.1 Boos and Theses Figre 3 shows the comparisons of performance crve of the model pmp trbine at the trbine mode with 6 opening of the gide vanes between experimental data ( Solid line ) and or predictions ( Open circle ). In Fig. 3 points G1 and G6 correspond to the maximm flow rate point and zero flow rate point respectively. For simlations at each point the rotational speed of rnner was set as a constant and the flow rate was adsted by setting the bondary condition (e.g. velocity) at the inlet of the pmp trbine. With the head of pmp trbine determined the nit speed (n11) and nit discharge (Q11) of the model pmp trbine cold be calclated sing the following formla nd1 Q n11 Q11 H ; D1 H. Based on Fig. 3 it is clear that the predictions agree well with the test data at G1 to G6 operation cases for the trbine mode. been focsed on the pressre flctations at vaneless space especially for small flow rate case (Hasmatchi et al. 011 Yan et al. 010) and even dring the design stage (Jng et al. 01). Becase there exist strong interactions between the rnner and the gide vanes of the pmp trbine the separation flow phenomenon and the rotating stall will happen at small flow rate operating conditions nder the trbine mode. Table Different points for calclations at the gide vanes opening angle 6 No. n11(rpm) Q11(L/s) G G G G G G Fig. 4. Pressre flctations verss time at the operating conditions G1 to G6. Fig. 3. Performance crve of the model pmp trbine. The prediction reslts of performance at G1 to G6 conditions on the gide vanes opening angle are listed in Table. 4. Pressre Flctation in the Vaneless Space In this section the amplitde and dominant freqency of pressre flctation at vaneless space between the rnner and gide vane of the pmp trbine will be investigated. In the literatre some of experimental and nmerical research wors have Figre 4 shows the pressre flctations in the vaneless space at time domain nder the operating conditions G1 to G6. The amplitde of the pressre flctation in the pmp trbine at these points is consistent. Table shows the comparisons between the predicted amplitdes and the experimental data of model test. The amplitde is measred in the time domain from pea to pea vales with 97% reliability. The agreement between predictions and experiments is considerably good. Frthermore both test and calclation have the same trends when pmp trbine is operated from case G1 to case G6. In Table 3 the amplitde of pressre flctations increases from case G1 to case G4. Therefore when pmp trbine starts from the best efficiency case G1 with the increase of the nit speed a significant increase of the amplitde of pressre flctations is observed in vaneless space between rnner and gide vanes. At the rnway (corresponding to zero load) the amplitde of case G4 is maximm. The amplitde gradally 665

6 J. T. Li et al. / JAFM Vol. 9 No. 6 pp decreases from case G4 to case G5 (corresponding to trbine brea case) then to case G6 (corresponding to zero flow rate).the above predicted trend of amplitde is nearly the same as experimental reslts by Hasmatchi et al. (009). (e) G5 (a) G1 (b) G (f) G6 Fig. 5. Pressre flctation on the measred points G1 to G6 at freqency domain (corresponding to (a)-(f)) in the freqency domain. f1 f and f3 indicate the primary secondary and third dominant freqency in the domain and their relationship with the freqency of the rotating rnner (fn). (c) G3 Table 3 omparison of predicted amplitdes of the model pmp trbine with experimental data (A is amplitde). f1 ΔH/H (%) al. Exp. A at 9fn(Pa) A at 18fn(Pa) G G G G G G (d) G4 The pressre flctations data in time domain (e.g. Fig. 4) is transformed into freqency spectrm in freqency domain throgh Fast Forier Transform (FFT) as shown in Fig. 5. The primary dominant freqency of pressre flctation is the rnner blade passing freqency and the secondary dominant freqency is doble of the rnner blade passing freqency. Frthermore the secondary dominant freqency is nearly eqal to gide vane passing freqency. 666

7 J. T. Li et al. / JAFM Vol. 9 No. 6 pp S1 stream srface of rnner at different operation cases. Fig. 9 only shows the trblent inetic energy distribtion at the case G1.As shown in Fig.6 the relative velocity is obviosly higher near the blade sction srface of the rnner blade passages. At the zero flow rate case in Fig. 7f the flow is almost bloced. At the rnway case (Fig.7d) the flow separations occr in the blade passage. The vortex magnitdes increase dramatically from trbine case (Fig. 8b) to trbine brae case (Fig. 8e). The third dominant freqency (4fn in Fig. 6b at case G and Fig. 6d at case G4) in pmp trbine may be cased by the blocage of flow in the blade passage. For example there are some flow blocs at the inlet of for blade passages of rnner at trbine case (Fig. 7b) and most of the blade passages are bloced at the rnway case (Fig. 7d). Fig. 6. Relative velocity distribtions on the S1 stream srface of rnner at different operating conditions G1-G6 (corresponding to (a)-(f) respectively). Fig. 8. Vortices distribtion on the S1 stream srface of rnner at different operating conditions G1-G6 (corresponding to (a)-(f) respectively). Fig. 7. Relative stream lines on the S1 stream srface of rnner at different operating conditions G1-G6 (corresponding to (a)-(f) respectively). Figres 6-8 show the relative velocity distribtions relative stream lines and vortex distribtions on the Fig. 9. Trblent inetic energy distribtions on S1 stream srface at operating condition G1. 667

8 J. T. Li et al. / JAFM Vol. 9 No. 6 pp From Fig. 6 8 and 9 at the inlet of rnner the velocity the vortex and the trblent inetic energy are very large near the pressre srface and leading edge of the blades leading to high pressre flctations on the vaneless spaces of the pmp trbine. Reslts reveal that the pressre flctation only contains rather high-freqency components (e.g. the rnner blade passing freqency and gide vane passing freqency). When the pmp trbine rns at trbine braing mode large vortex can been seen in the passage of the rnner. The stall phenomena will increase the pressre flctation in the vaneless space. 5. ONLUSIONS In order to stdy the pressre flctation of the model pmp trbine at the trbine mode three dimensional nsteady trblent flow simlations have been carried ot sing the PANS approach based on modifications of RNG -ε trblence model nder 6 o opening of the gide vanes. The predicted performance and relative amplitde of pea-to-pea pressre flctations at time domain in the vaneless space of the pmp trbine are both very close to the experimental data. (1) The maximm amplitde of pressre flctation in the vaneless space appears when the pmptrbine rns at rnaway point. The amplitde of pressre flctation increases first then decrease as the flow rate decrease from trbine mode. () The dominate freqency of pressre flctation in the vaneless space is the rnner blade passing freqency and the second dominate freqency is doble of the rnner blade passing freqency. The second dominate freqency is nearly eqal to gide vane passing freqency. (3) The relative velocity of near the blade sction srface of the rnner is considerably higher than one in other areas in rnner. At the rnway case the flow separations occr in the blade passage. The vortex magnitdes increase dramatically from trbine case to trbine brae case. (4) At the inlet of rnner the velocity the vortex and the trblent inetic energy are very large near the pressre srface and leading edge of the blades casing strong pressre flctations within the vaneless space of the pmp trbine which shold be avoided dring the design of pmp trbines especially those operated at high head conditions. AKNOWLEDGMENTS The athors wold lie to than proects spported by National Natral Science Fondation of hina and proect spported by open Research Fnd Program of State ey Laboratory of Hydroscience and Engineering NO. slhse-014-e- 0. REFERENES Ehrhard J. (1999). Research on linear and nonlinear eddy viscosity trblence models for bilding. Ph.D. thesis VDI Düsseldorf Germany. Germano M. (199). Trblence: The Filtering Approach. J. Flid Mech Girimai S R. Srinivasan and E. Jeong (003). PANS trblence models for seamless transition between RANS and LES: fixed point analysis and preliminary reslts. ASME paper FEDSM. Girimai S. (006). Partially-averaged navier stoes model for trblence: a Reynoldsaveraged Navier Stoes to direct nmerical simlation bridging method. ASME J. of Applied Mechanics 73() Hasmatchi V. M. Farhat P. Marzewsi and F. Avellan (009). Experimental investigation of a pmp-trbine at off-design operating conditions. In Proceedings of the 3rd International Meeting of the Worgrop on avitation and Dynamic Problems in Hydralic Machinery and Systems Brno zech Repblic Hasmatchi V. S. Roth F. Botero M. Farhat and F. Avellan (011). Hydrodynamics of a pmptrbine at off-design operating conditions: nmerical simlation. In Proceedings of ASME-JSME-KSME Joint Flids Engineering onference 011 Hamamats Japan Hang H R. F. Xiao W. S. Li and F. J. Wang (013). Analysis of S characteristics and pressre plsations in a pmp-trbine with misaligned gide vanes. ASME J. of Flids Engineering 135/ Ji B. X. W. Lo. Y. L. W X. X. Peng and Y. L. Dan (013). Nmerical analysis of nsteady cavitating trblent flow and shedding horseshoe vortex strctre arond a twisted hydrofoil. International Jornal of Mltiphase Flow Jng A. J. P. Yan and M. Giese (01). Development of a reliable very high-head pmp trbine considering challenging hydrodynamics. IOP onf. Series: Earth and Environmental Science 15. Lashmipathy S. (004). PANS Method for Trblence simlation of high and low Reynolds nmber flow past a circlar cylinder. M. Sc. Thesis Dept. of Aerospace Eng. Texas A. & M. University USA. Li J. T. S. H. Li Y. K. Sn Y. L. W and L. Q. Wang (01). Three dimensional flow simlation of load reection of a prototype pmp-trbine. Engineering with compters Li J. T. S. H. Li Y. K. Sn Y. L. W and L. Q. Wang (013). Three-dimensional flow simlation of transient power interrption process of a prototype pmp-trbine at pmp 668

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