CFD simulation of pressure and discharge surge in Francis turbine at off-design conditions

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1 IOP Conference Series: Earth and Environmental Science CFD simulation of pressure and discharge surge in Francis turbine at off-design conditions To cite this article: D Chirkov et al 01 IOP Conf. Ser.: Earth Environ. Sci View the article online for updates and enhancements. Related content - Numerical simulation of full load surge in Francis turbines based on threedimensional cavitating flow model D Chirkov, L Panov, S Cherny et al. - 3D numerical simulation of transient processes in hydraulic turbines S Cherny, D Chirkov, D Bannikov et al. - Transient two-phase CFD simulation of overload pressure pulsation in a prototype sized Francis turbine considering the waterway dynamics P Mössinger, P Conrad and A Jung Recent citations - Fatigue life estimation of Francis turbines based on experimental strain measurements: Review of the actual data and future trends Alexandre Presas et al - Suppression of unsteady swirl flow in the draft tube of a Francis hydro turbine model using J-Groove Zhenmu Chen et al - Experimental Hydro-Mechanical Characterization of Full Load Pressure Surge in Francis Turbines A Müller et al This content was downloaded from IP address on 30/01/019 at 0:4

2 6th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science 15 (01) doi: / /15/3/03038 CFD simulation of pressure and discharge surge in Francis turbine at off-design conditions D Chirkov 1, A Avdyushenko 1, L Panov 1, D Bannikov 1, S Cherny 1, V Skorospelov and I Pylev 3 1 Institute of Computational Technologies SB RAS, Novosibirsk, Russia Institute of Mathematics SB RAS, Novosibirsk, Russia 3 Branch LMZ OJSC «Power Machines», Hydraulic Machine Division, St-Petersburg, Russia chirkov@ict.nsc.ru Abstract. A hybrid 1D-3D CFD model is developed for the numerical simulation of pressure and discharge surge in hydraulic power plants. The most essential part the turbine itself is simulated directly using 3D unsteady equations of turbulent motion of fluid-vapor mixture, while the rest of the hydraulic system is simulated in frames of 1D hydro-acoustic model. Thus the model accounts for the main factors responsible for excitation and propagation of pressure and discharge waves in hydraulic power plant. Boundary conditions at penstock inlet and draft tube outlet are discussed in detail. Then simulations of dynamic behavior at part load and full load operating points are performed. It is shown that the numerical model is able to capture self-excited oscillations in full load conditions. The influence of penstock length and flow structure behind the runner are investigated. The presented approach seems to be a promising tool for prediction and investigation the dynamic behavior in hydraulic power plants. 1. Introduction Operation of hydraulic turbines in some off-design conditions exhibit, alone with local pressure pulsations, caused by rotor-stator interaction and draft tube vortex precession, also synchronous pulsations, that propagate along the whole water conduit. This behavior is typical for a wide range of off-design operating points, such as part load and full load [1]. Part load surge is forced by the rotation of helical vortex in an elbow draft tube. In full load the surge is excited by straight vortex with variable cavity volume. The resulting fluctuations of pressure and discharge propagate upstream the turbine, rousing penstock response, which can damp or increase the amplitude of turbine pulsations. The state-of-the-art approach for investigation the dynamic behavior of hydraulic circuits is based on 1D hydro-acoustic models [-6]. In case of hydraulic power plants all the elements of the circuit, including the turbine, are substituted by their 1D representations. The effect of cavitation is modeled by two lumped parameters, the cavitation compliance C = Vc / H and mass flow gain factor χ = Vc / Q [3]. These parameters are identified either from experiment [-3], or from steady state CFD computations (single phase or two phase), as in [3-4,6]. Time domain simulations require numerical solution of the set of ordinary differential equations. This approach it is fast, allowing Published under licence by Ltd 1

3 6th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science 15 (01) doi: / /15/3/03038 parametric studies. Stability analysis, based on eigenvalues of the system, is also available [9]. The shortcomings of 1D approach are evident: there is uncertainty in definition of some of the parameters, e.g., of mass flow gain factor [7]; in general the parameters depend on the operating point, and the determination of this dependency requires series of steady state CFD computations [3]; 1D approach gives no insight into complex 3D flow features of the process. Therefore it is desirable to develop a more general, namely 3D model, able to predict not only local, but also synchronous pulsations in water system. One step towards this was done in [7], where transient cavitiating flow in axially symmetric draft tube was simulated by means of -phase CFD. The present work suggests the hybrid 1D-3D CFD model of surge. The approach originates from that, suggested previously by the authors for simulation of transient processes [8]. In [8] the model was based on a coupled solution of 1D acoustics in the penstock and 3D URANS solution of single phase incompressible flow within the turbine. That approach has been successfully applied for simulation of runaway, power regulation and load rejection transients. In present work the original method of [8] is further developed by implementing two-phase cavitating flow model for the turbine domain, in order to simulate the mechanism of self-excited fluctuations of gaseous volume in the vortex core. Two-phase fluid flow equations are solved by strongly coupled artificial compressibility method, similar to that suggested in [9]. Boundary conditions at penstock inlet and draft tube outlet, as well as at penstock-turbine interface are discussed in detail. As an example application of the developed numerical model simulations of two off-design operating points are presented. The influence of vapor phase is analyzed for part-load vortex rope calculations. However the emphasis done to simulation of self-excited oscillations in full load operating point. Computations are carried out for Francis turbines with specific speed n s =40 (prototype head H=73m) and n s =170 (prototype head H=00m, model head H=1m).. Governing equations The whole water system of hydro power plant is divided in two parts, figure 1. First is a pipe line, where wave propagation is simulated using 1D hydro-acoustic equations. The second part is the turbine itself, where the flow-field is governed by unsteady 3D two-phase equations. The solution in both parts is found simultaneously. It should be noted that in present model the spiral case is omitted for simplicity and represented by its energy loss. The generalization to include spiral case in computational domain is straightforward. Figure 1 Schematic hydraulic power plant..1. Penstock domain In present study a simplified pipe line consisting of a single penstock of length l p and constant cross section S p is considered, see Fig 1. Elastic water hammer propagation in this penstock is described by the following one-dimensional hyperbolic system:

4 6th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science 15 (01) doi: / /15/3/03038 m a Q + = 0 t gsp x Q m + gs p = 0 t x where m= p/( ρlg) z is a piezometric head, Q is a discharge, a is a pipe wave speed. Friction loss and viscoelastic effect, caused by energy dissipation during the pipe wall deflection, are both neglected for simplicity... Turbine domain The cavitating flow-field inside the turbine is described as isothermal compressible liquid vapor mixture, where distribution of liquid volume fraction α L is described by transport equation with source terms, responsible for evaporation and condensation: (1) ρ + div( ρv ) = 0, () t ρv + div( ρv v) + pˆ = div( τ) + ρf, (3) t α L t div( α Lv ) = ( m + m ). (4) ρ L here ρ = α LρL + (1 α L) ρv is the mixture density, v is the velocity vector, pˆ = p+ ρk, p is the 3 static pressure; k is the turbulence kinetic energy. Absolute reference frame is used for static elements, while rotating reference frame is used for the runner, rotating with angular velocity ω around the Oz axis, directed downwards. Thus for runner sub-domain f = ( x1ω + uω, xω u1ω, g). Either standard or Kim-Chen k-ε turbulence model with log-law wall function near the solid walls is used to close the mean flow equations ()-(4). Evaporation (m ) and condensation (m + ) terms are evaluated using Singhal et. al. model [10]. m + C max[ p p,0] 1 = t ( ρlu /) ( α ) prod V L L [ ] ρ Cdest min 0, p pv ρlα L, m =. ρ t ρ U V ( L ) standard model constants С prod = 80, C dest = 1 are used. Characteristic time is taken t D /( U ) = 1, while characteristic velocity U = Q/ D1. Preliminary studies showed that the results do not depend significantly on the model, see also figure. 3. Numerical method Two-phase fluid flow equations ()-(4) are solved numerically using artificial compressibility method [11-1], based on approaches and experience of [13]. Dual time stepping is used for unsteady calculations. In pseudotime equations are marched using implicit finite volume scheme. Third order accurate MUSCL scheme is used for discretisation of convective terms, while nd order central difference scheme is used for viscous terms. Second order backward scheme is applied for physical time derivatives. Linearized system of discrete equations is solved using LU-SGS iterations [13]. All equations ()-(4) are solved in terms of (p,v,α L ) in a coupled manner, as suggested in [9]. For more details reader is referred to [11] and [1]. 3

5 6th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science 15 (01) doi: / /15/3/03038 Periodic stage approach is used for the turbine flow analysis, requiring computations only in one wicket gate (WG) channel, one runner channel, and the whole draft tube (DT). Water hammer equations (1) are solved using 1st order implicit finite difference scheme. Equations (1) and ()-(4) are iterated in pseudotime simultaneously until convergence. Interface boundary condition between penstock and turbine is described in the following section. 4. Implementation of boundary conditions 4.1. Penstock inlet boundary Total specific energy is fixed at the inlet of the penstock (head loss in penstock is neglected) Q E m+ = E + H = const. (5) 1 gs p in, pipe Evaluation of specific energy E at draft tube outlet is described in the following section. 4.. Draft tube outlet boundary Total specific energy E at draft tube outlet is obtained from a given Thoma number σ and net head H according to IEC standard. Let us assume that Oz axis is directed downwards and level z = 0 correspond to upper ring of wicket gate (figure 1). At that standard definition of σ is NPSH σ =, H p p v NPSH z z = abs, V + + ( r ρlg g ), v Q =, (6) S where p abs, is the average absolute pressure in draft tube outlet section S, z r is the reference level. Let us define the total specific hydraulic energy at the draft tube outlet as pabs, v E = z ρ g + g. (7) From (6) one can obtain L p = +. (8) V E σ H zr ρlg therefore for a given σ and head H the value of E is known and remains fixed. Note that neither discharge Q nor pressure p abs, is known a priory. So, during the numerical solution of the problem, energy E is fixed to (8). Velocity field is extrapolated from outside the computational domain Internal interface penstock wicket gate During the iterative solution of hydro-acoustic and two-phase equations flow parameters are exchanged through artificial penstock wicket gate interface. Namely, discharge Q obtained at the end of the penstock, together with flow angle δ sp is given as an inlet boundary condition for wicket gate computational domain. The pressure is transferred from wicket gate inlet to penstock outlet, taking into account energy loss Δh sp in the omitted spiral case. The link between wicket gate inlet pressure (p WG,in ) and penstock outlet pressure (p p,out ) is pp, out pwg, in Q 1 1 = + +Δh ρlg ρlg g sin δsp SWG, in S p sp. 5. Validation and steady state applications 4

6 6th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science 15 (01) doi: / /15/3/03038 Figure shows steady-state capabilities of the presented model in predicting turbine cavitation curve. The underlying physics seems to be rather conservative to the choice of a particular cavitation model. Figure 3 demonstrates the applicability of the stage approach to turbine hill-chart computation. 6. Simulation of part-load pulsations The analysis of part load surge is done for ns=40 turbine in prototype scale. Penstock length is 109 m, the wave speed a is taken 100 m/s. Relatively coarse structured mesh consisted of 17k cells for the wicket gate channel, 14k cells for the runner channel, and 80 k cells for the draft tube is used for the computations. Time step Δ t is taken 1/4 of the period of runner rotation. Preliminary tests showed that this value of Δ t is enough for obtaining time-step independent results. Figure. Prediction of cavitation curve for ns=40 turbine. Different cavitation models. Figure 3. Prediction of discharge in the whole operating range for ns=170 turbine. Figure 4 shows discharge and pressure fluctuations in different points of the turbine (wicket gate and draft tube cone, points T4 and T5 are 90 shifted) for single phase penstock-turbine computation. It can be seen that vortex precession rouses power and discharge surge of the same frequency. Figures 5-7 show the influence of cavitation for the case of single turbine computations. In both cases the frequency of vortex precession agrees well with the experimental data. However in twophase computations the amplitude of pulsations is almost times smaller. The reason can be insufficient grid resolution. The amplitude of pulsations in WG is just 3 times smaller than in the draft tube. Figure 4. Part-load pressure and discharge surge. 5

7 6th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science 15 (01) doi: / /15/3/03038 Figure 5. Pressure pulsations in the draft tube. Figure 6. Spectrum of pressure pulsations. c a b Figure 7. Part-load vortex rope for ns=40 turbine. (a) isosurface of pressure in 1-phase computations, isosurface α L =0.5 for -phase (b), and experiment (c). 7. Simulation of full-load pulsations The analysis of full load pulsations is done for ns=170 turbine. Simulations were carried out in model scale, D 1 =0.46m, H=1m. Since it is not possible to simulate the hydraulic circuit of the test rig, the penstock parameters were artificially set to l p =100m, wave speed a=500m/s. The Thoma number is taken σ = 0.07 to guarantee the presence of vapor phase in the draft tube. Computational mesh has 4k cells for the wicket gate channel, 4k cells for the runner channel, and 87 k cells for the draft tube. Time step Δ t corresponded 1/4 of the period of runner rotation. Previous experimental and numerical investigations showed that the flow at full load is almost axisymmetric. Thus currently exploited periodic stage approach, involving circumferential averaging in runner-draft tube interface, is a very good approximation. It should be noted that unsteady single phase computations give a steady state flow-field. Unsteady two-phase simulations are set up from the steady state two-phase solution. Figure 8 shows that cavity volume immediately starts to oscillate with increasing amplitude. Pressures in different points of the turbine start to oscillate accordingly. After approximately 1 second the fluctuations get into a limiting non-sinusoidal free-oscillations with frequency f=3.63hz=0.315f n. It is remarkable that pressure pulsations are of the same phase indicating the synchronous nature of the surge. The amplitude of pressure pulsations in wicket gate is larger than that in the draft tube. Relative peak-to-peak variation of pressure is about is about 8% of the net head for these artificial conditions. The influence of penstock length is analyzed in figure 9. It can be seen that longer penstock gives smaller pulsations. As expected, the frequency of oscillations reduces slightly for a longer penstock. 6

8 6th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science 15 (01) doi: / /15/3/03038 Figure 8. Self-excitation of pressure pulsations in full load. Figure 9. Influence of penstock length. Figure 10. Velocity profiles at runner outlet (line AB) in moments t 1 and t (see figure 8). Figure 11. Mass conservation check for full load simulation with Δ t = 1/(4 f n ). 8. Discussion Numerical experiments show that part load pulsations are well captured in single phase incompressible computations. Even more, the account of vapor phase reduces the amplitude of local pulsations. As expected, the account of vapor phase dynamics is crucial for capturing full load surge. In previous -dimensional axisymmetric study of Dörfler et al [7] strong dependency of predictions on numerical parameters is found out. It was reported that very fine mesh and time step required for - phase simulation. The cause could be the segregated solution strategy for momentum and phase volume fractions, used in CFD solver. As a measure of consistency of -phase solution the authors of [7] suggested to check the inaccuracy of mass conservation. Following [7] we have calculated both sides of the exact equation: dvc 1 = QDT1 QDT, where Vc = (1 α L) dv dt, Q= ρ( d ) ρ v S. (9) here Q DT1, Q DT are the volumetric discharges in draft tube entrance and elbow exit, respectively. Figure 11 shows that in present model equation (9) is fairly well fulfilled even for much larger time V L S 7

9 6th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science 15 (01) doi: / /15/3/03038 step. This surprising result may be due to the coupled solution of equations for pressure, momentum and α L. The suggested model can further be enhanced by switching from periodic stage computations to full turbine computations, including spiral case, all wicket gate and all runner channels. 9. Conclusions The method of CFD simulation of pressure and discharge surge in hydraulic power plants is suggested. The flowfield in turbine domain is simulated using 3D two-phase fluid-vapor mixture, while the rest of the hydraulic system is simulated in frames of 1D hydro-acoustic model. Thus the model accounts for the main factors responsible for excitation and propagation of surge (penstock inertia, vortex precession, cavitation), but is free of some shortcomings of existing 1D hydro-acoustic models. Most important, there is no need to determine cavitation compliance C and mass flow gain factor χ. The effect of runner and draft tube geometry is also inherently accounted for in the model. Unsteady simulations of part load and full load regimes are performed. Numerical experiments showed the capability of the presented model to capture pressure and discharge surge caused by both vortex rope precession and compliance of cavity volume. Acknowledgments This work was partially supported by grant of Russian Foundation for Basic Research. Nomenclature a Penstock wave speed [m/s] Q Discharge [m 3 /s] C Cavity compliance [m ] Q 11 Unit discharge ( = Q/ D1 H ) D 1 Runner diameter [m] S p Area of penstock cross section [m ] E Specific total energy [m] v Velocity vector [m/s] g Gravity [m/s ] V c cavity volume [m 3 ] H Net head [m] α L Liquid volume fraction [-] Δh SP Energy loss in spiral casing [m] δ sp stay vane outlet flow angle [rad] l p Penstock length [m] χ Mass flow gain factor [s] m Piezometric head ( = p / ρlg z) [m] ρ Mixture density [kg/m 3 ] n Rotational speed [rpm] ρ L Water density [kg/m 3 ] n 11 Unit rotational speed ( / 1 H ρ V Vapor density [kg/m 3 ] ns specific speed ( = 3.65n11 Q11η ) σ Thoma number [-] p Pressure [Pa] η Turbine efficiency [-] p V Vapor pressure [Pa] τ Stress tensor References [1] Jacob T and Prenat J E 1996 Francis Turbine Surge: Discussion and Data Base IAHR Symp.on Hydraulic machinery andsystems (Valencia, Spain) [] Doerfler P 198 System dynamics of the Francis turbine half load surge IAHR Symp. on Hydraulic Machinery and Systems (Amsterdam, Netherlands) [3] Koutnik J, Nicolet C, Schohl G A and Avellan F 006 Overload surge event in a pumped storage power plant IAHR Symp. on Hydraulic Machinery and Systems (Yokohama, Japan). [4] Flemming F, Foust J, Koutnik J and Fisher R K 008 Overload surge investigation using CFD data IAHR Symp. on Hydraulic Machinery and Systems (Foz do Iguassu, Brazil) [5] Alligne S, Nicolet C, Allenbach P, Kawkabani B, Simond J J and Avellan F 008 Influence of the vortex rope location of a Francis Turbine on the hydraulic system stability IAHR Symp. on Hydraulic Machinery and Systems (Foz do Iguassu, Brazil) [6] Alligne S, Maruzewski P, Dinh T, Wang B, Fedorov A, Iosfin J and Avellan F 010 Prediction 8

10 6th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science 15 (01) doi: / /15/3/03038 of a Francis turbine prototype full load instability from investigations on the reduced scale model IAHR Symp. on Hydraulic Machinery and Systems (Timisoara, Romania) [7] Dörfler P K, Keller M and Braun O 010 Francis full-load surge mechanism identified by unsteady -phase CFD IAHR Symp. on Hydraulic Machinery and Systems (Timisoara, Romania) [8] Cherny S, Chirkov D, Bannikov D, Lapin V, Skorospelov V, Eshkunova I and Avdushenko A 010 3D numerical simulation of transient processes in hydraulic turbines IAHR Symp. on Hydraulic Machinery and Systems (Timisoara, Romania) [9] Kunz R F, Boger D A and Stinebring D A, et al. 000 A preconditioned Navier-Stokes method for two-phase flows with application to cavitation prediction Computers & Fluids 9 pp [10] Singhal A K,Vaidya N and Leonard A D 1997 Multi-dimensional simulation of cavitating flows using a PDF model for phase change ASME-FEDSM [11] Panov L V, Chirkov D V and Cherny S G 011 Numerical algorithms for simulation of cavitating flows of viscous fluid Computational technologies (in Russian) [1] Panov L V, Chirkov D V, Cherny S G, Pylev I M and Sotnikov A A 01 Numerical modeling of steady-state cavitational flow of viscous fluid in Francis hydroturbine Thermophysics and Aeromechanics 3 (to appear) [13] Cherny S G, Chirkov D V, Lapin V N, Skorospelov V A and Sharov S V 006 Numerical Simulation of Fluid Flows in Turbomachines (Novosibirsk: Nauka) p 06 9