3D numerical simulation of transient processes in hydraulic turbines

Transcription

1 IOP Conference Series: Earth and Environmental Science 3D numerical simulation of transient processes in hydraulic turbines To cite this article: S Cherny et al 010 IOP Conf. Ser.: Earth Environ. Sci View the article online for updates and enhancements. Related content - CFD simulation of pressure and discharge surge in Francis turbine at off-design conditions D Chirkov, A Avdyushenko, L Panov et al. - Numerical simulation of full load surge in Francis turbines based on threedimensional cavitating flow model D Chirkov, L Panov, S Cherny et al. - Numerical modeling of flow in the Francis- 99 turbine with Reynolds stress model and detached eddy simulation method A V Minakov, A V Sentyabov, D V Platonov et al. Recent citations - A Hydrodynamic Study of a Propeller Turbine During a Transient Runaway Event Initiated at the Best Efficiency Point Mélissa Fortin et al - Influence of the clearance flow on the load reection process in a pump-turbine Xiaolong Fu et al - Dynamic instability of a pump-turbine in load reection transient process XiaoLong Fu et al This content was downloaded from IP address on /07/018 at 18:49

2 3D numerical simulation of transient processes in hydraulic turbines 1. Introduction S Cherny 1, D Chirkov 1, D Bannikov, V Lapin 1, V Skorospelov 3, I Eshkunova 1 and A Avdushenko 1 Institute of Computational Technologies SB RAS Acad. Lavrentev avenue 6, Novosibirsk, , Russia Department of Mechanics and Mathematics, Novosibirsk State University Pirogov st., Novosibirsk, , Russia 3 Institute of Mathematics SB RAS Acad. Koptug avenue 4, Novosibirsk, , Russia chirkov@ict.nsc.ru Abstract. An approach for numerical simulation of 3D hydraulic turbine flows in transient operating regimes is presented. The method is based on a coupled solution of incompressible RANS equations, runner rotation equation, and water hammer equations. The issue of setting appropriate boundary conditions is considered in detail. As an illustration, the simulation results for runaway process are presented. The evolution of vortex structure and its effect on computed runaway traces are analyzed. Transient processes in hydraulic turbines are transitions from one operating point to another, controlled by valve or wicket gate opening, payload applied to generator, etc. Examples of such processes are power increase/decrease, runaway, emergency turbine shutdown, and so on. The maority of them pass far from the best efficiency point, in areas of unstable operation, where strong non-stationarity of the flow is observed. Moreover, most of transient processes are associated with significant discharge changes, causing water hammer waves, traveling back and forth through the whole water system. These compressible effects introduce additional dynamics in transient processes, making the task of simulation rather complex. Nowadays the most robust approach for investigation of transient behavior in hydroelectric plants is 1D hydroacoustic theory. It is based on hyperbolic system of mass and momentum continuity equations for compressible fluid (see Krivchenko et al. [1], [] and Nicolet [3]). In frames of this approach and with the aid of electrical analogy one can consider branched pipe systems, and take into account all basic components of hydro power plant, such as surge tanks, valves, etc. [3]. At that the turbine itself is represented by its equivalent hydraulic resistance and inductance, taken from turbine efficiency hill-chart. Therefore application of this approach requires turbine hill-chart to be known a priory. Also 1D approach can not be used to describe and simulate unsteady three-dimensional flow structures, such as vortices, recirculations, cavitation, etc., arising in flow passage at transients. One way to overcome this difficulty is to assume that instantaneous flow field behavior in a given moment of transient process is the same as its behavior in a corresponding stationary operating point of a steady state hill-chart. However it is not quite true in reality (see Krivchenko et al. [1]). From the other hand in last two decades CFD models and algorithms well advanced in simulation of steady and unsteady three-dimensional turbulent flows in hydraulic machines. Both local flow structure and integral characteristics, such as energy losses can now be numerically analysed. As an example, Vu and Retieb [4] showed that steady-state stage computations are capable to accurately predict efficiency characteristics of Francis turbines near the optimum. Authors experience (see Cherny et al. [5]) shows good predicting capabilities of RANS models in computing local and integral flow parameters of turbines and pumps in a relatively wide range of regime parameters around best efficiency point. Of coarse, moving far from the optimum, for example to part load or towards runaway conditions, the flow becomes substantially unsteady, highly turbulent and cavitating, indicating that steady state single phase RANS assumptions become invalid and can not be used. c 010 Ltd 1

3 Although accurate and efficient simulation of unsteady flow phenomena remains one of the main challenges for CFD in hydraulic machinery, some authors gained success in this field. For example, Ruprecht et al. [6], who used VLES, and Vu et al. [7], who used standard k-ε model, accurately simulated vortex rope precession in draft tube at part load. The obective of the present work is to apply 3D unsteady incompressible fluid flow model to investigate nonstationary effects in transient processes of Francis turbine. As shown before, simulation of such processes require consideration of an extended water system, at least including the penstock. The idea is to combine unsteady RANS solver for the turbine domain with 1D water hammer equations for the penstock. An attempt to combine 1D equations of hydroacoustics with 3D CFD was undertaken previously by Ruprecht et al. [6], in order to investigate system response on pressure fluctuations induced by draft tube vortex rope precession. But in their simulations 3D model was used only for the draft tube, while the turbine itself was represented by its hill chart, as in 1D approach. In this work the methodology for simultaneous numerical solution of 1D penstock hydroacoustics and 3D incompressible fluid flow dynamics in wicket gates, runner, and diffuser, is developed. The numerical method is applied for computation of turbine runaway process.. Governing equations The idea of combined hydroacoustic 3D simulation of transient process is the following. The whole water system of hydro power plant is divided in two parts, Fig. 1. First is a pipe line where water hammer simulation is carried out using 1D theory. The second part is the turbine, consisted of distributor, runner and draft tube, where the flowfield is governed by 3D Navier-Stokes equations. The solution in both parts is found simultaneously. It should be noted that flow-field in spiral case is not computed. Instead, spiral case is represented by its energy loss. Fig. 1 Simplified water system of hydroelectric plant divided in two parts. Non-stationary flowfield inside the turbine passage is described by 3D unsteady Reynolds-averaged Navier- Stokes equations for incompressible fluid. Absolute reference frame is used for static elements (distributor and draft tube), while rotating reference frame is used for the runner, rotating with angular velocity ω around the Ox 3 axis, directed downwards. Thus for the runner domain governing equations are u = 0, (1) ui t ( uiu + ) pˆ + i = ν eff ui u + i + f i, 1,, 3 i =, ()

4 p where pˆ = k ρ +. Inertia and gravity terms in eq. () are ω 3 ω f 1 = x1 + u, f = xω u1ω, f 3 = g. Either standard or Kim-Chen [8] k-ε turbulence model with log-law wall function near the solid walls is used to evaluate effective viscosity ν and turbulence kinetic energy k needed for the mean flow equations eff (1), (). Runner angular velocity ω, appeared in the right hand side of eq. (), in general varies with time in accordance to angular momentum equation dω I z = M R(ω( t)) M Gen( t), (3) dt which is to be solved simultaneously with equations (1), (). In (3) I z is a summary moment of inertia of runner and generator; M R is a runner torque; M Gen is a payload torque, applied to the generator shaft. In present study a simplified pipe line consisting of a single penstock of length L and constant cross section S p is considered, see Fig 1. Elastic water hammer propagation in this penstock is well described by the following one-dimensional hyperbolic system (energy loss is neglected): m c Q + = 0 t gs p (4) Q m + gs p = 0 t where p m = + z is a piezometric head, Q is a discharge, c is a pipe wave speed. In present computations c ρ g was taken 100 m/s. 3. Numerical method Fluid flow equations (1), () are solved numerically using artificial compressibility method. Dual time stepping is used for unsteady problems. 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. For more details reader is referred to Cherny et al. [5]. 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). An example structured mesh in WG, runner and DT is shown in Fig.. Mixing plane boundary condition is applied on wicket gate runner and runner draft tube interfaces with circumferential averaging of all flow variables (p, u, v, w, k, ε). Being efficient in terms of storage and CPU requirements, this approach has two drawbacks: 1) rotor-stator interaction can not be taken into account; ) draft tube instabilities, such as vortex rope precession, are suppressed to a certain extent by averaging procedure applied at runner draft tube interface. Nevertheless in present pilot study the stage approach was adopted for its computational efficiency. The use of full flow analysis, involving computations of all WG and runner channels, which is free from the shortcomings indicated, is a future plan. Most of transient processes are controlled by opening/closing of the guide vanes, so flow-field computation in wicket gate region is carried out on moving mesh. The function of guide vane opening of time is an additional input data. Water hammer equations (4) 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. Having known the solution at n-th time level, prior to iterations for the next (n+1)-th one, new rotational speed ω n+1 is found from equation n+ ω 1 n ω n n I z = M R(ω ) M Gen( t ), (5) Δt which is a first order explicit discretisation of eq. (3). Different approximations of (3) as well as different 3

5 couplings with mean flow equations were examined, but they gave almost identical results. So the above algorithm was used in the present study as the most simple. Fig. Mesh in wicket gate, runner and draft tube for periodic stage analysis 4. Implementation of boundary conditions In CDF applications to hydraulic turbines a common practice for setting inlet and outlet boundary conditions is specifying velocity profile at the inlet and pressure at the outlet. Velocity profile is usually derived from discharge Q and inlet flow angle, which is rather conservative. In many problems however discharge is not known a priory and should be found as a part of the solution. Simulation of transient processes is the case, because of significant changes in discharge caused by guide vane opening, runner acceleration, etc. Therefore traditional boundary conditions can not be used for simulation of these phenomena. In order to resolve discharge variation during the transient process a new statement of inlet/outlet boundary conditions was developed Separate turbine computations For the case of isolated computations in wicket gate runner draft tube domain (WG-R-DT domain) novel conditions are the following. At the inlet section of wicket gate domain total specific hydraulic energy E in,wg and flow angle are specified, while at the draft tube outlet section total specific energy E out,dt is set together with pressure profile (typically simple hydrostatic distribution). Total specific hydraulic energy E in cross section S is determined as 1 p v E = z + (v ds). (6) Q S ρg g Note that no reference value of pressure is prescribed at the outlet. Instead it is adusted iteratively in the process of solution to provide given total energy E out,dt. In WG-R-DT simulations the inlet and outlet energies are linked together by the following relation: E E = H h (7) in,wg out,dt SP where H is the net head, h SP is the head loss in spiral casing and stay vane channels. In present simulations head loss h SP is a priory estimated as 0.01H. To the present time head loss h SP is assumed to be constant throughout the unsteady process, which is not true in reality. More accurate estimations can be used for h SP, accounting discharge variations, see for example Topa [9]. Computations in the reduced domain wicket gate runner (WG-R) are also available. This case is essentially the same, except for the treatment of outlet section of runner domain. Here radial equilibrium condition is specified for the pressure profile, and outlet energy E out,r is adusted to satisfy the relation E E = H h h. (8) in,wg out,r SP DT 4

6 In eq. (8) h DT is the head loss in draft tube, which is calculated using empirical formula (Topa [9]) Cz Cu hdt = ξ0 +, (9) g g where C z and C u are the averaged axial and absolute peripheral flow velocities, ξ 0 is an empirical constant. As follows from the above, new inlet/outlet boundary conditions prescribe head rather than discharge. The corresponding discharge is found from the solution. This statement has been tested for a wide range of operating regimes and proved to be reliable. 4.. Combined penstock-turbine computations Equations (7), (8) automatically neglect the effect of water hammer on wicket gate inlet energy. Therefore they can be used to simulate flow-fields in fixed operating points or transient processes with a weak water hammer effects (slow regulation, short penstock, etc). However most of real transient processes yield significant water hammer waves affecting the pressure in spiral case and wicket gate, and thus increasing or decreasing effective turbine head. In order to adequately set up inlet boundary condition for WG one need to consider extended water system, including the penstock. In case of computations in the extended domain penstock wicket gate runner draft tube (penstock-wg-r-dt) total energy Q E in, pipe = m + = const (10) gs is specified at the inlet of the penstock, meaning that water level in upper reservoir is assumed constant throughout the process. After each iteration in pseudotime penstock and turbine exchange pressure and discharge at their interface, as suggested in Ruprecht [6]. From CFD results pressure p at the WG inlet is averaged and given as an outlet boundary condition to water hammer model (4). Penstock outlet discharge Q, obtained in frames of water hammer model, together with flow angle are given as an inlet boundary condition for 3D RANS model of flow in WG-R-DT domain, see also Fig Steady state hill chart prediction Accurate resolution of efficiency and discharge is a necessary condition for numerical method to be used as a transient simulation tool. In order to demonstrate the capabilities of the present solver, it was applied to computation of efficiency hill chart of 57MW Francis turbine. Runner speed is 00 rpm, net head is 73.5 m, runner diameter is 3.15 m. A series of operating points have been computed, with discharge ranging from 30% to +0% of BEP discharge, and unit speeds n 11 raging from 60 to 90. For each regime steady state solution was sought in WG-R-DT domain. In order to demonstrate grid sensitivity three sets of computational meshes have been used: mesh 1 (coarse) 16k cells for WG, 4k cells for runner, and 4k cells for the DT (shown in fig. ); mesh (medium) 40k cells for WG, 54k cells for runner, and 68k cells for the DT; mesh 3 (fine) 110k cells for WG, 146k cells for runner, and 194k cells for the DT. In wicket gate and runner domains maximum cell skewness is 0.7, while in draft tube it reaches 0.9 near the solid wall of the cone. Since the comparison was made with experimental data, measured in a laboratory test rig, the laminar flow viscosity was adusted to ensure dynamic similarity to scale model conditions. Standard k-ε model was used for the turbulence. Experimental investigation of turbine scale model was performed according to IEC standard in the Laboratory of Water Turbines of JSC Power Machines LMZ, St.-Petersburg, Russia. Runner diameter of the scale model was 0.46 m, model head was 4 m. Relative error in the efficiency measurements was 0.%. Fig. 3 shows comparison of the computed and measured efficiency. All three meshes give good qualitative and quantitative agreement with experimental distributions. As expected, coarse mesh introduces excessive numerical dissipation, leading to a lesser value of turbine efficiency. Аs for medium and fine meshes, at n 11 = n 11,BEP variation of discharge gives maximum error less than 1%, while variation of n 11 at constant guide vane opening (GVO) gives the error less than 1.5%, which is concentrated in area n 11 < n 11,BEP. Compared to experimental data, the computed discharges are uniformly underestimated by %, which seems to be acceptable. 5

7 Fig. 3 Comparison of experimental and computed hill-charts: at constant unit speed n 11 = n 11,BEP =73.5 (left) and at constant guide vane opening a 0 = 178 mm (right) 6. Simulation of transient behavior at runaway As an example, the developed simulation tool is applied to analyze transient behavior during runaway from BEP point for the same turbine. Emergency runaway process is determined by sudden decrease of generator payload to zero (M Gen =0). According to eq. (3) runner speed starts growing gradually reaching runaway speed n r, satisfying the condition M R (n r ) =0. Guide vane opening a 0 remains constant throughout the process. According to the developed statement, time evolution of all the regime parameters n(t), Q(t), M R (t) and water hammer H(t) as well as local flow-fields should be obtained as the result of simulation. Computations in three different statements have been carried out: 1) in WG-R domain without the penstock, ) in WG-R-DT domain without the penstock, 3) in penstock-wg-r-dt domain. Mesh 1 (coarse) was used in order to reduce computational time. Less dissipative Kim-Chen k-ε model was used for turbulence in order to better resolve vortex structures. Time step was Δt = 0.005s, corresponding to 1/60 of runner rotation period at startup. Figure 4 shows the obtained traectories of operating point in Q n plane, along with experimental runaway curve and lines of constant GVO. It is expected that the runaway traectories would go along lines of constant GVO. However WG-R simulation deviate to the grater discharge, which is explained by the loss of applicability of formula (9), as we move away from the optimum. Computations including the draft tube are closer to experiment. Up to speed n = 75 their traectories go along the GVO line. Then, with greater speeds the traectories start to oscillate due to discharge pulsations, which however do not affect runner acceleration curve, Fig. 5. Such an oscillating behavior is not observed in WG-R computation. It is concluded that discharge oscillations are caused entirely by diffuser instabilities. As can be seen in Fig. 6, vortex rope forms and then breaks down in the draft tube cone during the process. Note that no vortex rope was observed in unsteady simulation of BEP point. The influence of turbulence modeling on the evolution of the vortex is under investigation. Figure 7 (left) illustrate pressure pulsations in a point of draft tube surface, showing that first 7 sec of the process pressure behavior is the same for both WG-R-DT and penstock-wg-r-dt computations. The appearance of high-frequency pressure oscillations in the latter are connected to the high-frequency water hammer waves, shown in Fig. 7 (right). 6

8 Fig. 4 Computed runaway traectories Fig. 5 Evolution of runner speed A C E F 7

9 G H I Fig. 6 Instantaneous draft tube pressure iso-surfaces, WG-R-DT computation. Letters correspond to time moments indicated in Fig. 4 on curve J Fig. 7 Computed pressure pulsations in the draft tube (left), pressure increase at wicket gate inlet due to water hammer (right) obtained in penstock-wg-r-dt simulation 7. Conclusion An approach is developed for numerical simulation of complex unsteady flow phenomena in transient regimes. The method is based on 3D unsteady RANS equations for the turbine with variable runner speed, which is governed by angular momentum equation. Dynamic variation of effective turbine head is accounted by simultaneous solution of 1D elastic water hammer equations for the penstock. Discharge is found as a part of solution, that is guaranteed by new type of inlet/outlet boundary conditions, prescribing head rather than discharge. The developed simulation tool allows to predict time evolution of basic regime parameters and 8

10 estimate dynamic forces and pressure pulsations in turbine passage during the process. One of the advantages of the presented approach is that it does not require any a priori knowledge about efficiency hill-chart of the turbine. The tool is applied for simulation of flow evolution during runaway process. It is shown that far from the optimum numerical flow analysis should be carried out with the draft tube. The appearance of vortex rope is observed in computations, including wicket gate, runner and draft tube. For the time being this methodology is applied to investigation of the other transient processes, such as power regulation and emergency shutdown. Acknowledgments Authors would like to thank their colleagues A. A. Sotnikov, I. M. Pilev, V. N. Stepanov and V. E. Rigin from JSC Power machines LMZ for valuable laboratory data and helpful discussions. This work has been partially supported by grant of Russian Foundation for Basic Research. Nomenclature a 0 Guide vane opening [mm] n Rotational speed [rpm] c Pipe wave speed [m/s] n 11 Unit rotational speed ( = nd 1 / H ) D 1 Runner diameter [m] p Pressure [Pa] E Specific total energy [m] Q Discharge [m 3 /s] g Gravity [m/s ] Q 11 Unit discharge ( = Q / D1 H ) H Net head [m] S p Pipe cross section [m ] h SP Energy loss in spiral casing [m] u i Mean velocity components (i =1,, 3) [m/s] h DT Energy loss in draft tube [m] v Absolute velocity vector [m/s] I z Moment of inertia [kg m ] t Time [s] L Pipe length [m] ρ Water density [kg/m 3 ] m Piezometric head ( = z + p / ρg ) [m] ω Runner angular velocity (= πn/30) [rad/s] M R Runner torque [N m] ν eff Eddy viscosity (=ν + ν turb ) [m /s] Payload generator torque [N m] M Gen References [1] Krivchenko G I, Arshenevskiy N N, Kvyatkovskiy E E and Klabukov V M 1975 Hydro-mechanical transient processes in hydro-energetic plants (Moscow: Energy, in Russian) [] Krivchenko G I and Gubin F F 1980 Hydroelectric plants (Moscow: Energy, in Russian) [3] Nicolet C 007 Hydroacoustic modelling and numerical simulation of unsteady operation of hydroelectric systems PhD Thesis (EPFL 3751, [4] Vu T C and Retieb S 00 Accuracy Assessment of Current CFD Tools to Predict Hydraulic Turbine Efficiency Hill Chart Proc. of the XXIst IAHR Symp. on Hydraulic Machin. and Syst. (Lausanne, Switzerland) [5] 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) (in Russian) [6] Ruprecht A, Helmrich T, Aschenbrenner T and Scherer T 00 Simulation of Vortex Rope in a Turbine Draft Tube Proc. of the XXIst IAHR Symp. on Hydr. Machin. and Syst. (Lausanne, Switzerland) [7] Vu T C, Nennemann B, Ciocan G D, Iliescu M S, Braun O and Avellan F 004 Experimental Study and Unsteady Simulation of the FLINDT Draft Tube Rotating Vortex Rope Proc. of the Hydro 004 Conf. (Porto, Portugal) FE [8] Chen Y S and Kim S W 1987 Computation of turbulent flows using an extended k-ε turbulence closure model (NASA CR-17904) [9] Topa G I 1989 Computation of integral hydraulic characteristics of hydromachines Publishing house of Leningrad University (Leningrad, in Russian) 9