Effects of uncertainties in positioning of PIV plane on validation of CFD results of a high-head Francis turbine model

The use of Computational Fluid Dynamics (CFD) for the design of modern hydraulic turbines has increased and matured significantly the last decades. More recently, CFD is also used to understand how to safely widen the hydraulic turbine operating ranges, and to avoid hazardous conditions during transient operation. The accuracy of such CFD results relies on validation with experimental data. There are many uncertainties in both numerical and experimental studies of flow in hydraulic turbines. The present work is focusing on the effects of the uncertainties in the positioning of the experimental Particle Image Velocimetry (PIV) plane on the validation of CFD results of the high-head Francis-99 turbine model. A transient shutdown sequence is considered, where the available experimental and numerical data are considered accurate according to a conventional thorough validation procedure. A part of that validation procedure is the comparison of spatially and temporally varying velocity profiles along three lines of the experimental PIV plane. The positioning of this PIV plane is here considered uncertain, using three translational and three rotational stochastic parameters with uniform probability distribution functions. The validated CFD results are used to extract the data that depends on these uncertainties, while this is not possible for the experimental data. The polynomial chaos expansion method is employed for the Uncertainty Quantification (UQ) study while Sobol’ indices are utilized for the Sensitivity Analysis (SA). The UQ can be used to show how the considered uncertainties impact the extracted components of the velocity field, and the sensitivity analysis reveals the relative contribution of each uncertain parameter on the quantity of interest. For this particular Francis-99 case it is shown that the so-called horizontal velocity component is most sensitive to the plane-normal positioning of the PIV plane. This is also the velocity component where all the numerical results found in the literature differ most from the experimental results. It is also shown that the probability distribution function of the numerical horizontal velocity is covered by the experimental standard deviation bounds, which means that it is quantified that the numerical and experimental results are similar within the range of the uncertainties

Flow-induced pulsations in Francis turbines during startup - A consequence of an intermittent energy system

Hydraulic turbines are increasingly responsible for regulating the electric grid, due to the rapid growth of the intermittent renewable energy resources. This involves a large increase in the number of starts and stops, which cause severe flow-induced pulsations and fluctuating forces that deteriorate the machines. Better knowledge of the evolution of the flow in the machines during transients makes it possible to avoid hazardous conditions, plan maintenance intervals, and estimate the costs of this new kind of operation. The present work provides an in-depth and comprehensive numerical study on the flow-induced pulsations and evolution of the flow field in a high-head model Francis turbine during a startup sequence. The flow simulation is carried out using the OpenFOAM open-source CFD code. A thorough frequency analysis is conducted on the fluctuating part of different pressure probes and force components, utilizing Short-Time Fourier Transform (STFT) to extract the evolution of the frequency and amplitude of pulsations. Low-frequency oscillations are detected during the startup, which are induced by the complex flow structure in the draft tube. A decomposition is performed on the draft tube pressure signals, and the variations of the synchronous (plunging) and asynchronous (rotating) modes are studied. The plunging mode is stronger at minimum and deep part load conditions, whereas the rotating mode is dominant during the presence of the Rotating Vortex Rope (RVR) at part load. The velocity field in the draft tube is validated against experimental data, and the complex flow structures formed during the startup procedure are explained using the λ2 vortex identification method

OpenFOAM for Francis turbine transients

The flexibility and fast responsiveness of hydropower systems make them a reliable solution to overcome the intermittency of renewable energy resources and balance the electrical grid. Therefore, investigating the complex flow fields during such operation is essential to increase the reliability and lifetime of future hydropower systems. The current article concerns the utilization of OpenFOAM for the numerical study of Francis turbines during transient load change operations. The details of employed models and numerical schemes are thoroughly explained. The Laplacian smoothing algorithm is applied for the deformation of the guide vane domain. The impact of different mesh diffusivity parameters on both load rejection and acceptance operations is studied. It is shown that general slip boundary conditions cannot be used for slipping points on the guide vane upper and lower surfaces. Instead, different alternatives are introduced and compared. The developed framework is tested on a high-head Francis turbine. Different transient operations are simulated and results are compared to the experimental data. It is shown that OpenFOAM can be employed as a trustworthy CFD solver for numerical investigation of Francis turbines transient operations

A semi-implicit slip algorithm for mesh deformation in complex geometries, implemented in OpenFOAM

Many engineering applications of computational fluid dynamics (CFD) comprise extensive movement of objects that necessitate complex dynamic mesh treatments. In particular, the mesh motion process frequently requires a proper slipping of mesh points on highly curved surfaces. The currently available implementation of explicit slip boundary conditions in OpenFOAM fails to allow large deformations of the mesh without severely degrading the mesh quality and inverting some of the cells. Thus, a robust semi-implicit slip algorithm, based on the Laplacian smoothing methodology, is developed in the present work to tackle this issue. The algorithm is in fact performed in two steps, one explicit and one implicit. The OpenFOAM implementation of the algorithm includes different mesh motion solvers and boundary conditions, based on the displacement or velocity of points. The method is first verified using simple, yet relevant, test cases, and it is shown that the developed algorithm significantly outperforms some of the well-known proprietary CFD codes. Then, it is applied to a complex practical CFD case study. An engineering application that requires the features of the developed mesh motion algorithm is the transient operation of Kaplan turbines. These double-regulated machines simultaneously adjust the guide vane and runner blade angles while changing the operating condition. CFD simulations of such transient operations are highly complex, as they involve mesh deformation of the guide vane passage and simultaneous mesh deformation and rigid-body rotation of the runner blade passage. The mesh deformation requires points to slip on the curved hub and shroud surfaces while preserving the cell quality in tiny blade clearances. Therefore, the feasibility of the developed algorithm is evaluated for a load rejection sequence of a Kaplan turbine model. Program summary: Program Title: Semi-implicit slip mesh motion CPC Library link to program files: https://doi.org/10.17632/wztc26vh7b.1 Developer\u27s repository link: https://github.com/salehisaeed/semiImplicitSlip Licensing provisions: GPLv3 Programming language: C++ Nature of problem: CFD simulations of numerous engineering fluid flows, such as transient operation of hydraulic turbines, involve an immensely complicated mesh motion process consisting of simultaneous mesh deformation and mesh slipping on highly curved surfaces. The available standard mesh motion methodology in OpenFOAM lacks some features to simulate this elaborate mesh motion. The introduced program addresses this problem by developing a new dynamic mesh algorithm. Solution method: The program implements a robust semi-implicit algorithm for slipping the mesh points on curved surfaces. The algorithm includes two steps, namely, an explicit step based on the general slip condition and an implicit step based on the Dirichlet condition. It employs the Laplacian smoothing equations to spread the mesh deformation into the domain. Additionally, a solid-body rotation may be added on top of the deformed mesh, which could be useful for modeling the runner region in transient operation of Kaplan turbines which contains simultaneous mesh deformation and solid-body rotation of the mesh

Implementation of deep reinforcement learning in OpenFOAM for active flow control

Recent advancements in artificial intelligence and machine learning have enabled tackling high-dimensional controlling and decision-making problems. Deep Reinforcement Learning (DRL), as a combination of deep learning and reinforcement learning, can perform immensely complicated cognitive tasks at a superhuman level. DRL can be utilized in fluid mechanics for different purposes, for instance, training an autonomous glider [1], exploring swimming strategies of multiple fish [2, 3], controlling a fluid-directed rigid body [4], proposing shape optimization [5, 6]. DRL can also be utilized for Active Flow Control (AFC) [7], which is of crucial importance for mitigating damaging effects or enhancing favourable consequences of fluid flows. Optimizing the AFC strategy using classical optimization methods is usually a highly non-linear problem and involves designing various parameters, while DRL can learn sophisticated AFCstrategies and fully exploit the abilities of the actuator. It is based on the reinforcement learning concept that explores the state-action-reward sequence and offers a powerful tool for conducting closed-loop feedback control.In the present work, a coupled DRL-CFD framework was developed within OpenFOAM, as opposed to previous attempts in the literature in which the CFD solver was treated as a black box. Here, the DRL agent is implemented as a boundary condition that is able to sense the environment state, perform some action, and record the corresponding reward. Figure 1 displays a simple flowchart of the developed DRL framework in which a deep neural network (DNN) is used as the decision maker (i.e., policy function).To test and verify the performance of the developed DRL-CFD software, the simple test case of vortex shedding behind a 2D cylinder is investigated. The actuator is a pair of synthetic jets on top and bottom of the cylinder. The reward function is defined as the reduction of drag and the absolute value of lift. Thereby, the DRL agent (which is a deep neural network here) learns to minimize the drag and lift coefficients by applying the optimum jet flow at each time step. The DRL agent was trained through a total of 1000 CFD simulations. Figure. 2 presents the variation of drag and lift coefficients of the cylinderfor both cases. The controlling mechanism starts at t = 40 s and it can be seen that both forces reduce significantly. The contours of vorticity behind the cylinder for the uncontrolled (baseline) and controlled cases, after reaching quasi-stationary condition (t = 200 s), are presented in Fig. 3. The vortex shedding effect is considerably reduced in the controlled case

A Head Loss Pressure Boundary Condition for Hydraulic Systems

Despite the increase in computational power of HPC clusters, it is in most cases not possible to include the entire hydraulic system when doing detailed numerical studies of the flow in one of the components in the system. The numerical models are still most often constrained to a small part of the system and the boundary conditions may in many cases be difficult to specify. The headLossPressure boundary condition is developed in the present work for the OpenFOAM open-source CFD code to include the main effects caused by a large hydraulic system onto a component in the system. The main motivation is to provide a boundary condition for incompressible hydraulic systems where known properties are specified by the user and unknown properties are calculated. This paper is a guide to the developed headLossPressure boundary condition. It is based on the extended Bernoulli equation to calculate the kinematic pressure on the patch. An arbitrary number of minor and friction losses are considered to describe the system in terms of head losses. The boundary condition also provides the opportunity to specify the head (difference in height) in relation to a reference elevation. System changes during operations are modelled through Function1 variables, which enables time-varying inputs. The developments are validated against experimental test data, where the varying head between two free surfaces and a valve closing and opening sequence are modelled with the boundary condition. The main effects of the system are well captured by the headLossPressure boundary condition. It is thus a useful and trustworthy boundary condition for incompressible flow simulations of components in a hydraulic system

Evaluation of startup time for a model contra-rotating pump-turbine in pump-mode

A larger part of the electricity is today from intermittent renewable sources of energy. However, the energy production from such sources varies in time. Energy storage is one solution to compensate for this variation. Today pumped hydro storage (PHS) is the most common form of energy storage. Usually, it requires a large head, which limits where it can be built. In the EU project ALPHEUS, PHS technologies for low- to ultra-low heads are explored. One of the concepts is a contra-rotating pump-turbine (CRPT). The behaviour of this design at time-varying load conditions is today scarce. In the present work, the impact of the startup time for a CRPT is analysed through computational fluid dynamics (CFD) simulations. The analysis includes a comparison between a coarse and a fine CFD model. The coarse model produces acceptable results and is 50 times cheaper, this model is thus used to assess the startup time. It is found that longer startup times generate lesser loads and peak values. A startup time of 10 s may be a sufficient alternative as the peak loads are heavily reduced compared to faster startups. Furthermore, there is not much difference between a startup time of 20–30 s

Flow Characteristics of Preliminary Shutdown and Startup Sequences for a Model Counter-Rotating Pump-Turbine

Pumped Hydropower Storage (PHS) is the maturest and most economically viable technology for storing energy and regulating the electrical grid on a large scale. Due to the growing amount of intermittent renewable energy sources, the necessity of maintaining grid stability increases. Most PHS facilities today require a geographical topology with large differences in elevation. The ALPHEUS H2020 EU project has the aim to develop PHS for flat geographical topologies. The present study was concerned with the initial design of a low-head model counter-rotating pump-turbine. The machine was numerically analysed during the shutdown and startup sequences using computational fluid dynamics. The rotational speed of the individual runners was decreased from the design point to stand-still and increased back to the design point, in both pump and turbine modes. As the rotational speeds were close to zero, the flow field was chaotic, and a large flow separation occurred by the blades of the runners. Rapid load variations on the runner blades and reverse flow were encountered in pump mode as the machine lost the ability to produce head. The loads were less severe in the turbine mode sequence. Frequency analyses revealed that the blade passing frequencies and their linear combinations yielded the strongest pulsations in the system

A Low-Head Counter-Rotating Pump-Turbine at Unsteady Conditions

With the increased amount of energy produced from variable renewable energy sources, such as wind and solar power, the need to store energy increases. The reason is that it is necessary to cope with the variation in energy being produced by the renewables to stabilise the electrical grids. The most widely used technology for energy storage on a large scale is today pumped hydro storage (PHS). For PHS to be economically feasible, a high head is typically required, which puts topographical constraints on where it can be built. However, the EU project ALPHEUS aims to develop PHS for low-head applications, hence allowing PHS at yet unexplored sites. In the project, new reversible counter-rotating pump-turbine (CRPT) concepts are explored as an alternative runner design for low-head situations. The CRPT consists of two runners rotating in opposite direction from one another and it is suggested that it can reach higher efficiencies and be more compact compared to a single runner arrangement.In the present work a model counter-rotating pump-turbine for the ALPHEUS project is numerically analysed with computational fluid dynamics (CFD) simulations. The simulations are carried out using unsteady CFD in OpenFOAM-v2012. In the simulations, the two runners rotate individually via prescribing a solid body rotation to the runner domains. The individually rotating runners causes a intricate rotor-rotor interaction which is resolved by the numerical model. An example of this is shown in Figure, where a complex vortical structure is developing by the runners and support-structures. Furthermore, the CRPT is in reality part of large hydraulic system which effects the performance of the machine. The system includes bends, valves, long pipes, and two large water reservoirs. To restrict the size of the computational domain, the novel \verb|headLossPressure| boundary condition, developed by Fahlbeck et al., is used to include the main effects of the hydraulic system. To summarise, this study will show the potentials with a CPRT in a PHS application through CFD simulations, explain the used numerical framework, and demonstrate a use case for the new headLossPressure boundary condition

NUMERICAL SIMULATIONS OF COUNTER-ROTATING PUMP-TURBINE WITH A NEW HEAD-LOSS PRESSURE BOUNDARY CONDITION

With an increasing amount of energy from renewable sources, such as wind and solar, the need of complementary controllable energy sources increases. Hydropower plays a key role to provide a stable and flexible electrical grid. By storing large amount of water when there is excess power in the grid, and later utilise the stored water when there is a lack of power, hydropower is a stabilising unit for the electrical grid [1]. The ALPHEUS EU project has the aim to develop a low-head to ultra low-head seawater based Pumped Hydropower Storage (PHS) solution with a pump-turbine unit [2, 3]. The main goal of the ALPHEUS project is that the pump-turbine unit should have a round-trip efficiency of 70 - 80 % and a switching time of about 120 s. PHS use the potential energy by pumping water to a reservoir. The potential energy is later extracted by reversing the pump to a turbine. Three pump-turbine concepts are to be investigated, a counter-rotating shaft-driven, a counter-rotating rim-driven, and a positive-displacement alternative. A rigorous optimisation process will be applied to maximize the round-trip efficiency for a wide range of operating conditions. In this work an initial design of a counter-rotating shaft-driven alternative is considered. In the ALPHEUS project an optimised counter-rotating shaft-driven pump-turbine will be experimentally evaluated in model scale, in the hydraulic laboratory at TU Braunschweig. The experiments are partly made in order to generate experimental test data. The numerical models are later going to be evaluated with the experimental test data. The experimental test facility consists of a two open reservoir surfaces, upper and lower. In turbine-mode, water flows from the upper to the lower reservoir, and it is pumped from the lower to the upper in pump-mode. The reservoirs are connected with a series of pipes, including bends and other obstacles in the flow path. The machine is going to be tested at different operating conditions and it is thus hard to estimate the flow rate for any given case. This is because head, or pressure, losses scale quadratic to a change in flow rate. An option to overcome this problem in a numerical framework is to include head losses at the boundaries of the computational domain. The flow rate in the simulation is calculated as a balance between the available pressure and the losses in the system. In OpenFOAM there is not any available boundary condition that can include up-/down-stream losses at a patch. This present work demonstrates a new pressure boundary condition, headLossPressure, developed by Fahlbeck [4]. The boundary condition is an extension of the available totalPressure boundary condition. It uses the volumetric flux to adjust the static pressure on the patch according the Bernoulli equation [5]. The headLossPressure is an incompressible pressure boundary condition for in-/outflow patches. If the patch has inflow the losses are subtracted, and for an outflow patch the losses are added.The basic functionality of the headLossPressure boundary condition is evaluated on a simple test case by Fahlbeck [4]. In this work the boundary condition is used together with the initial design of a model scale counter-rotating shaft-driven pump-turbine in the ALPHEUS project. The blade geometries shown in Figure 1a were designed by the Advanced Design Technology Ltd (ADT) company. The diameter of the runners is 27 cm, runner 1 (red) has eight blades, and runner 2 (blue) has seven blades. Runner 1 has a rotational speed of 1453 RPM in pump mode and 832 RPM in turbine mode, runner 2 rotates at 90 % of the speed of the first runner in each mode.The numerical simulations are made on the computational domain shown in Figure 1b. The numerical simulations are made with unsteady CFD at one operating condition in both pump and turbine modes. The numerical framework includes the two rotating runners, hub, support-struts, and contraction/extraction parts. The simulations utilise the unsteady incompressible pimpleFoam solver and the k-ω SST model is used to account for turbulence. The convective terms of the momentum equations are discretised using the LUST scheme, and temporal discretisation with the backward scheme. The pressureInletOutletVelocity and headLossPressure are used as boundary conditions for velocity and pressure, respectively, at both the inlet and the outlet. The pressure boundary condition is set to operate with a total height difference of 8 m, the full pipe length is roughly 16 m, one 90\ub0 bend, and some additional flow obstacles are included.The results from the unsteady simulations, shown in Figure 2, resolves the unsteady wakes of the runners and the support- struts. The complex flow pattern produced by the runners is caused by the downstream runner cutting the wakes of the upstream runner. The machine is operating at a high efficiency in both modes as the flow is rather axial after the runners. This is seen by that the vortex shedding of the support-strut is rather axial. A frequency analysis, not shown here, uncover that the pressure pulsations in the system are strongly connected to the blade passing frequencies and linear combinations of it.The headLossPressure boundary condition can be used to produce a plausible flow field as the solver calculates a flow rate that is not totally unphysical. The question still remains if the flow rate is correct and if the boundary condition can be used even for transient simulations. The numerical model and this new boundary condition will later be compared against experimental test data of an optimised counter-rotating pump-turbine.AcknowledgmentsThe authors thank all those involved in the organisation of OFW16 and to all the contributors that will enrich this event. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 883553. The computations were enabled by resources provided by the Swedish National Infrastructure for Computing (SNIC) at NSC and C3SE partially funded by the Swedish Research Council through grant agreement No. 2018-05973.References[1]\ua0\ua0\ua0 IEA,\ua0\ua0\ua0\ua0\ua0 \ua0Will\ua0\ua0\ua0\ua0\ua0 \ua0pumped\ua0\ua0\ua0\ua0\ua0 \ua0storage\ua0\ua0\ua0\ua0\ua0\ua0\ua0 hydropower\ua0\ua0\ua0\ua0\ua0\ua0\ua0 expand\ua0\ua0\ua0\ua0\ua0\ua0\ua0 more\ua0\ua0\ua0\ua0\ua0\ua0\ua0 quickly\ua0\ua0\ua0\ua0\ua0\ua0\ua0 than\ua0\ua0\ua0\ua0\ua0\ua0\ua0 stationary battery\ua0\ua0\ua0\ua0\ua0 \ua0storage?\ua0\ua0\ua0\ua0\ua0\ua0\ua0 \ua0IEA,\ua0\ua0\ua0\ua0\ua0 \ua0Paris,\ua0\ua0\ua0\ua0\ua0\ua0\ua0 \ua02019.\ua0\ua0\ua0\ua0\ua0 \ua0[Online].\ua0\ua0\ua0\ua0\ua0 \ua0Available:\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0 https://www.iea.org/articles/ will-pumped-storage-hydropower-expand-more-quickly-than-stationary-battery-storage[2]\ua0\ua0\ua0 ALPHEUS H2020. Accessed: 2021-02-12. [Online]. Available: https://alpheus-h2020.eu/[3]\ua0\ua0\ua0 M. Qudaih and et al., “The contribution of low-head pumped hydro storage to a successful energy transition,” inProceedings of the Virtual 19th Wind Integration Workshop, 2020.[4]\ua0\ua0\ua0 J. Fahlbeck, “Implementation of an incompressible headlosspressure boundary condition,” in Proceedings of CFD with OpenSource Software, 2020, Edited by Nilsson. H., http://dx.doi.org/10.17196/OS CFD#YEAR 2020.[5]\ua0\ua0\ua0 F. M. White, Fluid mechanics, ser. McGraw-Hill series in mechanical engineering.\ua0 \ua0McGraw-Hill, 2011