NUMERICAL ANALYSIS OF UNSTEADY PULSATING FLOWS USING A MODIFIED WALL-FUNCTION

The pressure fluctuation caused by swirling flow in draft tube is one of the main reasons of vibration in hydraulic turbine. It directly affects the steady operation of hydraulic turbine unit. The pressure fluctuation in draft tube of a large Francis turbine can’t be obtained accurately by similarity law from model test, and prototype test is difficult to carry out and costs too much. Therefore, it is necessary to predict pressure fluctuation in draft tube numerically and provide scientific reference for mitigating and suppressing pressure fluctuation. This paper describes a numerical study of unsteady flow in the draft tube of a large Francis turbine in a Hydropower Station of China by using the Reynolds averaged Navier–Stokes (RANS) approach with a Reynolds stress transport model (RSM), validating the numerical results against experimental data. The numerical results successfully represent the vortex rope. The pressure fluctuation patterns in different parts of the draft tube including the cone, elbow and diffuser are analyzed. The pressure fluctuation in the cone and elbow is relative steady, and it has an obvious dominant frequency which is approximately 0.28 and 0.3 times of the runner rotational frequency. These results show very good agreement with experiments. The largest pressure amplitude appears in the draft tube cone downstream side and the draft elbow inside. The pressure fluctuation in the diffuser is stochastic, and the amplitude is small. Additionally, the pressure distributions on the horizontal computational section of the draft tube are analyzed.

BACKGROUND: Cavitation is a phenomenon that occurs in vane hydraulic machines: pumps, hydraulic turbines, when the pressure in a certain area of the flow reaches the level of saturated steam pressure. Its occurrence depends on the design and mode of operation of the hydraulic turbine. In order to design a hydraulic turbine with high cavitation qualities, it is necessary to be able to reliably predict this phenomenon.
 AIMS: The article describes approaches to modeling the operation of Francis hydraulic turbines based on the ANSYS software package.
 METHODS: Using quasi-3D methods was modeled turbine blade system with 75 meters head. Hydrodynamic computation carried out in single-phase and two-phase formulations using the ANSYS CFX package.
 RESULTS: The design of a flow path Francis turbine 3D solid model with a specific speed coefficient ns =283 has been completed. The flow part of the hydraulic turbine includes a spiral case, a stator, a guide vane, an impeller and a draft tube. Computational modeling of the flow of a single-phase viscous fluid in a hydraulic turbine in different modes was carried out to construct a universal characteristic. The optimal efficiency is found and the flow characteristics are calculated. The losses in the elements of the flow part of the hydroturbine under various operating modes are determined, the zone of optimal operation is found. The cavitation flow is calculated using a two-phase flow model (water-steam). For both sides of the impeller blade, a pressure distribution was obtained, which can be used to judge the possibility of cavitation in areas where the pressure of the water column is less than the vaporization pressure. The value of the critical cavitation coefficient for the three most unfavorable modes was determined, and the dependence of the efficiency on the cavitation coefficient was constructed. The area occupied by steam on the blade during cavitation flow is visualized, its area is determined relative to the surface area of the blade.
 CONCLUSIONS: The designed hydraulic turbine has good energy and cavitation qualities, confirmed by the calculation. This version of the hydroturbine can be used as the initial one with further optimization of the blade system and elements of the flow path, to improve the energy and cavitation qualities.

Numerical simulations of axial hydraulic turbines away from the best efficiency point are challenging. Previous studies especially show difficulties predicting the tangential velocity at Part Load (PL) operating conditions, where the swirl is high, in comparison to experiments. This is a reoccurring problem, and it is essential to understand, as the high tangential velocity is a fundamental characteristic of the flow in hydraulic turbines and is directly related to the swirling flow stability and the turbine’s power output. The objective of this study is to numerically investigate and understand the origin of the tangential velocity deviation from experimental results by performing simulations with the finite volume method of an axial turbine operated at PL. A parametric study is performed to address the abovementioned. Specifically, the effects of the blade clearance, blade angle, flow rate, and different turbulence models are studied on this issue. Results are analyzed by comparing the predicted axial and tangential velocity profiles and torque to experimentally obtained values. Primarily the runner inter-blades flow is studied as there is a knowledge gap. In addition, the physical phenomena responsible for head losses are studied in detail. Results show that the model can predict the flow relatively well at optimal flow conditions with low swirl but has problems at part load; the tangential velocity between the runner blades is underestimated by ∼20%. The undervalued head losses are the root cause. They result in an overestimated torque and an underestimated tangential velocity as the runner extracts too much energy from the fluid. A small modeling error of 0.5° in the blade angle and a change of 3% in the flow rate significantly affect the tangential velocity and torque prediction. The studied parameters must be considered carefully when building a numerical model.

This work presents an experimental study about the application of acoustic emission (AE) techniques in the monitoring of cavitation erosion mass loss in small Francis turbines. A vertical Francis turbine test bench is specially devised to perform some experiments designed to evaluate the influence of small surface mass losses on turbine blades in the acoustic emission signals. An AE wideband transducer is employed in the test bench instrumentation system. In order to evaluate the AE levels associated with the turbine erosion stages, a small defect is introduced into the turbine runner. This defect is intended to simulate a small mass loss in the turbine runner. The measurements of the AE signals are performed in the Turbine Francis model at two situations: 1) turbine without defect, which means that the runner blades are free of apparent geometric imperfections; 2) turbine with defect, which is represented by a small hole drilled into a runner blade. The AE transducer is installed on the turbine draft tube and the AE measurements are performed at several operating conditions. The preliminary results obtained for the AE amplitude in this investigation show that the small defect introduced into a runner blade causes variations in the AE levels measured in the experiments, confirming that there is a large potential for the application of AE monitoring techniques in the accurate evaluation of cavitation wear on hydraulic turbines in field.

An improved method for preventing vortex rope formation and alleviating the associated pressure fluctuations in turbine draft tubes is investigated using baffles in the draft tube to hinder the swirling flow emerging from a Francis turbine runner. A strong swirl produces flow instabilities and pressure fluctuations. Partial load operating conditions at the rated water head and three flow rates are taken into consideration. It is demonstrated using a computational fluid dynamics simulation that this method effectively eliminates the vortex rope, particularly when using four baffles. The amplitude of the pressure pulsation in the draft tube modified with four baffles was 0.42 times that in a traditional draft tube. The baffles were found to reduce the tangential velocity of the flow in the draft tube and consequently hinder the development of the fierce swirling flow. This type of decrease is more significant compared to the gradual decay due to viscous effects of the solid wall in a traditional draft tube. The conclusion was verified by the results of experiments conducted using a novel device. The measured increase in turbine efficiency exceeded 3% at the evaluated partial loading point, indicating improved economic performance of the turbine.

Flow over a realistic car model: Wall modeled large eddy simulations assessment and unsteady effects

Past numerical and experimental research has shown that the draft tube inlet velocity is critically important to hydropower plant performance, especially in the case of low-head installations. However, less is known about the influence of flow parameters on turbine performance particularly swirl distribution. Based on the influence of draft tube flow characteristics on the overall performance of a low-head turbine, this research proposes a methodology for optimizing draft tube inlet velocity profiles as a new approach to controlling the flow conditions in order to yield better draft tube and turbine performance. Numerical optimization methods have been used successfully for a variety of design problems. However, addressing the optimization of boundary conditions in hydraulic turbines poses a new challenge. In this paper, three different vortex equations for representing the inlet velocity profile are applied to a cone diffuser, and the behavior of the objective function is analyzed. As well, the influence of the quantitative correlation between the swirling flow at the cone inlet and the analytical blade shape, flow rate, and swirl number using the best inlet velocity profiles is evaluated. We also include a discussion on the development of a flow structure caused by the inlet swirl parameters. Finally, we present an analysis of the influence of flow rate and swirl number on the behavior of the optimization process.

Francis turbines are most widely used in hydropower due to their characteristics which include a fast response and wide time-scale operation. The vortex rope inside Francis turbines is a common flow phenomenon, which always causes strong vibration, pressure pulsations, fatigue load, and even serious failure of the components. Vortex suppression methods can effectively change the velocity and pressure distribution of the flow field in the draft tube, reduce the volume of vortex rope and the amplitude of pressure pulsation, inhibit the development of cavitation erosion, and improve the operation stability of the hydro turbine. However, the vortex suppression method is not suitable for all working conditions, and the vortex suppression effect is also different. There are still many problems with how to analyze the vortex suppression effect and practicability of the turbine from multi-dimensions. It is of great significance to analyze the vortex suppression techniques and their practicability in hydraulic turbines from various aspects. The primary focus of the present study is to analyze the hazards of vortex rope in draft tubes and summarize the methods of suppressing vortex rope and pressure pulsation. This review article provides a basis for controlling the vortex rope in the draft tube, which can help the designers choose the suitable control method to mitigate it. Future research directions are also briefly discussed.

Effects of vortex rope formation in draft tube of reversible pump-turbine – A review

Hydraulic turbines need to operate at regimes other than designed ones. Off-design functioning of these turbines yields an inefficient and uneconomical operation of hydro projects. Performance and energy losses at different possible operating conditions need to be evaluated before finalizing the design of water turbines for satisfactory operations. Moreover, hydraulic turbines are unique machines designed for unique set of operating conditions and cost a huge percentage of the overall cost of the project. This work is compiled with twofold objectives; derivation of complete performance characteristics of a 48m head prototype Francis turbine in order to establish an optimum operating regime and, determination and analyses of head loss at different components of the turbine. Steady state flow simulations for four different load operations (60%, 80%, 100% and 120%) have been carried out using computational fluid dynamics. It is found that the optimum regime of operation lies within the speed factor range of 0.412-0.48 along with discharge factor range of 0.27-0.329 and maximum efficiency is obtained as 90.64% at full load operation. Maximum head loss in critical components of the turbine such as runner and draft tube is found as 12.7% at speed factor of 0.568 and 26.31% at 0.202 speed factor respectively. Also, the maximum total head loss in all the components is found as 47.8% at 60% load and 0.609 speed factor. It is concluded that the functioning of the turbine at higher speed factors is more detrimental than that at lower speed factors. Requirement of performance improvement at off-design conditions (especially at 60% load operation) is also suggested in order to widen the range of optimum operating regime. Obtained computational results are validated with experimental results and a strong agreement is found between the two.

Hydraulic turbines with high efficiency over a wide range of operating conditions offer a much sought-after flexibility to electricity producers. However, some low-head turbines exhibit sharp losses of efficiency close to their peak efficiency discharge that are linked to draft tube flow separations whose causes remain misunderstood. This paper presents the latest results obtained in the scope of the BulbT project that focused on the flow dynamics related to the efficiency drop. The main objectives are to document the transient characteristics of the flow in the hub-wake region and investigate interactions between the core flow and wall separations to identify potential mechanisms explaining the efficiency drop. Using proper orthogonal decompositions of synchronized time-resolved velocity and pressure measurements, highly energetic modes representing stochastic perturbations across BulbT's draft tube are identified. These perturbations occur only for the discharges affected by the efficiency drop, past the best efficiency point. Despite the absence of near-wall velocity measurements, the modal decompositions provide evidence that the onset of the efficiency drop is the result of two independent types of flow separation that occur on opposite sides of the draft tube. Upstream separations are found to happen simultaneously with an asymmetric acceleration of the flow in a region surrounding the turbine's axis and the tip of the runner hub and become the most important contributor to the efficiency drop at the highest measured flow rate. Furthermore, the likeliness of observing one kind of flow separation increases after it has already occurred, pointing to a strong history effect.

Investigations of the thermodynamic entropy evaluation in a hydraulic turbine under various operating conditions

At both partial and full load of Francis turbines, the unsteady behavior of cavitating draft tube vortices occurs and leads to undesirable matters such as power house vibration, noise and power swing in some cases. This paper presents the investigation of the interaction between the flow pattern at runner outlet and the unsteady behavior of cavitating vortices in draft tube with experimental and numerical approaches. On the experimental research, the pressure pulsation in the draft tube is measured and the unsteady behavior of cavitating vortices is taken pictures with a high speed camera in the model test. On the numerical research, by Computational Fluid Dynamics (CFD) adopting a two-phase unsteady analysis, the analysis domain from the guide vane to the draft tube is carried out for investigating the interaction between the runner outlet flow and the vortex pattern. The pressure pulsation at the upper draft tube and the unsteady behavior of cavitating vortices obtained from CFD results are similar to those obtained in the model test. Detailed analysis of CFD results at overload indicates the repeat of expansion and contraction of cavitating vortices, which were shaped helical vortices with opposite direction of runner rotation, and the corresponding flow pattern in every time step of the pressure pulsations.

The vortex rope in the draft tube is considered as the major contributor to pressure pulsation at partial load (PL) conditions, which causes the hydro unit to operate unstably. Based on the prototype Francis turbine HLA551-LJ-43 in the laboratory, J-grooves are designed on its conical section in this paper. We used numerical simulation to study the effect of the J-grooves on vortex suppression and energy dissipation in the draft tube. Four typical operating conditions were chosen to analyze the vortex suppression; the corresponding flow ratios Q* are 100%, 82%, 69%, and 53%, respectively. Entropy production theory is used to calculate the energy losses and assess the effect of the J-groove on energy dissipation under part-load conditions. By comparing entropy production, circumferential and axial velocity components, swirl intensity, pressure pulsation, and vortex distribution in a draft tube with and without J-grooves at different operating conditions, it can be concluded that the entropy production on the wall containing a conical section with J-grooves is obviously smaller than that without J-grooves, the effects of J-grooves on reducing circumferential velocity component Vu, pressure pulsation, and weakening vortex intensity and vortex rope in the conical section are obvious, especially at part load and deep part-load operating conditions. Using J-grooves shows better performance on vortex control and energy dissipation in the draft tube of a Francis turbine at partial load conditions.

ABSTRACTThe operation of Francis turbines at off-design conditions may cause the development of a cavitation vortex rope in the draft tube cone, acting as a pressure excitation source. The interactions between this excitation source and the hydraulic system at the natural frequency may result in resonance phenomena, causing serious hydro-mechanical oscillations. One-dimensional draft tube models for the simulation and prediction of part load resonances require an accurate modelling of the wave speed and the bulk viscosity for the draft tube flow. This paper introduces a new methodology for determining these two hydroacoustic parameters in the draft tube of a reduced scale physical model of a Francis turbine, based on experimental identification of the hydraulic natural frequency of the test rig. Finally, dimensionless numbers are derived to define both the wave speed and bulk viscosity for different operating points of the turbine.