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Guide vanes are a mechanical system used to direct flow in the desired direction. At lower operating conditions, implementing a guide vane system in the draft tube of a hydro-turbine can decrease the excess swirl in the flow and, thus, reduce pressure fluctuations. The present study discusses a numerical methodology to design an effective guide vane system in the draft tube of a high head Francis model turbine. The numerical method is computationally efficient and thus, saves excess computational time and data storage required for parametric analysis of the guide vane system. The aim is to mitigate the ‘rotating’ vortex rope with minimum additional losses in the turbine. The factors considered for the guide vane system design are a) number of guide vanes, b) chord length, c) span, d) inlet-outlet angles of the guide vanes, and e) their position in the draft tube. The parametric study comprises a) ideal guide vane design and b) realistic guide vane design study. The ideal guide vane design study was with the standalone draft tube domain. The realistic guide vane design study used the passage domains of the distributor, runner, and complete draft tube. From the ideal guide vane design study, a guide vane system with two or three guide vanes of chord 86% of runner radius and leading-edge span of 30% of runner radius effectively mitigates the rotating vortex rope. The system with three guide vanes is the most efficient when placed at some distance below the runner exit with mitigation above 95%. Validerad;2022;Nivå 1;2022-06-15 (hanlid)

The performance of energy recovery turbine (ERT) directly determines the cost and energy consumption of reverse osmosis desalination. In order to study the performance and loss mechanisms of ERT under different conditions, the external characteristics and the losses of different components were quantitatively analyzed. The loss mechanisms of each component in the turbine were revealed through the comparative analysis of the internal flow field. The results show that the efficiency is 2.2% higher than that at the design speed when turbine runs at n = 22000 r/min. The impeller losses account for more than 67% of the total losses. The impeller loss is mainly observed at the leading edge. The vortex on the pressure side of the leading edge is caused by the impact effect, while the vortex on the suction side of the leading edge is caused by the flow separation. With the increase in the rotating speed, the loss caused by flow separation in impeller decreases obviously. The volute loss is mainly observed near the tongue, which is caused by the flow separation at the tongue. The design of the tongue is very important to the performance of the volute. The turbulent kinetic energy (TKE) and loss decrease with the increase in the rotating speed. The loss in the draft tube is mainly observed at the inlet core. With the increase in the rotating speed, the turbulence pulsation and the radial pressure fluctuation amplitude reduce. Therefore, the turbine can be operated at the design or slightly higher than the design rotating speed under the condition that both the hydraulic condition and the intensity are satisfied, which are conducive to the efficient utilization of energy.

Flow instability and pressure fluctuation are common problems in hydro turbines, especially in partial flow conditions. When Francis hydro turbine operates at partial flow rate, swirl flow occurs at the runner outlet, which is the cause of pressure pulsations, vortex core, noise and vibration in the draft tube. Among various methods, J-groove was selected and mounted in the draft tube to suppress the swirl flow. The study focuses on the J-groove incorporation in a draft tube from the design process to optimization. The optimization focused on the suppression of swirl flow with minimum efficiency drop. The turbine efficiency and swirl number were selected for the optimization, which encounters global and local effects of J-groove installation on the Francis hydro turbine. J-groove shape optimization was performed by response surface methodology (RSM) and multi-objective genetic algorithm (MOGA). The flow behavior in the draft tube was compared without and with the initial and optimal J-groove shapes. The optimal J-groove shape is more effective in swirl flow suppression than the initial J-groove shape. Additionally, the installation of the J-groove did not hinder turbine performance. Therefore, the optimal J-groove shape improved flow behavior in the draft tube at the partial flow rate.

The vortex rope usually occurs in the draft tube of the Francis turbine operated under part-load conditions, to induce strong low-frequency pressure vibrations, and therefore, is very harmful to the safety of the hydropower unit. In the present work, three kinds of strategies are extensively investigated, i.e., the installations of the ventilation and the fin, as well as the hybrid strategy of the air admission through a fin, so as to effectively suppress the vortex rope oscillation and the pressure vibration in the draft tube of a Francis turbine, whose specific speed is 125 m-kW. For the unsteady flow simulation, the Reynolds averaged Navier-Stokes (RANS) method is applied coupled with the k-ω SST turbulence model and a homogeneous cavitation model. The flow analysis confirms that the low-frequency pressure vibrations are originated from the periodical oscillation of the vortex rope, and the cavitation usually enhances the vortex rope oscillation in the draft tube. Under the part-load condition, the dominant component of the pressure vibration in the draft tube has a frequency, for example, f1, lower than the runner rotating frequency fn. It is shown that all three strategies can be adopted to alleviate the vortex rope oscillation and the pressure vibrations in the draft tube, but their suppression mechanisms are quite different. The ventilation of an adequate amount from the turbine runner cone can change the vortex rope geometry from the spiral type to the cylindrical type, suppress the vortex rope oscillation, and consequently create the homogeneous distributions of the pressure and the pressure gradient in the draft tube. On the other hand, a fin installed at the draft tube wall can induce a small extra rope, and the interaction between the main vortex rope and the extra rope changes the flow field and alleviates the pressure vibration in the draft tube. It should be noted that a fin is much more effective to suppress the pressure vibration in the draft tube under the cavitation condition than under the non-cavitation condition. A better effect of suppressing the vortex rope oscillation can be achieved by the air admission through a fin, which is studied numerically in this paper. The result indicates that the air admission can further improve the effect of a fin for suppressing the pressure vibration in the inlet cone of the draft tube. This improvement is due to the stronger interaction between the main vortex rope and the extra air rope. However, the air admission through a fin should be carefully treated because the strong interaction may induce a larger pressure vibration in the elbow of the draft tube. Finally, it is clear that any strategy for suppressing the pressure vibration hardly changes the dominant component frequency f1, which is in the range of 0.22 fn-0.23 fn due to the main vortex rope oscillation in this study. The current results may be used in various engineering applications, where the active control of the vortex oscillation and the pressure vibrations with or without the cavitation is necessary.

A surrogate-model-based design optimization methodology using Genetic Algorithm to maximize the Static Pressure Rise (SPR) in conical draft tubes is presented. A set of accurate and computationally intensive data obtained from ANSYS-CFD simulations on space filling samples is used for developing a surrogate model. The methodology uses (i) A Latin hypercube experimental design for selecting space filling samples, (ii) Genetic Algorithm for determining parameters of a radial basis function based Kriging model formulated as minimization of a negative log-likelihood function and (iii) length of the straight portion (L), angle of divergence (αd) and inlet swirl angle (αsw) of draft tube as explanatory variables. Flow in the draft tube is characterized by the presence of wall separation, recirculation and axial vortex rope occurring under different inlet swirl and angle of divergence. The study shows that a flow consisting of a low intensity axial vortex rope near the exit of the draft tube is desirable for better distribution of flow in the radial direction for preventing the wall separation and recirculation in high area ratio draft tubes. It is found that the design variable that controls the development and structure of axial vortex rope is the inlet swirl. Verification using CFD analysis showed that the process of optimization has been able to fine-tune the inlet swirl angle that facilitated an optimum sized vortex rope at the center to cause uniform exit axial velocity and improved flow diffusion without wall separation, resulting in significant improvement in Static Pressure Rise.

Penetration of variable renewable energy into the electric grid requires parallel employment of power generation sources that can quickly balance the fluctuation in frequency of electric grid. Hydro power, being one of the most flexible power supplies, thus takes on an instrumental role in balancing the grid. However, in hydraulic turbines such flexibility is achieved at the expense of departure from turbine operation at the best efficiency point (BEP). Turbine operation at off-design conditions like part load (PL) or high load (HL) results in significant flow instability in the draft tube. Of particular prominence is the vortex breakdown phenomenon which manifests as a precessing vortex rope in the draft tube. The vortex rope causes dynamic pressure fluctuations in the system, additive to the compromise in efficiency. If resonant with the system natural frequency, these pressure fluctuations may affect the mechanical torque delivered by the turbine and cause a phenomenon called power swing. As such it is of paramount importance to circumvent the effects of the rope. Amidst many techniques developed by various investigators for mitigation of the rope, particularly recent the ancillary fluid injection technique exhibits promise. Ancillary fluid injection involves riddance of the stagnation zone that leads to rope formation, through transfer of momentum from a fluid injected at an appropriate location and velocity. This is usually accomplished using water. Admission of air for flow aeration is another method. An experimental as well as numerical perspective of these techniques as developed by various researchers is laid, to assess the benefit obtained alongside the entailing compromise.

The flow characteristics of the draft tube of a Francis turbine have a significant influence on turbine stability. Numerical simulations were performed for a Francis turbine under three different output conditions of 20%, 100%, and 120% at the rated and maximum heads. Laser Doppler velocimetry (LDV) tests were conducted to test the flow characteristics of the draft tube of the Francis turbine model. The flow characteristics in the draft tube, the mechanism of the flow characteristics change, and the effect of the opening on the vortex rope were analyzed. The results showed that the large and invisible vortex in the conical cross-section at the inlet of the draft tube gradually changed to a tangible vortex rope as the guide vane opening (GVO) increased. The pressure and velocity are significantly influenced by the GVO, and the flow characteristics in the draft tube improve as the GVO increases. Simultaneously, the influence range of the vortex rope increased as the head increased.

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.

The turbulent flow in the draft tube of a Francis turbine is very complicated while working under off-design conditions. Although the off-design conditions were widely studied, the vortex core line in the draft tube of a Francis turbine with splitter blades is not well understood, especially the vortex rope property. This letter presents a prediction of the behavior of the vortex rope in the draft tube of the Francis-99 turbine obtained by the computational fluid dynamics (CFD), where the Liutex/Rortex method, as the most recent vortex definition, is applied to analyze the periodical precession of the vortex rope in the draft tube cone. The advantage of this Liutex/Rortex method is shown by its enhanced ability to represent the vortex rope structurewith the vortex-core lines. Furthermore, since it seems to be very hard to define a sharp boundary surface for the whole vortex structure, it is advantageousfocusing only on the vortex core line,by which different vortex structures can be clearly differentiated. The evolution of the vortex core and the process of the vortex breakdown in the draft tube are revealed, which might help to comprehend the development of the turbulent flow in the draft tube.

International audience; Under the current global energy crisis the interests in developing a third generation of biofuels produced from non-food feedstock such as microalgae and cyanobacteria have clearly increased. Hydrodynamic stress, always present in cultivation process of these microorganisms, is an essential factor to ensure mixing inside bioreactors; however the importance of its intensity is usually ignored by applying a random agitation (energy consumption) which is unnecessarily overestimated. In this work, two types of agitation, stirring in agitated photobioreactors (APBR) and bubbling air in draft tube airlift photobioreactors (DPBR), are applied to study the effects of hydrodynamic stress on the growth and pigment content evolution of the cyanobacteria Synechocystis sp. PCC 6803, a self-propelled microorganism. The range of applied shear stress was between 0 and 400 mPa. Similar results are obtained for both agitation mechanisms, indicating that the effects of shear stress are limited to the breakdown of the cell colonies; once they are broken down any further increase in shear stress has no significant effect on their growth rate. Moreover, the variation in pigments concentration appeared to be linear with the cellular concentration and independent from shear intensity.

The swirling trajectory of the draft tube flow improves the pressure recovery. Resultant flow instabilities are still problematic for an optimized hydropower generation. Engineering solutions are getting increasing importance. However; the depth of wall-mounted countermeasures is a challenging parameter. Performance assessment of countermeasures would rate dampened pressure pulsations in terms of their sources so as to place them at a proper location. A method for evaluating the instability in the outlying domain of the draft tube cone is herein suggested. Two part-load operating points with opposite polarity in pressure pulsations have been investigated. The numerical approach of Shear Stress Transport has been used, and experimental agreement of measurements for the pressure spectra is verified at the wall. Inlet flow conditions and the growth of the core instability are described. The outlying domain of the draft tube has been found to be composed of three distinct zones of influence: the shortest upper cone with upstream travelling influences, the longest middle cone with core excitation, and the lowermost cone dominated by the backward elbow influence. The wall response lies within a definite high-frequency range proper to the operating point. During admission, the frequency range becomes even wider due to high kinetic energy and the highest pressure amplitude of the draft tube is developed by the impact of blade passing frequency. The excitation from the vortex rope precession in the outlying domain strongly depends on the operating condition. Thus, further works should extend this study over a wider operation range, and mount pressure sensors on countermeasures in order to identify their own instability contribution.

This paper focuses on the generation of twin vortex rope in the draft-tube elbow of a Francis turbine at deep part-load operation through analyzing the results of model tests along with numerical simulations. Model tests, including pressure fluctuations measurements, are conducted over ten speed factors. By considering the frequency of the pressure fluctuations with respect to the swirl intensity at the runner outlet, the part-load operating range is divided into three regimes, with two clear transitions between each occurring at swirl numbers 0.4 and 1.7. For operating conditions with a swirl number S > 0.4, a linear correlation between the frequency of the precessing vortex core and the swirl number is established. During the deep part-load regime (S > 1.7), low-frequency pressure fluctuations appear. Their frequency features another linear correlation with the swirl number. Unsteady computational fluid dynamics simulation of the full domain is performed to elucidate the generation mechanisms of the low-frequency fluctuations. By tracking the center of the vortical structures along the draft-tube, generation of three vortices in the elbow responsible for the pressure fluctuations at the lowest frequency is highlighted: the main precessing vortex core (PVC) hits the draft-tube wall in the elbow resulting in its break down into three vortices rotating with half the rotational speed of the PVC. Two of the vortices rotate with opposite angular position, constituting a structure of twin vortices. The periodic rotation of these three vortices in the elbow induces low-frequency pressure fluctuations.

Francis turbines operating at part load conditions develop a cavitation precessing vortex known as a vortex rope in the draft tube cone below the runner outlet. At part load conditions, this vortex precession acts as an excitation source inducing pressure pulsations in the whole hydraulic system at the vortex precession frequency. Simultaneously, the lower pressure levels in the vortex core can lead to cavitation development, increasing the local flow compliance and reducing drastically the pressure wave speed. As a result, the eigen-frequencies of the hydraulic circuit are lowered and may match the vortex rope excitation frequency, leading to undesired resonance conditions. This paper presents a procedure to predict this type of resonance phenomenon in turbine prototypes by performing reduced scale physical turbine model measurements and eigenvalue calculations with linearized system matrices. This new procedure requires the transposition of hydroacoustic parameters from the reduced scale physical model to the prototype scale based on the swirl number and the local cavitation coefficient similarity. The procedure is validated by measurements performed on a turbine prototype featuring a peak of power swings and pressure pulsations in the predicted operating conditions. (C) 2019 Elsevier Ltd. All rights reserved.

The flow in the draft tube of a Francis turbine is highly complex and unstable when the turbine operates far from its design point. To extend the Francis turbine operation range to meet the variable energy demand, a J-groove technology is introduced on the turbine draft tube wall to stabilize the unsteady flow in the draft tube. However, J-groove contributes to energy losses in the draft tube. In this study, the J-groove shape optimization process is proposed based on steady flow analysis using the response surface method. The energy loss and swirl intensity in the draft tube are selected as objectives for the optimization design. The flow characteristics in the draft tube without J-groove and with initial J-groove and optimized J-groove shape are compared. Results show that the swirl intensity in the draft tube with the optimized J-groove is suppressed effectively with the low energy loss in the draft tube. Moreover, the pressure fluctuation in the draft tube with the optimized J-groove is mitigated significantly to stabilize the Francis turbine operation under the off-design point condition.

The cavitation developed in the Francis turbine draft tube is known to be a source of the hydraulic instability, especially under the conditions with columnar cavitation vortex rope occurring in the draft tube. The hydraulic system will suffer from the risk of the self-excitation and the high pressure pulsations because of the dynamic features of the complex cavitation vortex rope. The links between the cavitation dynamic characteristics and the hydraulic system stability are important for an accurate system instability prediction. For this purpose, the cavitating flows in a Francis turbine operating under the overload conditions are simulated by using the Zwart-Gerber-Belamri (ZGB) cavitation model. The cavitation dynamic parameters in different cavitation development stages and the evolutions under various overload conditions are analyzed and compared in this paper. It is shown that the cavitation dynamic parameters, including the cavitation compliance, the mass flow gain factor and the wave speed, can well represent the cavitation characteristics with the vortex rope evolution. The predicted cavitation dynamic parameters are in a reasonable agreement with other available results, with an obvious dependency on the loads. The results obtained in this study are relevant to the system stability analysis.

The vibration problem of hydraulic generating unit and plant structures in hydropower station influenced mainly by pressure fluctuation of draft tube and other factors during the transient process is dramatic, whereas the relevant theoretical research is seriously lagged behind the actual engineering practice. Aiming at this present condition, firstly, a mathematical expression of hydraulic excitation induced by draft tube vortex under different load conditions is proposed from the perspective of theoretical analysis. Then, based on the hydraulic-mechanical-electrical-structural model of hydroelectric generation system established previously, the sudden load increasing transition process is incorporated into the investigation system of unit-plant structure vibration, and the corresponding dynamic characteristics under this non-stable operation condition are studied. The calculation results show that, compared with steady working condition, the operation stability of unit shaft system is decreased and the matching vibration amplitude is obviously increased during the transient process. Meanwhile, in contract to the unit shaft system, the oscillation phenomenon of generator floor in hydropower plant is more significant. In particular, the vertical direction vibration is extremely prominent that the displacement amplification can even reach several times of that when the system is operated stably. The research in this paper can not only reflect the vibration behavior of unit-plant structure in sudden load-up process to some extent, but also provide reasonable and reliable analysis model and method for dynamic response exploration, stability investigation, as well as fault diagnosis for the hydraulic generating unit and hydropower plant structures.

The synchronous pressure surge effect is a critical phenomenon occurring in Francis turbines operating at part load conditions. In this regime, pressure fluctuations are predominantly coming from the temporal rotation of a single helical vortex inside the turbine draft tube, called the part load vortex rope. However the combination of multi-physics interactions, geometry, cavitation, swirling flow and acoustic waves leads to a pressure amplification, called the synchronous pressure surge effect, which is more dangerous than the fluctuations resulting from the precessing vortex rope. While this subsequent amplification mechanism has been unraveled, the physical mechanism originating in the synchronous pressure wave remains poorly understood. We have therefore investigated the birth and the growth of the synchronous pressure wave in Francis turbines. By energy consideration of an azimuthal–temporal Fourier decomposition of the three dimensional numerical flow solutions in an axisymmetric draft tube geometry that is slightly disturbed at the wall, the source of the synchronous pressure and its amplification region are identified. In addition, the origin of this wave as the interaction of a wall disturbance with the part load vortex rope, is investigated using an asymptotic analysis and brings deeper comprehension of the synchronous wave generation mechanism.

The present research aims at understanding the mass transfer of air into water in a reversible pump turbine operating in condenser mode. In particular, the diffusion of oxygen through the water free-surface both in the vaneless gap between the impeller blades and the closed guide vanes and in the cone of the draft tube is investigated. A theoretical framework is carried out to compute the diffusion equation describing the oxygen diffusion process in the investigated machine. Oxygen concentration measurements together with temperature and wall pressure measurements are performed to validate the theoretical model of the mass transfer of oxygen in the water volume and to evaluate the influence of the densimetric Froude number, of the gauge pressure and of the cooling discharge on the diffusion process. Moreover, the analytical solution of the diffusion equation applied to both the free surfaces in the vaneless gap and in the cone of the draft tube allows computing the global diffusion coefficient for each air–water free-surface. The results show that the oxygen concentrations computed by the analytical model of the oxygen diffusion are in agreement with the measurements. The dependency of the oxygen concentration in water on the densimetric Froude number, on the gauge pressure and on the water cooling discharge is also observed. The computed global diffusion coefficients are mainly dependent on the densimetric Froude number in the vaneless gap and in the cone of the draft tube. Finally, the results achieved allow estimating the air losses correlated to the oxygen diffusion causing the increase of the water level in the cone of the draft tube.

Large eddy simulations of a ventilated pump-turbine were conducted using LES-mixture model. Peripheral and central aeration were applied to study the effectiveness of oxygen dissolution and the pump-turbine performance. The peripheral draft tube aeration was performed by air injection through (1) a continuous orifice and (2) a series of discrete orifices along the surface of the draft tube. The simulations were performed when the system is operating in the turbine mode. Peripheral aeration was more effective for the achieved dissolved oxygen level and the oxygen dissolution efficiency. The mean dissolved oxygen concentration and the dissolution efficiency inside the draft tube were predicted to be 1.8 mg/l and 80% using the continuous or discrete peripheral aeration and 1.4 mg/l and 25% using the central aeration. A mean value ranging from 1.0 mg/l to 2.0 mg/l was considered to be sufficient for aerobic bacteria to treat the wastewater. Aeration resulted in a minor penalty on the power generation, while it provided a significant reduction in the flow-induced vibration. The central aeration was more effective in reducing the amplitude of pressure fluctuations and yielded more stable turbine operating conditions.

Undesirable pressure pulsations will be induced by flow instabilities in the draft tube when the Francis turbine operates at off-design conditions, which have multiple effects on the steady operation, and the effects vary with the operating condition. Therefore, the establishment of a comprehensive state evaluation index of the draft tube pressure pulsation (DTPP) is of great practical significance. In this study, a comprehensive evaluation method of DTPP has been proposed based on Ensemble Empirical Mode Decomposition (EEMD) and information entropy. First, the frequency components of DTPP are separated by the EEMD method which is more suitable for the analysis of non-stationary pressure pulsation signal. Second, to eliminate the effects of noise, a targeted EEMD noise reduction method which is combined with autocorrelation analysis and wavelet soft-threshold de-noising method is designed for the DTPP signal. Then, index energy values of all frequency components are calculated and normalized, and the values of the signals’ characteristic entropy are obtained by using the normalized index energy vector as the input vector. Finally, characteristic entropy values of all pressure pulsation signals measured from the draft tube are integrated into an index, which is named as the comprehensive characteristic entropy of DTPP (E_DTPP). The state of DTPP is comprehensively evaluated by E_DTPP. This method was evaluated by the actual measuring data of a 200 MW hydroelectric generating unit. The case study indicates that this single index can be utilized to evaluate the actual state of DTPP, and pressure pulsations will have distinct influence on the operation stability when E_DTPP increases obviously. The efforts of this study provide a novel and useful method for the comprehensive state evaluation of DTPP, and the E_DTPP could be used as an index for the stability of Francis turbine.

To develop an optimum design method for impulse water turbines with low specific speed, a representative impulse water turbine with low specific speed used in agricultural irrigation machinery was optimized with a combination of an orthogonal experimental design, a genetic algorithm, and a BP neural network in this study. Numerical calculation was applied to analyze interflow characteristics for optimized and original water turbines. Results showed that the internal flow characteristics of the optimized water turbine presented remarkable improvement compared with the original water turbine. Pressure distribution increased, the vortex strip in the draft tube was reduced remarkably, and impeller torque increased by 26 %. In addition, the optimized impeller was manufactured by 3D printing, and performance comparison was conducted between experiments of the optimized and original water turbines. The efficiency of the optimized water turbine reached 42.5 %, which exceeded the original water turbine’s of 8.5 %. With increasing rotating speed, maximum efficiency running point moved to a high flow rate, and highly efficient areas expanded. Internal characteristic analysis and a full-scale experiment for both water turbines showed that the performance of the optimized water turbine exhibited substantial improvement. The analysis and experiment also verified the theoretical correctness and feasibility of the proposed optimum design method.

Intense vibrations in hydraulic turbine generator unit draft tubes lead to a run-out of the unit shafting and threaten its safe and stable operation. Correct maintenance is therefore important for the safe operation of such units. This study involves assessing the condition of the turbine generator unit by extracting the feature information of its vibration signals. Based on previous research, we present an enhanced Hilbert–Huang transform (HHT) method with an energy-correlation fluctuation criterion to extract feature information and effectively verify the method with simulated signals. An inspection application based on the signal from a vortex strip in the draft tube of a prototype turbine under suboptimal operating conditions indicates that this method is more effective than the traditional one, with a better component identification capability and better suited to the analysis of the complex and dynamic feature information of hydro turbines.

The effective utilization of micro hydropower sources is often realized through the use of pumps as turbines (PAT). The efficiency of PAT is about the same as that of the original pump. A further increase in efficiency and power output can be achieved by modifying the parts interacting with the flow, especially the impeller and the adjacent volute casing and draft tube. This paper presents a user-friendly calculation model of Francis turbine design and its application for PAT geometry modification. Two different modifications of a single-stage radial centrifugal pump were designed according to this model. The first modification (Turbine) consisted of a complete revision of the impeller geometry, volute casing and draft tube, which corresponded to a conventional Francis turbine. The second modification (Hybrid) was based on altered calculation model and consisted of a modification of only the impeller, which can be used in the original volute casing. Both modifications were tested on hydraulic test circuit at different heads. A comparison of the results of the Hybrid and the Turbine modification with the unmodified machine (Original) proved an increase in overall efficiency by 10%. Both modifications provided a higher flow rate and torque. This resulted in an overall power output increase—an increase of approximately 25% and 40% due to the Turbine and Hybrid modifications, respectively.

Numerical investigation was performed on a semi-model (one stay vane, two guide vanes, one runner passage inclusive of one main and one splitter blade, and the draft tube) of a high-head Francis turbine model with adjustable guide vanes in the draft tube. The motive of the present study is to investigate the possibility to mitigate the rotating vortex rope (RVR) formed at part load operating condition. Each guide vane in the draft tube consists of two hydrofoils. The upper hydrofoil is adjustable according to the flow angles leaving the runner. The lower hydrofoil is stationary and corresponds to the flow angle at best efficiency point (BEP).The factors considered while designing these guide vanes were a) number of guide vanes, b) chord length, c) span and d) position in the draft tube. The preliminary results indicate that the RVR pressure amplitude was suppressed by 97% compared to the reference model with no guide vanes at part load (PL) operating condition. An 8.7% increment in the draft tube pressure recovery was obtained which indicates that implementation of the guide vanes in the draft tube could positively impact the turbine efficiency beside the mitigation of the pressure pulsations at PL operation.

In the present study, a reduced model of the Francis-99 model turbine was investigated numerically at part load operating condition. The reduced model consists of a standalone draft tube domain of the Francis-99 model turbine. Numerical studies performed in the past on nearly complete hydro-turbine models (inclusive of the spiral casing, distributor domains, runner, and draft tube) reportedly consist of a large number of computational grids. This may increase the computational costs and data storage required to perform numerical analysis, which could be a setback for future research on new design concepts and optimization study of the draft tube domain. The reduced model was developed by mapping the phase averaged axial, radial, and tangential velocity profiles from the runner exit to the inlet of the standalone draft tube domain. Additionally, turbulent kinetic energy (k) and turbulent eddy dissipation (ε) variables were also considered for better flow prediction inside the draft tube domain. Two methods for mapping inlet boundary conditions were considered in the present study. In the first method, the entire planar profile of the runner-draft tube interface was considered. In the second method, the variables along a radial profile at the runner exit were considered with an axis-symmetric flow assumption over the entire draft tube inlet plane. The numerical results obtained from the Francis-99 reduced model turbine were validated against the numerical model of the NVKS Francis-99 model turbine (with available structured mesh) that was also analysed using the passage flow numerical technique and available experimental results. The results were found to be in reasonable agreement, with each other. The present study could be useful for the future mitigation study of rotating vortex rope by modifying the draft tube domain. Validerad;2021;Nivå 2;2021-08-10 (alebob)

The draft tube of a hydraulic turbine plays an important role for the efficiency and power characteristics of the overall system. The shape of the draft tube affects its performance, resulting in an increasing need for data-driven optimisation for its design. In this paper, shape optimisation of an elbow-type draft tube is undertaken, combining Computational Fluid Dynamics and a multi-objective Bayesian methodology. The chosen design objectives were to maximise pressure recovery, and minimise wall-frictional losses along the geometry. The design variables were chosen to explore potential new designs, using a series of subdivision-curves and splines on the inflow cone, outer-heel, and diffuser. The optimisation run was performed under part-load for the Kaplan turbine. The design with the lowest energy-loss identified on the Pareto-front was found to have a straight tapered diffuser, chamfered heel, and a convex inflow cone. Analysis of the performance quantities showed the typically used energy-loss factor and pressure recovery were highly correlated in cases of constant outflow cross-sections, and therefore unsuitable for use of multi-objective optimisation. Finally, a number of designs were tested over a range of discharges. From this it was found that reducing the heel size increased the efficiency over a wider operating range.

The applicability of the spouted bed technique to drying of granular products that are too coarse to be readily fluidized was recognized in the early 1950s. The classic or conventional spouted bed is a cylindrical vessel with a conical bottom fitted with an inlet nozzle for introduction of the spouting air. The wheat drying studies were carried out in a spouted bed predryer of rectangular cross-section equipped with a draft tube, and also in a cylindrical afterdryer. A number of prototype spouted bed dryers have been used to dry shelled corn. The spouted bed is potentially an excellent alternative for drying such materials. Spouted beds for drying of granular materials, pastes, and slurries are an emerging technology. Two-dimensional spouted beds, such as those proposed by Mujumdar, have a decided advantage as far as scaleup and modular design are concerned.

The proficiency of a hydraulic reaction turbine is essentially influenced by the exhibition of its draft tube. The shape and speed dispersion at the bay are fundamental components which influences the exhibition of the draft tube. Customarily, the structure of this part has been based on improved analytical methods, test thumb rules and model tests. In the last decade or two, the use of computational liquid elements (CFD) has significantly expanded in the plan procedure and will keep on becoming due to is adaptability and cost-viability. A CFD-based structure search can additionally be supported with a hearty and easy to use advancement outline work hypothesis and building. In this paper, parametric modeling has been executed to adjust the elements of parts by methods for expert program to diminish geometric modeling time in the overhaul. The CFD examination has additionally been done for finding the pressure and velocity distribution, which are coordinating with test readings. The draft tube configuration has been adjusted dependent on writing and assembling potential outcomes. &nbsp

In load rejection transitional processes in pumped-storage plants (PSPs), the process of closing pump turbines, including guide vane (GVCS) and ball valve closing schemes (BVCS), is crucial for controlling pulsating pressures and water hammer. Extreme pressures generated during the load rejection process may result in fatigue damage to turbines, and cracks or even bursts in the penstocks. In this study, the closing schemes for pump turbine guide vanes and ball valves are optimized to minimize water hammer and pulsating pressures. A model is first developed to simulate water hammer pressures and to estimate pulsating pressures at the spiral case and draft tube of a pump turbine. This is combined with genetic algorithms (GA) or non-dominated sorting genetic algorithm II (NSGA-II) to realize single- or multi-objective optimizations. To increase the applicability of the optimized result to different scenarios, the optimization model is further extended by considering two different load-rejection scenarios: full load-rejection of one pump versus two pump turbines, simultaneously. The fuzzy membership degree method provides the best compromise solution for the attained Pareto solutions set in the multi-objective optimization. Employing these optimization models, robust closing schemes can be developed for guide vanes and ball valves under various design requirements.

Cavitation is recognized as a phenomenon that can cause serious damage to a hydro turbine and can reduce its performance when operating at off-design point. This is an undesired phenomenon, which needs to be improved. In order to suppress the cavitation in the Francis turbine draft tube, a technology with grooved draft tube named J-Groove is introduced in the Francis turbine. The Francis turbine performance and the internal flow characteristic are investigated both with and without J-Groove installation by the experimental method and numerical simulation. Visualization was used to capture the cavitation rope in the Francis turbine draft tube to compare with the computational fluid dynamics analysis result. The results show that the turbine performance both with and without J-Groove installation is quite similar. Regardless of impact on performance of Francis turbine by J-Groove, it suppresses the cavitation vortex rope and pressure fluctuation in the Francis turbine draft tube efficiently.

The transient flow in pump-turbines during the load rejection process is very complex. However, few studies have been conducted on three-dimensional (3-D) numerical simulation. Hence, we simulated 3-D transient turbulent flow in a pump-turbine during the load rejection process using the calculation method of coupling the flow with the rotor motion of rigid body. To simulate the unsteady boundary conditions, the dynamic closing process of the guide vanes was simulated with the dynamic mesh technology. The boundary conditions at the spiral-casing inlet and the draft tube outlet were determined using the user defined functions (UDF) according to the experimental data. The numerical results of the rotational speeds show a good agreement with the experimental data. Then, the complex transient flow in the pump-turbine during the load rejection process was analyzed based on the numerical results. The results show that there are severe unsteady vortex flows in the vaneless space near the conditions under which the hydraulic torque on the runner equals to zero. When the pump-turbine operates into the maximum reverse discharge condition in the reverse pump operating process, the unsteady vortex flows in the vaneless space are instantaneously impacted into the region between the guide vanes and the stay vanes by the sudden reverse flows. The formation and development mechanism of the unsteady vortex flow in the vaneless space is associated with the distribution characteristic of the velocity field.

Owing to the part-load operations for the enhancement of grid flexibility, the Francis turbine often suffers from severe low-frequency and large-amplitude hydraulic instability, which is mostly pertinent to the highly unsteady swirling vortex rope in the draft tube. The influence of disturbances in the upstream (e.g., large-scale vortex structures in the spiral casing) on the draft-tube vortex flow is not well understood yet. In the present paper, the influence of the upstream disturbances on the vortical flow in the draft tube is studied based on the vortex identification method and the analysis of several important parameters (e.g., the swirl number and the velocity profile). For a small guide vane opening (representing the part-load condition), the vortices triggered in the spiral casing propagate downstream and significantly affect the swirling vortex-rope precession in the draft tube, leading to the changes of the intensity and the processional frequency of the swirling vortex rope. When the guide vane opening approaches the optimum one (representing the full-load condition), the upstream disturbance becomes weaker and thus its influences on the downstream flow are very limited.

We report on experimental study of flow and pressure pulsations in draft-tube of a laboratory air model of Francis-99 hydro-turbine operating over a broad range of regimes employing a rapid prototyping of the swirl generators and computerized measurements. In total, 867 operating regimes were examined corresponding to different combinations of the runner rotation speed and flowrates. The velocity measured by a computer-automated laser-Doppler anemometer and the pressure recording by wall-mounted acoustic sensors for a selection of operating conditions reveal a variety of patterns of the flow and vortex structures, with clearly identifiable regimes with the maximum coherent flow pulsations at non-optimal operating conditions. The regimes with distinct precessing vortex cores show notable rearrangement of the velocity and vorticity fields, accompanied by a sharp increase in the amplitude of the coherent pressure pulsations, as also confirmed by the peak cross-correlation of the spectra of pressures signals from two diametrally placed wall-mounted microphones. The paper closes with a scrutiny of the swirl number, its distribution and the relation of zero-swirl with the isogonal best-efficiency loci in a broad range of operating conditions. For the nominal best efficiency regime, the integral swirl number appears to have a small positive value of about S = 0.11, but the tangential velocity distribution reveals two concentric counter-rotating cylindrical rod-like streams with a negative swirl (relative to the runner rotation direction) in the inner region and positive in the outer. In the regimes with the PVC formation, as illustrated for the maximum pressure pulsations regime at S > 0.5, the axial velocity appears to be almost stagnant in the core (though positive apart from the cowl wake), the flow being pushed into the peripheral annular region.

The vortex rope phenomena appearing in a draft tube under partial load operations were investigated. The efforts were carried out by using a homogeneous equilibrium vapor-liquid two-phase model and a blending SST turbulence model, and the former takes account of the weak compressibility of mixed media. The vortex rope phenomena were induced by the radial impeller and three kinds of flow regimes were illustrated. Vortex rope was visible at some conditions and it displayed various patterns, while no obvious vortex rope was found under some conditions. It was found that the plant cavitation number determines that whether the vortex rope was visible or invisible. An interesting profile was that a secondary vortex filament ring entwining the vortex rope appeared clearly near the design condition. Both flow structures and pressure characteristics were studied to depict the vortex mechanism and the characteristics of the η-σ curves. Further analysis found that the shedding frequency of the vortex ring is similar with that of the precession movement.

The pressure fluctuations of the turbines are caused by the swirl component in the draft tube, which is an undesired phenomenon that needs to be improved when the turbine operates in the off-design condition. In order to avoid these kinds of unsteady flow phenomena, a technology of J-Groove on the draft tube wall is investigated by numerical method. The validation test of performance is conducted to compare the result of numerical and experimental methods. The steady and unsteady state analyses are conducted to investigate the internal flow of a Francis hydro turbine model draft tube with and without J-Groove. The swirl flow in the draft tube is significantly suppressed by the J-Groove installation. Moreover, according to the unsteady state analysis, the amplitude of pressure fluctuation in the draft tube is reduced effectively by the J-Groove.

Performance of flotation cells heavily relies on their hydrodynamics inside cells and interactions among the solid, liquid and gas phases. The flotation process in conjunction with the bubble-particle interactions in three-phase flow were experimentally investigated in an industrial Wemco 56 cell. Various methods were developed to measure and analyse the flotation process, in which the velocity field of liquid phase was measured using Particle Image Velocimetry (PIV). Particle/Droplet Image Analysis (PDIA) technique was developed to capture and measure bubble sizes, while a conductivity-based probe system was designed to evaluate the mixing status of solid, liquid and gas phases. The flotation kinetics were found relatively inhomogeneous and anisotropic in most regions, while possible flow short-circuiting was identified near bottom corner of the tank. The bubble mix was found insufficient near the cell bottom, although void fractions near the bottom slightly increased after adding particles. The investigation revealed significant impacts of the solid phase, which stimulated bubble to breakup and reattach more actively and promoted bubbles to penetrate further downwards to the bottom. A solid deposition layer of 30 mm was observed near bottom of the Wemco 56 cell, which requires optimisation of draft tube and false bottom designs.

Electricity is a necessity that must exist today, its use is always subject to binding. Most of the electricity comes from fossil energy-based power plants such as PLTU. Therefore, a solution was made by making a vortex water turbine to produce electrical energy. Utilizing a river flow with a small head of water, the water will enter the cross section. The flow will form a vortex because the shape of the section and the draft tube makes the lower side of the section have lower pressure. The vortex turbine will be designed to use a permanent magnet 150 watt AC generator. With a cross section of 60 x 55 x 150cm, draft tube 9.6 mm and turbine blade 30 x 50cm made of aluminum. On the framework will be used a 3 x 3.5 cm strip plate which is rolled. In order to withstand the impact of water on the blade, a 7 mm shaft is used and a nominal bearing life of 10274 hours. The resulting rotation is continued with a pulley with a diameter of 30 mm, 180 mm and with a belt type V material JIS K 6323 A 34.

Automatic optimization is becoming increasingly important in turbomachinery design to improve the performance of machine components and Evolutionary Algorithms (EAs) play a very important role in this task. The main drawback of EAs is the large number of evaluations that are required to obtain an “optimal” result. Consequently, in order to keep the computational time in an affordable frame for design purposes, either the mesh size has to be limited, thus reducing the resolution of the flow phenomena, or the number of free parameters must be kept small. Adjoint optimization does not suffer from these restrictions, i.e. the optimization time is not affected by the number of parameters. The computational effort for the adjoint method scales only with the grid size and is usually in the range of two times the CFD simulation alone. In this paper, a discrete adjoint method based on a coupled pressure based RANS solver is presented and applied to draft tube optimization. The adjoint solver is general and can therefore deal with any turbulence model supported by the CFD solver as well as any boundary condition, including mixing planes and mesh interfaces needed for multi-stage simulations. Furthermore, there is no restriction on the choice of objective function. The adjoint method is first applied to a baseline draft tube geometry and then again to its EA optimized geometry where the objective function was the minimization of losses in the draft tube. To reduce the complexity for this proof of concept but still including multiple operating points in the optimization, only peak efficiency and full-load were optimized simultaneously. The adjoint optimization can significantly improve the draft tube performance in both cases (baseline and EA optimization). The interplay between local and global optimization seems to be a promising strategy to find optimal geometries for multi-operating point/multi-objective optimization and will be further investigated in subsequent research.

Some methods are developed for generating a set of surfaces of the smooth hydroturbine draft tube depending on the nine geometric parameters, and also for constructing meshes in the region of the draft tube for the subsequent optimization of its shape based on numerical simulation of flows.

1. Though multistage axial turbines are being widely used since many decades for water steam expansion or in gas turbines, their use in ORCs has traditionally found limitations as a consequence of the choice of designing turbines with cantilever arrangements. 2. The choice of the cantilever arrangement is mainly related to the advantages of having simple shaft bearings design, only one rotating seal system in contact with the working fluid, a lighter and more compact turbine casing, only one side of the turbine casing occupied with the bearing and sealing systems (leaving the other side free to host the outlet duct for working fluid expanded vapour which often features very large volumetric flow rates), easiness of access for ordinary and extraordinary maintenance. Hence cantilever arrangement involves definitely lower turbine costs, both in terms of Capex and Opex and is practically the only solution adopted by the industrial suppliers of ORC turbines. 3. By adopting the cantilever arrangement the installation of several turbine discs hosting several expansion stages, traditionally installed one close to the other, would increase the overhang mass of the turbine rotor and decrease the natural frequencies of the system, yielding some mechanical problems and, at the end, limiting the possibility of installing, practically, more than 2-3 stages with this kind of arrangement. 4. On the other hand, however, modern ORC turbines require to increase number of stages to better exploit the expansion enthalpy drop, in order to increase turbine efficiency and/or to allow to adopt a low rotating speed (even 1,500 rpm) for a direct connection with synchronous generator. 5. The paper will describe an innovative solution that has allowed to increase the number of stages from the traditional 2-3 to at least 5 without leaving the effective cantilever arrangement, keeping the concept of ‘rigid’ rotor (i.e. operating below the first flexional natural frequency), with very low measured vibrations. 6. Operating data of a 9 MW 5 stage ORC turbine put in operation in 2016 will also be presented.

Hydraulic turbines are operated over an extended operating range to meet the real time electricity demand. Turbines operated at part load have flow parameters not matching the designed ones. This results in unstable flow conditions in the runner and draft tube developing low frequency and high amplitude pressure pulsations. The unsteady pressure pulsations affect the dynamic stability of the turbine and cause additional fatigue. The work presented in this paper discusses the flow field investigation of a high head model Francis turbine at part load: 50% of the rated load. Numerical simulation of the complete turbine has been performed. Unsteady pressure pulsations in the vaneless space, runner, and draft tube are investigated and validated with available experimental data. Detailed analysis of the rotor stator interaction and draft tube flow field are performed and discussed. The analysis shows the presence of a rotating vortex rope in the draft tube at the frequency of 0.3 times of the runner rotational frequency. The frequency of the vortex rope precession, which causes severe fluctuations and vibrations in the draft tube, is predicted within 3.9% of the experimental measured value. The vortex rope results pressure pulsations propagating in the system whose frequency is also perceive in the runner and upstream the runner. This is a submitted manuscript of an article published by Springer Verlag in Journal of The Institution of Engineers (India): Series C, 07 July 2017. Locked until 2018-07-08.

In the present work, flow around a horizontal axis wind turbine is investigated in co-rotating and counter-rotating configurations. Large Eddy Simulation (LES) has been employed in order to study the effect of rotation direction of the downstream turbine in a two in-line setup. The results are in good agreement with presenting experimental data in literatures. The power efficiency of the downstream turbine has increased about 4% in the counter-rotating configuration rather than co-rotating configuration with the same separation distance (3D). The power efficiency of the downstream turbine increased about 7% by decreasing the separation distance to 1D. The improved efficiency in the counter-rotating configuration is due to the flow rotation direction of the upstream turbine. The results revealed in both configurations that streamwise velocity is almost identical, while lateral velocities are changed greatly. Lateral velocities are decreased by moving in a downstream direction. Hence, the benefit of this configuration is obtained by lower separation distance. The authors suggested counter-rotating configuration for the terrain with a high density of installed wind turbines and believed that operating the wind turbines in counter-rotating configuration will not only improve the total efficiency of two in-line turbines, but will also considerably reduce the space they require. Since the oscillations of power coefficient are so high, the exact location of encountering the vortices on downstream blades should be determined to improve the power coefficient of two in line turbines. So, further studies are suggested to extract and track the vortices for future work to increase the efficiency of wind farms.

Francis turbines are often operated over a wide load range due to high flexibility in electricity demand and penetration of other renewable energies. This has raised significant concerns about the ...

Due to the low electricity prices in central Europe, cost optimisations related to all parts of a new hydropower plant have become increasingly important. In case of a run-of-river hydropower plant using a vertical axis Kaplan turbine, one of the cost drivers are the excavation works. Thus, a decisive factor for the reduction of construction costs is the minimisation of the construction depth of the elbow-type draft tube. In course of the design phase of a new hydropower plant in Austria, an analysis of the impact of draft tube modifications on the performance of the Kaplan turbine was carried out by applying computational fluid dynamics. The net head of the turbine with a diameter of D = 3.15 m accounts for Hnet = 9.00 m and the maximum discharge per unit is Qmax = 57.5 m3/s. After it was proven that there is a good agreement of the numerically calculated and experimentally measured turbine efficiency for the original turbine configuration, various draft tube designs were tested in order to find out their impact on the turbine efficiency and to analyse the sources of draft tube losses in detail. Finally, it was possible to find a new draft tube design representing a compromise of reduced construction costs and acceptable turbine efficiency.

This research investigated a high drying rate solar dryer with low-intensity energy consumption. In a brief issue, the solar spouted bed dryer was designed, fabricated and tested through this study. To cover this purpose, a 1D dynamic model was developed for this dryer's bed section. The mentioned accurate model is able to predict this type of solar dryer behavior which includes mass, momentum and energy transfer phenomena. The mentioned model solves the governing equations-mass, momentum, and energy balance equations-simultaneously using MATLAB software. By this system test pilot modeling and experiments, Design and manufacture of a high drying rate solar dryer with low energy intensity are achieved. Comparison between the model and experimental results shows that the maximum error percentage related to output profiles were approximately less than 3.6% that consider an appropriate band of errors. Based on experiments, the system is able to eliminate 85,500 mg water from 150 g corn grains during 90 min test interval. The considerable achievement contributed to the energy consumption intensity is equal to 93.3 kJ/g of corn, which can be a valuable energy heat rate. © 2017 American Institute of Chemical Engineers Environ Prog, 2017

Because of the important role of pumped storage stations in the peak regulation and frequency control of a power grid, pump turbines must rapidly switch between different operating modes, such as fast startup and load rejection. However, pump turbines go through the unstable S region in these transition processes, threatening the security and stability of the pumped storage station. This issue has mainly been investigated through numerical simulations, while field experiments generally involve high risks and are difficult to perform. Therefore, in this work, the model test method was employed to study S-induced security and stability issues for a pumped storage station in transition processes. First, a pumped storage system model was set up, including the piping system, model units, electrical control systems and measurement system. In this model, two pump turbines with different S-shaped characteristics were installed to determine the influence of S-shaped characteristics on transition processes. The model platform can be applied to simulate any hydraulic transition process that occurs in real power stations, such as load rejection, startup, and grid connection. On the experimental platform, the S-shaped characteristic curves were measured to be the basis of other experiments. Runaway experiments were performed to verify the impact of the S-shaped characteristics on the pump turbine runaway stability. Full load rejection tests were performed to validate the effect of the S-shaped characteristics on the water-hammer pressure. The condition of one pump turbine rejecting its load after another defined as one-after-another (OAA) load rejection was performed to validate the possibility of S-induced extreme draft tube pressure. Load rejection experiments with different guide vane closing schemes were performed to determine a suitable scheme to adapt the S-shaped characteristics. Through these experiments, the threats existing in the station were verified, the appropriate measures were summarized, and an important experimental basis for the safe and stable operation of a pumped storage station was provided.

In a hydraulic turbine, approximately three quarters of the energy recovery by the draft tube are obtained at the runner outlet, in its conical part. The performance of this component is a strong function of many flow variables as well as geometric aspects. Until now, different cone geometries have been created by changing lengths, diffuser angles, or shapes. However, the best cone angle for a specific inlet flow, shape, and length has not been well established. Moreover, there is a lack of information in terms of the exact position of the opening angle of a conical-duct shape diffuser to give the highest performance. To find this angle, an automatic optimization process manipulated by the Multi-Island Genetic Algorithm was created to generate different diffuser geometries to be evaluated through CFD simulations. Its computational cost has been overcome using a distributed computing evaluation established in a computational cluster. The methodology has allowed the location of the exact opening angle, improving approximately $$1.2 \%$$ the diffuser performance. A quantitative and qualitative analysis of the flow has been undertaken to understand how the optimum opening angle of a diffuser modifies the flow pattern to achieve the highest performance.

Hydro turbines operating at partial flow conditions usually have vortex ropes in the draft tube that generate large pressure fluctuations. This unsteady flow phenomenon is harmful to the safe operation of hydropower stations. This paper presents numerical simulations of the internal flow in the draft tube of a Francis turbine with particular emphasis on understanding the unsteady characteristics of the vortex rope structure and the underlying mechanisms for the interactions between the air and the vortices. The pressure fluctuations induced by the vortex rope are alleviated by air admission from the main shaft center, with the water-air two phase flow in the entire flow passage of a model turbine simulated based on the homogeneous flow assumption. The results show that aeration with suitable air flow rate can alleviate the pressure fluctuations in the draft tube, and the mechanism improving the flow stability in the draft tube is due to the change of vortex rope structure and distribution by aeration, i.e. a helical vortex rope at a small aeration volume while a cylindrical vortex rope with a large amount of aeration. The preferable vortex rope distribution can suppress the swirl at the smaller flow rates, and is helpful to alleviate the pressure fluctuation in the draft tube. The analysis based on the vorticity transport equation indicates that the vortex has strong stretching and dilation in the vortex rope evolution. The baroclinic torque term does not play a major role in the vortex evolution most of the time, but will much increase for some specific aeration volumes. The present study also depicts that vortex rope is mainly associated with a pair of spiral vortex stretching and dilation sources, and its swirling flow is alleviated little by the baroclinic torque term, whose effect region is only near the draft tube inlet.