Increasing the operating range of existing plants and flexibility of new units are important for both equipment manufacturers and utilities.
By Christof Gentner, Pierre-Yves Lowys, Florian Duparchy and Renaud Guillaume
Driven by the short-term trade in current electricity markets, utilities increasingly operate plants equipped with Francis or pumped-storage units with more frequent starts and stops and at lower loads than just a few years ago. Therefore, power producers and manufacturers emphasize extending the operating range of existing power plants and increasing flexibility for new units.
With that in mind, GE Renewable Energy developed an approach to assess the mechanical behavior of the runner using unsteady numerical analysis and advanced mechanically homologous scale model tests.
Markets demand flexible machines
As running plants under partial load conditions can be damaging to the units, specific developments are necessary to extend the operating range of single-regulated machines and yet to ensure minimum fatigue damage to the runners and other parts of the turbines. One main concern is to guarantee structural integrity for their long-term operation at low discharge considering the highly unsteady and often random pressure load in wide areas of the operating range.
Static computations do not provide enough information to assess the mechanical behavior of critical components under dynamic load. Moreover, the indirect measurement of excitation forces (i.e. of pressure fluctuations) does not give information about the behavior and mechanical response of the affected structure.
For mechanical properties, similar rules did not exist in a standard form. Recent research now makes it possible to predict the mechanical parameters of a prototype runner using data measured on a model.
GE has developed an approach that includes unsteady numerical investigations using coupled computational fluid dynamics (CFD) and mechanical finite element analysis (FEA), as well as mechanically homologous scale model tests that provide the needed mechanical behavior information. 1
In these model tests, a dedicated model runner is equipped with on-board stress measurement, which makes it possible to correlate the mechanical behavior of the runner with the hydraulic excitation. Unlike in prototype measurements, the mechanical model test delivers the mechanical behavior of the runner for the entire hill chart.
GE validated this approach by comparison of numerical simulations with model and prototype tests after transposition of the dynamic results. This combined methodology, based on unsteady simulation and dedicated measurements — both on model and prototype — makes it possible to extend the operating range of hydraulic machines with maximum information about the inflicted cost of life time due to dynamic loading. It is possible, for example, to associate cumulative damage to the runner with a particular operating condition.
Combining numerical simulation with measurements
The dynamic load on the runner of a radial machine consists of deterministic and stochastic components. The individual contribution of these components to the overall dynamic load depends on the operating point. Generally, stable frequency loads, such as rotor-stator interaction (RSI), are important between high part load and full load, whereas stochastic load patterns predominate at low and very low part load.
Established numerical methods combining CFD and FEA make it possible to determine the RSI contribution to the dynamic load with high accuracy, in addition to the static mechanical validation.
When it is important to extend the operating range to very low loads, purely numerical approaches reach their limits as it is a challenge to predict stochastic flow patterns with CFD simulations. GE developed a process wherein dedicated mechanical model tests supplement this design practice (see Figure 1 on page 38).
For existing machines, mechanical model tests and unsteady simulation enable identifying the most damaging operating conditions for the turbine and the most stressed areas on the runner. This process allows focusing site tests on the most severe operating zones and thus reducing the required scope significantly. Evidently, the possibilities for corrective modifications on existing runners are restricted. However, this approach permits GE in collaboration with the plant owner to define an extended operating domain with better knowledge of the stress patterns and with a higher level of confidence compared with numerical analysis alone.
For new machines, site data is not available beforehand. In this case, the combination of mechanical model tests and unsteady simulations delivers a good overview of the expected dynamic behavior of the turbine at the design stage. GE verified the ability of the scale model to accurately predict the runner stresses of the real machine on a recent pump-turbine project. Consequently, the criticality of the dynamic phenomena can be evaluated on the test rig. This feature allows modifying hydraulic and mechanical design in order to decrease the dynamic stresses at part load. The procedure shows both the influence of the hydraulic shape on the excitation due to hydraulic phenomena and the impact of the mechanical design on the stresses.
Validation with measurements on the prototype
Stress measurements on the prototype runner directly show the actual dynamic behavior of the turbine without the influence of the modelling hypothesis or transposition uncertainty. Site tests, here described on the example of a pump-turbine, reveal the most severe running conditions and the associated hydraulic phenomena. Additionally, they serve as a reference for calculation and validation of the scale model.
Site measurements of runner stresses require that both rotating and non-rotating parts of the machine are equipped with sensors. On fixed parts, the main components are instrumented to get a fingerprint of the unit. Commercially available dynamic pressure sensors are mounted in the draft tube and at the high-pressure side of the machine. The operating conditions of the unit are monitored to record net head, guide vane opening, power output and relative discharge. These measurements permit the association of the hydraulic and mechanical behavior of the machine with the operating point on the hill chart. A trigger synchronizes these measurements with the measurements on the rotor. On the turbine runner, strain gauges and pressure sensors are mounted on the blades.
The sensors and the data acquisition system in the runner are subjected to significant loadings. Therefore, it is beneficial to reduce the complexity of the rotating equipment as much as possible. Usually, strain gauges are located in areas of expected high stress and in areas of low stress gradients in order to minimize the uncertainty due to the positioning. Most strain gauges are placed at the junctions of the blades with crown and band on both pressure and suction sides.
The test program in turbine mode includes stepwise load variation in steady state conditions and transient records of startups, shut downs and trips. The on-board instrumentation is designed to operate safely and continuously in these conditions. In addition, the testing sequences are planned to acquire the most important data first, then to repeat and extend the survey progressively and finally to duplicate some sequences in order to secure the database.
The analysis of load ramps provides a good overview of the various hydraulic phenomena encountered by the turbine over the entire output range. From no load to maximum output, five main operating zones can be identified. For a deeper understanding, the signal of a strain gauge on the blade is associated with the corresponding spectrogram, where the coordinate represents the signal frequency as a multiple of rotation speed.
At deep part load, the signal shows high broad band fluctuations covering a frequency range of up to five times the rotation frequency. An intermediate smooth zone with low dynamic stress close to the level observed around the best efficiency point (BEP) is visible between the deep part load and part load zones. At part load operation, the highest dynamic levels are observed at the vortex-rope frequency.
Measurements at steady-state conditions complement the data acquired during the transient ramp. These measurements allow positioning precisely the operation point on the hill chart in terms of discharge and head. The dynamic stress level measured on the runner blades versus relative power output shows that the possibility to extend the operating range toward part load depends on the ability of the runner to sustain the excitation caused by the part load rope.
Numerical simulation delivers comprehensive stress data
Strain gauges on the prototype deliver local information and are usually not placed exactly in the points of highest stress. The evaluation of the runner fatigue life requires taking into account the actual dynamic stress in these hotspots, which is typically higher than the value measured at the strain gauge location. Thanks to coupled CFD and FEA, it is possible to compute the transfer functions that permit the extrapolation of the measured stresses to the entire runner, including the hotspots.
To determine the transfer functions, unsteady CFD delivers the fluctuating pressure field acting on the structure that is used as a loading for the FEA.
According to GE experience, CFD is able to simulate dynamic hydraulic phenomena with distinct frequency such as part load vortex rope or RSI. GE developed a CFD/FEA process to take into account the unsteady pressure loading at part load. The effect of the rotating vortex rope can be seen clearly in the Von Mises stress distribution on the runner for different points in time.
The coupled CFD/FEA unsteady simulation is then validated by checking the correlation with the experimental results, as shown for the dynamic strain measured by the gauges. This procedure allows computing with confidence the transfer functions that will enable extrapolating the locally measured data to the most stressed areas of the runner.
After the extrapolation, a rain-flow counting algorithm is used to extract the number of cycles and the corresponding mean and peak-to-peak stress levels. For a given peak-to-peak stress ∆σi on the runner, it is possible to evaluate the associated elementary damage di by relating the number of cycles applied at amplitude ∆σi to the number of cycles to failure. Using the Miner’s rule cumulative damage model, all elementary damages are added linearly to obtain the total damage D=Σidi.
Using the determined transfer functions, a fatigue analysis of the runner can then be performed for the areas of high stress.
After this calculation is repeated for the entire operating range of the turbine, the different zones identified with the stress measurement are shown as relative damage normalized by the damage at the BEP (value 1) (see Figure 2 on page 38). The red line indicates the limit of infinite life time. Below this limit, the stress level is considered low enough as not to induce significant damage to the structure.
Model test allows assessment for entire operating domain
Site measurements combined with unsteady CFD and FEA provide a reliable damage estimate, but this is obviously restricted to the testing conditions available during the field test campaign. To cover a wider range of working conditions, GE has developed an approach including a dedicated scale model test. The company started using model tests for mechanical research before 2001 and has since accumulated a valuable database covering numerous runner designs. The mechanical model runner is assembled differently than the typical model runners for hydraulic testing in order to achieve meaningful stress measurements.
Unlike prototype measurements, mechanical model tests allow exploring the entire range of head and submergence. The reduced scale model uses all dynamic and time-averaging sensors that are used in a conventional model measurement, such as torque, radial and axial thrusts and dynamic pressure measurements at non-rotating parts.
Beyond this typical instrumentation, strain gauges and dynamic pressure sensors are mounted on the blades and in the runner channels. The strain gauges are located close to the areas of the expected maximum stress. The on-board measurements allow validating the calculation from the hydraulic and mechanical perspective and also make possible the analysis of complex phenomena using techniques such as spatial harmonic decomposition.
For validating the methodology, some strain gauges are located at similar positions on the prototype and model runners. The first step of validation is comparing dynamic stresses in terms of amplitude and frequency. For this purpose, the load ramps recorded on the industrial turbine are reproduced on the test rig. Model stresses are transposed to the industrial scale using geometrical and mechanical similarity.
The results illustrate the relationship of the dynamic behavior of model and prototype. Both in terms of amplitude, shown over the full load range, and spectral field at the maximum of the part load rope, model and prototype show similar behavior.
Not all values can be scaled from the test rig to the industrial installation with the same accuracy. When the natural frequency of the runner and resonance phenomena are important, model and prototype will show significantly different behavior. This constraint has to be considered, for example, when assessing the high-frequency RSI in the power range above the BEP. As numerical simulation using CFD/FEA is able to predict this load case reliably, the mechanical validation can be carried out without input from the mechanical model test.
When large volumes of cavitation are present, Froude similarity might play a role and significant differences between pressure and stress measurement can be observed on the model. By varying the Thoma number (i.e. the downstream pressure level) on the model, a rope resonance was deliberately created in order to compare the response of the pressure and stress gauges. For a certain pressure level, the rope causes a synchronous pressure pulsation, visible as an elevation of peak-to-peak levels at the inlet pressure sensor. Maximum stress measurements recorded at the same time are insensitive to this resonance phenomenon. This example shows that the stress measurement in the rope zone can be less sensitive to the test conditions than the pressure pulsation and thus provides more reliable information regarding life time calculation.
The comparison of dynamic pressure typically recorded in conventional model tests with stresses measured in the runner shows that both quantities are only loosely linked in substantial areas of the operating range.
Whereas the pressure pulsations show a significant rise in the area of hydro acoustic resonance at Q/Qopt=0.81, the stresses remain unchanged. In the area of the vortex rope (Q/Qopt=0.7), pressure and stresses show a somewhat correlated trend, while at very low part load, the stresses increase independent from the pressure pulsation measured in the non-rotating system.
Put to practice: extending the operating range
Using the described procedure, the mechanical model test provides a hill chart showing the dynamic response of a prototype pump turbine (see Figure 3). It is possible to define iso-lines of dynamic stress that limit the area of continuous operation, in particular when operating at low head in very low part load. This information allows defining low load operation limits that ensure safe long-term behavior of the turbine.
In the design phase, the mechanical model test is an important tool to reconcile hydraulic and mechanical design targets with maximum possible reliability. For a Francis design, it was possible to reduce the dynamic stress on the runner while achieving a similar hydraulic performance (see Figure 4).
The newly-designed runner was manufactured and tested respecting hydraulic and mechanical similitude. The mechanical model test delivers information on the mechanical behavior of the runner at the design stage and thus allows a targeted balancing of efficiency and mechanical properties of the runner before prototype manufacturing.
Conclusion and perspectives
When respecting the restrictions of the method, the hydraulic and mechanical behavior of the mechanical model can be used to predict prototype behavior, especially in operating areas where CFD simulations reach their limits, such as very low part load.
In particular, the dynamic stress levels can be reproduced accurately on the reduced scale model runner as long as the conditions of transposition are fulfilled. The flexibility of the model test allows determining the dynamic behavior of the turbine in the entire range of operation.
Unsteady numerical simulations provide a dependable pressure loading and thus allow predicting accurately the dynamic behavior of the structure in the areas of part-load rope and RSI.
The hydro-mechanical model test and field measurements are two complementary ways to understand the dynamic behavior of a turbine. The association of measurements with numerical simulation offers a methodology to optimize the operating range of a hydro plant without compromising the life-time of the turbine.
This approach delivers reliable and extensive information about the mechanical behavior of new projects during the design phase. For plants already in operation, it is possible to map areas of safe operation in the hill chart when flexibility and the extension of the operating range need to be evaluated.
The prediction of the mechanical stresses in a prototype turbine runner based on homologous model tests will support to prepare hydro power plants for the challenges associated with future dispatching strategies.
Christof Gentner is responsible for technical tendering, Pierre-Yves Lowys is an engineer specializing in the analysis of field data, turbine behavior feedback and diagnostics, Florian Duparchy concentrates on fatigue and fracture mechanics analyses and turbine behaviors, and Renaud Guillaume works on the interaction of hydraulic and mechanical subjects. All the authors work for GE Renewable Energy.
1 Lowys, P.Y., et al, “Alqueva II and Salamonde II: Extending the Operating Range of Single Regulated Turbines,” Viennahydro 2016 Conference, Vienna, Austria, 2016.
This article has been evaluated and edited in accordance with reviews conducted by two or more professionals who have relevant expertise. These peer reviewers judge manuscripts for technical accuracy, usefulness, and overall importance within the hydroelectric industry.