Unsteady BEMT for fault diagnosis and prognosis in tidal stream turbines Michael Togneri Ian Masters
Matthew Allmark
Faris Elasha
Cranfield University School of Engineering, Cardiff University Bedford, MK3 0SU, UK The Parade, Cardiff, CF24 3AA, UK College of Engineering, Swansea University E-mail:
[email protected] E-mail:
[email protected] Singleton Park, Swansea, SA2 8PP, UK E-mail:
[email protected] [email protected]
Abstract—We present the results of simulations carried out with a robust blade element momentum theory (BEMT) model. This model includes several modifications to classical BEMT, including the addition of tip/hub losses, high induction effects and, most importantly for this work, the ability to deal with arbitrary inflow conditions (i.e., including time variation and spatial non-uniformity). We use this capacity to simulate the response of tidal stream turbines (TSTs) to turbulent inflow conditions. The discussion presented centres firstly on the method of generating these inflow conditions, and secondly on how the simulation results can be used both to diagnose fault conditions during TST operation, and to prognose the fatigue lifespan of gearbox components. Index Terms—BEMT, turbulence, simulation, fatigue, fault detection
I. I NTRODUCTION A. Blade element momentum theory (BEMT) The results presented in this paper rely on a robust BEMT code developed at Swansea University [1]. As with all BEMT, the code determines hydrodynamic loads on a rotor by finding agreement between two models of a tidal stream turbine (TST): firstly as a collection of annular elements comprising a rotor disc, each of which acts as a sink to absorb momentum from the fluid flow, and secondly as a collection of two-dimensional blade sections approximating the real blade shape, subject to lift and drag forces due to the impinging flow. The essential theory of BEMT is covered in many standard texts (e.g., [2]), so we do not cover it in detail. Nonetheless, we would draw attention to some modifications to classical BEMT theory incorporated into the solver used here. As is common in BEMT, tip and hub losses are corrected for using the formulation of Glauert [3]. The code also incorporates a generalised high-induction correction based on the work of Buhl [4]. The most important modification for simulating unsteady conditions with BEMT is the inclusion of arbitrary inflow conditions, as opposed to the classical formulation which assumes an unchanging plug flow and a steady operational condition. Our code incorporates two important innovations that make this possible. To start with, we model each blade separately, rather than using
a single blade to represent all others, and we track the position of each blade element individually, meaning that we can apply different inflow conditions to each blade element depending on its position in space. Further, we treat the hydrodynamic forces obtained from the BEMT as representing an instantaneous solution rather than steady state. In conjunction with a specified time-step and a model for resistive torque from the turbine generator, we can then calculate how far the blades will travel from moment to moment, and how the forces acting on them will alter. This scheme is described in [5], where it is used to analyse blade loading in response to wave conditions. It is not limited to use in wave conditions, however, as the scheme is agnostic to the nature of the unsteady flow applied. Here, we are interested specifically in turbulent flow conditions. The marine environment presents many engineering challenges for the deployment of TSTs, and turbulence must be included in any serious accounting of these, as a factor that affects both fatigue loads [6] and strong transient spikes but is also not well understood. Thus, we must find a way to specify a suitable turbulent flow field for use in our BEMT model. B. Synthetic eddy method (SEM) Unfortunately, it is not possible to obtain the type of direct measurements that would fully specify a turbulent velocity field - that is to say, measurements of all three velocity components at sufficiently many points to capture all important turbulent structures that impinge on a rotor disc. We need to find a way to recreate a turbulent flow field from a smaller data set. The method we have elected to use is the synthetic eddy method, originally developed as a way of generating inflow conditions for large eddy simulations [7]. We have elected to use this method because the inputs it requires are turbulent velocity covariances (i.e., Reynolds stresses) and turbulent lengthscales - precisely the data that are easily obtained with the most common tools (acoustic Doppler current profilers, or ADCPs, and acoustic Doppler velocimeters, or ADVs) for measuring turbulent flowfields both in the field and in the laboratory.
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The details of SEM are described in [7], [8], so again we will not deal with it in depth here. The basic approach of the method is to populate a space with randomly-placed eddies of a specified shape (here we use a three-dimensional tent function, although other shapes are possible) and with intensities given by the elements of the Cholesky decomposition of the Reynolds stress tensor. The fluctuating velocity field produced in this way recreates the Reynolds stresses of the ‘template’ data, and is thus representative in a second-order statistical sense of the turbulence from which the data is derived (see figures 2 and 6). II. ROTOR GEOMETRY AND TEST CASES We intend to demonstrate the usefulness of BEMT for predicting turbulent effects on TSTs by presenting results from two test cases. Both cases use a rotor geometry based on a flume-scale turbine (radius 0.237m) that has been used for laboratory tests at the University of Liverpool [9], [10]. We show the geometry of the rotor blades in figure 1; a Wortmann FX 63-137 blade profile is used for the entire blade span. The first test case uses a version of the rotor scaled up by a factor of ten and simulated in turbulent conditions that are based on ADCP measurements taken in Ramsey Sound, a channel off the coast of Pembrokeshire; data from this case are used to investigate the fatigue life of gearbox components. The second test case simulates the turbine at its original flume scale, but changes the pitch of a single blade - this models an offset blade fault condition, as might happen in a turbine with active pitch control for its blades. A. Gearbox prognostics In order to make a meaningful assessment of the fatigue life of the gearbox components, we must determine the range of loads it is likely to experience. The field data that we have available from the Ramsey Sound site was gathered with a bed-mounted ADCP and spans a complete spring-neap cycle
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Fig. 3. Mean absolute error between template turbulent covariances and synthetic turbulent covariances vs. duration of synthetic turbulence record. Blue line shows error in hu02 i; green shows hv 02 i; red shows hw02 i; cyan shows hu0 w0 i; magenta shows hv 0 w0 i.
(from 11/09/09 to 29/09/09), and as such is representative of all flow conditions a turbine deployed there will be be subject to. Since the turbine will not generate power during slack water, we consider only flood and ebb conditions. We thus elected to create from the field data a series of fourteen synthetic turbulence fields, each generated from the statistical properties of a single flood or ebb phase. In figure 2, we compare the measured Reynolds stresses for a representative ebb phase with the corresponding values from a synthetic turbulent flow field generated using these measurements as a template. We can see that the agreement is very good - perfect agreement is only obtained for a synthetic record of infinite duration, which is for fairly obvious reasons not practical. We found that a record of only ten minutes’ duration was sufficient to replicate the template Reynolds stresses with very small error (on the order of 1 × 10−4 , see figure 3), and will therefore also be long enough to be representative of all turbulence impinging on the turbine during the template tidal phase. Note that it is not possible to resolve the streamwise-spanwise covariance component of Reynolds stress (i.e., h−u0 v 0 i) from ADCP measurements, and so this is set to zero when generating the synthetic turbulence field. Figure 4 shows the torque record obtained from BEMT when the rotor experiences the turbulent flow whose statistics are depicted in figure 2 above. There is no obvious periodicity in the record, but from the extrema it is apparent that turbulent structures impinging on the rotor disc are inducing strong transient loads on the blades and that these ultimately appear in the shaft torque as well. A torque record like this is generated for each of the fourteen cases described above. If we assume that these cases give us a representative sample of the loads experienced throughout the entire tidal cycle, we can use them to create a load probability density function for the full range of
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permissible limits. The relationship between the shaft torque and the contact or bending stresses is complex and depends on a great many factors; however, there is an international standard for estimating the gearbox component stresses from the shaft torque [11], and our estimates of fatigue life are obtained by following its procedures.
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Fig. 4. Representative torque record for the gearbox prognostics test case this corresponds to the rotor geometry shown in figure 1 and the synthetic turbulence shown in figure 2
turbulent flow conditions experienced by the turbine. We also create, in the same manner, a corresponding rotational speed probability density function. With these together, we are able to determine the number of gearbox cycles corresponding to each load level, and therefore to predict the fatigue life of each gearbox component. We consider two failure modes for gearbox components: pitting of the contact surfaces, and cracking due to bending moments on gear teeth. Fatigue failure will occur when the cumulative load in either of these two modes exceeds
Tidal turbine gearboxes fulfil the same role as wind turbine gearboxes i.e., they transmit power from a low-speed, high-torque rotor shaft to a high-speed, low-torque generator shaft. In this test case, we consider a configuration similar to those used in wind turbines called the GB-R100-A [12], depicted schematically in figure 5. Gearboxes of this type have been extensively studied for fatigue failure in wind turbine gearboxes [13], [14], making it an obvious choice for fatigue studies in tidal turbines.
The life predictions for the gearbox components are presented in table I. We see that for all components failure is liable to occur due to surface pitting rather than cracking resulting from bending moment on the gear teeth. Most importantly, the component that we predict to fail first is the pinion gear of the high-speed stage; in other words, the fastest and smallest gear. In the load conditions predicted by our BEMT model with synthetic turbulence, this component is expected to undergo pitting failure after 135 lunar cycles, or slightly less than 11 years of operation.
this case we have included the hu0 v 0 i component that was omitted in figure 2; as the template data came from a flume rather than field measurements, the statistics were measured with an acoustic Doppler velocimeter rather than an ADCP, and thus all velocity covariances are available. Also of note is the fact that we use ADV measurements from a single point to represent the entire working section of the flume i.e., we assume that the turbulence statistics are uniform across the disc span. Again we see that the synthetic turbulence satisfactorily captures the second-order statistics of the template flow.
Fig. 5. Schematic depiction of three-stage gearbox configuration used in the current study. LS-PS: low-speed planetary stage; IS-PS: intermediate-speed planetary stage; HSS: high-speed stage. Component
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232.05 157.80 347.16 238.25 162.01 356.91 135.00 145.80
335.82 194.80 487.05 356.80 207.00 518.30 177.00 180.90
TABLE I FATIGUE LIFE IN LUNAR CYCLES FOR THE COMPONENTS OF THE GEARBOX CONFIGURATION DEPICTED IN FIGURE 5.
B. Offset blade fault detection In our second test case, we use measurements from an experimental flume as the template for our synthetic inflow turbulence. Experiments are planned for this flume that will replicate the simulations whose results we present in this section, and whose results will be used to validate our model. The purpose of this test case is to investigate whether it is possible to determine if a turbine has entered a fault state known as the ‘offset blade condition’ without physically examining the device. In normal operation, all blades of a TST rotor will be geometrically identical. In the offset blade condition, one blade is pitched relative to the others. This could be a result of physical deformation of the blades, but is more likely to occur as a fault in an active pitch control system. Ideally, detection of an offset blade would be possible simply by monitoring the power or torque output, since this is almost certainly the easiest parameter to measure on the fly. Figure 6, like figure 2 did for the turbulence in the gearbox prognostics case, compares the template turbulence statistics and those obtained from the SEM. Note that in
We run four simulations of the rotor in this synthetic turbulent flowfield: with no blade offset, and with offsets of 0.5, 3 and 6 degrees. On initial inspection of the loads and spectra, as shown in figure 7, there is no obvious distinction to be made between the different cases. The three highest spectral peaks appear on first glance to correspond to the rotational frequency and its first and second harmonics (the second harmonic being equal to the blade pass frequency), but examination of the actual rotational and blade pass frequencies shows that this is merely approximate. This implies that there is no loading corresponding to the natural period of the rotor. In the BEMT model used here, tower shadowing is not included, and so the only source of periodicity in the loads would be due to blades encountering the same turbulent structures on subsequent rotations (so-called ‘eddy slicing’). That this is not evident in the load spectra indicates that the turbulent structures in an SEM flow may not be sufficiently distinct from one another as to have a consistent effect in terms of structural loading from one blade rotation to the next. Since we cannot detect the offset blade condition from the shaft torque, we must look elsewhere to see if its effects can be detected. In figure 8, we show excerpts from the thrust records for individual blades, with the offset blade record picked out in red. This data is trivial to obtain from our BEMT results, but in a physical rotor would require the installation of individual load cells at the base of each blade. Immediately we can see that these measurements offer a means to detect the offset blade condition: as the pitch angle moves further from the design case, thrust on this blade decreases noticeably. These results are tabulated in table II, where these observations are confirmed. In moving from zero pitch offset to an offset of six degrees, the thrust contribution of the offset blade drops from a third of the total rotor thrust to less than a quarter. III. D ISCUSSION AND CONCLUSIONS We have shown that unsteady BEMT, in conjunction with SEM, can be used to predict some turbulence effects on TSTs, and to investigate how these effects can be ameliorated. The synthetic eddy method has been shown in figures 2 and 6 to yield a velocity field that, while non-physical, statistically reproduces measured turbulence. This means we are able to simulate a TST’s response to turbulence of known statistical properties without the need for either detailed velocity
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0 Blade 1 mean thrust (N) Blade 2 mean thrust (N) Blade 3 mean thrust (N) Offset blade contribution to total thrust
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Blade offset angle (◦ ) 0.5 3 6 21.444 22.266 22.313 0.325
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TABLE II M EAN THRUST VALUES FOR INDIVIDUAL BLADES ( BLADE 1 IS THE OFFSET BLADE ). F INAL LINE SHOWS PROPORTION OF TOTAL DISC THRUST CONTRIBUTED BY OFFSET BLADE .
life estimate. Our investigation of offset blade detection in turbulent conditions used only a single simulation, and its conclusions should therefore be regarded as preliminary. However, what it does indicate is that it may not be possible to detect fault conditions such as the offset blade from the torque on the rotor shaft alone, and therefore that detection will require additional instrumentation. Examination of the loads on individual blades has shown that we can detect an offset blade by the reduction in its thrust compared to other blades: this is a potential solution, although instrumenting the blade with a load cell that will allow such measurements will not be straightforward.
measurements or expensive computation. Our gearbox prognostics test case indicated that the high-speed pinion gear will be the first component to fail (after approximately eleven years of operation), and that all gearbox components will undergo pitting failure before cracking failure. This is beneficial in not only giving us an estimate for when maintenance ought to be scheduled, but also in telling us which components need to be redesigned or improved to lengthen the gearbox’s fatigue life. It is worth considering that eleven years may be too pessimistic an estimate for the gear’s lifespan: the probability distributions of load and speed that we used are based on data from the fastest segments of flood and ebb phases across the spring-neap cycle, and thus they neglect both slack water and the less-intense portions of floods and ebbs. A probability distribution of loads that did incorporate these times with lower loading would almost certainly yield a longer fatigue
The synthetic eddy method, although it provides satisfactory turbulent flowfields in a statistical sense, is not the only way of predicting fluctuating velocities on a TST. There are well-validated spectral methods that are widely used in the wind turbine industry, and some recent work has indicated that the spectral properties of tidal currents are sufficiently similar that these atmospheric methods could be adapted for use in marine flows [15]. A fruitful avenue of research, then, would be to attempt analysis of the test cases presented in this paper in the case where artificial turbulence is generated with spectral methods adapted for tidal flow, rather than with SEM. ACKNOWLEDGMENT This work was undertaken as part of the Low Carbon Research Institute Marine Consortium (www.lcrimarine.org.uk), and as part of SuperGen UK Centre for Marine Energy
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Fig. 7. Comparison of torque record (top panel) and torque spectra (bottom panel) for different blade offset angles in synthetic flume turbulence. On the spectrum plot, rotational frequency is marked by a solid black line and blade pass frequency by a dotted black line. Apparent spectral peaks are picked out with red circles.
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Research (UKCMER). The authors wish to acknowledge the financial support of the Welsh Assembly Government, the Higher Education Funding Council for Wales, the Welsh European Funding Office and the European Regional Development Fund Convergence Programme. The authors would also like to acknowledge the support of EPSRC through grant EP/J010200/1, which funds the UKCMER project. R EFERENCES [1] I. Masters, J. Chapman, J. Orme, and M. Willis, “A robust blade element momentum theory model for tidal stream turbines including tip and hub loss corrections,” Proceedings of IMarEST-Part A-Journal of Marine Engineering and Technology, vol. 10, no. 1, pp. 25–35, 2011. [2] T. Burton, D. Sharpe, N. Jenkins, and E. Bossanyi, Wind Energy Handbook. John Wiley and Sons, Ltd., 2001. [3] H. Glauert, Aerodynamic Theory, W. Durand, Ed. California Institute of Technology, 1943, vol. 4. [4] J. Chapman, I. Masters, M. Togneri, and J. Orme, “The buhl correction factor applied to high induction conditions for tidal stream turbines,” Renewable Energy, vol. 60, pp. 472–480, 2013. [5] H. Buckland, “Combined current, wave and turbulent flow and their effects on tidal energy devices,” Ph.D. dissertation, Swansea University, 2014. [6] D. Val, L. Chernin, and D. Yurchenko, “Reliability analysis of rotor blades of tidal stream turbines,” Reliability Engineering and System Safety, vol. 121, pp. 26–33, 2014. [7] N. Jarrin, S. Benhamadouche, D. Laurence, and R. Prosser, “A syntheticeddy-method for generating inflow conditions for large-eddy simulations,” International Journal of Heat and Fluid Flow, vol. 27(4), pp. 585–593, 2006. [8] N. Jarrin, “Synthetic inflow boundary conditions for the numerical simulation of turbulence,” Ph.D. dissertation, University of Manchester, 2008. [9] S. Tedds, I. Owen, and R. Poole, “Near-wake characteristics of a model horizontal axis tidal stream turbine,” Renewable Energy, vol. 63, pp. 222–235, 2014. [10] T. de Jesus Henriques, S. Tedds, A. Botsari, G. Najafian, T. Hedges, C. Sutcliffe, I. Owen, and R. Poole, “The effects of wave-current interaction on the performance of a model horizontal axis tidal turbine,” International Journal of Marine Energy, vol. 8, pp. 17–35, 2014. [11] ISO, “Calculation of load capacity of spur and helical gears,” 2008. [12] J. Cotrell, “A preliminary evaluation of a multiple-generator drivetrain configuration for wind turbines,” in ASME 2002 Wind Energy Symposium. American Society of Mechanical Engineers, 2002, pp. 345–352. [13] P. Tavner, J. Xiang, and F. Spinato, “Reliability analysis for wind turbines,” Wind Energy, vol. 10, no. 1, pp. 1–18, 2007. [14] F. Spinato, P. Tavner, G. van Bussel, and E. Koutoulakos, “Reliability of wind turbine subassemblies,” IET Renewable Power Generation, vol. 3, no. 4, pp. 387–401, 2009. [15] I. Milne, R. Sharma, R. Flay, and S. Bickerton, “Characteristics of the turbulence in the flow at a tidal stream power site,” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 371, no. 1985, 2013.
