By Eric Scheibler and Matt Clemmer
The Tennessee Valley Authority operates numerous hydroelectric facilities that utilize 1940s-era wicket gates. Cascading wicket gate failures in Unit 1 of the 140.4-MW Guntersville power station, which was constructed in 1935, and concerns raised after inspections of similar gates prompted TVA engineers to pursue comprehensive evaluations of similar- vintage wicket gates.
TVA chose to develop a risk ranking criteria for 1940s-era wicket gates, based on the calculated stresses due to gate stem torque during shear-pin activation versus the yield strength of gate material. These findings were compared to linear elastic finite element analyses (FEA) to help confirm ranking philosophy.
Based on wicket gates evaluated throughout corresponding TVA facilities, Unit 2 at the 124-MW Hiwassee facility was identified as posing the highest risk. Hiwassee, constructed in 1940, is located in Murphy, N.C.
The original Hiwassee powerhouse design consisted of a single conventional Francis turbine, with space in the powerhouse for an additional unit. In 1956, TVA installed Unit 2, a reversible Francis pump-turbine, which at the time was the world’s largest pump-turbine. It was also the first reversible pump-turbine in the country to use wicket gate control for both output and pumping.
TVA worked with Quest Integrity in 2014 to perform destructive material testing on a similar-vintage wicket gate, located at the Wilson plant, also cast from ASTM – A27 steel. This provided accurate material properties values necessary for comprehensive fitness-for-service (FFS)1 evaluations on the Hiwassee Unit 2 wicket gate.
|This figure shows the finite element mesh refinement of the wicket gate stem-to-leaf intersection. Refinement in this location of stress raisers (e.g., wicket gate stem-collar and leaf-collar) is necessary to accurately capture stress and non-recoverable strain results.|
The main objectives of this project were to provide TVA with a comprehensive condition assessment and remaining life estimate of the 1940s-era wicket gate types, based on quantitative evidence and supported by a recognized engineering standard.
A three-dimensional geometry model of the Unit 2 wicket gate at Hiwassee was developed using SolidWorks commercial CAD software2 and was based on the information found in the engineering and refurbishment drawings provided by TVA. A feature of particular interest was the stem-to-leaf boundary region that had been subject to machining during a recent refurbishment.
At the request of TVA, and in order to maintain conservatism, the stress relief radius at this location, specified only by a 0.06 inch maximum, was assumed to be zero.
The solid geometry was discretized and meshed using Abaqus CAE pre-processing software.3 Discretizing the geometry into “elements” of finite size allows for numerical approximation of the mathematical model representing the physical response of the structure subjected to various loads and boundary conditions. The stem, stem sleeves, and majority of the leaf and end plates were represented using reduced integration hexahedral elements. The leaf-collar and stem-collar boundary regions were modeled using quadratic tetrahedral elements. To accurately capture material response, the average characteristic element length was refined to 0.05 inches along the boundaries of interest (see Figure 1, page 34).
Material testing was conducted to obtain specific properties of the vintage A27 leaf and stem material.
Finite element modeling was conducted using Simulia’s Abaqus FEA software. Multiple stress analyses were performed based on routine gate squeeze and safety element activation (shear-pin breakage) conditions. Gate squeeze loading represents the daily operation and a shear-pin event represents an upper-limit loading event. The frequency of gate squeeze events – 730 events per year in this case – were based on operational records supplied by TVA.
TVA requested the frequency of shear-pin activation events model, a one-in-five-year occurrence.
An FFS assessment is a multi-disciplinary engineering approach to determine if a given structure is fit for continued service. The outcome of an FFS assessment supports decisions to operate as is, repair, retire or re-rate. The FFS approach also provides a quantitative means for determining when and where to inspect.
Comprehensive guidelines for FFS assessments are contained in the API 579-1/ASME FFS-1 standard.1
A limit load analysis addresses the failure mode of ductile rupture and detects the onset of gross plastic deformation (i.e., plastic collapse) of the structure. It provides a lower bound limiting load of the structure as the solution to a numerical model. The limit load is the load at which overall structural instability occurs. It is numerically identified as a point in the analysis where for a small increase in load, equilibrium (convergence) is no longer achieved.
Stem loading was linearly ramped from gate squeeze loading until the onset of plastic collapse could be distinguished. The load factor is a multiple by which the normal operational loads have been increased in that analysis step.
This analysis was conducted for each of the boundary conditions evaluated (i.e., once for the gate squeeze and once for the shear-pin activation).
To ensure the wicket gate is protected against localized failure, elastic-plastic analyses were conducted. Equivalent plastic strain (PEEQ) was monitored at peak locations as the stem loading was linearly ramped to the onset of plastic collapse. Values were compared to the limiting strain as outlined in the ASME FFS-1 standard.
The strain damage was quantified at each load factor as the strain limit damage ratio (SLDR). SLDR compares the local PEEQ to the limiting strain. Locations of peak PEEQ on the wicket gate were considered acceptable for the specified load factor if the SLDR was less than or equal to unity.
Cyclic fatigue – ratcheting
Cycle-by-cycle accumulation of equivalent plastic strain (ratcheting) is a mode of fatigue where crack-like flaws can initiate in a small number of load cycles. To ensure the wicket gate is protected against ratcheting, computationally intensive cycle-by-cycle elastic-plastic analyses including kinematic material hardening were conducted. In the FEA model, each loading and unloading is represented by an analysis step.
Crack stability and limiting flaw curves
One of the first tasks of a damage tolerance analysis is estimating critical flaw sizes. The failure assessment diagram (FAD) method found in the ASME FFS-1 standard describes the measure of acceptability of a component that contains a crack-like flaw.
The FAD method considers both unstable (brittle) fracture and limit load (plastic overload). In a FFS assessment of a crack-like flaw, the results from stress analyses, stress intensity factor and limit load solutions, material strength, and fracture toughness are combined to compute a non-dimensional toughness ratio and load ratio. The computed point, toughness ratio (vertical coordinate) and load ratio (horizontal coordinate), represents the crack-like flaw’s acceptability. If the point falls on or below the FAD curve, the component is considered safe for continued operation; outside of the curve, the component is considered unsafe for continued operation.
Alternatively, by plotting a limiting flaw curve based on methods found in the API 579-1/ASME FFS-1, combinations of flaw length and depth are determined that pose a risk for sudden failure due to brittle fracture or plastic collapse. Thus, these flaw dimensions represent points that fall exactly on the FAD. If the characteristic flaw dimensions (e.g., length and height) fall under the limiting flaw curve, then the flaw is considered acceptable; outside the limiting flaw curve, the flaw is unacceptable. The limiting flaw curve provides a means to evaluate many combinations of potential flaw sizes.
Fatigue-driven crack growth
Once critical flaw sizes are determined, the next task in the damage tolerance approach is to grow a flaw to failure. The outcome of this analysis will provide an estimate of remaining life and govern how inspection intervals may be determined.
Extensive empirical data has demonstrated that the rate of fatigue crack growth in metals can be characterized by the following expression:
- a is a characteristic crack dimension (length or depth),
- dal dN is the crack growth per load cycle,
- âˆ†K is the cyclic stress intensity factor,
- âˆ†Kth is the threshold value of âˆ†K, and
- C & m are material constants.
The stress intensity factor, K, is a fracture mechanics parameter that characterizes the stresses near the tip of a crack.
The cyclic stress intensity factor is defined as the difference between the maximum and minimum value of K in a given loading cycle. It is related to stress and crack size as follows:
- Y is a geometry factor that depends on the crack dimensions as well as the size and shape of the component, and
- âˆ†Ïƒ is the cyclic stress.
Life assessment can be performed by integrating Equation 1, and because constant- amplitude loading (i.e., âˆ† does not vary from one cycle to the next) was assumed, the number of loading cycles required to grow the crack from an initial flaw size, ao, to a final size, af, is given by:
It should also be noted that Equation 1 includes a threshold, âˆ†Kth, below which the crack growth rate is zero. Consequently, some of the load cycles may not contribute to fatigue damage because âˆ†K is below the threshold. The threshold cyclic stress is given by:
After the life of the component has been estimated from the crack growth assessment, the final step in the damage tolerance approach is to determine appropriate inspection intervals.
The FFS method is interlinked to nondestructive evaluation. The results from a nondestructive evaluation can be used as input for both the crack stability and crack growth analyses, the outcome of which can be used to define inspection intervals.
|This figure shows key areas of interest along the boundary of the upper journal and the leaf of the wicket gate.|
Stress results for each load case, gate squeeze and safety element activation were verified against closed form calculations (e.g., shear stress in shaft cross-section due to torsion) to confirm correct application of loads and boundary conditions. The entire wicket gate was evaluated and “key” locations of interest were identified for further FFS evaluation (see Figure 2).
The applied moment and directional loads were increased until numerical convergence of the elastic-plastic analysis was no longer achieved.
For the current shear-pin rating of 160 kips, the maximum expected wicket gate loading produces a SLDR of 0.281. Therefore, the local equivalent plastic strain is less than the limiting strain at every location and the wicket gate satisfies the criteria for protection against local failure.
|This figure shows a cutaway view of the wicket gate stem-collar and leaf-collar locations and illustrates the wicket gate response during progressive gate-squeeze loading. The leftmost image represents normal operation; the middle image represents shear-pin activation loading; and the rightmost image represents plastic-collapse. The color grey in false color stress contour (psi) indicates areas that have exceeded the von Mises yield criterion.|
Six elastic-plastic “cycle-by-cycle” gate squeeze load and unload cycles were modeled (see Figure 3), representing about three days of operation. Eight elastic-plastic “cycle-by-cycle” shear-pin activation load and unload cycles were modeled, representing 40 years of occurrences. The area of peak plastic accumulation was consistently found to occur at the leaf-collar boundary. Because the plastic strain continues to accumulate and does not elastically “shakedown,” in both cases the “no plastic action” criterion cannot be used to ensure protection from plastic ratcheting. These results are useful, however, in identifying the leaf-collar region as a possible site of crack initiation.
Crack stability and limiting flaw curves
Based on the stress analysis, the most likely scenario for the formation and propagation of a crack-like flaw would occur along the stem-to-collar and leaf-to-collar boundaries. Upper bound primary through thickness stress profiles that occurred at the maximum stress location in both the stem-to-collar and leaf-to-collar boundaries were used in the FFS assessment. The limiting flaw curves were calculated with the material parameters gathered from the material tests using Quest Integrity’s Signalâ„¢ Fitness-for-Service software.
Crack dimensions that fall below the curves are considered sub-critical, whereas those that fall outside of the curves are critical. Thus, these curves represent combinations of crack lengths and depths that could pose a significant risk of sudden failure. These curves were used to determine future inspection requirements and to evaluate the stability of any measured linear indications.
Based on the analyses, the following conclusions were established:
- The global stability criterion, which ensures protection against plastic collapse, was satisfied by the model’s numerical convergence to a stable solution under expected loading conditions. Analyses showed a continued linearly stable global response up to about 3.5 times the loading at gate squeeze, or about twice the loading required to break the shear pin.
- The highest equivalent plastic strain experienced under gate squeeze conditions was about 5% of the limiting strain value. Shear-pin activation conditions elevated the maximum equivalent plastic strain to 30% of the limiting value. Because both conditions produced a maximum below the failure condition defined at 100%, the wicket gate satisfies the requirement for protection against local failure.
- Under both gate squeeze and shear-pin activation loading conditions, cyclic loading of the component revealed isolated areas of plastic equivalent strain accumulation. However, the retention of an elastic core in the primary-load- bearing cross section of the component satisfies the ratcheting assessment.
- Conservative modeling of fatigue-driven crack growth produced a remaining life estimate of 46 years. This provides 16 years in excess of the proposed disassembly and wicket gate inspection interval of 30 years. This implies that if crack initiation were to occur, the crack could be detected by routine inspection prior to causing failure.
Based on these findings, TVA can likely meet the desired 30-year interval between major disassembly before a required inspection of the wicket gates.
1Fitness-For-Service, Fitness-for-Service API 579-1/ASME FFS-1, American Petroleum Institute and American Society of Mechanical Engineers, 2007.
2SolidWorks Premium, x64 SP5.0 ed., Dassault Systà¨;mes Solidworks Corp., Waltham, Mass., USA.
3Abaqus CAE/Standard 6.13, Dassault Systà¨;mes Simulia Corp., Providence, R.I., USA.
Scheibler, Eric, et al., “Fitness-for-Service Assessment on 1940’s Era Wicket Gates,” Proceedings of HydroVision International 2015, PennWell Corp., Tulsa, Okla., 2015.
Eric Scheibler is a senior consulting engineer and the global manager for hydropower with Quest Integrity. Matt Clemmer is hydro generation engineering manager for the Tennessee Valley Authority.
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.