Press Room - Getting rid of bad vibes.

	Getting rid of bad vibes.

	Bill Clark, CD-adapco, USA

	Psychics aren’t the only ones concerned with bad vibrations. They are also the bête noire of engineers. Perhaps the most spectacular example of this was the Tacoma Narrows Bridge disaster of 1940. The third longest suspension bridge in the world at that time, it was constructed using a lighter design than its predecessors. However, this also made it prone to vibrations from wind gusts. The bridge began oscillating and finally collapsed when the frequency of wind gusts matched the bridge’s own motion, compounding the magnitude of the oscillations. Engineers learned a lot from that bridge collapse, and it hasn’t been repeated. But the same factors influence the operation of gas turbine engines. To cut weight and boost performance, compressor and turbine blades need to be made as light as possible. However, this also makes them more susceptible to a type of vibratory damage called high cycle fatigue (HCF), resulting in premature failures. Unlike bridges, however, you can’t build a scale model of a turbine rotor and stick it in a wind tunnel to see how it performs. New techniques for merging the fields of computational fluid dynamics (CFD), finite element analysis (FEA) and computer aided design (CAD), however, make it possible to predict HCF and model how using selective mistuning of the blades can mitigate the damage caused by HCF. A major cause of crashes HCF is caused by vibratory stress cycles arising from a variety of aeromechanical forces. The frequencies involved are often in the thousands of cycles per second. HCF is of particular concern with jet airplanes, being a major cause of engine failures and sometimes resulting in the loss of the plane. According to the High Cycle Fatigue Science and Technology Program (HCF S&T Program), a group led by the United States Air Force, between 1982 and 1996, HCF was responsible for 56 percent of all Class A engine-related failures (a Class A mishap is one that results in over $1,000,000 damage, loss of a plane, loss of a life or permanent total disability). Annual HCF-related losses are estimated at $400 million, and an expenditure of 850,000 man-hours for risk management inspections. HCF, however, is not limited to the military or to jets. It also impacts commercial and land-based equipment. In fact, HCF is a potential problem with any rotating machine - turbo chargers, compressors, pumps, turbines, fans and so on. It is of concern for power producers using aeroderivative or other turbines, bu fortunately not to the same level as in aviation. To begin with, if a turbine generator throws a blade you have an unscheduled outage, but you don’t die. Secondly, a difference between a jet engine and a turbine used in power generation is that in power generation there is typically a single speed that is maintained throughout operation. The consequence of a constant RPM is that the unsteady forcing functions (rotor/stator interactions) are all known and hence it is a little easier to avoid resonance. Resonance is a situation where a forcing on a blade occurs at one of the blade’s natural frequencies, e.g. first bend mode. If the unsteady forcing functions - wake passing for instance - occur at this frequency, a large amplitude response will occur, thus limiting the life of the component. HCF and turbine design Designers of high-performance turbomachines have long recognized the need to compromise between steady aerodynamic performance, structural integrity, and the dynamic properties of turbomachinery blading. For example, improvements in steady aerodynamic performance can be obtained simply by reducing blade thickness, eliminating part-span shrouds or modifying the blade sweep. Eventually, however, a structural design limit is reached; the fatigue life of the blade becomes unacceptably low due to excessive flow-induced vibrations, or the blade flutters leading to catastrophic blade failure. Thus, the aeroelastic behavior of the airfoil, and in particular the unsteady aerodynamic response, should be of central importance in any compressor or turbine development program that attempts to optimize steady aerodynamic performance. With current trends in compressor or turbine designs calling for greater loading, higher speed, and increased efficiency, the ability to predict accurately the unsteady behavior becomes increasingly important. This is especially true because empirical design rules derived from past experiences cannot be effectively extrapolated into the operating regimes of new designs. Because engineers are already using such sophisticated tools in the design and development of turbomachinery, it is rare that HCF will occur at “design point” operation. Usually conditions where HCF (flutter and/or forced response) are likely to occur are at off-design conditions such as part speed or close to the surge line. The two major players in high cycle fatigue are forced response and flutter. Forced response is an external fluid dynamic forcing on a blade which causes the blade to vibrate. These forcing functions can be caused by the wakes emanating from upstream blade rows and/or the potential (pressure) fields developed from the neighboring blade rows. As there are so many blade rows, each with a different number of blades, it is virtually impossible to avoid the natural frequency of all blade rows under all operational speeds. The trick is to pass through resonance conditions quickly so as not to excite the offended blade row. Flutter on the other hand, is a fluid dynamic instability resulting in self-excited motion of a blade. That is, no external forcing functions are required to initiate large amplitude vibrations. This is the more difficult case to predict as we cannot merely look at the number of blades and o p e r a t i n g conditions (speed, pressure ratio and flow). Instead, one needs to be able to compute the aerodynamic damping present in the system. As contemporary turbomachines are becoming increasingly sophisticated while striving for higher pressure ratios, greater efficiency and reduced stages, the likelihood that flutter will occur is on the rise. It is very rare that we can make such appreciable gains in performance without paying a penalty somewhere else. In this case the penalty comes in the form of reduced component life. Modeling unsteady flows Aeroelasticians (people who study the interactions between aerodynamic forces and structural deformation) require accurate and efficient models of the unsteady flow fields that result from blade motion and incident gusts. These flows, however, are in general, time-dependent, three dimensional, compressible, and viscous, making their computation a challenging task. Until recently, the computer storage and computational time required to resolve accurately the boundary layers adjacent to the airfoil surfaces and endwalls have made threedimensional unsteady viscous calculations prohibitively expensive for routine design applications. While previous uncoupled analyses have gone a long way toward meeting the needs of turbomachinery designers by providing efficient unsteady aerodynamic response predictions, they fail to model potentially important unsteady flow phenomena associated with viscous boundary layer displacement and flow separation, large shock motions, finite amplitude blade vibrations and gust loads. With the advent of ever more powerful computers, a number of computational fluid dynamics (CFD) techniques have been developed which apply to the field of aeroelasticity. The method I will discuss here uses finite element modeling (FEM) software to compute the mass, damping and stiffness matrices required to solve the transient structural dynamics equations of motion. (See Table 1, Two-Dimensional Blade Structural Parameters). The matrices are then reduced to the most essential degrees of freedom. These matrices are used to compute the deformations of the structure within the CFD analysis itself. Constructed in this manner, the computational effort required to solve both the fluid and structural equations of motion is minimized, resulting in a methodology viable for industrial aeroelastic design assessment. STAR-CD, has numerous capabilities essential for modeling the complex aerodynamics associated with typical rotor-stator interaction analyses. The fully three-dimensional, viscous and compressible solver and may be used to compute either steady-state or transient flow problems using a variety of turbulence models. The structural analysis is performed by the CFD software using an extended application module called es-fsi (Expert System - Fluid-Structure Interaction) which computes the required load vector and the resulting time-dependen deformations as the unsteady flow develops. A fluid-structure interaction simulation entails three tasks: • Preprocessing - Building the computational models of the fluid and solid domains. These may be meshed separately, if desired, but must match reasonably well at the surface. Then certain surface nodes are selected out and designated as Master Degrees of Freedom (MDOF). Limiting the modeling to these MDOFs, reduces the size of the matrix used in the simulation and thereby speeds up the processing. • FSI simulation - During each time step, CFD software computes the fluid pressures, flow velocities, scalar quantities such as temperature, and turbulence kinetic energy and dissipation. These pressures act on the fluid-solid interface areas so that equivalent forces at the vertices corresponding to the MDOF can be computed. These forces therefore form the load vector on the right hand side of the dynamic equations of motion - [M]{u}+[C]{u}+[K]{u}={F} - where [M], [C] and [K] are the reduced mass, damping and stiffness matrices for the MDOF. Once the MDOF displacements are computed at a particular tim step, displacements for the non- MDOF surface vertices are interpolated. The new surface vertex positions are then used to move the surface mesh, and the internal mesh is filled and smoothed to maintain good mesh quality. The new pressures, velocities and other conserved variables are computed at the next time level and the entire process is repeated until the transient analysis is complete • Post-processing - The final task consists of reading the unsteady fluid pressures computed by the CFD analysis into an FEM code so that a transient dynamic analysis can be performed. Throughout the solution procedure, surface pressures are written to an external file for later post-processing. These may be used to prescribe the boundary conditions at various times in the transient dynamic analysis. The results of the FEM transient dynamics analysis include the nodal stresses which may be used to predict the fatigue life of the structure. The results can be analyzed in either a two-dimensional or three dimensionalmodel. Selective mistuning In theory, every blade in a typical blade row is deemed to be identical. Selective mistuning is a process whereby each blade in the row is slightly altered in a mechanical sense (i.e. slightly more or less thickness, camber, etc.). These differences, albeit subtle, change the natural frequencies for each blade. One could argue that normal variation in the manufacturing process already does this - and they would be correct. The difference in selective mistuning is the level to which the variations occur and how the mistuned blades are located around the wheel during assembly. With each blade on the wheel being slightly different it is now more difficult to excite the entire row, thus mitigating HCF. To use the modeling discussed above to selectively mistune an engine, one first has to realize that as the blade is altered (mistuned), not only are the structural properties of the blade affected, but so also is the aerodynamic performance. The first step in a detailed, three-dimensional assessment of the unsteady performance would be to propose a mistuning pattern or collection of blades. Next, one has to, for each blade, construct a computational model that includes both the structural properties (i.e. finite element model which reports the mass, stiffness and damping characteristics) and the detaile aerodynamic shape. As in all CFD analyses this involves the construction of a computational mesh. Next, the multiple numerical analyses must be performed to simulate a range of operating conditions to assess the effectiveness of the proposed mistuning pattern. While this sounds complex, in actuality it is quite straightforward and small improvements in unsteady performance translate to millions of dollars in savings in lost aircraft, warranty claims and maintenance costs. At this point, fundamental research is being conducted at several universities, and Wright-Patterson Air Force Base has conducted detailed analysis and experimentation to assess the value of mistuning. The analysis techniques are gaining acceptance and are being applied to help predict live and call attention to problematic designs. Once adopted, HCF analysis and selective mistuning would be done by the manufacturer as part of the original equipment design, not by the user as part of a maintenance outage. However at this time, HCF mitigation has been relegated to a secondary concern. This is due, in part, to the fact that only recently have we begun to understand how to predict enough of the salient physics to make aeroelastic calculations worthwhile. It would be difficult, if not impossible, for anyone other than the OEM to perform a full aeroelastic analysis because of the detailed technical information required for a successful simulation.