The Optimum Design of Stepped Shafts: A Study in Computational Optimization

Optimum stepped shaft designs are obtained through an application of Pontryagin’s Minimum Principle. Optimum designs are obtained for a given critical speed of specified order. Indexes of Performance to be minimized include mass and rotating inertia. A general problem formulation illustrates how constraints on stress, deflections, and geometric design are taken in account. Numerical solutions are obtained to nonlinear multi-point-boundary-value-problems. A Newton-Raphson algorithm was developed to determine step locations precisely in order to facilitate the convergence of the shooting method used to solve the boundary value problem. Numerical solutions are determined with an assumed critical speed; a Rayleigh quotient calculation is used to verify that the optimum design possesses the assumed value.

Tuning of Turbine Blades: A Theoretical Approach

A perturbation method is described which predicts the changes in eigenfrequencies resulting from geometrical changes of a structure. This dependence is represented by dimensionless functions, one for each eigenfrequency, which vary over the surface of the structure. The functions are presented for each eigenfrequency as isoline plots. An easily estimated integration of these functions allows one to predict a geometrical change which results in a desired change in the resonance frequencies. The method was applied to a turbine blade and a rectangular beam. For the turbine blade isoline plots are presented for the first five eigenfrequencies. Eigenfrequency changes up to 8 percent were modeled accurately.

Ceramic Thermal Barrier Coatings for Turbine Engine Components

The durability of plasma sprayed ceramic thermal barrier coatings subjected to cyclic thermal environments has been improved substantially by improving the strain tolerance of the ceramic structure and also by controlling the substrate temperature during the application of the coating. Improved strain tolerance was achieved by using ceramic structures with increased porosity, microcracking or segmentation. Plasma spraying on a controlled-temperature substrate also has been shown to improve durability by reducing harmful residual stresses. The most promising of the strain tolerant ceramic coatings have survived up to 6000 cycles of engine endurance testing with no coating or vane platform damage. In side-by-side engine tests, thermal barrier coatings have shown that they greatly reduce platform distress compared to conventionally coated vanes in addition to permitting reductions in cooling air and attendant increases in engine efficiency.

Unsteady Gapwise Periodicity of Oscillating Cascaded Airfoils

Tests were conducted on a linear cascade of airfoils oscillating in pitch to measure the unsteady pressure response on selected blades along the leading edge plane of the cascade and over the chord of the center blade. The pressure data were reduced to Fourier coefficient form for direct comparison, and were also processed to yield integrated loads and, particularly, the aerodynamic damping coefficient. In addition, results from two unsteady theories for cascaded blades with nonzero thickness and camber were compared with the experimental measurements. The three primary results that emerged from this investigation were: (a) from the leading edge plane blade data, the cascade was judged to be periodic in unsteady flow over the range of parameters tested, (b) as before, the interblade phase angle was found to be the single most important parameter affecting the stability of the oscillating cascade blades, and (c) the real blade theory and the experiment were in excellent agreement for the several cases chosen for comparison.

The Effect of NaCl(g) in High Temperature Oxidation

Sodium chloride can be present in gas turbine hot sections in the vapor as well as the condensed state. Particles containing sodium chloride may randomly break from compressor components, then impinge upon and stick to turbine components further down the gas path. However, NaCl vapor can deleteriously affect processes involving the formation and maintenance of protective oxide layers on turbine components. The relative importance of these two distinctly different mechanisms involving NaCl in corrosion processes is currently unknown. Numerous studies have dealt with the effect on corrosion behavior of Na2SO4-NaCl condensed mixtures with appreciable amounts of NaCl. However, the possibility that low NaCl vapor activities effect major changes in oxide scale formation and retention is equally as probable as that involving condensed NaCl. Therefore, the results presented here will deal with effects of low activities of NaCl vapor (0.1–100 ppm) upon scales formed by selected high temperature materials.

The Fluid Dynamics of Turbomachinery Program: Objectives, Organization and Results

Since 1968, an advanced educational program in the fluid dynamics of turbomachinery has been offered by the ASME Turbomachinery Institute at Iowa State University. Initiated by concerned individuals to help meet the need for high-level, continuing education in this field of specialization, the course appears to be accomplishing its original intent. The success of the program can be attributed to a number of factors including a good faculty, an eager and qualified group of participants, and scholarly surroundings. As might be expected, timely and thoughtful planning, good luck and competent support are also essential. Of the many lessons learned about this kind of educational effort, several seem important enough to report in this paper.

Combustion Turbine Deposition Observations From Residual and Simulated Residual Oil Studies

Burning residual oil in utility combustion turbines and the consequent deposition on blades and vanes may adversely affect reliability and operation. Corrosion and deposition data for combustion turbine materials have been obtained through dynamic testing in pressurized passages. The deposition produced by the 1900°F (1038°C) combustion gases from a simulated and a real residual oil on cooled Udimet 500 surfaces is described. Higher deposition rates for the doped fuel than for the real residual oil raised questions of whether true simulation with this approach can be achieved. Particles 4–8 μ m in dia predominated in the gas stream, with some fraction in the 0.1–12 μ m range. Deposition rates seemed to be influenced by thermophoretic delivery of small molten particles, tentatively identified as magnesium pyro and metavanadates and free vanadium pentoxide, which may act to bond the larger, solid particles arriving by inertial impaction to turbine surfaces. Estimated maintenance intervals for current utility turbines operating with washed and treated residual oil agreed well with field experience.

Experimental Evaluation of Squeeze Film Supported Flexible Rotors

This paper describes the experimental investigations which were conducted to verify existing theoretical vibration amplitude predictions for centrally preloaded, squeeze film supported flexible rotors. The influence of measurement errors and operating condition uncertainties are quantified. The agreement between theory and experiment was excellent, and it is shown that any discrepancy can be explained in terms of errors in determining the mean lubricant viscosity and the orbit magnitudes. Hence, for the range of parameters investigated, the theoretical model and predictions therefrom are validated.

Solution to a Bistable Vibration Problem Using a Plain, Uncentralized Squeeze Film Damper Bearing

During service introduction of an uprated turbojet engine, which has a three-bearing rotor support system with an overhung turbine, several problems related to system vibration were encountered — cabin noise and high engine vibration levels. These problems led to a factory and field investigation which showed that the source of the problem was a nonlinear interaction between rotor and casing modes coupled through bearing clearance. This interaction led to a bistable vibration of the system. This paper documents the results of this investigation and demonstrates that the use of a plain, uncentralized, squeeze film damper to support the turbine rotor solves all vibration problems by reducing the turbine critical speed and separating it from the casing mode. Also included are effects of exhaust system weight on engine vibration and cabin noise levels.

A Theoretical Investigation of an Overhung Flexible Rotor Mounted on Uncentralized Squeeze-Film Damper Bearings and Flexible Supports

Previous investigations have shown that the uncentralized type of squeeze-film damper is an effective means of reducing the transmission of unbalance forces into the supporting structure. In this theoretical study a more complex model, which includes an overhung “fan” disc and a noncentral “turbine” disc, has been employed. This model represents the conventional gas turbine somewhat closer than does the previously studied single disc system. This investigation has shown that it is possible to minimize the force transmitted into the surrounding structure by a careful selection of squeeze-film damper characteristics, although it may be found that some larger amplitudes of motion accompany the minimized transmissibility.