Timothy C. Allison

A Deconvolution-Based Approach to Structural Dynamics System Identification and Response Prediction

Two general linear time-varying system identification methods for multiple-input multiple-output systems are proposed based on the proper orthogonal decomposition (POD). The method applies the POD to express response data for linear or nonlinear systems as a modal sum of proper orthogonal modes and proper orthogonal coordinates (POCs). Drawing upon mode summation theory, an analytical expression for the POCs is developed, and two deconvolution-based methods are devised for modifying them to predict the response of the system to new loads. The first method accomplishes the identification with a single-load-response data set, but its applicability is limited to lightly damped systems with a mass matrix proportional to the identity matrix. The second method uses multiple-load-response data sets to overcome these limitations. The methods are applied to construct predictive models for linear and nonlinear beam examples without using prior knowledge of a system model. The method is also applied to a linear experiment to demonstrate a potential experimental setup and the methods feasibility in the presence of noise. The results demonstrate that while the first method only requires a single set of load-response data, it is less accurate than the multiple-load method for most systems. Although the methods are able to reconstruct the original data sets accurately even for nonlinear systems, the results also demonstrate that a linear time-varying method cannot predict nonlinear phenomena that are not present in the original signals.

Testing and Modeling of an Acoustic Instability in Pilot-Operated Pressure Relief Valves

Pressure relief valves are included as an essential element of many compressor piping systems in order to prevent overpressurization and also to minimize the loss of process gas during relief events. Failure of the valve to operate properly can result in excessive quantities of vented gas and/or catastrophic failure of the piping system. Several mechanisms for chatter and instability have been previously identified for spring-loaded relief valves, but pilot-operated relief valves are widely considered to be stable. In this paper, pilot-operated pressure relief valves are shown to be susceptible to a dynamic instability under certain conditions where valve dynamics couple with upstream piping acoustics. This self-exciting instability can cause severe oscillations of the valve piston, damaging the valve seat, preventing resealing and possibly causing damage to attached piping. Two case studies are presented that show damaging unstable oscillations in a field installation and a blowdown rig, and a methodology is presented for modeling the instability by coupling a valve dynamic model with a 1-D transient fluid dynamics simulation code. Modeling results are compared with measured stable and unstable operation in a blowdown rig to show that the modeling approach accurately predicts the observed behaviors.© 2015 ASME

MANUFACTURING AND TESTING EXPERIENCE WITH DIRECT METAL LASER SINTERING FOR CLOSED CENTRIFUGAL COMPRESSOR IMPELLERS

Direct Metal Laser Sintering (DMLS) is an additive manufacturing process that utilizes a high-powered laser to build up a metal part by selectively melting thin layers of metal powder. This process is attractive for the manufacturing of parts with complex geometry such as closed centrifugal compressor impellers. DMLS allows closed impellers to be made in a single piece and eliminates the shroud joint that results from two-piece manufacturing processes. Using a monolithic impeller can allow higher tip speeds with improved fatigue characteristics compared with two-piece and three-piece designs. Prototype parts can be made more economically than investment casting when considering the tooling costs. Manufacturing costs for DMLS parts are marginally higher than for two-piece machined impellers, but qualification efforts for the braze/weld joint at the cover are circumvented. The DMLS process introduces several factors that must be considered in the impeller design to achieve a successful build with the proper strength and surface finish. This paper describes the authors’ experience with manufacturing and testing multiple closed impeller designs constructed from Inconel 718, 17-4 PH Stainless Steel, and Titanium 6Al-4V. A detailed discussion of design factors and manufacturing experience with a DMLS vendor is included for the various metals. Dimensional, post-test destructive inspection, and material test results are provided showing that the DMLS process can produce an impeller with good dimensional accuracy, surface finish, and material strength. Finally, overspeed test results up to maximum tip speeds of over 1400 ft/s (425 m/s) and aerodynamic performance test results are presented and discussed.

Free-Response Simulation via the Proper Orthogonal Decomposition

The proper orthogonal decomposition is applied to the response of linear and nonlinear beam models to construct a reduced-order model for predicting the response to various initial conditions without requiring the equations of motion for the structure. The proper orthogonal decomposition is interpreted as a modal sum, and the structural response to an initial condition is expressed as a weighted summation of proper orthogonal modes and corresponding proper orthogonal coordinate histories. A method for calculating the weights of each mode in the response to an altered initial condition is presented. This method is applied to predict the responses of a linear undamped beam model and a damped beam model with a nonlinear spring to various initial displacement and velocity profiles. The results obtained are compared with those from respective finite element models for each beam.

Effects of Stator Flow Distortion on Rotating Blade Endurance: Part 2—Stress Analysis and Failure Criteria

Blade vibrations, with the possibility of failure, is one of the major factors controlling the reliability of compressors and turbines. The prospects of encountering high alternating stress environments in blades make efficient turbomachine operation a very challenging task. In many cases the compressor or turbine functions through a wide range of load, flow, temperature, and speed which affect blade vibration, thus the stress environment continuously changes as the operating conditions changes. Any flow disturbance upstream of the rotating blades and some disturbances downstream will produce repetitive wake pulses that excite the blades. Resonance occurs with any coincidence of repetitive pulses with structural natural frequencies of rotating blades or impellers resulting in substantial amplification of alternating stresses. Most OEM design practices control vibratory stresses by avoiding resonance with expected stator sources; those excitations that cannot be avoided are designed with sufficient endurance to prevent failure. Thus three aspects of rotor/ blade design affect reliability: 1) aerodynamic excitation level and frequency, 2) structural response and resonance margins, and 3) selection and control of materials, coatings and their fabrication process to withstand the service environment. The main objective of this study is to develop a mathematical model to simulate the stresses in the rotating blade row that evaluates all three aspects of design to assess long term endurance.This is a two part paper on high cycle fatigue (HCF) failure analysis procedure of rotating blades and impellers. Part 1 [1] discusses aerodynamic excitation caused by stator vane and its role in generation of blade vibration. Here comprehensive computational fluid dynamics (CFD) is used to get a better understanding of the stator-rotor flow interactions at different operating conditions. The results of the aerodynamic simulations are order related excitation spectrum that can be applied to the stress/pulsation relationship defined in this part of the paper.This paper, Part 2, discusses an empirical dynamic stress model developed by impulse testing, assessing material endurance strength, and evaluation of criteria for failure by HCF.Copyright

Experimental Validation of Empirical Methods for Dynamic Stress Prediction in Turbomachinery Blades

Turbomachinery blade fatigue life estimation requires reliable knowledge of actual static and dynamic stresses occurring within the blades. A common method for predicting dynamic stresses is to construct a finite element model of the blade and simulate the dynamic response to aerodynamic loads. Although this method is powerful and very useful, modeling errors (geometry, boundary conditions, stress concentrations, damping, etc.) may result in inaccurate stress predictions. Furthermore, unavoidable variability in manufacturing results in blade mistuning, which significantly affects stress amplification at resonance. This paper presents two empirical methods for predicting dynamic stresses in turbomachinery blades that include the actual effects of structural damping and mistuning. Both methods use strain gauge measurements from a blade modal test to obtain load to strain transfer functions, which are applied to predict the blade strain or stress response to a simulated load. The advantages and disadvantages of each method are discussed. The predictions of each method are compared with dynamic blade strain data acquired during a rotating test of a centrifugal compressor impeller.Copyright

Revisiting the SAFE Diagram for Analysis of Mistuned Bladed Disks

The SAFE diagram is a design tool that is often used for analyzing modes of concern in bladed disks. The diagram implements the concept of phase cancellation in order to show what bladed disk modes can and cannot be excited by upstream flow obstructions. In many cases, phase cancellation theory dictates that even if a modal frequency corresponds with an excitation order, the mode may not be excited if the total work calculated by integrating the excitation profile around the mode shape is equal to zero. This paper reviews the theory behind the SAFE diagram and explores the effects of blade mistuning on SAFE diagram analysis from both theoretical and experiential viewpoints. Modal test data, mistuned finite element analysis, and two case studies all indicate that mistuned modes may not exhibit the pure nodal diameter patterns that are predicted by a symmetric analysis and are required for phase cancellation. These mistuned asymmetric modes may result in high blade stresses and blade failure even if a SAFE diagram analysis indicates that the mode will not be excited.© 2012 ASME

Development of an Internally Cooled Centrifugal Compressor for Carbon Capture and Storage Applications

In order to reduce the amount of carbon dioxide (CO2) released into the atmosphere, significant progress has been made into capturing and storing CO2 from power plants and other major producers of greenhouse gas emissions. The compression of the captured carbon dioxide stream requires significant amounts of power and can impact plant availability, and increase operational costs. Preliminary analysis has estimated that the CO2 compression process reduces plant efficiency by 8% to 12% for a typical power plant. This project supports the U.S. Department of Energy (DOE) National Energy Technology Laboratory (NETL) objective of reducing energy requirements for carbon capture and storage in electrical power production. The primary objective of this study is to boost the pressure of CO2 to pipeline pressures with the minimal amount of energy required. Previous thermodynamic analysis identified optimum processes for pressure rise in both liquid and gaseous states. Isothermal compression is well known to reduce the power requirements by minimizing the temperature of the gas entering subsequent stages. Intercooling is typically accomplished using external gas coolers and integrally geared compressors. For large scale compression, use of straight through centrifugal compressors, similar to those used in oil and gas applications including LNG production, is preferred due to the robustness of the design. However, intercooling between each stage is not feasible. The current research develops an internally cooled compressor diaphragm that removes heat internal to the compressor. Results documenting the design process are presented including 3D conjugate heat transfer CFD studies. Experimental demonstration of the design is performed on a sub scale centrifugal compressor closed loop test facility for a range of suction pressures.Copyright

OPEN-LOOP AERODYNAMIC PERFORMANCE TESTING OF A 105,000 RPM OIL- FREE COMPRESSOR-EXPANDER FOR SUBSURFACE NATURAL GAS COMPRESSION AND REINJECTION

An aerodynamic performance test stand has been developed for validation of the performance of a 105,000 rpm compressor-expander which is intended for subsurface natural gas reinjection. The turbomachine consists of a two-stage centrifugal compressor, which is driven by a single-stage expansion turbine. The rotor is supported by foil gas journal bearings and a spiral-groove gas thrust bearing. The test stand is configured for open-loop testing of the overall compressor and turbine performance with air as the working fluid and atmospheric pressure at the compressor suction and turbine discharge locations. Several performance curves were generated for each component ranging from 73,500–115,500 rpm (70–110% of design speed). In general, measured compressor head was slightly lower than predictions, while measured efficiencies were close to predicted values. The turbine had higher flow than predicted, due in part to a larger flow area in the turbine. The turbomachine has shown acceptable performance on the open-loop test stand, and further testing at higher-pressure closed-loop conditions are planned.Copyright

Qualification Testing of a Liquid CO2 Turbopump for Carbon Capture and Sequestration Applications

In order to reduce the amount of carbon dioxide (CO2 ) greenhouse gases released into the atmosphere, significant progress has been made in developing technology to sequester CO2 from power plants and other major producers of greenhouse gas emissions. The compression of the captured carbon dioxide stream requires a sizeable amount of power, which impacts plant availability, capital expenditures and operational cost. Preliminary analysis has estimated that the CO2 compression process reduces the plant efficiency by 8% to 12% for a typical power plant. The goal of the present research is to reduce this penalty through development of novel compression and pumping processes. The research supports the U.S. Department of Energy (DOE) National Energy Technology Laboratory (NETL) objectives of reducing the energy requirements for carbon capture and sequestration in electrical power production. The primary objective of this study is to boost the pressure of CO2 to pipeline pressures with the minimal amount of energy required. Previous thermodynamic analysis identified optimum processes for pressure rise in both liquid and gaseous states. At elevated pressures, CO2 assumes a liquid state at moderate temperatures. This liquefaction can be achieved through commercially available refrigeration schemes. However, liquid CO2 turbopumps of the size and pressure needed for a typical power plant were not available. This paper describes the design, construction, and qualification testing of a 150 bar cryogenic turbopump. Unique characteristics of liquid CO2 will be discussed.© 2011 ASME