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The programming routines for the NASTRAN Level 16program are presented. Particular emphasis is placed on its application to aeroelastic analyses, mode development, and flutter analysis for turbomachine blades.
To be of quantitative value to the designer and analyst, it is necessary to experimentally verify the flow modeling and the numerics inherent in calculation codes being developed to predict the three dimensional flow through turbomachine blade rows. This experimental verification requires that predicted flow fields be correlated with three dimensional data obtained in experiments which model the fundamental phenomena existing in the flow passages of modern turbomachines. The Purdue Annular Cascade Facility was designed specifically to provide these required three dimensional data. The overall three dimensional aerodynamic performance of an instrumented classical airfoil cascade was determined over a range of incidence angle values. This was accomplished utilizing a fully automated exit flow data acquisition and analysis system. The mean wake data, acquired at two downstream axial locations, were analyzed to determine the effect of incidence angle, the three dimensionality of the cascade exit flow field, and the similarity of the wake profiles. The hub, mean, and tip chordwise airfoil surface static pressure distributions determined at each incidence angle are correlated with predictions from the MERIDL and TSONIC computer codes.
The LINFLUX-AE computer code predicts flutter and forced responses of blades and vanes in turbomachines under subsonic, transonic, and supersonic flow conditions. The code solves the Euler equations of unsteady flow in a blade passage under the assumption that the blades vibrate harmonically at small amplitudes. The steady-state nonlinear Euler equations are solved by a separate program, then equations for unsteady flow components are obtained through linearization around the steady-state solution. A structural-dynamics analysis (see figure) is performed to determine the frequencies and mode shapes of blade vibrations, a preprocessor interpolates mode shapes from the structural-dynamics mesh onto the LINFLUX computational-fluid-dynamics mesh, and an interface code is used to convert the steady-state flow solution to a form required by LINFLUX. Then LINFLUX solves the linearized equations in the frequency domain to calculate the unsteady aerodynamic pressure distribution for a given vibration mode, frequency, and interblade phase angle. A post-processor uses the unsteady pressures to calculate generalized aerodynamic forces, response amplitudes, and eigenvalues (which determine the flutter frequency and damping). In comparison with the TURBO-AE aeroelastic-analysis code, which solves the equations in the time domain, LINFLUX-AE is 6 to 7 times faster.
The characteristics of the flow field about highly loaded turbocompressor blades in a cascade wind tunnel were investigated. Experimental tests were conducted at chord Reynolds number (R sub c) near 500,000. A laser Doppler anemometer was employed in flow velocity measurement. Suction surface mean velocity and turbulence intensity profiles at a single incidence angle are presented. These data contribute to further understanding of two-dimensional boundary layer profiles, points of separation, and transition zones for turbomachine blades, and concomitantly, to compressor cascade predictive models.
Summarized here are key advances in experimental techniques and theoretical applications which point the way to a broad understanding and control of turbomachinery noise. On the experimental side, the development of effective inflow control techniques makes it possible to conduct, in ground based facilities, definitive experiments in internally controlled blade row interactions. Results can now be valid indicators of flight behavior and can provide a firm base for comparison with analytical results. Inflow control coupled with detailed diagnostic tools such as blade pressure measurements can be used to uncover the more subtle mechanisms such as rotor strut interaction, which can set tone levels for some engine configurations. Initial mappings of rotor wake-vortex flow fields have provided a data base for a first generation semiempirical flow disturbance model. Laser velocimetry offers a nonintrusive method for validating and improving the model. Digital data systems and signal processing algorithms are bringing mode measurement closer to a working tool that can be frequently applied to a real machine such as a turbofan engine. On the analytical side, models of most of the links in the chain from turbomachine blade source to far field observation point have been formulated. Three dimensional lifting surface theory for blade rows, including source noncompactness and cascade effects, blade row transmission models incorporating mode and frequency scattering, and modal radiation calculations, including hybrid numerical-analytical approaches, are tools which await further application.
A method for analyzing the nonadiabatic viscous flow through turbomachine blade passages was developed. The field analysis is based upon the numerical integration of the full incompressible Navier-Stokes equations, together with the energy equation on the blade-to-blade surface. A FORTRAN IV computer program was written based on this method. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system. The flow may be axial, radial or mixed and there may be a change in stream channel thickness in the through-flow direction. The inputs required for two FORTRAN IV programs are presented. The first program considers laminar flows and the second can handle turbulent flows. Numerical examples are included to illustrate the use of the program, and to show the results that are obtained.
Three dimensional aerodynamic data, required to validate and/or indicate necessary refinements to inviscid and viscous analyses of the flow through turbomachine blade rows, are discussed. Instrumentation and capabilities for pressure measurement, probe insertion and traversing, and flow visualization are reviewed. Advanced measurement techniques including Laser Doppler Anemometers, are considered. Data processing is reviewed. Predictions were correlated with the experimental data. A flow visualization technique using helium filled soap bubbles was demonstrated.
Three-dimensional viscous and inviscid numerical analyses are currently being developed to predict the complex flow through turbomachine blade passages. To be of value to the designer, these numerical solutions must be evaluated and subsequent refinements directed by correlating predicted flow fields with data obtained from experiments which model the fundamental three-dimensional flow phenomena inherent in blade rows. This paper describes a series of experiments to provide such data. In particular, the effect of a potential and a rotational inlet flow field on the detailed three-dimensional aerodynamic performance of an extensively instrumented cambered airfoil cascade has been determined at two levels of aerodynamic loading. Data presented quantify the pressure and suction surface static pressure chordwise distributions on the hub, mean, and tip streamlines; the velocity distribution in the cascade aft-passage region; and the cascade exit region flow field. Appropriate data are correlated with predictions.
The unsteady airloads generated by the vibrations of turbomachine blades operating at transonic Mach numbers are predicted by a linearized potential flow analysis whose unsteady aerodynamics model encompasses the effects of blade geometry, nonzero mean pressure variation across the blade row, high frequency blade motion, and shock motion, all within the framework of a linearized frequency-domain formulation. A numerical solution for the entire unsteady flow field is determined by matching a solution covering an extended blade passage region to another covering, and extending beyond, the supersonic region(s) adjacent to a blade surface. Results are given for cascades of double circular arc and flat plate blades, in order to demonstrate the unsteady analysis and to partially illustrate the effects of blade geometry, inlet Mach number, vibration frequency and shock motion on unsteady response.
The effect of aerodynamic detuning on the supersonic flow induced forced response behavior of a turbomachine blade row is analyzed using an aeroelastic model. The rotor is modeled as a flat plate airfoil cascade representing an unwrapped rotor annulus; the aerodynamic detuning is achieved by alternating the circumferential spacing of adjacent rotor blades. The total unsteady aerodynamic loading on the blading, due to the convection of the transverse gust past the airfoil cascade as well as that resulting from the motion of the cascade, is developed in terms of influence coefficients. The model developed here is then used to analyze the effect of aerodynamic detuning on the flow induced forced response behavior of a twelve-bladed rotor with Verdon's Cascade B flow geometry.
Models to predict the complex three-dimensional flow through turbomachine blade rows are being developed. To verify these models and direct necessary refinements, it is necessary that predictions be correlated with data obtained in experiments which model the fundamental three-dimensional blade row flow phenomena. This paper describes a series of experiments performed in a large scale, subsonic, annular cascade facility specifically designed to provide such data. In particular, the effect of incidence angle on the three-dimensional passage flow field through an annular cascade of cambered airfoils is investigated and quantified, accomplished by obtaining detailed and expensive LDA data. These data demonstrate and quantify the development of the passage vortices through the airfoil passage and their strong interaction with the endwall boundary layers.
The present method for the implementation of nonreflecting boundary conditions in 2D and 3D linearized unsteady flow computations is applied to cases of unsteady flows in turbomachine blade rows. The eigenmodes of a discrete representation of the governing equations are computed and used to construct nonreflecting boundary conditions. In 3D, a mixed numerical method is used; in 2D, the discrete representation of the governing equations is obtained from the discretized equations used by the flow solver itself. Wavenumbers and radial mode shapes are computed.
The fundamental forcing function unsteady aerodynamics for application to turbomachine blade row forced response are considered, accomplished through a series of experiments performed in a rotating annular cascade and a research axial flow turbine. In particular, the unsteady periodic flowfields downstream of rotating rows of perforated plates, airfoils and turbine blade rows are measured with a cross hot-wire and an unsteady total pressure probe. The unsteady velocity and static pressure fields were then analyzed harmonically and split into vortical and potential gusts, accomplished by developing a gust splitting analysis which includes both gust unsteady static pressure and velocity data. The perforated plate gusts closely were found to be linear theory vortical gusts, satisfying the vortical gust constraints. The airfoil and turbine blade row generated velocity perturbations did not satisfy the vortical gust constraints. However, the decomposition of the unsteady flow field separated the data into a propagating vortical component which satisfied these vortical gust constraints and a decaying potential component.
The exact transport equations for turbulent (Reynolds) stresses have left-hand sides representing the 'substantial derivatives' of the Reynolds stresses, i.e., the rates of change of stress with respect to time, as seen by an observer following the mean motion of the fluid. Here the 'mean' is a statistical average for the turbulent motion, distinguished from the ordered unsteadiness on which it is superimposed: for a turbomachine blade or a cyclically-pitching airfoil, the mean is a phase average. Written in coordinates fixed with respect to a solid surface, the substantial derivative appears partly as an Eulerian time derivative at given spatial coordinate position and partly as a spatial derivative. Separation presents two specific problems to a turbulence model: (1) prediction of the flow near separation depends critically on the 'near-wall' part of the turbulence model, and (2) downstream of separation, a boundary layer changes gradually to a mixing layer.
A preconditioning scheme has been implemented into a three-dimensional viscous computational fluid dynamics code for turbomachine blade rows. The preconditioning allows the code, originally developed for simulating compressible flow fields, to be applied to nearly-incompressible, low Mach number flows. A brief description is given of the compressible Navier-Stokes equations for a rotating coordinate system, along with the preconditioning method employed. Details about the conservative formulation of artificial dissipation are provided, and different artificial dissipation schemes are discussed and compared. The preconditioned code was applied to a well-documented case involving the NASA large low-speed centrifugal compressor for which detailed experimental data are available for comparison. Performance and flow field data are compared for the near-design operating point of the compressor, with generally good agreement between computation and experiment. Further, significant differences between computational results for the different numerical implementations, revealing different levels of solution accuracy, are discussed.
The Five-Axis, Three-Magnetic-Bearing Dynamic Spin Rig is an apparatus for vibration testing of turbomachine blades in a vacuum at rotational speeds from 0 to 40,000 rpm. This rig includes (1) a vertically oriented shaft on which is mounted an assembly comprising a rotor holding the blades to be tested, (2) two actively controlled heteropolar radial magnetic bearings at opposite ends of the shaft, and (3) an actively controlled magnetic thrust bearing at the upper end of the shaft. This rig is a more capable successor to a prior apparatus, denoted the Dynamic Spin Rig (DSR), that included a vertically oriented shaft with a mechanical thrust bearing at the upper end and a single actively controlled heteropolar radial magnetic bearing at the lower end.
Topics covered include: Optoelectronic Tool Adds Scale Marks to Photographic Images; Compact Interconnection Networks Based on Quantum Dots; Laterally Coupled Quantum-Dot Distributed-Feedback Lasers; Bit-Serial Adder Based on Quantum Dots; Stabilized Fiber-Optic Distribution of Reference Frequency; Delay/Doppler-Mapping GPS-Reflection Remote-Sensing System; Ladar System Identifies Obstacles Partly Hidden by Grass; Survivable Failure Data Recorders for Spacecraft; Fiber-Optic Ammonia Sensors; Silicon Membrane Mirrors with Electrostatic Shape Actuators; Nanoscale Hot-Wire Probes for Boundary-Layer Flows; Theodolite with CCD Camera for Safe Measurement of Laser-Beam Pointing; Efficient Coupling of Lasers to Telescopes with Obscuration; Aligning Three Off-Axis Mirrors with Help of a DOE; Calibrating Laser Gas Measurements by Use of Natural CO2; Laser Ranging Simulation Program; Micro-Ball-Lens Optical Switch Driven by SMA Actuator; Evaluation of Charge Storage and Decay in Spacecraft Insulators; Alkaline Capacitors Based on Nitride Nanoparticles; Low-EC-Content Electrolytes for Low-Temperature Li-Ion Cells; Software for a GPS-Reflection Remote-Sensing System; Software for Building Models of 3D Objects via the Internet; "Virtual Cockpit Window" for a Windowless Aerospacecraft; CLARAty Functional-Layer Software; Java Library for Input and Output of Image Data and Metadata; Software for Estimating Costs of Testing Rocket Engines; Energy-Absorbing, Lightweight Wheels; Viscoelastic Vibration Dampers for Turbomachine Blades; Soft Landing of Spacecraft on Energy-Absorbing Self-Deployable Cushions; Pneumatically Actuated Miniature Peristaltic Vacuum Pumps; Miniature Gas-Turbine Power Generator; Pressure-Sensor Assembly Technique; Wafer-Level Membrane-Transfer Process for Fabricating MEMS; A Reactive-Ion Etch for Patterning Piezoelectric Thin Film; Wavelet-Based Real-Time Diagnosis of Complex Systems; Quantum Search in Hilbert Space; Analytic Method for Computing Instrument Pointing Jitter; and Semiselective Optoelectronic Sensors for Monitoring Microbes.
Blading models added to TURBAN, an axial turbine meanline design code, and CSPAN, an axial compressor spanline design code, are presented. Calculations of blade chord length, blade axial length, and number of blades for each blade row are now provided by each code. In order to accomplish this, computational models for axial solidity and stagger angle were added to TURBAN. For a compressor, where solidity and chord were already available from input, the modeling additions to CSPAN were for stagger angle and for the blade angles to include incidence and deviation. All added computations utilized models already available in the literature.