scholarly journals Three-Dimensional Elasticity-Based Solutions for Natural Vibrations of Low Aspect Ratio Compressor Blades

1993 ◽  
Author(s):  
Oliver G. McGee
Keyword(s):  
Aspect Ratio ◽  
Twist Angle ◽  
Ritz Method ◽  
Three Dimensional ◽  
Natural Vibrations ◽  
Compressor Blades ◽  
Low Aspect Ratio ◽  
Plate And Shell ◽  
Convergence Study ◽  
Three Dimensional Elasticity

This paper offers three-dimensional (3-D) vibration frequency solutions for low aspect ratio compressor blades. The Ritz method is used to minimize the 3-D elasticity-based dynamical energies with displacements approximated by mathematically complete polynomials satisfying the clamped boundary conditions exactly. The accuracy of the method is established by a convergence study explicitly showing the influence of solution determinant size. Several tables are presented which show the variation of natural frequencies with twist angle in the presence of skewness of low aspect ratio compressor blades. Results obtained using the present Ritz method are used to elucidate those frequency solutions which are inaccessible using beam, plate and shell theories, since kinematic constraints associated with these theories are eliminated in the present 3-D approach.

Vibration Characteristics of Low Aspect Ratio Compressor Blades

1971 ◽  
Vol 93 (1) ◽  
pp. 103-112 ◽  
Author(s):  
Ralph Petricone ◽  
Fernando Sisto
Keyword(s):  
Aspect Ratio ◽  
Contact Point ◽  
Twist Angle ◽  
Ritz Method ◽  
Three Dimensional ◽  
Beam Theory ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Compressor Blades ◽  
Low Aspect Ratio

This paper presents the results of a study of the vibration characteristics of low aspect ratio compressor blades. The treatment is based on thin shell theory and the Rayleigh-Ritz method is used to obtain the eigenvectors and eigenvalues. The object is to elucidate those characteristics which are inaccessible using beam theory. Results are presented which show the variation of the natural frequencies and mode shapes with angle of twist, aspect ratio, and angle of inclination of the base of the blade. A three-dimensional plot of the bending mode frequencies versus aspect ratio and twist angle is presented. Although the surfaces describing the variation of frequencies for specific modes do not intersect, there is a point of contact. This contact point is significant in the transition of mode shapes along the frequency surfaces. It is demonstrated that the “stiff-direction” or “in-plane” vibration of the untwisted plate evolves into coupled bending modes as the twist angle increases from zero and that the character of these modes changes in the vicinity of the contact point.

Three-Dimensional Vibration Analysis of Twisted Cylinder With Sectorial Cross Section

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
D. Zhou ◽  
S. H. Lo
Keyword(s):  
Cross Section ◽  
Chebyshev Polynomial ◽  
Numerical Solutions ◽  
Twist Angle ◽  
Ritz Method ◽  
Three Dimensional ◽  
Cylindrical Domain ◽  
Linear Elasticity Theory ◽  
Boundary Functions ◽  
Polynomial Series

The three-dimensional (3D) free vibration of twisted cylinders with sectorial cross section or a radial crack through the height of the cylinder is studied by means of the Chebyshev–Ritz method. The analysis is based on the three-dimensional small strain linear elasticity theory. A simple coordinate transformation is applied to map the twisted cylindrical domain into a normal cylindrical domain. The product of a triplicate Chebyshev polynomial series along with properly defined boundary functions is selected as the admissible functions. An eigenvalue matrix equation can be conveniently derived through a minimization process by the Rayleigh–Ritz method. The boundary functions are devised in such a way that the geometric boundary conditions of the cylinder are automatically satisfied. The excellent property of Chebyshev polynomial series ensures robustness and rapid convergence of the numerical computations. The present study provides a full vibration spectrum for thick twisted cylinders with sectorial cross section, which could not be determined by 1D or 2D models. Highly accurate results presented for the first time are systematically produced, which can serve as a benchmark to calibrate other numerical solutions for twisted cylinders with sectorial cross section. The effects of height-to-radius ratio and twist angle on frequency parameters of cylinders with different subtended angles in the sectorial cross section are discussed in detail.

Calculation of the Rise and Pitch of a Three-Dimensional Low-Aspect-Ratio Flat Ship

1991 ◽  
Vol 35 (04) ◽  
pp. 314-324
Author(s):  
Todd McComb
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Static Case ◽  
Equilibrium Flow ◽  
Low Aspect Ratio ◽  
Fast Speed ◽  
Flow Past

Using low-aspect-ratio flat ship theory, this paper defines a procedure to determine the position of a hull which is in equilibrium at some "fast" speed in terms of a given hull shape for the same hull at rest. This procedure is then used to find the equilibrium flow past a moving ship, when given the shape of the hull at rest. The method is then extended to find the hull configuration at various speeds based on either the configuration in the static case or at some other equilibrium speed, leading to a calculation of drag versus speed. Some general formulas and some simple examples are given.

Improving the Performance of a Turbine With Low Aspect Ratio Stators by Aft-Loading

2004 ◽  
Vol 128 (3) ◽  
pp. 492-499 ◽  
Author(s):  
Graham Pullan ◽  
John Denton ◽  
Eric Curtis
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Loss Reduction ◽  
Low Aspect Ratio ◽  
Surface Pressure Distribution ◽  
Loaded Surface ◽  
Nozzle Guide ◽  
Nozzle Guide Vanes ◽  
Stage Efficiency

Experimental data and numerical simulations are presented from a research turbine with low aspect ratio nozzle guide vanes (NGVs). The combined effects of mechanical and aerodynamic constraints on the NGV create very strong secondary flows. This paper describes three designs of NGV that have been tested in the turbine, using the same rotor row in each case. NGV 2 used three-dimensional design techniques in an attempt to improve the performance of the datum NGV 1 blade, but succeeded only in creating an intense vortex shed from the trailing edge (as previously reported) and lowering the measured stage efficiency by 1.1% points. NGV 3 was produced to avoid the “shed vortex” while adopting a highly aft-loaded surface pressure distribution to reduce the influence of the secondary flows. The stage with NGV 3 had an efficiency 0.5% points greater than that with NGV 1. Detailed comparisons between experiment and computations, including predicted entropy generation rates, are used to highlight the areas where the loss reduction has occurred and hence to quantify the effects of employing highly aft-loaded NGVs.

The Lift on Wings at Sonic Speeds by Means of an Electrical Resistance Analogue

1956 ◽  
Vol 60 (542) ◽  
pp. 137-139
Author(s):  
P. J. Palmer
Keyword(s):  
Aspect Ratio ◽  
Electrical Resistance ◽  
Close Agreement ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Sonic Velocity ◽  
Dimensional Problem ◽  
Low Aspect Ratio ◽  
Small Incidence ◽  
Low Aspect Ratio Wings

This note shows how a pure resistance analogue can be used to find the lift on low aspect ratio wings travelling, with small incidence, at speeds close to the sonic velocity.The method is applicable to flat, twisted or cambered wings and is simple in operation; the results obtained being in close agreement with those obtained by calculations based on the same theory.The solutions given in this note are essentially those corresponding to the Jones theory, which is applicable to low aspect ratio wings at small incidence, travelling with velocity close to the sonic value. Under these conditions it has been shown that the three-dimensional problem reduces to a series of two-dimensional problems in planes perpendicular to the direction of motion. Thus the wing can be considered as a series of spanwise sections, the solution for each section, in terms of the velocity potential, being considered in turn.

Unsteady Aerodynamics of a Low Aspect Ratio Turbine Stage: Modeling Issues and Flow Physics

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
G. Persico ◽  
A. Mora ◽  
P. Gaetani ◽  
M. Savini
Keyword(s):  
Aspect Ratio ◽  
Coming Out ◽  
Three Dimensional ◽  
Unsteady Aerodynamics ◽  
Fast Response ◽  
Operating Conditions ◽  
Pressure Probe ◽  
Turbine Stage ◽  
Time Resolved ◽  
Low Aspect Ratio

In this paper the three-dimensional unsteady aerodynamics of a low aspect ratio, high pressure turbine stage are studied. In particular, the results of fully unsteady three-dimensional numerical simulations, performed with ANSYS-CFX, are critically evaluated against experimental data. Measurements were carried out with a novel three-dimensional fast-response pressure probe in the closed-loop test rig of the Laboratorio di Fluidodinamica delle Macchine of the Politecnico di Milano. An analysis is first reported about the strategy to limit the CPU and memory requirements while performing three-dimensional simulations of blade row interaction when the rotor and stator blade numbers are prime to each other. What emerges as the best choice is to simulate the unsteady behavior of the rotor alone by applying the stator outlet flow field as a rotating inlet boundary condition (scaled on the rotor blade pitch). Thanks to the reliability of the numerical model, a detailed analysis of the physical mechanisms acting inside the rotor channel is performed. Two operating conditions at different vane incidence are considered, in a configuration where the effects of the vortex-blade interaction are highlighted. Different vane incidence angles lead to different size, position, and strength of secondary vortices coming out from the stator, thus promoting different interaction processes in the subsequent rotor channel. However some general trends can be recognized in the vortex-blade interaction: the sense of rotation and the spanwise position of the incoming vortices play a crucial role on the dynamics of the rotor vortices, determining both the time-mean and the time-resolved characteristics of the secondary field at the exit of the stage.

The method of caustics for the determination of normal loads acting on surfaces of elastic bodies

1980 ◽  
Vol 15 (1) ◽  
pp. 37-41 ◽  
Author(s):  
P S Theocaris ◽  
N I Ioakimidis
Keyword(s):  
Three Dimensional ◽  
Contact Problems ◽  
Two Dimensional ◽  
Concentrated Force ◽  
Elastic Bodies ◽  
Plate And Shell ◽  
Elasticity Problems ◽  
Three Dimensional Elasticity ◽  
Quantities Of Interest

The optical method of caustics constitutes an efficient experimental technique for the determination of quantities of interest in elasticity problems. Up to now, this method has been applied only to two-dimensional elasticity problems (including plate and shell problems). In this paper, the method of caustics is extended to the case of three-dimensional elasticity problems. The particular problems of a concentrated force and a uniformly distributed loading acting normally on a half-space (on a circular region) are treated in detail. Experimentally obtained caustics for the first of these problems were seen to be in satisfactory agreement with the corresponding theoretical forms. The treatment of various, more complicated, three-dimensional elasticity problems, including contact problems, by the method of caustics is also possible.

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