Validation of Three-Dimensional Euler Methods for Vibrating Cascade Aerodynamics

1996 ◽  
Vol 118 (4) ◽  
pp. 771-782 ◽  
Author(s):  
G. A. Gerolymos ◽  
I. Vallet
Keyword(s):  
Subsonic Flow ◽  
Three Dimensional ◽  
Computational Results ◽  
Two Dimensional ◽  
Flat Plates ◽  
Dimensional Theory ◽  
Code Comparison ◽  
Euler Solver ◽  
Euler Methods ◽  
Theoretical Results

The purpose of this work is to validate a time-nonlinear three-dimensional Euler solver for vibrating cascades aerodynamics by comparison with available theoretical semi-analytical results from flat-plate cascades. First the method is validated with respect to the purely two-dimensional theory of Verdon (for supersonic flow) by computing two-dimensional vibration (spanwise constant) in linear three-dimensional cascades. Then the method is validated by comparison with the theoretical results of Namba and the computational results of He and Denton, for subsonic flow in a linear three-dimensional cascade with three-dimensional vibratory mode. Finally the method is compared with results of Chi from two subsonic rotating annular cascades of helicoi¨dal flat plates. Quite satisfactory agreement is obtained for all the cases studied. A first code-to-code comparison is also presented.

Validation of 3-D Euler Methods for Vibrating Cascade Aerodynamics

1994 ◽  
Author(s):  
Georg A. Gerolymos ◽  
Isabelle Vallet
Keyword(s):  
Subsonic Flow ◽  
Three Dimensional ◽  
Computational Results ◽  
Two Dimensional ◽  
Flat Plates ◽  
Dimensional Theory ◽  
Code Comparison ◽  
Euler Solver ◽  
Euler Methods ◽  
Theoretical Results

The purpose of this work is to validate a time-nonlinear three-dimensional Euler solver for vibrating cascades aerodynamics by comparison with available theoretical semi-analytical results from flat-plate cascades. First the method is validated with respect to the purely two-dimensional theory of Verdon (for supersonic flow) by computing two-dimensional vibration (spanwise constant) in linear three-dimensional cascades. Then the method is validated by comparison with the theoretical results of Namba and the computational results of He and Denton, for subsonic flow in a linear three-dimensional cascade with three-dimensional vibratory mode. Finally the method is compared with results of Chi from two subsonic rotating annular cascades of helicoïdal flat-plates. Quite satisfactory agreement is obtained for all the cases studied. A first code-to-code comparison is also presented.

Membrane theory

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Three Dimensional ◽  
Thin Sheets ◽  
Two Dimensional ◽  
Leading Order ◽  
Membrane Theory ◽  
Dimensional Theory ◽  
Small Thickness

This chapter develops two-dimensional membrane theory as a leading order small-thickness approximation to the three-dimensional theory for thin sheets. Applications to axisymmetric equilibria are developed in detail, and applied to describe the phenomenon of bulge propagation in cylinders.

An Investigation of the Predicting Capabilities of a Variable Flow Stress Machining Theory

2001 ◽  
Author(s):  
P. Mathew
Keyword(s):  
Flow Stress ◽  
Material Flow ◽  
Three Dimensional ◽  
Experimental Results ◽  
Two Dimensional ◽  
Variable Flow ◽  
Comparative Results ◽  
Intermittent Cutting ◽  
Theoretical Results ◽  
Modelling Approach

Abstract The Oxley Machining Theory, which has been developed over the last 40 years, is presented in this paper. The capability of the model is described with its initial two-dimensional machining approach followed by the extension to the generalised model for three-dimensional machining. The theoretical results from the model are compared with the experimental results to determine the model capability. A brief description of the work associated with the effect of strain hardening at the interface is presented and comparative results are shown. A further extension of the model to intermittent cutting process of reaming is also presented and a comparison with the experimental results indicates the model developed is quite capable of predicting cutting forces for reaming. In explaining the results obtain, the assumptions made are explained and the inputs required. The limitations of the modelling approach are presented. It is pointed out that the Oxley model is a versatile model as long as proper description of the material flow stress properties is presented.

Contact Temperature in Dry Bearings. Three Dimensional Theory and Verification

1981 ◽  
Vol 103 (2) ◽  
pp. 243-251 ◽  
Author(s):  
A. Floquet ◽  
D. Play
Keyword(s):  
Fourier Transform ◽  
Boundary Conditions ◽  
Experimental Verification ◽  
Three Dimensional ◽  
Contact Temperature ◽  
3D Analysis ◽  
New Work ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Infra Red

Boundary conditions were arbitrarily specified in an earlier two dimensional (2D) analysis of contact temperature. In this new work a general three dimensional (3D) Fourier transform solution is obtained from which for specific cases, the boundary conditions can be estimated. Further, experimental verification of 3D analysis was performed using infra-red technique.

CHARACTERISTICS OF MESOSCOPIC PHASE TRANSITIONS IN TWO-DIMENSIONAL SIMPLE NANOSTRUCTURED MATERIALS

2003 ◽  
Vol 17 (25) ◽  
pp. 4539-4554 ◽  
Author(s):  
YOSHITAKE YAMAZAKI ◽  
HERBERT GLEITER ◽  
CHENXU WU ◽  
VLADISLAV ALYOSHIN ◽  
JULY KRASILNIKOVA ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Nanostructured Materials ◽  
Critical Phenomena ◽  
Experimental Studies ◽  
Inert Gas ◽  
Computational Results ◽  
Two Dimensional ◽  
Metropolis Monte Carlo ◽  
Renormalization Theory ◽  
Theoretical Results

In order to study nanostructured materials, a fundamental framework of the theory and the computer-experimental studies is established. The essential characteristics of the mesoscopic phase transitions and critical phenomena in these materials are evaluated by means of this approach. For nanostructured materials consisting of inert gas atoms, we study mesoscopic phase transitions and critical phenomena by generalizing the renormalization theory and the Metropolis Monte Carlo method. The results obtained by the both methods are reported in two papers: computational results in the present paper and the theoretical results in the paper which follows.

Lattice-Boltzmann simulations of particles in non-zero-Reynolds-number flows

1999 ◽  
Vol 385 ◽  
pp. 41-62 ◽  
Author(s):  
DEWEI QI
Keyword(s):  
Reynolds Number ◽  
Cross Section ◽  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Spherical Particles ◽  
Computational Results ◽  
Two Dimensional ◽  
Lattice Boltzmann Simulations ◽  
Boltzmann Method ◽  
Reynolds Number Flows

A lattice-Boltzmann method has been developed to simulate suspensions of both spherical and non-spherical particles in finite-Reynolds-number flows. The results for sedimentation of a single elliptical particle are shown to be in excellent agreement with the results of Huang, Hu & Joseph (1998) who used a finite-element method. Sedimentation of two-dimensional circular and rectangular particles in a two-dimensional channel and three-dimensional spherical particles in a tube with square cross-section is simulated. Computational results are consistent with experimentally observed phenomena, such as drafting, kissing and tumbling.

Directed fluid sheets

1976 ◽  
Vol 347 (1651) ◽  
pp. 447-473 ◽  
Keyword(s):  
Water Waves ◽  
Three Dimensional ◽  
Steady Motion ◽  
Finite Depth ◽  
Free Surface Flows ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Inviscid Fluids ◽  
Two Dimensional Flows

This paper is concerned mainly with incompressible inviscid fluid sheets but the incompressible linearly viscous fluid sheet is also considered. Our development is based on a direct formulation using the two dimensional theory of directed media called Cosserat surfaces . The first part of the paper deals with the formulation of appropriate nonlinear equations (which may include the effects of gravity and surface tension) governing the two dimensional motion of incompressible inviscid media for two categories, namely those ( a ) for two dimensional flows confined to a plane perpendicular to a specified direction and ( b ) for propagation of fairly long waves in a stream of variable initial depth. The latter development is a generalization of an earlier direct formulation of a theory of water waves when the fixed bottom of the stream is level (Green, Laws & Naghdi 1974). In the second part of the paper, special attention is given to a demonstration of the relevance and applicability of the present direct formulation to a variety of two dimensional problems of inviscid fluid sheets. These include, among others, the steady motion of a class of two-dimensional flows in a stream of finite depth in which the bed of the stream may change from one constant level to another, the related problem of hydraulic jumps, and a class of exact solutions which characterize the main features of the time-dependent free surface flows in the three dimensional theory of incompressible inviscid fluids.

Cavity Flow Predictions Based on the Euler Equations

1994 ◽  
Vol 116 (1) ◽  
pp. 36-44 ◽  
Author(s):  
Manish Deshpande ◽  
Jinzhang Feng ◽  
Charles L. Merkle
Keyword(s):  
Numerical Solutions ◽  
Three Dimensional ◽  
Leading Edge ◽  
Cavity Flow ◽  
Cavity Surface ◽  
Computational Domain ◽  
Two Dimensional ◽  
Sheet Cavitation ◽  
Inception Point ◽  
Euler Solver

An Euler solver based on artificial-compressibility and pseudo-time stepping is developed for the analysis of partial sheet cavitation in two-dimensional cascades and on isolated airfoils. The computational domain is adapted to the evolution of the cavity surface and the boundary conditions are implemented on the cavity interface. This approach enables the cavitation pressure condition to be incorporated directly without requiring the specification of the cavity length or the location of the inception point. Numerical solutions are presented for a number of two-dimensional cavity flow problems, including both leading edge cavitation and the more difficult mid-chord cavitation condition. Validation is accomplished by comparing with experimental measurements and nonlinear panel solutions from potential flow theory. The demonstrated success of the Euler cavitation procedure implies that it can be incorporated in existing incompressible CFD codes to provide engineering predictions of cavitation. In addition, the flexibility of the Euler formulation may allow extension to more complex problems such as viscous flows, time-dependent flows and three-dimensional flows.

scholarly journals The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Henry Maxfield ◽  
Gustavo J. Turiaci
Keyword(s):  
Classical Solution ◽  
Path Integral ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Matrix Integral ◽  
Pure Gravity ◽  
Extremal Limit ◽  
3D Gravity

Abstract We propose that a class of new topologies, for which there is no classical solution, should be included in the path integral of three-dimensional pure gravity, and that their inclusion solves pathological negativities in the spectrum, replacing them with a nonperturbative shift of the BTZ extremality bound. We argue that a two dimensional calculation using a dimensionally reduced theory captures the leading effects in the near extremal limit. To make this argument, we study a closely related two-dimensional theory of Jackiw-Teitelboim gravity with dynamical defects. We show that this theory is equivalent to a matrix integral.

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