Irrotational flow past bodies close to a plane surface

1971 ◽  
Vol 50 (3) ◽  
pp. 481-491 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Asymptotic Expansion ◽  
Numerical Computation ◽  
Potential Flow ◽  
Close Agreement ◽  
Plane Surface ◽  
Three Dimensional ◽  
Ground Surface ◽  
Two Dimensional ◽  
General Shape ◽  
Irrotational Flow

A theroetical analysis is given for potential flow over, around and under a vehicle of general shape moving close to a plane ground surface. Solutions are given both in the form of a small-gap asymptotic expansion and a direct numerical computation, with close agreement between the two for two-dimensional flows with and without circulation. Some results for three-dimensional bodies are discussed.

scholarly journals Design and Testing of Swept and Leaned Outlet Guide Vanes to Reduce Stator-Strut-Splitter Aerodynamic Flow Interactions

1998 ◽  
Author(s):  
A. R. Wadia ◽  
P. N. Szucs ◽  
K. L. Gundy-Burlet
Keyword(s):  
Dimensional Analysis ◽  
Test Performance ◽  
Potential Flow ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Angle Distribution ◽  
Two Dimensional ◽  
Guide Vanes ◽  
Flow Interactions ◽  
Design And Testing

Large circumferential varying pressure levels produced by aerodynamic flow interactions between downstream stators and struts present a potential noise and stability margin liability in a compression component. These interactions are presently controlled by tailoring the camber and/or stagger angles of vanes neighboring the fan frame struts. This paper reports on the design and testing of a unique set of swept and leaned fan outlet guide vanes (OGVs) that do not require this local tailoring even though the OGVs are closely coupled with the fan frame struts and splitter to reduce engine length. The swept and leaned OGVs not only reduce core-duct diffusion, but they also reduce the potential flow interaction between the stator and the strut relative to that produced by conventional radial OGVs. First, the design of the outlet guide vanes using a single bladerow three-dimensional viscous flow analysis is outlined. Next, a two-dimensional potential flow analysis was used for the coupled OGV-frame system to obtain a circumferentially non-uniform stator stagger angle distribution to further reduce the upstream static pressure disturbance. Recognizing the limitations of the two-dimensional potential flow analysis for this highly three-dimensional set of leaned OGVs, as a final evaluation of the OGV-strut system design, a full three-dimensional viscous analysis of a periodic circumferential sector of the OGVs, including the fan frame struts and splitter, was performed. The computer model was derived from a NASA-developed code used in simulating the flow field for external aerodynamic applications with complex geometries. The three-dimensional coupled OGV-frame analysis included the uniformly-staggered OGVs configuration and the variably-staggered OGVs configuration determined by the two-dimensional potential flow analysis. Contrary to the two-dimensional calculations, the three-dimensional analysis revealed significant flow problems with the variably-staggered OGVs configuration and showed less upstream flow non-uniformity with the uniformly-staggered OGVs configuration. The flow redistribution in both the radial and tangential directions, captured fully only in the three-dimensional analysis, was identified as the prime contributor to the lower flow non-uniformity with the uniformly-staggered OGVs configuration. The coupled three-dimensional analysis was also used to validate the design at off-design conditions. Engine test performance and stability measurements with both uniformly- and variably-staggered OGVs configurations with and without the presence of inlet distortion confirmed the conclusions from the three-dimensional analysis.

scholarly journals A Justification of Two-Dimensional Nonlinear Viscoelastic Shells Model

2012 ◽  
Vol 2012 ◽  
pp. 1-24
Author(s):  
Fushan Li
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Analysis ◽  
Laplace Transformation ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Nonlinear Viscoelastic ◽  
Leading Term ◽  
Viscoelastic Shells

By applying formal asymptotic analysis and Laplace transformation, we obtain two-dimensional nonlinear viscoelastic shells model satisfied by the leading term of asymptotic expansion of the solution to the three-dimensional equations.

Design Methods of Volute Casings for Turbocharger Turbine Applications

1996 ◽  
Vol 210 (2) ◽  
pp. 149-156 ◽  
Author(s):  
H Chen
Keyword(s):  
Experimental Data ◽  
Potential Flow ◽  
Design Method ◽  
Three Dimensional ◽  
Design Methods ◽  
Two Dimensional ◽  
Aerodynamic Design ◽  
3D Design ◽  
Flow Equations ◽  
Good Agreement

This paper discusses aerodynamic design methods of volute casings used in turbocharger turbines. A quasi-three-dimensional (Q-3D) design method is proposed in which a group of extended two-dimensional potential flow equations and the streamline equation are numerically solved to obtain the geometry of spiral volutes. A tongue loss model, based on the turbulence wake theory, is also presented, and good agreement with experimental data is shown.

Design and Testing of Swept and Leaned Outlet Guide Vanes to Reduce Stator–Strut–Splitter Aerodynamic Flow Interactions

1999 ◽  
Vol 121 (3) ◽  
pp. 416-427 ◽  
Author(s):  
A. R. Wadia ◽  
P. N. Szucs ◽  
K. L. Gundy-Burlet
Keyword(s):  
Dimensional Analysis ◽  
Potential Flow ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Angle Distribution ◽  
Two Dimensional ◽  
Guide Vanes ◽  
Flow Interactions ◽  
Design And Testing ◽  
Flow Nonuniformity

Large circumferentially varying pressure levels produced by aerodynamic flow interactions between downstream stators and struts present a potential noise and stability margin liability in a compression component. These interactions are presently controlled by tailoring the camber and/or stagger angles of vanes neighboring the fan frame struts. This paper reports on the design and testing of a unique set of swept and leaned fan outlet guide vanes (OGVs) that do not require this local tailoring even though the OGVs are closely coupled with the fan frame struts and splitter to reduce engine length. The swept and leaned OGVs not only reduce core-duct diffusion, but they also reduce the potential flow interaction between the stator and the strut relative to that produced by conventional radial OGVs. First, the design of the outlet guide vanes using a single blade row three-dimensional viscous flow analysis is outlined. Next, a two-dimensional potential flow analysis was used for the coupled OGV–frame system to obtain a circumferentially nonuniform stator stagger angle distribution to reduce the upstream static pressure disturbance further. Recognizing the limitations of the two-dimensional potential flow analysis for this highly three-dimensional set of leaned OGVs, as a final evaluation of the OGV–strut system design, a full three-dimensional viscous analysis of a periodic circumferential sector of the OGVs, including the fan frame struts and splitter, was performed. The computer model was derived from a NASA-developed code used in simulating the flow field for external aerodynamic applications with complex geometries. The three-dimensional coupled OGV–frame analysis included the uniformly staggered OGV configuration and the variably staggered OGV configuration determined by the two-dimensional potential flow analysis. Contrary to the two-dimensional calculations, the three-dimensional analysis revealed significant flow problems with the variably staggered OGV configuration and showed less upstream flow nonuniformity with the uniformly staggered OGV configuration. The flow redistribution in both the radial and tangential directions, captured fully only in the three-dimensional analysis, was identified as the prime contributor to the lower flow nonuniformity with the uniformly staggered OGV configuration. The coupled three-dimensional analysis was also used to validate the design at off-design conditions. Engine test performance and stability measurements with both uniformly and variably staggered OGV configurations with and without the presence of inlet distortion confirmed the conclusions from the three-dimensional analysis.

Surface Vorticity Theory for Axisymmetric Potential Flow past Annular Aerofoils and Bodies of Revolution with Application to Ducted Propellers and Cowls

1972 ◽  
Vol 14 (4) ◽  
pp. 280-296 ◽  
Author(s):  
R. I. Lewis ◽  
P. G. Ryan
Keyword(s):  
Integral Equation ◽  
Experimental Test ◽  
Potential Flow ◽  
Three Dimensional ◽  
Classical Solutions ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Bodies Of Revolution ◽  
Dimensional Flow ◽  
Ducted Propeller

The well known surface vorticity method originally due to Martensen for calculating two-dimensional aerofoil and cascade flows is extended to axisymmetric flows past annular aerofoils, bodies of revolution and interacting combinations of these. A variety of solutions is presented in comparison with experimental test or classical solutions. A generalized surface vorticity integral equation for fully three-dimensional flow is developed in curvilinear co-ordinates from which the two-dimensional axisymmetric equations are shown to be reducible. This paper is aimed at ship ducted propeller problems but is of wider application to fan cowls, nozzles, bodies of revolution or engine intakes.

The Application of Limit Analysis to Punch-Indentation Problems

1953 ◽  
Vol 20 (4) ◽  
pp. 453-460
Author(s):  
R. T. Shield ◽  
D. C. Drucker
Keyword(s):  
Limit Analysis ◽  
Plane Surface ◽  
Plastic Material ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Upper And Lower Bounds ◽  
Two Dimensional ◽  
Flat Punch ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Abstract Limit analysis is applied to obtain upper and lower bounds for the punch pressure in the indentation of the plane surface of an elastic-perfectly plastic material by a flat rigid punch. The two-dimensional flat punch and the three-dimensional flat square and rectangular punch problems are considered. The analysis assumes Tresca’s yield criterion of constant maximum shearing stress k, during plastic deformation. It is shown that the pressure required to produce indentation in the two-dimensional problem lies between 5k and (2 + π)k. The lower bound obtained for any rectangular punch is again 5k while the upper bound for a smooth punch lies between 5.71k for a square and (2 + π)k for a very long rectangle. A value of 5.36k is found for a ratio of length to breadth of 3. The limit pressure for a uniformly loaded area, as distinguished from an area loaded by a punch, is bracketed by 5k and (2 + π)k when the area is convex.

Nonlinear electroviscoelastic potential flow instability theory of two superposed streaming dielectric fluids

2014 ◽  
Vol 92 (10) ◽  
pp. 1249-1257 ◽  
Author(s):  
M.F. El-Sayed ◽  
N.T. Eldabe ◽  
M.H. Haroun ◽  
D.M. Mostafa
Keyword(s):  
Surface Tension ◽  
Electric Field ◽  
Potential Flow ◽  
Flow Instability ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Physical Parameters ◽  
Two Dimensional ◽  
Dielectric Fluids ◽  
Fluid Velocities

The nonlinear electrohydrodynamic Kelvin–Helmholtz instability of two superposed viscoelastic Walters B′ dielectric fluids in the presence of a tangential electric field is investigated in three dimensions using the potential flow analysis. The method of multiple scales is used to obtain a dispersion relation for the linear problem, and a nonlinear Ginzburg–Landau equation with complex coefficients for the nonlinear problem. The linear and nonlinear stability conditions are obtained and discussed both analytically and numerically. In the linear stability analysis, we found that the fluid velocities and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities, and surface tension have stabilizing effects; and that the system in the three-dimensional disturbances is more stable than in the corresponding case of two-dimensional disturbances. While in the nonlinear analysis, for both two- and three-dimensional disturbances, we found that the fluid velocities, surface tension, and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities have stabilizing effects, and that the system in the three-dimensional disturbances is more unstable than its behavior in the two-dimensional disturbances for most physical parameters except the kinematic viscosities.

scholarly journals Extrapolation Algorithm for Computing Multiple Cauchy Principal Value Integrals

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Jin Li ◽  
Yongling Cheng
Keyword(s):  
Asymptotic Expansion ◽  
Density Function ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Cauchy Principal ◽  
Numerical Examples ◽  
Extrapolation Algorithm ◽  
Expansion Formulae ◽  
Error Functional ◽  
Principal Value

In this paper, the computation of multiple (including two dimensional and three dimensional) Cauchy principal integral with generalized composite rectangle rule was discussed, with the density function approximated by the middle rectangle rule, while the singular kernel was analytically calculated. Based on the expansion of the density function, the asymptotic expansion formulae of error functional are obtained. A series is constructed to approach the singular point, then the extrapolation algorithm is presented, and the convergence rate is proved. At last, some numerical examples are presented to validate the theoretical analysis.

scholarly journals On Unsteady Effects in WIG Craft Aerodynamics

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Nikolai Kornev
Keyword(s):  
Time Domain ◽  
Potential Flow ◽  
Three Dimensional ◽  
Ground Effect ◽  
Two Dimensional ◽  
Unsteady Forces ◽  
Longitudinal Plane ◽  
Ground Effects ◽  
Unsteady Effects

The paper presents the analysis of unsteady forces and their influence on the aerodynamics and motion of a wing-in-ground (WIG) effect craft. Two-dimensional and three-dimensional aerodynamic models based on the potential flow are coupled with time domain simulations in the longitudinal plane. A special attention is paid to the explanation of the dynamic ground effect on both the sink and pitching motions. The influence of unsteady and quasi-steady forces on the dynamic ground effects and the craft motion is analyzed for different heights of flight.

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