Islands in three-dimensional steady flows

1991 ◽  
Vol 227 ◽  
pp. 527-542 ◽  
Author(s):  
C. C. Hegna ◽  
A. Bhattacharjee
Keyword(s):  
Boundary Layer ◽  
Classical Theory ◽  
Three Dimensional ◽  
Rational Surface ◽  
Steady Flows ◽  
Rational Surfaces ◽  
Boundary Layer Analysis ◽  
Layer Analysis ◽  
Euler Flows ◽  
Critical Layers

We consider the problem of steady Euler flows in a torus. We show that in the absence of a direction of symmetry the solution for the vorticity contains δ-function singularities at the rational surfaces of the torus. We study the effect of a small but finite viscosity on these singularities. The solutions near a rational surface contain cat's eyes or islands, well known in the classical theory of critical layers. When the islands are small, their widths can be computed by a boundary-layer analysis. We show that the islands at neighbouring rational surfaces generally overlap. Thus, steady toroidal flows exhibit a tendency towards Beltramization.

A Quasi-Three-Dimensional Blade Surface Boundary Layer Analysis for Rotating Blade Rows

1982 ◽  
Vol 104 (2) ◽  
pp. 439-449 ◽  
Author(s):  
W. T. Thompkins ◽  
W. J. Usab
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Normal Vector ◽  
Surface Boundary ◽  
Nasa Lewis Research ◽  
Surface Boundary Layer ◽  
Boundary Layer Analysis ◽  
Rotating Blade ◽  
Layer Analysis ◽  
Coordinate Lines

A quasi-three-dimensional, finite difference boundary layer analysis for rotating blade rows has been developed which uses pressure distribution and streamline position data from a three-dimensional Euler equation solver. This analysis uses as coordinate lines the blade normal vector, the local inviscid streamline direction and a crossflow coordinate tine perpendicular to both normal and streamline coordinate lines. The equations solved may be determined either by assuming the crossflow velocity to be small or that its variation in the crossflow direction is small. Thus the analysis would not apply to a region where the boundary layer character changes rapidly such as a corner but could be expected to provide good results away from hub or tip casing boundary layers. Modified versions of Keller’s box scheme are used to solve the streamwise and crossflow momentum equations as well as the energy equation. Results are presented for a high-tip speed, low aspect ratio rotor designed by NASA Lewis Research Center which show that the three-dimensional boundary layer separates significantly sooner and has a much larger influence on rotor performance than would be expected from a two-dimensional analysis.

Calculation of Three-Dimensional Boundary Layers on Rotating Turbine Blades

1987 ◽  
Vol 109 (1) ◽  
pp. 41-49 ◽  
Author(s):  
O. L. Anderson
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Pressure Surface ◽  
Boundary Layer Analysis ◽  
Layer Analysis ◽  
Edge Conditions ◽  
Dimensional Boundary ◽  
Pressure Suction

An assessment has been made of the applicability of a three-dimensional boundary-layer analysis to the calculation of heat transfer and streamline flow patterns on the surfaces of both stationary and rotating turbine passages. In support of this effort, an analysis has been developed to calculate a general nonorthogonal surface coordinate system for arbitrary three-dimensional surfaces and also to calculate the boundary-layer edge conditions for compressible flow using the surface Euler equations and experimental pressure distributions. Using available experimental data to calibrate the method, calculations are presented for the endwall, and suction surfaces of a stationary cascade and for the pressure surface of a rotating turbine blade. The results strongly indicate that the three-dimensional boundary-layer analysis can give good predictions of the flow field and heat transfer on the pressure, suction, and endwall surfaces in a gas turbine passage.

scholarly journals Boundary layer analysis and heat transfer of a nanofluid

2014 ◽  
Vol 17 (2) ◽  
pp. 401-412 ◽  
Author(s):  
M. M. MacDevette ◽  
T. G. Myers ◽  
B. Wetton
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layer Analysis ◽  
Layer Analysis

A Systematic Computational Design System for Turbine Cascades, Airfoil Geometry and Blade-to-Blade Analysis

1983 ◽  
Author(s):  
Z.-Q. Ye
Keyword(s):  
Boundary Layer ◽  
Leading Edge ◽  
Computational Design ◽  
Design System ◽  
Finite Area ◽  
Streamline Curvature ◽  
Boundary Layer Analysis ◽  
Curvature Analysis ◽  
Layer Analysis ◽  
Turbine Cascades

This paper describes a systematic computational design system for two-dimensional turbine cascades. The system includes a sequence of calculations in which airfoil profiles are designed from velocity diagram requirements and specified geometric parameters, followed by an inviscid global streamline curvature analysis, a magnified reanalysis around the leading edge, and a transitional profile boundary layer and wake mixing analysis. A finite area technique and a body-fitted mesh are used for the reanalysis. The boundary layer analysis is performed using the dissipation-integral method of Walz which has been modified in the present application. Several turbine airfoil profile geometry designs are presented. Also two sample cascade design cases and their calculated performance for a range of Mach numbers and incidence angles are given and discussed.

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