An Accurate and Efficient Euler Solver for Three-Dimensional Turbomachinery Flows

1987 ◽  
Vol 109 (3) ◽  
pp. 346-353 ◽  
Author(s):  
C. F. Shieh ◽  
R. A. Delaney
Keyword(s):  
Numerical Solution ◽  
Euler Equations ◽  
Numerical Scheme ◽  
Three Dimensional ◽  
Curvilinear Coordinates ◽  
Analysis Method ◽  
Surfaces Of Revolution ◽  
Conservative Form ◽  
Turbine Cascades ◽  
Euler Solver

Accurate and efficient Euler equation numerical solution techniques are presented for analysis of three-dimensional turbomachinery flows. These techniques include an efficient explicit hopscotch numerical scheme for solution of the three-dimensional time-dependent Euler equations and an O-type body-conforming grid system. The hopscotch scheme is applied to the conservative form of the Euler equations written in general curvilinear coordinates. The grid is constructed by stacking from hub to shroud two-dimensional O-type grids on equally spaced surfaces of revolution. Numerical solution results for two turbine cascades are presented and compared with experimental data to demonstrate the accuracy of the analysis method.

An Accurate and Efficient Euler Solver for Three-Dimensional Turbomachinery Flows

1986 ◽  
Author(s):  
C. F. Shieh ◽  
R. A. Delaney
Keyword(s):  
Numerical Solution ◽  
Euler Equations ◽  
Numerical Scheme ◽  
Three Dimensional ◽  
Curvilinear Coordinates ◽  
Analysis Method ◽  
Surfaces Of Revolution ◽  
Conservative Form ◽  
Turbine Cascades ◽  
Euler Solver

Accurate and efficient Euler equation numerical solution techniques are presented for analysis of three-dimensional turbomachinery flows. These techniques include an efficient explicit hopscotch numerical scheme for solution of the 3-D time-dependent Euler equations and an O-type body-conforming grid system. The hopscotch scheme is applied to the conservative form of the Euler equations written in general curvilinear coordinates. The grid is constructed by stacking from hub to shroud 2-D O-type grids on equally spaced surfaces of revolution. Numerical solution results for two turbine cascades are presented and compared with experimental data to demonstrate the accuracy of the analysis method.

Time-Marching Analysis of Steady Transonic Flow in Turbomachinery Cascades Using the Hopscotch Method

1983 ◽  
Vol 105 (2) ◽  
pp. 272-279 ◽  
Author(s):  
R. A. Delaney
Keyword(s):  
Experimental Data ◽  
Euler Equations ◽  
Transonic Flow ◽  
Numerical Scheme ◽  
Curvilinear Coordinates ◽  
Two Dimensional ◽  
Analysis Method ◽  
Time Marching ◽  
Turbine Cascades ◽  
Turbomachinery Cascades

A rapid, time-marching, numerical scheme based on the hopscotch method is presented for solution of steady, two-dimensional, transonic flow in turbomachinery cascades. The scheme is applied to the strong-conservation form of the unsteady Euler equations written in arbitrary curvilinear coordinates. Cascade solutions are obtained on an orthogonal, body-centered coordinate system. Numerical solution results for two turbine cascades are presented and compared with experimental data to demonstrate the accuracy and computational efficiency of the analysis method.

Time-Marching Analysis of Steady Transonic Flow in Turbomachinery Cascades Using the Hopscotch Method

1982 ◽  
Author(s):  
R. A. Delaney
Keyword(s):  
Experimental Data ◽  
Euler Equations ◽  
Transonic Flow ◽  
Numerical Scheme ◽  
Curvilinear Coordinates ◽  
Two Dimensional ◽  
Analysis Method ◽  
Time Marching ◽  
Turbine Cascades ◽  
Turbomachinery Cascades

A rapid, time-marching, numerical scheme based on the hopscotch method is presented for solution of steady, two-dimensional, transonic flow in turbomachinery cascades. The scheme is applied to the strong-conservation form of the unsteady Euler equations written in arbitrary curvilinear coordinates. Cascade solutions are obtained on an orthogonal, body-centered coordinate system. Numerical solution results for two turbine cascades are presented and compared with experimental data to demonstrate the accuracy and computational efficiency of the analysis method.

Mass transport in three-dimensional water waves

1991 ◽  
Vol 231 ◽  
pp. 417-437 ◽  
Author(s):  
Mohamed Iskandarani ◽  
Philip L.-F. Liu
Keyword(s):  
Mass Transport ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Steady Flow ◽  
Water Waves ◽  
Numerical Scheme ◽  
Three Dimensional ◽  
Langmuir Circulation ◽  
Circulation Patterns ◽  
Wave Trains

A spectral scheme is developed to study the mass transport in three-dimensional water waves where the steady flow is assumed to be periodic in two horizontal directions. The velocity–vorticity formulation is adopted for the numerical solution, and boundary conditions for the vorticity are derived to enforce the no-slip conditions. The numerical scheme is used to calculate the mass transport under two intersecting wave trains; the resulting flow is reminiscent of the Langmuir circulation patterns. The scheme is then applied to study the steady flow in a three-dimensional standing wave.

scholarly journals Analysis of Three-Dimensional Turbomachinery Flows on C-Type Grids Using an Implicit Euler Solver

1989 ◽  
Author(s):  
K. F. Weber ◽  
D. W. Thoe ◽  
R. A. Delaney
Keyword(s):  
Euler Equations ◽  
Periodic Boundary ◽  
Three Dimensional ◽  
External Flow ◽  
Compressor Cascade ◽  
Nasa Ames Research ◽  
Point Calculation ◽  
Grid Construction ◽  
Euler Solver ◽  
Calculation Procedures

A 3-D Euler analysis for turbomachinery flows on a C-type grid is presented. The analysis is based on the Beam and Warming implicit algorithm for solution of the unsteady Euler equations and is derived from the ARC3D code developed by Pulliam at NASA Ames Research Center. Modifications made to convert this code from external flow applications to internal turbomachinery flows are given in detail. These changes include the addition of inflow, outflow, and periodic boundary point calculation procedures. Also presented are the C-grid construction procedures. Finally, results of code experimental verification studies for 3-D compressor cascade and rotor flows are presented.

Quasi-Three-Dimensional Numerical Solution of Flow in Turbomachines

1977 ◽  
Vol 99 (1) ◽  
pp. 132-140 ◽  
Author(s):  
C. Bosman ◽  
M. A. I. El-Shaarawi
Keyword(s):  
Numerical Solution ◽  
Centrifugal Compressor ◽  
Three Dimensional ◽  
Computer Programs ◽  
Two Dimensional ◽  
Surfaces Of Revolution ◽  
Single Mass ◽  
The Mean ◽  
Better Than ◽  
Turbomachine Blade

The paper demonstrates the operational feasibility of obtaining flow detail through turbomachine blade passages by working iteratively with existing two-dimensional computer programs which solve alternately for S1 and S2 streamsheets. The resulting solution is regarded as “quasi-three-dimensional” because of the constraints implied by the use of S1 streamsurfaces which are surfaces of revolution and of a single, mass averaged S2 streamsurface. Since the S1 streamsheet thickness distributions are determined by the mean S2 solution and the mean S2 streamsurface shape is determined from the set of S1 solutions, the results obtained are anticipated to be better than could have been obtained by either program individually, since the latter application would necessarily have required the user to assume arbitrary variations for these factors. Comparisons of two and quasi-three dimensional results for a centrifugal compressor and a radial inflow turbine are presented.

Analysis of Three-Dimensional Turbomachinery Flows on C-Type Grids Using an Implicit Euler Solver

1990 ◽  
Vol 112 (3) ◽  
pp. 362-369 ◽  
Author(s):  
K. F. Weber ◽  
D. W. Thoe ◽  
R. A. Delaney
Keyword(s):  
Euler Equations ◽  
Periodic Boundary ◽  
Three Dimensional ◽  
External Flow ◽  
Compressor Cascade ◽  
Nasa Ames Research ◽  
Point Calculation ◽  
Grid Construction ◽  
Euler Solver ◽  
Calculation Procedures

A three-dimensional Euler analysis for turbomachinery flows on a C-type grid is presented. The analysis is based on the Beam and Warming implicit algorithm for solution of the unsteady Euler equations and is derived from the ARC3D code developed by Pulliam at NASA Ames Research Center. Modifications made to convert this code from external flow applications to internal turbomachinery flows are given in detail. These changes include the addition of inflow, outflow, and periodic boundary point calculation procedures. Also presented are the C-grid construction procedures. Finally, results of code experimental verification studies for three-dimensional compressor cascade and rotor flows are presented.

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