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.

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.

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.

Numerical Solution of Inviscid Two-Dimensional Transonic Flow Through a Cascade

1987 ◽  
Vol 109 (1) ◽  
pp. 108-113
Author(s):  
J. Forˇt ◽  
K. Kozel
Keyword(s):  
Experimental Data ◽  
Weak Solution ◽  
Numerical Solution ◽  
Transonic Flow ◽  
Numerical Procedure ◽  
Numerical Results ◽  
Two Dimensional ◽  
System Of Difference Equations ◽  
Flow Through ◽  
Turbine Cascades

The paper presents a method of numerical solution of transonic potential flow through plane cascades with subsonic inlet flow. The problem is formulated as a weak solution with combined Dirichlet’s and Neumann’s boundary conditions. The numerical procedure uses Jameson’s rotated difference scheme and the SLOR technique to solve a system of difference equations. Numerical results of transonic flow are compared with experimental data and with other numerical results for both compressor and turbine cascades near choke conditions.

The Computation of Transonic Flow Through Two-Dimensional Gas Turbine Cascades

1971 ◽  
Author(s):  
P. W. McDonald
Keyword(s):  
Flow Field ◽  
Gas Turbine ◽  
Transonic Flow ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Airfoil Surface ◽  
Pressure Distributions ◽  
Flow Through ◽  
Turbine Cascades ◽  
Definition Of

Steady transonic flow through two-dimensional gas turbine cascades is efficiently predicted using a time-dependent formulation of the equations of motion. An integral representation of the equations has been used in which subsonic and supersonic regions of the flow field receive identical treatment. Mild shock structures are permitted to develop naturally without prior knowledge of their exact strength or position. Although the solutions yield a complete definition of the flow field, the primary aim is to produce airfoil surface pressure distributions for the design of aerodynamically efficient turbine blade contours. In order to demonstrate the accuracy of this method, computed airfoil pressure distributions have been compared to experimental results.

Navier–Stokes Solution for Steady Two-Dimensional Transonic Cascade Flows

1988 ◽  
Vol 110 (3) ◽  
pp. 339-346 ◽  
Author(s):  
O. K. Kwon
Keyword(s):  
Stokes Equations ◽  
Solution Procedure ◽  
Curvilinear Coordinates ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Turbine Cascade ◽  
Navier Stokes Equations ◽  
Time Marching ◽  
Transonic Turbine ◽  
Transonic Cascade

A robust, time-marching Navier–Stokes solution procedure based on the explicit hopscotch method is presented for solution of steady, two-dimensional, transonic turbine cascade flows. The method is applied to the strong conservation form of the unsteady Navier–Stokes equations written in arbitrary curvilinear coordinates. Cascade flow solutions are obtained on an orthogonal, body-conforming “O” grid with the standard k–ε turbulence model. Computed results are presented and compared with experimental data.

scholarly journals Transonic Flow Through Turbine Cascades With Nonuniform Pitch

1992 ◽  
Author(s):  
R. Kurz
Keyword(s):  
Experimental Data ◽  
Measurement System ◽  
Transonic Flow ◽  
Reynolds Numbers ◽  
Calculation Procedure ◽  
Flow Through ◽  
Turbine Cascades

The flow behind linear turbine cascades with uniform and nonuniform pitches was investigated both theoretically and experimentally. A calculation procedure based on an Euler–code for nonuniform pitch to chord ratios is presented. Experimental data were obtained by using a Laser–2–Focus measurement system and Kiel probes. Outlet Laval numbers range from 0.7 to 1.0, corresponding to Reynolds numbers from 380,000 to 700,000. The pitch–to–chord ratio of the investigated configurations reaches from 0.771 to 0.877.

Selection of Models to Assess the Profile Losses in Blade Rows Using the Methods of Mathematical Statistics

2015 ◽  
Author(s):  
Oleg Baturin ◽  
Daria Kolmakova ◽  
Aleksey Gorshkov ◽  
Grigorii Popov
Keyword(s):  
Experimental Data ◽  
Turbine Engines ◽  
Gas Turbine Engines ◽  
Analysis Method ◽  
Distribution Law ◽  
Profile Losses ◽  
Calculation Results ◽  
Turbine Cascades ◽  
Axial Turbines ◽  
Selection Of

An investigation of five models used to assess the profile losses in axial turbine cascades appears in this article: Soderberg model, Ainley&Mathieson model, Dunhem&Came model, Kaker&Ocapu model and Central Institute of Aviation Motors (CIAM, Russia) model. Using them, the calculation results were compared with experimental data for 170 airfoil cascades of axial turbines. These cascades include a diversity of blade profiles of axial turbines used in aircraft gas turbine engines. Direct comparison of the calculated and experimental results did not make it possible to uniquely choose the best model. For this reason, the analysis method of loss models based on the statistical analysis of calculation and experimental data deviation was developed. It is shown that the deviations are subject to the normal distribution law. Based on the analysis of mathematical expectations μΔζ and standard deviation σΔζ, it was found that CIAM model gives the results closest to the experimental data. It shows the deviation from the real values of the loss 2±82% with a probability of 95%.

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