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 Adaptive Unstructured 2D Navier-Stokes Solutions on Mixed Quadrilateral/Triangular Meshes

1993 ◽  
Author(s):  
Stuart D. Connell ◽  
D. Graham Holmes ◽  
Mark E. Braaten
Keyword(s):  
Stokes Equations ◽  
Solution Procedure ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Quadrilateral Elements ◽  
Time Marching ◽  
Transonic Turbine ◽  
The One ◽  
Marching Scheme

This paper presents a solution adaptive scheme for solving the Navier-Stokes equations on an unstructured mixed grid of triangles and quadrilaterals. The solution procedure uses an explicit Runge-Kutta finite volume time marching scheme with an adaptive blend of second and fourth order smoothing. The governing equations are solved in a 2D, axisymmetric or quasi-3D form. In viscous regions quadrilateral elements are used to facilitate the one dimensional refinement required for the efficient resolution of boundary layers and wakes. The effect of turbulence is incorporated through using either a Baldwin-Lomax or k-ε turbulence model. Solutions are presented for several examples that illustrate the capability of the algorithm to predict viscous phenomena accurately. The examples are a transonic turbine, a nozzle and a combustor diffuser.

scholarly journals Viscous Flow Computations in Turbomachine Cascades

1990 ◽  
Author(s):  
P.-A. Chevrin ◽  
C. Vuillez
Keyword(s):  
Stokes Equations ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Turbine Cascade ◽  
Compressor Cascade ◽  
Navier Stokes Equations ◽  
Transonic Compressor ◽  
Different Types ◽  
Time Marching ◽  
Transonic Turbine

Accurate prediction of the flow in turbomachinery requires numerical solution of the Navier-Stokes equations. A two-dimensional Navier-Stokes solver developed at ONERA for the calculation of the flow in turbine and compressor cascades was adapted at SNECMA to run on different types of grid. The solver uses an explicit, time-marching, finite-volume technique, with a multigrid acceleration scheme. A multi-domain approach is used to handle difficulties due to the geometry of the flow. An H-C grid was used in the calculations. Two turbulence models, based on the mixing length approach, were used. The flow in a transonic compressor cascade, a subsonic and a transonic turbine cascade were computed. Comparison with experiments is presented.

Inverse Design of and Experimental Measurements in a Double-Passage Transonic Turbine Cascade Model

2005 ◽  
Vol 127 (3) ◽  
pp. 619-626 ◽  
Author(s):  
G. M. Laskowski ◽  
A. Vicharelli ◽  
G. Medic ◽  
C. J. Elkins ◽  
J. K. Eaton ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Design Procedure ◽  
Cascade Model ◽  
Inverse Design ◽  
Navier Stokes ◽  
Turbine Cascade ◽  
Flow Conditions ◽  
Navier Stokes Equations ◽  
Attached Flow ◽  
Transonic Turbine

A new transonic turbine cascade model that accurately produces infinite cascade flow conditions with minimal compressor requirements is presented. An inverse design procedure using the Favre-averaged Navier-Stokes equations and k‐ε turbulence model based on the method of steepest descent was applied to a geometry consisting of a single turbine blade in a passage. For a fixed blade geometry, the passage walls were designed such that the surface isentropic Mach number (SIMN) distribution on the blade in the passage matched the SIMN distribution on the blade in an infinite cascade, while maintaining attached flow along both passage walls. An experimental rig was built that produces realistic flow conditions, and also provides the extensive optical access needed to obtain detailed particle image velocimetry measurements around the blade. Excellent agreement was achieved between computational fluid dynamics (CFD) of the infinite cascade SIMN, CFD of the designed double passage SIMN, and the measured SIMN.

A Fully Three-Dimensional Inverse Method for Turbomachinery Blading With Navier-Stokes Equations

1998 ◽  
Author(s):  
Zhengming Wang ◽  
Ruixian Cai ◽  
Hongji Chen ◽  
Dong Zhang
Keyword(s):  
Inverse Problem ◽  
Stokes Equations ◽  
Interpolation Method ◽  
Three Dimensional ◽  
Curvilinear Coordinates ◽  
Navier Stokes ◽  
Special Treatment ◽  
Blade Profile ◽  
Navier Stokes Equations ◽  
Time Marching

A new numerical method for solving fully three-dimensional inverse shape design problem of turbomachinery blading has been developed. The general inverse problem refers to the problem in which the pressure distributions on suction and pressure surfaces of blade are given, but the corresponding blade profile is unknown. In this paper, the calculations are based on the 3D Navier-Stokes equations expressed in terms of nonorthogonal curvilinear coordinates and corresponding nonorthogonal velocity components, and the explicit time marching algorithm and Baldwin-Lomax turbulence model are adopted. A special treatment for boundary conditions on blade surfaces is employed to satisfy the given pressure distribution. In computational process, an initial blade profile is supposed at starting, and then the blade surfaces will move regularly with time steps in the time marching process until the convergence is reached. The movement velocities at every point of blade surfaces are obtained from the solution of the Navier-Stokes equations. After each revision of the blade profile, the grid is reconstructed, and the aerodynamic parameters need to be transferred between the old and new grid points by an accurate interpolation method. Thus the viscous inverse problem is solved in a new process. The computational results for two test cases indicate that the method presented in this paper is very effective.

scholarly journals Application of a Navier-Stokes Analysis to Transonic Cascade Flow Fields

1982 ◽  
Author(s):  
S. J. Shamroth ◽  
H. McDonald ◽  
W. R. Briley
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Solution Procedure ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Controlled Diffusion ◽  
Cascade Flow ◽  
Model Predictions ◽  
Flow Through ◽  
Transonic Cascade

A numerical solution procedure for the ensemble-averaged compressible time-dependent Navier-Stokes equations is applied to the transonic cascade flow field. The equations are solved by the consistently split linearized block implicit (LBI) method of Briley and McDonald. Boundary conditions are set so as to specify upstream total pressure and downstream static pressure. Turbulence is modeled by a mixing length model. Predictions are made for flow through a Jose Sanz controlled diffusion cascade and the method yields converged solutions within a relatively small number of time steps (≈ 150). Although to date comparisons with data have not been made, the results show the expected cascade flow field features.

Direct simulation of transition in an oscillatory boundary layer

1998 ◽  
Vol 371 ◽  
pp. 207-232 ◽  
Author(s):  
G. VITTORI ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Temporal Development ◽  
Direct Simulation ◽  
Navier Stokes Equations ◽  
Oscillatory Boundary Layer

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

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