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.

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.

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.

Development of a 3D Navier Stokes Solver for Application to all Types of Turbomachinery

1988 ◽  
Author(s):  
W. N. Dawes
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Basic Algorithm ◽  
Navier Stokes Equations ◽  
Transonic Compressor ◽  
Stage Of Development ◽  
Code Performance

This paper describes the current stage of development of a code aimed at solving the 3D Navier-Stokes equations in any type of turbomachinery geometry. The basic algorithm time marches the fully 3D unsteady equations of motion expressed in finite volume form with a two step explicit / one step implicit method. Full multigrid acceleration is used to reduce solution time and maintain code performance on fine meshes. Turbulence modelling is via mixing-length closure and the widely used Baldwin-Lomax model. The generality and robustness of the code is demonstrated by application to five different test cases, three axial and two radial configurations. Also included is a grid independence study which demonstrates near grid independent solutions for transonic compressor cascade flow (albeit with the actual result subject to transition modelling constraints). For two of the axial cases (transonic compressor in cascade, secondary flow in a high speed compressor) and one radial case (Eckardt high speed impellor) sufficient mesh is employed for the predictions to be essentially quantitative. The other two cases (radial inflow turbine with clearance and compressor stator with hub clearance) are really simulations rather than predictions, but are included as the flows are novel and provide much physical insight.

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.

The Simulation of Three-Dimensional Viscous Flow in Turbomachinery Geometries Using a Solution-Adaptive Unstructured Mesh Methodology

1991 ◽  
Author(s):  
W. N. Dawes
Keyword(s):  
Unstructured Mesh ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Mean Value ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Three Dimensional Flow ◽  
Navier Stokes Equations ◽  
Transonic Compressor

This paper presents a numerical method for the simulation of flow in turbomachinery blade rows using a solution-adaptive mesh methodolgy. The fully three dimensional, compressible, Reynolds averaged Navier-Stokes equations with k-ε turbulence modelling (and low Reynolds number damping terms) are solved on an unstructured mesh formed from tetrahedral finite volumes. At stages in the solution, mesh refinement is carried out based on flagging cell faces with either a fractional variation of a chosen variable (like Mach number) greater than a given threshold or with a mean value of the chosen variable within a given range. Several solutions are presented, including that for the highly three-dimensional flow associated with the corner stall and secondary flow in a transonic compressor cascade, to demonstrate the potential of the new method.

The Simulation of Three-Dimensional Viscous Flow in Turbomachinery Geometries Using a Solution-Adaptive Unstructured Mesh Methodology

1992 ◽  
Vol 114 (3) ◽  
pp. 528-537 ◽  
Author(s):  
W. N. Dawes
Keyword(s):  
Unstructured Mesh ◽  
Turbulence Modeling ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Mean Value ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Navier Stokes Equations ◽  
Transonic Compressor

This paper presents a numerical method for the simulation of flow in turbomachinery blade rows using a solution-adaptive mesh methodology. The fully three-dimensional, compressible, Reynolds-averaged Navier–Stokes equations with k–ε turbulence modeling (and low Reynolds number damping terms) are solved on an unstructured mesh formed from tetrahedral finite volumes. At stages in the solution, mesh refinement is carried out based on flagging cell faces with either a fractional variation of a chosen variable (like Mach number) greater than a given threshold or with a mean value of the chosen variable within a given range. Several solutions are presented, including that for the highly three-dimensional flow associated with the corner stall and secondary flow in a transonic compressor cascade, to demonstrate the potential of the new method.

Unsteady Navier-Stokes Simulation of a Transonic Flutter Cascade Near Stall Conditions Applying Algebraic Transition Models

2005 ◽  
Author(s):  
Hans Thermann ◽  
Reinhard Niehuis
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Strong Shock ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Implicit Time ◽  
Compressor Cascade ◽  
Transonic Compressor ◽  
Transition Models ◽  
Operating Points

Due to the trend in the design of modern aeroengines to reduce weight and to realize high pressure ratios, fan and first stage compressor blades are highly susceptible to flutter. At operating points with transonic flow velocities and high incidences stall flutter might occur involving strong shock-boundary layer interactions, flow separation and oscillating shocks. In this paper, results of unsteady Navier-Stokes flow calculations around an oscillating blade in a linear transonic compressor cascade at different operating points including near stall conditions are presented. The nonlinear unsteady Reynolds-averaged Navier-Stokes equations are solved time-accurately using implicit time-integration. Different Low-Reynolds-Number turbulence models are used for closure. Furthermore, empirical algebraic transition models are applied to enhance the accuracy of prediction. Computations are performed two-dimensionally as well as three-dimensionally. It is shown that, for the steady calculations, the prediction of the boundary layer development and the blade loading can be substantially improved compared with fully turbulent computations when algebraic transition models are applied. Furthermore, it is shown that the prediction of the aerodynamic damping in the case of oscillating blades at near stall conditions can be dependent on the applied transition models.

Unsteady Navier-Stokes Simulation of a Transonic Flutter Cascade Near-Stall Conditions Applying Algebraic Transition Models

2005 ◽  
Vol 128 (3) ◽  
pp. 474-483 ◽  
Author(s):  
Hans Thermann ◽  
Reinhard Niehuis
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Strong Shock ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Implicit Time ◽  
Compressor Cascade ◽  
Transonic Compressor ◽  
Transition Models ◽  
Operating Points

Due to the trend in the design of modern aeroengines to reduce weight and to realize high pressure ratios, fan and first-stage compressor blades are highly susceptible to flutter. At operating points with transonic flow velocities and high incidences, stall flutter might occur involving strong shock-boundary layer interactions, flow separation, and oscillating shocks. In this paper, results of unsteady Navier-Stokes flow calculations around an oscillating blade in a linear transonic compressor cascade at different operating points including near-stall conditions are presented. The nonlinear unsteady Reynolds-averaged Navier-Stokes equations are solved time accurately using implicit time integration. Different low-Reynolds-number turbulence models are used for closure. Furthermore, empirical algebraic transition models are applied to enhance the accuracy of prediction. Computations are performed two dimensionally as well as three dimensionally. It is shown that, for the steady calculations, the prediction of the boundary layer development and the blade loading can be substantially improved compared with fully turbulent computations when algebraic transition models are applied. Furthermore, it is shown that the prediction of the aerodynamic damping in the case of oscillating blades at near-stall conditions can be dependent on the applied transition models.

scholarly journals Analysis of Transonic Turbomachinery Flows Using a 2-D Explicit Low-Reynolds k-ε Navier-Stokes Solver

1994 ◽  
Author(s):  
F. Dejean ◽  
C. Vassilopoulos ◽  
G. Slmandirakis ◽  
K. C. Giannakoglou ◽  
K. D. Papailiou
Keyword(s):  
Stokes Equations ◽  
Guide Vane ◽  
Navier Stokes ◽  
Fractional Step ◽  
Flow Conditions ◽  
Compressor Cascade ◽  
Navier Stokes Equations ◽  
Time Marching ◽  
Low Reynolds ◽  
The Stability

An explicit, time-marching fractional-step solver for the calculation of the two-dimensional compressible Navier-Stokes equations is presented. The advantage of using a fractional-step analysis is its simplicity and the fact that greater time-steps are allowed, since the stability criterion is less strict compared to other explicit solvers. Turbulence is modeled through a low-Reynolds k-ε model, for which a novel artificial viscosity scheme is implemented, ensuring a smooth ε-distribution close to solid walls. The method is used in order to numerically investigate the flow field in three different cascades, namely a highly loaded transonic linear turbine guide vane cascade in six different flow conditions, a transonic steam turbine cascade in two different flow conditions and a low supersonic compressor cascade. Calculations are performed using both H- and C-type grids.

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