Implicit time-stepping methods for the Navier-Stokes equations

AIAA Journal ◽  
1996 ◽  
Vol 34 (3) ◽  
pp. 555-559 ◽  
Author(s):  
K. J. Badcock ◽  
B. E. Richards
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Implicit Time ◽  
Navier Stokes Equations ◽  
Time Stepping

Rotor-Stator Interaction Analysis Using the Navier-Stokes Equations and a Multigrid Method

1995 ◽  
Author(s):  
Andrea Arnone ◽  
Roberto Pacciani
Keyword(s):  
Stokes Equations ◽  
Interaction Analysis ◽  
Time Discretization ◽  
Navier Stokes ◽  
Implicit Time ◽  
Navier Stokes Equations ◽  
Time Stepping ◽  
Fully Implicit ◽  
Rotor Stator Interaction ◽  
Stage Analysis

A recently developed, time-accurate multigrid viscous solver has been extended to the analysis of unsteady rotor-stator interaction. In the proposed method, a fully-implicit time discretization is used to remove stability limitations. By means of a dual time-stepping approach, a four-stage Runge-Kutta scheme is used in conjunction with several accelerating techniques typical of steady-state solvers, instead of traditional time-expensive factorizations. The accelerating strategies include local time stepping, residual smoothing, and multigrid. Two-dimensional viscous calculations of unsteady rotor-stator interaction in the first stage of a modem gas turbine are presented. The stage analysis is based on the introduction of several blade passages to approximate the stator:rotor count ratio. Particular attention is dedicated to grid dependency in space and time as well as to the influence of the number of blades included in the calculations.

Multigrid Computations of Unsteady Rotor-Stator Interaction Using the Navier-Stokes Equations

1995 ◽  
Vol 117 (4) ◽  
pp. 647-652 ◽  
Author(s):  
A. Arnone ◽  
R. Pacciani ◽  
A. Sestini
Keyword(s):  
Stokes Equations ◽  
Time Discretization ◽  
Navier Stokes ◽  
Implicit Time ◽  
Navier Stokes Equations ◽  
Time Stepping ◽  
Fully Implicit ◽  
Local Time Stepping ◽  
Rotor Stator Interaction ◽  
Residual Smoothing

A Navier-Stokes time-accurate solver has been extended to the analysis of unsteady rotor-stator interaction. In the proposed method, a fully-implicit time discretization is used to remove stability limitations. A four-stage Runge-Kutta scheme is used in conjunction with several accelerating techniques typical of steady-state solvers, instead of traditional time-expensive factorizations. Those accelerating strategies include local time stepping, residual smoothing, and multigrid. Direct interpolation of the conservative variables is used to handle the interfaces between blade rows. Two-dimensional viscous calculations of unsteady rotor-stator interaction in a modern gas turbine stage are presented to check for the capability of the procedure.

Rotor-Stator Interaction Analysis Using the Navier–Stokes Equations and a Multigrid Method

1996 ◽  
Vol 118 (4) ◽  
pp. 679-689 ◽  
Author(s):  
A. Arnone ◽  
R. Pacciani
Keyword(s):  
Stokes Equations ◽  
Interaction Analysis ◽  
Time Discretization ◽  
Navier Stokes ◽  
Implicit Time ◽  
Navier Stokes Equations ◽  
Time Stepping ◽  
Fully Implicit ◽  
Rotor Stator Interaction ◽  
Stage Analysis

A recently developed, time-accurate multigrid viscous solver has been extended to the analysis of unsteady rotor–stator interaction. In the proposed method, a fully implicit time discretization is used to remove stability limitations. By means of a dual time-stepping approach, a four-stage Runge–Kutta scheme is used in conjunction with several accelerating techniques typical of steady-state solvers, instead of traditional time-expensive factorizations. The accelerating strategies include local time stepping, residual smoothing, and multigrid. Two-dimensional viscous calculations of unsteady rotor–stator interaction in the first stage of a modern gas turbine are presented. The stage analysis is based on the introduction of several blade passages to approximate the stator:rotor count ratio. Particular attention is dedicated to grid dependency in space and time as well as to the influence of the number of blades included in the calculations.

scholarly journals Navier-Stokes Analysis of Unsteady Transonic Flows Through Gas Turbine Cascades With and Without Coolant Ejection

1997 ◽  
Author(s):  
T. Tanuma ◽  
N. Shibukawa ◽  
S. Yamamoto
Keyword(s):  
Gas Turbine ◽  
Stokes Equations ◽  
Viscous Flows ◽  
Navier Stokes ◽  
Implicit Time ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Time Marching ◽  
Turbine Cascades ◽  
Annular Cascade

An implicit time-marching higher-order accurate finite-difference method for solving the two-dimensional compressible Navier-Stokes equations was applied to the numerical analyses of steady and unsteady, subsonic and transonic viscous flows through gas turbine cascades with trailing edge coolant ejection. Annular cascade tests were carried out to verify the accuracy of the present analysis. The unsteady aerodynamic mechanisms associated with the interaction between the trailing edge vortices and shock waves and the effect of coolant ejection were evaluated with the present analysis.

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