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

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.

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.

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

A Navier–Stokes Solver for Turbomachinery Applications

1993 ◽  
Vol 115 (2) ◽  
pp. 305-313 ◽  
Author(s):  
A. Arnone ◽  
R. C. Swanson
Keyword(s):  
Stokes Equations ◽  
Computer Code ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Stepping ◽  
Eddy Viscosity Model ◽  
Local Time Stepping ◽  
Grid Independence ◽  
Full Multigrid Method ◽  
Transonic Rotor

A computer code for solving the Reynolds-averaged full Navier–Stokes equations has been developed and applied using H- and C-type grids. The Baldwin–Lomax eddy-viscosity model is used for turbulence closure. The integration in time is based on an explicit four-stage Runge–Kutta scheme. Local time stepping, variable coefficient implicit residual smoothing, and a full multigrid method have been implemented to accelerate steady-state calculations. A grid independence analysis is presented for a transonic rotor blade. Comparisons with experimental data show that the code is an accurate viscous solver and can give very good blade-to-blade predictions for engineering applications.

scholarly journals Strong $L^2$ convergence of time numerical schemes for the stochastic two-dimensional Navier–Stokes equations

2018 ◽  
Vol 39 (4) ◽  
pp. 2135-2167 ◽  
Author(s):  
Hakima Bessaih ◽  
Annie Millet
Keyword(s):  
Stokes Equations ◽  
Random Perturbation ◽  
Time Discretization ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Exponential Moment ◽  
Navier Stokes Equations ◽  
Fully Implicit ◽  
Moment Estimates ◽  
Discretization Schemes

Abstract We prove that some time discretization schemes for the two-dimensional Navier–Stokes equations on the torus subject to a random perturbation converge in $L^2(\varOmega )$. This refines previous results that established the convergence only in probability of these numerical approximations. Using exponential moment estimates of the solution of the stochastic Navier–Stokes equations and convergence of a localized scheme we can prove strong convergence of fully implicit and semiimplicit temporal Euler discretizations and of a splitting scheme. The speed of the $L^2(\varOmega )$ convergence depends on the diffusion coefficient and on the viscosity parameter.

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