Stability Analysis of a Galerkin/Runge–Kutta Navier–Stokes Discretisation on Unstructured Tetrahedral Grids

1997 ◽  
Vol 132 (2) ◽  
pp. 201-214 ◽  
Author(s):  
M.B. Giles
Keyword(s):  
Stability Analysis ◽  
Navier Stokes ◽  
Tetrahedral Grids ◽  
Runge Kutta

Advanced Numerical Methods for the Prediction of Tonal Noise in Turbomachinery—Part I: Implicit Runge–Kutta Schemes

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Graham Ashcroft ◽  
Christian Frey ◽  
Kathrin Heitkamp ◽  
Christian Weckmüller
Keyword(s):  
Stokes Equations ◽  
Temporal Integration ◽  
Aerodynamic Noise ◽  
Navier Stokes ◽  
Noise Generation ◽  
Academic Problems ◽  
Tonal Noise ◽  
Navier Stokes Equations ◽  
Runge Kutta ◽  
The Stability

This is the first part of a series of two papers on unsteady computational fluid dynamics (CFD) methods for the numerical simulation of aerodynamic noise generation and propagation. In this part, the stability, accuracy, and efficiency of implicit Runge–Kutta schemes for the temporal integration of the compressible Navier–Stokes equations are investigated in the context of a CFD code for turbomachinery applications. Using two model academic problems, the properties of two explicit first stage, singly diagonally implicit Runge–Kutta (ESDIRK) schemes of second- and third-order accuracy are quantified and compared with more conventional second-order multistep methods. Finally, to assess the ESDIRK schemes in the context of an industrially relevant configuration, the schemes are applied to predict the tonal noise generation and transmission in a modern high bypass ratio fan stage and comparisons with the corresponding experimental data are provided.

Spatial Stability Analysis of a Flap Side Edge Vortex

2005 ◽  
Vol 4 (1-2) ◽  
pp. 37-47
Author(s):  
Jean-Philippe Brazier ◽  
Frédéric Moens ◽  
Philippe Bardoux
Keyword(s):  
Stability Analysis ◽  
Temporal Stability ◽  
Low Frequency ◽  
Aerodynamic Noise ◽  
Navier Stokes ◽  
Mean Flow ◽  
Side Edge ◽  
Amplification Rate ◽  
Edge Vortex ◽  
Flap Deflection

The flap side edge vortex is suspected to contribute to aerodynamic noise generation. Using a temporal stability analysis, Khorrami and Singer have shown that unstable modes could exist in this vortex. Due to the convective nature of this instability, a spatial analysis is more suitable. This is the subject of the present work. The mean flow past a 2D wing with a half-span flap has been computed with a steady 3D Navier-Stokes code. Then, local linear stability calculations are performed in several planes perpendicular to the vortex axis. The vortex is assumed axisymmetric and modelled with Batchelor's analytical vortex. Using Gaster's relation, the spatial amplification rate is calculated, giving by integration the relative amplitude of the fluctuations. Some low-frequency fluctuations are seen to be preferentially amplified by the vortex, but the amplifications remain small, so that this mechanism alone should not produce important noise in this particular configuration, where the flap deflection angle is moderate.

2D and 3D Stability of Cavity Flows in High Mach Number Regimes

2019 ◽  
Author(s):  
Parshwanath S. Doshi ◽  
Rajesh Ranjan ◽  
Datta V. Gaitonde
Keyword(s):  
Stability Analysis ◽  
Mach Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Cavity Flows ◽  
Flame Holder ◽  
High Mach Number ◽  
Eddy Simulation ◽  
High Mach ◽  
The Stability

Abstract The stability characteristics of an open cavity flow at very high Mach number are examined with BiGlobal stability analysis based on the eigenvalues of the linearized Navier-Stokes equations. During linearization, all possible first-order terms are retained without any approximation, with particular emphasis on extracting the effects of compressibility on the flowfield. The method leverages sparse linear algebra and the implicitly restarted shift-invert Arnoldi algorithm to extract eigenvalues of practical physical consequence. The stability dynamics of cavity flows at four Mach numbers between 1.4 and 4 are considered at a Reynolds number of 502. The basic states are obtained through Large Eddy Simulation (LES). Frequency results from the stability analysis show good agreement when compared to the theoretical values using Rossiter’s formula. An examination of the stability modes reveals that the shear layer is increasingly decoupled from the cavity as the Mach number is increased. Additionally, the outer lobes of the Rossiter modes are observed to get stretched and tilted in the direction of the freestream. Future efforts will extend the present analysis to examine current and potential cavity flame holder configurations, which often have downstream walls inclined to the vertical.

Sign in / Sign up

Export Citation Format

Share Document