• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.39 no.9
• /
• pp.805-815
• /
• 2011

Nonlinear Parabolized Stability Equations(NSPE) can be effectively used to study more throughly the transition process. NPSE can efficiently analyze the stability of a nonlinear region in transition process with low computational cost compared to Direct Numerical Simulation(DNS). In this study, NPSE in general coordinate system is formulated and a computer code to solve numerically the equations is developed. Benchmark problems for incompressible and compressible boundary layers over a flat plate are analyzed to validate the present code. It is confirmed that the NPSE methodology constructed in this study is an efficient and effective tool for nonlinear stability analysis.

• International Journal of Aeronautical and Space Sciences
• /
• v.7 no.2
• /
• pp.155-174
• /
• 2006

Parabolized stability equations for compressible flows in general curvilinear coordinate system are derived to deal with a broad range of transition prediction problems on complex geometry. A highly accurate finite difference PSE code has been developed using an implicit marching procedure. Compressible and incompressible flat plate flow stability under two-dimensional and three¬dimensional disturbances has been investigated to test the present code. Results of the present computation are found to be in good agreement with the multiple scale analysis and DNS data. Stability calculation results by the present PSE code for compressible boundary layer at Mach numbers ranging from 0.02 to 1.5 are also presented and are again seen to be as accurate as the spectral method.

• 한국전산유체공학회:학술대회논문집
• /
• 2006.10a
• /
• pp.110-119
• /
• 2006

An accurate and cost efficient method PSE is used for the stability analysis of 2D or 3D compressible boundary layers. A highly accurate finite difference PSE code has been developed at a general curvilinear coordinate system using an implicit marching procedure to deal with a broad range of transition predictions problems. Evolution of disturbances in compressible flat plate boundary layers are studied for free-stream Mach numbers ranging from 0 to 1.5. The effect of mean-flow nonparallelism is found to be weak on two dimensional waves and strong on three dimensional waves. The maximum amplification rate increases monotonically with Mach number. The present PSE solutions are compared with previous numerical investigations and experimental results and are found to be in good agreement.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.37 no.11
• /
• pp.1055-1065
• /
• 2009

In this study, stability analysis of boundary layers on airfoils is performed by using parabolized stability equations(PSE). Boundary layer edge conditions are obtained by compressible inviscid flow calculations. Mean velocity and temperature profiles of the laminar boundary layer are obtained by solving compressible boundary layer equations in generalized curvilinear coordinates with fourth order accuracy in the wall normal direction. Laminar mean flow profiles are used as input data for PSE to investigate growth rates of disturbances and stability characteristics. For the cases of boundary layer on NACA0012 and HSNLF(1)-0213 airfoils at Mach number 0.5, growth rates with respect to disturbance frequencies and profiles of disturbance amplitude are investigated. The effect of angle of attack on stability characteristics are examined at both upper and lower surfaces. The neutral stability curves, effect of Mach number and effect of airfoil section shapes are also analyzed.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.38 no.5
• /
• pp.403-413
• /
• 2010

Transition location of boundary layers over airfoils is predicted by using PSE(Parabolized Stability Equations) and $e^N$-method. Growth rates of disturbances are obtained from the PSE analysis and the N-factor curves are calculated by integrating the growth rates. The computational code developed in the present study is validated by comparing the computed results with the well known data for the cases of flat plate boundary layers and airfoils. Predictions of transition location are made for the boundary layers over NACA0012, NLF(1)-0414F, and NLF(1)-0416 airfoil. Predicted transition locations are found to be in good agreement with the experimental data.

• 한국전산유체공학회:학술대회논문집
• /
• 2007.10a
• /
• pp.134-140
• /
• 2007

Nonlinear parabolized stability equations for compressible flow in general curvilinear coordinate system are derived to deal with a broad range of transition prediction problems on complex geometry. A highly accurate finite difference PSE code has been developed using an implicit marching procedure. Blasius flow is tested. The results of the present computation show good agreement with DNS data. Nonlinear interaction can make the T-S fundamental wave more unstable and the onset of its amplitude decay is shifted downstream relative to linear case. For nonlinear calculations, rather small difference in initial amplitude can produce large change during nonlinear region. Compressible secondary instability at Mach number 1.6 is also simulated and showed that 1.1% initial amplitude for primary mode is enough to trigger the secondary growth.