OS-Stab: Orr-Sommerfeld Stability Solver

Description

Performs stability analsysis for incompressible flows by solving the Orr-Sommerfeld equation for planar channel flow, the Blasius boundary layer, or for a given arbitary mean velocity profile. Note that in all cases, the parallel-flow approximation is made.

Background

Several different solvers are provided using different numerical methods including stablized shooting, Chebyschev spectral collocation, and finite-difference discretization. Solvers are also provided for both temporal analysis (real wavenumber, complex wave speed) and the more realistic spatial analysis (real frequency, complex wavenumber).

Also includes bl.f which is a spectral collocation Blasius flow solver and there are also shooting-based Blasius solvers embedded within the stability solvers (see below).

As an example, the mean Blasius velocity profile and second derivative of that profile computed using contebl.f is shown below.

The eigenfunction for the most unstable Tollmien-Schlichting wave (TS-wave) at Re=5800, alpha=0.179 is shown in the following figure with an complex valued wave speed (eigenvalue) of c = 0.36412287E+00 + i 0.79597206E-02.

These results are from running contebl.f using default input parameters as described below.

Note that there are example scripts for making plots of results using gnuplot. These scripts have files *.com such as mean.com for plotting the mean flow profile and phi.com for plotting the eigenfunction, phi.

There are also example scripts for plotting these same results using Python and matplotlib. See mean.py and phi.py and these are used by typing

python mean.py

which generates the file mean.png. Similarly for phi.py.

Building

Should build on Linux and MacOS platforms with Gfortran. First, as usual, you will clone the repository from GitHub using a command such as:

git clone https://github.com/sscollis/os-stab.git

You can get simple help on building the applications(s) by typing:

make help

And the default build is simply:

make 

Recommended build is:

make USE_RKCK45=1

You can make the Doxygen documentation using:

make docs

and then you can view the documentation locally by pointing your browser at html/index.html. For example, on a Mac you type

open html/index.html

from within the main os-stab directory to view the Doxygen documentation.

Running

The simplest case is temporal stability analysis for a planar channel using Conte's method and shooting:

./conte

Enter "d" for default values

A similar analysis for the Blasius boundary layer is done using:

./contebl

Enter "d" for default values

or the similar which takes input fron stdin

./orrsom < test.inp

Just computing the Blasisus boundary layer alone (no eigenanalysis):

./bl < bl.inp

A spatial analysis for BL is done using:

./orrspace 

And then type space.inp for input file.

You can do a sweep through the stability curve using:

./orrspace

And enter sweep.inp as the input file.

Additional examples

These examples require that one currently builds with USE_ALL_NR=1 that requires the user to supply commercially licenses code from Numerical Recipes in a file called nr.f. These routines are currently only used sparingly and can/should be replaced with open source code as time permits.

Nevertheless, you must have a valid license to use Numerical Recipes code and you must now check such code into this repository!

To do a sweep in alpha using finite-differences:

orrfdchan < fd-128.inp

or a single alpha and printing the eigenfunction:

orrfdchan < fdchan.inp

NOTE: There currently are not example inputs for all codes!

Updates as of 12-30-2019

Updated Orr-Sommerfeld solvers for gfortran

Code	Description
conte.f	Solves OS for channel using Godunov-Conte shooting
contebl.f	Solve Blasius and then OS for boundary layer using Conte
bl.f	Spectral collocation solver for Blasius equation
orrsom.f	Similar to contebl.f
shoot.f	Collection of general routines for shooting
orrspace.f	Solves spatial problem for boundary layers can sweep in frequency
orrfdchan.f	Solves temporal channel problem using finite-differences including sweeps

Numerous updates in this version include:

1. Fixed bug in eigenfunction values at nstep
2. Improved orthonormalization criteria
3. Switch from IMSL to LAPACK (need to test still)
4. Updated to support gfortran in makefile
5. Added scripts for gnuplot output
6. Improved some inline documentation
7. Use OpenBLAS for numerical linear algebra
8. Works on Mac OS-X (Darwin)

Updates as of 7-13-97

Incompressible Orr--Sommerfeld Solvers for Channel flow and Blasius Boundary Layer. Also bl.f is a spectral blasius flow solver.

Updates as of 3-07-2001

I have updated the following codes to use LAPack routines

orrncbl.f This finds the neutral curve for Boundary layer and channel profiles

orrcolchan.f Solve Orr-Sommerfeld for channel profile

S. Scott Collis
[email protected]