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Evaluating pressure coefficient at the top wall of the channel

pressure coefficient is in general^4.1:

$\displaystyle C_{p} = \frac{p - p_{\infty}}{\frac{1}{2}\rho_{\infty} U_{\infty}^{2}}$

(4.1)

We are going to evaluate pressure coefficient at the boundary, specifically at the UpperWall patch.
It means we need to know value of pressure at the boundary.
We use OpenFOAM post-processing functionality for sampling value of pressure.
The postProcess utility employs function object framework.
We use function object surfaceFieldValue.
An example of using this function object can be seen in its header file
# cat $FOAM_SRC/functionObjects/field/fieldValues/surfaceFieldValue/surfaceFieldValue.H
We create a new file called sampleUpperPatch in system directory.

(It can be done for example by command # touch system/sampleUpperPatch . The ‘touch’ command creates an empty text file. Use mcedit, or other text editor, to add following text to the file.)

type            surfaceFieldValue;
libs            ("libfieldFunctionObjects.so");

writeControl    writeTime;
writeFields     true;

surfaceFormat   raw;
regionType      patch;
name            upperWall;

operation       none;

fields
(
    p
);

We would like to sample field ‘p’ at the regionType ‘patch’ with name ‘upperWall’. The data will be stored in raw format.
The function object can be launched from case directory:
# cd $FOAM_RUN/pitzDaily
# postProcess -func sampleUpperPatch

Output is following:

/*---------------------------------------------------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  dev                                   |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
Build  : dev-e2ccbbbb
Exec   : postProcess -func sampleUpperPatch
Date   : Jun 16 2017
Time   : 12:00:00
Host   : $HOSTNAME
PID    : $$
Case   : $FOAM_RUN/pitzDaily
nProcs : 1
sigFpe : Enabling floating point exception trapping (FOAM_SIGFPE).
fileModificationChecking : Monitoring run-time modified files using timeStampMaster (fileModificationSkew 10)
allowSystemOperations : Allowing user-supplied system call operations

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
Create time

Create mesh for time = 0

surfaceFieldValue sampleUpperPatch:
    total faces  = 223
    total area   = 0.00031106


Time = 0

Reading fields:
    volScalarFields: p

Executing functionObjects


Time = 100

Reading fields:
    volScalarFields: p

Executing functionObjects


Time = 200

Reading fields:
    volScalarFields: p

Executing functionObjects


Time = 287

Reading fields:
    volScalarFields: p

Executing functionObjects


End

In test case directory is directory postProcessing containing new folder sampleUpperPatch, look inside:
# cd ./postProcessing
# ls
```
sampleUpperPatch  sets
```
# cd ./sampleUpperPatch
# ls
```
surface
```
# cd ./surface
# ls
```
0  100  200  287
```
# cd ./287
# ls
```
patch_upperWall.raw  p_patch_upperWall.raw
```

Look at file data:
# more ./p_patch_upperWall.raw

# p  FACE_DATA 223
#  x  y  z  p
-0.0198086 0.0254 0 -1.90829
-0.0182574 0.0254 0 -3.67105
-0.0167681 0.0254 0 -4.67569
-0.0153384 0.0254 0 -4.97477
-0.0139658 0.0254 0 -5.12385
-0.012648 0.0254 0 -5.26736
-0.0113829 0.0254 0 -5.38125
-0.0101683 0.0254 0 -5.46206

For plotting at top wall channel we use e.g. an open-source program gnuplot
${\textcolor{blue}{\mathsf {In \ Linux: }}}$ Run gnuplot:
# gnuplot
${\textcolor{red}{\mathsf {In \ Windows: }}}$ Run gnuplot outside of terminal. Use File > Change Directory and navigate to the location of file p_upperWallData.raw and confirm with OK.
In gnuplot environment type command:
gnuplot> plot './p_patch_upperWall.raw' using 1:($4/(0.5*100)) with lines
$p_{\infty} = 0\ m^2s^{-2},\ U_{\infty} = 10.0\ m\,s^{-1}$

Figure: at the top wall, Backward-Facing-Step OpenFOAM tutorial

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