# Sig Turbulence / Dellenback Abrupt Expansion

## 1 Testcase description and experimental results

The OpenFOAM case-study was developed by:

Håkan Nilsson, Chalmers University of Technology, Gothenburg, Sweden

The turbulent swirling flow in an abrupt expansion was experimentally investigated by Dellenback, Metzger, and Neitzel [1]. The geometry is illustrated in Figure 1. The inlet is located at the smaller diameter, where either a pure axial, or swirling flow at different swirl and Reynolds numbers is imposed.

Figure 1: Dellenback Abrupt Expansion geometry. Inlet at the small diameter.

The geometric data used in this case-study are the following:

 Inlet diameter $D_{in} = 50.78 mm$ Outlet diameter $D_{out} = 98.5 mm$ Expansion ratio $D_{out}/D_{in} = 1.94$ Inlet length $2*D_{in}$ Outlet length $10*D_{in}$

Dellenback presented 9 cases: 3 with purely axial flow, and 6 with swirl:

 $Re = \frac{U_{b,in}D_{in}}{\nu}$ $S = \left. \frac{\int_0^{R_{in}}V_\theta V_zr^2dr}{R_{in}\int_0^{R_{in}}V_z^2rdr}\right|_{z/D_{in}=-2.00}$ 30,000 0.00, 0.60, 0.98 60,000 0.00, 1.16 100,000 0.00, 0.17, 0.74, 1.23

The measurements were taken at the cross-sections shown in figure 2.

Figure 2: Measurement cross-sections. Numbers refer to Z/D, where D is the inlet diameter, and Z=0 at the abrupt expansion.

At each cross-section the following data is available:

• Axial mean velocity profiles.
• Tangential mean velocity profiles.
• Axial RMS velocity profiles.
• Tangential RMS velocity profiles.
• Most data sets show measurements on both sides of the centerline as a check for symmetry.
• Only some of the experimental data are arranged for the automatic post-processing. Please help arrange the rest in a similar way!

The case-study is thoroughly described in [7] (Slides), where there are also some preliminary results.

Future work using this case-study should refer to Gyllenram and Nilsson [4], Nilsson and Gyllenram [5], and Nilsson [7].

## 2 Published computational results

Computations have been performed by Schluter et al. [2], Gyllenram, Nilsson and Davidson [3], Gyllenram and Nilsson [4,5,8], Gyllenram [6], and Nilsson [7]. Gyllenram and Nilsson [4] validated the filtered k-omega SST model using the Dellenback Abrupt Expansion case. Gyllenram and Nilsson [8] determined the optimal filter width ($\alpha=3$). Nilsson and Gyllenram [5] implemented the kOmegaSSTF model in OpenFOAM, and validated it in the Dellenback Abrupt Expansion case. The OpenFOAM case-study was developed and first presented by Nilsson [7], at the 4th OpenFOAM Workshop in Montreal.

## 3 References

[1] Dellenback, P.A., Metzger, D.E., and Neitzel, G.P., "Measurements in Turbulent Swirling Flow Through an Abrupt Expansion", AIAA Journal, 26(6), pp.669-681 , 1987.

[2] Schluter, J.U., Pitsch, H., and Moin, P., "Large Eddy Simulation Inflow Conditions for Coupling With Reynolds-Averaged Flow Solvers", AIAA Journal, 42(3), pp. 478-484, 2004.

[3] Gyllenram, W., Nilsson, H., and Davidson, L., "Large Eddy Simulation of Turbulent Swirling Flow Through a Sudden Expansion", IAHR 2006, Yokohama, 2006, Paper, Slides

[4] Gyllenram, W., and Nilsson, H., "Design and Validation of a Scale-Adaptive Filtering Technique for LRN Turbulence Modeling of Unsteady Flow", Journal of Fluids Engineering, May 2008, Vol 130.

[5] Nilsson, H., and Gyllenram, W., "Experiences with OpenFOAM for water turbine applications", 1st OpenFOAM Conference, Old Windsor, London, 2007. Paper, Slides

[6] Gyllenram, W., "Analytical and Numerical Studies of Internal Swirling Flows", PhD Thesis, Chalmers University of Technology, Gothenburg, Sweden, 2008, ISBN 978-91-7385-104-6, CPL, Thesis, Errata, Slides

[7] Nilsson, H., "The Dellenback Abrupt Expansion OpenFOAM Case-Study, and the kOmegaSSTF turbulence model", 4th OpenFOAM Workshop, Montreal, June 1-4, 2009. Slides

[8] Gyllenram, W. and Nilssson, H., Very Large Eddy Simulation of Draft Tube Flow, IAHR Symposium, Yokohama, 2006. Paper.

[9] Paik, J, Sotiropoulos, F., "Numerical simulation of strongly swirling turbulent flows through an abrupt expansion", International Journal of Heat and Fluid Flow 31 (2010) 390–400

[10] Nilsson, H. "Simulations of the vortex in the Dellenback abrupt expansion, resembling a hydro turbine draft tube operating at part-load", IOP Conf. Ser.: Earth Environ. Sci. 15 022016. 15 p. Article number 022016

[11] Javadi, A. and Nilsson H. "LES and DES of Strongly Swirling Turbulent Flow through a Suddenly Expanding Circular Pipe". Computers & Fluids (2014). In Press. doi:10.1016/j.compfluid.2014.11.014

## 4 How to get the files

The OpenFOAM Dellenback Abrupt Expansion cases described in the following sections were developed as a case-study for the Fourth OpenFOAM Workshop, Montréal, 2009, and can be found at the OpenFOAM-extend SourceForge project. It includes complete OpenFOAM cases and automatic post-processing of the results. The block-structured hexahedral meshes are parameterized and generated with m4 and blockMesh. Instructions on how to run the cases follow below.

Get all the current case files by doing:


cd $FOAM_RUN svn checkout svn://svn.code.sf.net/p/openfoam-extend/svn/trunk/Breeder_1.5/OSIG/Turbulence/dellenbackAbruptExpansion In the descriptions below, we thus assume that the dellenbackAbruptExpansion directory is located in the$FOAM_RUN directory

Update your files every now and then by doing:


cd $FOAM_RUN/dellenbackAbruptExpansion svn update In the dellenbackAbruptExpansion directory you find three directories: dellenbackAbruptExpansion/ |-- cases |-- measurements -- optionalMeshes  In the measurements directory, you can find the original experimental results that were kindly provided by Dellenback, for use in this OpenFOAM case-study. The directory must be located next to the cases directory for the automatic post-processing to work. Unfortunately, the data was only available on paper, which is what can be found in the scanned dellenbackData.pdf file. An attempt to automatically extract (OCR) the data in the pdf file to a text file can be found in the dellenbackData.OCR file. This file can be used as a basis for generating the final files for comparisons. The data that has already been extracted and checked thoroughly are available as groups of four files for each operating condition: Re?????Sw***AxialMean Re?????Sw***AxialRMS Re?????Sw***TangentialMean Re?????Sw***TangentialRMS  where '?????' and '***' refer to the Reynolds number and swirl number for each case. In the cases directory, you find the currently available test cases. Those are described in detail below. In the optionalMeshes directory you find other meshes that might be of interest, for instance the ICEM files for generating the meshes used by Gyllenram and Nilsson, referred to as the 'coarse' and 'fine' mesh. These are the required libraries, except for what is already available in OpenFOAM-1.5-dev: See further info at OpenFOAM-extend webpage ## 5 Test cases Here you can find generic test cases that can be modified for your purposes. The test cases include parameterized mesh generation with several meshes, complete case set-up, and automatic post-processing using sample, foamLog and gnuplot. You can contribute cases if you come up with more ideas. In that case, please try to follow the same directory structure and name conventions. Add instructions on the new cases in this Wiki. ### 5.1 DAEsimpleFoam This case is set up for simpleFoam and kOmegaSST, but can be used to run any other steady RAS simulation, by editing constant/RASProperties, and choosing the most appropriate m4 script in constant/polyMesh for mesh generation (wall-functions or low-Re). The mesh is parametrized using m4. Figures 3-5 show most of the parameters. There are some additional parameters that are explained in the m4 scripts. Figure 3: The mesh planes used in the m4 parametrization Figure 4: The m4 parametrization of the O-grid at mesh plane A Figure 5: The m4 parametrization of the O-grid at mesh plane B-H Run the case by doing (remember that you need libOpenFoamTurbo.so available!): cd$FOAM_RUN/dellenbackAbruptExpansion/cases/DAEsimpleFoam
./Allrun


Note that you can modify the Allrun script to use one of the alternative meshed provided, for Low-Re simulations.

Post-process the case (when the simulation is done - 10000 iterations takes a looong time) by following the instructions in the postProcessing/README file.

Clean up everything from the simulation (not from post-processing) by doing:

cd $FOAM_RUN/dellenbackAbruptExpansion/cases/DAEsimpleFoam ./Allclean  There is an xFig directory that contains files for generation of the drawings in this Wiki, to be used with xfig. ### 5.2 DAEtransientSimpleFoam This case is set up for transientSimpleFoam and kOmegaSSTF, but can be used to run any other transient RAS simulation, by editing constant/RASProperties, and choosing the most appropriate m4 script in constant/polyMesh for mesh generation (wall-functions or low-Re). The case is set up and run similar to the DAEsimpleFoam case, described above. Run the case by doing (remember that you need OpenFOAM-1.5-dev, libaddedIncompressibleRASModels.so, and libOpenFoamTurbo.so available!): cd$FOAM_RUN/dellenbackAbruptExpansion/cases/DAEtransientSimpleFoam
./Allrun


Note that you can modify the Allrun script to use one of the alternative meshed provided, for Low-Re simulations.

Post-process the case (when the simulation is done - 10000 iterations takes a looong time) by following the instructions in the postProcessing/README file. Note that there are prepared, but commented, lines in the files for plotting mean probes and profiles if you have activated the averaging at time 9.358, and run the case until time 16.8 (which is the default endTime).

Clean up everything from the simulation (not from post-processing) by doing:

cd \$FOAM_RUN/dellenbackAbruptExpansion/cases/DAEtransientSimpleFoam
./Allclean
`

There is an xFig directory that contains files for generation of the drawings in this Wiki, to be used with xfig

See references [4,5,7] for a description of kOmegaSSTF.

## 6 Others

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