Non-Newtonian Flow Through Expansion Channel
Overview
The purpose of this numerical simulation is to validate the flow velocity profile for a Non-Newtonian fluid via the Power-Law model.
The numerical simulation were carried out using the Reynolds-Averaged Navier–Stokes (RANS) approach at laminar flow conditions. The results of SimScale simulation runs were compared to the analytical results shown in [1] [2]. The flow regime selected for the study has a Reynolds number of Re=40
.
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Geometry
The geometry of the study is a 2 dimensional channel with a 3:1 expansion (see Fig.1.). A brief description of the dimensions are provided by the table below.
- with respect to expansion step.
Domain and Analysis type
The domain is the internal region of the geometry with the domain extents same as the geometrical dimensions. For this study a full hexahedral structured mesh was created with the “blockMesh” open-source tool (see Fig.2.). The Mesh was refined at the expansion step in both horizontal and vertical directions. Two meshes, mesh M_2 (intermediate) and mesh M_3 (fine) were used for the study to check for mesh independence of results. The details of the mesh are listed in the following table:
Mesh and Element types :
| Mesh type | Number of cells | Type |
|---|---|---|
| blockMesh | 30.7 – 77.6 thousand | 3D hexahedral |
The numerical analysis performed is detailed as follows:
Tool Type : OPENFOAM®
Analysis Type : In-Compressible Steady-State
Turbulence Model : Laminar
Non-Newtonian model : Power-Law
Simulation Setup
Fluid:
Non-Newtonian
- normalized Consistancy Index (by density): k[m2/s]
based on Re=40
- Flow/Power Index n=0.5−2
Boundary Conditions:
For the inlet boundary, a fixed velocity condition was applied, while a pressure boundary condition was applied at the outlet. No-slip condition was applied for the walls and empty condition for the side faces. The following table provides the further details.
| Boundary type | Velocity | Pressure |
|---|---|---|
| Inlet | laminar Fixed Value: 0.5 ms−1
|
Zero Gradient |
| Outlet | Zero Gradient | Fixed Value: 0 Pa
|
| Wall no-slip | Fixed Value: 0.0 ms−1
|
Zero Gradient |
| Custom | 2D Empty | 2D Empty |
Results
The numerical simulation results for the various Power Index ranging from n=0.5−2
for a Re=40
are compared with analytical formulation given by Tanner [1] and shown by [2]. The formulations for the Generalized Reynolds number for non-Newtonian flows for this case is as follows:
Generalized Reynolds number: Re=ρ V2−nHnK
where, ρ
is the density, V
is the flow inlet velocity, H
is the inlet height, n
is the power index and K
is the consistency factor. All quantities here are in standard S.I units.
Two meshes M_2 and M_3 were analyzed. As no further improvement was observed for mesh M_3 the results presented are for mesh M_2. A comparison of the velocity profile in the fully developed region downstream of the expansion at X=28
is shown in fig.3. The figure shows the normalized velocity profile along the normalized channel height for n>1
shear thickening or dilatant fluid (e.g corn starch water), n=1
Newtonian fluid and n<1
Shear thinning or pseudoplastic fluids (e.g ketchup, paint, blood).
The Velocity contours with streamlines and corresponding profiles for Power Index n=0.5,1.0,2.0
are shown in the figure Fig.4 below.
References
| [1] | (1, 2)
|
| [2] | (1, 2)
|
Disclaimer
This offering is not approved or endorsed by OpenCFD Limited, producer and distributor of the OpenFOAM software and owner of the OPENFOAM® and OpenCFD® trade marks. OPENFOAM® is a registered trade mark of OpenCFD Limited, producer and distributor of the OpenFOAM software.