COMSOL 6.2 - Turbulent Flow over a Backward-Facing Step

Turbulent Flow over a Backward-Facing Step

The backward-facing step has long been a central benchmark case in computational fluid dynamics. The geometry is shown in Figure 1.

Figure 1: Backstep geometry. Dimensions in SI units.

Fully developed channel flow enters at the domain from the left. When the flow reaches the step, it detaches and a recirculation zone is formed behind the step. Because of the expansion of the channel, the flow slows down and eventually reattaches. The flow field is displayed in Figure 2.

Figure 2: Resulting flow field.

Though seemingly simple, the flow field is a challenge for turbulence models that utilize wall functions. The reason is that wall functions are derived by invoking equilibrium assumptions. Separation and reattachment do not adhere to these assumptions and it must therefore be asserted by numerical experiments that the wall functions can give accurate results even if the underlying theoretical assumptions are not strictly satisfied. The experiment is motivated by the fact that flow with separation and subsequent reattachment are of central importance in many engineering applications.

Model Definition

The model data is taken from Ref. 1. The parameters are given in Table 1. The Reynolds number based on Uav and the step height, S, is 47625 and the flow is therefore clearly turbulent.

Table 1: Model Parameters.
Property	Value	Description
S	0.0381 m	Step height
hc	2·S	Inlet channel height
H	3·S	Outlet channel height
L1	0.3048 m	Inlet channel length
L2	1.3335 m	Outlet channel length
ρ	1.23 kg/m3	Density
μ	1.79·10-5	Dynamic viscosity
Re	47625	Reynolds number
Uav	Re·μ/ρ/S	Mean inlet velocity

Results and Discussion

As shown in Figure 3, the recirculation length normalized by the step height becomes close to 6.7. Ref. 2 gives an experimental result of 7.1. The result provided by COMSOL Multiphysics is well within the range shown by other investigations (see Ref. 1 and Ref. 3). The separation lengths in Ref. 1 ranges between 6.12 and 7.24. In Ref. 3, recirculation lengths between 5.4 and 7.1 are obtained. Furthermore, Ref. 3 shows that the recirculation length can differ significantly by just changing some implementation details in the wall functions.

Figure 3: Contour plot of streamwise velocity equal to zero, colored by x/S where S is the step height.

Finally, note that the recirculation length can shift quite significantly with the mesh resolution. The current result does not shift much if the mesh is refined, but coarser meshes can yield very different recirculation lengths. This emphasizes the need to ensure that the mesh is fine enough.

Notes About the COMSOL Implementation

There are two aspects of the backward-facing step that need special consideration.

Mesh Generation

It is important to apply a fine enough mesh at the separation point to accurately capture the creation of the shear layer. It must also be remembered that both the flow field and turbulence variables can feature strong gradients close to the walls and that the mesh must be fine enough there to represent these gradients.

Inlet Boundary Conditions

To simulate fully developed channel flow that enters the domain, choose Fully developed flow option in the Inlet boundary condition, enforcing an average inlet velocity Uav based on the Reynolds number.

References

1. 1st NAFEMS Workbook of CFD Examples. Laminar and Turbulent Two-Dimensional Internal Flows, NAFEMS, 2000.

2. J. Kim, S.J. Kline, and J.P. Johnston, “Investigation of a Reattaching Turbulent Shear Layer: Flow Over a Backward Facing Step”, Transactions of the ASME, vol. 102, p. 302, 1980.

3. D. Kuzmin, O. Mierka, and S. Turek, “On the Implementation of the k-ε Turbulence Model in Incompressible Flow Solvers Based on a Finite Element Discretization”, Int’l J Computing Science and Mathematics, vol. 1, no. 2–4, pp. 193–206, 2007.

Heat_Transfer_Module/Verification_Examples/turbulent_backstep

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select ε .

Click .

Click

In the tree, select .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
S	0.0381[m]	0.0381 m	Step height
hc	0.0762[m]	0.0762 m	Inlet channel height
H	0.1143[m]	0.1143 m	Outlet channel height
L1	0.3048[m]	0.3048 m	Inlet channel length
L2	1.3335[m]	1.3335 m	Outlet channel length
rhof	1.23[kg/m^3]	1.23 kg/m³	Density
muf	1.79e-5[Pa*s]	1.79E-5 Pa·s	Dynamic viscosity
Re	47625	47625	Reynolds number
Uav	Re*muf/rhof/S	18.191 m/s	Mean inlet velocity

Geometry 1

Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type L1+L2.

In the text field, type hc.

Locate the section. In the text field, type -L1.

In the text field, type S.

Rectangle 2 (r2)

In the toolbar, click

In the window for , locate the section.

In the text field, type L2.

In the text field, type S.

Click

Mesh Control Edges 1 (mce1)

In the toolbar, click

and choose .

On the object , select Boundary 6 only.

It might be easier to select the correct boundary by using the window. To open this window, in the toolbar click and choose . (If you are running the cross-platform desktop, you find in the main menu.)