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ASBL: Axisymmetric Separated Boundary Layer

The purpose here is to provide a validation case for turbulence models. Unlike verification, which seeks to establish that a model has been implemented correctly, validation compares CFD results against data in an effort to establish a model's ability to reproduce physics. A large sequence of nested grids of the same family are provided here if desired. Data are also provided for comparison. For this particular "essentially incompressible" axisymmetric separated boundary layer case (from Driver), the data are from an experiment.

The experiment utilized a cylinder of 0.140 m diameter in a tunnel in which an adverse pressure gradient was imposed over a portion of the flow by diverging the four tunnel walls. Each wall was deflected by as much as 0.045 m, resulting in an area expansion ratio of about 1.6. In the experiment, the tunnel sidewall boundary layers were thinned via suction. In experimental case C (used here), the adverse pressure gradient was severe enough that the flow on the cylinder separated, resulting in a bubble of length approximately 0.2 m.

The experimentalist provided a streamline shape well outside of the cylinder's boundary layer that can be used as an inviscid surface for defining the upper boundary condition in a CFD simulation. The inflow to the domain is adjusted so that the naturally developing turbulent boundary layer on the cylinder in the CFD solution grows to approximately 0.012 m thick near the position x = -0.3 m (just upstream of the adverse pressure gradient), as noted in the experiment. A short region with symmetry is imposed upstream to avoid possible incompatibilities between freestream inflow and wall BCs. (Note that particular variations of the BCs at the inflow and outflow may also work and yield similar results for this problem.)

It is important to note that this axisymmetric case is not a 2-D computation; it uses a periodic (rotated) grid system with appropriate boundary conditions on the periodic sides of the grid.

GRIDS

Some of the experimental data for this case are shown below. Velocity and turbulence profiles of interest are chosen at the following x-locations: x=-0.3302, -0.0762, 0.0508, 0.1016, 0.1524, 0.2286, and 0.3048 (all in meters). Note that for the Driver data, the wall-normal coordinate y' is defined such that y'=0 on the cylinder surface.

The experimental data reference is: Driver, D. M., "Reynolds Shear Stress Measurements in a Separated Boundary Layer Flow," AIAA Paper 91-1787, from the AIAA 22nd Fluid Dynamics, Plasma Dynamics, and Lasers Conference, June 1991, Honolulu, HI, https://doi.org/10.2514/6.1991-1787.

For the pressure coefficient data, note that it is relative to conditions at the position near x=-0.4 or so upstream; i.e., Cp is defined to be 0 near this location.

The experimental data used are provided here:

• Driver Cp data
• Driver Cf data
• Driver velocity profiles
• Driver u'v' profiles

What to Expect:

RESULTS	LINK TO EQUATIONS	MRR Level
SA	SA eqns	4
SSTm	SSTm eqns	3
SSG/LRR-RSM-w2012	SSG/LRR-RSM-w2012 eqns	3
Wilcox2006-klim-m	Wilcox2006-klim-m eqns	2
EASMko2003-S	EASMko2003-S eqns	1
K-e-Rt	K-e-Rt eqns	1

(Other turbulence model results may be added in the future.)

Note that the OVERFLOW code has documented its results for this validation case (for the SA-noft2 and SST turbulence models) in NAS Technical Paper 2016-01 (pdf file) (18.3 MB) by Jespersen, Pulliam, and Childs.
 
 

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Last Updated: 11/12/2021