3. Group assignment: Flow around a cylindrical body
In low
Reynolds number regime (Re=50…200), two-dimensional time dependent (periodic)
flow takes place around cylindrical bodies. The laminar boundary layer separates
on both sides of the frontal surface, producing free shear layers, the vorticity of which is being accumulated in large eddies
downstream from the cylinder. The interaction between large eddies give rise to
the well-known von Karman vortex sheet.
This
investigation is aimed at the understanding of flow phenomenon, as well as the
application of error estimation methodology in the case of time dependent flow.
The shape
and proportions of the simulation domain will be chosen on the basis of Betti Bolló’s recommendations
according to Fig.1. Let d¥/d = 100. u¥ velocity shall be used as boundary
condition at the outer boundary.
Figure 1. Geometrical
parameters and boundary conditions.
Task 1. (3 points)
Preparation
of 3 meshes of different numbers of elements by maintaining element size ratios
within each mesh and keeping similarity between corresponding elements. In
order to achieve comparable results both ratio of side length and angles need
to be identical in corresponding elements. Please consider the applicability of
Richardson-extrapolation when choosing the number of mesh elements.
Task 2. (3 points)
Chose air
as working fluid and set the value of viscosity on the way the Reynolds-number
be equal to 110! Make a pre-calculation with your coarsest mesh and check the
Courant number distribution! Set the time step size on each mesh corresponding
to C=1 maximum Courant number! Estimate the necessary computation time, by
assuming, that the periodic solution takes 120 * d/u¥ flow time to develop! Change mesh
sizes if necessary!
Task 3. (3 points)
Run
simulations with your 3 meshes until reaching the periodic solution, meanwhile
monitoring lift force FL and drag FD !
Task 4. (3 points)
Calculate FD,avg (average value
of of FD), as well as f frequency and FL,rms (RMS of FL) for the periodic
solution. Evaluate the following dimensionless quantities:
, 
, 
.
Estimate
the error of above quantities for your finest mesh and extrapolate mesh
independent values! Please, compare your computational results with experimental
data specified in Table 1!
|
Re |
50 |
70 |
90 |
110 |
130 |
150 |
170 |
Referencia |
|
St |
0.122 |
0.144 |
0.159 |
0.169 |
0.177 |
0.183 |
0.189 |
Williamson (1998) |
|
cL,rms |
0.0466 |
0.138 |
0.199 |
0.254 |
0.306 |
0.356 |
0.404 |
Norberg (2001) |
|
cD,avg |
1.45 |
1.39 |
1.36 |
1.34 |
1.33 |
1.33 |
1.33 |
Henderson (1995) |
Table 1. Experimental data
Task 5. (3 points)
Summarize the
investigation aims and methodology as well as the results of flow pattern, time
functions and average quantities!
The report should be prepared in PowerPoint
(.PPT) file which is to be up-loaded to the personal result folder.
References:
Bolló, B,
Baranyi, L., 2010. Computation of low-Reynolds number
flow around a stationary circular cylinder. Proc. 7th International Conference
on Mechanical Engineering, Budapest, pp. 891-896.
Henderson,
R.D., 1995. Details of the drag curve near the onset of vortex shedding. Physics of Fluids 7, 2102–2104.
Norberg, C.,
2001. Flow around a circular cylinder: aspects of fluctuating lift. Journal of
Fluids and Structures 15, 459-469.
Williamson,
C.H.K., Brown, G.L., 1998. A series in 1/√Re to
represent the Strouhal-Reynolds number relationship
of the cylinder wake. Journal of Fluids and Structures 12(8), 1073-1085.