Forced convection around a cylinder
We consider the forced convection of an heat source at the entrance of a channel with a cylinder inside.
1. Running the case
The command line to run this case is
mpirun -np 4 feelpp_toolbox_heatfluid --case "github:{repo:toolbox,path:examples/modules/heatfluid/examples/TurekHron}"
--case "github:{repo:toolbox,path:examples/modules/heatfluid/examples/TurekHron}"
The report of the execution of the command above is available here. |
2. Data files
The case data files are available in Github here
3. Geometry
A channel with a cylinder inside
We consider a 2D model representative of a laminar incompressible flow around an obstacle. The flow domain, named ΩfΩf, is contained into the rectangle [0,Long]×[0,Haut][0,Long]×[0,Haut]. It is characterised, in particular, by its dynamic viscosity μfμf and by its density ρfρf.
In order to describe the flow, the incompressible Navier-Stokes model is chosen for this case, define by the conservation of momentum equation and the conservation of mass equation. At them, we add the material constitutive equation, that help us to define σfσf
The goal of this benchmark is to couple the Naviers-Stockes equations and the heat equations We remind that the Naviers-Stokes equation are
And the Heat equations is
The toolbox is HeatFluid
4. Input parameters
The following table displays the various fixed and variables parameters of this test-case.
Name |
Description |
Units |
u |
fluid velocity |
m/s |
ρ |
density of the fluid |
kg/m3 |
ν |
dynamic viscosity |
kg/(m×s) |
p |
pression |
Pa |
f |
source term |
kg/(m3×s) |
Cp |
thermal capacity |
J/(kg∗K) |
T |
Temperature |
K |
Q |
heat source |
W.m−3 |
k |
Thermal conductivity |
W⋅m−1⋅K−1 |
4.1. initial condition
For the fluid:
We use a parabolic velocity profile, in order to describe the flow inlet by Γin, which can be express by
where ˉU is the mean inflow velocity.
However, we want to impose a progressive increase of this velocity profile. That’s why we define
With t the time.
For the temperature:
We give as source this temperature
4.2. Materials
"Materials":
{
"Fluid":{
"rho":"1.0e3",
"mu":"1.0",
"k":"2.9e-5",
"Cp":"4185"
}
},
4.3. Boundary conditions
For the fluid:
We set
-
On Γin, an inflow Dirichlet condition : uf=(vin,0)
-
On Γwall and Γobst, a homogeneous Dirichlet condition : uf=0
-
On Γout, a Neumann condition : σfnf=0
For the heat:
-
On Γin, an inflow Dirichlet condition : Tf=Tin