OpenFoam Simulation of Flow through a Backward Facing Step

 

Problem  SetUp:

q

Velocity  =  0.05  m/sec

Start  Time  =  0  sec

End  Time  =  1  sec

delta  Time  for  0.2  Graded  Mesh  =  0.00001  sec

delta  Time  for  0.5  Graded  Mesh  =  0.0001  sec

delta  Time  for  0.8  Graded  Mesh  =  0.0001  sec

Number of Cells in X direction  (Longer  Dimension =  200

Number of Cells in Y direction  (Each  Block =  10

OpenFoam  Solver  =  icoFoam

 

 

CONTOURS  Obtained:

 

(A)  0.2  Graded  Mesh:

11

 

Velocity  Distribution  without  Mesh:

fff

 

Velocity  Distribution  with  Mesh:

1

 

 

 

(B)  0.5  Graded  Mesh:

hh

 

Velocity  Distribution   without  Mesh:

kk

 

Velocity  Distribution  with  Mesh:

22

 

 

 

(C)  0.8  Graded  Mesh:

uyy

 

Velocity  Distribution  without  Mesh:

ffd

 

Velocity  Distribution   with  Mesh:

cc

 

 

 

PLOT  of  Velocity  Variation  @  0.085  m  from  Inlet  (for  different  Graded  Mesh):

s

 

 

CFL  Number:

Mean  Courant  Number  for  0.2  Graded  Mesh:  0.000325646

Mean  Courant  Number  for  0.5  Graded  Mesh:  0.00326564

Mean  Courant  Number  for  0.8  Graded  Mesh:  0.00327031

 

 

CONCLUSION:

NB:   `CFL=(Velocitytimes dt)/(trianglex)`

   The CFL numbers for Convergence are different for all the three Graded Mesh Simulations. For 0.2 Graded Mesh, simulation converges at delta time  =  0.00001 sec. But for 0.5 and 0.8 Graded Meshes, convergence delta time is 0.0001 sec. 

OBSERVATION:

   0.2 Graded Mesh < 0.5 Graded Mesh < 0.8 Graded Mesh

=> (delta time of 0.2 Graded Mesh) < (delta time of 0.5 Graded Mesh)=(delta time of 0.8 Graded Mesh)

=> 0.2 Graded CFL Number < 0.5 Graded CFL Number < 0.8 Graded CFL Number

=> 0.2 Graded Convergence Time > 0.5 Graded Convergence Time > 0.8 Graded Convergence Time

  So, 0.8 Graded Mesh Simulation converges at the fastest rate among all the three Graded Mesh Simulations.

  Again from the above Plot, we can conclude --> Velocity Distributions are almost same for all the Graded Mesh.

 

 


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