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This tutorial analyses the boundary layer development of a flow over a plate with an edge facing the stream. Flow velocity and fluid density and viscosity are specified to yield a laminar Reynolds number. The figure below shows the flow in the boundary layer over the plate. The model is solved using a 2D quadrilateral structured mesh.
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* [Steady state flow](case_venturi.html#Steady_state_flow) : description of the problem
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* [domain Boundaries](case_venturi.html#Domain_boundaries) : boundaries of the computational domain
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* [Convergence of the case](case_venturi.html#Convergence) : numerical and physical convergence of the model
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* [Shear stress and pressure on the plate](case_blasius.html#shear_pressure_on_plate) : post-processing of shear and pressure forces on the plate
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* [Bibliography](case_blasius.html#Bibliography) : bibliographic references
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* [Input files ](case_venturi.html#Input_files) : detailed description of case input files
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* [blasius.dat (case global parameters)](case_blasius.html#blasius_dat)
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* [blasius.dom.dat (domain input data)](case_blasius.html#blasius_dom_dat)
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* [blasius.geo.dat (mesh data)](case_blasius.html#blasius_geo_dat)
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* [blasius.set.dat (set data: groups for post-processing, optional)](case_blasius.html#blasius_set_dat)
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* [blasius.fix.dat (boundary conditions data)](case_blasius.html#blasius_fix_dat)
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* [blasius.ker.dat (kernel input data)](case_blasius.html#blasius_ker_dat)
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* [blasius.nsi.dat (incompressible Navier-Stokes solver parameters)](case_blasius.html#blasius_nsi_dat)
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* [blasius.post.alya.dat (alya2pos parameters)](case_blasius.html#blasius_post_alya_dat)
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* * *
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* * *
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# <a class="anchor" id="Steady_state_flow"></a>Steady state flow
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<center>blasius case - solution of the steady state flow</center>
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Plate is on plane Y=0, begins at X=0 and ends at X=1\. Simulation settings are specified to analyse a steady state flow. Integration TIME_INTERVAL is set from 0 to 1e5 (infinity) and so is NUMBER_OF_STEPS, in order to let iterate.
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* * *
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* * *
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# <a class="anchor" id="Domain_boundaries"></a>domain Boundaries
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Boundary numbers are as follows, inlet on the left end.
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<center>blasius case - domain boundaries</center>
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Boundary conditions are: inflow (1), outflow (2), wall (3) and symmetry (4).
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* * *
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* * *
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# <a class="anchor" id="Convergence"></a>Convergence of the case
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Next figure shows the convergence plot (alya-all-nsi app) of the simulation.
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<center>blasius case - numerical convergence</center>
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* * *
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* * *
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# <a class="anchor" id="shear_pressure_on_plate"></a>Shear stress and pressure on the plate
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As with the rest of the tutorials in this manual, the results have been postprocessed using the open-source software ParaView. In order to obtain X shear stress distribution and the accumulated Cf value on the wall, ParaView spreadsheet filter has been used to export velocity numerical values to an excel sheet, where velocity grandients and Cf integral
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```math
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{C_f} = \int_0^x \rho \frac{dU}{dy} {dx}
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```
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have been calculated numerically, giving this results:
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<center>blasius case - shear stress and Cf along the plate</center>
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<center>blasius case - pressure along the plate</center>
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From the technical literature (3) we obtain the following expression to calculate the Skin Friction Coefficient as a function of the Reynolds number:
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in a laminar boundary layer, $` \displaystyle{C_f} = \frac{0.664}{\sqrt{Re}} = \frac{0.664}{\sqrt{1000}} `$ = 0.0209975
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which correlates pretty well with the value obtained from the simulation with Alya: 0.022809309
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* * *
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* * *
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# <a class="anchor" id="Bibliography"></a>Bibliography
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(3) Measurement of Boundary Layer on a Flat Plate Kay Gemba (California State University, Long Beach) March 25, 2007
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* * *
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* * *
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# <a class="anchor" id="Input_files"></a>Input files
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* * *
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## <a class="anchor" id="blasius_dat"></a>blasius.dat (case global parameters)
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```
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$----------------------------------------------------------—
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RUN_DATA
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ALYA: blasius $ case name
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END_RUN_DATA
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$----------------------------------------------------------—
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PROBLEM_DATA
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TIME_COUPLING: Global, From_critical $ global time step is calculated by Alya
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TIME_INTERVAL= 0.0, 1.0e6 $ integration time domain from t=0 to t=1.0e6s
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TIME_STEP_SIZE= 0.001 $ prescribed time step (no effect, since TIME_COUPLING = From_critical)
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NUMBER_OF_STEPS= 2000 $ maximum number of time steps
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NASTIN_MODULE: On $ nastin module (Incompressible Navier-Stokes) is used
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END_NASTIN_MODULE
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PARALL_SERVICE: On $ parallelization module can be used
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End_PARALL_SERVICE
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END_PROBLEM_DATA
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$----------------------------------------------------------—
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```
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* * *
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## <a class="anchor" id="blasius_dom_dat"></a>blasius.dom.dat (domain input data)
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```
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$----------------------------------------------------------—
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DIMENSIONS
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NODAL_POINTS= 3721 $ number of nodes
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ELEMENTS= 3600 $ number of elements
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SPACE_DIMENSIONS= 2 $ 2D mesh
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TYPES_OF_ELEMENTS= 12 $ 4 node quadrilateral elements
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BOUNDARIES= 240 $ number of boundary edges
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END_DIMENSIONS
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$----------------------------------------------------------—
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STRATEGY $ integration strategy
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INTEGRATION_RULE: Open $ open rule is the default
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DOMAIN_INTEGRATION_POINTS: 0 $ 0 = automatic, depending on each element type
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END_STRATEGY
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$----------------------------------------------------------—
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GEOMETRY $ mesh definition
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GROUPS= 0 $ number of groups (for deflation based solvers)
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INCLUDE blasius.geo.dat $ include geometry file (nodes, elements & boundaries)
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END_GEOMETRY
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$----------------------------------------------------------—
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SETS $ sets definition
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INCLUDE blasius.set.dat $ include set file (groups for post-processing)
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END_SETS
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$----------------------------------------------------------—
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BOUNDARY_CONDITIONS, EXTRAPOLATE $ edge BC’s extrapolate to nodes
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INCLUDE blasius.fix.dat $ include boundary conditions file
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END_BOUNDARY_CONDITIONS
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$----------------------------------------------------------—
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```
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* * *
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## <a class="anchor" id="blasius_geo_dat"></a>blasius.geo.dat (mesh data)
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```
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$----------------------------------------------------------—
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NODES_PER_ELEMENT $ nodes per element list
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1 4 $ element number, number of nodes 2 4 3 4 : : 3599 4 3600 4
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END_NODES_PER_ELEMENT
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$----------------------------------------------------------—
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ELEMENTS $ element connectivity list
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1 3720 3718 3719 3721 $ element number, node number 1, node number 2, ...
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2 3717 3715 3718 3720
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3 3712 3710 3715 3717
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:
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:
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:
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3599 122 29 28 123
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3600 30 118 29 122
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END_ELEMENTS
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$----------------------------------------------------------—
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COORDINATES
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1 4.248591e-03 3.000000e+00 $ node number, coord X, coord Y
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2 9.318577e-03 3.000000e+00
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3 1.533496e-02 3.000000e+00
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:
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:
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:
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3720 -9.350762e-01 0.000000e+00
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3721 -1.000000e+00 0.000000e+00
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END_COORDINATES
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$----------------------------------------------------------—
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BOUNDARIES, ELEMENT
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1 3721 3720 1 $ boundary element #, node #s, element # boundary belongs to
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2 3720 3717 2
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3 3717 3712 3
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:
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:
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:
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239 2 1 3572
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240 1 121 3571
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END_BOUNDARIES MATERIALS, FLUID_MATERIAL=1, NUMBER=0, DEFAULT=1 all elements have material 1 END_MATERIALS CHARACTERISTICS END_CHARACTERISTICS
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$----------------------------------------------------------—
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```
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* * *
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## <a class="anchor" id="blasius_set_dat"></a>blasius.set.dat (set data: groups for post-processing, optional)
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```
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$----------------------------------------------------------—
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ELEMENTS $ element sets definition
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1 1 $ element number, set number
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2 1
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3 1
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:
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:
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:
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3599 1
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3600 1
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END_ELEMENTS
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$----------------------------------------------------------—
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BOUNDARIES $ boundary sets definition
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1 1 $ boundary element number, boundary set number
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2 1
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3 1
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:
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:
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:
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239 4
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240 4
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END_BOUNDARIES
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$----------------------------------------------------------—
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NODES $ node sets definition
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0
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END_NODES
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$----------------------------------------------------------—
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```
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* * *
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## <a class="anchor" id="blasius_fix_dat"></a>blasius.fix.dat (boundary conditions data)
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```
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$----------------------------------------------------------—
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ON_BOUNDARIES
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1 4 $ boundary element number, boundary number
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2 4
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3 4
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:
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:
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:
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239 4
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240 4
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END_ON_BOUNDARIES
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$----------------------------------------------------------—
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```
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* * *
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## <a class="anchor" id="blasius_ker_dat"></a>blasius.ker.dat (kernel input data)
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```
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$---------------------------------------------------------—
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PHYSICAL_PROBLEM
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MATERIAL=1
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PROPERTIES $ fluid physical properties
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DENSITY: CONSTANT, PARAMETERS = 1.0 $ mass density
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VISCOSITY: CONSTANT, PARAMETERS = 0.001 $ dynamic viscosity (μ)
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END_PROPERTIES
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END_PHYSICAL_PROBLEM
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$---------------------------------------------------------—
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NUMERICAL_TREATMENT
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MESH
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DIVISION=2 $ mesh subdivisions
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END_MESH
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ELSEST $ element search strategy
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STRATEGY: BIN $ BIN divide mesh into boxes to find elements that host
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witness points (suited for structured meshes)
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NUMBER: 100,33 $ 2D domain divided in 100 x 10 boxes
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END_ELSEST
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END_NUMERICAL_TREATMENT
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$---------------------------------------------------------—
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OUTPUT_&_POST_PROCESS
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ON_LAST_MESH
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STEPS=100 $ write post-process file every ‘STEPS’ time steps
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END_OUTPUT_&_POST_PROCESS
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$---------------------------------------------------------—
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```
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* * *
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## <a class="anchor" id="blasius_nsi_dat"></a>blasius.nsi.dat (incompressible Navier-Stokes solver parameters)
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```
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$---------------------------------------------------------—
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PHYSICAL_PROBLEM
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PROBLEM_DEFINITION
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TEMPORAL_DERIVATIVES: On $ transient problem
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CONVECTIVE_TERM: On $ off for Stokes flow (negligible for high viscosity fluids)
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VISCOUS_TERM: LAPLACIAN $ suitable for constant viscosity fluid assumption
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END_PROBLEM_DEFINITION
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END_PHYSICAL_PROBLEM
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$---------------------------------------------------------—
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NUMERICAL_TREATMENT
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ELEMENT_LENGTH: Minimum $ element length for Alya to calculate critical time step
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STABILIZATION: ASGS $ numerical stabilization method
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TIME_INTEGRATION: Trapezoidal, ORDER: 1, EULER=20 $ time integration scheme
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SAFETY_FACTOR: 1.6e5 $ multiply global time step: Alya calculates critical time step
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as required by explicit solvers, which is suited for transient
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analysis but makes stationary solutions converge very slowly
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STEADY_STATE_TOLER: 1.0e-10 $ convergence tolerance for steady state
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MAXIMUM_NUMBER_OF_IT: 1 $ max number of inner NS iterations
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CONVERGENCE_TOLERANCE: 1.0e-3 $ convergence tolerance for inner NS loop (useless in this case)
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ALGORITHM: SCHUR $ NS solution algorithm (uncouples p & V)
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SOLVER: ORTHOMIN, CONTINUITY_PRESERVING if not specifyed, default is MOMENTUM_PRESERVING
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PRECONDITION: DT
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END_ALGORITHM
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MOMENTUM $ velocity solver
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ALGEBRAIC_SOLVER
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SOLVER: GMRES, KRYLOV=10 $ solver suited for asymmetric matrix
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CONVERGENCE: ITERA=1000, TOLER=1.0e-12, ADAPTIVE, RATIO=0.01 $ max iter #, convergence criteria
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ADAPTIVE, RATIO=0.001 means that the loop will end also if the difference of the norm of convergence value changes less than 0.1% in two consecutive iterations
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OUTPUT: CONVERGENCE $ solver convergence file (.cso) is generated
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PRECONDITIONER: DIAGONAL $ matrix preconditioner type
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END_ALGEBRAIC_SOLVER
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END_MOMENTUM
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CONTINUITY $ pressure solver
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ALGEBRAIC_SOLVER
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SOLVER: DEFLATED_CG, COARSE: SPARSE $ CG solvers are suited for symmetric matrix
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CONVERGENCE: ITERA=1000, TOLER=1.0e-12, ADAPTIVE, RATIO=0.01 $ max iter #, convergence criteria
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ADAPTIVE, RATIO=0.001 means that the loop will end also if the difference of the norm of convergence value changes less than 0.1% in two consecutive iterations
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OUTPUT: CONVERGENCE $ solver convergence file (.cso) is generated
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PRECONDITIONER: LINELET $ matrix preconditioner type
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END_ALGEBRAIC_SOLVER
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END_CONTINUITY
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END_NUMERICAL_TREATMENT
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$---------------------------------------------------------—
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OUTPUT_&_POST_PROCESS
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START_POSTPROCES_AT STEP = 0 $ initial step to post process
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POSTPROCESS VELOCITY STEPS = 1 $ post process velocity every 10 steps (priority ker.dat)
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POSTPROCESS PRESSURE STEPS = 1 $ post process pressure every 10 steps (priority ker.dat)
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BOUNDARY_SET
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FORCE $ obtain pressure & velocity forces acting on boundaries
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TORQUE, CENTER=0,0,0 $ obtain torque of forces acting on boundaries, related to CENTER
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MASS $ obtain mass flow through boundaries
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END_BOUNDARY_SET
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END_OUTPUT_&_POST_PROCESS
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$---------------------------------------------------------—
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BOUNDARY_CONDITIONS
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PARAMETERS
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INITIAL: CONSTANT, VALUE=1.0, 0.0 $ domain velocity initialization (constant and equal to inlet velocity)
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|
|
END_PARAMETERS
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|
CODES, NODES $ Boundary Conditions
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|
1 11 1.000000 0.000000 $ inflow
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2 00 0.000000 0.000000 $ outflow
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3 11 0.000000 0.000000 $ wall
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4 01 0.000000 0.000000 $ symmetry
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1 & 4 11 1.000000 0.000000 $ vertex...
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2 & 3 11 0.000000 0.000000
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|
2 & 4 01 0.000000 0.000000
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|
3 & 4 11 0.000000 0.000000
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|
END_CODES $ (note that BC’s apply to boundaries, not to boundary sets)
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END_BOUNDARY_CONDITIONS
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|
|
|
$---------------------------------------------------------—
|
|
|
|
```
|
|
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|
* * *
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|
|
## <a class="anchor" id="blasius_post_alya_dat"></a>blasius.post.alya.dat (alya2pos parameters)
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|
|
|
```
|
|
|
|
$----------------------------------------------------------------—
|
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|
|
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|
DATA
|
|
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FORMAT: visit $ also valid for ParaView
|
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|
|
MARK_ELEMENTS: type $ to create automatic layers in post process according to some criterion
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|
ELIMINATE_BOUNDARY_NODES: yes $ for parallel runs, to avoid node duplicity between subdomain
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|
|
BOUNDARY: ON $ to post process boundary mesh
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|
SUBDOMAINS, ALL $ subdomains (parallel partitions) to post process
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|
END_SUBDOMAINS
|
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$ SUBDOMAINS
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$ 2 $ post process only subdomain 2
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$ END_SUBDOMAINS
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END_DATA
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$----------------------------------------------------------------—
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|
```
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|
* * * |
