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This tutorial analyses the flow through an elbow discretized with a 3D tetrahedral unstructured mesh.
* [Steady state flow](case_elbow.html#Steady_state_flow_2) : description of the problem
* [Domain Boundaries](case_elbow.html#Domain_boundaries_2) : boundaries of the computational domain
* [Case convergence](case_elbow.html#Convergence_2) : numerical convergence of the model
* [Velocity field](case_elbow.html#Velocity_profiles_2) : post-processing of velocity field and pressure drop according to Re
* [Pressure drop](case_elbow.html#Pressure_drop) : pressure drop vs. Reynolds number
* [Input files](case_elbow.html#Input_files_2) : detailed description of case input files
* [elbow.dat (case global parameters)](case_elbow.html#elbow_dat)
* [elbow.dom.dat (domain input data)](case_elbow.html#elbow_dom_dat)
* [elbow.geo.dat (mesh information)](case_elbow.html#elbow_geo_dat)
* [elbow.set.dat (groups for post-processing, optional)](case_elbow.html#elbow_set_dat)
* [elbow.fix.dat (boundary conditions data)](case_elbow.html#elbow_fix_dat)
* [elbow.ker.dat](case_elbow.html#elbow_ker_dat)
* [elbow.nsi.dat (incompressible Navier-Stokes solver parameters)](case_elbow.html#elbow_nsi_dat)
* [elbow.post.alya.dat (alya2pos parameters)](case_elbow.html#elbow_post_alya_dat)
* * *
* * *
# <a class="anchor" id="Steady_state_flow_2"></a>Steady state flow
![image](uploads/ba9d7c69e8fd8c107569559d101d6776/image.png)
<center>elbow case – 3D turbulent flow (Re=1e4) [(click for Turbulent Flow Development animation)](http://www.youtube.com/watch?feature=player_embedded&v=65YWYUH7zB8)</center>
Simulation settings are specified to reach a steady state flow condition. The case is run with different Reynolds numbers, by changing the viscosity of the fluid, in order to analyze pressure drop variation. Total pipe length is roughly 6m.
# <a class="anchor" id="Domain_boundaries_2"></a>Domain Boundaries
* * *
* * *
Boundary numbers are as follow, outlet on the short straight. Inlet velocity is specified with a paraboloid surface function.
![image](uploads/54403dd217af405828671cba2ed5e2da/image.png)
<center>elbow case – domain boundaries</center>
* * *
* * *
# <a class="anchor" id="Convergence_2"></a>Case convergence
Time iteration is let to calculate automatically the time increment within each timestep and the maximum number of iterations is set to infinity (1e6), so that the simulation will finish when convergence criteria are reached. Next figure show two convergence plot (alya-all-nsi app) of the simulations with Re=150.
![image](uploads/4c348a489ec56cba7f40864931e9fce1/image.png)
<center>elbow case – numerical convergence</center>
* * *
* * *
# <a class="anchor" id="Velocity_profiles_2"></a>Velocity field
An animation of the resulting turbulent flow is found in this link: see elbow case animation. This is only a roughly approximate solution, since Re=1.0e4 is much beyond the limit of laminar flow and no turbulence model is used in the simulation. Next figure shows velocity results for Re=100:
![image](uploads/1108db062f9faef759de3057ea12ab2b/image.png)
<center>elbow case – velocity distribution (Re = 100)</center>
* * *
* * *
# <a class="anchor" id="Pressure_drop"></a>Pressure drop
In the following, pipe pressure drop results are compared to semi-empirical results calculated with classical engineering methods, such as Poiseuille and Darcy equations.
![image](uploads/ddd0bb885f070b40945b343527a6639a/image.png)
<center>elbow case – empirical data</center>
The relation between flow pressure drop and Reynolds number is analyzed from the previous runs.
Reynolds number is calculated as follows (taking ‘l’ as pipe diameter):
```math
\textnormal{Re} = \frac{(\rho \cdot {U} \cdot {l})}{\mu}
```
Theoretical pressure drop calculations have been performed using Poiseuille equation to account for pressure losses along pipe length, and an empirical formula to add minor fitting pressure loss:
```math
{\Delta p} = 8 \cdot \frac{{Q} \cdot \nu \cdot {l}}{\pi{R}^4} + \frac{1}{2}{k} \rho {U}^2}
```
being,
* Q = mass rate
* ν = dynamic viscosity
* l = pipe axis lenght
* k = elbow pressure loss coefficient (diagram)
* ρ = density
Next table and plot show the correlation between results calculated by Alya and the theoretical-empirical ones:
<center>
<table class="doxtable">
<tbody>
<tr>
<td>mu</td>
<td>2.000E-02</td>
<td>1.000E-02</td>
<td>6.667E-03</td>
</tr>
<tr>
<td>Re</td>
<td>5.000E+01</td>
<td>1.000E+02</td>
<td>1.500E+02</td>
</tr>
<tr>
<td>Alya pressure drop</td>
<td>2.0903</td>
<td>1.0934</td>
<td>0.7906</td>
</tr>
<tr>
<td>Theoretical pressure drop</td>
<td>2.0515</td>
<td>1.0315</td>
<td>0.6982</td>
</tr>
<tr>
<td>error</td>
<td>1.9%</td>
<td>6.0%</td>
<td>13.2%</td>
</tr>
</tbody>
</table>
</center>
![image](uploads/62a37c3d2782b7b0fa63330040cd65db/image.png)
<center>elbow case – pressure drop vs. Reynolds number</center>
Pressure drop values from the different Alya runs are obtained from the file elbow-boundary.nsi.set, by reading inlet and outlet mean pressure values from the last time step results, corresponding in this case boundary sets 9 and 13 to inlet and outlet surfaces respectively.
* * *
* * *
# <a class="anchor" id="Input_files_2"></a>Input files
* * *
## <a class="anchor" id="elbow_dat"></a>elbow.dat (case global parameters)
```
$----------------------------------------------------------—
RUN_DATA
ALYA: elbow $ case name
END_RUN_DATA
$----------------------------------------------------------—
PROBLEM_DATA
TIME_COUPLING: Global, From_critical $ global time step is prescribed
TIME_INTERVAL= 0.0, 1.0e6 $ integration time domain from t=0 to t=10s
NUMBER_OF_STEPS= 1e5 $ infinite time steps
MAXIMUM_NUMBER_GLOBAL= 1 $ only used when coupling modules
NASTIN_MODULE: On $ nastin module (Incompressible Navier-Stokes) is used
END_NASTIN_MODULE
PARALL_SERVICE: On
END_PARALL_SERVICE
END_PROBLEM_DATA
$----------------------------------------------------------—
```
* * *
```
## <a class="anchor" id="elbow_dom_dat"></a>elbow.dom.dat (domain input data)
$----------------------------------------------------------—
DIMENSIONS
NODAL_POINTS= 5682 $ number of nodes
ELEMENTS= 26410 $ number of elements
SPACE_DIMENSIONS= 3 $ 3D mesh
TYPES_OF_ELEMENTS= 30 $ 4 node tetrahedral elements
BOUNDARIES= 4046 $ number of boundary edges
END_DIMENSIONS
$----------------------------------------------------------—
STRATEGY
INTEGRATION_RULE: Open $ open rule is the default
DOMAIN_INTEGRATION_POINTS: 0 $ 0 = automatic, depending on each element type
END_STRATEGY
$----------------------------------------------------------—
GEOMETRY
GROUPS=100 $ number of groups (for deflation based solvers)
INCLUDE elbow.geo.dat $ include geometry file (nodes, elements & boundaries)
END_GEOMETRY
$----------------------------------------------------------—
SETS
INCLUDE elbow.set.dat $ include set file (groups for post-processing)
END_SETS
$----------------------------------------------------------—
BOUNDARY_CONDITIONS, EXTRAPOLATE $ edge BC’s extrapolate to nodes
INCLUDE elbow.fix.dat $ include boundary conditions file
END_BOUNDARY_CONDITIONS
$----------------------------------------------------------—
```
* * *
## <a class="anchor" id="elbow_geo_dat"></a>elbow.geo.dat (mesh information)
```
$----------------------------------------------------------—
NODES_PER_ELEMENT
1 4 $ element number, # nodes
2 4
3 4
:
:
26409 4
26410 4
END_NODES_PER_ELEMENT
$----------------------------------------------------------—
ELEMENTS (element connectivity list)
1 5585 5586 5518 5562 $ element number, node number 1, node number 2, ...
2 5660 5630 5629 5613
3 5676 5662 5647 5666
:
:
26409 1638 1433 1313 1315
26410 1491 1638 1313 1315
END_ELEMENTS
$----------------------------------------------------------—
COORDINATES
1 1.638713e+00 -2.971132e+00 2.893691e-02 $ node number, coord X, coord Y , coord Z
2 1.533333e+00 -2.971132e+00 2.886751e-02
3 1.873338e+00 -2.971128e+00 2.852064e-01
:
:
5681 1.045415e+00 0.000000e+00 0.000000e+00
5682 1.000000e+00 0.000000e+00 0.000000e+00
END_COORDINATES
$----------------------------------------------------------—
BOUNDARIES, ELEMENT
1 5681 5676 5682 9402 $ boundary element #, node #s, element # boundary belongs to
2 5666 5676 5681 9399
3 5666 5638 5660 9763
:
:
4045 54 71 12 24996
4046 12 67 54 26111
END_BOUNDARIES MATERIALS, NUMBER=0, DEFAULT=1 $ vall elements have material 1 END_MATERIALS CHARACTERISTICS END_CHARACTERISTICS
$----------------------------------------------------------—
```
* * *
## <a class="anchor" id="elbow_set_dat"></a>elbow.set.dat (groups for post-processing, optional)
```
$----------------------------------------------------------—
ELEMENTS
1 1 $ element number, set number
2 1
3 1
:
:
:
26409 1
26410 1
END_ELEMENTS
$----------------------------------------------------------—
BOUNDARIES (boundary sets definition)
1 2 $ boundary element number, boundary set number
2 2
3 2
:
:
:
4045 13
4046 13
END_BOUNDARIES
$----------------------------------------------------------—
NODES (node sets definition)
0
END_NODES
$----------------------------------------------------------—
```
* * *
## <a class="anchor" id="elbow_fix_dat"></a>elbow.fix.dat (boundary conditions data)
```
$----------------------------------------------------------—
ON_BOUNDARIES
1 4 $ boundary element number, boundary set number
2 4
3 4
:
:
:
4045 1
4046 1
END_ON_BOUNDARIES
$----------------------------------------------------------—
```
* * *
## <a class="anchor" id="elbow_ker_dat"></a>elbow.ker.dat
```
$---------------------------------------------------------—
PHYSICAL_PROBLEM
PROPERTIES $ fluid physical properties (water)
DENSITY: CONSTANT, PARAMETERS = 1.0 $ mass density
VISCOSITY: CONSTANT, PARAMETERS = 0.0005 $ dynamic viscosity (μ)
END_PROPERTIES
END_PHYSICAL_PROBLEM
$---------------------------------------------------------—
NUMERICAL_TREATMENT
MESH
DIVISION=1 $ 2 automatic mesh subdivisions
END_MESH
ELSEST $ element search strategy
STRATEGY: BIN BIN divide mesh into boxes to find elements that host
witness points (suited for structured meshes)
NUMBER: 20, 20, 20
DATAF: LINKED_LIST
END_ELSEST
SPACE_&_TIME_FUNCTIONS
FUNCTION=INFLOW
-4*y**2-4*z**2+12*y-8 $ paraboloid surface function (Umax=1)
END_FUNCTION
END_SPACE_&_TIME_FUNCTIONS
END_NUMERICAL_TREATMENT
$---------------------------------------------------------—
OUTPUT_&_POST_PROCESS
ON_LAST_MESH
STEPS=10 $ post-process every ‘STEPS’ time steps
END_OUTPUT_&_POST_PROCESS
$---------------------------------------------------------—
```
* * *
## <a class="anchor" id="elbow_nsi_dat"></a>elbow.nsi.dat (incompressible Navier-Stokes solver parameters)
```
$---------------------------------------------------------—
PHYSICAL_PROBLEM
PROBLEM_DEFINITION
TEMPORAL_DERIVATIVES: On $ transient problem
CONVECTIVE_TERM: On $ off for Stokes flow (negligible for high viscosity fluids)
VISCOUS_TERM: LAPLACIAN $ suitable for constant viscosity fluid assumption
END_PROBLEM_DEFINITION
END_PHYSICAL_PROBLEM
$---------------------------------------------------------—
NUMERICAL_TREATMENT
ELEMENT_LENGTH: Minimum $ element length for Alya to calculate critical time step
STABILIZATION: ASGS $ numerical stabilization method
TIME_INTEGRATION: Trapezoidal, ORDER: 1, EULER=20 $ time integration scheme
SAFETY_FACTOR: 100.0 $ multiply global time step: Alya calculates critical time step
as required by explicit solvers, which is suited for transient
analysis but makes stationary solutions converge very slowly
STEADY_STATE_TOLER: 1.0e-10 $ convergence tolerance for steady state
MAXIMUM_NUMBER_OF_IT: 1 $ max number of inner NS iterations
CONVERGENCE_TOLERANCE: 1.0e-3 $ convergence tolerance for inner NS loop (useless in this case)
ALGORITHM: SCHUR $ NS solution algorithm (uncouples p & V)
SOLVER: ORTHOMIN, CONTINUITY_PRESERVING $ default is MOMENTUM_PRESERVING
PRECONDITION: DT
END_ALGORITHM
MOMENTUM $ velocity solver
ALGEBRAIC_SOLVER
SOLVER: GMRES, KRYLOV=10 $ solver suited for asymmetric matrix
CONVERGENCE: ITERA=1000, TOLER=1.0e-12, ADAPTIVE, RATIO=0.01 $ max iter #, convergence criteria
ADAPTIVE, RATIO=0.01 means that the loop will end also if the difference of the norm of convergence value changes less than 1% in two consecutive iterations
OUTPUT: CONVERGENCE $ solver convergence file (.cso) is generated
PRECONDITIONER: DIAGONAL $ matrix preconditioner type
END_ALGEBRAIC_SOLVER
END_MOMENTUM
CONTINUITY $ pressure solver
ALGEBRAIC_SOLVER
SOLVER: DEFLATED_CG, COARSE: SPARSE $ CG solvers are suited for symmetric matrix
CONVERGENCE: ITERA=1000, TOLER=1.0e-12, ADAPTIVE, RATIO=0.01 $ max iter #, convergence criteria
ADAPTIVE, RATIO=0.01 means that the loop will end also if the difference of the norm of convergence value changes less than 1% in two consecutive iterations
OUTPUT: CONVERGENCE $ solver convergence file (.cso) is generated
PRECONDITIONER: DIAGONAL $ matrix preconditioner type
END_ALGEBRAIC_SOLVER
END_CONTINUITY
END_NUMERICAL_TREATMENT
$---------------------------------------------------------—
OUTPUT_&_POST_PROCESS
START_POSTPROCES_AT STEP = 0 $ initial step to post process
POSTPROCESS VELOCITY STEPS = 10 $ post process velocity every 10 steps (priority ker.dat)
POSTPROCESS PRESSURE STEPS = 10 $ post process pressure every 10 steps (priority ker.dat)
POSTPROCESS MEAN_PRESSURE, STEPS = 1
BOUNDARY_SET
FORCE
TORQUE, CENTER=0,0,0
MASS
MEAN_PRESSURE
END_BOUNDARY_SET
END_OUTPUT_&_POST_PROCESS
$---------------------------------------------------------—
BOUNDARY_CONDITIONS
PARAMETERS
VARIATION: NON_CONSTANT $ there will be parameters specifyed by function
INITIAL: COARSE $ domain velocity initialization
END_PARAMETERS
CODES, NODES $ Boundary Conditions
1 000 0.000000 0.000000 0.000000 $ outlet
2 111 1.000000 0.000000 0.000000, SPACE_TIME_FUNCTION=INFLOW $ inlet
3 111 0.000000 0.000000 0.000000 $ wall
4 001 0.000000 0.000000 0.000000 $ symmetry
1 & 3 111 0.000000 0.000000 0.000000 $ edges...
1 & 4 001 0.000000 0.000000 0.000000
2 & 3 111 0.000000 0.000000 0.000000
2 & 4 111 1.000000 0.000000 0.000000, SPACE_TIME_FUNCTION=INFLOW $ inlet
3 & 4 111 0.000000 0.000000 0.000000
1 & 3 & 4 111 0.000000 0.000000 0.000000 $ $ vertex...
2 & 3 & 4 111 0.000000 0.000000 0.000000
END_CODES $ inlet(note that BC’s apply to boundaries, not to boundary sets)
END_BOUNDARY_CONDITIONS
$---------------------------------------------------------—
```
* * *
## <a class="anchor" id="elbow_post_alya_dat"></a>elbow.post.alya.dat (alya2pos parameters)
```
$----------------------------------------------------------------—
DATA
FORMAT: visit $ also valid for ParaView
MARK_ELEMENTS: type $ to create automatic layers in post process according to some criterion
ELIMINATE_BOUNDARY_NODES: yes $ for parallel runs, to avoid node duplicity between subdomain
BOUNDARY: ON $ to post process boundary mesh
SUBDOMAINS, ALL $ subdomains (parallel partitions) to post process
END_SUBDOMAINS
END_DATA
$----------------------------------------------------------------—
```
* * *