|
|
|
<div class="textblock">
|
|
|
|
|
|
|
|
This tutorial analyses the Venturi effect on a 2D quadrilateral structured mesh.
|
|
|
|
|
|
|
|
* [Steady state flow](case_venturi.html#Steady_state_flow) : description of the problem
|
|
|
|
* [domain Boundaries](case_venturi.html#Domain_boundaries) : boundaries of the computational domain
|
|
|
|
* [Convergence of the case](case_venturi.html#Convergence) : numerical and physical convergence of the model
|
|
|
|
* [Velocity profiles](case_venturi.html#Velocity_profiles) : post-processing of velocities in different venturi sections
|
|
|
|
* [Input files ](case_venturi.html#Input_files) : detailed description of case input files
|
|
|
|
* [venturi.dat (case global parameters)](case_venturi.html#venturi_dat)
|
|
|
|
* [venturi.dom.dat (domain input data)](case_venturi.html#venturi_dom_dat)
|
|
|
|
* [venturi.geo.dat (mesh data)](case_venturi.html#venturi_geo_dat)
|
|
|
|
* [venturi.set.dat (set data: groups for post-processing, optional)](case_venturi.html#venturi_set_dat)
|
|
|
|
* [venturi.fix.dat (boundary conditions data)](case_venturi.html#venturi_fix_dat)
|
|
|
|
* [venturi.ker.dat (kernel input data)](case_venturi.html#venturi_ker_dat)
|
|
|
|
* [venturi.nsi.dat (incompressible Navier-Stokes solver parameters)](case_venturi.html#venturi_nsi_dat)
|
|
|
|
* [venturi.post.alya.dat (alya2pos parameters)](case_venturi.html#venturi_post_alya_dat)
|
|
|
|
|
|
|
|
* * *
|
|
|
|
|
|
|
|
* * *
|
|
|
|
|
|
|
|
# <a class="anchor" id="Steady_state_flow"></a>Steady state flow
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<center>Solution of the steady state flow</center>
|
|
|
|
|
|
|
|
Simulation settings are specified to reach a steady state flow condition.
|
|
|
|
|
|
|
|
Velocity and fluid properties give a low Re number for this case.
|
|
|
|
|
|
|
|
Integration time interval is set to infinity (1e6), and so is maximum number of timesteps. Alya run can be stopped after a few timesteps because the steady state solution converges very quickly with the specified settings. Otherwise the job will do 1e6 time iterations!
|
|
|
|
|
|
|
|
For every time step, time increment is automatically calculated. Only 1 Navier-Stokes iteration is specified to be performed at every time step. The two iterative solvers used by Navier-Stokes solution of Momentum and Continuity, are allowed to do 1000 iterations each unless convergence tolerances are reached (1.0e-12 in both cases).
|
|
|
|
|
|
|
|
Venturi length is 6m, half height is 1m and inlet velocity has a parabolic profile with a maximum value in the symmetry plane of 1 m/s.
|
|
|
|
|
|
|
|
Density is set to 1 and dynamic viscosity μ equals 1e-2, so that Reynolds number is about 100\. For much higher Reynolds in turbulent regime, the solution may diverge ([as shown in the following animation](http://www.youtube.com/watch?feature=player_detailpage&v=lqJsO7gC02w)), indicating that TURBUL module has to be used with NASTIN module in order to simulate such a case.
|
|
|
|
|
|
|
|
* * *
|
|
|
|
|
|
|
|
* * *
|
|
|
|
|
|
|
|
# <a class="anchor" id="Domain_boundaries"></a>domain Boundaries
|
|
|
|
|
|
|
|
Boundary numbers are as follow, inlet is on the left, +X direction is upwards.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
* * *
|
|
|
|
|
|
|
|
* * *
|
|
|
|
|
|
|
|
# <a class="anchor" id="Convergence"></a>Convergence of the case
|
|
|
|
|
|
|
|
Next figure shows the convergence plot (alya-all-nsi app) of the simulation after 989 time steps, when convergence criteria is reached. Since the analysis looks for a steady state solution, time integration is a matter of solving strategy, with no physical sense. Alya is doing ‘transient’ all the time.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Further on, the effect of mesh refinement is analyzed looking at the convergence of two variables: the total viscous force acting on the wall and the maximum velocity at the central venturi section. The same case has been calculated with different values of the parameter DIVISION: 0, 1, 2 and 3, which produce mesh sizes of 4200, 16800, 67200 and 268800 elements respectively. The following plots show the convergence of wall viscous force and maximum velocity with mesh refinement.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
# <a class="anchor" id="Velocity_profiles"></a>Velocity profiles
|
|
|
|
|
|
|
|
The following figure shows the velocity profiles of inlet, outlet and minimum venturi section.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
To practice a little bit with this case, you may increase inlet velocity or fluid viscosity in order to increase Re number. With Reynolds two orders of magnitude higher, the flow is not stationary and the simulation diverges at t≃21s ([see venturi case animation](http://www.youtube.com/watch?feature=player_detailpage&v=lqJsO7gC02w)).
|
|
|
|
|
|
|
|
* * *
|
|
|
|
|
|
|
|
* * *
|
|
|
|
|
|
|
|
# <a class="anchor" id="Input_files"></a>Input files
|
|
|
|
|
|
|
|
* * *
|
|
|
|
|
|
|
|
## <a class="anchor" id="venturi_dat"></a>venturi.dat (case global parameters)
|
|
|
|
|
|
|
|
```
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
|
|
|
|
RUN_DATA
|
|
|
|
|
|
|
|
ALYA: venturi $ case name
|
|
|
|
RUN_TYPE: Preliminary, Frequency=1e6 \ $ initial solution, write restart file frequency
|
|
|
|
No_restart
|
|
|
|
|
|
|
|
|
|
|
|
END_RUN_DATA
|
|
|
|
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
|
|
|
|
PROBLEM_DATA
|
|
|
|
|
|
|
|
TIME_COUPLING: Global, From_critical $ Alya calculates global time step
|
|
|
|
TIME_INTERVAL= 0.0, 1.0e6 $ infinite integration time domain
|
|
|
|
NUMBER_OF_STEPS= 1.0e6 $ infinite time steps
|
|
|
|
NASTIN_MODULE: On $ nastin module (Incompressible Navier-Stokes) is used
|
|
|
|
END_NASTIN_MODULE
|
|
|
|
MAXIMUM_NUMBER_GLOBAL= 1 $ only used when coupling modules
|
|
|
|
|
|
|
|
|
|
|
|
END_PROBLEM_DATA
|
|
|
|
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
```
|
|
|
|
* * *
|
|
|
|
|
|
|
|
## <a class="anchor" id="venturi_dom_dat"></a>venturi.dom.dat (domain input data)
|
|
|
|
```
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
|
|
|
|
DIMENSIONS
|
|
|
|
|
|
|
|
NODAL_POINTS= 4361 $ number of nodes
|
|
|
|
ELEMENTS= 4200 $ number of elements
|
|
|
|
SPACE_DIMENSIONS= 2 $ 2D mesh
|
|
|
|
TYPES_OF_ELEMENTS= 12 $ 4 node quadrilateral elements
|
|
|
|
BOUNDARIES= 340 $ number of boundary edges
|
|
|
|
|
|
|
|
|
|
|
|
END_DIMENSIONS
|
|
|
|
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
|
|
|
|
STRATEGY $ integration strategy
|
|
|
|
|
|
|
|
INTEGRATION_RULE: Open $ open rule is the default
|
|
|
|
DOMAIN_INTEGRATION_POINTS: 0 $ 0 = automatic, depending on each element type
|
|
|
|
|
|
|
|
|
|
|
|
END_STRATEGY
|
|
|
|
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
|
|
|
|
GEOMETRY $ mesh definition
|
|
|
|
|
|
|
|
GROUPS= 20 $ number of groups (for deflation based solvers)
|
|
|
|
INCLUDE venturi.geo.dat $ include geometry file (nodes, elements & boundaries)
|
|
|
|
|
|
|
|
|
|
|
|
END_GEOMETRY
|
|
|
|
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
|
|
|
|
SETS $ sets definition
|
|
|
|
|
|
|
|
INCLUDE venturi.set.dat $ include set file (groups for post-processing)
|
|
|
|
|
|
|
|
|
|
|
|
END_SETS
|
|
|
|
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
|
|
|
|
BOUNDARY_CONDITIONS, EXTRAPOLATE $ edge BC’s extrapolate to nodes
|
|
|
|
|
|
|
|
INCLUDE venturi.fix.dat $ include boundary conditions file
|
|
|
|
|
|
|
|
|
|
|
|
END_BOUNDARY_CONDITIONS
|
|
|
|
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
|
|
|
|
* * *
|
|
|
|
```
|
|
|
|
## <a class="anchor" id="venturi_geo_dat"></a>venturi.geo.dat (mesh data)
|
|
|
|
```
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
|
|
|
|
NODES_PER_ELEMENT $ nodes per element list
|
|
|
|
|
|
|
|
1 4 $ element number, number of nodes 2 4 3 4 : : 4199 4 4200 4
|
|
|
|
|
|
|
|
END_NODES_PER_ELEMENT
|
|
|
|
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
|
|
|
|
ELEMENTS $ element connectivity list
|
|
|
|
|
|
|
|
1 4370 4368 4369 4371 $ element number, node number 1, node number 2, ...
|
|
|
|
2 4367 4365 4368 4370
|
|
|
|
3 4362 4360 4365 4367
|
|
|
|
:
|
|
|
|
:
|
|
|
|
4199 32 29 28 33
|
|
|
|
4200 62 30 29 32
|
|
|
|
|
|
|
|
|
|
|
|
END_ELEMENTS
|
|
|
|
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
|
|
|
|
COORDINATES
|
|
|
|
|
|
|
|
1 9.867555e-01 -6.000000e+00 $ node number, coordinate X, coordinate Y 2 9.710386e-01 -6.000000e+00 3 9.525975e-01 -6.000000e+00 : : 4370 9.867555e-01 6.000000e+00 4371 1.000000e+00 6.000000e+00
|
|
|
|
|
|
|
|
END_COORDINATES
|
|
|
|
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
|
|
|
|
BOUNDARIES, ELEMENT
|
|
|
|
|
|
|
|
1 3471 3470 30 $ boundary element #, node #s, element # boundary belongs to
|
|
|
|
2 3470 3469 60
|
|
|
|
3 3469 3468 90
|
|
|
|
:
|
|
|
|
:
|
|
|
|
339 4366 4369 31
|
|
|
|
340 4369 4371 1
|
|
|
|
|
|
|
|
|
|
|
|
END_BOUNDARIES
|
|
|
|
|
|
|
|
MATERIALS, NUMBER=0, DEFAULT=1 $ all elements have material 1
|
|
|
|
|
|
|
|
END_MATERIALS
|
|
|
|
|
|
|
|
CHARACTERISTICS
|
|
|
|
|
|
|
|
END_CHARACTERISTICS
|
|
|
|
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
```
|
|
|
|
* * *
|
|
|
|
|
|
|
|
## <a class="anchor" id="venturi_set_dat"></a>venturi.set.dat (set data: groups for post-processing, optional)
|
|
|
|
```
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
|
|
|
|
ELEMENTS $ element sets definition
|
|
|
|
|
|
|
|
1 1 $ element number, set number
|
|
|
|
|
|
|
|
2 1
|
|
|
|
|
|
|
|
3 1
|
|
|
|
|
|
|
|
:
|
|
|
|
|
|
|
|
:
|
|
|
|
|
|
|
|
:
|
|
|
|
|
|
|
|
4199 1
|
|
|
|
|
|
|
|
4200 1
|
|
|
|
|
|
|
|
|
|
|
|
END_ELEMENTS
|
|
|
|
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
|
|
|
|
BOUNDARIES $ boundary sets definition
|
|
|
|
|
|
|
|
1 1 $ boundary element number, boundary set number
|
|
|
|
|
|
|
|
2 1
|
|
|
|
|
|
|
|
3 1
|
|
|
|
|
|
|
|
:
|
|
|
|
|
|
|
|
:
|
|
|
|
|
|
|
|
:
|
|
|
|
|
|
|
|
339 4
|
|
|
|
|
|
|
|
340 4 $ 4 sets in total, 1 for each domain boundary
|
|
|
|
|
|
|
|
|
|
|
|
END_BOUNDARIES
|
|
|
|
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
|
|
|
|
NODES $ node sets definition
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
|
|
|
|
END_NODES
|
|
|
|
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
```
|
|
|
|
* * *
|
|
|
|
|
|
|
|
## <a class="anchor" id="venturi_fix_dat"></a>venturi.fix.dat (boundary conditions data)
|
|
|
|
```
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
|
|
|
|
ON_BOUNDARIES
|
|
|
|
|
|
|
|
1 1 $ boundary element number, boundary number
|
|
|
|
2 1
|
|
|
|
3 1
|
|
|
|
:
|
|
|
|
:
|
|
|
|
:
|
|
|
|
339 4
|
|
|
|
340 4
|
|
|
|
|
|
|
|
|
|
|
|
END_ON_BOUNDARIES
|
|
|
|
|
|
|
|
$----------------------------------------------------------—
|
|
|
|
```
|
|
|
|
* * *
|
|
|
|
|
|
|
|
## <a class="anchor" id="venturi_ker_dat"></a>venturi.ker.dat (kernel input data)
|
|
|
|
```
|
|
|
|
$---------------------------------------------------------—
|
|
|
|
|
|
|
|
PHYSICAL_PROBLEM
|
|
|
|
|
|
|
|
PROPERTIES $ fluid physical properties
|
|
|
|
DENSITY: CONSTANT, PARAMETERS = 1.0 $ mass density
|
|
|
|
VISCOSITY: CONSTANT, PARAMETERS = 1.0e-2 $ dynamic viscosity (μ)
|
|
|
|
END_PROPERTIES
|
|
|
|
|
|
|
|
|
|
|
|
END_PHYSICAL_PROBLEM
|
|
|
|
|
|
|
|
$---------------------------------------------------------—
|
|
|
|
|
|
|
|
NUMERICAL_TREATMENT
|
|
|
|
|
|
|
|
MESH
|
|
|
|
DIVISION=0 $ mesh subdivisions (further runs with DIVISION=1, 2, 3)
|
|
|
|
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: 100,10 $ 2D domain divided in 100 x 10 boxes
|
|
|
|
END_ELSEST
|
|
|
|
SPACE_&_TIME_FUNCTIONS
|
|
|
|
FUNCTION=INFLOW $ function definition
|
|
|
|
1-x**2 $ parabolic function for inlet velocity
|
|
|
|
END_FUNCTION
|
|
|
|
END_SPACE_&_TIME_FUNCTIONS
|
|
|
|
|
|
|
|
|
|
|
|
END_NUMERICAL_TREATMENT
|
|
|
|
|
|
|
|
$---------------------------------------------------------—
|
|
|
|
|
|
|
|
OUTPUT_&_POST_PROCESS
|
|
|
|
|
|
|
|
ON_LAST_MESH
|
|
|
|
STEPS=10 $ write post-process file every ‘STEPS’ time steps
|
|
|
|
|
|
|
|
|
|
|
|
END_OUTPUT_&_POST_PROCESS
|
|
|
|
|
|
|
|
$---------------------------------------------------------—
|
|
|
|
```
|
|
|
|
* * *
|
|
|
|
```
|
|
|
|
## <a class="anchor" id="venturi_nsi_dat"></a>venturi.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 $ 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)
|
|
|
|
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=0.001 $ max iter #, convergence criteria
|
|
|
|
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
|
|
|
|
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=0.001 $ max iter #, convergence criteria
|
|
|
|
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
|
|
|
|
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 SHUR STEPS = 10 $ post process shur every 10 steps (priority ker.dat)
|
|
|
|
BOUNDARY_SET
|
|
|
|
FORCE $ obtain pressure & velocity forces acting on boundaries
|
|
|
|
TORQUE, CENTER=0,0,0 $ obtain torque of forces acting on boundaries, related to CENTER
|
|
|
|
MASS $ obtain mass flow through boundaries
|
|
|
|
END_BOUNDARY_SET
|
|
|
|
|
|
|
|
|
|
|
|
END_OUTPUT_&_POST_PROCESS
|
|
|
|
|
|
|
|
$---------------------------------------------------------—
|
|
|
|
|
|
|
|
BOUNDARY_CONDITIONS
|
|
|
|
|
|
|
|
PARAMETERS
|
|
|
|
INITIAL: COARSE $ domain velocity initialization (helps convergence)
|
|
|
|
END_PARAMETERS
|
|
|
|
CODES, NODES $ Boundary Conditions
|
|
|
|
1 00 0.000000 0.000000 $ outlet: free condition for Ux and Uy (p~0)
|
|
|
|
2 11 0.000000 -1.000000, SPACE_TIME_FUNCTION=INFLOW $ inlet: Uy = -1*INFLOW(x) ,inlet velocity parabolic
|
|
|
|
profile
|
|
|
|
3 11 0.000000 0.000000 $ wall condition: Ux = Uy = 0
|
|
|
|
4 10 0.000000 0.000000 $ symmetry condition: Ux = 0 , Uy = free
|
|
|
|
1 & 4 10 0.000000 0.000000 $ right lower corner
|
|
|
|
1 & 3 11 0.000000 0.000000 $ right upper corner
|
|
|
|
2 & 4 11 0.000000 -1.000000 $ left lower corner
|
|
|
|
2 & 3 11 0.000000 0.000000 $ left upper corner
|
|
|
|
END_CODES $ (note that BC’s apply to boundaries, not to boundary sets)
|
|
|
|
|
|
|
|
|
|
|
|
END_BOUNDARY_CONDITIONS
|
|
|
|
|
|
|
|
$---------------------------------------------------------—
|
|
|
|
```
|
|
|
|
* * *
|
|
|
|
|
|
|
|
## <a class="anchor" id="venturi_post_alya_dat"></a>venturi.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
|
|
|
|
$ SUBDOMAINS
|
|
|
|
$ 2 $ post process only subdomain 2
|
|
|
|
$ END_SUBDOMAINS
|
|
|
|
|
|
|
|
|
|
|
|
END_DATA
|
|
|
|
|
|
|
|
$----------------------------------------------------------------—
|
|
|
|
```
|
|
|
|
* * * |
