エルボ配管内の流れ （流れ）¶
シミュレーション名： flow__in_a_curved_pipe_XYZ3D
シミュレーション体系¶
Navier-Stokes方程式
エルボの内径、外径はそれぞれ 160 mm, 200 mm ( 半径はそれぞれ 80 mm, 100 mm )．
エルボは直角 ( 90 deg )に、曲率半径は 1.0 m で曲がる．
曲がり部分の両端に 1.0 m の直管部分がある．
流入側の配管外側には、外径 300mm のヒーターを取り付けている（本問題には無関係）．
メッシュ¶
メッシュ生成スクリプト ( mesh.py )
mesh.py ( flow__in_a_curved_pipe_XYZ3D )¶
import numpy as np
import os, sys
import gmsh
# ========================================================= #
# === make__geometry === #
# ========================================================= #
def make__geometry( dimtags={} ):
surfDim, voluDim = 2, 3
# ------------------------------------------------- #
# --- [1] parameter --- #
# ------------------------------------------------- #
radius_1 = 0.1
radius_2 = 0.08
radius_3 = 0.15
heater_s = 0.30
heater_e = 0.70
angle = 90.0 * np.pi/180.0
# ------------------------------------------------- #
# --- [2] design pipe1 --- #
# ------------------------------------------------- #
cylinder_1s = gmsh.model.occ.addCylinder( 0,0,0, 1.0, 0,0, radius_1 )
disk_1 = gmsh.model.occ.addDisk( 1,0,0, radius_1, radius_1 )
rotate = gmsh.model.occ.rotate( [(surfDim,disk_1)], 1,0,0, 0,1,0, angle )
revolve_1 = gmsh.model.occ.revolve( [(surfDim,disk_1)], 1,1,0, 0,0,1, angle )
cylinder_1e = gmsh.model.occ.addCylinder( 2,1,0, 0,1,0, radius_1 )
object_1 = [ (dim,tag) for dim,tag in revolve_1 if ( dim == 3 ) ]
tools_1 = [ (voluDim,cylinder_1s), (voluDim,cylinder_1e) ]
gmsh.model.occ.synchronize()
pipe1,maps = gmsh.model.occ.fuse( object_1, tools_1, removeObject=True, removeTool=True )
gmsh.model.occ.synchronize()
# ------------------------------------------------- #
# --- [3] design pipe2 --- #
# ------------------------------------------------- #
cylinder_2s = gmsh.model.occ.addCylinder( 0,0,0, 1.0, 0,0, radius_2 )
disk_2 = gmsh.model.occ.addDisk( 1,0,0, radius_2, radius_2 )
rotate = gmsh.model.occ.rotate( [(surfDim,disk_2)], 1,0,0, 0,1,0, angle )
revolve_2 = gmsh.model.occ.revolve( [(surfDim,disk_2)], 1,1,0, 0,0,1, angle )
cylinder_2e = gmsh.model.occ.addCylinder( 2,1,0, 0,1,0, radius_2 )
object_2 = [ (dim,tag) for dim,tag in revolve_2 if ( dim == 3 ) ]
tools_2 = [ (voluDim,cylinder_2s), (voluDim,cylinder_2e) ]
gmsh.model.occ.synchronize()
pipe2,maps = gmsh.model.occ.fuse( object_2, tools_2, removeObject=True, removeTool=True )
gmsh.model.occ.synchronize()
pipe1,maps = gmsh.model.occ.cut ( pipe1, pipe2, removeObject=True, removeTool=False )
gmsh.model.occ.synchronize()
# ------------------------------------------------- #
# --- [4] design heater --- #
# ------------------------------------------------- #
length = heater_e - heater_s
cylinder_3o = gmsh.model.occ.addCylinder( heater_s,0,0, length, 0,0, radius_3 )
cylinder_3i = gmsh.model.occ.addCylinder( heater_s,0,0, length, 0,0, radius_1 )
heater,maps = gmsh.model.occ.cut( [(voluDim,cylinder_3o)], [(voluDim,cylinder_3i)], \
removeObject=True, removeTool=True )
gmsh.model.occ.synchronize()
# ------------------------------------------------- #
# --- [3] register dimtags --- #
# ------------------------------------------------- #
dimtags["pipe"] = pipe1
dimtags["fluid"] = pipe2
dimtags["heater"] = heater
dimtags["inlet"] = [(2,9)]
dimtags["outlet"] = [(2,10)]
dimtags["inner_pipe"] = [(2,6),(2,7),(2,8)]
dimtags["outer_pipe"] = [(2,23),(2,24),(2,25),(2,26)]
dimtags["pipeEnd_inlet"] = [(2,27)]
dimtags["pipeEnd_outlet"] = [(2,28)]
dimtags["heater_contact"] = [(2,19)]
dimtags["heater_surface"] = [(2,20),(2,21),(2,22)]
return( dimtags )
# ========================================================= #
# === 実行部 === #
# ========================================================= #
if ( __name__=="__main__" ):
# ------------------------------------------------- #
# --- [1] initialization of the gmsh --- #
# ------------------------------------------------- #
gmsh.initialize()
gmsh.option.setNumber( "General.Terminal", 1 )
gmsh.option.setNumber( "Mesh.Algorithm" , 5 )
gmsh.option.setNumber( "Mesh.Algorithm3D", 4 )
gmsh.option.setNumber( "Mesh.SubdivisionAlgorithm", 0 )
gmsh.model.add( "model" )
# ------------------------------------------------- #
# --- [2] Modeling --- #
# ------------------------------------------------- #
sample__model = "make" # -- [ "import" / "make" ] -- #
if ( sample__model == "import" ):
dimtagsFile = None
stpFile = "msh/model.stp"
import nkGmshRoutines.import__stepFile as isf
dimtags = isf.import__stepFile( inpFile=stpFile, dimtagsFile=dimtagsFile )
elif ( sample__model == "make" ):
dimtags = {}
dimtags = make__geometry( dimtags=dimtags )
gmsh.model.occ.synchronize()
gmsh.write( "msh/model.stp" )
gmsh.model.occ.synchronize()
gmsh.model.occ.removeAllDuplicates()
gmsh.model.occ.synchronize()
# ------------------------------------------------- #
# --- [3] Mesh settings --- #
# ------------------------------------------------- #
mesh_from_config = True # from nkGMshRoutines/test/mesh.conf, phys.conf
uniform_size = 0.05
if ( mesh_from_config ):
meshFile = "dat/mesh.conf"
physFile = "dat/phys.conf"
import nkGmshRoutines.assign__meshsize as ams
meshes = ams.assign__meshsize( meshFile=meshFile, physFile=physFile, dimtags=dimtags )
else:
import nkGmshRoutines.assign__meshsize as ams
meshes = ams.assign__meshsize( uniform=uniform_size, dimtags=dimtags )
# ------------------------------------------------- #
# --- [4] post process --- #
# ------------------------------------------------- #
gmsh.model.occ.synchronize()
gmsh.model.mesh.generate(3)
gmsh.write( "msh/model.msh" )
gmsh.finalize()
phys.conf
phys.conf ( flow__in_a_curved_pipe_XYZ3D )¶
# <names> key type dimtags_keys physNum
fluid volu [fluid] 301
pipe volu [pipe] 302
heater volu [heater] 303
inlet surf [inlet] 201
outlet surf [outlet] 202
inner_pipe surf [inner_pipe] 203
outer_pipe surf [outer_pipe] 204
pipeEnd_inlet surf [pipeEnd_inlet] 205
pipeEnd_outlet surf [pipeEnd_outlet] 206
heater_surface surf [heater_surface] 207
heater_contact surf [heater_contact] 208
mesh.conf
mesh.conf ( flow__in_a_curved_pipe_XYZ3D )¶
# <names> key physNum meshType resolution1 resolution2 evaluation
fluid 301 constant 0.02 - -
pipe 302 constant 0.02 - -
heater 303 constant 0.03 - -
inlet 201 constant 0.0 - -
outlet 202 constant 0.0 - -
inner_pipe 203 constant 0.0 - -
outer_pipe 204 constant 0.0 - -
pipeEnd_inlet 205 constant 0.0 - -
pipeEnd_outlet 206 constant 0.0 - -
heater_surface 207 constant 0.0 - -
heater_contact 208 constant 0.0 - -
生成したメッシュを次に示す．
Elmer シミュレーションファイル¶
シミュレーションファイル ( ns.sif )を以下に示す．
ns.sif ( flow__in_acurved_pipe_XYZ3D )¶
include "./msh/model/mesh.names"
Header
CHECK KEYWORDS Warn
Mesh DB "." "msh/model"
Include Path ""
Results Directory "out/"
End
Simulation
Max Output Level = 3
Coordinate System = string "Cartesian"
Coordinate Mapping(3) = 1 2 3
Simulation Type = "Transient"
TimeStepping Method = BDF
BDF Order = 2
Timestep sizes(1) = 0.1
Timestep Intervals(1) = 50
Steady State Max Iterations = 1
Post File = output.vtu
End
Constants
Gravity(4) = 0 0 -1 9.82 !! m/s^2
End
Solver 1
Equation = Navier-Stokes
Linear System Solver = Iterative
Linear System Direct Method = UMFPACK
Linear System Iterative Method = BiCGStab
Linear System Convergence Tolerance = 1.0e-6
Linear System Max Iterations = 5000
Linear System Preconditioning = ILUT
Nonlinear System Convergence Tolerance = Real 1.0e-7
Nonlinear System Max Iterations = Integer 1000
Nonlinear System Relaxation Factor = Real 1.0
Nonlinear System Newton After Iterations = 15
Nonlinear System Newton After Tolerance = 1.0e-3
Steady State Convergence Tolerance = 1.0e-5
stabilize = True
Div Discretization = False
End
Body 1
Name = "fluid"
Target Bodies(1) = $fluid
Equation = 1
Material = 1
End
Equation 1
Name = "Fluid"
Active Solvers(1) = 1
Navier-Stokes = True
End
Material 1
Name = "Air"
Density = 1.2e0 !! kg/m3
Viscosity = 1.0e-3 !!
End
Boundary Condition 1
Name = "inlet"
Target Boundaries(1) = $inlet
Velocity 1 = 1.0
Velocity 2 = 0
Velocity 3 = 0
End
Boundary Condition 2
Name = "outlet"
Target Boundaries(1) = $outlet
End
Boundary Condition 3
Name = "inner_pipe"
Target Boundaries(1) = $inner_pipe
!! Velocity 1 = 0
!! Velocity 2 = 0
!! Velocity 3 = 0
End
