水中に沈めた鉄塊からの自然対流冷却¶
シミュレーション名 :: heatConduction__box_in_water_XYZ3D
シミュレーション体系¶
基本方程式は、 熱輸送方程式( Heat Equation ) と Navier-Stokes方程式
流体は、 非圧縮 , Boussinesq近似
熱輸送は、 熱伝導、熱対流、輻射を取り扱う．
シミュレーション対象は直方体 ( 50 [cm] x 50 [cm] x 50 [cm] )の箱のなかに、直方体の鉄塊が ( 20 [cm] x 20 [cm] x 20 [cm] ) が安置してあり、周囲を水が満たしている．
初期温度、 20 [℃] の水が鉄塊に触れて、自然対流し、鉄塊が冷却される．
流体は、すべり境界条件とする．
物性条件¶
Target |
Parameters |
Value |
Unit |
Description |
|---|---|---|---|---|
空気 |
Heat Conductivity |
0.0257 |
W/m.K |
熱伝導度 |
Heat Capacity |
1.005e+3 |
J/kg.K |
比熱 |
|
Density |
1.166e+0 |
kg/m3 |
密度 |
|
Heat Expansion Coefficient |
3.665e-3 |
1e-6 |
体積膨張率(1K毎に(0.29e-3)分の体積増加(線形近似)) |
|
Reference Temperature |
293.15 |
K |
参照温度 (体積膨張率の測定温度：Boussinesq近似) |
|
viscosity |
1.512e-5 |
Pa.s |
粘度 |
|
水 |
Heat Conductivity |
0.602 |
W/mK |
熱伝導度 |
Heat Capacity |
4.18e3 |
J/kg K |
比熱 |
|
Density |
9.97e3 |
J/kg K |
密度 |
|
Reference Temperature |
293.15 |
K |
参照温度 |
|
Heat Expansion Coefficient |
0.29e-3 |
1/K |
体積膨張率 (体積膨張率の測定温度：Boussinesq近似) |
|
viscosity |
1.18e-3 |
Pa s |
粘度 |
|
SS400 |
Heat Conductivity |
51.6 |
W/m.K |
熱伝導度 |
Heat Capacity |
473.0 |
J/kg.K |
比熱 |
|
Density |
7.85e+3 |
kg/m3 |
密度 |
|
定数 |
gravity |
0,0,-1,9.8 |
m/s2 |
重力加速度 |
Stefan Boltzmann |
5.68e-8 |
W/m2K4 |
Stefan-Boltzmann係数 |
メッシュ¶
メッシュ生成スクリプト ( mesh.py )
mesh.py ( heatConduction__box_in_water_XYZ3D )¶
import numpy as np
import os, sys
import gmsh
import nkGmshRoutines.geometrize__fromTable as gft
import nkGmshRoutines.load__dimtags as ldt
# ========================================================= #
# === 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 --- #
# ------------------------------------------------- #
dimtags = {}
inpFile = "dat/geometry.conf"
dimtagFile = "dat/boundary.json"
dimtags = gft.geometrize__fromTable( inpFile=inpFile )
dimtags = ldt.load__dimtags( inpFile=dimtagFile, dimtags=dimtags )
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 = 0.050
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()
geometry.conf
geometry.conf ( heatConduction__box_in_water_XYZ3D )¶
# <define> @cbox.thick = 5e-3
# <define> @cbox.wx = 500e-3
# <define> @cbox.wy = 500e-3
# <define> @cbox.wz = 500e-3
# <define> @cbox.xMin = ( -0.5 ) * @cbox.wx
# <define> @cbox.yMin = ( -0.5 ) * @cbox.wy
# <define> @cbox.zMin = 0.0
# <define> @water.wx = @cbox.wx - 2.0*( @cbox.thick )
# <define> @water.wy = @cbox.wx - 2.0*( @cbox.thick )
# <define> @water.wz = @cbox.wx - ( @cbox.thick )
# <define> @water.xMin = ( -0.5 ) * @water.wx
# <define> @water.yMin = ( -0.5 ) * @water.wy
# <define> @water.zMin = @cbox.thick
# <define> @metal.wx = 200e-3
# <define> @metal.wy = 200e-3
# <define> @metal.wz = 200e-3
# <define> @metal.xMin = ( -0.5 ) * @metal.wx
# <define> @metal.yMin = ( -0.5 ) * @metal.wy
# <define> @metal.zMin = @cbox.thick
# <names> key geometry_type centering xc yc zc wx wy wz
metal cube False @metal.xMin @metal.yMin @metal.zMin @metal.wx @metal.wy @metal.wz
water.00 cube False @water.xMin @water.yMin @water.zMin @water.wx @water.wy @water.wz
cbox cube False @cbox.xMin @cbox.yMin @cbox.zMin @cbox.wx @cbox.wy @cbox.wz
# <names> key boolean_type targetKeys toolKeys removeObject removeTool
container cut [cbox] [water.00] True False
water cut [water.00] [metal] True False
boundary.json
boundary.json ( heatConduction__box_in_water_XYZ3D )¶
{
"container.bdr": [ [2,7],[2,8],[2,9],[2,10],[2,19],[2,20] ],
"metal.bdr" : [ [2,1],[2,2],[2,3],[2,4],[2,6] ]
}
phys.conf
phys.conf ( heatConduction__box_in_water_XYZ3D )¶
# <names> key type dimtags_keys physNum
metal volu [metal] 301
water volu [water] 302
container volu [container] 303
metal.bdr surf [metal.bdr] 201
container.bdr surf [container.bdr] 202
mesh.conf
mesh.conf ( heatConduction__box_in_water_XYZ3D )¶
# <names> key physNum meshType resolution1 resolution2 evaluation
metal 301 constant 0.040 - -
water 302 constant 0.040 - -
container 303 constant 0.040 - -
metal.bdr 201 constant 0.0 - -
container.bdr 202 constant 0.0 - -
生成したメッシュを次に示す．
Boussinesq近似の確認¶
シミュレーション設定¶
流体境界を (i) 鉄塊境界, (ii) 容器境界 の２つに分ける．
鉄塊境界に温度のDirichlet境界条件 T= 600 [K] = 330 [℃] を課す．
流体としては、 "Normal-Tangential velocity = True" を指定し、滑り壁条件 (
) を課した．Boussinesq近似の挙動を確認する．
boussinesq.sif ( heatConduction__box_in_water_XYZ3D )¶
!! =============================================================== !!
!! === boussinesq.sif ( heatConduction__box_in_water_XYZ3D ) === !!
!! =============================================================== !!
!! -- Boussinesq Approx. Confirmation -- !!
!!
!! * target fluid is "Air"
!! * heat Eqs. in metals is not solved.
!!
!! ------------------------------------- !!
!! ------------------------------------------------- !!
!! --- [1] basics --- !!
!! ------------------------------------------------- !!
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) = 10e-2
Timestep Intervals(1) = 50
Steady State Max Iterations = 5
End
Constants
Stefan Boltzmann = 5.6703e-8 !! -- [ W / m^2 K^4 ] -- !!
gravity(4) = 0 0 -1 9.82 !! -- [ m/s^2 ] -- !!
End
!! ------------------------------------------------- !!
!! --- [2] solvers / Equations --- !!
!! ------------------------------------------------- !!
Solver 1
Equation = "HeatEquations"
Procedure = "HeatSolve" "HeatSolver"
Variable = "Temperature"
Exec Solver = "Always"
Stabilize = True
Bubbles = False
Optimize Bandwidth = True
Steady State Convergence Tolerance = 1.0e-5
Nonlinear System Convergence Tolerance = 1.0e-3
Nonlinear System Max Iterations = 1
Nonlinear System Newton After Iterations = 3
Nonlinear System Newton After Tolerance = 1.0e-3
Nonlinear System Relaxation Factor = 1
Linear System Solver = Iterative
Linear System Iterative Method = BiCGStab
Linear System Max Iterations = 500
Linear System Convergence Tolerance = 1.0e-10
BiCGstabl polynomial degree = 2
Linear System Preconditioning = ILU0
Linear System ILUT Tolerance = 1.0e-3
Linear System Abort Not Converged = False
Linear System Residual Output = 20
Linear System Precondition Recompute = 1
End
Solver 2
Equation = "Navier-Stokes"
Procedure = "FlowSolve" "FlowSolver"
Variable = Flow Solution[velocity:3,pressure:1]
Stabilize = True
Bubbles = True
Optimize Bandwidth = True
Linear System Solver = Iterative
Linear System Scaling = Logical False
Linear System Direct Method = UMFPACK
Linear System Iterative Method = BiCGStab
Linear System Convergence Tolerance = 1.0e-6
Linear System Max Iterations = 3000
Linear System Preconditioning = ILUT
Nonlinear System Convergence Tolerance = Real 1.0e-5
Nonlinear System Max Iterations = Integer 300
Nonlinear System Relaxation Factor = Real 0.7
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 = True
End
Solver 3
Exec Solver = after saving
Equation = "Result output"
Procedure = "ResultOutputSolve" "ResultOutputSolver"
Output File Name = "heat"
Vtu Format = Logical True
Binary Output = Logical True
Scalar Field 1 = String Temperature
Scalar Field 2 = String pressure
Vector Field 1 = String velocity
End
Equation 1
Name = "water"
Active Solvers(3) = 3 2 1
Convection = Computed
End
!! ------------------------------------------------- !!
!! --- [3] Bodies & Materials --- !!
!! ------------------------------------------------- !!
Body 1
Name = "water"
Target Bodies(1) = $water
Equation = 1
Material = 1
Initial Condition = 1
Body Force = 1
End
Material 1
Name = "Air"
Heat Conductivity = 0.0257 !! W/m.K
Heat Capacity = 1.005e+3 !! J/kg.K
Reference Temperature = 293.15 !! K
Density = 1.166e+0 !! kg/m3
Heat Expansion Coefficient = 3.665e-3 !! 1e-6
viscosity = 1.512e-5 !! Pa.s
End
!! ------------------------------------------------- !!
!! --- [5] initial & boundary Condition --- !!
!! ------------------------------------------------- !!
Initial Condition 1
Name = "water.initial"
Temperature = 293.15 !! = 20 degree
End
Boundary Condition 1
Name = "metal.bdr"
Target Boundaries(1) = $metal.bdr
Normal-Tangential Velocity = True
velocity 1 = 0.0
Temperature = 600.0
End
Boundary Condition 2
Name = "container.bdr"
Target Boundaries(1) = $container.bdr
Normal-Tangential Velocity = True
velocity 1 = 0.0
End
!! ------------------------------------------------- !!
!! --- [6] others --- !!
!! ------------------------------------------------- !!
Body Force 1
Name = "BoussinesqApprox"
Boussinesq = Logical True
End
水中の鉄塊における自然対流冷却¶
シミュレーション設定¶
Dirichlet条件の場合、空気の動きは見えても、鉄塊内部の冷却の様子はわからない．
解析対象を鉄塊部分の熱伝導も含めて解く．
空気→水へ変更する．
heat.sif ( heatConduction__box_in_water_XYZ3D )¶
!! ========================================================= !!
!! === heat.sif ( heatConduction__box_in_water_XYZ3D ) === !!
!! ========================================================= !!
!! -- Boussinesq Approx. Confirmation -- !!
!! * target fluid is "Air"
!! * heat Eqs. in metals is not solved.
!! ------------------------------------------------- !!
!! --- [1] basics --- !!
!! ------------------------------------------------- !!
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) = 10e-2
Timestep Intervals(1) = 30
Steady State Max Iterations = 5
End
Constants
Stefan Boltzmann = 5.6703e-8 !! -- [ W / m^2 K^4 ] -- !!
gravity(4) = 0 0 -1 9.82 !! -- [ m/s^2 ] -- !!
End
!! ------------------------------------------------- !!
!! --- [2] solvers / Equations --- !!
!! ------------------------------------------------- !!
Solver 1
Equation = "HeatEquations"
Procedure = "HeatSolve" "HeatSolver"
Variable = "Temperature"
Exec Solver = "Always"
Stabilize = True
Bubbles = False
Optimize Bandwidth = True
Steady State Convergence Tolerance = 1.0e-5
Nonlinear System Convergence Tolerance = 1.0e-3
Nonlinear System Max Iterations = 1
Nonlinear System Newton After Iterations = 3
Nonlinear System Newton After Tolerance = 1.0e-3
Nonlinear System Relaxation Factor = 1
Linear System Solver = Iterative
Linear System Iterative Method = BiCGStab
Linear System Max Iterations = 500
Linear System Convergence Tolerance = 1.0e-10
BiCGstabl polynomial degree = 2
Linear System Preconditioning = ILU0
Linear System ILUT Tolerance = 1.0e-3
Linear System Abort Not Converged = False
Linear System Residual Output = 20
Linear System Precondition Recompute = 1
End
Solver 2
Equation = "Navier-Stokes"
Procedure = "FlowSolve" "FlowSolver"
Variable = Flow Solution[velocity:3,pressure:1]
Linear System Solver = Iterative
Linear System Scaling = Logical False
Linear System Direct Method = UMFPACK
Linear System Iterative Method = BiCGStab
Linear System Convergence Tolerance = 1.0e-6
Linear System Max Iterations = 3000
Linear System Preconditioning = ILUT
Nonlinear System Convergence Tolerance = Real 1.0e-7
Nonlinear System Max Iterations = Integer 500
Nonlinear System Relaxation Factor = Real 0.7
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
Solver 3
Exec Solver = after saving
Equation = "Result output"
Procedure = "ResultOutputSolve" "ResultOutputSolver"
Output File Name = "heat"
Vtu Format = Logical True
Binary Output = Logical True
Scalar Field 1 = String Temperature
Scalar Field 2 = String pressure
Vector Field 1 = String velocity
End
!! Equation 1
!! Name = "Metals"
!! Active Solvers(2) = 3 1
!! !! Convection = Computed
!! End
Equation 1
Name = "water"
Active Solvers(3) = 3 2 1
Convection = Computed
End
!! ------------------------------------------------- !!
!! --- [3] Bodies & Materials --- !!
!! ------------------------------------------------- !!
!! Body 1
!! Name = "metal"
!! Target Bodies(1) = $metal
!! Equation = 1
!! Material = 1
!! Initial Condition = 1
!! End
Body 1
Name = "water"
Target Bodies(1) = $water
Equation = 1
Material = 1
Initial Condition = 1
Body Force = 1
End
!! Body 3
!! Name = "container"
!! Target Bodies(1) = $container
!! Equation = 1
!! Material = 1
!! Initial Condition = 3
!! End
!! Material 1
!! Name = "SS400"
!! Heat Conductivity = 51.6 !! W/m.K
!! Heat Capacity = 473.0 !! J/kg.K
!! Reference Temperature = 293.15 !! K
!! Density = 7.85e+3 !! kg/m3
!! End
!! Material 2
!! Name = "H2O"
!! Heat Conductivity = 0.602 !! W/m.K
!! Heat Capacity = 4.18e3 !! J/kg.K
!! Reference Temperature = 293.15 !! K
!! Density = 9.97e+3 !! kg/m3
!! Heat Expansion Coefficient = 0.29e-3 !! 1e-6
!! viscosity = 1.18e-3 !! Pa.s
!! End
Material 1
Name = "Air"
Heat Conductivity = 0.0257 !! W/m.K
Heat Capacity = 1.005e+3 !! J/kg.K
Reference Temperature = 293.15 !! K
Density = 1.166e+0 !! kg/m3
Heat Expansion Coefficient = 3.665e-3 !! 1e-6
viscosity = 1.512e-5 !! Pa.s
End
!! ------------------------------------------------- !!
!! --- [5] initial & boundary Condition --- !!
!! ------------------------------------------------- !!
!! Initial Condition 1
!! Name = "SS400.initial"
!! temperature = 673.15 !! = 400 degree
!! End
Initial Condition 1
Name = "water.initial"
Temperature = 293.15 !! = 20 degree
End
!! Initial Condition 3
!! Name = "water.initial"
!! Temperature = 293.15 !! = 20 degree
!! End
Boundary Condition 1
Name = "metal.bdr"
Target Boundaries(1) = $metal.bdr
Normal-Tangential Velocity = True
velocity 1 = 0.0
Temperature = 600.0
End
Boundary Condition 2
Name = "container.bdr"
Target Boundaries(1) = $container.bdr
Normal-Tangential Velocity = True
velocity 1 = 0.0
End
!! ------------------------------------------------- !!
!! --- [6] others --- !!
!! ------------------------------------------------- !!
Body Force 1
Name = "BoussinesqApprox"
Boussinesq = Logical True
End
シミュレーション結果¶
結果は以下の通り．
