エルボ配管内の流れ （熱伝導）

  • 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

  • エルボ配管内の流れを参考に

  • 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た．

  • ヒータを 5 kW で加熱し、ヒータ→パイプ、及び、パイプ→水（静止）への熱伝導をみる．

    • パイプ、及び、水の初期温度は20℃ = 293.15 Kとした．

    • 熱源としては、"Heat Source" keywordを用いて、重量密度あたりの熱源( 5.0e3 / 8.96e3 )を設定．

    • 時間としては、10 (s) 毎に 50回の書き出しを実行する． ( Total = 500 (s) )

  • ヒータが熱が他に逃げる場所がないので、無限大に温度が上がっていってしまうが、ここでは無視する．

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 ( heat.sif )を以下に示す．

heat.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)                        = 10.0
  Timestep Intervals(1)                    = 50

  Steady State Max Iterations              = 10
End

Constants
  Gravity(4)                               = 0 0 -1 9.82	!! m/s^2
End

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
  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
End


Body 1
  Name                                     = "pipe"
  Target Bodies(1)                         = $pipe
  Equation                                 = 1
  Material                                 = 1
  Initial Condition                        = 1
End


Body 2
  Name                                     = "heater"
  Target Bodies(1)                         = $heater
  Equation                                 = 1
  Material                                 = 1
  Initial Condition                        = 2
  Body Force                               = 1
End

Body 3
  Name                                     = "fluid"
  Target Bodies(1)                         = $fluid
  Equation                                 = 1
  Material                                 = 2
  Initial Condition                        = 3
End


Equation 1
  Name                                     = "ThermalConduction"
  Active Solvers(2)                        = 1 2
End


Material 1
  Name                                     = "Cupper" 
  Heat Conductivity                        = 398.0    !! W/m.K
  Heat Capacity                            = 379.0    !! J/kg.K
  Reference Temperature                    = 293.0    !! K
  Density                                  = 8.96e+3  !! kg/m3 
End

Material 2
  Name                                     = "water"
  Heat Conductivity                        = 0.602    !! W/m.K
  Heat Capacity                            = 4.182e3  !! J/kg.K
  Reference Temperature                    = 293.15   !! K
  Density                                  = 997.0    !! kg/m3 
End


Initial Condition 1
  Name                                     = "pipeInitial"
  temperature                              = 293.15
End                                      

Initial Condition 2
  Name                                     = "heaterInitial"
  temperature                              = 293.15
End                                      

Initial Condition 3
  Name                                     = "fluidInitial"
  temperature                              = 293.15
End                                      

Body Force 1
  Name                                     = "HeatSource"
  Heat Source                              = 2.0e3 / 8.96e3
End

シミュレーション結果

結果は以下の通り．

  • ヒータの熱が時間経過に伴い、パイプ内を伝導していく．

  • 水へはほぼ熱伝導しない．（銅の熱伝導率：398 [W/mk] ⇔ 水の熱伝導率：0.6 [W/mK]）

  • 水と銅の比熱差も関係あり． ( 銅の定圧比熱： 379 [J/kgK] ⇔ 水の定圧比熱：4180 [J/kgK] )

  • 実際は、水と銅は比重が10倍弱異なるので、熱容量としてはそこまで大きな差はないが．

../../../_images/heatConduction.gif