/ALE/GRID/FLOW-TRACKING

Block Format Keyword Mean velocity within ALE mesh is used to determine automatically mesh displacement, mesh deformation, and also mesh rotation. The general idea is to have an ALE mesh acting as a tracking window.

Figure 1.


Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/ALE/GRID/FLOW-TRACKING
I_def scale_def
I_rot scale_rot

Definition

Field Contents SI Unit Example
I_def Enable deformation flag.
= -1
Disabled
= 1 (Default)
Enabled
scale_def Deformation scale factor.

Default = 1.0 (Real)

I_rot Enable rotation flag.
= -1
Disabled
= 1 (Default)
Enabled
scale_rot Rotation scale factor.

Default = 1.0 (Real)

Comments

  1. The grid velocity is calculated based on the mass-weighted average velocity of the material within the ALE mesh. A common application is modeling ALE impactors, such as ALE birdstrikes.
  2. For all nodes i, the mesh velocity i, is set as:
    w i = u a v g + D a v g X i C + Ω a v g × X i C MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4DamaaBa aaleaacaWGPbaabeaakiabg2da9iaadwhadaWgaaWcbaGaamyyaiaa dAhacaWGNbaabeaakiabgUcaRmaadmaabaGaamiraaGaay5waiaaw2 faamaaBaaaleaacaWGHbGaamODaiaadEgaaeqaaOWaaeWaaeaacaWG ybWaaSbaaSqaaiaadMgaaeqaaOGaeyOeI0Iaam4qaaGaayjkaiaawM caaiabgUcaRiabfM6axnaaBaaaleaacaWGHbGaamODaiaadEgaaeqa aOGaey41aq7aaeWaaeaacaWGybWaaSbaaSqaaiaadMgaaeqaaOGaey OeI0Iaam4qaaGaayjkaiaawMcaaaaa@55C3@
    Where,
    u a v g MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaBa aaleaacaWGHbGaamODaiaadEgaaeqaaaaa@39EB@
    Mass averaged velocity
    X i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwamaaBa aaleaacaWGPbaabeaaaaa@37EF@
    Node coordinates
    C MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qaaaa@36C0@
    Center of mass
    D a v g = 1 2 L a v g + L t a v g MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaaca WGebaacaGLBbGaayzxaaWaaSbaaSqaaiaadggacaWG2bGaam4zaaqa baGccqGH9aqpdaWcaaqaaiaaigdaaeaacaaIYaaaamaabmaabaWaam WaaeaacaWGmbaacaGLBbGaayzxaaWaaSbaaSqaaiaadggacaWG2bGa am4zaaqabaGccqGHRaWkdaahbaWcbeqaaiaadshaaaGcdaWadaqaai aadYeaaiaawUfacaGLDbaadaWgaaWcbaGaamyyaiaadAhacaWGNbaa beaaaOGaayjkaiaawMcaaaaa@4D6B@
    Average strain rate tensor
    Ω a v g = 1 2 L a v g L t a v g MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuyQdC1aaS baaSqaaiaadggacaWG2bGaam4zaaqabaGccqGH9aqpdaWcaaqaaiaa igdaaeaacaaIYaaaamaabmaabaWaamWaaeaacaWGmbaacaGLBbGaay zxaaWaaSbaaSqaaiaadggacaWG2bGaam4zaaqabaGccqGHsisldaah baWcbeqaaiaadshaaaGcdaWadaqaaiaadYeaaiaawUfacaGLDbaada WgaaWcbaGaamyyaiaadAhacaWGNbaabeaaaOGaayjkaiaawMcaaaaa @4C49@
    Average spin tensor
    L a v g = m i L i m i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaaca WGmbaacaGLBbGaayzxaaWaaSbaaSqaaiaadggacaWG2bGaam4zaaqa baGccqGH9aqpdaWcaaqaamaaqaeabaGaamyBamaaBaaaleaacaWGPb aabeaaaeqabeqdcqGHris5aOWaamWaaeaacaWGmbaacaGLBbGaayzx aaWaaSbaaSqaaiaadMgaaeqaaaGcbaWaaabqaeaacaWGTbWaaSbaaS qaaiaadMgaaeqaaaqabeqaniabggHiLdaaaaaa@48EF@
    Average gradient of velocity
    L = u = x u x x u y x u z y u x y u x y u x z u x z u x z u x MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaaca WGmbaacaGLBbGaayzxaaGaeyypa0Jaey4bIeTaamyDaiabg2da9maa dmaabaqbaeqabmWaaaqaaiabgkGi2oaaBaaaleaacaWG4baabeaaki aadwhadaWgaaWcbaGaamiEaaqabaaakeaacqGHciITdaWgaaWcbaGa amiEaaqabaGccaWG1bWaaSbaaSqaaiaadMhaaeqaaaGcbaGaeyOaIy 7aaSbaaSqaaiaadIhaaeqaaOGaamyDamaaBaaaleaacaWG6baabeaa aOqaaiabgkGi2oaaBaaaleaacaWG5baabeaakiaadwhadaWgaaWcba GaamiEaaqabaaakeaacqGHciITdaWgaaWcbaGaamyEaaqabaGccaWG 1bWaaSbaaSqaaiaadIhaaeqaaaGcbaGaeyOaIy7aaSbaaSqaaiaadM haaeqaaOGaamyDamaaBaaaleaacaWG4baabeaaaOqaaiabgkGi2oaa BaaaleaacaWG6baabeaakiaadwhadaWgaaWcbaGaamiEaaqabaaake aacqGHciITdaWgaaWcbaGaamOEaaqabaGccaWG1bWaaSbaaSqaaiaa dIhaaeqaaaGcbaGaeyOaIy7aaSbaaSqaaiaadQhaaeqaaOGaamyDam aaBaaaleaacaWG4baabeaaaaaakiaawUfacaGLDbaaaaa@6A52@
    Gradient of velocity
  3. It is possible to disable mesh deformation and/or mesh rotation. It can also be amplified or reduced using scale factors scale_def and scale_rot.
    Figure 2.


  4. It is recommended to define Non-Reflecting Frontier on ALE mesh boundaries (/EBCS/NRF).
    Figure 3.


  5. A specific treatment is introduced to amplify mesh deformation to track material that tends to escape the ALE boundaries. Without this treatment, average quantities may not adequately track the main flow when there are large velocity gradient differences.
    Figure 4.