Ityp = 3

This law enables to model a non-reflecting boundary (NRF).


law11_ityp3
Figure 1.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW11/mat_ID or /MAT/BOUND/mat_ID
mat_title
ρi ρ0            
Ityp   Psh          
Ityp = 3 - Non-Reflecting Boundary
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
    c l c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiBamaaBa aaleaacaWGJbaabeaaaaa@37FB@        
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Definitions

Field Contents SI Unit Example
mat_ID Material identifier

(Integer, maximum 10 digits)

 
mat_title Material title

(Character, maximum 100 characters)

 
ρ i Initial density 3

(Real)

[ kg m 3 ]
ρ 0 Reference density used in E.O.S (equation of state)

Default ρ 0 = ρ i (Real)

[ kg m 3 ]
Ityp Boundary condition type 1
= 0
Gas inlet (from stagnation point data)
= 1
Liquid inlet (from stagnation point data)
= 2
General inlet/outlet
= 3
Non-reflecting boundary

(Integer)

 
Psh Pressure shift 2

(Real)

[ Pa ]
c Outlet sound speed 1

(Real)

[ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
l c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiBamaaBa aaleaacaWGJbaabeaaaaa@37FB@ Characteristic length 1

(Real)

[ m 3 ]

Comments

  1. Non-Reflecting Boundary formulation is based on Bayliss & Turkel. 1 The objective is to impose a mean pressure which fluctuate with rapid variations of pressure and velocity:
    (1)
    P t = ρ c ( t ( V n ) V n d i v ( V V n n ) ) + c ( P P ) 2 l c
    Pressure in the far field P MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaBa aaleaacqGHEisPaeqaaaaa@3868@ is imposed with a function of time. The transient pressure is derived from P MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaBa aaleaacqGHEisPaeqaaaaa@3868@ , the local velocity field V and the normal of the outlet facet:
    • density, energy, temperature, turbulent energy and dissipation are imposed with a function of time as in Ityp = 2
    • if the function number is 0, the neighbor element value is used to respect continuity
    • acoustic impedance will be ρ c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyWdiNaam 4yaaaa@389E@
    • typical length l c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiBamaaBa aaleaacaWGJbaabeaaaaa@37FB@ is used to relax the effective pressure towards its imposed value. It should be large compared to the highest wave length of interest in the problem. The relaxation term acts as high pass filter whose frequency cut-off is:(2)
      f c = c 4 π l c

      Where, sound speed c and characteristic length l c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiBamaaBa aaleaacaWGJbaabeaaaaa@37FB@ are two required parameters (non zero).

  2. The Psh parameter enables shifting the output pressure which also becomes P-Psh. If using Psh=P(t=0), the output pressure will be Δ P MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeiLdiaadc faaaa@37E5@ , with an initial value of 0.0.
  3. With thermal modeling, all thermal data ( T 0 , ρ 0 C P , ...) can be defined with /HEAT/MAT.
  4. It is not possible to use this boundary material law with multi-material ALE laws 37 (/MAT/LAW37 (BIPHAS)) and 51 (/MAT/LAW51 (MULTIMAT)).
1 A. Bayliss, E. Turkel, "Outflow Boundary Condition for Fluid Dynamics", NASA-CR-170367, Institute for Computer Application in Science and Engineering, August 7, 1980