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Shock Tube with rhoCentralFoam, sonicFoam, Lax-Friedrichs and MacCormacks

Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

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Page 1: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

Shock Tube with rhoCentralFoam,sonicFoam, Lax-Friedrichs and

MacCormacks

Page 2: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

Hypothesis• Compressible flow

• Viscous flow

• Bi-dimensional flow 𝜕

𝜕𝑧= 0

• Laminar

Page 3: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

Temperature

P = ρRTR = 286.9 J/Kg.K.

P1 = 100,000 N/m2

ρ1 = 1 kg/m3

P2 = 10,000 N/m2

ρ2 = 0.125 kg/m3

Hence,

T1 = 348.432 K T2 = 278.746 K

Respectively,

μ1= 2.099e-05 μ1 = 1.764e-05

μavg = 1.932e-05

Page 4: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

Mesh

Geometry size is 10*5*2

[-5 -2.5 -1] to [5 2.5 1]

Page 5: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

rhoCentralFoam

𝑟ℎ𝑜𝐶𝑒𝑛𝑡𝑟𝑎𝑙𝐹𝑜𝑎𝑚

0 ቐ𝑝𝑇𝑈

𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 ቐ𝑝𝑜𝑙𝑦𝑀𝑒𝑠ℎሼ𝑏𝑙𝑜𝑐𝑘𝑀𝑒𝑠ℎ𝐷𝑖𝑐𝑡𝑡ℎ𝑒𝑟𝑚𝑜𝑝ℎ𝑦𝑠𝑖𝑐𝑎𝑙𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑖𝑒𝑠𝑡𝑢𝑟𝑏𝑢𝑙𝑒𝑛𝑐𝑒𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑖𝑒𝑠

𝑠𝑦𝑠𝑡𝑒𝑚

𝑐𝑜𝑛𝑡𝑟𝑜𝑙𝐷𝑖𝑐𝑡𝑓𝑣𝑆𝑐ℎ𝑒𝑚𝑒𝑠𝑓𝑣𝑆𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠𝑎𝑚𝑝𝑙𝑒𝐷𝑖𝑐𝑡𝑠𝑒𝑡𝐹𝑖𝑒𝑙𝑑𝑠𝐷𝑖𝑐𝑡

Page 6: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

rhoCentralFoam vs Lax Friedrichs

Page 7: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

rhoCentralFoam vs Lax Friedrichs

Page 8: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

rhoCentralFoam vs Lax Friedrichs

Page 9: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

rhoCentralFoam vs MacCormack

Page 10: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

rhoCentralFoam vs MacCormack

Page 11: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

rhoCentralFoam vs MacCormack

Page 12: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

rhoCentralFoam

Page 13: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

rhoCentralFoam

Page 14: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

rhoCentralFoam

Page 15: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

rhoCentralFoam

Page 16: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

rhoCentralFoam

Page 17: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

rhoCentralFoam vs sonicFoam

Page 18: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

rhoCentralFoam vs sonicFoam

Page 19: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

rhoCentralFoam vs sonicFoam

Page 20: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

Conclusions• rhoCentralFoam works well and in coherence with MacCormack solution

• Minor changes in physical properties by introducing viscosity

• rhoCentralFoam is more accurate than sonicFoam

• rhoCentralFoam is faster solver than sonicFoam

Page 21: Shock Tube with rhoCentralFoam sonicFoam, Lax-Friedrichs and … · 2016-12-22 · Temperature P = ρRT R = 286.9 J/Kg.K. P 1 = 100,000 N/m2 ρ 1 = 1 kg/m 3 P 2 = 10,000 N/m2 ρ 2

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