University:
Boston University
Course:
MET CS 201 | Introduction to Programming
Academic year:

2024
Views:

81

Pages:

19
Author:

Gironetzbk3n

The Shock Tube Problem The Shock Tube problem ● ● ● ● Studied by Gary A. Sod in 1978 1D problem analytical solutions are known used to test and validate computational fluid models The Shock Tube problem ● ● ● ● Studied by Gary A. Sod in 1978 1D problem analytical solutions are known used to test and validate computational fluidmodels diaphragm y x z p = 100 kPa u = 0 m/s ρ = 1.000 kg/m3 p = 10 kPa u = 0 m/s ρ = 0.125 kg/m3 The Shock Tube problem ● ● ● ● Studied by Gary A. Sod in 1978 1D problem analytical solutions are known used to test and validate computational fluid models diaphragm rarefaction wave shock wave contact discontinuity Governing Equations Conservation of mass Conservation of momentum Conservation of energy Governing Equations Conservation of mass Conservation of momentum Conservation of energy Assume: ● inviscid flows (no viscosity) ● no heat transfer Analytical solutions diaphragm rarefaction wave shock wave contact discontinuity OpenFOAM 2D shock tube set-up y 2m x 2 0. z m 10 m 2 3 y 6 7 x 0 4 z 1 5 OpenFOAM 2D shock tube set-up y 2m x 2 0. z m 10 m 2 3 y 7 6 grid refinement x 0 4 z 1 5 OpenFOAM 2D shock tube set-up y 2m x 2 0. z m 10 m 2 3 y 6 7 x 0 4 z 1 empty walls 5 OpenFOAM 2D shock tube set-up y 2m x 2 0. z m 10 m non-uniform internal flow y x z p = 100 kPa u = 0 m/s T = 348.432 K p = 10 kPa u = 0 m/s T = 278.746 K OpenFOAM 2D shock tube set-up y 2m x 2 0. z m 10 m Δt = 10-6 s t = 10 ms sampling rate: 0.5 ms resolution cases: 20x20x1 30x30x1 50x50x1 100x100x1 300x300x1 400x400x1 OpenFOAM rhoCentralFoam solver ● Greenshields et al., 2010 ● compressible fluids ● finite volumes method ● values are provided at the centroid of the volume cell ● cells are contiguous polyhedral volumes ● volume integrals in divergence and gradient terms are converted to surface integrals via Gauss’s theorem Results: time evolution line cuts along x-axis Results: time evolution 20x20x1 line cuts along x-axis pressure temperature speed density Results: time evolution 20x20x1 line cuts along x-axis pressure temperature speed density 50x50x1 Results: time evolution 100x100x1 line cuts along x-axis pressure temperature speed density 300x300x1 Results: resolution line cuts along x-axis Results: resolution line cuts along x-axis pressure temperature speed density