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** Shock Tube **

## Shock Tube

**Figure 1. Shock tube at initial state.**

### Flow Description

This validation case involves an unsteady flow in a shock tube. The
tube is a cylinder. A diaphragm separates the gas at two states. Fig.
1 shows the shock tube at the initial states.

**Table 1. Initial conditions. **
Region |
Pressure (psia) |
Temperature (R) |
Density |

1 |
1.0 |
416.0 |
0.125 |

4 |
10.0 |
520.0 |
1.0 |

As the diaphragm bursts a shock, slip surface, and expansion waves
form a propagate through the tube. Fig. 2 shows the state of the flow
a short time after the burst of the diaphragm.

**Figure 2. Shock tube shortly after diaphragm has burst.**

### Geometry

The shock tube is a cylinder of length 1.0 ft and a inside radius
of 0.1 ft. Fig. 1 shows the geometry.

### Computational Domain and
Boundary Conditions

The tube is closed at the ends, thus all boundaries of the
computational domain are ideally solid walls. The inside surface of
the tube is assumed a slip surface. Since the time span of the
unsteady flow is short, the waves never reach the end walls, and so,
conditions at these boundaries are held fixed.

### Comparison Data

The classical shock tube solution provides data for comparison.
The text by Anderson discusses this solution. The Fortran program stubex.f creates the data files containing the
pressure stp.dx, density
str.dx, axial velocity stu.dx, and Mach
number stm.dx along the tube at the final time,
which is at t = 2.11725E-04 seconds. The pressure and density has
been non-dimensionalized by the pressure
at state 4.

### Computational Grid

The computational grid was generated by the Fortran program stubeic.f. The number of axial and radial grid
points are input and then are evenly spaced. Fig. 3 below shows an
example planar grid.

**Figure 3. Computational grid (coarsened for display).**

### Computational Studies

** Table 2. Computational studies peformed for the
shock tube case. **
Study |
Category |
Person |
Comments |

Study #1 |
Example |
J.W. Slater |
Explicit, Runge-Kutta Operator. |

Study #2 |
Example |
J.W. Slater |
Explicit. Comparison with NPARC. |

Study #3 |
Example |
J.C. Dudek |
Implicit, Point Jacobi Operator. |

### References

1. Anderson, J.D., * Modern Compressible Flow *, McGraw Hill
Inc., New York, 1984.

Last Updated: Monday, 30-Apr-2012 14:02:04 EDT