Phase 1 of the Caltech ASC converging shock experiments.

The lensing of the shock by a contact is not a trivial problem. At the point where the lens and wedge meet there are three requirements outlined by P. Dimotakis and R. Samtaney

• The transmitted shock must be perpendicular to the wedge face
• The reflected wave must be cancled to minimize wave reflections from the the wedge walls
• the angle by wich the flow turns across the transmitted shock should be such that the flow is radial immediately behind the transmitted shock

The particular case identified has a lens to driver gas density ratio of 1.4, with gamma =1.4 for the lens gas and 1.5 for the driver. The incoming shock strength is M=1.3122 in the driver gas, and the wedge half-angle is 11.617degrees. For these particular conditions, the lens shape is very close to an ellipse of aspect ratio 4.448 centered at x=2.14R to the right of the apex ( where R is the lengh of the wedge plates)

The code is documented and the VTF repository holds the Phase 1 input files.

An example of the circular shock produced by Phase 1 (color density contours shown):

To illustrate the smoothness of the shock produced by the lensing procedure, the shockspeed along the centerline is calculated and comparied with an equivelent Phase 0 (no lens) case.

Notice that the Phase 0 has sharp changes in shock speed as the mach-stem reaches the centerline, these are absent in the Phase 1 simulations. Also, here is an animation of the pressure along the center-line (y=0) of the wedge produced to aid the experimental design : CenterlinePressure.avi.

Here is an example of the circular shock being produced by the gas lens in the case where the contact between the lens and driver gas has a "membrane" consisting of a thin layer of a very heavy gas.

• At a later time:
  

• In polar coordinates:
  

• shock closeup in polar: