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Next: Piston Velocity Up: Moving Shock into Stationary Previous: Moving Shock into Stationary Index General Velocities IssuesWhen a valve or membrane is suddenly opened, a shock is created and propagates downstream. With the exception of close proximity to the valve, the shock moves in a constant velocity (5.12(a)). Using a coordinates system which moves with the shock results in a stationary shock and the flow is moving to the left see Figure (5.12(b)). The ``upstream'' will be on the right (see Figure (5.12(b))).
The ``downstream'' Mach number is Note that in this case the stagnation temperature in stationary coordinates changes (as in the previous case) whereas the thermal energy (due to pressure difference) is converted into velocity. The stagnation temperature (of moving coordinates) is A similar rearrangement to the previous case results in The same question that was prominent in the previous case appears now, what will be the shock velocity for a given upstream Mach number? Again, the relationship between the two sides is Since M_{sx} can be represented by M_{sy} theoretically equation (5.63) can be solved. It is common practice to solve this equation by numerical methods. One such methods is ``successive substitutions.'' This method is applied by the following algorithm:
Subsections Next: Piston Velocity Up: Moving Shock into Stationary Previous: Moving Shock into Stationary Index Created by:Genick Bar-Meir, Ph.D. On: 2007-11-21 |