Lecture 10 Flashcards
What does theta* represent?
Local flow angle with which M=1 is reached
Explain how the epicycloid diagram works
So with this diagram, you are always dealing with critical Mach numbers
1. You calculate M* from given M (equations will be given)
2. You follow the black line until reaching the vertical line in our angle
3. Then, you move following a blue line until the vertical line of your turning angle
4. Following a black line, you go back again until the critical-Mach edge –> Obtaining the critical Mach number after the expansion.
5. With the given equations, you convert it again to the “normal” Mach number (no critical)
Now you can draw the expansion fan. You need to calculate the Mach angles: sin(alpha) = 1/M
What’s the Prandtl’s shock relation?
Page 16
What happens with the tangential component of the velocity (Mach) in a supersonic flow before and after a shock?
It is unchanged
Draw the sketches of the components of the Mach numbers before and after the shock, in the case of supersonic and subsonic flows
What’s the consequence, in each case, regarding the value of the critical Mach number after the shock?
Sketches are in page 17
The consequences are that
Supersonic flow: Critical Mach number post-shock –> >1
Subsonic flow: Critical Mach number post-shock –> <1
For a Normal Shock, what’s the result of the multiplication of the critical Mach number before and after the shock?
How is it for oblique shock and what’s the name?
Normal shock: 1
Oblique shocks: The name is Prandtl’s shock relation. The equation is in slide 16
In the Busemann‘s shock polar, which solution is the more probable to happen?
The supersonic one. It impplies less losses and that what nature wants.
Explain how we can use the Busemann‘s shock polar
- We calculate M* before the shock, and highlight the polar correspondent to that M*
- We draw the line correspondent to the deflection angle theta (line from the origin and that has theta to the x axis)
- Wher it intersects to that polar, we join the 2 points –> This last point is the M* after the shock.
- 90° line from the (0,0) to the last line we draw –> That’s the shock angle
What’s the difference between Busemann‘s shock polar and the epicycloid diagram
Busemann‘s shock polar: For calculating the critical Mach number and shock angle after a shock (when turning flows)
Epicycloid diagram: For calculating the critical Mach number after the expansion fan (when turning flows)
It goes without saying, but when we calculate M*, we can compute easily M; therefore we have the velocity and therefore we can compute things with the pressure.
How are normal shocks related to oblique shocks?
If the tangent component of the oblique shock is 0, then it is a normal shock
So normal shock and oblique shocks, they are related to the tangent component. If it is different of 0 or not
Can normal shocks lead to post-shock Mach numbers > 1?
No
Can oblique shocks lead to M=1 after the shock?
Yes
They can lead to supersonic, sonic and subsonic conditions
Is it important to use the red or the blue curve in the epicycloid diagram?
No
It is exactly the same, only considering deflection upwards or downwards
How does the shock angle relate to the Mach angle for very weak shocks?
For very weak shocks, Mach number after the shock will be nearly Mach number before the shock.
In oblique shocks, this will lead to Mach numbers being nearly the same. If the intensity of the shock goes to 0, then Mach angle and shock angle will be identical.
To which direction do we have to sketch nonlinear waves?
Always to the local flow velocity
It is basically considering the flow and then how the after-shock flow would be, but in regard of the flow before the shock.
We have no longer any reference states
