Supersonic Flow Flashcards
What is an isentropic process? Give an example
A reversible adiabatic process (C/D nozzle)
Are all adiabatic processes reversible?
No! Ie) before and after a shockwave.
Although there is not heat transfer in this process, there is an entropy change as energy is used to form/consumed by the shockwave. In thermodynamics, because the entropy change has occurs, the process is irreversible.
How does Tstag, Pstag and Ptotal change after a normal shockwave?
How is stagnation temperature calculated?
Tstag remains the same.
Pstag will decrease
Ptotal drops (but static increases)
Rayleigh supersonic pilot tube equation, or adiabatic equations
When will an oblique shockwave form?
Pressure waves will form and accumulate if supersonic flow encounters a compression pressure disturbance (concave corner) and an oblique shockwave will form.
The angle between the DIRECTION of the incoming airflow and the shockwave is less than 90*.
How do air properties change after an oblique shockwave?
What two factors make the difference?
(No need to list equations)- but still know them
An oblique is a form of normal shock, so will experience similar change in air properties. Difference is the properties are broken into components, 2 orthogonal components: parallel (T) and perpendicular (n).
The surface deflection angle is ‘theta’ or the change in airspeed direction (as flows parallel). The angle between the shockwave and the surface before deflection is ‘beta’ aka shock angle.
What is assumed with the airflow parallel to the shockwave?
It does not cross a shockwave and assumes no particle slip… hence the value is same before/after the shockwave.
What does each and every line on the B-0-M diagram represent?
Black line represents a relationship between B & 0 for a given M1>1.
Red line represents the maximum 0, will be at the turning point if the black lines.
Blue line indicated where M2=1.
Go in detail further about what can be determined from the red and blue lines
Red line:
If 0>0max, then the oblique shockwave from the leading edge, if Mfs reaches Mdet then it will form a bow shock.
If 0<0max, then an oblique shock will form attached to the surface. There will also be 2 possible types of oblique shockwaves formed… discussed next.
Blue line: (critical Mach line)
If below the blue line then ‘weak shock’ where M2>1.
If above the blue line then ‘strong shock’ where M2<1.
What two times is the deflection angle (0) equal to 0?
When B=90 (then normal shock will always form).
Or when B=u= sin^-1
What is assumed with the red/blue lines at high Mach numbers?
They begin to approximate each other so it is assumed when M2=1 then 0=0max.
What is an expansion wave?
Is an isentropic process where supersonic airflow encounters a convex corner (area increasing, or a pressure decreasing location). Expansion waves form at the LE of the surface forming an expansion region with a series of expansion waves inside.
Explain what occurs if supersonic airflow encounters a small change (increase) in area
If supersonic airflow encounters a small change in area, velocity will increase and pressure decreases.
A singular Mach wave will form.
What occurs if supersonic airflow encounters a larger change (increase) in area?
What are the 2 factors that influence the size?
Draw the diagram
The deflection angle (0) is the sum of many small 0 so an infinite number of expansion waves form, creating an expansion region.
U is the angle between the shockwave and incoming airflow (where airflow is parallel to the surface), while 0 is the angle between the airflow and surface deflection.
Velocity will increase and pressure will decrease.
The size of the expansion region is determined by incoming M and deflection angle.
How are air properties affected by a greater deflection angle?
A greater deflection angle means a lower pressure and a greater velocity. In theory, when P2=0Pa, M2=infinity and 0=0max.
Is the previous card about 0=0max realistic?
No, airflow can’t not expand further beyond 0max. The end of 0max is labelled the slipstream. The area between the surface (end of deflection angle) and the slipstream is known therefore as the stagnation region. As in the slipstream P2=0 and V=infinity, while in the stagnation region P2=0 and V=0, there is a large change in speed. But in the real world, this is almost unachievable as P=0 is difficult to get as well as due to the viscosity of air, vortices will form within the stagnation region causing oscillations in the airflow.
