Normal and oblique shocks

[Dick Whittingham]

In wannabes Rowley UK has posed a question, from ATPL exam feedback. It is:

When comparing a normal and an oblique shockwave, the normal shockwave:

A) has a higher total pressure
B) has a higher total temperature
C) has a lower static pressure
D) has a lower total pressure

I've brought it over here where all the experts are. My guess is that at the same Mfs the normal shock is going to have a higher pressure and temperature rise, so the answer is both A and B.

Help.

Dick W

[RowleyUK]

Cheers Dick, your a gent!


What i could really do with knowing is which shockwave has the highest Total,Static,Dynamic Pressure/Temperature and the like.

Any help would be much appreciated.

Oh and btw, Do any of you guys know what speed the bow wave APPEARS?(Also another Feedback question}

[Dick Whittingham]

I've had time to think about this, and below I give my latest thoughts. I had hoped one of the real experts would have definitive data to answer these points, and I still hope someone will check this out for you.

Shock Waves

Shock waves are a thin surface in the airflow where there is a sudden fall in true airspeed and a sudden rise in static pressure behind the shockwave. These two effects lead to a sudden rise in air temperature and density also rises as the effect of the increased pressure overcomes the effect of increased temperature.

In an adiabatic change, as this is, total energy in the airflow remains constant, but now, post Bernoulli, some of the energy is thermal, so it is no longer true that static pressure energy plus dynamic pressure energy equals total energy. The thermal energy – the high temperature air – is lost downstream. Lost energy means drag, and this is wave drag, always present when shockwaves form.

Shockwaves can be normal to the airflow - at 90º to the flow - or oblique. Normal shockwaves bring the airspeed down to subsonic values, which is a big jump, so the pressure and temperature rises are large, as is the energy loss. The higher the freestream speed ahead of the normal shockwave, the greater the effects, so minimum energy is lost in a normal shockwave that forms in airflow just at or just above M1.0.

Oblique shockwaves at angles of less than about 70º to the flow only bring the flow down to a lower value that is still supersonic. For any given freestream speed oblique shockwaves are less intense than normal shockwaves, pressure and temperature rises are smaller and less thermal energy is lost.

Expansion waves are diffuse areas where supersonic flow is accelerated. Through an expansion wave airspeed and pressure fall, and so do density and temperature.

Ambient static pressure is constant, unless the aircraft is climbing or descending. This is not the same as static pressure in the airflow, which goes up through a shockwave and down through an expansion wave.


Q. What happens to total energy? A. Remains constant all the time.
Q. Static pressure? A. Up through a shockwave, down through an expansion wave.
Q. Air Temperature? A. Up through a shockwave, down through an expansion wave.
Q. Total head pressure? A. Down through a shockwave, up through an expansion wave. Note that total head pressure is not total energy because of the missing thermal energy.
Q. Least energy loss? A. Shockwave at just over M1.0 freestream. Has to be a normal shockwave as you can’t get oblique shockwaves at this Mach number.

This makes the answer B, as the higher temperature energy in the normal shock means a lower pressure energy if the total is to remain the same.

Any comment, experts all?

Dick W

[Keith.Williams.]

Before going further let me state that I do not consider myself to be an expert on anything! (people who consider themsleves to be experts are often just people who have stopped learning).

I agree with most of what you have said Dick, but I'm note sure that total pressure increases in an expansion wave. I think it is just another case of swapping static pressure energy for dynamic pressure (kinetic) energy, with no energy being gained.

I'm also not entirely sure that you cannot get a normal shockwave if the freestream flow is more than M1.

JAR exam questions often ask things like:

If a supersonic airflow is to be compressed by passing it through a shockwave or series of shockwaves, which will produce the least energy loss?

a. Normal
b. Slightly oblique.
c. Highly oblique.
d. Expansion wave.


My initial response to these questions was that supersonic airflows produce only oblique shockwaves so the questions are meaningless. This is probably true (of shockwaves) in most cases, but even an oblique shockwave is normal over a very narrow area at the leading edge of the object that is creating it.
If the object is very blunt then the normal part of the shockwave might be be quite wide.

I believe that these questions are really probing the students' knowledge of the relative magnitudes of the decelerations and heat losses. But even this is a bit problematic. A normal shock wave produces a greater temperature rise and hence greater energy loss, per unit area of shockwave. But oblique shockwaves tend to be more extensive so there is a greater surface area over which to lose energy.

My answer to this type of question is that a series of oblique shock waves followed by a very weak normal one is the most efficient method, but I am quite prepared to be proved wrong.

The original question in this string is also a bit ambiguous, in that it does not state whether we are to consider the total pressure of the airflow going into or coming out of the shockwave.

If we consider an object in flight (rather than an airflow through a duct) a supersonic flow going into an oblique shockwave will clearly have more total pressure than sonic airflow going into a normal one. But a Mach 5 zero degree C airflow going into a normal shock wave will come out at about 1300 degrees C at Mach 0.4, whereas a mach 2 flow going into a 60 degree oblique wave will come out at more than mach 1. The normal shockwave has clearly caused a great deal of kinetic energy to be converted into heat, so the total pressure must have been reduced by quite a bit. So which of the emerging airflows has the greatest total pressure? I suspect that it is the (originally) slower airflow coming out of the oblique wave.

[Dick Whittingham]

Keith, Thanks for your reply

My guess at the energy content in an expansion wave was based on the idea that some of the heat energy generated in the shockwave would be given back as pressure energy in the expansion wave, so dynamic plus static should go up slightly. It was only a guess.

I am absolutely sure you can have normal shocks in airflow over M1.0, if the object in the flow is blunt. In fact, turning to energy loss, a pitot intake at supersonic freestream speeds has a huge normal shock across the front of it, hence the rapid change from the P1 to the Lightning, to a pitot with a conical shock body to generate oblique shocks to recover the ram pressure in a more efficient way. The final shock, the air having decelerated a lot, was usually given as a normal shock just at the end of the conical body. Likewise the 2-dimensional wedge shock bodies on, eg, Concorde.

My throwaway line was that you couldn't have oblique shocks at M1.0, which is true exactly at M1.0, and unlikely at just above M1.0 unless you have a very small deflection angle.

I think we are agreed, if no speed is given, the lowest energy loss is at just above M1.0, and the shock is a small normal one. For deceleration from any given supersonic speed to subsonic speed, then a series of oblique shocks is better than one big normal shock.

What is truth, said jesting Pilate, and would not stay for an answer. I had hoped some ace aerodynamicist would have helped out here.

Regards, Dick

[Zeke]

Dick,

An example may help with some numbers ...

Say free stream M=1.5 with a wedge of
12 degrees = oblique shock
13 degrees = normal shock

Ratio is the relationship between the value before the shock to after the shock. p = static pressure, pt = total pressure, T =temperature, r = density

For the normal shock
Shock angle = 90 degrees
Mach = 0.701
p ratio = 2.458
pt ratio = 0.929
T ratio = 1.32
r ratio = 1.862

For the oblique shock
Shock angle = 64.371 degrees
Mach = 0.959
p ratio = 1.969
pt ratio = 0.969
T ratio = 1.224
r ratio = 1.608


Q -When comparing a normal and an oblique shockwave, the normal shockwave:

A) has a higher total pressure - no
B) has a higher total temperature - yes
C) has a lower static pressure - no
D) has a lower total pressure - no

The trick question is how in JAR does this improve delivering passengers and freight to the destination safely.

Regards

Z

[Dick Whittingham]

Thanx a million. Just what I needed!

The problem for us at Bristol is not that we have to know the answer, but that we have to know why that answer is correct, so we have gone pretty deep into this particular problem - more than anyne would need to know for the exam.

As a general problem, the JAR syllabus keeps on expanding as one nerd after another tries to add in his own bit of specialist knowledge - but don't get me going on that one.

Hope you got the answer, Rowley!

Dick W