Fluid Compression

[Ciro Pabón]

...

BTW: water is compressible, it's bulk modulus elasticity is 2.15 N/m2.

Actually, it is 2150000000 N/m2. That is, one thousand million times larger. Ehem. Talking about basics...

If water had this kind of bulk modulus (2.15 Pascals) it would be the most compressible thing in the Universe. It would diminish 50% in volume under 1 Pascal of pressure.

For example, 1 Pascals is the pressure of a peso bill (or a pound banknote) on a counter...

Air, for example, has a bulk modulus of 105000 N/m2 (at constant temperature), that is, 4 orders of magnitude smaller than water.

So, air is 20000 times more compressible than water. Water is less compressible than solid rock (around 0.7 times).

At 300 kph, which is like 0.25 Mach, air is compressed around 5%, but only in stagnation points. Around the rest of the car, the air is compressed much less.

On the other hand, the pressure of a regular turbo compressor is somewhere between 15 and 20 pounds per square inch. As atmospheric pressure is .... (wait a minute) around 14 pounds per square inch (not sure, darn american units!), you can see that a turbo is increasing density over 100%.

Now, if you compare the 5% increase in density at some points of an F1 car with the 100% increase in density of a turbo compressor, it's easy to understand why you could assume that air is incompressible when doing some calculations on the aerodynamic of a car, while you cannot discard the compressibility of air when designing a turbo.

[Raptor22]

Yes Buddy I understand that. I simply used examples of where the different assumptions are applicable. Propellors in air, axial flow compressors, this is where we deal compressibility. In freestream problems we don't bother because the effect is so small.

That's the thing though. A freestream problem can also be supersonic or close to supersonic (with airplane fuselages for example). So even though you might know that, someone else reading this might misuse your classification, leading to confusion, leading to the usual endless arguments that pollute posts. I just wanted to make it clear to everyone that it's about flow conditions (pressure, temperature, speed), not about the type of problem.

Marekk, thanks for the quick math. I think that pretty much establishes we are nowhere near sound speed, so we can assume incompressibility...

100%, we on the same page.

[ringo]

No you are allowed to neglect changes in density provided temperature is constant.

You cannot declare incompressibility. Incompressible and neglecting density is 2 different things. That is a definite assertion which is not true.

Especially with temperature and energy change in the exhaust stream being so drastic.

Density will go from 0.3kg/m3 all the way up to 1.2kg/m3 in the case of a blown floor, and this is happening over a good distance along the floor.

The density can only be neglected where energy changes are small, and it's more like a neglection than anything, it's not a confirmation that air is incompressible like water.

[volarchico]

...Density will go from 0.3kg/m3 all the way up to 1.2kg/m3 in the case of a blown floor, and this is happening over a good distance along the floor.
...

Where will the density be so low as 0.3kg/m3? Is that right at the exhaust exit? That's a similar density as what you'd find up at 39,000 ft altitude!

[ringo]

The temperature is very high. I think it took this value a little after the exit.

edit: wait a minute.


r is 287.

Now P is absolute pressure and T temperature.

Both these things vary on an F1 car and so will density.

at 850 degrees C, it's: 101325 Pa/ 287 J/kgK * (850 + 273)K = 0.314 Kg/m3

at 25 degrees it's = 1.184

Now vary the pressure along the car and it gets even more impossible to guess what is happening on the car.

Incompressible is just the wrong word to describe air at any rate.
It's like saying someone is invincible because they don't die when you punch them. The intention is somewhat understandable but it's misleading.

[Just_a_fan]

Incompressible is just the wrong word to describe air at any rate.

As has been pointed out to you already, the term is used in the context of "at the speeds being considered, air can be considered to be incompressible". This allows for a much simpler calculation whilst not adding an appreciable error in the results.

The fact that this is a reasonable method is highlighted by the development of high performance aircraft. During WW2 piston-engined fighters were topping out at around 450mph. They were designed on the assumption that air behaved as an incompressible fluid. All was well - the aircraft performed as designed.

However, in power-dives the pilots were starting to find that the aircraft weren't controllable, in the usual sense, as speeds exceeded c.600mph. This is because at those speeds, the air was starting to exhibit compressible characteristics and shockwaves were interferring with control operations.

So, at the speeds at which F1 cars operate (much less than a Spitfire), air can be taken as incompressible in calculations without loss of accuracy in the results.

However, I think you know that this is what is meant hereabouts and are just doing a bit of friendly trolling...

[segedunum]

Sorry Seg, but there is no static pressure increase. At this speed of flow (way below speed of sound) exhaust gases and air are incompressible.

I don't understand what you're postulating. Hotter gases will increase static pressure. Bernoulli is absolutely steadfast on that one. We can't just wave away a physical principle. Correct me if I'm wrong as well, but I always thought gases were compressible certainly at low mach numbers (just think about it), not incompressible? Nevertheless, Bernoulli will still apply to them.

You simply can't increase static pressure of gas/fluid by blowing another gas/fluid in it until the speed is comparable to speed of sound, at which shock waves start to form.

You're comparing the wrong things here. Static pressure of the environment will increase.

Just take a look at hot-air balloons - you can blow as much hot air into it as you will - static pressure inside this balloon remains at ambient level all the time.

You're looking at this in the wrong way. The volume of air is not important. However, if you introduce hotter air somewhere than the surrounding environment static pressure will increase. As sure as eggs is eggs. That's what we're looking at. Static pressure will increase, with a corresponding decrease in dynamic pressure, compared with not doing anything at all. That's not what we want underneath a floor.

[Just_a_fan]

Bernoulli is absolutely steadfast on that one. We can't just wave away a physical principle. Correct me if I'm wrong as well, but I always thought gases were compressible certainly at low mach numbers (just think about it), not incompressible? Nevertheless, Bernoulli will still apply to them.

Strictly speaking Bernoulli doesn't apply to compressible gases...

Bernoulli developed his theorem using incompressible fluids, not air. If you want to use Bernoulli then you need to assume that air is incompressible. And that is only valid at low speeds.

There are other ways of doing it using conservation laws etc. but they're not strictly Bernoulli.

Fun this, isn't it.

[volarchico]

The temperature is very high. I think it took this value a little after the exit.

edit: wait a minute.


r is 287.

Now P is absolute pressure and T temperature.

Both these things vary on an F1 car and so will density.

at 850 degrees C, it's: 101325 Pa/ 287 J/kgK * (850 + 273)K = 0.314 Kg/m3

at 25 degrees it's = 1.184

Now vary the pressure along the car and it gets even more impossible to guess what is happening on the car.

Incompressible is just the wrong word to describe air at any rate.
It's like saying someone is invincible because they don't die when you punch them. The intention is somewhat understandable but it's misleading.

Makes sense. I guess I was thinking about the pressure being higher due to the compression and combustion in this equation, but it makes sense that the exhaust has to return to atmospheric pressure on exit. Thanks!