I know that-- Temperature,Pressure,Density increases. Total temp, total enthalpy remains constant. Total Pressure increases. But why it happens?
1. Why total temp remains same but static temp increases?
2. If total temp remains same, then why total Pressure get increased?
3. Static temperature increases but total temperature remains same because the kinetic energy part of total temp transform into thermal energy and due to that static temperature increases but total temp remains same. For pressure, static pressure increases but total pressure decreases. If we explain that the kinetic energy part of total pressure transform into pressure energy, so that increasing the static pressure. As we have seen in the case of temperature. Then the total pressure should remain same. Why it is decreasing?
4. I have learned that we do not apply or extract work from flow across shock wave. Then how the static pressure & temperature increases though the process is adiabatic? Shock wave is not doing any work on the flow, then why we say that across shock wave flow gets compressed?
5. As soon as the flow approaches the shock wave, what exactly happens inside the flow? Pressure gets increased or temperature gets increased first?
Sorry for this long question list in one page.
hi Subhankar,
it would take a very long post to answer to your questions clearly and carefully.
But i can help you in the approach of getting answers to these problems in the physics of shock waves. By the nature of your questions i can understand that you want to know the unsteady aspects of the shock waves.
rather than trying to answer for a stationary shock try looking at the moving shock waves.
you have to understand why and how moving shock waves are generated and how do they affect the matter behind it. And you also need to understand about weak waves and strong waves.
Try looking at "The Piston Problem" in unsteady gas dynamics.
have a look at these references to help in your understanding,
Physics of shock waves by Zeldovich and Raizer
The dynamics and thermodynamics of compressible flows by A.H.Shapiro (volume 1)
(try understanding the formation of shock waves)
if you are asking for the flow through a normal (steady, adiabatic, inviscid) shock wave I suggest to see the books of Zucrow.
Furthermore, you can find useful to study the viscous structure of the shock wave and discover similarity with the Fanno flow.
Dear Subhankar,
all your answer are in chapter 4 of compressible fluid flow for Dr M. Saad
and part 1,2 The Dynamics and Thermodynamics of Compressible Fluid Flow
Ascher H. Shapiro because understanding Prandtl and Rankine -Hugonoiot relations will be more affected when you studing the NSW
BUT first you need to chose your case becasue you need to knew you type of flow ( fanno . CD nozzel , diffuser, shock tube . supersonic wind tunnels ... ) and the shock if it is moving or not.
You have one wrong assumption: The total pressure does not increase; it decreases because the shock causes an irreversible alteration of the flow state. There is a loss in usable energy (exergy). The shock is a consequence of information running upstream against the flow, but of course that can not happen easily if the flow is supersonic. Think of a body fixed in a flow, with a loudspeaker mounted on the body sending sound against the flow direction. If the oncoming flow is subsonic there is no problem, the information travels just upstream and an observer far upstream will hear the sound. If the flow is supersonic, the information ends exactly at the (normal) shock position because only in the region downstream the shock the sound can travel upstream to it. All sound waves are stopped at this point and superpose forming the shock. In fact, the sound waves are always there due to the existence of the body ("pressure information"), and the loudspeaker is not needed. The flow must come to a halt on the front side of the body, with increasing static pressure. Eventually there is a sharp border between the supersonic flow and the slow, subsonic flow right in front of the body: the shock.
The total temperature, a measure of the total energy (=exergy+anergy) is constant because no energy is taken out, and since the flow looses kinetic energy, the static temperature must go up. The mass flow (density times velocity in a 1-d situation) is also constant, that means that the density must also go up; then the equation of state for the gas, relating T, rho and p, gives the p. If the flow comes to a halt, the recovered pressure is not the one before the shock but smaller, depending on the shock strength. The stronger the shock (or, the higher the Mach number of the oncoming flow) the higher the total pressure loss is. With it the entropy increases, a direct measure for the degree of irreversibility. Hence a shock throttles the flow and reduces its ability to provide "work". (At equal formal energy, i.e. equal total temperature, a higher total pressure is always favorable because it increases the easily usable energy of the system, and it has less entropy.)
lets look to your question from another side . what is causing a shock wave to be appears in your system ? and is it in the same direction of the flow or against?
ANSWER: As the free energy equation of GIBBS .The work that should be done in the system as the flow cross the line of sonic speed ,the entropy will decreases rapidly casing increasing in Gibbs energy and this energy will be on the opposite direction of the flow but in the same direction with speed of sound ,so the free energy will interferes with the energy of sound instructively , being like the ice ball growing fast to compensate the total energy of the system to be adiabatic. sorry being to late to answer but i just see the question .
Dear Subhankar Ghosh
I do agree with Markus J. Kloker .
I wanted to add an explanation, but I found the answer by dear Markus J. Kloker a complete one.
Hello Subhankar Ghosh , I have a series of short lectures about compressible flows if you are interested in this topic. In this lecture I derive the equations related to Normal Shocks:
https://www.youtube.com/watch?v=qwQ_qHZj1LU
But I recommend you watch the previous videos as well. You can access the entire playlist here:
https://www.youtube.com/watch?v=EuYcv8ytZfk&list=PLWIeEaC-UXrWjUnmyUqh9s0csLsgxgs-u
I hope this can be helpful!
Dear Subhankar,
Shock waves are very small regions in the gas where the gas properties change by a large amount. Two types of shock waves are there one is oblique and other is normal shock waves. It is formed when a pressure front moves at supersonic speeds and pushes on the surrounding air. This is not a conventional sound waves; a shock wave takes the form of a very sharp change in the gas properties. Shock waves in air are heard as a loud "crack" noise. Across a shock wave, the static pressure, temperature, and gas density increases almost instantaneously. If the shock wave is perpendicular to the flow direction it is called a normal shock. Shock wave is perpendicular to flow. It is seen that properties change across the shock wave.
Why temperature remains constant?
The ratio of stagnation temperatures remains constant across a normal shock since the process is adiabatic, irreversible process; and entropy rises. The entropy values of the two points are not the same. Entropy can change across a shock wave.
What exactly happens when a supersonic flow go through or cross a normal shock wave?
If the flow is supersonic, the information ends exactly at the (normal) shock position because only in the region downstream the shock the sound can travel upstream to it. what happens exactly, all sound waves are stopped at this point and superpose forming the shock.
For a perfect gas, it is seen by plotting between entropy change is plotted against the upstream mach number, shocks are possible only in supersonic flow. Since the flow across a shock wave is irreversible, the downstream state must have the higher entropy. The upstream state is supersonic and the downstream state is subsonic. Thus, shock waves can happen only in supersonic flow and the flow becomes subsonic once it crosses a shock wave.
In case of compression waves
Across a compression wave, the flow decelerates and the pressure increases. Because, any new disturbance created here will travel at a faster speed than wave speed c, since the pressure and temperature might have now risen here. The wave traveling is behind a higher wave speed, hence compression waves getting closer and closer.
In case of expansion waves
Across an expansion wave, the flow accelerates and the pressure decreases. Since the expansion waves cannot catch up with one another, a shock wave can not form with expansion waves. Similarly as compression, any new disturbance created here will travel at a slower speed than c, because the pressure and temperature have dropped here.
Formation of a shock wave (it may be dangerous)
A shock wave can move through any material. Piston accelerated from rest to finite velocity, series of waves created (wave front). Shock waves occur when objects move faster than the speed of sound, which is 1,236 kilometers (768 miles) per hour. Shock waves make bombs more dangerous and sometimes are the most dangerous part of an explosion. However, the shock wave moves much faster than the rest of the bomb's energy, and fades away quickly.
Ashish
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