Enthalpy Explained: All You Need to Know

[Sailor Al]

Yes there is. Just master the material that I recommended for you and you will how this equation is derived.

I know it's not a perfect tool, but I get exactly zero hits in a Google search for "conservation of enthalpy"

 

[Chestermiller]

I know it's not a perfect tool, but I get exactly zero hits in a Google search for "conservation of enthalpy"

Look. I gave you the exact materials you need to learn to accomplish what you want. Do you have the determination to learn these materials or not? I'm not going to spoon feed this to you. You need to study and do lots of problems. I'm sorry if I'm being blunt. I'm giving you this advice based on over 50 years of engineering experience.

 

[Sailor Al]

My question was pretty simple: How is the consideration of enthalpy relevant in the study of aerodynamics of aircraft wings and yacht sails, i.e. in (dry) air at wind speeds of 0 to 300 kts, in temps of 0 to 25°C in the normal atmosphere below say 10,000 ft?
Aerodynamics is about the understanding of the aerodynamic force that results in lift and drag over a wing.
I have asked why H = U + PV has any bearing on this study?
You are saying "useful to solve for the temperature distribution in a fluid flow (and its feedback effect on the flow)." but that doesn't seem to have anything to do with the subject at hand - especially when in a separate post you are saying that " you can treat the flow as isothermal".
I'm not being deliberately obtuse, and I am reading most of the material being offered, but none of it explains my problem.

 

[Chestermiller]

My question was pretty simple: How is the consideration of enthalpy relevant in the study of aerodynamics of aircraft wings and yacht sails, i.e. in (dry) air at wind speeds of 0 to 300 kts, in temps of 0 to 25°C in the normal atmosphere below say 10,000 ft?

My answer was that I don't think it is relevant, and that you can solve this isothermally..

Aerodynamics is about the understanding of the aerodynamic force that results in lift and drag over a wing.
I have asked why H = U + PV has any bearing on this study?

In your situation, temperature can have a negligible effect of the forces, but if you want to include this effect, you also need to include a heat balance equation (based on enthalpy) and the effect of temperature on the fluid mechanics equations. Have you had a course in fluid dynamics, including the Navier Stokes equations?

You are saying "useful to solve for the temperature distribution in a fluid flow (and its feedback effect on the flow)." but that doesn't seem to have anything to do with the subject at hand - especially when in a separate post you are saying that " you can treat the flow as isothermal".

If the flow is isothermal (negligible effect of temperature), then you don't need to solve for the temperature distribution. You just solve the isothermal fluid dynamics equations. You can then substitute the calculated flow velocity distribution into the enthalpy balance equation to check to see whether the calculated temperature distribution is indeed negligible.

I'm not being deliberately obtuse, and I am reading most of the material being offered, but none of it explains my problem.

In my judgment, you're "in over your head."

 

[Sailor Al]

My answer was that I don't think it is relevant, and that you can solve this isothermally..

If the flow is isothermal (negligible effect of temperature), then you don't need to solve for the temperature distribution. You just solve the isothermal fluid dynamics equations. You can then substitute the calculated flow velocity distribution into the enthalpy balance equation to check to see whether the calculated temperature distribution is indeed negligible.

In my judgment, you're "in over your head."

If you cast your mind back to the reason I asked the question in post #17, you will note I said:
"I have done a lot of reading, including Marchaj, Fossati, Gentry and I have studied Eiffel's research report in his book. I am now three weeks into reading Anderson to see if he can provide some answers and have come unstuck at Section 7.2 when for some unexplained reason, he introduces:
"A related quantity is the specific enthalpy, denoted by h and defined as h = e + pv (7.3)""
And I asked "why it is important?"
I 100% concur with your answer " I don't think it is relevant", and is 100% correct. But now I have to ask why the heck did Anderson include it in his book entitled "Fundamentals of Aerodynamics"?
Also as I said in #17 "Because I'm trying to understand the "air can be considered incompressible below Mach 0.3" assumption which he "proves" in an incredibly long and complex argument which, inter alia, includes, and thus relies upon, the differentiation of the enthalpy equation at (7.19)"
If the introduction of enthalpy is not relevant, but is a part of the justification of the <M0.3 argument, doesn't that invalidate the whole argument?
I am ensuring that I don't go "in over my head" by working painstakingly through Anderson's line of reasoning.
Your response clearly confirms my conclusion that his reasoning is deeply flawed.
I know I'm not ready to "solve the isothermal fluid dynamics equations", and before I do I want to have some confidence I need to. If Anderson's reasoning is so flawed, and he's one of the top dudes in the field, then I'm pretty sure I can save myself a lot of time and frustration by staying well away.

 

[Chestermiller]

Please consider delving into the references I recommended.

As far as the books you have been studying, if they have problems at the end of the chapters, please consider solving a major fraction of these problems. Reading is good, but only solving problems can solidify your understanding and give you a working knowledge of the subject.

 

[Sailor Al]

Please consider delving into the references I recommended.

As far as the books you have been studying, if they have problems at the end of the chapters, please consider solving a major fraction of these problems. Reading is good, but only solving problems can solidify your understanding and give you a working knowledge of the subject.

But if the references are explaining enthalpy, and enthalpy is not relevant to aerodynamics, what's the point of that if my study is aerodynamics. Don't you see the contradiction?
I have my answer, you have confirmed enthalpy is irrelevant to aerodynamics.

 

[Motore]

I have my answer, you have confirmed enthalpy is irrelevant to aerodynamics.

Read post #19!

 

[Sailor Al]

Read post #19!

Yes, I know, it is a conundrum. But when I press him for why he qualifies his answer with "As long as the temperature of the air does not change much" he ducks for the undergrowth .
What is your view: is enthalpy useful in describing the process in #17?

 

[Motore]

What is your view: is enthalpy useful in describing the process in #17?

In that specific scenario in my opinion, it complicate things because the change in temperature is small, but it is useful if you want a precise way to compute things. But you said it's irrelevant to aerodynamics which is not the case as people solving aerodynamics questions use it often.
https://www.grc.nasa.gov/www/k-12/airplane/enthalpy.html

 

[Sailor Al]

Thanks for that link.
It relates to a very special situation where heat is added to a closed system in which pressure remains constant.
But in aerodynamics heat is never added to the system, and I don't think you can remove heat from a system without changing its pressure.

I'm not sure what it has to do with aerodynamics.

 

[vanhees71]

Particularly in fluid dynamics enthalpy plays an important role. In ideal fluid dynamics (adiabatic motion) it's the right thermodynamic potential to use. Euler's equation reads
$$\rho \mathrm{D}_t \vec{v}=\rho (\partial_t \vec{v} + (\vec{v} \cdot \vec{\nabla}) \vec{v})=-\vec{\nabla} P.$$
With $h$ the enthalpy per unit mass of the fluid and thus
$$\mathrm{d}h=T \mathrm{d} S + \frac{1}{\rho} \mathrm{d} P$$
you get, for adiabatic motion, $\vec{\nabla} P=\rho \vec{\nabla} h$ and thus
$$\mathrm{D}_t \vec{v}=-\nabla h.$$
Another very valuable source is vol. 6 of Landau and Lifshitz (fluid dynamics).

 

[Sailor Al]

Particularly in fluid dynamics enthalpy plays an important role.

But I'm not necessarily interested in fluid dynamics.
I'm interested in the aerodynamics of yachts' sails. Where is enthalpy useful in the aerodynamics of sails or wings?

 

[Motore]

But I'm not necessarily interested in fluid dynamics.
I'm interested in the aerodynamics of yachts' sails.

Wikipedia:
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion).

 

[vanhees71]

But I'm not necessarily interested in fluid dynamics.
I'm interested in the aerodynamics of yachts' sails. Where is enthalpy useful in the aerodynamics of sails or wings?

Aerodynamics is a subfield of fluid dynamics.

 

[Chestermiller]

But if the references are explaining enthalpy, and enthalpy is not relevant to aerodynamics, what's the point of that if my study is aerodynamics. Don't you see the contradiction?
I have my answer, you have confirmed enthalpy is irrelevant to aerodynamics.

It is irrelevant only if you are assuming that the flow is isothermal (i.e., non-isothermal effects are negligible).

 

[Chestermiller]

But I'm not necessarily interested in fluid dynamics.
I'm interested in the aerodynamics of yachts' sails. Where is enthalpy useful in the aerodynamics of sails or wings?

It is useful only when the amount of viscous frictional heating and compressional heating are sufficient (i.e., high Mach numbers) for the temperature to change significantly. For the range of operating conditions you have enumerated, it is not useful.

 

[vanhees71]

Then the free enthalpy (or Gibbs energy), $G=U-ST+PV=H-ST$ is the right potential:
$$\mathrm{d} F=\mathrm{d} U -S \mathrm{d} T -T \mathrm{d} S + P \mathrm{d} V + V \mathrm{d} P = -S \mathrm{d} T + V \mathrm{d} P.$$

 

[Steve4Physics]

I want to understand why Anderson introduced enthalpy.

You could read-ahead through the text in Anderson’s book after he defines enthalpy - to see how he then uses enthalpy. Or have you already done that and found it is not used?

 

[Sailor Al]

You could read-ahead through the text in Anderson’s book after he defines enthalpy - to see how he then uses enthalpy. Or have you already done that and found it is not used?

Ha! Yes, and that is the nub.
I have read through the text, and he does use it, specifically Section 7.4.2 where he uses it to derive (7.19)

Then via a very long and complex route* he "proves" that the errors in using air as compressible below M 0.3 are negligible.

*I'm working on a way to show the argument, but it needs work:

Here's a link to the analysis, please feel free to comment.

 

[som]

I can find no "rules" for its use. No-one is saying there is a law of conservation of enthalpy.

I am a layman in aerodynamics. However, this is my view on your concern. In thermodynamics, $$dH=TdS+VdP$$ So, in an adiabatic, isobaric reversible process, $dS=0, dP=0$ the enthalpy$(H)$ remains conserved.

Air is normally considered as insulator of heat. So if you consider a chunk of air as your system, all the thermodynamical changes within it are assumed to occur in the adiabatic way. In atmospheric science, adiabatic lapse rate is an example of such assumption which works well.

In addition, if some aerodynamical study is meant to pursue in a constant pressure zone, say, at a narrow range of altitude, then the study eventually becomes adiabatic, isobaric where H is constant as mentioned above. That may be the reason to introduce enthalpy.

Having said so, I don't know and couldn't realise either what kind of thermodynamical changes we see for a parcel of air, if the process is simultaneously adiabatic and isobaric. For an ideal gas, adiabaticity implies $PV^{\gamma}=$constant. If we further set $P$ constant for isobaric process, then $V$ must become constant. Hence, no work done, no heat exchange and $dU=0$. So everything stand still.

For a non-ideal gas, some meaningful changes may occur.