Talk:Rankine–Hugoniot conditions

Greater explanation needed

I find this article very difficult to understand. It seems to have much assumed knowledge, and many of the symbols are undefined. It would benefit greatly from practical examples and applications, and full definitions of symbols. (Not to mention reputable references) Sholto Maud 02:38, 31 May 2006 (UTC)

I have expanded this article with the intention of making it clearer and to provide some additional references. However, unfortunately, this subject does require some familiarity with thermodynamics and a reasonable level of mathematics. I hope this helps. Griffgruff (talk) 23:18, 6 July 2009 (UTC)

I also added some introductory remarks to guide non-expert readers towards the central idea of treating the jumps as discontinuities, which wasn't previously explained. For the moment these remarks need some hyperlinks and citations. I will put these in when I have a bit more time; folks should also feel free to pitch in and edit as they see fit. Rtfisher (talk) 08:28, 15 October 2023 (UTC)

difficult article

i do agree that this article is based on previous knowledge i would need some change do be more understandable

Problem on the energy flux equation

The last equation (energy flux) contains a unit mismatch, that is to say, different units are added.

The first component (e- Internal energy) is [Cv x T] (Cv- specific heat in constant volume, T- temperature) the unit is [J/mol]

The two other added parts are [P/roh] and [1/2 x u^2] both of which have the same unit [(m/sec)^2] yet different from the first (e).

I don't see how you can add the three [ e+P/roh+(1/2 x u^2) ].

... unless the equation is per unit mass...

Is it?

Yes. Lowercase e and ρ indicate that the quantities are specific (meaning, that they are per unit mass). Titoxd^{(?!? - cool stuff)} 20:56, 1 March 2008 (UTC)

This is very complicated to understand, as it requires a great deal of knowledge, I will provide a simpler derivation of the Rankine-hugoniot equations using only simple algebra. —Preceding unsigned comment added by 86.160.174.17 (talk) 10:52, 31 August 2009 (UTC)

Inviscid

A shcok is always a dissipative phenomenon, requiring viscosity. The Rankine-Hugoniot relations only assume that the fluid is non-viscous outside the shock. — Preceding unsigned comment added by Mkovari (talk • contribs) 10:37, 16 November 2012 (UTC)

Error in 1D Euler equation - momentum equation

Correct me if I am mistaken, but I believe that equation number 2 i.e. 1-D euler momentum equation has a mistke in it : on the right hand side, shouldn't the convective term be :

${\frac {\partial }{\partial x}}{\frac {\rho u^{2}}{2}}$

instead of :

${\frac {\partial }{\partial x}}\rho u^{2}$

--GLorieul (talk) 19:20, 4 March 2014 (UTC)

No, the momentum equation does not have a factor of 1/2 missing. To see why you can take a look at the derivation of these equations @ [1].Bbanerje (talk) 21:11, 5 March 2014 (UTC)

Derivation of Rankine-Hugoniot jump condition from PDE is wrong

Note that jump conditions (for discontinuous functions) could not be obtained from differential equations in principle, so the derivation oj jump conditions in section “The jump condition” is erroneous. Re-casting of differential equations in another form would result, for this approach, in another (incorrect) “conservation law”. For example, the equation

${\frac {\partial u}{\partial t}}+u{\frac {\partial u}{\partial x}}=0$

can be rewritten in two equivalent forms (for smooth solutions):

${\frac {\partial u}{\partial t}}+{\frac {\partial u^{2}/2}{\partial x}}=0$

and

${\frac {\partial u^{2}/2}{\partial t}}+{\frac {\partial u^{3}/3}{\partial x}}=0$,

so this way of reasoning would give two (contradictory) jump conditions.

Albina-belenkaya (talk) 20:36, 9 January 2015 (UTC)

For physical reasons behind jump conditions in nonlinear hyperbolic PDEs see PDE Notes by J. Shatah. Bbanerje (talk) 04:55, 12 January 2015 (UTC)

The Rankine -- Hugoniot conditions are not, of course, incorrect. What I mean is that the way of reasoning (i.e., derivation of jump conditions by integrating PDEs) is wrong. The right way is postulating the integral relations for hyperbolic system (or derivation of jump conditions from a more complicated system for viscous heat-conducting gas; in this case the shock wave is a narrow zone with large gradients). In present version of the article this point is not clearly stated. Albina-belenkaya (talk) 18:42, 12 January 2015 (UTC)

I agree that a more rigorous approach would be better. You could add a section below the textbook derivation to explain the problems with this approach and what the solution is. Bbanerje (talk) 00:20, 13 January 2015 (UTC)

Equations not in frame of shock

The article states that "In a coordinate system that is moving with the shock, the Rankine–Hugoniot conditions can be expressed as:" but the equations given are in the frame of the pre-shock medium, no? --129.11.68.6 (talk) 14:04, 8 October 2015 (UTC)

Incorrect jump conditions

The jump conditions are incorrect. This is a major mistake. Should be fixed. Here are the correct equations:

  \frac{\rho_2}{\rho_1} = \frac{v_1}{v_2}=\frac{\gamma+1}{\gamma-1+2M_1^{-2}}

  \frac{p_2}{p_1}&=&\frac{2\gamma M_1^2 - (\gamma-1)}{\gamma+1}
                   

where M_1=\frac{v_1}{c_{s,1}} is the Mach number of the upstream flow. The pressure behind a strong shock depends on the upstream ram pressure, not on the upstream pressure. That's why the Mach number appears on the right hand side. On the other hand, the density jump has an upper limit. There is no symmetry as shown in the article.

See for example section 7.2 in http://www.astronomy.ohio-state.edu/~dhw/A825/notes7.pdf

— Preceding unsigned comment added by 141.213.169.21 (talk) 01:20, 14 March 2018 (UTC)

Misattribution to Albert Michelson

The article attributes the "Michelson-Rayleigh" line to Albert Michelson. I do not believe this is the correct Michelson. Landau & Lifschitz's text on Fluid Mechanics (section 129, 1987 edition) cites "V. A. Mikhel'son, 1890." While Albert Michelson was alive at that time, the earliest papers in the archive at the University of Chicago only date back to 1891. https://www.lib.uchicago.edu/e/scrc/findingaids/view.php?eadid=ICU.SPCL.MICHELSON#:~:text=,Palomar%20Observatories%2C%20reprints%20of. I have also found the citation to the original paper and will include it and correct the misattribution.

Rtfisher (talk) 07:47, 15 October 2023 (UTC)

Rankine-Hugoniot condition does not apply to shock waves

The article incorrectly describes the Rankine-Hugoniot condition as describing "the relationship between the states on both sides of a shock wave or a combustion wave (deflagration or detonation) "

The Rankine-Hugoniot condition actually only describes the relationship between the states on both sides of a combustion wave and not a shock wave.

My reference is Williams [1] which defines the scope of the Rankine-Hugoniot condition quite explicitly:

"Such a classification provides a framework within which plane deflagration and detonation waves may be investigated." (my emphasis)

Williams restricts his use of "shock wave" to the pressure wave generated by supersonic bodies and the separate pressure wave that is followed by the deflagration.

The conditions relating to shock waves are quite different and are discussed in shock wave in which the confusion is exacerbated by its reference to the Rankine-Hugoniot condition. I plan to start a talk on that page in an attempt to unravel the confusion.

[1]Williams, F. A. (2018). Combustion theory. CRC Press. p. 19

Gpsanimator (talk) 06:19, 13 November 2023 (UTC)

Hi @Gpsanimator: I think the RH conditions do apply to shocks. I am not very familiar with combustion waves, but I am with shock physics; and, from my experience, the RH conditions almost always come up in introductory texts on shocks. For example,

The Rankine-Hugoniot relations are the expressions for conservation of mass, momentum and energy across a shock front. They apply just as well to blast waves as to shock waves because they express the conditions at the shock front, which, at this point, we will treat as a discontinuity.

and

The famous Rankine-Hugoniot (RH) relations [...] are widely used in shock physics, because they quickly provide data of shock parameter values for many practical applications rather than obtaining more precise data by elaborately solving hyperbolic differential equations.

And many other examples can be found by searching Rankine-Hugoniot in, for example, Google Scholar. CoronalMassAffection (talk) 20:42, 28 November 2023 (UTC)

Unfortunately both of your references are behind paywalls and not accessible and, being privately published papers, should not be considered "introductory texts". There is much misinformation to be found behind commercial paywalls.

I have used Williams[1] as my source and they are very specific.

Can you cite any published textbook that uses RH condition for shocks other than in combustion waves? Gpsanimator (talk) 21:11, 28 November 2023 (UTC)

I do not know of any such textbooks that are not behind paywalls, but the second paper I reference above might be accessible via this link. And another relevant book chapter might be available via this link. Regardless, the RH conditions are used for shocks in plasma, as can be seen by checking out the papers referenced here. Also, although less authoritative, the lecture notes of Ian Cross (MIT) and the lecture notes of David Weinberg (Ohio State University) also discuss RH conditions in terms of shocks. CoronalMassAffection (talk) 03:31, 29 November 2023 (UTC)

Hi, Trestan, Thanks for your response. My degree is in Mathematical Physics, and my current interest is in the propagation of large amplitude acoustic waves.

To clarify William's use of the  term "combustion wave (deflagration or detonation) ", it's important to distinguish between how the two terms relate to the nature of the combustion, or exothermic process yielding hot gaseous products.

Deflagration is when the speed of the process is subsonic, as in the case of black powder (gunpowder) and detonation is when the speed is supersonic, as in the case of high explosives like TNT, C4, ammonium nitrate (as in the Beirut Port explosion in 2020), etc.

Deflagration will only generate an explosion if the chemical reaction is contained in a casing such as the cardboard of a firework or the metal casing of a bullet cartridge.

Detonation is the explosion of uncontained HE. It spontaneously explodes when detonated.

I haven't checked all of your references, but the ones I have are from commercial journals (Springer, Shock Waves, IOP Astrophysical Journal, etc.) and are not peer reviewed, nor are they standard textbooks. As such, they cannot be cited as reputable sources, and certainly not, in your terms, as "introductory texts on shocks".

I really would encourage you to access an authoritative source if you intend to pursue a career in technical writing. Gpsanimator (talk) 21:04, 17 December 2023 (UTC)

As an undergraduate, you could access authoritative texts through your university library. Gpsanimator (talk) 21:11, 17 December 2023 (UTC)

Hi @Gpsanimator: Thanks for your concern regarding my career; however, this is not the appropriate forum for that sort of discussion per WP:FOC, and I feel that your concluding remark was not made in the spirit of Wikipedia's founding principles WP:5P4. Regardless, I do not think it is really up for debate whether the references I give above come from reputable, peer-reviewed journals/publishers. As far as Wikipedia is concerned, them being from commercial journals and not being "standard" textbooks does not preclude WP:REPUTABILITY. Furthermore, you can easily verify that these journals are in fact peer reviewed (see for example Springer (books) and ApJ). Also, looking at citation count, you can get a good understanding that the ideas presented are mainstream. CoronalMassAffection (talk) 22:31, 17 December 2023 (UTC)

No, your journal articles are not peer reviewed:

Springer (books): "All books published by Springer Nature undergo review. This usually involves a review by experts"

Note "usually"

ApJ: "ApJ articles are generally sent to one reviewer, although at the discretion of the editor two or more may be used.

Note... "generally"

Please, use your university library tyo get reliable sources. Gpsanimator (talk) 23:31, 17 December 2023 (UTC)

These resources were accessed through my university library. CoronalMassAffection (talk) 02:01, 18 December 2023 (UTC)

Reliable sources are not limited to just peer-reviewed papers and standard textbooks. Books published by reliable academic presses such as Springer are reliable sources.

I don't think the statement quoted above implies that any ApJ articles do not go through peer review. The statement seems to imply that the number of reviewers is typically one, but sometimes two.

Whether a source is behind a paywall is irrelevant. Many reliable sources are not widely available on the internet. There is no requirement that a reliable source be accessible for free, or online, or to any specific Wikipedia editor. --Srleffler (talk) 18:10, 24 December 2023 (UTC)

Chiming in here a bit late perhaps, but the RH conditions themselves clearly reduce to a non-reactive hydrodynamic discontinuity (eg, a shock) in the case of zero added enthalpy (alpha = 0 in dimensionless form). The CRC reference cited was a combustion reference and should be understood in that context.Rtfisher (talk) 21:31, 29 December 2023 (UTC)

Dear @Gpsanimator, the Rankine-Hugoniot equations can be used to describe shock waves, no doubt about that. One prominent historical example of their use is the Sedov-Taylor-von Neumann point blast wave problem, which was used by Taylor in 1941 to estimate the yield of the first atomic bomb explosion, much of the annoyance to the U.S. government. (I'm very sure this was not a deflagration event.) The original (peer reviewed) articles are available at [2] and [3]. Since they may be behind a paywall, there is a recent interesting article on that problem entitled On the Symmetry of Blast Waves, which is both peer reviewed and open access. I know the Rankine-Hugoniot equations are also used at e.g. LANL in evaluating experiments with various high explosives. I'm sure you can find lots of LANL reports as examples at osti.gov. Just search for "Rankine-Hugoniot explosives" or similar. -- Robin 88.64.171.181 (talk) 17:41, 8 May 2024 (UTC)

References