Page 43 - 48Fundamentals of Compressible Fluid Mechanics

1.3. HISTORICAL BACKGROUND 5
1.3.2 The shock wave puzzle

Here is where the politics of science was a major obstacle to achieving an ad-
10
vancement . In the early 18xx, conservation of energy was a concept that was
applied only to mechanical energy. On the other side, a different group of scientists
dealt with calorimetry (internal energy). It was easier to publish articles about the
second law of thermodynamics than to convince anyone of the first law of thermo-
dynamics. Neither of these groups would agree to “merge” or “relinquish” control
11
of their “territory” to the other. It took about a century to establish the first law .
At first, Poisson found a “solution” to the Euler’s equations with certain
boundary conditions which required discontinuity 12 which had obtained an implicit
form in 1808. Poisson showed that solutions could approach a discontinuity by
using conservation of mass and momentum. He had then correctly derived the
jump conditions that discontinuous solutions must satisfy. Later, Challis had no-
ticed contradictions concerning some solutions of the equations of compressible
13
gas dynamics . Again the “jumping” conditions were redeveloped by two different
researchers independently: Stokes and Riemann. Riemann, in his 1860 thesis,
was not sure whether or not discontinuity is only a mathematical creature or a real
creature. Stokes in 1848 retreated from his work and wrote an apology on his
“mistake.” 14 Stokes was convinced by Lord Rayleigh and Lord Kelvin that he was
mistaken on the grounds that energy is conserved (not realizing the concept of
internal energy).
At this stage some experimental evidence was needed. Ernst Mach
studied several fields in physics and also studied philosophy. He was mostly in-
terested in experimental physics. The major breakthrough in the understanding
of compressible flow came when Ernest Mach “stumbled” over the discontinuity.
It is widely believed that Mach had done his research as purely intellectual re-
search. His research centered on optic aspects which lead him to study acoustic
and therefor supersonic flow (high speed, since no Mach number was known at
that time). However, it is logical to believe that his interest had risen due to the
10 Amazingly, science is full of many stories of conflicts and disputes. Aside from the conflicts of
scientists with the Catholic Church and Muslim religion, perhaps the most famous is that of Newton’s
netscaping (stealing and embracing) Leibniz[’s] invention of calculus. There are even conflicts from not
giving enough credit, like Moody not giving the due credit to Rouse. Even the undersigned encountered
individuals who have tried to ride on his work. The other kind of problem is “hijacking” by a sector. Even
on this subject, the Aeronautic sector “took over” gas dynamics as did the emphasis on mathematics like
perturbations methods or asymptotic expansions instead on the physical phenomena. Major material
like Fanno flow isn’t taught in many classes, while many of the mathematical techniques are currently
practiced. So, these problems are more common than one might be expected.
11 This recognition of the first law is today the most “obvious” for engineering students. Yet for many it
was still debatable up to the middle of the nineteen century.
12 Sim´ eon Denis Poisson, French mathematician, 1781-1840 worked in Paris, France. ”M’emoire sur
la th’eorie du son,” J. Ec. Polytech. 14 (1808), 319-392. From Classic Papers in Shock Compression
Science, 3-65, High-press. Shock Compression Condens. Matter, Springer, New York, 1998.
13 James Challis, English Astronomer, 1803-1882. worked at Cambridge, England UK. ”On the veloc-
ity of sound,” Philos. Mag. XXXII (1848), 494-499
14 Stokes George Gabriel Sir, Mathematical and Physical Papers, Reprinted from the original journals
and transactions, with additional notes by the author. Cambridge, University Press, 1880-1905.