Facing the Heat Barrier - NASA's History Office
Facing the Heat Barrier - NASA's History Office
Facing the Heat Barrier - NASA's History Office
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<strong>Facing</strong> <strong>the</strong> <strong>Heat</strong> <strong>Barrier</strong>: A <strong>History</strong> of Hypersonics<br />
The HGS swept over a small model of a nose cone placed within <strong>the</strong> stress. The<br />
time for passage was of <strong>the</strong> order of 100 microseconds, with <strong>the</strong> shock tube thus<br />
operating as a “wind tunnel” having this duration for a test. This never<strong>the</strong>less was<br />
long enough for photography. In addition, specialized instruments permitted study<br />
of heat transfer. These included thin-gauge resistance <strong>the</strong>rmometers for temperature<br />
measurements and thicker-gauge calorimeters to determine heat transfer rates.<br />
Metals increase <strong>the</strong>ir electrical resistance in response to a temperature rise. Both<br />
<strong>the</strong> <strong>the</strong>rmometers and <strong>the</strong> calorimeters relied on this effect. To follow <strong>the</strong> sudden<br />
temperature increase behind <strong>the</strong> shock, <strong>the</strong> <strong>the</strong>rmometer needed a metal film that<br />
was thin indeed, and Avco researchers achieved a thickness of 0.3 microns. They did<br />
this by using a commercial product, Liquid Bright Platinum No. 05, from Hanovia<br />
Chemical and Manufacturing Company. This was a mix of organic compounds of<br />
platinum and gold, dissolved in oils. Used as a paint, it was applied with a brush<br />
and dried in an oven.<br />
The calorimeters used bulk platinum foil that was a hundred times thicker, at<br />
0.03 millimeters. This thickness diminished <strong>the</strong>ir temperature rise and allowed <strong>the</strong><br />
observed temperature increase to be interpreted as a rate of heat transfer. Both <strong>the</strong><br />
<strong>the</strong>rmometers and calorimeters were mounted to <strong>the</strong> surface of nose-cone models,<br />
which typically had <strong>the</strong> shape of a hemisphere that faired smoothly into a cylinder<br />
at <strong>the</strong> rear. The models were made of Pyrex, a commercial glass that did not readily<br />
crack. In addition, it was a good insulator. 37<br />
The investigator Shao-Chi Lin also used a shock tube to study <strong>the</strong>rmal ionization,<br />
which made <strong>the</strong> HGS electrically conductive. To measure this conductivity,<br />
Shao used a nonconducting shock tube made of glass and produced a magnetic field<br />
within its interior. The flow of <strong>the</strong> conducting HGS displaced <strong>the</strong> magnetic lines<br />
of force, which he observed. He calibrated <strong>the</strong> system by shooting a slug of metal<br />
having known conductivity through <strong>the</strong> field at a known speed. Measured HGS<br />
conductivities showed good agreement with values calculated from <strong>the</strong>ory, over a<br />
range from Mach 10 to Mach 17.5. At this highest flow speed, <strong>the</strong> conductivity of<br />
air was an order of magnitude greater than that of seawater. 38<br />
With shock tubes generating new data, <strong>the</strong>re was a clear need to complement<br />
<strong>the</strong> data with new solutions in aerodynamics and heat transfer. The original Allen-<br />
Eggers paper had given a fine set of estimates, but <strong>the</strong>y left out such realistic effects<br />
as dissociation, recombination, ionization, and changes in <strong>the</strong> ratio of specific heats.<br />
Again, it was necessary to make simplifying assumptions. Still, <strong>the</strong> first computers<br />
were at hand, which meant that solutions did not have to be in closed form. They<br />
might be equations that were solvable electronically.<br />
Recombination of ions and of dissociated diatomic molecules—oxygen and<br />
nitrogen—was particularly important at high Mach, for this chemical process could<br />
deliver additional heat within <strong>the</strong> boundary layer. Two simplified cases stood out. In<br />
34<br />
Nose Cones and Re-entry<br />
“equilibrium flow,” <strong>the</strong> recombination took place instantly, responding immediately<br />
to <strong>the</strong> changing temperature and pressure within <strong>the</strong> boundary layer. The extent of<br />
ionization and dissociation <strong>the</strong>n were simple point functions of <strong>the</strong> temperature and<br />
pressure at any location, and <strong>the</strong>y could be calculated directly.<br />
The o<strong>the</strong>r limiting case was “frozen flow.” One hesitates to describe a 9000 K<br />
airstream as “frozen,” but here it meant that <strong>the</strong> chemical state of <strong>the</strong> boundary layer<br />
retained its condition within <strong>the</strong> free stream behind <strong>the</strong> bow shock. Essentially this<br />
means that recombination proceeded so slowly that <strong>the</strong> changing conditions within<br />
<strong>the</strong> boundary layer had no effect on <strong>the</strong> degrees of dissociation and ionization. These<br />
again could be calculated directly, although this time as a consequence of conditions<br />
behind <strong>the</strong> shock ra<strong>the</strong>r than in <strong>the</strong> boundary layer. Frozen flow occurred when <strong>the</strong><br />
air was rarefied.<br />
These approximations avoided <strong>the</strong> need to deal with <strong>the</strong> chemistry of finite reaction<br />
rates, wherein recombination would not instantly respond to <strong>the</strong> rapidly varying<br />
flow conditions across <strong>the</strong> thickness of a boundary layer but would lag behind<br />
<strong>the</strong> changes. In 1956 <strong>the</strong> aerodynamicist Lester Lees proposed a heat-transfer <strong>the</strong>ory<br />
that specifically covered those two limiting cases. 39 Then in 1957, Kantrowitz’s colleagues<br />
at Avco Research Laboratory went considerably fur<strong>the</strong>r.<br />
The Avco lab had access to <strong>the</strong> talent of nearby MIT. James Fay, a professor<br />
of mechanical engineering, joined with Avco’s Frederick Riddell to treat anew <strong>the</strong><br />
problem of heat transfer in dissociated air. Finite reaction-rate chemistry was at <strong>the</strong><br />
heart of <strong>the</strong>ir agenda, and again <strong>the</strong>y needed a simplifying assumption: that <strong>the</strong><br />
airflow velocity was zero. However, this condition was nearly true at <strong>the</strong> forward tip<br />
of a nose cone, where <strong>the</strong> heating was most severe.<br />
Starting with a set of partial differential equations, <strong>the</strong>y showed that <strong>the</strong>se equations<br />
reduced to a set of nonlinear ordinary differential equations. Using an IBM<br />
650 computer, <strong>the</strong>y found that a numerical solution of <strong>the</strong>se nonlinear equations was<br />
reasonably straightforward. In dealing with finite-rate chemistry, <strong>the</strong>y introduced<br />
a “reaction rate parameter” that attempted to capture <strong>the</strong> resulting effects. They<br />
showed that a re-entering nose cone could fall through 100,000 feet while transitioning<br />
from <strong>the</strong> frozen to <strong>the</strong> equilibrium regime. Within this transition region,<br />
<strong>the</strong> boundary layer could be expected to be partly frozen, near <strong>the</strong> free stream, and<br />
partly in equilibrium, near <strong>the</strong> wall.<br />
The Fay-Riddell <strong>the</strong>ory appeared in <strong>the</strong> February 1958 Journal of <strong>the</strong> Aeronautical<br />
Sciences. That same issue presented experimental results, also from Avco, that<br />
tested <strong>the</strong> merits of this treatment. The researchers obtained shock-tube data with<br />
shock Mach numbers as high as 17.5. At this Mach, <strong>the</strong> corresponding speed of<br />
17,500 feet per second approached <strong>the</strong> velocity of a satellite in orbit. Pressures<br />
within <strong>the</strong> shock-tube test gas simulated altitudes of 20,000, 70,000, and 120,000<br />
feet, with equilibrium flow occurring in <strong>the</strong> models’ boundary layers even at <strong>the</strong><br />
highest equivalent height above <strong>the</strong> ground.<br />
35