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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

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