Correspondence between Normal-Shock and Blunt-Body Flows

Gibson, Walter E.; Marrone, Paul V.

doi:10.1063/1.1706576

Cited by 20 publications

(6 citation statements)

References 11 publications

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“…In fact, formulas (14) and (15) generally will be preferable to (6) and (7) for near-parabolic orbits (frequently encountered in lunar transfer trajectories) where (6) and (7) begin to lose accuracy. During the lunar approach, a high-precision position determination from the earth can be reduced to position and velocity errors at the last guidance maneuver by means of (14, 15, and 11).…”

Section: Applicationsmentioning

confidence: 96%

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Approximate Method for Hypersonic Nonequilibrium Blunt Body Airflows

Ellington¹

1963

AIAA Journal

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Section: Applicationsmentioning

confidence: 96%

“…However, for the parabolic case one may write e = 1 + e, de = e, and 1 -e 2 = -2e + 0(e 2 ), so that 8a(l -e 2 ) = 25p -2p (1 + e). Reformulating (6) and (7) in this fashion and retaining terms of 0(5p) and 0(e) in place of 0(5a) and 0(8e) for the elliptic orbit, one arrives at in 2 / 1 . 1/1 -cos/\ 2 \ _ 5V1 + cos/y f 5r -…”

mentioning

confidence: 98%

Approximate Method for Hypersonic Nonequilibrium Blunt Body Airflows

Ellington¹

1963

AIAA Journal

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“…• at impact velocity of Vsinθ (Gibson & Marrone 1962). In the present study, we calculate chemical reactions for shock angles of 90…”

Section: Methodsmentioning

confidence: 99%

“…In the shock model, we considered chemical reactions along a streamline behind a bow shock as those behind a onedimensional steady-state plane shock (Gibson & Marrone 1962;Hall et al 1962). In this approximation, the enthalpy of postshocked gas species behind the steady-state plane shock is given by that of the streamline behind the bow shock.…”

Section: Methodsmentioning

confidence: 99%

OXIDIZING PROTO-ATMOSPHERE ON TITAN: CONSTRAINT FROM N₂FORMATION BY IMPACT SHOCK

Ishimaru¹,

Sekine²,

Matsui³

et al. 2011

ApJ

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Titan is the only satellite that possesses a thick atmosphere, composed mainly of N 2 and CH 4 . However, its origin and evolution remain largely unknown. Knowledge of the acquirement of a N 2 atmosphere on Titan would provide insights into nitrogen evolution in planetary atmospheres as well as the formation of satellite systems around gas giants. Previous studies have proposed that the atmospheric N 2 would have been converted from NH 3 via shock heating by accreting satellitesimals in the highly reducing proto-atmosphere composed of NH 3 and CH 4 . Nevertheless, the validity of this mechanism strongly depends on both the composition of the proto-atmosphere and kinetics of shock chemistry. Here, we show that a CO 2 -rich oxidizing proto-atmosphere is necessary to form N 2 from NH 3 efficiently by atmospheric shock heating. Efficient shock production of N 2 is inhibited in a reducing protoatmosphere composed of NH 3 and CH 4 , because CH 4 plays as the coolant gas owing to its large heat capacity. Our calculations show that the amount of N 2 produced in a CO 2 -rich proto-atmosphere could have reached ∼20 times that on the present Titan. Although further quantitative analysis are required (especially, the occurrence of catalytic reactions), our results imply that the chemical composition of satellitesimals that formed the Saturnian system is required to be oxidizing if the current atmospheric N 2 is derived from the shock heating in the proto-atmosphere during accretion. This supports the formation of regular satellites in an actively supplied circumplanetary disk using CO 2 -rich materials originated from the solar nebula at the final stage of gas giant formation.

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“…More specific investigations on the range of applicability of binary scaling were then performed by Gibson, Marrone, and Sowyrda [58,61,59] and summarized in a chapter written for the AGARD meeting on The High Temperature Aspect of Hypersonic Flows, held at VKI in April 1962 [60]. In that chapter, they develop an analytical method based on the shock-mapping technique to determine the chemical state of shock layers around hypersonic blunt bodies.…”

Section: Binary Scaling 241 State Of the Artmentioning

confidence: 99%

On binary scaling and ground-to-flight extrapolation in high-enthalpy facilities

Looringhe¹,

Arwid²

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The binary scaling law is commonly used to study the aerothermodynamics of hypersonic vehicles in high-enthalpy facilities. It enables the duplication of the shock layer in the vicinity of the stagnation point, including binary chemistry and nonequilibrium processes, through the reproduction of the Péclet and wall Damköhler numbers. These are both conserved through the duplication of the composition of the gas, the free-stream enthalpy h ∞ and the product of a density and a length-scale of the flow ρL.Binary scaling is built on the assumption of a flow devoid of radiation coupling and governed by binary reactions. These two conditions drastically narrow down the envelope of flows for which binary scaling can be used. Moreover, diffusive transport and wall chemistry have never been addressed although they can have an important impact on the wall heat flux.The first part of this thesis consists in an effort to better understand the theoretical role and effect of the different assumptions done to build the binary scaling. It is first shown that diffusive transport and wall chemistry should scale appropriately. Second, that non-binary chemistry will cause the shock layer in the laboratory flow to be hotter and less dissociated. A methodology is proposed to identify clearly what free-stream conditions will affect the least the flow variables of interest. Lastly, that radiation coupling will be weaker in the laboratory flow than in flight, causing the enthalpy contained in the shock layer to be greater in the laboratory flow.These findings are verified in the second part with two experiments. The first experiment was performed in the Plasmatron plasma wind tunnel at the von Karman Institute, Belgium. Binary scaled boundary layers were obtained for flows where diffusion and wall chemistry contribute significantly to the heat flux. The stagnation point heat fluxes were measured and exhibit a good agreement with the theoretical scaling law. This also validates the use of the binary scaling law in subsonic high-enthalpy facilities.The second experiment was performed in the X2 expansion tube at the Centre for Hypersonics, Australia. Three flows were obtained over cylinders of different radii, adapting the free-stream density according to the binary scaling law. The free-stream conditions were determined in order to ensure a significant radiative coupling. Its effect could clearly be identified through measurements of the shock standoff distance, stagnation point heat flux, and shock layer radiation. A new method, based on a mix of experiments, computational fluid dynamics, and informed use of engineering correlations is proposed to perform ground to flight extrapolation for cases for which the radiative coupling is non-negligible. Declaration by authorThis thesis is composed of my original work, and contains no material previously published or written by another person except where due reference has been made in the text. I have clearly stated the contribution by others to jointly-authored works that I have include...

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Correspondence between Normal-Shock and Blunt-Body Flows

Cited by 20 publications

References 11 publications

Approximate Method for Hypersonic Nonequilibrium Blunt Body Airflows

Approximate Method for Hypersonic Nonequilibrium Blunt Body Airflows

OXIDIZING PROTO-ATMOSPHERE ON TITAN: CONSTRAINT FROM N₂FORMATION BY IMPACT SHOCK

On binary scaling and ground-to-flight extrapolation in high-enthalpy facilities

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Correspondence between Normal-Shock and Blunt-Body Flows

Cited by 20 publications

References 11 publications

Approximate Method for Hypersonic Nonequilibrium Blunt Body Airflows

Approximate Method for Hypersonic Nonequilibrium Blunt Body Airflows

OXIDIZING PROTO-ATMOSPHERE ON TITAN: CONSTRAINT FROM N2FORMATION BY IMPACT SHOCK

On binary scaling and ground-to-flight extrapolation in high-enthalpy facilities

Contact Info

Product

Resources

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OXIDIZING PROTO-ATMOSPHERE ON TITAN: CONSTRAINT FROM N₂FORMATION BY IMPACT SHOCK