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Hypersonic flow over spherically blunted cone capsules for atmospheric entry, Part I: The sharp cone and the sphere

Hornung, Hans G. and Martinez Schramm, Jan and Hannemann, Klaus (2019) Hypersonic flow over spherically blunted cone capsules for atmospheric entry, Part I: The sharp cone and the sphere. Journal of Fluid Mechanics, 871, pp. 1097-1116. Cambridge University Press. doi: 10.1017/jfm.2019.342. ISSN 0022-1120.

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Official URL: https://doi.org/10.1017/jfm.2019.342


Depending on the cone half-angle and the inverse normal-shock density ratio, hypersonic flow over a spherically blunted cone exhibits two regimes separated by an almost discontinuous jump of the body end of the sonic line from a point on the spherical nose to the shoulder of the cone, here called sphere behaviour and cone behaviour. The inflection point of the shock wave in sphere behaviour is explained. In Part 1 we explore the two elements of the capsule shape, the sphere and the sharp cone with detached shock, theoretically and computationally, in order to put the treatment of the full capsule shape on a sound basis. Starting from the analytical expression for the shock detachment angle of a cone given by Hayes & Probstein (Hypersonic Flow Theory, 1959, Academic Press) we make a hypothesis for the sharp cone, about the functional form of the dependence of dimensionless quantities on the inverse normal-shock density ratio and a cone angle parameter. In the critical part of atmospheric entry the shock shape and drag of the capsule are insensitive to viscous effects, so that much can be learned from inviscid studies. Accordingly, the hypothesis is tested by making a large number of Euler computations to cover the parameter space: Mach number, specific heat ratio and cone angle. The results confirm the hypothesis in the case of the dimensionless shock stand-off distance as well as for the drag coefficient, yielding accurate analytical functions for both. This reduces the number of independent parameters of the problem from three to two. A functional form of the shock stand-off distance is found for the transition from the cone to the sphere. Although the analysis assumes a calorically perfect gas, the results may be carried over to the high-enthalpy real-gas situation if the normal-shock density ratio is replaced by the density ratio based on the average density along the stagnation streamline.

Item URL in elib:https://elib.dlr.de/126008/
Document Type:Article
Title:Hypersonic flow over spherically blunted cone capsules for atmospheric entry, Part I: The sharp cone and the sphere
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Hornung, Hans G.California Institute of Technology, Pasadena, CAUNSPECIFIEDUNSPECIFIED
Martinez Schramm, JanUNSPECIFIEDhttps://orcid.org/0000-0002-8891-6253UNSPECIFIED
Date:3 June 2019
Journal or Publication Title:Journal of Fluid Mechanics
Open Access:No
Gold Open Access:No
In ISI Web of Science:Yes
Page Range:pp. 1097-1116
Publisher:Cambridge University Press
Keywords:hypersonics flow, spherically blunt cone, sonice line, shock stand off distance
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space Transportation
DLR - Research area:Raumfahrt
DLR - Program:R RP - Space Transportation
DLR - Research theme (Project):R - Reusable Space Systems and Propulsion Technology
Location: Göttingen
Institutes and Institutions:Institute for Aerodynamics and Flow Technology > Spacecraft, GO
Deposited By: Martinez Schramm, DR Jan
Deposited On:12 Jul 2019 15:11
Last Modified:21 Sep 2023 12:46

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