Aerothermodynamic correlations for high-speed flow

Heat flux and drag correlations are developed for high-speed flow over spherical geometries that are accurate for any Knudsen number ranging from continuum to free-molecular conditions. A stagnation point heat flux correlation is derived as a correction to the continuum (Fourier model) heat flux and also reproduces the correct heat flux in the free-molecular limit by use of a bridging function. In this manner, the correlation can be combined with existing continuum correlations based on computational fluid dynamics simulations, yet it can now be used accurately in the transitional and free-molecular regimes. The functional form of the stagnation point heat flux correlation is physics based, and was derived via the Burnett and super-Burnett equations in a recent article, Singh & Schwartzentruber (J. Fluid Mech., vol. 792, 2016, pp. 981–996). In addition, correlation parameters from the literature are used to construct simple expressions for the local heat flux around the sphere as well as the integrated drag coefficient. A large number of direct simulation Monte Carlo calculations are performed over a wide range of conditions. The computed heat flux and drag data are used to validate the correlations and also to fit the correlation parameters. Compared to existing continuum-based correlations, the new correlations will enable engineering analysis of flight conditions at higher altitudes and/or smaller geometry radii, useful for a variety of applications including blunt body planetary entry, sharp leading edges, low orbiting satellites, meteorites and space debris.

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Large Eddy Simulations of High Speed Flows

Volume 2, Parts A and B ◽

10.1115/ht-fed2004-56162 ◽

2004 ◽

Cited By ~ 6

Author(s):

C. Kannepalli ◽

S. Arunajatesan ◽

W. H. Calhoon ◽

S. M. Dash

Keyword(s):

Flow Regime ◽

High Speed ◽

Turbulent Transport ◽

Measurement Techniques ◽

Model Development ◽

High Speed Flow ◽

Speed Flow ◽

Wide Range ◽

Schmidt Numbers ◽

High Speed Flows

RANS models are required for the prediction of scalar fluctuations and turbulent transport in the high speed flow regime. These models will have application, for example, in missile exhaust plume signature analyses, scramjet combustors and other important areas. However, experimentally derived scalar fluctuation data needed to develop these models for the high speed flow regime is not readily available due to the inability of relevant experimental measurement techniques (e.g. hot wires) to cope with this flowfield environment. This issue poses significant difficulties for model development in this flow regime. Researchers have used different values for the turbulent Prandtl and Schmidt numbers but no consensus has been reached as to what these values have to be for high speed flows. To address this difficulty, a two part program has been initiated to fill the data gap and thus facilitate model development. Part I of this program involves the collection of LES data over a wide range of conditions. Part II involves the use of these data to evaluate and develop RANS tools to improve predictive capabilities. This paper presents results and findings of Part I of this program. Several flow fields of relevance to the problems mentioned above are studied. These include classical unit problems such as high and low Mach number shear layers, boundary layers and separated flows such as compression corner flows. In the process we are gradually extending the applicability of LES to more complex flows and at the same time enabling RANS model development by facilitating flow databases in the high speed flight regime. The findings of this study elucidate the effects of compressibility on the character of mean scalar profiles, variations in turbulent Prandtl number, and on scalar rms fluctuations.

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A Transient Global Heat-Flux Measurements for High-Speed Flow over a Wall-Mounted Cylinder in a Shock Tube

22nd AIAA International Space Planes and Hypersonics Systems and Technologies Conference ◽

10.2514/6.2018-5384 ◽

2018 ◽

Author(s):

Hiroshi Ozawa ◽

Stuart J. Laurence

Keyword(s):

Heat Flux ◽

Shock Tube ◽

High Speed ◽

High Speed Flow ◽

Speed Flow ◽

Flux Measurements

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Heat flux correlation for high-speed flow in the transitional regime

Journal of Fluid Mechanics ◽

10.1017/jfm.2016.118 ◽

2016 ◽

Vol 792 ◽

pp. 981-996 ◽

Cited By ~ 8

Author(s):

Narendra Singh ◽

Thomas E. Schwartzentruber

Keyword(s):

Heat Flux ◽

Flow Regime ◽

Stagnation Point ◽

High Speed ◽

Higher Order ◽

Molecular Flow ◽

Free Molecular Flow ◽

Burnett Equations ◽

Transition Flow ◽

Stagnation Point Heat Flux

An analytical correlation is developed for stagnation-point heat flux on spherical objects travelling at high velocity which is accurate for conditions ranging from the continuum to the free-molecular flow regime. Theoretical analysis of the Burnett and super-Burnett equations is performed using simplifications from shock-wave and boundary-layer theory to determine the relative contribution of higher-order heat flux terms compared with the Fourier heat flux (assumed in the Navier–Stokes equations). A rarefaction parameter ($W_{r}\equiv M_{\infty }^{2{\it\omega}}/Re_{\infty }$), based on the free-stream Mach number ($M_{\infty }$), the Reynolds number ($Re_{\infty }$) and the viscosity–temperature index (${\it\omega}$), is identified as a better correlating parameter than the Knudsen number in the transition regime. By studying both the Burnett and super-Burnett equations, a general form for the entire series of higher-order heat flux contributions is obtained. The resulting heat flux expression includes terms with dependence on gas properties, stagnation to wall-temperature ratio and a main dependence on powers of the rarefaction parameter $W_{r}$. The expression is applied as a correction to the Fourier heat flux and therefore can be combined with any continuum-based correlation of choice. In the free-molecular limit, a bridging function is used to ensure consistency with well-established free-molecular flow theory. The correlation is then fitted to direct simulation Monte Carlo (DSMC) solutions for stagnation-point heat flux in high-speed nitrogen flows. The correlation is shown to accurately capture the variation in heat flux predicted by the DSMC method in the transition flow regime, while limiting to both continuum and free-molecular values.

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