### Abstract

Language | English |
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Title of host publication | 2nd European Conference on Aero-Space Sciences (EUCASS) |

Number of pages | 8 |

Publication status | Published - Jul 2007 |

Event | 2nd European Conference on AeroSpace Sciences (EUCASS), 2007 - Brussels, Belgium Duration: 1 Jul 2007 → 6 Jul 2007 |

### Conference

Conference | 2nd European Conference on AeroSpace Sciences (EUCASS), 2007 |
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Abbreviated title | EUCASS 2007 |

Country | Belgium |

City | Brussels |

Period | 1/07/07 → 6/07/07 |

### Fingerprint

### Keywords

- fluid dynamics
- aerospace
- structures
- composites
- design engineering

### Cite this

*2nd European Conference on Aero-Space Sciences (EUCASS)*

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*2nd European Conference on Aero-Space Sciences (EUCASS).*2nd European Conference on AeroSpace Sciences (EUCASS), 2007, Brussels, Belgium, 1/07/07.

**The structure of hypersonic shock waves using Navier-Stokes equations modified to include mass diffusion.** / Greenshields, C.J.; Reese, J.M.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

TY - GEN

T1 - The structure of hypersonic shock waves using Navier-Stokes equations modified to include mass diffusion

AU - Greenshields, C.J.

AU - Reese, J.M.

PY - 2007/7

Y1 - 2007/7

N2 - Howard Brenner has recently proposed modifications to the Navier-Stokes equations that relate to a diffusion of fluid volume that would be significant for flows with high density gradients. In a previous paper (Greenshields & Reese, 2007), we found these modifications gave good predictions of the viscous structure of shock waves in argon in the range Mach 1.0-12.0 (while conventional Navier-Stokes equations are known to fail above about Mach 2). However, some areas of concern with this model were a somewhat arbitrary choice of modelling coefficient, and potentially unphysical and unstable solutions. In this paper, we therefore present slightly different modifications to include molecule mass diffusion fully in the Navier-Stokes equations. These modifications are shown to be stable and produce physical solutions to the shock problem of a quality broadly similar to those from the family of extended hydrodynamic models that includes the Burnett equations. The modifications primarily add a diffusion term to the mass conservation equation, so are at least as simple to solve as the Navier-Stokes equations; there are none of the numerical implementation problems of conventional extended hydrodynamics models, particularly in respect of boundary conditions. We recommend further investigation and testing on a number of different benchmark non-equilibrium flow cases.

AB - Howard Brenner has recently proposed modifications to the Navier-Stokes equations that relate to a diffusion of fluid volume that would be significant for flows with high density gradients. In a previous paper (Greenshields & Reese, 2007), we found these modifications gave good predictions of the viscous structure of shock waves in argon in the range Mach 1.0-12.0 (while conventional Navier-Stokes equations are known to fail above about Mach 2). However, some areas of concern with this model were a somewhat arbitrary choice of modelling coefficient, and potentially unphysical and unstable solutions. In this paper, we therefore present slightly different modifications to include molecule mass diffusion fully in the Navier-Stokes equations. These modifications are shown to be stable and produce physical solutions to the shock problem of a quality broadly similar to those from the family of extended hydrodynamic models that includes the Burnett equations. The modifications primarily add a diffusion term to the mass conservation equation, so are at least as simple to solve as the Navier-Stokes equations; there are none of the numerical implementation problems of conventional extended hydrodynamics models, particularly in respect of boundary conditions. We recommend further investigation and testing on a number of different benchmark non-equilibrium flow cases.

KW - fluid dynamics

KW - aerospace

KW - structures

KW - composites

KW - design engineering

UR - http://arxiv.org/abs/0706.0141

M3 - Conference contribution book

BT - 2nd European Conference on Aero-Space Sciences (EUCASS)

ER -