# Accession Number:

## ADA231565

# Title:

## On the Goertler Instability in Hypersonic Flows: Sutherland Law Fluids and Real Gas Effects

# Descriptive Note:

## Contractor rept.

# Corporate Author:

## INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

# Personal Author(s):

# Report Date:

## 1990-12-01

# Pagination or Media Count:

## 71.0

# Abstract:

The Goertler vortex instability mechanism in a hypersonic boundary layer on a curved wall is investigated in this paper. The aim is to clarify the precise roles of the effects of boundary layer growth, wall cooling and gas dissociation in the determination of stability properties. First assume that the fluid is an ideal gas with viscosity given by Sutherlands law. When the free stream Mach number M is large, the boundary layer divides into two sublayers a wall layer of OMexp 32 thickness over which the basic state temperature is OM-sq and a temperature adjustment layer of O1 thickness over which basic state temperature decreases monotonically to its free stream value. Goertler vortices which have wavelength comparable with the boundary layer thickness i. e. have local wavenumber of order M exp -32 are referred to as wall modes. Their downstream evolution is governed by a set of parabolic partial differential equations and that they have the usual features of Goertler vortices in incompressible boundary layers. As the local wavenumber increases, the neutral Goertler number decreases and the centre of vortex activity moves towards the temperature adjustment layer. Goertler vortices with wavenumber of order one or larger must be necessarily be trapped in the temperature adjustment layer and it is this mode which is most dangerous. For this mode the leading order term in the Goertler number expansion is independent of the wavelength number and is due to the curvature of the basic state. This term is also the asymptotic limit of the neutral Goertler numbers of the wall mode. To determine the higher order correction terms in the Goertler number expansion, one has to distinguish between two wall curvature cases.

# Descriptors:

- *FREQUENCY
- THICKNESS
- STABILITY
- LAYERS
- GROWTH(GENERAL)
- BOUNDARY LAYER
- VORTICES
- COOLING
- GASES
- CURVATURE
- PRECISION
- EVOLUTION(GENERAL)
- PARABOLAS
- PARTIAL DIFFERENTIAL EQUATIONS
- WALLS
- FLUIDS
- FREE STREAM
- VISCOSITY
- DISSOCIATION
- DETERMINATION
- CORRECTIONS
- INCOMPRESSIBILITY
- BOUNDARY LAYER FLOW
- HYPERSONIC FLOW
- TEMPERATURE

# Subject Categories:

- Fluid Mechanics