# Numerical Modeling of Blunt-Body Flows—Problems and Prospects

## Abstract

The problems associated with numerical modeling of blunt-body flows are discussed. An efficient modeling technique should ideally incorporate the interactions between the turbulent boundary layer near the body, the unsteady, highly vortical wake flow behind the body, and the potential-flow regions outside these. The incomplete understanding of vortical unsteady flow fields, in particular, turbulent boundary layers and their separation behavior, will for the foreseeable future preclude accurate modeling; but even coarse modeling methods could serve an important role in establishing cause-and-effect relationships. In particular, one should aim at finding methods which can be used to predict, at least qualitatively, the effect of small local body changes on local flow patterns and on the overall drag. A case is made for flow-field calculation methods based on the vorticity equations. Such methods have proved successful in aeronautical and meteorological applications. The overall drag and lift can be calculated in terms of the vorticity shed into the wake; in particular, the vortex drag associated with longitudinal vortices due to aerodynamic lift can be analyzed.

## Keywords

Turbulent Boundary Layer Vortex Core Separation Line Vortex Sheet Side Force## Notation

- a
vortex core radius

- A, B
0(1) parameters depending on vorticity distribution in vortex core

- D
drag

- L
lift

- n
unit binormal

- r
radius vector

- R
local radius of curvature of a vortex filament

- Re
Reynolds number

- u
velocity vector field

- U
velocity of body

- U
_{t} velocity just outside boundary layer

- v = ∇
_{φ} potential flow field

- Γ
circulation around vortex filament

- ρ
density

- ω=∇×u
vorticity, ω=(ω

_{1}, ω_{2}, ω_{3})

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