ESDU 09015:2010

INTRODUCTION

The general principles, by which aft-fixing of transition can be
used in wind-tunnel testing to simulate flow characteristics* at a
Reynolds number higher than the test value, are described in
Reference 1. As part of that process it is essential to obtain a
good physical understanding of important flow features, such as
shock/boundary-layer interaction, likely flow separations
etc., at the test Reynolds number, full-scale Reynolds
number and any other intermediate Reynolds numbers that are of
interest. Prior to the test programme, this understanding is
obtained by the use of CFD methods and past experience of similar
configurations. It is also important to have a clear understanding
of the test objective(s).

Following Reference 1, a simulation criterion is then selected
that is closely linked to a dominant flow feature and the objective
of the test. For example, where conditions at the shock are of
particular significance, the transition band positions may be
selected to match the shock position at the Reynolds number it is
desired to simulate in the test. Alternatively, a boundary-layer
parameter (e.g. momentum thickness) immediately upstream
of the shock may be chosen. If upper-surface separation near the
trailing edge is of particular significance, then the momentum
thickness at the trailing edge is an appropriate parameter to
choose. Once a suitable criterion has been chosen, forced
transition locations (x_tru and
x_trl) used in low-Reynolds-number tests can be
directly mapped to a higher Reynolds number
(Re_eff) simulated by the use of aft fixing. It
should be noted that it is not possible to satisfy all possible
criteria simultaneously and the degree to which the selected
criterion is satisfied will be a compromise. For example, if shock
position is the chosen criterion, care must be taken to ensure that
accurate matching of this parameter does not result in a serious
mismatch in the boundary-layer condition immediately upstream of
the shock.

Because of these difficulties it is hard to provide a general
"rule-of-thumb" procedure and the purpose of this document is to
illustrate the procedure through the particular example of the F4
wing/body combination at its design condition. It is shown how
suitable simulation criteria may be selected and how upper-surface
and lower-surface transition locations, suitable for a test at low
Reynolds number, may be chosen. Although the framework outlined in
Reference 1 is generally followed, other flow parameters are
examined where it is thought these are useful in developing a sound
understanding of the flow.

In this example the test objective is taken to be the estimation
of drag at the design condition. A real test programme will cover a
range of C_L, rather than being focussed on a
single design point but the detailed analysis at the design point
serves to illustrate the procedure that should be applied over the
range to be tested. However, as outlined in Reference 1, at other
values of C_L, the investigation may lead to the
adoption of different simulation criteria and CFD extrapolation
procedures.

* It is implicit that the simulation represents a flow where
transition on both upper and lower surfaces occurs at or close to
the leading edge, as is usually the case at full scale.