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.