INTRODUCTION

This Item is the third in a sequence dealing with the VGK aerofoil method. The Item describes the use of VGK to estimate a separation boundary for two-dimensional aerofoils in transonic flow in terms of lift coefficient and freestream Mach number. The basis of the Item is the method described in Transonic Data Memorandum No. 81020 (Reference 1), and the separation boundary corresponds to conditions on the upper surface of the aerofoil for which the shock strength and the adverse pressure gradient(s) are sufficiently severe for the trailing-edge pressure coefficient, relative to its trend with increasing lift coefficient or Mach number in attached flow, to have decreased by 0.05.

The full description of the underlying principles and limitations of the method, which is essentially based on ‘calibrating' VGK results against experimental data, is given in Reference 1. The present describes only the detailed organisation of the computation involving VGK runs so as to obtain points on the separation boundary in a reliable and efficient way. For a description of the principles and typical results of the VGK method, reference should be made to Part 1 of the sequence of Items (ESDU 96028), whilst details of the various types of VGK runs, the naming convention and functions of various files and the use of the program VGKCON (the VGK ‘control' program) are given in Part 2 (ESDU 96029).

The estimation of a single point on an aerofoil separation boundary requires a number of VGK runs to be performed. These runs constitute a ‘sequence'. The first of such runs would normally relate to a combination of Mach number and incidence at which there were significant positive margins in terms of both the ‘shock-upstream criterion' and the ‘trailing-edge criterion'. These criteria are reproduced from Reference 1 as Figures 1a and 1b, where examples of positive margins are indicated. Successive VGK runs in the sequence are carried out at the same Mach number, with various values of incidence, until two successive VGK runs yield one or other of the margins sufficiently close to zero. (Two successive runs are required so as to ensure that VGK has adequately converged – see Section 4.) The values of Mach number and lift coefficient of the last VGK run in the sequence then constitute the single point on the separation boundary. The sequence of VGK runs is controlled by a Fortran program, SEPCON. This program produces a record of the flow conditions and criterion margins of the VGK runs, and at each stage in the sequence produces the files necessary for the next VGK run. The organisation of the commands to execute the VGK and SEPCON programs in a batch file is described in Section 5. Procedures for obtaining a number of points on an aerofoil separation boundary are also presented.

Estimated separation boundaries obtained using the present method are presented and compared with observed results in Section 6.