INTRODUCTION VGK is a CFD (computational fluid dynamics) method coded in Fortran for predicting the aerodynamic characteristics of a two-dimensional single-element aerofoil?? in a subsonic freestream@ including the effects of viscosity (boundary layers and wake) and shock waves. VGK uses an iterative approach to solve coupled finite-difference equations for the inviscid flow region and the viscous flow region (represented by integral equations). The aerofoil boundary-layers must be attached for VGK to produce results that correspond to the real flow@ but the code has been calibrated against experimental data to provide a method of estimating a separation boundary - see Ref. 2 and Part 3. VGK was developed over a period of years at RAE (now DERA@ Farnborough)@ and is made available by ESDU International plc under the terms of an agreement with DERA?. Crown copyright is retained in the VGK source code. The Data Items dealing with VGK@ of which this is the first@ are: Part 1: Principles and results@ Part 2: User manual for operation with MS-DOS and UNIX systems@ Part 3: Estimation of a separation boundary in transonic flow@ Part 4: Use of VGK to calculate excrescence drag magnification (to be issued)@ Part 5: User manual for ESDUview variant (to be issued). VGK can be used to determine inviscid as well as viscous flows. For viscous cases it is necessary to specify the locations of boundary-layer transition- see Section 4 for guidance on this. The main features of VGK are described in Section 3@ including the inviscid and viscous flow elements@ the computational grids@ and the solution process. Drag determination is given particular consideration in Section 3.4. The precise forms of finite-difference scheme and iteration procedure employed in a particular VGK 'run' are governed by a number of parameters@ which are listed in Section 3.3. The values of these parameters may be selected by the user. Default values for these parameters are given@ together with comments on the effects on VGK results of variations from these values. The performance of VGK@ in terms of the accuracy of its results@ is considered in Section 5 for inviscid flows@ where comparisons with other theoretical methods are given@ and in Section 6 for viscous flows@ where comparisons with experiment are presented. For flows where the aerofoil boundary-layer is attached and any shock waves present are relatively weak (which thus include most aerofoil design conditions) the performance of VGK is good@ with drag coefficient being well predicted. Where the boundary-layer is locally separated or close to separation@ VGK can still give a valuable indication of the flow parameters@ but its accuracy is then not as good. In References 2 and 22 calculations utilising an early version of the VGK code are presented. When such calculations are repeated with the current version of VGK slightly different results are obtained@ due to minor changes in the code that have been incorporated over a period of years. However@ repeat calculations that have been carried out have revealed no differences of any significance. Because of its good performance@ VGK can be utilised effectively to investigate a number of factors@ such as: (a) The influence of aerofoil geometry changes (profile and camber changes) on aerofoil characteristics at and around cruise conditions. (b) The influence of changes in Mach number@ Reynolds number and transition locations on aerofoil characteristics. (c) The influence of deflection through small angles of leading- and/or trailing-edge controls. (d) The influence of over-fixing transition in wind-tunnel tests on aerofoils. ?? This does not entirely preclude its use for aerofoils with deflected controls@ see Section 6 (item (c)) and Section 6.3. ? VGK has been extended (as BVGK) to deal additionally with the effects of low Reynolds numbers and with boundary-layers with (small) regions of separation (Ref. 1)@ see Section 6.
ESDU 96028 A-1997 history
1997ESDU 96028 A-1997 VGK METHOD FOR TWO-DIMENSIONAL AEROFOIL SECTIONS PART 1: PRINCIPLES AND RESULTS