Abstract:

VGK is a CFD (computational fluid dynamics) method for predicting the aerodynamic characteristics of a two-dimensional single-element aerofoils in a subsonic and high-transonic freestream, including the effects of viscosity (boundary layers and wake) and shock waves.

The ESDU VGK Toolbox app is a web-based interface to this VGK code that requires no downloading or local installing of software and is designed to be easy to use and to give instant results.

The app provides a simple interface that enables users to specify an aerofoil and flow characteristics (for inviscid and viscous flow). The pressure coefficient C_p vs non-dimensional chordwise coordinate ξ graph for that aerofoil under those flow conditions is calculated and presented, along with numerous other graphs and tables.

The calculation can further be configured for multiple Mach numbers or multiple angles of incidence.

VGK uses an iterative approach to solve coupled finite-difference equations for the inviscid flow region (assumed to be potential) and the viscous flow region represented by integral boundary-layer equations. The aerofoil boundary-layers must be attached for VGK to produce results that correspond to the real flow.

The original command-line VGK code is also available (see ESDU 96029 and other Data Items from the Transonic Aerodynamics Series, Section 6b), however you are recommended to use the ESDU VGK Toolbox for most common circumstances, particularly those in which repetitive calculations are to be performed, for example optimisation studies.

ESDU 96028 describes the main features of the original VGK method, including the inviscid and viscous flow elements, the computational grids, and the solution process. The performance of VGK, in terms of the accuracy of its results, is considered both for inviscid flows, where comparisons with other theoretical methods are given, and for viscous flows, where comparisons with experiment are presented. For flows where the aerofoil boundary layer is attached and with any shock waves present being typical of transonic aerofoil design conditions, the performance of VGK is good, with drag coefficient being well predicted.

Because of its good performance, VGK can be utilised effectively to investigate a number of factors, such as: the influence of aerofoil geometry (profile and camber) changes on aerofoil characteristics at and around cruise conditions; the influence of changes in Mach number, Reynolds number and transition locations on aerofoil characteristics; the influence of deflection through small angles of leading- and/or trailing-edge flaps; the influence of over-fixing transition in wind-tunnel tests on aerofoils.