An analysis of aerodynamic forces on a delta wing

The present study aims at relating lift and drag to flow structures around a delta wing of elliptic section. Aerodynamic forces are analysed in terms of fluid elements of non-zero vorticity and density gradient. The flow regime considered is M(infinity) = 0.6 similar to 1.8 and alpha = 5 degrees similar to 19 degrees, where M(infinity) denotes the free-stream Mach number and alpha the angle of attack. Let rho denote the density, u velocity, and omega vorticity. It is found that there are two major source elements R(e)(x) and V-e(x) which contribute about 95% or even more to the aerodynamic forces for all the cases under consideration, Re(x) = -1/2u(2) del rho . del phi and V-e(x) = -rho u x omega . del phi, where phi is an acyclic potential, generated by the delta wing moving with unit velocity in the negative direction of the force (lift or drag). All the physical quantities are non-dimensionalized. Detailed force contributions are analysed in terms of the flow structures and the elements R(e)(x) and V-e(x). The source elements R(e)(x) and V-e(x) are concentrated in the following regions: the boundary layer in front of (below) the delta wing, the primary and secondary vortices over the delta wing, and a region of expansion around the leading edge. It is shown that V-e(x) due to vorticity prevails as the source of forces at relatively low Mach number, M(infinity) < 0.7. Above about M(infinity) = 0.75, R(e)(x) due to compressibility generally becomes the dominating contributor to the lift, while the overall contribution from V,(x) decreases with increasing M(infinity), and even becomes negative at M(infinity) = 1.2 for the lift, and at a higher M(infinity) for the drag. The analysis is carried out with the aid of detailed numerical results by solving the Reynolds-averaged Navier-Stokes equations, which are in close agreement with experiments in comparisons of the surface pressure distributions.