Shock-Vortex Interactions In Transonic Flow Over A Delta Wing Aircraft

The Delta wing forms a critical component in various applications involving high-speed flight over subsonic, transonic and supersonic regimes. Vortex breakdown in the delta wing is accompanied by a sudden change in the pressure distribution and has a detrimental effect on the aerodynamic characteristics, such as lift distribution and stall. In particular, transonic flow conditions in delta wings at a moderately high Angle of Attack (AoA) give rise to complex interactions between shock waves and the leading-edge vortex system. The appearance of shock waves, caused by the localised supersonic flow regions over the wing, further complicates the flow structures.

This work investigates the transonic flow over a 650 swept-back delta wing with a sharp leading edge. To study the onset of the vortex breakdown on the wing in the presence of shocks, we carried out simulations at AoA of 23.60. The high-fidelity simulations are carried out using the higher order Entropic Lattice Boltzmann Method (ELBM) for transonic flows, developed at SankhyaSutra Labs (SSL).

The computational domain used in the simulations is 15Cr x 6Cr x 6Cr, where Cr is the root chord of the wing measuring 65.364 cm. In order to reduce the computational resources needed, the simulations are performed with a symmetry boundary condition along the longitudinal plane. The no-slip boundary condition is applied over the surface of the delta wing. A Mach number of 0.85 (transonic flow) is chosen along with a Reynolds number of 6 × 106, calculated based on the mean aerodynamic chord of 43.576 cm.

Streamlines coloured by Mach number capturing the vortical flow and localised supersonic regions over the delta wing;
Figure 1(a) Streamlines coloured by Mach number capturing the vortical flow and localised supersonic regions over the delta wing;
Coefficient of pressure distribution compared against experimental data at AoA = 23.6o
Figure 1(b) Coefficient of pressure distribution compared against experimental data at AoA = 23.6o
The simulation results are compared against the experimental database from Langley National Transonic Facility (NTF). Qualitative and quantitative comparisons are made with experimental data to understand the phenomenon of shock-vortex interactions with the ELBM solver. The sharp leading edge and the slender body cause the flow to separate early, which leads to a primary vortex that dominates the upper surface of the wing. This primary vortex can be observed from the streamlines plotted in Figure 1(a). The streamlines in blue show the low-velocity vortical structures at the sharp leading edge. Supersonic structures are shown at the core of the primary vortex. Simulation results are validated by comparing the pressure distribution with experimental data. Figure 1(b) shows the pressure distribution at selected chord wise locations over the wing. These locations are taken in accordance with the experimental data. Simulations show a good match in the suction peak close to the apex of the wing, i.e. x/Cr = 0.2. Although values further downstream exhibit slight under-prediction, overall pressure distribution matches well when compared with the experiments. The pressure distribution along the leading edge denoted by the corresponding root chord location is plotted in Figure 2. These leading edge suction pressure values, which are a subset of Figure 1(b), agree well with the reference data.
Coefficient of pressure on upper surface near leading edge along root chord
Figure 2 Coefficient of pressure on upper surface near leading edge along root chord

One of the major challenges with existing CFD solvers is the ability to detect secondary vortex and cross flow shock over the delta wing in transonic flow conditions. Though this phenomenon is well established experimentally, capturing the same in simulations has been a challenge. The solver from SankhyaSutra Labs has not only successfully captured the pressure losses, secondary vortex structures and the presence of terminating and cross-flow shocks over the wing platform, but has also demonstrated a good match with experimental data.

Further Reading: Milind D et. al., Transonic flow over Delta Wing using Entropic Lattice Boltzmann Method, 33rd Congress of the International Council of the Aeronautical Science, Sweden, 2022

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