TA5: Shock control bump optimization on a transonic laminar flow airfoil
Reducing aircraft drag has a huge impact on reducing aviation emission, therefore, for greener air transport. Shock control bumps are effective in reducing the wave drag, a component of the total drag, at high subsonic or transonic speed range.
The challenges are: (1) to assure good accuracy of aerodynamic force calculation; (2) to assure high quality and consistant meshes for all the designs; (3) to find the global optimum.
The Navier-Stokes equations are to be solved and there are a large number of flow solvers. Comparison of the solution for the original airfoil flow forms a good starting point.
Drag reduction for transonic wings is crucial for the aeronautical industry, for control of aviation emission and operational efficiency.
Shock control bumps were found to be effective in reducing the wave drag and the total drag if installed on transonic airfoils or wings. However, their effectiveness relies on the position, height, and size of the bumps. In this test case, we will look into the optimal design parameters for a given laminar flow airfoil, i.e. RAE5243 airfoil, at the design Mach number and Reynolds number. It will be divided into two cases: (1) fully turbulent flow; (2) fixed transition at 45%c. The optimization will be constrained by the given lift condition.
Navier-Stokes flow solver with turbulence modelling
Optimization method with lift constraint
Figures 1 and 2 below show the airfoil, the bump and its parameterisation. The computational domain is suggested to be 20 chord length away from the airfoil in all directions.
Air as perfect gas
Laminar or turbulent flow (fixed transition)
| Aerofoil | $M_\infty$ | $\textrm{Re}_{c,\infty}$ | $C_l$ | Flow condition |
|---|---|---|---|---|
| RAE5243 | 0.68 | $19 \times 10^6$ | 0.82 | Fully turbulent |
| RAE5243 | 0.68 | $19 \times 10^6$ | 0.82 | 45% transition |
Steady state solution
No-slip boundary condition at wall and far field boundary condition
Fully turbulent or fixed transition
Minimum total drag Min $ C_d $ for given $ C_l $
Bump height, position, length and crest position
Bounds of design parameters:
Bump crest position
$ 0 < X_{cre} / C < 1 $
Bump starting point to crest
$ 0 < X_{bumprelative} / C < X_{bumplength} / C $
Bump total length
$ 0 < X_{bumplength} / C < 0.4 $
Bump height
$ 0 < \Delta Y_{h} / C < 0.05 $
Total drag of the airfoil $ C_{d} = C_{d, pressure} + C_{d,friction} $
Results for datum airfoil:
Lift curve, drag polar and flowfield at the given $C_{l} $
Results for optimized airfoil:
Bump shape and position parameters
Lift, drag (both components) and pitching moment at the design condition
Lift curve and drag polar for a range of lift around the design point
Data to be stored requested from Analysis
Flow field data