Design of low-speed slotted, natural-laminar-flow airfoil reproducing transonic behaviors

Airfoils tested at low speeds generally produce surface pressure distributions that differ substantially from those measured at transonic conditions, which in turn results in very different boundary-layer characteristics even for the same Reynolds number. A methodology is presented for mapping transonic pressure gradients to an equivalent low-speed airfoil. It is applied to the design of a low-speed, slotted, natural-laminar-flow (SNLF) airfoil intended to emulate the pressure gradients of a SNLF airfoil designed for a transonic commercial transport with a Reynolds number of 13.2 million. The on-design cruise operating condition of the original airfoil was chosen as the reference condition; however, the design lift coefficient of the new airfoil was lowered to account for both compressibility effects and suitability for low-speed wind-tunnel testing. The overall design process mirrors the development of the transonic airfoil by beginning with a single-element airfoil and then modifying it to include an aft element. An inverse design method based on conformal mapping was developed and employed to determine the necessary geometry of the low-speed single-element airfoil. Analysis of the new SNLF airfoil confirms that the design objectives were met, and the airfoil is found to be well behaved down to a Reynolds number of 1 million.