An inverse design method based on conformal mapping was developed and employed to determine the necessary geometry of the low-speed single-element airfoil. 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. 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. 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. A methodology is presented for mapping transonic pressure gradients to an equivalent low-speed airfoil. 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.
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