# Multipoint inverse airfoil design method based on conformal mapping

Michael S. Selig, Mark D. Maughmer

Research output: Contribution to journalArticle

86 Citations (Scopus)

### Abstract

A method of multipoint inverse airfoil design for incompressible potential flow is presented. Multipoint design is handled by dividing the airfoil into a number of desired segments. For each segment, the velocity distribution is prescribed together with an angle of attack at which the prescribed velocity distribution is to be achieved. In this manner, multipoint design objectives can be taken into account in the initial specification of the velocity distribution. In order for the multipoint inverse airfoil design problem to be well posed, three integral constraints and several conditions arise that must be satisfied. Further restrictions are imposed if the airfoil is to have a specified pitching moment, thickness ratio, or other constraints. The system of equations is solved partly as a linear system and partly through multidimensional Newton iteration. Since the velocity distribution is prescribed about the circle in terms of the arc limit, specification of the velocity in terms of arc length is also handled through multidimensional Newton iteration.

Original language English (US) 1162-1170 9 AIAA journal 30 5 https://doi.org/10.2514/3.11046 Published - May 1992

### Fingerprint

Conformal mapping
Velocity distribution
Airfoils
Specifications
Potential flow
Angle of attack
Linear systems

### All Science Journal Classification (ASJC) codes

• Aerospace Engineering

### Cite this

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title = "Multipoint inverse airfoil design method based on conformal mapping",
abstract = "A method of multipoint inverse airfoil design for incompressible potential flow is presented. Multipoint design is handled by dividing the airfoil into a number of desired segments. For each segment, the velocity distribution is prescribed together with an angle of attack at which the prescribed velocity distribution is to be achieved. In this manner, multipoint design objectives can be taken into account in the initial specification of the velocity distribution. In order for the multipoint inverse airfoil design problem to be well posed, three integral constraints and several conditions arise that must be satisfied. Further restrictions are imposed if the airfoil is to have a specified pitching moment, thickness ratio, or other constraints. The system of equations is solved partly as a linear system and partly through multidimensional Newton iteration. Since the velocity distribution is prescribed about the circle in terms of the arc limit, specification of the velocity in terms of arc length is also handled through multidimensional Newton iteration.",
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In: AIAA journal, Vol. 30, No. 5, 05.1992, p. 1162-1170.

Research output: Contribution to journalArticle

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T1 - Multipoint inverse airfoil design method based on conformal mapping

AU - Selig, Michael S.

AU - Maughmer, Mark D.

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N2 - A method of multipoint inverse airfoil design for incompressible potential flow is presented. Multipoint design is handled by dividing the airfoil into a number of desired segments. For each segment, the velocity distribution is prescribed together with an angle of attack at which the prescribed velocity distribution is to be achieved. In this manner, multipoint design objectives can be taken into account in the initial specification of the velocity distribution. In order for the multipoint inverse airfoil design problem to be well posed, three integral constraints and several conditions arise that must be satisfied. Further restrictions are imposed if the airfoil is to have a specified pitching moment, thickness ratio, or other constraints. The system of equations is solved partly as a linear system and partly through multidimensional Newton iteration. Since the velocity distribution is prescribed about the circle in terms of the arc limit, specification of the velocity in terms of arc length is also handled through multidimensional Newton iteration.

AB - A method of multipoint inverse airfoil design for incompressible potential flow is presented. Multipoint design is handled by dividing the airfoil into a number of desired segments. For each segment, the velocity distribution is prescribed together with an angle of attack at which the prescribed velocity distribution is to be achieved. In this manner, multipoint design objectives can be taken into account in the initial specification of the velocity distribution. In order for the multipoint inverse airfoil design problem to be well posed, three integral constraints and several conditions arise that must be satisfied. Further restrictions are imposed if the airfoil is to have a specified pitching moment, thickness ratio, or other constraints. The system of equations is solved partly as a linear system and partly through multidimensional Newton iteration. Since the velocity distribution is prescribed about the circle in terms of the arc limit, specification of the velocity in terms of arc length is also handled through multidimensional Newton iteration.

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