Airfoil Chord Length Research Articles

Erratum: “Experiment of a Shockless Transonic Airfoil Partially Modified from an Arbitrary Airfoil”

An experiment is carried out on a transonic flow over an airfoil, which is partially modified from an arbitrary airfoil. The modification is made to satisfy the shockless condition predicted by the same author [Jour. Japan Soc. Aero. Space Sci. 26 (1978) 191]. Static pressures are measured at 88 points on the airfoil surface, when the Mach number at wind tunnel wall is 0.5∼0.8, the measuring angle of attack is 0°∼4° and the Reynolds number is 4.0∼4.6×10 6 . A shockless transonic flow is observed under a measuring condition close to the design condition. The supersonic region extends from 0.4% to 63% of airfoil chord length and the local maximum Mach number is 1.36. The results support that shockless airfoils can be designed by partial modifications of an arbitrary airfoil.

Experiment of a Shockless Transonic Airfoil Partially Modified from an Arbitrary Airfoil

An experiment is carried out on a transonic flow over an airfoil, which is partially modified from an arbitrary airfoil. The modification is made to satisfy the shockless condition predicted by the same author [Jour. Japan Soc. Aero. Space Sci. 26 (1978) 191]. Static pressures are measured at 88 points on the airfoil surface, when the Mach number at wind tunnel wall is 0.5∼0.8, the measuring angle of attack is 0°∼4° and the Reynolds number is 4.0∼4.6×10 6 . A shockless transonic flow is observed under a measuring condition close to the design condition. The supersonic region extends from 0.4% to 63% of airfoil chord length and the local maximum Mach number is 1.36. The results support that shockless airfoils can be designed by partial modifications of an arbitrary airfoil.

The discrepancy between the measured sound field of an oscillating solid and that predicted from the Kirchhoff formulation

Considerable discussion was evoked at the Miami meeting by T. F. Brooks' report [J. Acoust. Soc. Am. 62, S33(A)(1977) and NASA TP‐1048 (Dec. 1977)] that, for carefully performed experiments on sound radiation from a rotationally oscillating (peak angular displacement α) airfoil shaped solid, the Kirchhoff integral over surface pressures and accelerations consistently overpredict SPL's at moderate distances by 2–5 dB. The present paper gives quantitative development of explanation proposed at that time by J. E. Brooks and independently by the author. SPL data at 2.2 m radius from the airfoil (chord length 2b = 0.46 m) at f = 301 Hz (α = 82.1 and 259.3 μrad) and at f = 447 Hz (α = 30.8 and 97.6 μrad), respectively, suggest pattern can be regarded as a dipole‐quadrupole field superposition. Surface pressure amplitudes divided by f2α are nearly independent of f and α, so, even though kb is not extremely small, multipole concepts and matched asymptotic expansion formulation are applicable. Dipole moment vector [proportional to ∫pndS] would be identically zero were airfoil an elliptic cylinder, but is merely “small” for the actual experimental airfoil. Although accuracy of p measured at any one surface point is probably within 10%, p changes sign from leading to trailing edge and |∫pndS1| over top or bottom surface is less than 15% of corresponding ∫|p|dS1. The expected value of the experimentally derived [∫pndS]2 exceeds its error‐free value by N times the mean‐squared error in individually measured p's (N = 9). Consequently, the expected value of the square of the magnitude of the dipole vector moment calculated from surface measurements of p will be about 2–3 times its error‐free value, which is consistent with the 2–5 dB discrepancy reported by T. F. Brooks.