Trans RINA, Vol 157, Part A3, Intl J Maritime Eng, Jul-Sep 2015
5. COMPARISON OF TEST RESULTS WITH AEROFOIL THEORY AND DATA
5.1. STATIC TESTS
From the measured forces during the T-Foil model tests in the water tunnel, lift coefficients and drag coefficients in the static tests were investigated. Equations 5 and 6 were used to calculate the lift coefficients and drag coefficients respectively:
(5) (6)
Figures 14 and 15 show the magnitude of lift coefficients and drag coefficients of the T-Foil obtained from the static tests at various water flow velocities. In addition, the lift-to-drag ratio is plotted for different angles of attack in Figure 16.
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8
V=1.82 m/s V=2.30 m/s V=2.70 m/s
close to linear to calculate an average model T-Foil lift-
coefficient derivative ( over the incidence range ±15
degrees. This slope was found to be CLα = 2.45 per radian and was considered appropriate to calculate a quasi-static lift coefficient for the dynamic tests as the basis of comparison with measured dynamic lift coefficients.
It is known that the lift curve slope reduces as aspect ratio reduces. This is due to the downwash produced, which reduces the effective angle of attack of the foil. Glauert [19] has investigated the effect of aspect ratio on the slope of the lift curve for both elliptic and rectangular aerofoils. Although the T-Foil used here is not neither elliptic nor rectangular in
planform, the foil is approximately
-15 -12 -9 -6 -3 0 3 6 9 12 15 T-Foil angle of attack, α (º)
Figure 14: T-Foil static lift coefficient at different angles of attack and various water flow velocities.
0.06 0.08 0.10 0.12 0.14 0.16
V=1.82 m/s V=2.30 m/s V=2.70 m/s
intermediate in geometry between elliptic and rectangular planforms. Further, the results obtained using Glauert’s equations for aspect ratio of AR = 3.6 varied only slightly, being 3.89 per radian for the rectangular planform and 4.04 per radian for the elliptic planform on the basis of a two dimensional section lift curve slope of 2π per radian. We also note that Ol et al. [14] measured a two dimensional lift curve slope very close to 2π per radian at a Reynolds number of 60,000, significantly less than the Reynolds number of the T-foil tested here which was 105,305 based on the average chord. We therefore can expect that the present T-foil two dimensional section would also have a lift curve slope close to 2π per radian. The possible causes of the rather lower three dimensional CLα = 2.45 per radian measured on the model T-foil are the presence of the T-Foil strut, which obstructs the upper surface, the hinge mount which penetrates the foil to the lower surface and the precise design of the T-foil outboard ends which are approximately rectangular and smoothly contoured. The T-Foil strut in particular may be the cause of asymmetry of the lift curve for positive and negative angles of attack.
-5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0
-15 -12
V=1.82 m/s V=2.30 m/s V=2.70 m/s
-9
-6
-3 0369 12 T-Foil angle of attack, α (º)
-15 -12 -9 -6 -3 0 3 6 9 12 15 T-Foil angle of attack, α (º)
Figure 15: T-Foil static drag coefficient at different angles of attack and various water flow velocities.
As can be seen in Figure 14, the relationship between lift coefficient and angle of attack is not exactly linear. However, the relationship was considered sufficiently
Figure 16: T-Foil lift-to-drag ratio at different angles of attack and various water flow velocities.
5.2. DYNAMIC TESTS The quasi-static lift coefficient was calculated by
multiplying the T-Foil lift-coefficient derivative (
with the measured angles of attack. Figure 17 shows a sample comparison between quasi-static lift coefficient
15
A-180
©2015: The Royals Institution of Naval Architects
Static drag coefficient, CD
Static lift coefficient, CL
Lift-to-drag ratio, L/D
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