Wings using NACA four digit profiles are examples of foils with significative internal volume, where sectional method have normally a fast convergence. It will be used two NACA four digit foils in this Section. The first one, the NACA 0012 with aspect ratio
AR = 3.0 foil, will be analysed with the sectional method. Boundary layer variables
will be evaluated at the midspan section with the purpose of showing the numerical behaviour of boundary layer with free transition condition, and compare it qualitatively to the observations of Gad-el-Hak [1].
The second foil is the NACA 0020 foil with AR = 1.5, where sectional method,
Inviscid, RANS solution and experimental method can be compared in terms of lift and total drag.
7.1.1 The NACA 0012 foil
It was discussed in the previous Chapter that on NACA 0012 foils, apart from tip region, convergence is reached in an average of 7 iterations, using 20 sections and 160 nodes on each section, with the same panel mesh used in Chapter 6. The flow characteristics for NACA 0012 foil are listed in Table 7.1.
Aspect Ratio 3.0
Re∞ 6.0·105
˜
ncrit 9.0
Range ofα 0 to 10o
Table 7.1: Characteristics of NACA 0012 foil problem It was used a free transition condition with its limit at 90% c.
7.1.1.1 Varying the Angle of Incidence of the foil
The increase in the angle of incidence, according to Gad-el-Hak [1] and Drela and Giles [35], makes laminar flow to be increasingly more unstable. Then numerically, the increase in incidence angle should contribute to an earlier transition to turbulence.
The objective of the following numerical analysis is to show qualitatively, by means of graphics obtained from VIX analysis, that the increase in the angle of incidence will move the transition upstream, meaning an earlier transition. The transition point can be identified at the maximum of H shape parameter distribution.
Figure 7.1 shows H shape parameter distribution on the upper surface at midspan section, for three different angles: zero, 5oand 10o. The distribution presents a contin- uous curve, starting with a small oscillation near leading edge and increasing smoothly to a peak where transition happens. After the peak,Hdecreases smoothly to turbulent values, increasing later, near the trailing edge.
Figure 7.1: H shape parameter behaviour for different angles of incidence on a NACA 0012 foil
In this work, regions with H >2.5 are considered separated flow regions. Table 7.2 shows α and the point of transition, taken at the maximumH.
In Figure 7.1, the transition peak moves upstream with the increase in the angle of incidence. The peak also increases in height and decreases in width. H also an increases near the trailing edge when the incidence angle is increased.
With peaks becoming progressively narrower and higher as α increases, there is a trend to a discontinuous peak if α is large. In a limiting inclination, the appearance of a discontinuous and sharp peak can be understood as a stall.
α Average Upper degrees Transition (%c) 0 75 2 63 3 58 5 45 7 34 9 25 10 21
Table 7.2: Variation of transition and frictional force
7.1.1.2 Variation of Critical Amplification Ratio
According to Drela and Youngreen [62], the decrease on the amplification ratio ˜ncrit
has an effect of shortening the laminar length by imposing a lower limit for laminar momentum instability. In this test, using the NACA 0012 mesh at α = 0, it was used the free transition and ˜ncrit was reduced.
Table 7.3 shows the transition point on a chord percentage and the frictional drag coefficient CDf adopting two values for ˜ncrit.
Due to the difficulty to obtain experimental frictional drag data in which ˜ncrit is
controlled, just a qualitative analysis is performed. According to Drela and Youngreen [62], devices to force turbulence such as, turbulators or sand sheets on the leading edge of a wing, have a similar effect of reducing ˜ncrit and, according to Gad-el-Hak [1], it is
expected that frictional drag will increase.
Average ˜
ncrit Transition (% c) CDf
4.0 64 5.999·10−3
9.0 80 4.657·10−3
Table 7.3: Flow characteristics varying amplification ratio
Figure 7.2 shows the comparison ofH shape parameter using ˜ncrit= 4.0 and ˜ncrit=
9.0. In Figure 7.2 H peak is reduced and transition is moved upstream when using a lower amplification ratio. In this case, CDf increases, as shown in Table 7.3, because
transition length is shortened and separation bubble is reduced or, in some cases, eliminated due to the higher momentum of flow when ˜ncrit is decreased.
7.1.2 NACA 0020 Rudder
A NACA 0020 rudder of AR = 1.5 was investigated in order to compare with data
from the work of Turnock and Wright [72]. The rudder model is shown in Figure 7.3. In the work [72], authors used a coupled and uncoupled inviscid panel method, the PALISUPAN, to a finite element method (FEA) to analyse flow on a rudder. RANS analysis, uncoupled to the structural model was also done by the authors [72] and it is shown in Figures 7.4 and 7.5.
Figure 7.2: H shape parameter varying ˜ncrit on a NACA 0012 foil at zero angle of incidence
At rudder’s root, it was imposed a reflection condition in order to simulate wind tunnel wall. The VIX analysis was run using Re∞ = 1.0·106; ˜ncrit = 9.0 and a free
transition condition with xtr = 90% c. Figures 7.4 and 7.5 show lift and drag for the
rudder model compared to experimental results. Just data from the uncoupled model presented by Turnock and Wright [72] was considered.
At 12.5 degrees, VIX viscous flow did not converge so it is shown the underconverged data at the twentieth iteration.