Acceso y permanencia

NACA 0012 was chosen for the various tail rotor blades defined later in this work, which were developed from the baseline NACA0012 blade of the WHL model tail rotor. HMB predictions for the NACA 0012 are here validated against ARA wind tunnel test data and compared to MSES at a Mach number of 0.5, and a Reynolds number of 5 million (the effect of Reynolds number is covered in the following sub-subsection).

In contrast to the above comparisons where the data was from low-turbulence tunnels, the ARA 2D-transonic tunnel148_{is thought to have a moderate amount turbulence, but for many years the (steady and unsteady ramp}

and oscillatory pitch) data obtained has been taken to be representative of practical helicopter aerofoil sections, Wilby.318 _{Since the ARA tunnel is pressurised (up to 3 atmospheres), this data has the advantage that the}

Reynolds number is usually close to that of a typical full-size rotor blade (nominally Re=10 x M x 106_{, and}

in addition some limited data is also available at reduced pressure ratios, and hence lower Reynolds numbers, over the same range of Mach numbers, 0.3-0.85, for application to tail rotors.

The validations for NACA 0012 presented here have therefore been carried out at M=0.5, Re=5.0 million and 2.2 million, and an HMB case for Re=1 million has been included to highlight the trend with Reynolds

3.1 Aerofoils 3 VALIDATION

Figure 108: Comparison of HMB Predictions and Test Data: CM vs INCIDENCE

number. This Reynolds number is also of interest for the Navier-Stokes hover computations (presented later in this thesis), for a blade-section with chord based on the WHL model rotor, while M=0.5 relates to about 83%R and a tip Mach number of 0.6.

As for the above NACA 23012 validation, several turbulence models were used, including the modified k-ω

model which had been well tested for HMB Navier-Stokes hover cases due to its robustness. 5 _{A range of}

Ncrit (2.0, 0.5 and 0.1) was used for the MSES aerofoil analysis code to facilitate comparison with the HMB fully-turbulent model predictions and also to represent the effects of turbulence of the ARA tunnel (based WHL experience, see also Drela’s Turbulence-Ncrit graph in the MSES documentation98_).

The grid size used for these 2D aerofoil computations totalled 96,390 points, 291 around the aerofoil, 81 normal and 151 in the wake, the distance to the farfield boundary was 15 chords around the aerofoil and 20 chords downstream and the first cell height was set to 1 x 10−5_{to obtain a y+ value near unity.}

The following Figures present comparisons for NACA 0012 at a Reynolds number of 5 million. Figure 109 compares the CL-alpha curve for HMB predictions with the 3 turbulence models, as described above, with MSES predictions and the ARA test data. NACA 0012 was computed here with the standard finite thickness trailing edge to be compatible with the tests. Generally there is good agreement for the lift-curve slope, although on close examination, MSES shows the steepest slope, while HMB lies nearer to the test data, which has the lowest slope, with little difference whether transition free or fixed (with .0021”-.0025” balantini balls at 7% chord). As the stall is approached the lift-curve flattens at the Mach number and the lift does not break. Both MSES and HMB with the k-ω (3000) model capture the maximum lift, but all the predictions show a reduction in CL post-stall. While the data is thought to be reliable, the values must represent the mean of a signal with some unsteadiness and the stall pattern in the wind tunnel would be influenced by roof (vented to a plenum chamber) and wall effects, and perhaps even the formation of stall cells, in contrast to the purely 2D simulations.

5

Recently, main rotor hover cases have been run by the author at AW(Yeovil) using the range of HMB k-ω_{models, and the}

3.1 Aerofoils 3 VALIDATION

Figure 109: Predicted lift-curve for NACA 0012 at M=0.5 and Re=5.0 million together with ARA test data

While the 3000 turbulence model gives the highest CLmax, the 3007 and 3002 models are in close agreement with the MSES predictions with fairly low Ncrit, with the later turbulence model perhaps giving pessimistic results.

Figure 110 compares the drag. As found previously, the standard k-ω (3000) model tends to over-predict, while the modified model and SST k-ω models are in excellent agreement with the test data. MSES tends to under-estimate the drag, but both predictions cpature the drag divergence trend quite well. Figure 110 also shows the skin friction component of drag (obtained from the HMB .intv file, and from MSES), and this data is plotted on large scales in Figure 111 where it can be seen that the results from HMB straddle the skin friction values from MSES. The sst model (3007) is in close agreement with MSES with Ncrit=2.0. 6 As expected the skin friction drag gradually decreases with incidence while the pressure drag increases, slowly at first, but then diverges as the stall develops with increasing incidence, Figure 112. In terms of pressure drag the HMB estimates are slightly greater than those produced by MSES.7

Comparisons of predictions and test data for the pitching moment of NACA 0012 at M=0.5 and Re=5 million are shown in Figure 113. The moment increases strongly with incidence due to the formation of a shock on the upper surface near the leading edge. This trend tends to be over-predicted both MSES and HMB, although the moment break occurs at a similar incidence to the test, and shows a downward trend in the region of 12 degrees.

Figure 110 compares the MSES and HMB predictions for total drag and skin friction drag, both with the ARA test data, and with points obtained for the drag coefficient of the rotor blade as described above. While the steady drag test data at the higher Reynolds number lies close to the MSES predictions, the 3002 or 3007 turbulence model of HMB may be considered to provide a good estimate of the drag at a Reynolds number of 1 million. The solid points from the measured drag coefficients coincide with the 2D trends, giving confidence in the overall approach. Figure 111 shows the skin friction drag on an expanded scale, confirming good agreement between HMB and MSES, and Figure 112 shows the trends for the pressure drag to be similar for both sets of predictions, and with the residual pressure drag (obtained from the total minus the skin friction) showing similar drag divergence trends.

Finally, the predictions and test data are compared in terms of a CL-CD polar in Figure 114, and the HMB results are seen to be in excellent agreement with the test data, particularly for the modified and sst k-ωmodels

6

A value of Ncrit=2 was identified as matching the onset of transition from flow visualisation tests carried out by the author in the WHL wind tunnel in 1997.

7

While the static pressures measured on the surface of the wind tunnel model may be integrated to give an estimate of the pressure drag, the sparcity of data is generally considered to limit the accuracy of the integration, even with 39 tappings. While this topic has not been pursued further here, separate fitting of the skin friction and pressure drag has been used in methods developed at WHL by Beddoes30

3.1 Aerofoils 3 VALIDATION

Figure 110: Profile drag coefficient predicted from MSES and HMB compared to blade profile drag coefficient from Navier-Stokes hovering rotor simulations

Figure 111: Skin Friction drag predicted from MSES and HMB on expanded scale compared to blade skin- friction drag coefficient from Navier-Stokes hovering rotor simulations

3.1 Aerofoils 3 VALIDATION

Figure 112: Pressure drag predictions from HMB and MSES compared to ARA test data for NACA 0012 at M=0.5 and Re=5 million

Figure 113: Pitching Moment predictions from HMB and MSES compared to ARA test data for NACA 0012 at M=0.5 and Re=5 million

3.1 Aerofoils 3 VALIDATION

Figure 114: Lift-Drag Polar predictions from HMB and MSES compared to ARA test data for NACA 0012 at M=0.5 and Re=5 million

(3002 and 3007). As might be expected the MSES predictions tend to over-estimate the CL/CD at the top end of the drag bucket, while they also show good agreement at low lift.