Wind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics

Appendix A NFAC Characteristics

The main characteristics of the NFAC wind tunnel test sections are summarized in Table A . 1 and Table A . 2 .

Table A . 1 40 x 80 Foot Wind Tunnel Characteristics [21] .

40 x 80 Foot Wind Tunnel Width Test Section 24.38 m (80 ft) Height Test Section 12.19 m (40 ft ) Length Test Section 24.38 m (80 ft) Actual Width Test Section 24.08 m (79 ft) Actual Height Test Section 11.89 m (39 ft) Actual Length Test Section 24.38 m (80 ft) Approximate BL Thickness Floor (Start -­‐ End) .25 -­‐ .46 m (10 -­‐ 18 in) Approximate BL Thickness Top (Start -­‐ End) .08 -­‐ .15 m (3 -­‐ 6 in) Approximate BL Thickness Sides (Start -­‐ End) > .25 -­‐ .46 m (> 10 -­‐ 18 in) Maximal Test Section Velocity 154.33 m/s (300 kts) Table A . 2 80 x 120 Foot Wind Tunnel Characteristics [20] .

80 x 120 Foot Wind Tunnel Width Test Section 36.58 m (120 ft ) Height Test Section 24.38 m (80 ft) Length Test Section 36.58 m (120 ft ) Actual Width Test Section 35.97 m (118 ft) Actual Height Test Section 23.93 m (78.5 ft) Actual Length Test Section 36.58 m (120 ft ) Approximate BL Thickness Floor (Start -­‐ End) .76 -­‐ 1.12 m (30 -­‐ 44 in) Maximal Test Section Velocity 51.44 m/s (100 kts) W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning

Appendix B C81 Airfoil Adjustment Code Results

B.1 Angle of Attack and Mach number interpolation

The C81 airfoil files are obtained from experienced XV - 15 researchers [6] . The interpolation for angle of attack and Mach number is performed. Figure B . 1 shows part of the imported data for the 64 - X08 airfoil and the PCHIP interpolation for angles of attack and linear interpolation for Mach numbers.

(b) c vs. α at M = 0.60 [~] for 64-X08 (c) c vs. α at M = 0.40 [~] for 64-X08 (a) c vs. α at M = 0.85 [~] for 64-X08 l d m 0.5 1.8 [~] m [~] [~] 1.6 c l d c c 0.5 1.4 cient, 1.2 cient, cient, ffi ffi 0 ffi 0.8 lift coe 0.6 drag coe -0.5 moment coe 0.4 0.2 -1 -0.5 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 angle of attack, α [deg] angle of attack, α [deg] angle of attack, α [deg] (d) c vs. M at α = 4 [deg] for 64-X08 (e) c vs. M at α = 2 [deg] for 64-X08 (f) c vs. M at α = 6 [deg] for 64-X08 l d m -0.02 0.09 0.75 -0.04 0.08 [-] m [~] c [~] d -0.06 0.07 l c c 0.7 -0.08 0.06 cient, cient, ffi cient, -0.1 ffi 0.05 ffi 0.65 -0.12 0.04 lift coe -0.14 0.03 drag coe 0.6 moment coe -0.16 0.02 C81 data interpolation 0.01 -0.18 0.55 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 Mach number, M [~] Mach number, M [~] Mach number, M [~] Figure B . 1 Imported C81 data for NACA 64 - X08 airfoil.

Similar data is shown in Figure B . 2 , Figure B . 3 and Figure B . 4 for the 64 - X12, 64 - X18 and 64 - X25 airfoils, respectively.

W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning (a) c vs. α at M = 0.85 [~] for 64-X12 (b) c vs. α at M = 0.60 [~] for 64-X12 (c) c vs. α at M = 0.40 [~] for 64-X12 l d m 0.5 1.8 [~] [~] m d c 1.6 c [~] 0.5 l 1.4 c cient, 1.2 cient, ffi ffi 0 cient, 1 ffi 0.8 0.6 drag coe -0.5 lift coe 0.4 moment coe 0.2 -1 -0.5 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 angle of attack, α [deg] angle of attack, α [deg] angle of attack, α [deg] (d) c vs. M at α = 4 [deg] for 64-X12 (e) c vs. M at α = 2 [deg] for 64-X12 (f) c vs. M at α = 6 [deg] for 64-X12 l d m -0.02 0.16 -0.04 0.6 [~] [~] m 0.14 d -0.06 [~] c l c c 0.12 -0.08 0.55 cient, cient, -0.1 0.1 cient, ffi ffi ffi -0.12 0.08 0.5 -0.14 0.06 lift coe -0.16 drag coe 0.04 0.45 moment coe -0.18 C81 data 0.02 interpolation -0.2 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 Mach number, M [~] Mach number, M [~] Mach number, M [~] Figure B . 2 Imported C81 data for NACA 64 - X12 airfoil.

(a) c vs. α at M = 0.71 [~] for 64-X18 (b) c vs. α at M = 0.60 [~] for 64-X18 (c) c vs. α at M = 0.40 [~] for 64-X18 l d m 0.5 1.8 [~] m [~] 1.6 c [~] d l c c 0.5 1.4 cient, 1.2 cient, ffi cient, ffi ffi 1 0.8 lift coe 0.6 drag coe -0.5 moment coe 0.4 0.2 -1 -0.5 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 angle of attack, α [deg] angle of attack, α [deg] angle of attack, α [deg] (d) c vs. M at α = 4 [deg] for 64-X18 (e) c vs. M at α = 2 [deg] for 64-X18 (f) c vs. M at α = 6 [deg] for 64-X18 l d m 0.5 0.05 -0.015 0.45 0.045 [~] -0.02 m [~] 0.4 c [~] d 0.04 -0.025 l c c 0.35 0.035 -0.03 cient, cient, ffi 0.3 cient, -0.035 0.03 ffi ffi -0.04 0.25 0.025 -0.045 0.2 lift coe 0.02 drag coe -0.05 0.15 moment coe 0.015 -0.055 C81 data 0.1 interpolation 0.01 -0.06 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 Mach number, M [~] Mach number, M [~] Mach number, M [~] Figure B . 3 Imported C81 data for NACA 64 - X18 airfoil.

W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning (a) c vs. α at M = 0.75 [~] for 64-X25 (b) c vs. α at M = 0.75 [~] for 64-X25 (c) c vs. α at M = 0.45 [~] for 64-X25 l d m 0.5 1.8 1 [~] m [~] c 1.6 [~] d l c c 1.4 0.5 cient, cient, 1.2 ffi cient, ffi 0 ffi 0.8 lift coe drag coe 0.6 moment coe -0.5 0.4 0.2 -1 -0.5 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 angle of attack, α [deg] angle of attack, α [deg] angle of attack, α [deg] (d) c vs. M at α = 4 [deg] for 64-X25 (e) c vs. M at α = 16 [deg] for 64-X25 (f) c vs. M at α = 14 [deg] for 64-X25 l d m 0.7 -0.08 0.7 -0.1 [~] 0.6 m [~] c d -0.12 [~] 0.6 l c c 0.5 -0.14 cient, 0.5 cient, ffi cient, ffi -0.16 ffi 0.4 0.4 -0.18 lift coe 0.3 0.3 drag coe -0.2 moment coe 0.2 C81 data -0.22 0.2 interpolation -0.24 0.1 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 Mach number, M [~] Mach number, M [~] Mach number, M [~] Figure B . 4 Imported C81 data for NACA 64 - X25 airfoil.

B.2 Representative Stall Delay Plots

Figure B . 5 and Figure B . 6 show the effect of stall delay on the lift curve slope on a set of interp olated airfoil data at various radial stations.

(a) c vs. α at M = 0.50 [~] at r/R = 0.0875 [~] (b) c vs. α at M = 0.60 [~] at r/R = 0.2000 [~] (c) c vs. α at M = 0.71 [~] at r/R = 0.3000 [~] l l l 2 1.5 1.5 1.5 [~] [~] [~] 1 l l l c 0.5 cient, cient, c cient, c 0.5 ffi ffi ffi 0.5 lift coe lift coe lift coe -0.5 -0.5 -0.5 -1 -1 -1 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 angle of attack, α [deg] angle of attack, α [deg] angle of attack, α [deg] (d) c vs. α at M = 0.30 [~] for r/R = 0.5000 [~] (e) c vs. α at M = 0.85 [~] at r/R = 0.9700 [~] (f) c vs. α at M = 0.85 [~] at r/R = 1.0000 [~] l l l 1 1 [~] [~] [~] l l l c c c 0.5 0.5 0.5 cient, cient, cient, ffi ffi ffi lift coe lift coe lift coe Data -0.5 -0.5 -0.5 Data, stall delay PCHIP data PCHIP data, stall delay -1 -1 -1 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 angle of attack, α [deg] angle of attack, α [deg] angle of attack, α [deg] Figure B . 5 Effect of stall delay on lift curve slope.

W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning (a) c vs. M at α = 30 [deg] at r/R = 0.0875 [~] (b) c vs. M at α = 45 [deg] at r/R = 0.2000 [~] (c) c vs. M at α = -2 [deg] at r/R = 0.3000 [~] l l l 1.75 0.02 2.2 1.7 [~] [~] [~] 0.018 l l l c c c 1.65 0.016 cient, cient, cient, 1.8 ffi ffi 1.6 ffi 0.014 1.6 1.55 lift coe lift coe lift coe 0.012 1.5 1.4 1.45 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 Mach number, M [~] Mach number, M [~] Mach number, M [~] (d) c vs. M at α = 0 [deg] at r/R = 0.5000 [~] (e) c vs. M at α = 2 [deg] at r/R = 0.9700 [~] (f) c vs. M at α = 2 [deg] at r/R = 1.0000 [~] l l l 0.4 0.55 Data 0.04 Data, stall delay PCHIP data 0.35 0.02 PCHIP data, stall delay [~] [~] [~] 0.5 l l l c c c 0.3 0.45 cient, cient, cient, ffi ffi ffi -0.02 0.25 0.4 lift coe lift coe lift coe -0.04 0.2 -0.06 0.35 0.15 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 Mach number, M [~] Mach number, M [~] Mach number, M [~] Figure B . 6 Effect of stall delay on lift coefficient for set of airfoil data at various radial stations.

Figure B . 6 d shows the result of the assumption that the zero lift angle of attack is equal to zero. As a result the lift coefficient is slightly lowered at high Mach numbers. While the observed effect is small, future work could eliminate this error from the program.

W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning

Appendix C Steady XV - 15 Rotor Validation Results

All the plots for the steady results are presented in Section 0 .

C.1 Simulation Parameters

Table C . 3 shows a compact overview of the simulation parameters. ND stands for non - dimensionalized, the boundary size is ex pressed as the coordinates of the corners of a rectangular prism. The grid cells indicate the amount of cells on the x,y and z edge of the boundary, respectively. Rotor Grid Ref. and Grid Refinement indicate refinement of cells by multipl ying the amount of cells by a c ertain factor.

Table C . 3 Overview of steady simulation parameters .

Hover Parameters Boundary Conditions & Grid Simulation Variables ( -­‐ 38.1, -­‐ 38.1, -­‐ 68.58) Radius 3.81 m Boundary Size Simulated time 2.5 s (38.1, 38.1, 38.1) Cone angle 2.5 deg Grid cells [#] 30,30,42 Timesteps 3000 Tip speed 225.55 m/s Rotor Box Ref. 1,1 Δ T 2.50E -­‐ 03 Cutout 0.0875 r/R Rotor Grid Ref . 6x Δ X 0.0784 min Grid Refinement ( -­‐ 7.62, -­‐ 7.62, -­‐ 68.58) Solidity 0.081 Iterations 10 Box [m] (7.62, 7.62, 38.1) Power ND 6.41E+08 Grid Refinement 4x Relaxation ( u,v,w,p ) 0.1 Thrust ND 2.84E+06 Volume Ratio Max 8 Flight Condition hover Cells 1,053,948 Rotor Model steady Tilt and Advance Ratio Boundary Conditions & Grid Simulation Variables ( -­‐ 38.1, -­‐ 38.1, -­‐ 68.58) Radius 3.81 m Boundary Size Simulated time 1.25 s (38.1, 38.1, 38.10) Cone angle 2.5 deg Grid cells [#] 30,30,42 Timesteps 1000 Tip speed 221.17 m/s Rotor Box Ref. 1,1 Δ T 2.50E -­‐ 03 Cutout 0.0875 r/R Rotor Grid Ref . 6x Δ X 0.0784 min Grid Refinement ( -­‐ 15.24, -­‐ 7.62, -­‐ 68,58) Solidity 0.081 Iterations 10 Box [m] (7.62, 7.62, 38.10) Power ND 6.05E+08 Grid Refinement 4x Relaxation ( u,v,w,p ) 0.1 Thrust ND 2.73E+06 Volume Ratio Max 8 Flight Condition general Cells 2,029,692 (at 30 degree tilt) Rotor Model steady Airplane Mode Boundary Conditions & Grid Simulation Variables ( -­‐ 38.1, -­‐ 38.1, -­‐ 68.58) Radius 3.81 m Boundary Size Simulated time 1.25 s (38.1, 38.1, 38.10) Cone angle 2.5 deg Grid cells [#] 30,30,42 Timesteps 1000 Tip speed 183.76 m/s Rotor Box Ref. 1,1 Δ T 2.50E -­‐ 03 Cutout 0.0875 r/R Rotor Grid Ref . 6x Δ X 0.0784 min Grid Refinement ( -­‐ 15.24, -­‐ 7.62, -­‐ 68,58) Solidity 0.081 Iterations 10 Box [m] (7.62, 7.62, 38.10) Power ND 3.47E+08 Grid Refinement 4x Relaxation ( u,v,w,p ) 0.1 Thrust ND 1.89E+06 Volume Ratio Max 8 Flight Condition general Cells 1,053,948 Rotor Model steady W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning

C.2 Residual Overview

The present s ection shows the residuals for a representative airplane mode, tilt mode and hover mode case in Figure C . 7 , Figure C . 8 and Figure C . 9 , respectively.

Figure C . 7 Residual overview for representative airplane mode case.

Figure C . 8 Residual overview for representative tilt mode case with α p = 75.

W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning Figure C . 9 Residual overview for representative hover mode case.

C.3 Data Steady XV - 15 Rotor Results

The data used in the various plots is tabulated in Table C . 4 .

Table C . 4 Summary of steady RotCFD Validation Data α p V/ Ω R θ 0 M [ - ] or # Flight Mode File [deg] [m/s] [deg] TL SD T [N] P [J/s] C / σ [ - ] C / σ [ - ] η [ - ] T P 1 Hover 0.rpr 90 0.00 0.0 N N 1.467E+04 2.487E+05 6.373E -­‐ 02 4.790E -­‐ 03 0.675 2 Hover 2.rpr 90 0.00 2.0 N N 1.952E+04 3.483E+05 8.480E -­‐ 02 6.708E -­‐ 03 0.741 3 Hover 4.rpr 90 0.00 4.0 N N 2.457E+04 4.799E+05 1.067E -­‐ 01 9.243E -­‐ 03 0.759 4 Hover 6.rpr 90 0.00 6.0 N N 2.972E+04 6.474E+05 1.291E -­‐ 01 1.247E -­‐ 02 0.738 5 Hover 8.rpr 90 0.00 8.0 N N 3.466E+04 8.578E+05 1.506E -­‐ 01 1.652E -­‐ 02 0.710 6 Hover 10.rpr 90 0.00 10.0 N N 3.867E+04 1.122E+06 1.680E -­‐ 01 2.161E -­‐ 02 0.640 7 Hover 0_TL.rpr 90 0.00 0.0 Y N 1.450E+04 2.485E+05 6.299E -­‐ 02 4.786E -­‐ 03 0.665 8 Hover 2_TL.rpr 90 0.00 2.0 Y N 1.909E+04 3.464E+05 8.293E -­‐ 02 6.672E -­‐ 03 0.718 9 Hover 4_TL.rpr 90 0.00 4.0 Y N 2.373E+04 4.810E+05 1.031E -­‐ 01 9.264E -­‐ 03 0.720 10 Hover 6_TL.rpr 90 0.00 6.0 Y N 2.844E+04 6.612E+05 1.235E -­‐ 01 1.273E -­‐ 02 0.685 11 Hover 8_TL.rpr 90 0.00 8.0 Y N 3.282E+04 8.967E+05 1.426E -­‐ 01 1.727E -­‐ 02 0.678 12 Hover 10_TL.rpr 90 0.00 10.0 Y N 3.643E+04 1.180E+06 1.583E -­‐ 01 2.273E -­‐ 02 0.557 13 Hover 0_TL_SD.rpr 90 0.00 0.0 Y Y 1.669E+04 2.906E+05 7.250E -­‐ 02 5.597E -­‐ 03 0.703 14 Hover 2_TL_SD.rpr 90 0.00 2.0 Y Y 2.183E+04 4.060E+05 9.483E -­‐ 02 7.819E -­‐ 03 0.752 15 Hover 4_TL_SD.rpr 90 0.00 4.0 Y Y 2.712E+04 5.617E+05 1.178E -­‐ 01 1.082E -­‐ 02 0.753 16 Hover 6_TL_SD.rpr 90 0.00 6.0 Y Y 3.245E+04 7.686E+05 1.410E -­‐ 01 1.480E -­‐ 02 0.721 17 Hover 8_TL_SD.rpr 90 0.00 8.0 Y Y 3.759E+04 1.031E+06 1.633E -­‐ 01 1.986E -­‐ 02 0.669 18 Hover 10_TL_SD.rpr 90 0.00 10.0 Y Y 4.207E+04 1.338E+06 1.828E -­‐ 01 2.577E -­‐ 02 0.609 W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning 19 Tilt 15_18_TL.rpr 15 0.32 18.0 Y N 8.109E+03 6.146E+05 3.663E -­‐ 02 1.255E -­‐ 02 NA 20 Tilt 15_19_TL.rpr 15 0.32 19.0 Y N 1.208E+04 9.008E+05 5.457E -­‐ 02 1.840E -­‐ 02 NA 21 Tilt 15_20_TL.rpr 15 0.32 20.0 Y N 1.600E+04 1.193E+06 7.227E -­‐ 02 2.436E -­‐ 02 NA 22 Tilt 15_21_TL.rpr 15 0.32 21.0 Y N 1.985E+04 1.496E+06 8.966E -­‐ 02 3.055E -­‐ 02 NA 71 Tilt 15_175_TL.rpr 15 0.32 17.5 Y N 6.133E+03 4.765E+05 2.770E -­‐ 02 9.731E -­‐ 03 NA 72 Tilt 15_185_TL.rpr 15 0.32 18.5 Y N 1.009E+04 7.559E+05 4.558E -­‐ 02 1.544E -­‐ 02 NA 23 Tilt 30_155_TL.rpr 30 0.32 15.5 Y N 8.998E+03 5.399E+05 4.064E -­‐ 02 1.103E -­‐ 02 NA 24 Tilt 30_165_TL.rpr 30 0.32 16.5 Y N 1.289E+04 7.906E+05 5.822E -­‐ 02 1.615E -­‐ 02 NA 25 Tilt 30_175_TL.rpr 30 0.32 17.5 Y N 1.673E+04 1.046E+06 7.557E -­‐ 02 2.136E -­‐ 02 NA 26 Tilt 30_185_TL.rpr 30 0.32 18.5 Y N 2.045E+00 1.312E+06 9.237E -­‐ 06 2.679E -­‐ 02 NA 73 Tilt 30_15_TL.rpr 30 0.32 15.0 Y N 7.030E+03 4.174E+05 3.175E -­‐ 02 8.524E -­‐ 03 NA 74 Tilt 30_16_TL.rpr 30 0.32 16.0 Y N 1.095E+04 6.644E+05 4.946E -­‐ 02 1.357E -­‐ 02 NA 27 Tilt 60_8_TL.rpr 60 0.32 8.0 Y N 1.512E+04 5.360E+05 6.830E -­‐ 02 1.095E -­‐ 02 NA 28 Tilt 60_9_TL.rpr 60 0.32 9.0 Y N 1.865E+04 6.911E+05 8.424E -­‐ 02 1.411E -­‐ 02 NA 29 Tilt 60_10_TL.rpr 60 0.32 10.0 Y N 2.207E+04 8.546E+05 9.969E -­‐ 02 1.745E -­‐ 02 NA 30 Tilt 60_11_TL.rpr 60 0.32 11.0 Y N 2.525E+04 1.027E+06 1.141E -­‐ 01 2.097E -­‐ 02 NA 75 Tilt 60_6_TL.rpr 60 0.32 6.0 Y N 7.823E+03 2.571E+05 3.534E -­‐ 02 5.250E -­‐ 03 NA 76 Tilt 60_7_TL.rpr 60 0.32 7.0 Y N 1.149E+04 3.904E+05 5.190E -­‐ 02 7.972E -­‐ 03 NA 31 Tilt 75_2_TL.rpr 75 0.32 2.0 Y N 1.374E+04 3.304E+05 6.206E -­‐ 02 6.747E -­‐ 03 NA 32 Tilt 75_3_TL.rpr 75 0.32 3.0 Y N 1.716E+04 4.160E+05 7.751E -­‐ 02 8.495E -­‐ 03 NA 33 Tilt 75_4_TL.rpr 75 0.32 4.0 Y N 2.041E+04 5.117E+05 9.219E -­‐ 02 1.045E -­‐ 02 NA 34 Tilt 75_5_TL.rpr 75 0.32 5.0 Y N 2.358E+04 6.180E+05 1.065E -­‐ 01 1.262E -­‐ 02 NA 77 Tilt 75_1_TL.rpr 75 0.32 1.0 Y N 1.030E+04 2.575E+05 4.652E -­‐ 02 5.258E -­‐ 03 NA 35 Advance Ratio 75_2_TL.rpr 75 0.32 2.0 Y N 1.374E+04 3.304E+05 6.206E -­‐ 02 6.747E -­‐ 03 NA 36 Advance Ratio 75_3_TL.rpr 75 0.32 3.0 Y N 1.716E+04 4.160E+05 7.751E -­‐ 02 8.495E -­‐ 03 NA 37 Advance Ratio 75_4_TL.rpr 75 0.32 4.0 Y N 2.041E+04 5.117E+05 9.219E -­‐ 02 1.045E -­‐ 02 NA 38 Advance Ratio 75_5_TL.rpr 75 0.32 5.0 Y N 2.358E+04 6.180E+05 1.065E -­‐ 01 1.262E -­‐ 02 NA 81 Advance Ratio 75_1_TL.rpr 75 0.32 1.0 Y N 1.030E+04 2.575E+05 4.652E -­‐ 02 5.258E -­‐ 03 NA 39 Advance Ratio 27_75_2_TL.rpr 75 0.27 2.0 Y N 1.534E+04 3.345E+05 6.929E -­‐ 02 6.831E -­‐ 03 NA 40 Advance Ratio 27_75_3_TL.rpr 75 0.27 3.0 Y N 1.857E+04 4.099E+05 8.388E -­‐ 02 8.371E -­‐ 03 NA 41 Advance Ratio 27_75_4_TL.rpr 75 0.27 4.0 Y N 2.165E+04 4.965E+05 9.779E -­‐ 02 1.014E -­‐ 02 NA 82 Advance Ratio 27_75_1_TL.rpr 75 0.27 1.0 Y N 1.209E+04 2.673E+05 5.463E -­‐ 02 5.459E -­‐ 03 NA 42 Advance Ratio 18_75_3_TL.rpr 75 0.18 3.0 Y N 2.053E+04 3.982E+05 9.273E -­‐ 02 8.132E -­‐ 03 NA 43 Advance Ratio 18_75_4_TL.rpr 75 0.18 4.0 Y N 2.325E+04 4.704E+05 1.050E -­‐ 01 9.606E -­‐ 03 NA 44 Advance Ratio 18_75_5_TL.rpr 75 0.18 5.0 Y N 2.596E+04 5.519E+05 1.173E -­‐ 01 1.127E -­‐ 02 NA 86 Advance Ratio 18_75_1_TL.rpr 75 0.18 1.0 Y N 1.490E+04 2.792E+05 6.730E -­‐ 02 5.702E -­‐ 03 NA 87 Advance Ratio 18_75_2_TL.rpr 75 0.18 2.0 Y N 1.771E+04 3.349E+05 8.000E -­‐ 02 6.839E -­‐ 03 NA 45 Airplane Mode 40_23_TL.rpr 0 0.40 23.0 Y N 2.906E+03 2.762E+05 1.902E -­‐ 02 9.837E -­‐ 03 0.777 46 Airplane Mode 40_24_TL.rpr 0 0.40 24.0 Y N 5.753E+03 4.902E+05 3.765E -­‐ 02 1.746E -­‐ 02 0.866 47 Airplane Mode 40_25_TL.rpr 0 0.40 25.0 Y N 8.577E+03 7.101E+05 5.613E -­‐ 02 2.529E -­‐ 02 0.892 48 Airplane Mode 40_26_TL.rpr 0 0.40 26.0 Y N 1.140E+04 9.343E+05 7.461E -­‐ 02 3.328E -­‐ 02 0.901 78 Airplane Mode 40_225_TL.rpr 0 0.40 22.5 Y N 1.480E+03 1.706E+05 9.686E -­‐ 03 6.076E -­‐ 03 0.640 79 Airplane Mode 40_255_TL.rpr 0 0.40 25.5 Y N 9.988E+03 8.215E+05 6.537E -­‐ 02 2.926E -­‐ 02 0.898 49 Airplane Mode 70_375_TL.rpr 0 0.70 37.5 Y N 3.328E+03 5.535E+05 2.178E -­‐ 02 1.971E -­‐ 02 0.777 W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning 50 Airplane Mode 70_385_TL.rpr 0 0.70 38.5 Y N 7.193E+03 1.054E+06 4.707E -­‐ 02 3.754E -­‐ 02 0.882 51 Airplane Mode 70_395_TL.rpr 0 0.70 39.5 Y N 1.098E+04 1.559E+06 7.186E -­‐ 02 5.553E -­‐ 02 0.910 52 Airplane Mode 70_405_TL.rpr 0 0.70 40.5 Y N 1.471E+04 2.073E+06 9.627E -­‐ 02 7.383E -­‐ 02 0.917 80 Airplane Mode 70_37_TL.rpr 0 0.70 37.0 Y N 1.369E+03 3.036E+05 6.184E -­‐ 03 6.200E -­‐ 03 0.583 53 Hover 6_TL_SD_GC.rpr 90 0.00 6.0 Y Y NA NA NA NA NA 54 Hover 6_TL_SD_GE.rpr 90 0.00 6.0 Y Y NA NA NA NA NA 55 Hover 6_TL_SD_IR.rpr 90 0.00 6.0 Y Y NA NA NA NA NA 56 Hover 10_TL_SD_IR2.rpr 90 0.00 6.0 Y Y NA NA NA NA NA 57 Advance Ratio 27_75_2_TL_SD.rpr 75 0.27 2.0 Y N 1.812E+04 3.915E+05 8.185E -­‐ 02 7.995E -­‐ 03 NA 58 Advance Ratio 27_75_3_TL_SD.rpr 75 0.27 3.0 Y N 2.173E+04 4.780E+05 9.815E -­‐ 02 9.761E -­‐ 03 NA 59 Advance Ratio 27_75_4_TL_SD.rpr 75 0.27 4.0 Y N 2.530E+04 5.765E+05 1.143E -­‐ 01 1.177E -­‐ 02 NA 88 Advance Ratio 27_75_1_TL_SD.rpr 75 0.27 1.0 Y N NA NA NA NA NA 87 Advance Ratio 27_75_0_TL_SD.rpr 75 0.27 0.0 Y N 1.089E+04 2.507E+05 4.919E -­‐ 02 5.120E -­‐ 03 NA 61 Advance Ratio 18_75_3_TL_SD.rpr 75 0.18 3.0 Y N 2.368E+04 4.659E+05 1.070E -­‐ 01 9.514E -­‐ 03 NA 62 Advance Ratio 18_75_4_TL_SD.rpr 75 0.18 4.0 Y N 2.681E+04 5.488E+05 1.211E -­‐ 01 1.121E -­‐ 02 NA 63 Advance Ratio 18_75_5_TL_SD.rpr 75 0.18 5.0 Y N 2.988E+04 6.429E+05 1.350E -­‐ 01 1.313E -­‐ 02 NA 83 Advance Ratio 18_75_1_TL_SD.rpr 75 0.18 1.0 Y N 1.733E+04 3.264E+05 7.828E -­‐ 02 6.666E -­‐ 03 NA 84 Advance Ratio 18_75_2_TL_SD.rpr 75 0.18 2.0 Y N 2.049E+04 3.915E+05 9.255E -­‐ 02 7.995E -­‐ 03 NA 85 Advance Ratio 18_75_3_TL_SD.rpr 75 0.18 3.0 Y N 2.368E+04 4.659E+05 1.070E -­‐ 01 9.514E -­‐ 03 NA 86 Advance Ratio 18_75_0_TL_SD.rpr 75 0.18 0.0 Y N 1.415E+04 2.704E+05 6.392E -­‐ 02 5.522E -­‐ 03 NA 64 Hover 10_SD.rpr 90 0.00 10.0 N Y 4.447E+04 1.291E+06 1.932E -­‐ 01 2.486E -­‐ 02 0.688 65 Hover 0_SD.rpr 90 0.00 0.0 N Y 1.682E+04 2.903E+05 7.307E -­‐ 02 5.591E -­‐ 03 0.711 66 Hover 2_SD.rpr 90 0.00 2.0 N Y 2.237E+04 4.075E+05 9.718E -­‐ 02 7.848E -­‐ 03 0.773 67 Hover 4_SD.rpr 90 0.00 4.0 N Y 2.800E+04 5.617E+05 1.216E -­‐ 01 1.082E -­‐ 02 0.790 68 Hover 6_SD.rpr 90 0.00 6.0 N Y 3.391E+04 7.559E+05 1.473E -­‐ 01 1.456E -­‐ 02 0.781 69 Hover 8_SD.rpr 90 0.00 8.0 N Y 3.962E+04 9.945E+05 1.721E -­‐ 01 1.915E -­‐ 02 0.749 89 Tilt 15_18.rpr 15 0.32 18.0 N N 8.523E+03 6.435E+05 3.850E -­‐ 02 1.314E -­‐ 02 NA 90 Tilt 75_3.rpr 75 0.32 3.0 N N 1.705E+04 4.130E+05 7.701E -­‐ 02 8.434E -­‐ 03 NA 91 Advance Ratio 18_75_3.rpr 75 0.18 3.0 N N 2.075E+04 3.998E+05 9.373E -­‐ 02 8.164E -­‐ 03 NA 92 Airplane Mode 40_24 .rpr 0 0.40 24.0 N N 6.246E+03 5.274E+05 4.088E -­‐ 02 1.878E -­‐ 02 0.874 W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning

Appendix D Unsteady XV - 15 Rotor Validation Results

D.1 Simulations Parameters

Table D . 5 shows a compact overview of the simulation parameters. ND stands for non - dimensionalized, the boundary size is expressed as the coordinates of the corners of a rectangular prism. The grid cells indicate the amount of cells on the x,y and z edge of the boundary, respectively. Rotor Grid Ref. and Grid Refinement indicate refinement of cells by multiplying the amount of cells b y a certain factor.

Table D . 5 Overview of steady simulation parameters .

Hover Parameters Boundary Conditions & Grid Simulation Variables ( -­‐ 38.1, -­‐ 38.1, -­‐ 68.58) Radius 3.81 m Boundary Size Simulated time 2.5 s (38.1, 38.1, 38.1) Cone angle 2.5 deg Grid cells [#] 30,30,42 Timesteps 3000 Tip speed 225.55 m/s Rotor Box Ref. 1,1 Δ T 8.33E -­‐ 04 Cutout 0.0875 r/R Rotor Grid Ref . 6x Δ X 0.0784 min ( -­‐ 7.62, -­‐ 7.62, -­‐ 68.58) Solidity 0.081 Grid Refinement Box [m] Iterations 10 (7.62, 7.62, 38.1) Power ND 6.41E+08 Grid Refinement 4x Relaxation ( u,v,w,p ) 0.1 Thrust ND 2.84E+06 Volume Ratio Max 8 Flight Condition hover Cells 1,053,948 Rotor Model Tilt and Advance Ratio Boundary Conditions & Grid Simulation Variables ( -­‐ 38.1, -­‐ 38.1, -­‐ 68.58) Radius 3.81 m Boundary Size Simulated time 1.25 s (38.1, 38.1, 38.10) Cone angle 2.5 deg Grid cells [#] 30,30,42 Timesteps 1000 Tip speed 221.17 m/s Rotor Box Ref. 1,1 Δ T 8.33E -­‐ 04 Cutout 0.0875 r/R Rotor Grid Ref . 6x Δ X 0.0784 min ( -­‐ 15.24, -­‐ 7.62, -­‐ 68,58) Solidity 0.081 Grid Refinement Box [m] Iterations 10 (7.62, 7.62 38.10) Power ND 6.05E+08 Grid Refinement 4x Relaxation ( u,v,w,p ) 0.1 Thrust ND 2.73E+06 Volume Ratio Max 8 Flight Condition general Cells 2,029,692 (at 30 degree tilt) Airplane Mode Boundary Conditions & Grid Simulation Variables ( -­‐ 38.1, -­‐ 38.1, -­‐ 68.58) Radius 3.81 m Boundary Size Simulated time 1.25 s (38.1, 38.1, 38.10) Cone angle 2.5 deg Grid cells [#] 30,30,42 Timesteps 1000 Tip speed 183.76 m/s Rotor Box Ref. 1,1 Δ T 8.33E -­‐ 04 Cutout 0.0875 r/R Rotor Grid Ref . 6x Δ X 0.0784 min ( -­‐ 15.24, -­‐ 7.62, -­‐ 68,58) Solidity 0.081 Grid Refinement Box [m] Iterations 10 (7.62, 7.62 38.10) Power ND 3.47E+08 Grid Refinement 4x Relaxation ( u,v,w,p ) 0.1 Thrust ND 1.89E+06 Volume Ratio Max 8 Flight Condition general Cells 1,053,948 W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning

D.2 Hover - Unsteady

Figure D . 10 and Figure D . 11 show , analogous to the steady results obtained in Section 4.1 , the hover performance for the unsteady model of the XV - 15 rotor in RotUNS.

0.030 WTT (Mtip = .53) WTT (Mtip = .65) 0.025 CAMRAD I (Mtip = .66) Flight test (Mtip = .69) OARF data (Mtip = .66) RotCFD UNSTEADY (Mtip = .66) 0.020 RotCFD UNSTEADY TL (Mtip = .66) [~] RotCFD UNSTEADY TL SD (Mtip = .66) σ / RotCFD UNSTEADY TL SD E1 (Mtip = .66) P C 0.015 RotCFD UNSTEADY TL SD E2 (Mtip = .66) RotCFD UNSTEADY TL SD E4 (Mtip = .66) RotCFD UNSTEADY TL SD E3 (Mtip = .66) power, RotCFD UNSTEADY SD (Mtip = .66) 0.010 CAMRAD II (Mtip = .69) 0.005 0.000 0.00 0.05 0.10 0.15 0.20 blade loading, C / σ [~] T Figure D . 10 Unsteady results for X V - 15 rotor hov er power as a function of thrust [2], [28] .

Both graphs show serious error in excess of 10%, compared to the presented theoretical and experimental data.

1.000 0.800 [~] M 0.600 0.400 gure of merit, OARF Data (Mtip = 0.66) WTT (Mtip = .65) fi WTT (Mtip = .53) Flight test (Mtip = .69) CAMRAD I (Mtip = .66) RotCFD UNSTEADY (Mtip = .66) RotCFD UNSTEADY TL (Mtip = .66) RotCFD UNSTEADY TL SD (Mtip = .66) 0.200 RotCFD UNSTEADY TL SD E2 (Mtip = .66) RotCFD UNSTEADY TL SD E3 (Mtip = .66) RotCFD UNSTEADY TL SD E4 (Mtip = .66) RotCFD UNSTEADY SD (Mtip = .66) CAMRAD II (Mtip = .69) 0.000 0.00 0.05 0.10 0.15 0.20 blade loading, C / σ [~] T Figure D . 11 Unsteady results for XV - 15 rotor hover figure of Merit as a function of thrust [2], [28] .

D.3 Tilt Mode - Unsteady

Figure D . 12 and Figure D . 13 show , analogous to the steady results obtained in Section 4.2 , the tilt mode performance and the sensitivity to advance ratio variations for the unsteady model of the XV - 15 rotor in RotUNS.

W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning 0.022 0.018 0.014 [~] σ / 0.010 P C power, 0.006 WTTt α p = 15° (Mtip = .65) WTT α p = 30° (Mtip = .65) WTT α p = 60° (Mtip = .65) WTT α p = 75° (Mtip = .65) 0.002 CAMRAD I α p = 15° (Mtip = .65) CAMRAD I α p = 30° (Mtip = .65) CAMRAD I α p = 60° (Mtip = .65) CAMRAD I α p = 75° (Mtip = .65) RotCFD UNSTEADY TL α p = 15° (Mtip = .65) RotCFD UNSTEADY TL α p = 30° (Mtip = .65) RotCFD UNSTEADY TL α p = 60° (Mtip = .65) RotCFD UNSTEADY TL α p = 75° (Mtip = .65) -0.002 0.00 0.02 0.04 0.06 0.08 0.10 blade loading, C / σ [~] T Figure D . 12 Uns teady results for XV - 15 r otor power as a function of thrust for various pylon angles at V/ Ω R = .32 [2] .

The results for the various tilt modes correlate slightly better than the hover performance , t he steady model, however, outperforms the unsteady model in terms of accuracy.

0.014 0.012 0.010 [~] 0.008 σ / P Test V/ Ω R = 0.32 C Test V/ Ω R = 0.27 0.006 Test V/ Ω R = 0.18 power, Theory V/ Ω R = 0.32 Theory V/ Ω R = 0.27 0.004 Theory V/ Ω R = 0.18 RotCFD UNSTEADY TL V/ Ω R = 0.32 (Mtip = .65) RotCFD UNSTEADY TL V/ Ω R = 0.27 (Mtip = .65) 0.002 RotCFD UNSTEADY TL V/ Ω R = 0.18 (Mtip = .65) RotCFD UNSTEADY TL SD V/ Ω R = 0.27 (Mtip = .65) RotCFD UNSTEADY TL SD V/ Ω R = 0.18 (Mtip = .65) 0.000 0.03 0.05 0.07 0.09 0.11 0.13 blade loading, C / σ [~] T Figure D . 13 Uns teady results for XV - 15 rotor power as function of thrust, for α p = 75° and M tip = 0.65 [2] .

The variation of advance ratio shows similar performance to CAMRAD I.

W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning

D.4 Airplane Mode - Unsteady

Figure D . 14 shows , analogous to the steady results obtained in Section 4.3 , airplane mode performance for the unsteady model of the XV - 15 rotor in RotUNS.

1.000 0.800 [~] η ciency, 0.600 ffi Theory V/ Ω R = .70 (Mtip = .54) Theory V/ Ω R = .40 (Mtip = .54) fl ight test WTT V/ Ω R = .385 (Mtip = .62) propulsive e 0.400 WTT V/ Ω R = .46 (Mtip = .53) WTT V/ Ω R = .34 (Mtip = .53) RotCFD TL V/ Ω R = 0.40 (Mtip = .54) RotCFD TL V/ Ω R = 0.70 (Mtip = .54) 0.200 0.00 0.01 0.02 0.03 0.04 0.05 0.06 blade loading, C / σ [~] T Figure D . 14 Unsteady results for (r otor ) propulsive efficiency as function of thrust [2] .

D.5 Data Unsteady XV - 15 Rotor Results

The data used in the various plots is tabulated in Table D . 6 .

Table D . 6 Summary of unsteady RotCFD Validation Data .

α p V/ Ω R θ 0 M [ - ] or # Flight Mode File [deg] [m/s] [deg] TL SD T [N] P [J/s] C / σ [ - ] C / σ [ - ] η [ - ] T P 1 Hover 0.rpr 90 0.00 0.0 N N 1.100E+04 2.170E+05 4.778E -­‐ 02 4.179E -­‐ 03 0.505 2 Hover 2.rpr 90 0.00 2.0 N N 1.460E+04 3.020E+05 6.342E -­‐ 02 5.816E -­‐ 03 0.552 3 Hover 4.rpr 90 0.00 4.0 N N 1.820E+04 4.130E+05 7.906E -­‐ 02 7.954E -­‐ 03 0.562 4 Hover 6.rpr 90 0.00 6.0 N N 2.170E+04 5.510E+05 9.427E -­‐ 02 1.061E -­‐ 02 0.552 5 Hover 8.rpr 90 0.00 8.0 N N 2.500E+04 7.170E+05 1.086E -­‐ 01 1.381E -­‐ 02 0.524 6 Hover 10.rpr 90 0.00 10.0 N N 2.800E+04 9.080E+05 1.216E -­‐ 01 1.749E -­‐ 02 0.489 7 Hover 0_TL.rpr 90 0.00 0.0 Y N 1.070E+04 2.160E+05 4.648E -­‐ 02 4.160E -­‐ 03 0.481 8 Hover 2_TL.rpr 90 0.00 2.0 Y N 1.400E+04 3.000E+05 6.082E -­‐ 02 5.778E -­‐ 03 0.526 9 Hover 4_TL.rpr 90 0.00 4.0 Y N 1.730E+04 4.070E+05 7.515E -­‐ 02 7.839E -­‐ 03 0.531 10 Hover 6_TL.rpr 90 0.00 6.0 Y N 2.040E+04 5.410E+05 8.862E -­‐ 02 1.042E -­‐ 02 0.513 11 Hover 8_TL.rpr 90 0.00 8.0 Y N 2.350E+04 7.100E+05 1.021E -­‐ 01 1.367E -­‐ 02 0.483 12 Hover 10_TL.rpr 90 0.00 10.0 Y N 2.620E+04 9.070E+05 1.138E -­‐ 01 1.747E -­‐ 02 0.442 13 Hover 0_TL_SD.rpr 90 0.00 0.0 Y Y 1.270E+04 2.540E+05 5.517E -­‐ 02 4.892E -­‐ 03 0.545 14 Hover 2_TL_SD.rpr 90 0.00 2.0 Y Y 1.698E+04 3.492E+05 7.375E -­‐ 02 6.726E -­‐ 03 0.584 15 Hover 4_TL_SD.rpr 90 0.00 4.0 Y Y 2.020E+04 4.750E+05 8.775E -­‐ 02 9.148E -­‐ 03 0.573 16 Hover 6_TL_SD.rpr 90 0.00 6.0 Y Y 2.390E+04 6.310E+05 1.038E -­‐ 01 1.215E -­‐ 02 0.554 17 Hover 8_TL_SD.rpr 90 0.00 8.0 Y Y 2.730E+04 8.170E+05 1.186E -­‐ 01 1.574E -­‐ 02 0.520 18 Hover 10_TL_SD.rpr 90 0.00 10.0 Y Y 3.040E+04 1.040E+06 1.321E -­‐ 01 2.003E -­‐ 02 0.480 W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning 19 Tilt 15_18_TL.rpr 15 0.32 18.0 Y N 4.660E+03 3.970E+05 2.105E -­‐ 02 8.107E -­‐ 03 NA 20 Tilt 15_19_TL.rpr 15 0.32 19.0 Y N 7.020E+03 5.770E+05 3.171E -­‐ 02 1.178E -­‐ 02 NA 21 Tilt 15_20_TL.rpr 15 0.32 20.0 Y N 9.390E+03 7.670E+05 4.241E -­‐ 02 1.566E -­‐ 02 NA 22 Tilt 15_21_TL.rpr 15 0.32 21.0 Y N 1.160E+04 9.610E+05 5.240E -­‐ 02 1.962E -­‐ 02 NA 23 Tilt 30_155_TL.rpr 30 0.32 15.5 Y N 4.918E+03 3.443E+05 2.221E -­‐ 02 7.031E -­‐ 03 NA 24 Tilt 30_165_TL.rpr 30 0.32 16.5 Y N 7.218E+03 5.011E+05 3.260E -­‐ 02 1.023E -­‐ 02 NA 25 Tilt 30_175_TL.rpr 30 0.32 17.5 Y N 9.489E+03 6.648E+05 4.286E -­‐ 02 1.358E -­‐ 02 NA 26 Tilt 30_185_TL.rpr 30 0.32 18.5 Y N 1.175E+04 8.360E+05 5.307E -­‐ 02 1.707E -­‐ 02 NA 27 Tilt 60_8_TL.rpr 60 0.32 8.0 Y N 8.855E+03 3.655E+05 4.000E -­‐ 02 7.463E -­‐ 03 NA 28 Tilt 60_9_TL.rpr 60 0.32 9.0 Y N 1.104E+04 4.647E+05 4.985E -­‐ 02 9.489E -­‐ 03 NA 29 Tilt 60_10_TL.rpr 60 0.32 10.0 Y N 1.316E+04 5.738E+05 5.944E -­‐ 02 1.172E -­‐ 02 NA 30 Tilt 60_11_TL.rpr 60 0.32 11.0 Y N 1.524E+04 6.855E+05 6.884E -­‐ 02 1.400E -­‐ 02 NA 31 Tilt 75_2_TL.rpr 75 0.32 2.0 Y N 8.970E+03 2.660E+05 4.052E -­‐ 02 5.432E -­‐ 03 NA 32 Tilt 75_3_TL.rpr 75 0.32 3.0 Y N 1.120E+04 3.250E+05 5.059E -­‐ 02 6.637E -­‐ 03 NA 33 Tilt 75_4_TL.rpr 75 0.32 4.0 Y N 1.330E+04 3.920E+05 6.008E -­‐ 02 8.005E -­‐ 03 NA 34 Tilt 75_5_TL.rpr 75 0.32 5.0 Y N 1.543E+04 4.673E+05 6.970E -­‐ 02 9.544E -­‐ 03 NA 35 Advance Ratio 75_2_TL.rpr 75 0.32 2.0 Y N 8.970E+03 2.660E+05 4.052E -­‐ 02 5.432E -­‐ 03 NA 36 Advance Ratio 75_3_TL.rpr 75 0.32 3.0 Y N 1.120E+04 3.250E+05 5.059E -­‐ 02 6.637E -­‐ 03 NA 37 Advance Ratio 75_4_TL.rpr 75 0.32 4.0 Y N 1.330E+04 3.920E+05 6.008E -­‐ 02 8.005E -­‐ 03 NA 38 Advance Ratio 75_5_TL.rpr 75 0.32 5.0 Y N 1.543E+04 4.673E+05 6.970E -­‐ 02 9.544E -­‐ 03 NA 39 Advance Ratio 27_75_2_TL.rpr 75 0.27 2.0 Y N 1.007E+04 2.710E+05 4.548E -­‐ 02 5.533E -­‐ 03 NA 40 Advance Ratio 27_75_3_TL.rpr 75 0.27 3.0 Y N 1.220E+04 3.260E+05 5.511E -­‐ 02 6.657E -­‐ 03 NA 41 Advance Ratio 27_75_4_TL.rpr 75 0.27 4.0 Y N 1.424E+04 3.911E+05 6.431E -­‐ 02 7.987E -­‐ 03 NA 42 Advance Ratio 18_75_3_TL.rpr 75 0.18 3.0 Y N 1.390E+04 3.330E+05 6.279E -­‐ 02 6.800E -­‐ 03 NA 43 Advance Ratio 18_75_4_TL.rpr 75 0.18 4.0 Y N 1.577E+04 3.913E+05 7.123E -­‐ 02 7.991E -­‐ 03 NA 44 Advance Ratio 18_75_5_TL.rpr 75 0.18 5.0 Y N 1.760E+04 4.560E+05 7.950E -­‐ 02 9.312E -­‐ 03 NA 45 Airplane Mode 40_23_TL.rpr 0 0.40 23.0 Y N 1.404E+03 1.670E+05 6.341E -­‐ 03 3.410E -­‐ 03 0.621 46 Airplane Mode 40_24_TL.rpr 0 0.40 24.0 Y N 3.128E+03 3.016E+05 1.413E -­‐ 02 6.159E -­‐ 03 0.766 47 Airplane Mode 40_25_TL.rpr 0 0.40 25.0 Y N 4.820E+03 4.385E+05 2.177E -­‐ 02 8.955E -­‐ 03 0.811 48 Airplane Mode 40_26_TL.rpr 0 0.40 26.0 Y N 6.478E+03 5.794E+05 2.926E -­‐ 02 1.183E -­‐ 02 0.825 49 Airplane Mode 70_375_TL.rpr 0 0.70 37.5 Y N 1.397E+03 3.099E+05 6.308E -­‐ 03 6.329E -­‐ 03 0.582 50 Airplane Mode 70_385_TL.rpr 0 0.70 38.5 Y N 3.607E+03 6.043E+05 1.629E -­‐ 02 1.234E -­‐ 02 0.771 51 Airplane Mode 70_395_TL.rpr 0 0.70 39.5 Y N 5.737E+03 9.014E+05 2.591E -­‐ 02 1.841E -­‐ 02 0.822 52 Airplane Mode 70_405_TL.rpr 0 0.70 40.5 Y N 7.800E+03 1.200E+06 3.523E -­‐ 02 2.451E -­‐ 02 0.840 53 Hover 6_TL_SD_GC.rpr 90 0.00 6.0 Y Y 2.390E+04 6.159E+05 1.038E -­‐ 01 1.186E -­‐ 02 54 Hover 6_TL_SD_GE.rpr 90 0.00 6.0 Y Y 2.390E+04 6.300E+05 1.038E -­‐ 01 1.213E -­‐ 02 0.552 55 Hover 6_TL_SD_IR.rpr 90 0.00 6.0 Y Y 2.359E+04 6.299E+05 1.025E -­‐ 01 1.213E -­‐ 02 0.545 56 Hover 10_TL_SD_IR2.rpr 90 0.00 6.0 Y Y 2.980E+04 1.030E+06 1.295E -­‐ 01 1.984E -­‐ 02 0.472 58 Advance Ratio 27_75_2_TL_SD.rpr 75 0.27 2.0 Y N 1.202E+04 3.146E+05 5.428E -­‐ 02 6.425E -­‐ 03 NA 59 Advance Ratio 27_75_3_TL_SD.rpr 75 0.27 3.0 Y N 1.435E+04 3.789E+05 6.482E -­‐ 02 7.738E -­‐ 03 NA 60 Advance Ratio 27_75_4_TL_SD.rpr 75 0.27 4.0 Y N 1.669E+04 4.516E+05 7.539E -­‐ 02 9.222E -­‐ 03 NA 61 Advance Ratio 18_75_3_TL_SD.rpr 75 0.18 3.0 Y N 1.619E+04 3.868E+05 7.313E -­‐ 02 7.899E -­‐ 03 NA 62 Advance Ratio 18_75_4_TL_SD.rpr 75 0.18 4.0 Y N 1.832E+04 4.538E+05 8.275E -­‐ 02 9.267E -­‐ 03 NA 63 Advance Ratio 18_75_5_TL_SD.rpr 75 0.18 5.0 Y N 2.037E+04 5.276E+05 9.201E -­‐ 02 1.077E -­‐ 02 NA W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning 64 Hover 10_SD.rpr 90 0.00 10.0 N Y 3.267E+04 1.044E+06 1.419E -­‐ 01 2.010E -­‐ 02 0.526 65 Hover 0_SD.rpr 90 0.00 0.0 N Y 1.278E+04 2.525E+05 5.552E -­‐ 02 4.863E -­‐ 03 0.526 66 Hover 2_SD.rpr 90 0.00 2.0 N Y 1.696E+04 3.515E+05 7.368E -­‐ 02 6.769E -­‐ 03 0.608 67 Hover 4_SD.rpr 90 0.00 4.0 N Y 2.118E+04 4.801E+05 9.201E -­‐ 02 9.246E -­‐ 03 0.601 68 Hover 6_SD.rpr 90 0.00 6.0 N Y 2.512E+04 6.389E+05 1.091E -­‐ 01 1.231E -­‐ 02 0.593 69 Hover 8_SD.rpr 90 0.00 8.0 N Y 2.903E+04 8.273E+05 1.261E -­‐ 01 1.593E -­‐ 02 0.563 W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning

Appendix E Wind Tunnel Case Plots

Each of the wind tunnel subsets would have at least a couple of interesting velocity or vector plots to show, however, since a total of 28 subsets have been processed this woul d pose too much images in this A ppendix. Therefore only a selection of view per subset is presented here. The used coordinate system in the NFAC wind tunnels is shown in Figure E . 15 . The TTR will always rotate for the thrust to be (partially) aligned with the positive y - axis.

Figure E . 15 The boundaries of the extended test sections with TTR in edgewise and axial mode, respectively.

E.1 80 - by 120 - Foot Wind Tunnel Cases

E.1.1 Case 1, Edgewise, 0 kts.

Figure E . 16 Case 1, WTGE, Z Y - plane. Figure E . 17 Case 1, WTRO, Z Y - plane.

Figure E . 16 and Figure E . 17 show a velocity plot (with pressure plot on the geometry) of the Z Y - plane of case 1 for WTGE and WTRO, respectively. Figure E . 18 serves as the legend for the plots of case 1, all units are SI.

Pressure, p [Pa] : 1.020E+05 1.0 22E+05 1.024E+05 1.026E+05 1.028E+05 1.031E+05 1.033E+05 1.035E+05 Velocity Magnitude, V [m/s]: 0.00E+00 4.08E+00 8.16E+00 1.22E+01 1.63E+01 2.04E+01 2.45E+01 2.86E+01 3.27E+01 3.67E+01 4.08E+01 4.49E+01 4.9 0E+01 Figure E . 18 Legend for pressure and velocities for case 1.

W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning E.1.2 Case 2, Edgewise, 10 kts.

Figure E . 19 Case 2, FF GE, XY - plane. Figure E . 20 Case 2, WTGE , XY - plane.

Figure E . 19 and Figure E . 20 show a velocity plot (with pressure plot on the geometry) of the XY - plane of cas e 2 for FF GE and WT GE , respectively. Figure E . 21 serves as the legend for the plots of case 2.

Pressure, p [Pa] : 1.020E+05 1.0 22E+05 1.024E+05 1.026E+05 1.028E+05 1.031E+05 1.033E+05 1.035E+05 Velocity Magnitude, V [m/s]: 0.00E+00 4.08E+00 8.16E+00 1.22E+01 1.63E+01 2.04E+01 2.45E+01 2.86E+01 3.27E+01 3.67E+01 4.08E+01 4.49E+01 4.9 0E+01 Figure E . 21 Legend for pressure and velocities for case 2 .

W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning E.1.3 Case 3, Axial, 100 kts.

Figure E . 22 Case 3, WTGE, XZ - plane. Figure E . 23 Case 3, WTRO, XZ - plane.

Figure E . 22 and Figure E . 23 show a velocity plot (with pressure plot on the geo metry) of the ZY - plane of case 3 for WTGE and WTRO, respectively. Figure E . 24 serves as the legend for the plots of case 3.

p [Pa] V [m/s]: Figure E . 24 Legend for pr essure and velocities for case 3 .

W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning

E.2 40 - by 80 - Foot Wind Tunnel Cases

E.2.1 Case 5, Edgewise, 100 kts.

Figure E . 25 Case 5, FFGE, X Y - plane. Figure E . 26 Case 5, WTGE, X Y - plane.

Figure E . 25 and Figure E . 26 show a velocity plot (with pressure plot on the geometry) of the XY - plane of case 5 for FFGE and WTGE , respectively. Figure E . 27 serves as th e legend for the plots of case 5.

Pressure, p [Pa] Velocity Magnitude, V [m/s]: Figure E . 27 Legend for pre ssure and velocities for case 5 .

W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning E.2.2 Case 6, Axial, 200 kts.

Figure E . 28 Case 6, FFGE, XY - plane. Figure E . 29 Case 6, WTGE, XY - plane.

Figure E . 28 and Figure E . 29 show a velocity plot (with pressure plot on the geo metry) of the XY - plane of case 6 for FFGE and WTGE , respectively. Figure E . 30 serves as the legend for the plots of case 6 .

Pressure, p [Pa] Velocity Magnitude, V [m/s]: Figure E . 30 Legend for pr essure and velocities for case 6 .

E.2.3 Case 7, Tilt, 100 kts.

Figure E . 31 Case 7, WT GE, XY - plane. Figure E . 32 Case 7, WTRO , XY - plane.

Figure E . 31 and Figure E . 32 show a velocity plot (with pressure plot on the geo metry) of the XY - plane of case 7 for WTGE and WTRO , respectively. Figure E . 33 serves as the legend for the plots of case 7. The grid at the walls of the 40 - by 80 - Foot Wind Tun nel shows problems with gridding clearly, as shown in Figure E . 34 .

Pressure, p [Pa] Velocity Magnitude, V [m/s]: Figure E . 33 Legend for pr essure and velocities for case 7 .

W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning Figure E . 34 ZY - plane of case 7, just behind the rotor plane.

W ind Tunnel Interference Effects on Tilt Rotor Testing Using Computational Fluid Dynamics Witold J. F. Koning