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Figure 4: Change in shape of vortex ribbons at great distances behind the wing [16 Prandtl’s early work also applies the lifting-line theory to multiple wing configurations suggesting the elliptical lift distribution for a two-wing system. — Figure 4 Change in shape of vortex ribbons at great distances behind the wing [16 Prandtl’s early work also applies the lifting-line theory to multiple wing configurations suggesting the elliptical lift distribution for a two-wing system.

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This design follows in the footsteps of the Preliminary Research Aerodynamic Design to Lower Drag, or Prandtl-D platform developed at NASA Armstrong|2]. A combination of geometric and aerodynamic twist was utilized to ensure the lift distribution per unit span conformed to the bell shape proposed by Prandtl as a more efficient alternative to the ellipti- cal spanload when a span constraint is not present. Past research gives the expectation that the design will realize an up to 11.1% decrease in induced drag while increasing the span by 22.5% for a given structural weight, which this research effort intends to verify through more robust aerodynamic analysis than previous efforts have utilized.

ailerons are deflected anti-symmetrically, the lift vector on the high-lift wing will benefit from the upwash, and it can be thought of as tilting forward. Due to the negative angle of attack, the opposite wing tip is producing a negative lift vector, when the aileron is actuated upward, tilting in the direction of the freestream, and thus, it fails to utilize the region of upwash. This resultant force differential on the wingtips shows an ability for proverse yaw in roll. The movement of the upwash region inboard (Figure 2) matches what is believed to be exhibited by bird flight. This has been examined by the formation of flight. To achieve an optimal formation, birds overlap their wing tips such that they are capturing the entire region of upwash. The amount of overlap is congruent with the inboard region of upwash produced from the application of Prandtl’s revision of the most efficient spanwise lift distri- bution [2].

The influence of the vortical structure to the lifting surface increases the effective angle of attack and the induced drag as the ends of the vortex sheet are positioned closer together, which is to say the aspect ratio is inversely proportional to the induced drag (the next section will utilize this idea by the reframing of design constraints to achieve a new analytical solution). Prandtl uses this basis for the derivation of an elliptical shape of circulation distribution across the span having fixed wingspan, total lift, and velocity (derivation in text [16]). Vorticity and its relationship to the flow field and aerodynamic performance is an ongoing theme in this thesis that will draw qualitative and quantitative comparisons to the general overview provided in this section.

at the center of the wing, and y is a ratio of circulations across the span (Equation 2.1.6) for w = 0 representing the ELD. After allowing span to become a parameter, Equation 2.1.8 is substituted into Equation 2.1.4 to isolate the circulation at the center of the wing as a function of the gross lift, the freestream velocity, and the circulation ratio across the span (Equation 2.1.9). Transferring these variables to express induced drag yields Equation 2.1.10.

Figure 5: yw Variation in Relation to Aerodynamic Characteristics Ratios [14]

Figure 6: Induced drag ratio compared to the circulation ratio [14]

Figure 7: Circulation distribution of various spanloads [14]

The equations above, detailed in the research production [12], are obtained assuming . non-structural weight distribution given by 2.1.17 and only differ by the magnitude of a ‘ourier coefficient. This method holds for rectangular wings of constant chord and thick- 1ess. Variations of chord length and thickness along the span require numerical methods hat exceed the scope of the research. The research goes further and shows that for any ixed lift and distribution of weight there exists an optimum wingspan for which the condi- ion of minimal induced drag is satisfied. However, the solutions presented for each set of onstraints are derived specifically for rectangular wings and cannot be applied when wing weep is introduced. Though the solutions for the rectangular planform may not contribute o tailless flight, it provides groundwork for aircraft designers concerned with drag reduction, veight reduction, and fuel economy of commercial airliners.

Figure 9: Common cranes (grus grus) flying in formation over lake Fehér near Sdndorfalva, Hungary [14]

Figure 10: Aerodynamic Parameter Percent Change Between Y/b = 0.148 and -0.444 fo: the Trailing Wing Compared to the Leading Wing [14] optimization for an ELD system in flight formation.

bell-shaped lift distribution has sparked research that suggest that this spanload is the most efficient method of generating lift for a fixed amount of lift and a maximum root bending moment (or structural weight). Most notably, Dr. Bowers at NASA Armstrong is the first to measure proverse yaw by experimental flight data. The data materialized Horten’s theory which recognized the phenomenon of induced thrust as a consequence of inboard upwash to encourage favorable yaw without need for a vertical tail. NASA researchers correlate the characteristics of the BSLD wit analysis models. These correla h bird flight which has been previously understood with | ELD tions, advanced by Kyle Lukacovic of California Polytechnic State University [14], provide three explanations to bird flight being modeled by BSLD that have failed to be explained by | ELD:

Figure 13: Lift Distributions to be Matched

Figure 14: Region of Downwash Observed by XFLR5 Analysis

Figure 15: Polars of Interpolated Airfoils Figure 16: Interpolated Airfoil Cross Sections

Figure 18: Trefftz Plane Results from AVL

Figure 19: Flow Domain used for the Wing-Only Analysis of Bellwether

Figure 20: Physics Settings for the Wing-Only Analysis of Bellwether

Figure 21: Mesh Scene of Wing-Only Model

Figure 22: Planform Mesh Scene of Wing-Only Model

Figure 23: Prism Layer Mesh Scene of Wing-Only Model

greater validation of the mesh and physics reports. The physics ran 5000 steps reporting coefficients of lift and drag of 0.6363 and 0.03254 with a percent error of 0.1418% and 0.1346%, respectively, compared to the steady RANS physics solution.

Figure 25: Bellwether Wing-Only Unsteady RANS - Coefficients Monitor

is normal to the rotation of the flow (i.e. the rotation is spanwise with each vortex rotating towards the aircraft centerline). The difference in vector directions from port to starboard vortices indicate opposite directionality. The flow outboard of the vortex center is where the region of upwash occurs. The identification of the core location provides a qualitative understanding of the influence on the change in flow field to aerodynamic performance when this work turns to the comparison of the various lift distributions. ra Pr ‘/ ¥ . . INTRA TH NANA TT. . Z Ca ee | 1 1 é 1

Figure 27: Bellwether Wing-Only Unsteady RANS - Forces Monitor

Figure 28: Bellwether Wing-Only CFD - Wall Y+

Figure 29: Mesh Resolution Percent Error

Figure 30: Bellwether Wing-Only CFD - Vorticity Vector Top View

Figure 31: Bellwether Wing-Only CFD - Wake Vorticity Scalar Scene

Figure 32: Bellwether Wing-Only CFD - Vortex Core Scene

Figure 33: Comparison of Lift Curve Slopes of the Wing-Only Bellwether Model for VLM and CFD Analyses

Figure 34: Constrained Streamlines on Bellwether Wing-Only Planform View

Figure 35: Comparison of Vortex Lattice Methods’ c*CL Curves to a Scaled Curve of dL from CFD at a Common Lift Coefficient

Figure 36: Longitudinal Mesh at the Root Airfoil million cells. The computational burden is placed on the High-Powered Computing Cente1 (HPCC) at Oklahoma State University.

Figure 37: Horizontal Mesh with Wake Refinement Enabled

The lift distributions, dL, across the span are plotted against the desired curves in Figure 39 to confirm each wing is producing lift congruent with how it is designed. Next, the aerodynamic performance of each is measured in the ratio of lift to drag produced at the common flight condition. To save on computational expense, the Modern Bel and Cosine curves have not been iterated extensively to match their curves. Instead, they have been designed with enough distinction to provide significant differences to the flow fie ds produced by the Prandtl and ELD wings. The Bellwether design, applying the bell spanload outlined by Ludwig Prandtl, shows found to be operating at a much lower coefficient of lift (0.323) than the other d greatest efficiency in level flight (Figure 40). The ] so this comparison of the |] design failed to adhere to the fixed-lift design constraint placed upon the other d ELD to the other wings on this basis is ill-founded. ELD wing is istributions, The ELD istributions. This can be corrected by running an alpha sweep and comparing the performance of the

ELD at an incidence angle where the CL matches that of the other distributions. However, this method is likely to introduce greater parasitic drag, so a L/D comparison would not be representative of the efficiency of lift generation. A comparison could be made in setting up a Trefftz plane in STAR-CCM+ as a grid of planar probes from which the velocity vectors recorded are used to calculate induced drag from the flow field. This may be a suitable method of comparing induced drag computationally, and the truest comparison of aerodynamic efficiency in level flight, but it cannot entirely capture the aerodynamic performance without also accounting for the parasite drag by measuring the total drag and calculating induced drag (Cp = Cpo + Cp;). No clear comparison in level flight is made to ELD, but it is determined that increasing the centralization of lift deviating from the bell spanload results in decreased aerodynamic efficiency for this aircraft configuration in this flow regime. For a physical explanation of how the change in lift distribution affects the roll-yaw coupling response of the aircraft, we revert to the discussion of the regions of upwash and downwash discovered by Dr. Bowers and the research team at NASA responsible for the design and testing of the Prandtl-D flying wing [2]. Referencing Figure 2 de picts the sharp induction of upwash flow at the wingtips caused by the elliptical lift distribution. The bell spanload offers a smoother transition between regions of upwash and downwash that begin within the wingspan. Depictions of trailing vortices for Bellwether and the ] ELD model are observed to relate the computational findings to the Prandtl-D research and avian flight correlations [2] [14].

Figure 41: Bellwether Vorticity Vector Scene

Figure 42: Elliptical Model Vorticity Vector Scene

Yaw per Unit Roll with Aileron Deflection ‘igure 43: Yaw Control Power per Unit Roll from 20 Anti-Symmetric Aileron Deflection

Figure 44: Yaw Moment Monitor by Iteration of Steady RANS Solver in STAR-CCM+

Figure 45: Aileron Mesh Scene on Longitudinal Plane velocity gradients close to the surface boundary. Future CAD modeling could create a filled boundary by creating planar surfaces in the gaps of the ends of each aileron and a surface bounding the upper surfaces. This may also be remedied using a solid loft feature from creating a sketch profile in the corner gaps at the ends of each aileron and using the attach- ment surface as a guide curve to avoid a potential non-manifold-body error in STAR-CCM-.

structure for the propulsor shaft. This addition is adhered to the composite fuselage, and the motor shaft slides through the fuselage and the fin to drive the propeller. This design allows for the CFD analysis of pitch stability to be representative of the aircraft behavior without needing to account for the pitching moment induced by the propulsive system. Additionally, the propeller placement was chosen to operate aft of the fuselage as not to influence the freestream flow on the fuselage, since the lift generated by the body was included in the design and analysis to match the Prandtl bell lift distribution. Daw Lam ceiitadiwval ataktli¢ze LA ith ahaciesawwawnkt @whaAat Pha wc LAwn tran! Ate am claae Atl atdeaal

Figure 47: Propulsor Placement in Line with Center of Gravity ISO

Figure 48: Longitudinal Static Stability from CM v. Alpha Plot for Varying Center of Gravity Locations

Roll and Yaw Coefficients in Beta Sweep

The modeling begins with the importation of .dat files as x,y,z coordinates into SolidWorks to create splines of specific airfoil geometry. From these splines, sketch blocks are created so that they may be inserted as different sizes at different locations and angles of twist. The airfoils are positioned from BellwetherOne at the root to RAE 101 at the tip of the wing in accordance with Figure 50. The semispan wing sections are lofted together and connected to the fuselage cross sec tion at the centerline through the use of guide curves to obtain the desired biomimetic shape The fuselage shape was made iteratively through high-fidelity analysis to ensure it produce: the lift required to promote the smooth, continuous bell curve. The aerodynamic shape i: hollowed out for the creation of the structural components. The ribs are created at the semispan locations of the sketch blocks created from the .dat file splines and lofted to ar adjacent intersection curve made plane distanced the rib thickness over an extrusion to adhere to the from the interaction between the wing and a referenc« from the airfoil sketch block. A lofted feature is choser sweep and dihedral along the span. The fuselage ribs anc bulkheads are made using the same technique. Lightning holes are laser cut in the Aeroply ribs and bulkheads to reduce the support shear flow. The fuselage weight of the structural components while remaining t¢ internal structure harbors specific bays: camera system avionics, propulsion, and storage. composed from the fiberglass skin. Each compartment is accessible through magnetic hatche:

Figure 53: Bellwether - Front View

Figure 54: Port Wing Mold Assembly and the Integration of Leading-Edge Flow Sensors

Figure 55: Sensing Sleeve Mounted in the Endeavor Wind Tunnel on the leading edge to their respective pressure sensors. The pressure sensors are wired to an Arduino computer board responsible for applying the algorithm and storing the in-flight data to an SD card. The first sleeve (Figure 55) has been tested for basic readings of pressure data containing only 1 pressure sensor for the initial test. This model is representative of what will be included in the wing, but a second model (like the sleeve shown in Figure 54) is made to more accurately simulate the in-flight reading since the model will take the shape of the entire wing section housing the sensing mechanism.

Figure 57: Propulsor Placement in Line with Center of Gravity

Figure 58: Bellwether Planform View

Figure 59: Bellwether1

Figure 61: Bellwether3

Figure 63: Bellwether5

Figure 65: Lift and Drag Monitor of Bellwether - Unsteady RANS results

Figure 68: Cosine Model - Drag Distribution in Roll

Figure 69: Cosine Model - Lift Distribution in Roll

Figure 70: Modern Bell - Drag Distribution in Roll (bin direction is backwards on this plot)

Figure 71: Modern Bell - Lift Distribution in Roll (bin direction is backwards on this plot)

Figure 73: Prandtl - Lift Distribution in Roll Figure 72: Prandtl Bell - Drag Distribution in Roll

Figure 74: Elliptical - Drag Distribution in Roll (bin direction is backwards on this plot)

Figure 75: Elliptical - Lift Distribution in Roll

Figure 76: Combine Alpha Sweep

Figure 77: Distributions at Common CL of All Analysis Methods

Figure 78: Wake Refinement

Figure 79: Aileron Mesh 1

Figure 80: Aileron Mesh 2

Figure 81: Aileron Mesh 3

Figure 82: Aileron Mesh 4

Figure 85: Inboard Wing Mold - Top View

Figure 84: Inboard Wing Mold

Figure 87: Outboard Wing Mold - Top View Figure 86: Outboard Wing Mold

Figure 88: Mold 1

Figure 89: Mold 2

Figure 90: Mold3

Figure 91: System of Components for Leading-Edge Flow Sensing Sleeve

Figure 92: Wind Tunnel Setup for 3D-Printed Bellwether Model

Figure 93: Wind Tunnel Flow Visualization

Figure 94: Wind Tunnel 1

Figure 95: Wind Tunnel 2

Figure 96: Wind Tunnel 3

Figure 97: Wind Tunnel 4

Figure 98: Wind Tunnel 5

Figure 99: Water Tunnel 1

Figure 100: Water Tunnel 2

Figure 101: Water Tunnel 3

Figure 102: Water Tunnel 4

Figure 103: Water Tunnel 5

Figure 104: Bellwether Vorticity 1

Figure 108: Bellwether Vorticity 5

Figure 109: Elliptical Vorticity 1

Figure 110: Elliptical Vorticity 2

Figure 112: Cosine Vorticity 1

Figure 115: Modern Bell Vorticity 1

Figure 117: Bellwether Streamlines 1 Figure 116: Modern Bell Vorticity 2

Figure 118: Bellwether Streamlines 2

Figure 119: Bellwether Streamlines 3

Figure 120: Bellwether Vector Scene

Figure 121: Bellwether Vortex Core