Computational Analysis of the External Aerodynamics of the Unpowered X-57 Mod-III Aircraft

Computational Analysis

of the External Aerodynamics of the

Unpowered X - 57 Mod - III Aircraft

Seung Y. Yoo

NASA Armstrong Fli ght Research Center, Edwards, California, 93523 , USA

Jared C. Duensing

Scie nce & Technology Corporation, Moffet Field, California, 94035 , USA Investigation s of the external aerodynamics of the unpowered X - 57 Mod - III configuration using computational fluid dynamics are presented. Two different Reynolds - a veraged Navier - Stokes flow solvers were used in the analysis: the ST A R - CCM+ unstructured solver using polyhedral grid topology , and the L aunch Ascent Vehicle Aerodynamics (LAVA) structured curvilinear flow solver using structured overset grid topology . A g rid refinement study was conducted and suitable grid resolution was determined by examining the forces and moments of the aircraft . Code - to - code comparison show s that STAR - CCM+ and LAVA are in good agreement both in quantitative values and trends . The angl e - of - att ack sweep and sideslip - angle sweep were performed. Results indicate that lift coefficient s have a sharp dr o p at stall. At high angle of att ack , STAR - CCM+ and LAVA show different flow separation behavior possibly d ue to differences in the turbulence model. The sideslip - angle sweep result s show constant pitching moment from 0° to 15° , then a sharp increase between 15° and 20° sideslip angle .

I. Nomenclature AFRC = Armstrong Flight Research Center ARC = Ames Research Center C = d rag coefficient D C = l ift coefficient L C Y = s ide - force coefficient C = r olling - moment coefficient l C = p itching - moment coefficient m C = y awing - moment coefficient n CAD = c omputer - aided design CFD = c omputational f luid d ynamics LAVA = Launch Ascent Vehicle A erodynamics NASA = National Aeronautics and Space Administration RANS = Reynolds - a veraged Navier - Stokes y+ = n on - dimensional wall distance II. Introduction The X - 57 Maxwell, or Scalable Convergent Electric Propulsion Technology and Operations Research (SCEPTOR) , is o ne of the X - plane s funded by Flight Demonstration and Capabilities ( FDC ) under the Integrated Aerospace Engineer, Control s and Dynamics, P.O. Box 273, MS 4840D, Edwards, California, 93523 - 0273.

Computational Aerosciences Branch, NAS Division, Moffett Field, California, 94035 .

Aviation Systems Program ( IASP ) in the Aeronautics Research Mission Directorate ( ARMD ) of the National Aeronautics and Space Administration (NASA) . The X - 57 progr am has several key research objectives aimed at reducing aviation energy usage. The research objectives include demonstration of a propeller - based distributed electric propulsion (DEP) system, reduction of induced drag through wing - tip - mounted propeller s , and improved lift efficiency using leading - edge high - lift motors and nacelles.

The X - 57 progra m is divided into several phases , denoted by the modification (Mod) made to the ai rplane . Each M od mod if ies the existing T ECNAM P - 2006T aircraft (Costruzioni Ae ronautiche TECNAM S.p.A, Capua, Italy) in a systematic and modular manner to achieve each research objective . There are four Mods , as shown in Fig. 1 . The Mod - I , shown in Fig. 1(a) , is the original T ECNAM P - 2006T aircraft , which serve s as the baseline for the performance comparison . The Mod - II , shown in Fig. 1(b) , repla ces the original engine and propellers with an electric al propulsion system and optimized propellers. The Mod - III , shown in Fig. 1(c) , replaces the wing of Mod - II with a high - aspect - ratio wing with and wing - tip - mounted propellers . The wing - tip propellers rotate in the direction that counteract s the wing - t ip vortices, intended to reduce induced drag . The Mod - IV , shown in Fig. 1(d) , incorporates the leading - edge - mounted high - lift propellers to Mod - III to provide additional lift at takeoff and landing conditions .

Fig . 1 . X - 57 modification ( Mod ) comparison .

As the X - 57 is a manned experimental project , a significant amount of precaution is taken prior to the flight - test campaign. T he safety of the pilot and the aircraft are of the highest priority, thus the external flow physics of the aircraft are investigated and examined using c omputational f luid d ynamics (CFD) simulations and analysis techniques .

Due to limited wind tunnel testi ng, the CFD results are used in conjunction with wind - tunnel experimental data to develop the aerodynamics database that is used in the pilot - in - the - loop simulation. The pilot - in - the - loop simulation is used for aircraft familiarization trainings and for th e mission .

This paper presents the results of the CFD analysis that was performed , specifically angle - of - att ack sweeps and sideslip - angle sweeps, on the unpowered X - 57 Mod - III configuration. The angle - of - att ack sweeps and sideslip - angle sweeps were performed for three different flap - deflection angles: cruise (0.0°) ; takeoff (10.0°) ; and landing (30.0° ).

The work s presented are predecessor s o f the powered X - 57 Mod - III and Mod - IV analysis as well as aerodynamic database generation . T he term “aircraft” is used herein to describe the unpowered X - 57 Mod - III.

T he NASA Armstrong Flight Research Center (AFRC) and the NASA Ames Research Center (ARC) collaborated in the effort . The AFRC used a commercially available STAR - CCM+ [1] unstructured solver while ARC used the in - house - developed Launch Ascent Vehicle Aerodynamics (LAVA) structured curvilinear solver [2]. Simulation settings and modeling techniques were based on previous work that developed the best practices for si mulating the X - 57 wind - tunn el model using the same solvers [3].

Section II below describes the flow solvers and the numerical settings utilized in the investigation . Section III presents the geometry and grid generation process . Section IV presents results and assoc iated discussions . Section V summarizes the findings.

III. Flow Solvers This section presents the solver s and the numerical settings used to perform the simulations. Two different Reynolds - averaged Navier - Stokes (RANS) equation solvers were used to analyze the aircraft : the STA R - CCM+ unstructured solver , and the LAVA structured curvilinear solver .

A. STAR - CCM+ The STAR - CCM+ is a commercially available CFD package that include s geometry / computer - aided design ( CAD ) manipulation tools, a grid generator capable generating different unstructured grid topologies (polyhedral, Cartesian, tetrahedral), various flow solvers, and post - processing tools . The flow solvers of STAR - CCM+ solve the RANS equation in finite - volume, cell - centered formulation. The compressible flow solver using the s teady - state, implicit time - stepping scheme was utilized . The inviscid fluxes were discretized using the second - order Roe flux - difference splitting scheme. The algebraic multigrid linear solver using the Gauss - Seidel relaxation scheme was employed to solve the system of linearized equations. The gradients were computed using the h ybrid Gauss l east - s quare s m ethod and limited using the Venkatakrishanan scheme [4]. A l ow - Mach preconditioner was not utilized so as to be consistent with LAVA solver settings . The flow was assumed fully turbulent and the Spalart - Allmaras turbulence model with the rotational correction was used to resolve the turbulence [5]. The quadratic constitu tive relationship [6] was not utilized due to lack of availability in STAR - CCM+ for the Spalart - Allamaras model. The Courant - Friedrichs - Lewy (CFL) number was linearly ramped from 0.01 to 25.0 in the initial 100 iterations.

All simulations were performed using the freestream condition as the initial solution.

B. Launch A scent Vehicle Aerodynamic (LAVA) LAVA was developed and it is maintained by ARC . Similar to STAR - CCM+, it consists of several different flow solvers and it is capable of using various grid topology (Cartesian, unstructured polyhedral, structured overset) depending on th e choice of the solver. The structured curvilinear solver was used in this study . A second - order convective flux discretization with first - order upwind scheme in time was used with a Van - Albada slope limiter. F ully turbulent flow was assumed and the Sp alar t - Allmaras turbulence model [5] was used with the quadratic constitutive relation [6] and rotation correction. As with STAR - CCM+, the low Mach preconditioner was not utilized.

A ll simulations were performed using the freestream condition as the initial so lution. More detail can be foun d in the previous study [3].

IV. Geometry and Grid Generation This section presents the detail of the geometry and grid generation process . The 100 percent scale model of the X - 57 Mod - III configuration was used to perform the simulations . All control surfaces (aileron s , rudder , stabilator, and trim tab ) and their deflections were modeled . Three nominal flap - deflection angles were modeled : 0 ° deflection (cruise) ; 10 ° deflection (takeoff) ; and 30° deflection (land ing) . The flap deflection s are listed in Table 1.

Table 1. Flap - deflection angl es and associated flight phase.

Flight phase Flap - deflection angle , deg Cruise 0 Take off 10 Landing 30 Important dimension s and reference parameter s of the aircraft such as the mean the aerodynamic chord, span, and wing area are tabulated in Table 2 . The origin of the main coordinate system with respect to the nose leading edge of the aircraft and the moment reference center with respect of the origin of the main coo rdinate system are also tabulated in Table 2 . The main coordinate system is defined with the x - axis pointing in the direction from the nose to tail of the aircraft, the y - axis in the direction out the right wing, and the z - axis pointing up based on the rig ht - hand coordinate system. The body - axis coordinate system, with its origin at the moment reference center, is defined with the x - axis in the direction from tail to the nose of the aircraft, the y - axis in the direction out the right wing, and the z - axis po inting down based on the right - hand coordinate system. Figure 2 shows the main coordinate system and the body - axis coordinate system. The positive control surface def lections, defined based on the trailing edge orientation, are tabulated in Table 3 .

Table 2 . The X - 57 geometric parameters used in the study.

Parameter Value Mean aerodyn amic chord 2.13 ft Span 31.633 ft Wing area 66.667 ft Moment reference center with respect to origin (12.8997, 0.0, 5.377) ft Origin with respect to nose ( - 1.889, 0.0, 4.242) ft Table 3 . Positive control surface def lection orientation.

Control surface Positive deflection Aileron Trailing edge down Rudder Trailing edge left Stabilator Trailing edge down Pitch t rim tab Trailing edge down F ig. 2 . Coordinate system orientations and origins.

Using the identical underlying model , computational grid s were generated independently for STAR - CCM+ and LAVA as the two solvers utilize different type s of topology : STAR - CCM+ used the unstructured polyhedral grid topology while LAVA used the structured overset grid topology . The f ollowing subsections describe the grid generation process and settings . T he terminologies “ grid ” and “ mesh ” are used interchangeably herein .

A. Grid Generation with STAR - CCM+ As a comprehensive CFD p ackage, STAR - CCM+ contains its own geometry manipulation and grid generation tools which were utilized in th is work. Individual control surfaces ( aileron, rudder, stabilator, and pitch trim tab ) were modeled such that they can be deflected independently . T he flap deflection s were modeled in the CAD model , and thus were not manipulated within the STAR - CCM+ environment .

G rid s based on the STAR - CCM+ polyhedral grid topology combined with the prism layer grid were created using the STAR - CCM+ grid generator. Half of the aircraft was modeled utilizing the symmetry boundary condition unless asymmetric geometry (aileron or rudder deflection) or flow condition (nonzero sideslip condition) was present.

Essential grid parameters such as the growth ratio, cell size, far field length, et c etera were specified based on the gridding guidelines provided by the American Institute of Aeronautics and Astronautics ( AIAA ) CFD High Lift Prediction Workshop [7] as well as best practices developed during previous work [3]. The pr ism layer grid of 31 layers was created to capture the flow in the boundary layer . The total height of the prism layer was initially specified based on the turbulent boundary layer thickness , then adjusted based on the results of background studies .

Grid wall spacing was determined based on the wing y+ value of 0.3 . The far field distance was specified as a 50 wing - span length . The surface c ell size of individual components of the aircraft (fuselage, vertical tail, rudder, stabilator, and wing) were specif ied as a percentage of a grid reference length to simplify the process of systematically creating grid s of different resolution. A representative polyhedral surface grid of the aircraft is shown in Fig. 3 .

Fig . 3 . Representative STAR - CCM+ polyhedral surface grid of the X - 57 with all control surfaces deflected to maximum deflection angle.

B. Grid Generation with Lauch Ascent Vehicle Aerodynamics ( LAVA ) Structured overset grids were created to model the X - 57 Mod - III configuration. Various tools were utilized in the gr id generation process. The ANSA [8], a CAD and mesh generation software, was used to discretize the provided model which served as the basis for the overset grids. The Poi ntwise grid generation software [9] (Pointwise, Inc., Fort Worth, T exas) and Chimera Grid Tools [10] were used to create the structured overset grids. As with the model s used in STAR - CCM+ simulations, all of the control surfaces were modeled independently. A full span model was utilized regardless of the symmetry . The ini tial volume grid spacing w as based on the wing y+ value of 1.0 or smaller, depending on the grid resolution level. The nearfield grids were generated using the curvilinear grids and the farfield grids were created using the Cartesian grid s . A n in - house - dev eloped grid connecti vity tool was applied to the volume grids to interpolate the overlapping grids. The surface grids are shown in Fig. 4. Full details of the control - surface modeling and grid generation parameters are presented in a previously published s tudy [3].

Fig . 4 . Representative structured overset surface grid s used with Launch Ascent Vehicle Aerodynamics ( LAVA ) .

V. Results Computation al fluid dynamics simulation results are presented in this section. The force and moment coefficients are presented for all simulations performed. The lift coefficient (C ), drag coefficient (C ), and side - force coefficient L D (C ) were normalized u sing the wing area. The rolling - moment coefficient (C ) and yawing - moment coe fficient (C ) Y l n were normalized using the wingspan and wing area. The pitching - moment coefficient (C ) was normalized using the m mean aerodynamic chord and wing area. The moment coefficients were computed about the moment reference center provided in Table 2 . The C and C were computed about the stability axis and t he C , C , C , and C were computed D L Y l m n about the body axis coordinate system. The origin of the stability axis and the body axis were placed at the moment reference center.

The results are presented i n the following order. First, the results of the grid refinement study are presented which determined the grid re solution necessary to resolve the flow physics . Succeeding the grid refinement study , the angle - of - att ack sweep study and the sideslip - angle sweep study are presented.

The angle - of - att ack sweeps and sideslip - angle sweeps w ere conducted for three different flap - deflection angles as tabulated in Table 1 : 0 ° deflection (cruise) , 10 ° deflection (takeoff) , and 30 ° deflection (landing ) with th e respective atmospheric condition s associated with each flap - deflection angle . The atmospheric conditions per flap - deflection angles are tabulated in Table 4 . The angle s o f attack and sideslip angle s simulated for each flap deflection are tabulated in Table 5 .

All figures presented in the following sub section s identify the STAR - CCM+ results with blue color and the LAVA results with red color. All line plots presented show the 0 ° flap - deflection results with solid lines , the 10 ° flap - deflection results with dashed lines, and the 30 ° flap - deflection results with dash - dot lines.

Table 4. Atmospheric conditions for flap deflection s.

Flap = 0 ° Flap = 10 ° Flap = 30 ° Altitude , ft 8000 2500 2500 Mach 0.233 0.149 0.139 Density , slug/ft 1.8628E - 3 2.20782E - 3 2.20782E - 3 Static p ressure , lbf/ft 1571.9 1931.9 1931.9 Static t emperature , K 272.3 283.2 283.2 Coef ficient of viscosity , slug/ft/s 3.57532E - 7 3.68708E - 7 3.68708E - 7 Reynolds number 1.32E6 9.875E5 9.21E5 Table 5. Angle - of - att ack sweep and sideslip - angle sweep run matrix.

Flap deflection , deg Angle of att ack , deg Sideslip angle , deg - 2, 0, 2, 4, 8, 10, 12, 14, 15, 0 0 16, 17, 18, 19, 20, 22, 24 Angle - of - att ack - 2, 2, 4, 8, 10, 12, 13, 10 0 sweep 14, 15, 16, 18, 20, 22 - 2, 2, 4, 8, 9, 10, 11, 12, 13, 30 0 14, 15, 16, 17, 18, 20, 24 0, 5, 0 2 10 (STAR - CCM+ only) , 15 (STAR - CCM+ only) 0, 5, S ideslip - angle 10 2 10 (STAR - CCM+ only) , sweep 15 (STAR - CCM+ only) 0, 5, 30 2 10 (STAR - CCM+ only) , 15 (STAR - CCM+ only) A. Grid Refinement Study A grid refinement study was performed to determine the grid resolution requirement needed to resolve flow phenemona . The aircraft configura tion of maximum control surface deflection s, largest angle of att ack , and largest sideslip angle wa s used in the study. The freestream flow angles and control surface deflection angles are tabulated in Table 6 . The atmospheric condition used is tabulated in Table 7 .

Three different grid resolutions were simulated using STAR - CCM+ : a coarse grid of 4 5 million cells , a medium grid of 77 million cells , and a fine grid of 126 million cells. The force and moment coefficients for each grid resolution are tabulated in Table 8 . The relative errors of coarse and medium grid with respect to the fine grid are tabulated in Table 9 . Results show ed that, with the exception of C , the relative error of the force and moment coefficients of both l the coarse and the medium grid are under 3 percent with respect to the fine grid. The coarse grid under estimates the C by 17.7 percent relative to the fine grid , whereas the medium grid over - predicts C by 1.1 percent . T he values of C l l l are , however, small - close to zero - which is prone to large relative error. Based on the result presented, the coarse grid was selected to perform the STAR - CCM+ CFD simulations , identified in the tables using bold text .

For LAVA, five different grid reso lutions were simulated: a coarse grid of 60.1 milli on nodes, a medium grid of 95.2 million nodes, a fine grid of 148.6 mill ion nodes, a very - fine grid of 312.6 million nodes, and an extra - fine grid of 425.7 million nodes. The force and moment coefficients and their respective relative error to the extra - fine grid are presented in Table 10 and Table 11 , respectively. Similar to STAR - CCM+ results, r elative errors are small as they are under 4 percent except for C . T he relative errors of the rolling moment coefficient are , however, converging toward l the extra - fine grid , and the absolute value of the coefficient is small and susceptible to large relative error. Based on the results, the fine grid was selected to perform the LAVA CFD simulations , identified in the tables using bold text .

Using the LAVA results as the reference, the STAR - CCM+ result s are within 10 percent of th e LAVA results for the force and moments coefficients. The coefficient with the largest difference is C , with STAR - CCM+ l under estimat ing it by 9.9 percent relative to the LAVA solution. The C has the smallest relative difference , with D STAR - CCM+ over estima t ing it by 1.2 percent relative to LAVA. The force and moment coefficient of the selected grid resolution for the STAR - CCM+ and LAVA are summarized in Table 12.

Table 6. Aircraft orientation and control - surface - deflection used in grid refinement study.

Parameter Angle , deg Angle of att ack 10 Sideslip angle 20 Aileron - 25 Flap 30 Rudder - 28 Stabilator - 15 Trim tab - 18 Table 7. Atmospheric conditions used in grid refinement study.

Altitude , ft 2500 Mach 0.139 Density , slug/ft 2.20782E - 3 Static p ressure , lbf/ft 1931.9 Static t emperature , K 283.2 Coef fficient of viscosity , slug/ft/s 3.68708E - 7 Velocity , ft/s 153.87 Reynolds number 9.21E5 Table 8. STAR - CCM+ forces and moments for grid refinement study for full deflection; selected resolution shown in bold.

STAR - CCM+ C C C C C C D L Y l m n g rid r esolution coarse (45e6 cells) 0.30394 1.46749 - 0.61327 0.01631 2.41895 0.12050 medium (77e6 cells) 0.30623 1.47778 - 0.61585 0.02004 2.41327 0.12257 fine (126e6 cells) 0.30797 1.47193 - 0.61886 0.01982 2.38941 0.12337 Table 9 . STAR - CCM+ force and moment coefficient error with respect to fine grid; selected resolution shown in bold.

STAR - CCM+ C error , C error , C error , C error , C error , C error , D L Y l m n g rid r esolution % % % % % % coarse (45 mil. cell) - 1.1 - 0.3 - 0.9 - 17.7 1.2 - 2.3 medium (77 mil. cell) - 0.5 0.4 - 0.5 1.1 1.0 - 0.6 Table 10 . LAVA forces and moments for grid refinement study for full deflection; selected resolution shown in bold.

LAVA g rid r esolution C C C C C C D L Y l m n coarse (60.1 mil. nodes) 0.3024 1.57 - 0.6053 0.0135 2.396 0.1119 medium (95.2 mil. nodes) 0.29838 1.55 - 0.595 0.016 2.404 0.1117 fine (248.6 mil. nodes) 0.30036 1.56 - 0.5876 0.0181 2.398 0.1106 very - fine (312.6 mil. nodes) 0.30265 1.56 - 0.5844 0.0226 2.402 0.1121 extra - fine (425.7 mil nodes) 0.30237 1.56 - 0.582 0.0239 2.401 0.1126 Table 11 . LAVA force and moment coefficient error with respect to X - fine grid; selected resolution shown in bold.

C error , C error , C error , C error , C error , C error , D L Y l m n LAVA g rid r esolution % % % % % % coarse (60.1 mil. nodes) - 0.01 - 0.64 - 4.00 43.51 0.21 0.62 medium (95.2 mil. nodes) 1.32 0.51 - 2.23 33.05 - 0.12 0.80 fine (248.6 mil. nodes) 0.66 - 0.26 - 0.96 24.27 0.12 1.78 very - fine (312.6 mil. nodes) - 0.09 - 0.32 - 0.41 5.44 - 0.04 0.44 Table 12 . STAR - CCM+ and LAVA force and moment coefficients of selected grid resolution; selected resolution shown in bold.

Flow s olver C C C C C C D L Y l m n LAVA 0.30036 1.56 - 0.5876 0.0181 2.398 0.1106 STAR - CCM+ 0.30394 1.4 7 - 0.613 3 0 .0163 2.419 0.1205 B. Angle - of - A tt ack Sweep Results of the angle - of - att ack sweep for three flap deflection s , shown in Table 1 , are presented in this section.

C ontrol surfaces other than the flap were set to the neutral position (no deflection) . The atmospheric conditions for each flap deflection are tabulated in Table 4 . The f ollowing discussions analyze flow physics as well as the differences in solutions of th e two solvers.

The r esults of C , presented in Fig. 5, show that STARCCM+ and LAVA results compare well for the angles of L attack in the linear lift curve slope region for all three flap deflection s. R esults also show , however, that there is increase in dif ference in C between STAR - CCM+ and LAVA with an increase in flap - deflection angle in the linear L lift curve slope region. This trend can be analyzed using the surface pressure coefficient contours and streamline on the upper surface of the wing at 8 ° angle of att ack for 0 ° , 10 ° , and 30 ° flap deflection , shown in Fig. 6 . Blue arrows in the figure point to location s on the wing ha ving different flow feature between two solvers. At 0 ° flap deflection , shown in Fig 6(a) , STAR - CCM+ and LAVA both show similar sol ution of attached flow. At 10 ° flap deflection , shown in Fig. 6(b) , STAR - CCM+ show s a small separation region on the outboard trailing edge of the wing that is not present in the LAVA solution. At 30 ° flap deflection , shown in Fig. 6(c) , the STAR - CCM+ resu lt shows a clearly separated region on the outboard trailing edge of the wing , while the LAVA result shows attached flow . Thu s the STAR - CCM+ estimat es a lower C .

L Comparing the C at higher angle of att ack , near stall, the discrepancies in solution produced by STAR - CCM+ L and LAVA are large due to difference s in the separation behavior predicted by the two solvers. An example is shown in the surface pressure coefficient contour of the wing for the 30 ° flap - defl ection angle, presented in Fig. 7 . Blue arrows point to location s on the wing ha ving a different flow feature between two solvers. The surface pressure contour at 8 ° angle of att ack , shown in Fig 7(a) , show s the STAR - CCM+ result with a thin separation region in the outboard trailing edge , as discussed above . At 14 ° angle of att ack , shown in Fig 7(b) , the STAR - CCM+ result shows flow separation in the wing root region that is not present in the LAVA solution. The r esults of both solvers show separation at the outboard of the wing at 14 ° angle of att ack . At 18 ° angle of att ack , shown in Fig 7(c) , the STAR - CCM+ solution shows t hree separated region s while the lAVA solution shows the two separated regions. The differences in the flow separation are reflected in the C curve : STARCCM+ predicts a lower C in the post - stall angle of att ack compared L L to LAVA. The cause of the difference is possibly due to the quadratic constitutive relation that is used in LAVA but is not used in STAR - CCM+ , shown to affect the wing - fuselage j unction flow [6] .

Examining the C at the stall for all three flap deflection s , shown in Fig. 5 , the drop in C at the stall is not L L significant. The 0° flap deflection , shown with notation in Fig. 8 , is used as an example. The LAVA result show s an 11.7 - percent drop relative to the maximum C between the angle of att ack of 19° ( angle of att ack of maximum C ) L L and that of 22°. The STAR - CCM+ result show s a larger but more gradual drop in lift compared to LAVA : an 1 8.3 - percent drop relative to the maximum C between the angle of att ack of 17 ° ( angle of att ack of maximum C ) L L and that of 22°. To provide a basis of comparison, the STAR - CCM+ CFD analysis of the NASA Gulfstream G III (Gulfstream Aerospace Corporation, Savannah, Georgia) aircraft showed a 27.5 - percent sharp drop in lift at stall relative to maximum lift [11].

The C compar e well at low angle s of attack for all three flap deflection s , as shown in Fig. 9 . The STAR - CCM+ D pr edicts a higher C at 15 ° , 16 ° , and 17 ° angle s of attack for 0 ° , 10 ° , and 30 ° flap deflection , respectively. The C , D m presented in Fig. 10 , shows that STAR - CCM+ and LAVA compare well . Examining the C of the 0 ° flap deflection , m shown in Fig. 10 , t here can be seen a sudden increase in C at angle s of attack above 20 ° that is not shown in other m flap deflection s . For clarity, C as a function of angle of att ack for 0 ° flap deflection is shown in Fig. 11 . This m phenomena can be correlated to the surface p ressure coefficient contour of the aircraft at 22 ° angle attack for 0 ° and 10 ° flap deflection , shown in Fig. 12 . A large separation bubble that envelops the majority of the upper surface exist s on the stabilator at 0 ° flap deflection , shown in Fig. 12(a) . On the 10 ° flap deflection configuration , shown in Fig. 12(b) , the stabilator has a separation region that is localized to the inboard of the upper surface and grows from the leading edge to trailing edge. Based on the size of the separation region shown, the s tabilator of 10 ° flap - deflection configuration would produce more lift compared to that of the 0 ° flap - deflection configuration, hence producing more nose - down pitching moment.

Fig . 5 . Angle - of - att ack sweep: C L v ersu s angle of att ack for 0°, 10°, and 30° flap - deflection angles .

Fig . 6 . Surface pressure coefficient contour of the upper surface of the wing at 8° angle of att ack : a) flap = 0° ; b) flap = 10° ; and c) flap = 30°.

Fig . 7 . Surface pressure coefficient contour of the upper surface of the wing at 30° flap deflection at selected angles of attack : a) angle of att ack = 8° ; b) angle of att ack = 14° ; and c) angle of att ack = 18°.

Fig . 8 . Angle - of - att ack sweep: C L v ersu s angle of att ack for 0° flap - deflection angles ; m aximum C L and stall for STAR - CCM+ and LAVA denoted.

Fig . 9 . Angle - of - att ack sweep: C D v ersu s angle of att ack for 0°, 10°, and 30° flap - deflection angles.

Fig . 10 . Angle - of - att ack sweep: C m v ersu s angle of att ack for 0°, 10°, and 30° flap - deflection angles.

Fig . 11 . Angle - of - att ack sweep: C v ersu s angle of att ack for 0° flap - deflection angles.

m Fig . 12 . STARCCM+ s urface pressure coefficient contour at 22° angle of att ack for simulated flap - deflection angles : a) flap = 0° ; and b) flap = 10° .

C. Sideslip - Angle Sweep Results of the sideslip - angle sweep s at a constant angle of att ack of 2 ° are presented for 0 ° , 10 ° , and 30 ° flap deflection s: C in Fig. 13 , C in Fig. 14 , C in Fig. 15 , C in Fig. 16 , C in Fig. 17 , and C in Fig. 18 . The sideslip L D Y l m n angle s simulated are tabulated in Table 5 . It should be noted that not all sideslip angle s were simulated by LAVA; LAVA simulated 5 ° and 20 ° while STAR - CCM+ simulated 5 ° , 10 ° , 15 ° , and 20 ° . As with the angle - of - att ack sweep study, c ontrol surfaces other than the flap were set to the neutral position (no deflection). The atmospheric conditions for each flap deflection are tabulated in Table 4 .

Comparing the presented force and moment coefficients of STAR - CCM+ and LAVA, results from t he two solvers are in agreement in both values and trends. The C , shown in Fig. 13 , is approximately constant from 0 ° to 5 ° sideslip L angle , then decreases as sideslip angle increases for the simulated flap deflection s. The C , shown in Fig. 14 , d e creases D as the sideslip angle increases . The slope of C as a function of sideslip angle is identical for 0 ° , 10 ° , and 30 ° flap D deflection s. Similarly, t he C , shown in Fig. 15, decreases linearly with increase in sideslip angle with flap deflection Y having negligible effect. The C , Fig. 16, dec reases linearly with increase in sideslip angle , however, the rate of change l decreases with increase with flap - deflection angle. The C , Fig. 17, is approximately constant from 0 ° to 15 ° sideslip m angle , and then suddenly the C increases at 20 ° sideslip angle for all flap deflection s. This trend is only shown in m STAR - CCM+ result ( LAVA did not run 10 ° and 15 ° sideslip angle ) . The C at 5 ° and 20 ° sideslip angle , however, m compare well between STAR - CCM+ and LA VA.

The increase in pitching moment for sideslip angle above 20° can be analyzed by examining Fig. 19. Figure 19 shows the surface pressure coefficient contour of the upper surface of the stabilator for 0° flap deflection at 5°, 10°, 15°, and 20° sideslip angle s with constant angle of att ack of 2 ° . The surface pressure coefficient on the upper surface fo the stabilator for sideslip angle s of 5° to 15° remains approximately constant. A t 20°, however, there is increase in surface pressure on the upper surface of the stabilator , denoted by a blue arrow in the figure. This increase in the surface pressure decreases the lift generated by the stabilator , effectively increas ing the C , as seen in Fig. 17 .

m The surface pressure coefficient contour of 0 ° , 10 ° , and 30 ° flap deflection s at 2 ° angle of att ack and 20° sideslip angle are presented in Fig. 20 . The figure shows that there is a flow separation on the leading edge of the rudder for the simulated flap deflection s. T he size of the separation region is independent of the flap - deflection angle . The location of the separation region s are denoted in the figure by red arrow s . There is also flow separation on the leading edge of the right wing root section for the simulated fla p deflection s. T he size of the separation region grows in the spanwise direction with increas e in the flap - deflection angle. The separation region s are denoted by blue arrow s in the figure.

Fig . 13 . Sideslip - angle sweep at 2° angle of att ack : C v ersu s sideslip angle for 0°, 10°, and 30° flap - deflection L angles.

Fig . 14 . Sideslip - angle sweep at 2° angle of att ack : C D v ersu s sideslip angle for 0°, 10°, and 30° flap - deflection angles.

Fig . 15 . Sideslip - angle sweep at 2° angle of att ack : C v ersu s sid eslip angle for 0°, 10°, and 30° flap - deflection Y angles .

Fig . 16 . Sideslip - angle sweep at 2° angle of att ack : C v ersu s sideslip angle for 0°, 10°, and 30° flap - deflection l angles .

Fig . 17 . Sideslip - angle sweep at 2° angle of att ack : C v ersu s sidesli p angle for 0°, 10°, and 30° flap - deflection m angles .

Fig . 18 . Sideslip - angle sweep at 2° angle of att ack : C n v ersu s sideslip angle for 0°, 10°, and 30° flap - deflection angles .

Fig . 19 . STARCCM+ s urface pressure coeffi cient contour of stabilator : 0° flap - deflection , 2° angle of att ack : a) sideslip angle = 5° ; b) sideslip angle = 10° ; c) sideslip angle = 15° ; and d) sideslip angle = 20° .

Fig . 20 . STARCCM+ s urface pressure coefficient contour of aircraft at 2 0° sideslip angle for simulated flap deflection s at 2° angle of att ack : a) flap = 0 ° ; b) flap = 10° ; and c) flap = 30 °.

VI. Conclusion This paper presented computational analysis of t he unpowered, Mod - III of the X - 57 using the STAR - CCM+ and the Launch Ascent Vehicle Aerodynamics ( LAVA ) flow solvers . A grid refinement study showed that adequate grid resolution was used in the simulations , with force and moment coefficients predictions being within 3 percent except for rolling moment coefficient ( a small value for both flow solvers ) . Based on the grid resolution selecte d, angle - of - att ack sweep s and sideslip - angle sweep s were performed .

Results of the angle - of - att ack sweep s were presented with the results showing agreement between the two flow solvers. The discrepancies between the two solvers grow with increase in flap deflection due to STAR - CCM+ having outboard trailing edge separation that is not present in the LAVA solutions. The difference between the solutions of two solvers are present at angle of att ack near stall due to the different separation behaviors predicte d by the solvers - STAR - CCM+ does not us e quadratic constitutive relationship with the turbulence model. R esults also show that flap deflection s do not change the lift curve slope in the linear region ; h owever, increasing the flap - deflection angle increase s the maximum lift while lowering the angle of att ack at which the lift occurs. Additionally, a sharp increase in pitching moment was observed at 0 ° flap deflection due to flow separation on the upper surface of the stabilator that did not occur at higher flap - deflection angles.

Sideslip - angle sweep results showed that forces and moments change linearly with change in sideslip angle except for the pitching moment. I nvestigation of the flow over the stabilator showed that while surface pressure is approximately constant from 5 ° to 15 ° sideslip angle , it increases at 20 ° sideslip angle , decreasing the lift generated by the stabilator and producing a sharp increase in t he pitching moment. The s urface pressure coefficient also showed a separation region on the leading edge of the wing, near the wing - fuselage junction, that grows in spanwise direction with an increase in flap - deflection angle.

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