Dragonfly Preparation for Powered Flight Wind Tunnel and CFD Modelling

Dragonfly Preparation for Powered Flight Wind Tunnel and CFD Modelling

Peter Lorber Brian Wallace Kalki Sharma Patrick Bowles LM Fellow Aeronautical Engr, Staff Aeronautical Engr, Sr Computational Aero, Mgr Sikorsky, A Lockheed Martin Company, Stratford, CT Karl Edquist Brian McGrath William Kellermeyer Paul Gilles Senior Aerospace Engr Senior Professional Staff Test Engineer NASA Langley Research Johns Hopkins Applied Research Laboratory National Full Scale Aerodynamics Center, Hampton, VA Laurel, MD Complex, Moffett Field, CA ABSTRACT Preparation for Powered Flight (PPF) is a critical phase for Dragonfly, the National Aeronautics and Space Administration (NASA) mission to Saturn’s moon Titan. During PPF the descending lander has been lowered below the backshell and uses its rotors to remove or “despin” any residual yaw motion of the vehicle. A 1/2-scale model of the Dragonfly PPF configuration was tested in the National Full-Scale Aerodynamics Complex (NFAC) 80 by 120-foot wind tunnel to measure aerodynamic loads and surface pressures on the lander and backshell. The results were used to improve understanding of the complex aerodynamic interactions and provide validation data for the Computational Fluid Dynamics (CFD) simulations used to develop the required aerodynamic databases for full-scale, Titan conditions. Configurations tested in the wind tunnel included Lander- alone-no-rotors (L), Lander-alone-with-rotors (LR), and Lander-with-rotors-and-Backshell (LRB). Both LR and LRB configurations were tested at multiple descent velocities and pitch and roll attitudes. The eight powered rotors were operated in nine combinations of active and inactive rotors, using steps of increasing RPM from idle to maximum. The results were used to identify conditions that generated the desired yaw moment for despin, and those that generated reduced or opposite sign moment. In parallel, CFD simulations applied the STAR-CCM+ toolset to the experimental geometry. Time-averaged virtual disks added spatially varying axial and rotational momentum to the flow to represent the rotors. There was generally good agreement between experiment and CFD, but conditions having strong interactions between the rotors, Lander, and Backshell were found to require more sophisticated methods. These lessons are being applied to the CFD for the full-scale Lander under Titan conditions.

1  for developing the EDL phase, with implementation INTRODUCTION supported by APL, LM Space, and Sikorsky. Dragonfly is Dragonfly is a NASA New Frontiers mission led by the Johns scheduled for launch in July 2028 and arrival at Titan in late Hopkins University Applied Physics Laboratory (APL) to 2034, followed by a roughly three-year science mission.

study prebiotic chemistry on the surface of Titan, Saturn’s largest moon, using a relocatable rotorcraft lander, as discussed in Ref. (1) and (2). Getting the lander to the surface requires a precise Entry, Descent, and Landing (EDL) sequence starting with separating the cruise stage, atmospheric entry, deployment of parachutes, and heat shield jettison, as shown in Figure 1 . The lander is then posed (lowered) below the backshell to allow the rotors to spin, beginning the Preparation for Powered Flight (PPF) phase.

EDL During PPF pairs of rotors will be used to reduce residual spin of the vehicle prior to releasing the lander and initiating the Transition to Powered Flight (TPF) phase. During TPF, the lander falls for one second, spins up its rotors, and transitions to level flight, Ref. (3), (4), (5). After TPF, the lander Figure 1. Dragonfly Entry, Descent and Landing phase.

descends, searches for a safe landing site using Light Detection and Ranging (LiDAR) sensors and cameras, and The PPF sequence is a unique portion of EDL and includes lands for the first time. The PPF phase is the focus of the requirements that reflect the need to understand the state of experimental and computational efforts described in this the posed lander during use of the rotors and prior to lander paper. NASA Ames and Langley have primary responsibility st P resented at the Vertical Flight Society’s 81 Annual Forum & Technology Display, Virginia Beach, VA, USA, May 20-22, 2025.

Copyright © 2025 by the Vertical Flight Society. All rights reserved.

release, to ensure high likelihood of a successful TPF installed at tunnel centerline height on a tower located 295ft sequence. One aspect of PPF that required special attention upstream of the inlet plane. This weather station measures was the use of computational fluid dynamics (CFD) methods atmospheric wind speed and direction.

to predict the aerodynamics of the combined LRB configuration with and without spinning rotors, a continuation of efforts started in Ref. (6).

Given the unique nature of the PPF sequence and the fact that no relevant test or flight aerodynamics data from previous EDL missions existed for building confidence in the CFD methods for PPF, tailored wind tunnel testing was conducted by the Dragonfly EDL team to generate such data. Previous Dragonfly wind tunnel tests have used NASA Langley facilities to investigate entry vehicle aerodynamics, coaxial rotor pair aerodynamics and vibratory loads, and powered lander aerodynamics for TPF and forward flight conditions.

Figure 2. NFAC configured for 80-x 120-ft testing The 80- by 120-ft section of the National Full Scale Aerodynamics Complex (NFAC), operated by the United These measurements are converted into centerline parameters States Air Force (USAF) at NASA Ames Research Center, by regular calibration, most recently in 2019. Figure 3 shows was chosen for Dragonfly PPF testing. The large test section how the systematic uncertainty of q obtained using the  was attractive because it to minimized wall interaction at low static/total pressure system grows for q <5psf and is  speed simulated descent. The test article included an unquantified below 1psf. This systematic uncertainty is approximately ½ scale model of the backshell and the lander dominated by measurement uncertainties in the transducers with eight powered rotors. The parachute was not included.

plus the uncertainty reported for the centerline pitot/static The test was conducted in December 2023 to February 2024 calibration probe.

by a team from NASA, APL, NFAC, and Sikorsky.

Computational Fluid Dynamics (CFD) modelling of Dragonfly in the Titan environment is critical to designing the vehicle and its flight control systems. Validation with wind tunnel data increases confidence and reduces uncertainty in the CFD-based aerodynamic databases required for the PPF and rotorcraft flight phases. The primary CFD for database generation couples a steady Navier-Stokes flow field solution with blade element based virtual disk models of the rotors, as discussed in Ref. (7). More sophisticated unsteady and discrete blade models are also used as part of a multi-fidelity CFD workflow, see Ref. (8).

Figure 3. Systematic uncertainties for the 80- by 120-ft centerline dynamic pressure.

EXPERIMENTAL METHODOLOGY The desired free stream velocities were 4 to 6.9m/s (q  =10- The success of the test depended on integration of the NFAC 30Pa or 0.2-0.6psf), in order to overlap Titan climb to hover wind tunnel, anemometry towers, and model positioning induced velocity ratios, assuming maximum rotor RPM of system with the separately developed models of the lander 1100 for Titan and 3800 at NFAC. These were below the and its rotors and the backshell. Each hardware element had calibrated operating range of the standard system. To its own set of instrumentation with software for calibration, accurately measure and set such low velocities, two 20ft tall data acquisition, real time monitoring, and post-test analysis.

towers were installed 69ft upstream, 27ft from each wall. The The eight rotors had independent speed control. Effective installation is depicted in Figure 4 . Each tower mounted four application of the experimental results required quantitative RM Young 81000 3-axis ultrasonic anemometers and two estimates of the uncertainty and appreciation of the relevant multi-instrument weather stations. A test-specific calibration scaling parameters.

was performed relative to a 3-axis Gill anemometer mounted at the model location. Calibration runs were performed at Test Facility each nominal speed across a variety of ambient conditions, as well as for perturbed conditions.

The NFAC configured to use the 80- by 120-ft indraft test section is shown in Figure 2 from Ref. (9). Standard facility A first-order combination of the two top 3-component instrumentation includes a probe system to obtain an averaged anemometers mounted on each tower yielded the best static pressure and total pressure at the test section inlet, Ref.

performance across the calibration dataset (Table 7) and was (9), plus measurements of barometric pressure, total implemented for the test. The 95% confidence uncertainty temperature, and relative humidity. A weather station is was ±0.3m/s. Test conditions could typically be set within ±0.15m/s. Testing was conducted in the late evening/night to directions for the rotors. The test envelope was +50  to +130  maximize productivity in prevailing weather conditions.

lander pitch and -5  to +30  lander roll. At 90  pitch and 0  Testing was paused whenever the atmospheric wind speed roll the bottom of the lander pointed upstream (toward the and direction created unacceptable variation in the velocities.

tunnel inlet), simulating a pure axial descent.

Figure 5. LRB and LR models installed Figure 4. Low speed anemometer calibration Table 1: Anemometer Calibration Model Results Anemometers Cal Check Check Data Used Bias [kt] Residual  Data  [kt] [kt] Top 2 (Avg) 0.071 0.081 - 0.011 Top 2 (Ind) 0.070 0.080 - 0.012 Figure 6. Installation overview, looking downstream Top 4 0.066 0.085 -0.029 Top 6 0.066 0.087 -0.026 All 8 0.053 0.083 -0.034 Dragonfly Model The ½ scale Dragonfly lander model represented the 2023 configuration of the full-scale lander but was not strictly geometrically scaled. The geometry was based on the Integrated Test Program flying drone and this model was originally used for a prior test in the NASA Langley 14x22.

The vertical fins and the cradle used to attach the pose Figure 7. Lander axis and rotor definitions mechanism were added. The pose mechanism itself was not The model had eight 30.5in. diameter, two-bladed, constant included. The Lander model has a nominal length of 1.95m pitch, variable RPM rotors. The carbon fiber blades were and was designed and fabricated by APL. The similarly scaled purchased from KDE Direct, who also provided the blade Backshell model has a diameter of D=2.6m and was geometry information for CFD validation. Each rotor was fabricated by NASA Langley. The Lander and Backshell each attached directly to a 5.7kW, three-phase, brushless outrunner have dedicated 6-component force and moment balances. The drive motor. Each rotor pair was coaxial, counter-rotating, interface hardware includes two independent stings to capture and canted laterally 5  bottom-out. The four rotors on the left each non-metric balance taper. The Lander sting passes side of the lander were mounted on ATI Industrial Delta 6- through the Backshell model with clearance to avoid fouling component load cells. Figure 9 shows the arrangement for one the two metric systems.

counter rotating rotor pair.

Figure 5 shows the Lander plus Backshell (LRB) configuration from upstream at the left, and a top view of the Lander (LR) at the right. Figure 6 shows the model positioned at test section mid-height, mounted to an NFAC variable pitch mechanism which in turn was mounted to the test section yaw mechanism The mid-point of the model was above the yaw table axis of rotation, 15ft (4.5m) ahead of the vertical strut.

Figure 7 shows a definition of the pitch and roll motions, the lander coordinate axis, and the numbering system and rotation Figure 8. Coaxial rotor pair assembly Model Rotor Control and Data Acquisition Table 2. Rotor RPM sequences Precise and stable rotor speed control was essential for the Sequence Active Rotors collection of quality data. The test matrix required rotor ZF All at 0 RPM control from 0 to 3800RPM at shaft torques from zero to Q1, Q7 2 Diagonal Lower Rotors R5+7, R6+8 4.9Nm. Model rotor speed control was established by incorporating eight independent Elmo model G-DRU100/100 Q5 4 Diagonal Rotors Electronic Speed Controllers (ESCs) located remote to the Q6 4 CCW Rotors model to alleviate volumetric constraints. Renishaw A5 8 Rotors incremental encoders were incorporated within the motor sub- RPM= 380 (idle) to 3800 (max) assemblies to provide relative rotor/motor position measurements. The ESCs minimized speed error with a tuned speed control loop utilizing differentiated position measurement as velocity feedback. The speed loop was carefully tuned to minimize overshoot or oscillations that could excite model dynamic responses that would contaminate balance and load cell measurements.

The large distance (90-ft) between the ESCs and the motors presented two challenges for routing the motor lead wires.

First, the driving voltage supplied to the ESCs was set Figure 9. Q1 and Q7 operating rotors and intended sufficiently high to overcome resistive and inductive losses in system torque for PPF despin. Q1 produces a +M z and the cables. Second, routing 24 current carrying conductors (3 Q7 produces a -M .

z phases x 8 motors) from the ESC to the motors presented the The model control software was designed to minimize model risk of bridging the metric model frame to the non-metric pilot fatigue for sustained testing. Figure 10 shows the sting that held the model. Ideally all model loads are designed organized layout of the model control and real time data to pass from the model frame through the balance to the sting.

interface. This single interface controls both rotor speed In reality, all sensor and motor conductors must also pass commanding and data recording.

from the metric model frame to the sting. Care was taken to minimize this bridging through the careful positioning of a service loop. Check load pull tests were conducted to confirm minimal bridging after final assembly.

Speed commands were sent to the eight ESCs from a remotely located host computer that was operated by a model pilot through a custom software interface developed in LabVIEW.

The software operated in either manual or automatic mode. In manual mode, the model pilot would pre-populate individual motor speed commands as prescribed by the test director/test matrix and simultaneously send the commands to the eight rotors. In automatic mode, the model pilot selected and initiated a preprogrammed rotor RPM sequence.

Figure 10. Model software control interface Each rotor RPM sequence was comprised of independent time series speed commands for each rotor. Table 2 lists the Both the ATI load cells and the NASA balance were sensitive primary sequences utilized in testing. The “Active Rotors” to large amplitude model dynamic oscillations that could step through a series of RPM commands and hold for enough exceed their load limits. In consideration of these instruments, time to assure stable speed control before proceeding to the the model control software included multiple safety features.

next step and RPM. The remaining rotors hold at idle speed These features include an automated rotor stop for the cases (380 RPM) for the entirety of the RPM sequence. The specific of rotor velocity limit exceedance, load cell limit exceedance, RPM steps were prescribed by the test matrix to satisfy test and NASA balance limit exceedance. For safety objectives. The automated rotor RPM sequences produce a considerations, the model pilot also had the options of multitude of unique model states in quick succession to triggering either a software stop sequence or pressing an minimize testing time. emergency stop button that disconnected power to the ESCs.

This paper is focused on the Q1 and Q7 rotor sequences which APL’s Data Acquisition System (DAS) recorded motor ESC despin the vehicle during PPF. Figure 9 provides a graphic of telemetry which included motor speed, bus voltage, ESC bus the rotor state and desired system control moment. current, and ESC temperature. The APL DAS also recorded ATI load cell force, moment and temperature data.

Thermocouples were placed on either side of each ATI load cell to measure the temperature gradient through the load cell.

The temperature gradient was monitored by the model pilot initial wind-off, rotors-off condition and subtracted from the and testing was paused when the gradient exceeded 4°F as wind-on measurements.

recommended by the load cell manufacturer to assure accurate load cell data.

In summary, this experiment employed a sophisticated rotor control system to manage the eight powered rotors of the 1/2- scale Dragonfly model. The system utilized three-phase brushless outrunner drive motors, ESCs, and a custom software interface to achieve precise control over rotor speed and sequence execution. By carefully designing and implementing the rotor control and data acquisition systems, Figure 11. Lander and Figure 12. Pressure tap the experiment was able to collect high-quality data on the backshell body axes. distributions.

aerodynamic interactions between the rotors, lander, and backshell, which is essential for understanding the complex The reported pressures are the differential relative to dynamics involved in the PPF phase.

freestream static, P-P , and the pressure coefficient C = (P -  P P ) / q . The pressures were scanned at a rate of 10Hz, giving   Lander and Backshell Instrumentation a potential unsteady bandwidth of up to 5Hz. The frequency response from the 25-100 cm pneumatic lines was estimated The Lander and Backshell force and moment balances were using the method of Ref. (10), which converts the unsteady provided by NASA Langley Research Center and were Navier-Stokes equations to a one-dimensional wave equation specified as model LRC-716-1K-1.50A and LRC-711B, having an analytical solution. The first resonance is at 65 to respectively. They are single-piece direct-read 6-component 350 Hz and for 10 Hz and below the amplification ratio is less balances which were calibrated at Langley in 2023. Table 3 than 1.03, indicating that the unsteady pressures could be used shows the full scale (FS) load ranges and calibration accuracy.

for at least qualitative purposes.

Table 3. Model balances range and accuracy The relatively sparse tap distribution was interpolated onto surface patch representations of the Lander and Backshell and Lander NF (N) AF(N) PM(Nm) RM(Nm) YM(Nm) SF(N) colored by the time averaged pressure, as in Figure 12 . This F S Range 4448 890 288 113 113 2224 Accuracy (%FS) 0.08 0.20 0.06 0.24 0.14 0.09 proved to be quite useful for developing understanding of the Backshell NF (N) AF(N) PM(Nm) RM(Nm) YM(Nm) SF(N) load measurements and correlating to CFD. The grey surfaces F S Range 2224 2224 435 81 239 1557 had no pressure taps.

Accuracy (%FS) 0.49 0.39 0.11 0.42 0.11 0.14 Rotor Fx (N) Fy(N) Fz(N) Tx(N) Ty(N) Tz(N) Wind Tunnel Data Acquisition F S Range 660 660 1980 60 60 60 Accuracy (%FS) 1.25 1.25 1.50 1.00 1.25 1.75 The NFAC Data Acquisition System (DAS) was used to The force and moment loads in the balance-axis systems were acquire the outputs from both internal balances, the standard converted to model body- and wind-axis systems. This and supplemental wind tunnel instrumentation, and model process includes translation, rotation, and converting all attitude surface pressures. Critically, a synthetic nominal rotor moments to right hand rule. Figure 11 shows the three primary RPM signal was acquired from the APL DAS to synchronize body axis systems for F , F , F , M , M , and M , aligned in the two datasets. In addition to acquiring the raw signals, the x y z x y z direction but translated in z.. The individual rotor forces and NFAC DAS was programmed to reduce the measurements to moments were reported initially in shaft axes, rotated to critical parameters. The data reduction included standard remove the cant, and then translated to the lander body axes. balance computations, coordinate transformations, weight tares, and tunnel condition computations (using the test- In addition to the force and moment measurements, there specific calibration). The NFAC DAS was configured to were 55 Lander static pressure taps and 49 Backshell taps, acquire analog signals, including the balance raw outputs, at shown by the markers in Figure 12 . These were acquired 2KHz. Data from digital instruments, including the model using two 64-port electronic pressure scanners, one for the surface pressure measurements, were recorded at 10Hz.

Lander and one for the Backshell. The calibration accuracy was ±0.06% of the 2500Pa (0.36psi) full scale. The reference The primary test objective was to produce a set of body force was the tunnel barometric manifold, as measured by an and moment measurements across a variety of pre-scripted absolute pressure sensor installed at the sting head. rotor control sweeps and attitudes. The volume of test conditions posed practical challenges for researchers due to Care was required because the aerodynamic pressures were the primary data (body force & moment, rotor performance) normally of the order 𝑞 = 10-30Pa, small compared to the ∞ being split between the APL DAS and the NFAC Steady DAS hydrostatic pressure, 𝜌𝑔ℎ~150 Pa, between the sting and the and Basic DAS. The first challenge was synchronizing the barometer in the control room and the ~10 Pa range of the acquisition start and the duration between the systems to absolute pressure transducers. Reference readings for all ensure all desired data were collected. This challenge was scanner ports and the two absolute sensors were taken at an solved with a straightforward “take data” trigger and by administratively adjusting the NFAC DAS point duration to a 0.5s running average to produce an assessment on the encompass the rotor sequence being executed. The second variation of the average during that period. The precision challenge was to identify each RPM step and align the three uncertainty error bars shown in plots in this paper correspond data streams. As shown in Figure 13 , the rising edge of the to the 95% (2σ) confidence interval from the running average.

RPM signal in each stream was used to align the start times.

Manual review was required to resolve noise spikes on the NFAC RPM signal, inconsistent skew in clock times, truncated point durations, and missing, mis-placed, or corrupted data files. Data alignment, application of data corrections, and generation of statistical and time series files was performed post-test by Sikorsky.

Figure 14. Test condition matrices for ZH, Q1, Q7, and A5 sequences at V = 5.3m/s  Figure 13. Merger of NFAC and APL data acquisition The resultant of systematic uncertainty and precision streams uncertainty is the total uncertainty reported in this paper.

Test Conditions 2 2 𝑈 ≈ √𝑈 + 𝑈 .

𝑠 𝑟 Testing was completed across 26 runs spanning just over 1 month. One major model change (adding the Backshell) took approximately a week midway through testing. The approach to data collection was to set freestream velocity and model pitch and roll, and then step the RPM up and back down for each selected rotor operating sequence ( Table 2 ).

Figure 14 shows the pitch/roll (P/R) test points for four primary rotor sequences: Zero Hold (ZH) with all rotors at 0 RPM, Q1 and Q7 with diagonal lower rotors spinning and stepped in RPM with the other 6 rotors at idle, and A5 with Figure 15. Sequence analysis and uncertainty example all eight rotors stepped at the same RPM. A total of 13,051 specific combinations of velocity, pitch, roll, rotor sequence, RPM, and model configuration were acquired. Gas Properties, Scaling and VRS The most relevant scaling parameters for this test are Experimental Uncertainty Reynolds number, Mach number, and the ratios between the freestream and the rotor tip and induced velocities. Table 4 Data processing procedures for this test were devised to compares gas properties at NFAC in air, at Titan, and at the minimize errors and uncertainties, but due to the nature of NASA Langley Transonic Dynamics Tunnel (TDT) in R- wind tunnel testing, inaccuracies are assured. The uncertainty 134A heavy gas. The TDT is included since it was used for can be divided into two components: systematic uncertainty prior full-scale Dragonfly rotor tests, Ref (11).

(U ) and precision uncertainty (U ). Systematic uncertainties r s are largely derived from calibration of the wind tunnel Freestream velocities were set so that Titan and NFAC conditions and lander, backshell, and rotor balances.

freestream dynamic pressures and Mach numbers were Precision uncertainty (data reduction uncertainty) lends itself reasonably close, q  ~10-30Pa and M  ~0.01-0.02, as shown to varied interpretation. Figure 15 gives an example of the in Table 5 . Compared to Titan, the combined scaling of process used in this paper to determine precision uncertainty. density (0.22), velocity (1.8), geometry (0.5) and viscosity A sequence in the dataset was extracted to produce a (2.7) leads to a 10-15x difference in Reynolds number, waveform duration which was representative of that test 𝜌𝑉 𝐷/𝜇 . Since Re is still greater than 800,000 and the ∞ condition, typically 4-8s. The waveform is processed through geometry is angular, separation locations should be generally

consistent, with the possible exception of the outside of the backshell at high pitch or roll angles. Viscous shear forces are no more than 5-10% of the pressure forces, based on selected CFD solutions.

Table 4. Titan and wind tunnel conditions - 5 T a P  𝜇 , 10  5 3 K m/s 10 Pa kg/m kg/(m-s) NFAC 1.01 293 1.2 1.81 339 Titan, 4 km 1.19 89 4.6 0.64 203 Titan, surface 1.47 94 5.4 0.67 195 TDT 1.01 303 4.0 1.24 170 Figure 16. Rotor flow states adapted from (12) and (13) Table 5. NFAC and Titan scaling using freestream velocity and Backshell diameter, D COMPUTATIONAL METHODOLOGY Reynolds V  q  Mach U  /a m/s Pa ( V , D) The CFD aerodynamic database is used in the flight dynamics  simulations of the lander in the APL developed Closed Loop 4.0 10 0.010 8.0 x10 Simulation (CLS) and NASA Program to Optimize Simulated 5.3 17 0.016 1.1 x10 Trajectories II (POST2) tools. Over 3000 simulations are 6.9 29 0.020 1.4 x10 required to populate the database. That number of 3.0 Titan 24 0.015 1.3 x10 simulations necessitates a multi-fidelity CFD workflow that strikes a balance between computational efficiency and Rotor RPM was set so blade tip Mach numbers were similar accuracy. Currently, mid-fidelity CFD is used for the database to those at Titan, M ~ 0.4. Ratios were maintained between tip while high-fidelity is used for cross-checks. The NFAC test V , V =  R, and hover induced velocity, v =Thrust/ . vs. CFD validation quantifies the error as uncertainty of the  t h √2𝜌𝜋𝑅 PPF aerodynamics. That uncertainty is then scaled to Titan Table 5 compares model scale rotor properties at NFAC with conditions and used with the Titan CFD database in CLS and those at 1100RPM at Titan. The 10-15x reduction in chord POST2. The use of mid-fidelity CFD is, of course, a risk – Reynolds number is the same. Also shown for reference are higher fidelity CFD is often more accurate in capturing nominal values for single rotor thrust and v .

h complex physics. The multi-tool and multi-fidelity analysis is Table 6. NFAC and Titan scaling using rotor tip speed shown in Figure 17 . CFD fidelity, accuracy, and resource and chord at 75% radius expense increase left to right.

V Mach V Re T v t t 1R h RPM m/s /a (V t c .75 ) N m/s 1200 49 0.14 1.7 x10 12 3.0 2400 97 0.29 3.3 x10 50 6.5 3800 154 0.45 5.2 x10 120 10.0 1100 Titan 78 0.40 5.6 x10 400 5.1 Figure 17. CFD methods used for the NFAC CFD Since PPF is a descent condition with rotors operating at validation, illustrated by vorticity visualizations.

varying RPM, penetration into Vortex Ring State (VRS) is an STAR-CCM+ is a commercial, multi-physics software important consideration. VRS has been extensively studied, package. The mid-fidelity model used a coupled, implicit e.g., Refs (12), (13), but data for coaxial rotors next to a wall steady-state Reynolds Averaged Navier Stokes (RANS) (the Lander) and below a solid shell is limited at best. Figure solver. The volume discretization used a second order, central 16 shows how the ratio of climb velocity, V = -V  , to hover C differencing scheme with boundedness. The turbulence model induced velocity, v , aligns to the Ref. (13) single rotor model h was Spalart-Almaras (SA). The Virtual Disk Model (VDM) as the flow state varies from hover (V =0m/s) through mild C used for the rotors is described below. The combined to severe (red) VRS. The vertical axis is the ratio of actual methodology is denoted RANS-VDM.

power to hover power. All tested conditions measured the rotors absorbing power, rather than operating in a windmill Unsteady simulations in this paper maintain second order brake state. spatial discretization and use a second order dual-time stepping scheme with either unsteady RANS (URANS) or the SA Improved Delayed Detached Eddy Simulation (IDDES) turbulence model. When IDDES is used with the VDM, these results are denoted IDDES-VDM.

Due to the low Mach numbers of this test, constant density and used for each simulation condition. This allows direct was used for both RANS and IDDES. All other solver comparison to the measured forces to calculate error.

settings, including the VDM and mesh described later, were constructed to follow the full-scale Titan CFD workflow Rotor Model described in Ref. (7).

The VDM simulates the aerodynamic effects of a rotor by High-fidelity CFD using NASA OVERFLOW (2.4) was also representing it as a disk within the fluid flow. It utilizes Blade used to compare, contrast, and help understand the NFAC test Element Momentum Theory (BEMT) to calculate time- results. Details and results are provided in Ref. (8). This averaged but spatially varying forces and moments on the disk approach used Detached Eddy Simulation and discrete blades, elements from inputs such as rotation rate and rotor geometry.

referenced as DES-DB in Figure 17 . Blade section lift and drag forces are computed from local flow velocities and C81 airfoil coefficient tables generated To accomplish the large number of RANS-VDM simulations using the OVERFLOW solver at test-appropriate Mach and required to cover the attitudes and RPMs investigated in the Reynolds numbers, as in Ref. (14). The VDM settings and test, a streamlined workflow was established to convert test mesh are consistent with Ref (7). A half-cosine tip loss conditions to CFD inputs, run the simulations, and collect the function was applied to the VDM model starting at r/R=0.85.

results. This workflow was also used in Ref. (7). Batches of Comparisons of STAR-CCM+ RANS-VDM to full-scale 50 cases were distributed across multiple High Performance Dragonfly rotor forces and moments had correlation similar Computers (HPC) and scheduled using Design Manager to that shown in Refs. (11) and (15) for RotCFD.

within STAR-CCM+. Individual simulations were set up to stop once the windowed average of the yaw moments of the Mesh rotors, lander, and backshell were each within a specified asymptotic tolerance. The simulations were set to run from a An unstructured polyhedral mesher generated the surface and minimum of 1750 up to a maximum of 8000 iterations.

volume mesh. The surface mesh of the backshell and lander is shown in Figure 20 . The cell size was chosen such that a Domain and Components minimum of five cells existed between two sharp edges, and all the intricate features of the internal components would be The CFD model included the Dragonfly lander and backshell, captured to avoid defeaturing. The near-body cross-section of support structures, and the wind tunnel domain. An image of the volume mesh is also shown in Figure 20 . The boundary the components is shown in Figure 18 . The tunnel domain layer mesh settings were chosen to ensure a 𝑦 + of 1 at 5.3 consisted of a rectangular prism to model the 80 x 120ft m/s. The off-body volume mesh is shown in Figure 21 . The NFAC wind tunnel. CFD boundary conditions are shown in tunnel walls had a cell size of 1 m, and refinement regions for Figure 19 . Because of the small size of the model (0.1% the rotors’ near- and far-wake and backshell had cells sizes of blockage), and avoiding operation with high inlet cross flows, 0.022m, 0.044m, 0.022m, respectively. All the refinement the inlet contraction was not modeled and the walls used regions rotate with the lander orientation except for the inviscid slip boundary conditions.

backshell wake region, which remains parallel to the tunnel axis to resolve its wake.

Figure 18. Dragonfly CFD model components and assembly.

Figure 20. Surface meshes (top) and volume mesh slices at y=0 (bottom left) and through the forward rotors (right).

Figure 19. Computational domain used to simulate the Dragonfly NFAC installation.

The simulation ambient conditions (pressure and temperature), lander pitch and roll, rotor RPMs, and test section velocity were extracted from the experimental data Figure 21. Volume mesh slice at y=0m.

Unmodeled Geometry EXPERIMENTAL RESULTS The CFD model does not include the following items: Lander-Only (L)  Lander motor and load cell wires The first configuration tested was the lander without the  Lander and Backshell openings or "leakages" backshell or rotor blades (L). Figure 24 shows the body axis  Wires secured to the mounting stings forces (as defined in Figure 7 ) as a function of the roll and  Small fasteners, gaps, and other hardware features pitch attitude, all at V  =5.3m/s. Variations are small for ±10   Blade attachment or hub from axial descent, P/R = 90/0°. At higher angles, F and F x y  Blade elasticity of the KDE blades forces from wind axis drag appear. The lower image shows pressure coefficient values and mapped colors at P/R=90/0°.

These omissions should have minimal impact on the overall Yellow is stagnation on the lower surface, C =1 aerodynamics, but potentially affect sensitive quantities, e.g. P .

drag, in areas or conditions where flow separation is altered causing cascading impacts. Scans of the NFAC installation were not available, but images of the test and CFD geometry are compared in Figure 22 . Several KDE blades were 3D scanned, showing modest blade-to-blade and blade-to-design differences such as flatwise bending deflections and hand sanding effects on the leading- and trailing edges. Overall the RANS-VDM thrust and torque will be shown to compare well to the rotor test data despite such nuances.

Figure 24. Lander without rotors (L) body-axis forces vs. Pitch and Roll at V=5.3m/s and C at P/R=90/0° P Lander Plus Rotors (LR) Figure 22. Test and CFD geometry comparisons Figure 25 shows the F (thrust/drag) force and M (yaw) z z moment as functions of rotor RPM in axial descent, Discrete Blade Analysis P/R=90/0°. The upper row shows the sum of lander and rotor Analysis was also performed for a smaller subset of cases loads in body axis. The blue and black symbols are for using discrete blades (DB) and the unsteady RANS (URANS) sequences Q1 (Rotors 5 and 7 active) and Q7 (Rotors 6 and 8 solver. Cases used a temporal resolution of 1° per timestep, active) in hover at V =0m/s. The loads increase quadratically  16 sub-iterations, and total time of 20 rotor revolutions.

from idle at 380 RPM to a maximum of F = -240N at 3800 z Averages were taken over the last 4 revolutions. Two rotors RPM with M = +16Nm for Q1 and -16Nm for Q7. As V is z  are set up for simulation (R3 and R8). Figure 23 contains increased to 6.9m/s, the LR drag at idle increases to F =-55N.

z images of the rotors, off-body mesh, and the surface mesh.

The variation in F with V  is reduced at higher RPM as the z rotor-induced velocities interact with the lander body.

The yaw moment varies with V  and RPM depending on VRS penetration and rotor-lander interactions. For Q1 at V =6.9m/s (red circles), M increases from 380 to 1000RPM,  z drops until 2000 RPM, and then rises to 15Nm at 3800RPM, compared to 16 Nm in hover. The VRS metric V C /v h is -1.9 at 1000RPM, -1.3 at 2000RPM, and -0.7 at 3800RPM.

Consistent generation of M requires sufficient rotor thrust to z achieve V /v > -1.2 and avoid strong VRS ( Figure 16 ). At C h Figure 23 Surface and volume mesh for isolated rotor lower V this boundary is reached at lower RPM.

 discrete blade (DB) setup.

The lower row in Figure 25 shows Rotor 8 shaft axis F F and F are most affected by the respective roll and pitch z y x angles, as expected. M maintains authority within ±20% for (thrust) and Mz (torque). The influence of V  is small, z implying only limited effects of VRS on the time averaged pitch within ±10  of 90  and roll below 25  , but M shows up z rotor loads themselves. The figure also shows the lander body to a 50% reduction at more extreme attitudes.

axis M from Rotor 8, adding the moment from the 5  canted z thrust to the shaft torque. The canted thrust contribution is ~2x that from shaft torque. Doubling the Rotor 8 M (-8Nm at z 3450RPM and V =5m/s) to account for the unmeasured Rotor  6 gives -16Nm from the rotors, compared to -11Nm for the entire vehicle, indicating that the lander body produces a +5Nm or -30% counteracting moment.

Figure 27. LR F x , F y , F z , and M z vs. pitch and roll for Q1 at 3450 RPM and V  =5.3m/s.

Lander Plus Rotors Plus Backshell (LRB) After examining the LR results, the number of pitch/roll attitudes for the LRB test phase was increased to better define the despin envelope. The number of RPM steps was reduced, but the record at each step was increased to 8 seconds. Figure 28 shows F (top) and M (bottom) vs RPM for sequences Q1 z z and Q7 at V =4.0, 5.3, 6.9m/s, P/R=90/0°. The LRB total is  on the left, the LR in the middle, and the Backshell on the right. The LRB F shows a strong increase with V  at RPM< z 2500, which weakens at higher RPM, especially at lower Figure 25. LR and Rotor 8 F and M for Q1 and Q7 at z z velocities. The LR F trends are more consistent, reaching - z P/R=90/0°, V =0, 4, 5.3, 6.9 m/s.

 250N at 3800RPM, similar to the Figure 25 results for the Figure 26 shows Lander surface pressures during the Q1 RPM lander alone. The Backshell F (drag) weakens as rotor thrust z sweep at V =5.3m/s and P/R=90/0°. In the upper left, at 600 increases, approaching zero at the lower velocities. This will  RPM and low thrust, the lower surface sees yellow stagnation be discussed further below.

pressures, and the sides and nose see moderate suction, C ~ P The LRB and LR M in Figure 28 are low below 2000RPM, z -0.5. At 1400RPM, the increased rotor thrust generates much with consistent increases from 2500 to 3800RPM. At the more forward suction. Integrating the yaw moment from the highest velocity, M is reduced by up to 5Nm (25%). The z measured C produces an adverse M of 10Nm. As RPM P z backshell M is small, providing up to a 2Nm addition at z increases further, the increased induced velocities from the 1750RPM, and up to a 1Nm reduction above 3000RPM.

rotors flip the pressures on the lower surface from stagnation to suction. This reduction in body drag is responsible for the lowered effect of V  on F z that was observed in Figure 25 .

Figure 28. LRB F z and M z for Q1 and Q7 at P/R=90/0° Figure 26. LR body C suction opposing rotor +M for P z and V =4.0, 5.3, 6.9m/s.

 sequence Q1 at V =5.3 m/s and P/R=90/0°.

 Figure 29 shows the progression in surface pressures with The effect of pitch and roll attitude on the lander plus rotors increased RPM with and without the backshell. At idle, both forces and yaw moment at 3450RPM, V =5.3m/s is shown in  the lander and the inside of the backshell are near stagnation Figure 27 . Body axis F increases noticeably for P/R > ±10  .

z pressure (C > +0.8), consistent with the measured near-zero P lander F and strong negative backshell F (drag). As rotor not pressure-instrumented. As with pitch, the higher roll z z thrust increases, the induced flow along the backshell into the angles allow the freestream to produce positive pressure on rotors flips the pressure inside the backshell to a level of the inside of the backshell, increasing drag.

suction, C ~ -0.5, similar to outside the backshell, consistent P with near zero backshell F . Compared to the LR pressures, z with the backshell present the Lander lower surface stagnation pressure flips to suction at lower RPM, and the suction on the side does not get as strong or generate as strong an adverse M . This is consistent with the reduced adverse M z z seen in Figure 28 for the LRB.

Figure 31. Pitch dependence of LRB F , M , and C for z z P Q1 at 3480RPM, Roll=0, and V  = 5.3 m/s.

Figure 29. Comparison of LRB and LR pressures for Q1 at 380 to 3470 RPM, P/R=90/0°, V = 5.3 m/s.

 Shaft axis thrust and torque for Rotors 3 and 8 during Q7 sequences are shown in Figure 30 . Runs 12 and 13 are LR and Runs 17-25 are LRB. There is very little difference for Rotor 8 (active), while F on Rotor 3 (idle) is slightly larger at z V  =5.3 m/s without the backshell.

Figure 32. Roll dependence of LRB F z , M z , and C P for Q1 at 3480RPM, Pitch=0, and V  = 5.3 m/s.

LRB forces and yaw moment for all measured attitudes are plotted in Figure 33 , for Q1 at 3480 RPM and V  =5.3m/s. As noted above, F increases at higher pitch and roll, as the z backshell drag is recovered. F and F are generally small at y x lower angles, and higher at higher angles. M authority is z generally maintained for pitch attitudes of 80  to 130  , but substantially reduced at 60  and 50  .

Figure 30. Rotor F and M with and without the z z backshell for Q7 at V  =4.0, 5.3, 6.9m/s, P/R=90/0°.

Varying the model pitch attitude can have a substantial effect on the loads, as shown in Figure 31 for pitch sweeps at zero roll. There is higher drag, -F and reduced M at higher pitch z, z and roll angles. M remains strongly positive from 65 to 130  z pitch, but was significantly reduced at 50  pitch. The Figure 33. LRB F x , F y , F z & M z vs. pitch and roll for pressures show very strong suction at the nose, caused by a Q1 at 3480 RPM and V =5.3m/s.

combination of freestream and rotor induced velocities. At  zero RPM and 50  pitch, the nose suction is absent. The Figure 34 compares M for Q1 at 3480 RPM for V  = 4.0, 5.3, z pressures also show that at the higher pitch angles of 50  ,70  , and 6.9 m/s. At the lowest speed there is a strong favorable and 115  , there is positive pressure on the inside of the yaw moment generated at all tested attitudes. At the highest backshell creating a drag force which combines with rotor speed, the region of strong favorable M is reduced to 90±15  z thrust to generate F = -320N compared to -180N at low pitch.

z pitch, and there is a region of adverse yaw moment at 50  The effect on F z , M z , and C P of varying roll attitude from -5  pitch. As noted in the figure, the VRS metric, V /v increases C h to +30  is illustrated in Figure 32 for Q1 and Q7 sequences at from -0.4 at V = 4m/s to -0.7 at V =6.9 m/s. While all of   3480 RPM. For Q1, positive roll does increase nose suction these are below the axial flow stability boundary in Figure 16 , up to C = -3.5. This is consistent with the measured 25% P Refs (13) and (5) do show that the boundary moves to reduced reduction in M . Q7 has a similar reduction in M , but the z z V /v when in-plane velocity is present, as occurs at larger C h suction is not seen, likely because the aft fin and cradle are pitch and roll angles.

average applied. The backshell F has the highest amplitude z low frequency variation, at 0.2 to 0.8Hz. This content is also seen at lower amplitude in the lander F and in the pressures z on the inside of the backshell and the bottom of the lander.

This again appears to be caused by interaction between the rotor wakes and the flow along the backshell. Further investigation using CFD will be described below.

Figure 34. LRB M vs. pitch and roll for Q1 at 3480 z RPM, and V  =4.0, 5.3, 6.9 m/s.

Unsteady Loads and Pressures Figure 35 shows time histories of selected lander, backshell, and rotor loads, RPM, and V for a Q1 sequence at P/R= 90/0.

 Each step is ~8 seconds long, is shown in a different color, and had a 4Hz digital low pass filter applied. This format Figure 36. Lander and Backshell force and moment provides a qualitative indication of the unsteady content as spectra for Q1 at 3480 RPM, V  =5.3 m/s, P/R=90/0°.

rotor RPM varies. Lander unsteady amplitudes increased above 1750 RPM, and were generally higher during the reducing RPM half of the sequence. Backshell, F and F z x amplitudes were notably higher above 3000 RPM.

Figure 37. Extended record of Lander and Backshell F z and pressure, for Q7 at 3840 RPM, P/R=90/0°, V  =6.9m/s.

Figure 35. Lander, Backshell, and Rotor 5 load time histories for Q1 at P/R=90/0° and V =5.3 m/s.

 COMPUTATIONAL RESULTS Figure 36 shows spectra for the three forces plus Mz at In this section, the CFD results for the vehicle are compared 3480RPM. The primary plots are not filtered and extend to with the wind tunnel data, with a focus on the metrics of 120Hz. The rotor 2p is present at 115Hz for the lander, plus vertical force, F , and yawing moment, M . The primary z z model structural responses previously identified by rap testing objective is to evaluate the correlation between the simulation of the installed model. The inset plots focus on the 0 to 4Hz results and wind tunnel measurements, while identifying range, consistent with the filtered time histories. The peaks methodologies to enhance the consistency and accuracy of the near 0.5 to 1.0Hz observed for both Lander and Backshell correlation.

forces are of interest since they are believed to represent unsteady aerodynamic interaction between the rotor-induced velocities, the Lander and Backshell wakes, and the external Lander-only (L) flow. The magnitudes at the 0-1Hz frequencies are ~3x higher for Backshell F than for Lander F . In Figure 38 the aerodynamic loads are plotted as a function z z of the roll and pitch attitude, all at V =5.3m/s. The results are  A small number of test conditions were acquired for an for the lander-only configuration (no backshell, no rotors).

extended record of 90 sec. Figure 37 shows lander and The RANS results show good trending with test, with F x backshell F and surface pressure vs. time for a case with large z ~0.5N lower than the test and F ~1N lower. Additional mesh z rotor-backshell interaction: V  =6.9 m/s, Q7 at 3480RPM and refinements (not shown) did not improve the correlation.

P/R=90/0°. The blue curves are unfiltered with 1kHz Similar results were found at 4.0m/s and 6.9m/s.

bandwidth, and the red curves have a 4 second moving block To further verify the VDM, isolated discrete blade cases were simulated for the A5 rotor sequence in descent at 6.9m/s. As outlined previously, only R3 and R8 were simulated. An isolated rotor was also set up for the RANS-VDM approach, and the computational results are compared with the rotor load cell, as shown in Figure 40 . For the RANS-VDM and URANS-DB Rotors 3 and 8 torque predictions are within 0.2Nm for all cases. The computational torque also aligns well with test in trend and magnitude. Both computational methods under-predict Rotor 3 thrust for RPM<2500. At higher rotor speeds, both computational approaches capture the test data well, with the URANS-DB approach showing better agreement in Rotor 3 thrust, and RANS-VDM showing Figure 38. Lander-only loads vs. pitch at R=0, V  =5.3m/s better agreement in Rotor 8 thrust. Overall, this effort provides confidence that in complex flow domains, such as Lander + Rotors (LR) VRS, the lower order VDM approach can provide adequate To present the LR correlation results, data is plotted across results for rotor thrust and torque.

sweeps of rotor RPM, starting with the individual rotor thrust and torque results in Figure 39 to highlight the RANS-VDM ability to accurately model the rotor’s installed physics. The shaded green region and the error bars correspond to the second standard deviation of the CFD iteration history and the second standard deviation of the test processed data as described previously. The shaded green region is not strictly physical for the RANS-VDM data, but instead indicate the solver’s ability to converge to a single value in these difficult flow scenarios. The values above the F and M plots’ x-axes z z are the difference between the test and CFD results. The largest error in rotor F z is ~7.5%, and for M z the RANS-VDM torque is within 0.2Nm. The in-plane rotor forces and lateral and longitudinal moments, though not plotted here, are st relatively small, and well within the 1 standard deviation of Figure 40. Comparison of RANS-VDM, URANS-DB, and test for R3 (left) and R8 (right) thrust and torque in the test error bars. Similar F and M correlations were z z observed across the test matrix.

descent at V  =6.9m/s for the A5 rotor sequence.

The Q1 rotor rpm sequence during descent, P/R= 90/0°, and at a tunnel speed of 6.9m/s is illustrated in Figure 41 . In these plots, the four of the six-component loads are plotted in the lander balance (LB) frame against the despin rotors’ RPM (Rotors 5 and 7 in this case). The LR results at P/R=130/30° are plotted in Figure 42 . The RANS-VDM results agree well with the test data F and M , even following some of the more z z subtle variations in the M z as RPM increases. The error in F z between the experimental and RANS-VDM data for both the P/R=90/0° and 130/30° datasets is approximately 4.7N, relative to peak loads of ~250N. For M , the error for the two z orientations is ~1.2Nm, with peak yaw values of ~16Nm. The variance in the test data increases with rotor speed, indicating flow unsteadiness, as discussed in the experimental section at these conditions. As with the rotor balance correlation, the CFD and test in-plane loads are small, with CFD typically within 1-2σ.

Figure 39 Rotor thrust and torque at P/R=90/0°, Q7, and V  =6.9m/s In-plane forces show larger percent-error but are small in absolute magnitude compared to F . These loads are a z stronger relative function of the non-modeled geometries in these conditions. For brevity, the in-plane loads are not plotted in the Figure 43 format; throughout the P/R angles investigated, in-plane forces and moment behave similar to that shown vs. RPM in, e.g., Figure 41 and Figure 42 .

Figure 43. LR Q1 sequence at 3450RPM, V  =5.3m/s, F z and M vs. pitch and roll z The Test v. CFD error is shown for 2700RPM and V =5.3m/s  in Figure 44 . At this lower rotor speed, RANS-VDM still Figure 41. LR sequence Q1 at V  =6.9 m/s, P/R=90/0°.

tends to underestimate F at an absolute error up to 12N z relative to system loads of -150N. Overall, these correlations highlight the RANS-VDM ability to accurately capture the LR configuration F and M to within ~20% of the test data.

z z The RANS-VDM and test LR F and pressure contours for the z P/R=80/10°, Q1, and V =5.3m/s conditions are shown in ∞ Figure 45 . At 1740RPM, the RANS-VDM exhibits an F error z of 2.5N compared to a test F of ~-65N. The error at 3400RPM z in LR F is ~-20N relative to a test F of ~-240N. These errors z z are primarily due to differences in bottom plate pressure. At 3400RPM, RANS-VDM predicts C ≈ -1, whereas the test p measures C ≈ -0.3. This disparity arises from rotor-lander p interaction, which RANS-VDM can struggle to accurately model near descent orientation at higher rotor speeds. The F z errors are similar at 3100 to 3800RPM.

Figure 42. LR sequence Q1 at V =6.9 m/s, P/R=130/30°.

 The impact of pitch and roll attitude on the LR forces and yaw Figure 44 CFD Results for LR, Q1 at 2700RPM, moment at 3450RPM and V  =5.3m/s is shown in Figure 43 where the color range is consistent with Figure 27 . The first V  =5.3m/s, F x , F y , F z , and M z vs. pitch and roll two columns present the RANS-VDM F and Test - CFD F , z z while the third and fourth show M . RANS-VDM z underestimates F across all orientations by 10N to 40N, z relative to peak loads of ~250N. The error is larger than that observed in the lander-only comparison, indicating growth related to the increasing complexity of the blade installation and rotor induced aerodynamic interactions. It accurately predicts the yaw moment direction of the vehicle with an average error margin of 1.7Nm, relative to peaks near 15Nm and RANS-VDM backshell F show a significant increase, z driven by an internal backshell pressure change as depicted in in Figure 47 . Both the test and simulation pressure contours show the pressure drop within the backshell, with the CFD results exhibiting a more pronounced change.

Figure 45. LR F and pressures: P/R=80/10°, Q1 z sequence, V = 5.3m/s.

 Lander+Backshell (LRB) Figure 46 plots the results for the PPF LRB configuration during descent at 6.9m/s, for a rotor speed sweep of the Q1 rotor sequence. The F (top row) and M results (bottom row) z z Figure 47. Backshell interior pressure at 6.9m/s, LRB are displayed in the lander balance (LB) frame, with the first descent orientation, sequence Q1 at 3470 & 3800RPM column showing the lander and the second column the backshell. There is a strong correlation between RANS-VDM Figure 48 plots results at 6.9 m/s, P/R=130/30°. In this and test data, except for the 3800RPM case where RANS- orientation, the backshell does not exhibit the same increase VDM overestimates F for the backshell by 87N. The z in F at higher rotor speeds observed in straight descent. The z 3800RPM condition also shows a growth in the test F σ bars z rotors do not prevent the wind tunnel flow from entering the caused by increased low frequency load fluctuations. RANS- backshell, so that F z is more influenced by tunnel speed than VDM appears to lock onto a solution near the upper limit of rotor speed. The RANS-VDM F error is minimal, as is the z the test oscillation range. This behavior will later be compared unsteadiness in the test data throughout the RPM sweep. The to the IDDES results.

largest relative discrepancies are in lander M at RPM> 3000.

z Figure 46. LRB F and M for rotor sequence Q1 at z z Figure 48. Lander (left) and Backshell (right) F and M z z V =6.9m/s, P/R=90/0°.

 for rotor sequence Q1 at V  =6.9m/s, P/R=130/30°.

In the descent orientation, the rotors’ wake acts in opposition Lander surface pressures are compared in Figure 49 for 2400 to the wind tunnel flow entering the backshell while the rotors and 3800RPM. At 2400RPM, with RANS-VDM under- simultaneously reduce the pressure inside the backshell as predicting lander M by 1.2Nm, the pressures are quite close z they generate increasing thrust. At 3800RPM, both the test to the test data. At 3800RPM, the RANS-VDM under- predicts lander M by 9.1Nm. The test provides pressure z readings on the port side of the lander while there are RANS- VDM pressure contours on both sides. From these two views it can be seen that on the port side RANS-VDM under- predicts the pressure relative to the test, and on the starboard side it shows a negative pressure region on the tail. The lander shows a -M in both the test and RANS-VDM, but the z stronger rotor induced negative pressure is likely the cause of larger -M lander contribution from RANS-VDM.

z Figure 51. LRB F z & M z for Q1 at 3480RPM, V  =5.3m/s A lower rotor speed, 2400RPM, was also investigated to identify the effect of rotor thrust. Figure 52 shows the forces and yaw moment results. The error in F shows a significant z drop in magnitude compared to 3800RPM, while the M z errors at the orientation limits remains similar in magnitude.

Figure 49. Lander pressures for Q1 at V =6.9m/s,  P/R=130/30°.

Figure 52. LRB F & M for Q1 at 2400 RPM, V =5.3m/s z z  Time-averaged F and M generally show strong correlation z z between RANS-VDM and test. Weaker F correlations arise z at operating conditions with strong lander and rotor interactions with the backshell, typically at higher RPM when the vehicle is in descent at V /v > -0.6. These conditions can C h also have large Backshell oscillatory forces ( Figure 37 ).

Weaker M correlation occurs at higher pitch and roll z orientations. The steady RANS-VDM trends parallel to the test data, but it struggles to adequately capture details of the flow physics and loses accuracy. This implies that higher fidelity unsteady methods such as IDDES-VDM are needed.

Unsteady Loads To understand the impact of switching from RANS to IDDES, cases with both good and poor correlation were simulated using IDDES. The wake structure of the IDDES-VDM cases at P/R=90/0°, V =6.9m/s, Q1 rotor sequence, 3400RPM is  Figure 50. LRB M for Q1 at 3480RPM at V =4.0, 5.3, z  shown in Figure 53 . The flow demonstrates the complexity 6.9 m/s that IDDES is able to capture, which should better model the The impact of pitch and roll attitude on the lander and actual flow in the test run, as opposed to the RANS-VDM solver, which captures the average flow characteristics.

backshell F z and M z at 3480RPM and V  =5.3m/s is plotted in Figure 51 . CFD under-predicts F relative to test with the z greatest error near the P/R=90/0° descent orientation. The F z error at higher P/R is significantly lower. The story is simpler for M : increased error is found at distinct incidences far from z P/R=90/0°, at high descent velocity, and high RPM. This behavior is visualized by the 130° pitch data in Figure 50 .

DISCUSSION The wind tunnel and accompanying CFD validation study provided valuable insights into the aerodynamics of the Dragonfly mission during the PPF phase. The NFAC test campaign verified that the yaw control authority required to null the spin rate of the Lander and Backshell prior to TPF was not always available. In combination with full-scale Titan CFD for both PPF and surface flight, this helped finalize the program decision to reorient the rotors to the configuration shown at the right of Figure 56 , as described in Ref (7). The Figure 53 Wake structure for rotor sequence Q1, new configuration reduces adverse rotor-lander interactions and provides robust yaw authority throughout the expected 3400RPM, V  =6.9m/s, P/R=90/0°.

mission envelope.

Figure 54 shows Backshell F during descent at 5.3m/s for a z rotor speed sweep of the Q1 rotor sequence. The figure plots Backshell F against rotor speed, with IDDES results as z yellow stars plus violin plots of the IDDES solution history.

At 1740RPM, the RANS-VDM and IDDES-VDM solutions converge to a similar value; each agrees with the test data. At 3400RPM, the RANS solution falls near the upper bounds of the IDDES solution while the mean of the IDDES agrees very Figure 56. Renderings of 2023 NFAC model basis (left) well with the mean of the test data. As noted previously, the and 2024 Critical Design Review configuration (right).

RANS results lock onto a state near the test maximum as well.

The time-accurate IDDES solutions permit a more physical The many thousands of unique data points from the NFAC unsteady shed wake to form, which produces a time-averaged test provide a comprehensive database for CFD validation.

F much closer to experiment.

z The complex flow physics, which involve multi-body interactions, rotor-body interactions, body-rotor interactions, flow separation and bluff body shedding of numerous length scales represent a challenge to modern numerical methods which need to comprehensively and accurately model such phenomenon throughout the flight envelope. To focus on the scale of the validation performed here, parity plots of the RANS-VDM correlation for the primary F and M loads are z z shown in Figure 57 . Here, test data and CFD are plotted directly against each other without attention to the underlying incidence, RPM, etc. CFD that correlates perfectly against Figure 54. Backshell F z for LRB Q7 Sequence at test would show a line with unity slope and no variance.

P/R=90/0° and V  = 5.3 m/s.

Clearly, the CFD is well correlated to the test data, although Figure 55 plots the lander M at P/R=130/30° and 6.9m/s for variance increases from the rotor loads to the LR, and then to z the Q1 rotor sequence. The error in M is highest for cases the LRB, following the increasing complexity associated with z above 3000RPM. Rotor speeds of 2400RPM and 3800RPM the flow field and aerodynamic interactions with each step.

were simulated using IDDES. The mean of the IDDES M z Although High Performance Computers are consistently shows substantial error reduction.

growing, low- and mid-fidelity CFD methods are still required to team with high-fidelity methodologies once the number of CFD cases grow past a few dozen. The RANS- VDM method used here did well overall. Key errors were identified based on the test vs. CFD error and were studied with the IDDES-VDM approach. The introduction of IDDES improved the correlation against the test data while incurring a 5x increase in computational resources. A multi-fidelity approach, combining the RANS-VDM and IDDES-VDM is a cost-effective and accurate approach for the CFD required for Titan. High-fidelity simulations, however, are still used and Figure 55. Lander M z for P/R=130/30  , LRB Q1 at V  = recommended as cross-checks when possible. This approach 6.9 m/s.

will be implemented on the program to reduce the uncertainty currently carried by the flight dynamics tools using the CFD data for the full-scale Titan configurations.

4. Synchronizing the multiple data streams from the NFAC and APL systems and parsing the 90 to 150 sec points into individual records for each rotor RPM.

5. Defining the experimental uncertainties driven by measurement precision plus low frequency load variation.

Specific experimental observations include: 1. The yaw moments, M , were categorized as Favorable z (>80% of the hover M ) at low V and/or low Pitch/Roll (<10- z ∞ 15  ), Reduced at high V OR high Pitch/Roll (>20  ), or ∞ Adverse (<15% or Swapped Sign) for High V AND high ∞ Pitch/Roll. The Backshell M magnitudes were generally z small compared to the M from the Lander plus Rotors.

z 2. The individual rotors had consistent thrust and torque (~RPM ) for almost all conditions. Thrust was reduced for some high V , high Pitch/Roll conditions. Vortex ring state ∞ penetration is modest (V C /v h > -0.8) for combined lower V ∞ and higher rotor thrust, and substantial (V /v < -2) at C h combined high V and low thrust.

∞ 3. Lander lower surface pressures show relatively uniform positive pressures (C > 0.5) approaching stagnation at low P rotor thrust, which transitions to suction (C < -0.5) for P increased rotor thrust and induced velocity.

4. Lander left side suction pressures behind the rotors were consistent with the Lander reduced or adverse M , particularly z for the Q1 sequences with the forward Rotor 5 active.

5. Backshell drag with the rotors off or at low thrust was consistent with that expected for an open cup, but it was Figure 57. Test v. CFD parity plots for LRB F z (left reduced by aerodynamic interaction.at high thrust and column) and M (right column), for R8 (top), LR z |Pitch/Roll|<20  . At higher |Pitch/Roll|, the Backshell could (middle), and Backshell (bottom).

maintain positive inner surface C and high drag. There were P low frequency (<1Hz) F variations of substantial magnitude, z mostly on the Backshell, at maximum V and maximum rotor ∞ thrust.

CONCLUSIONS 7. The Q1 and Q7 sequences with the two diagonal lower A 1/2 scale model of the Dragonfly PPF lander plus backshell rotors active were most efficient generating M since they had z configuration was tested in NFAC to determine its canted thrust and shaft torque contributions aligned. Q5 with aerodynamic characteristics, emphasizing the ability of the four diagonal rotors active and Q6 with four counterclockwise rotors to generate a consistent yaw moment to counteract rotors active were less efficient than Q1 since either the shaft vehicle spin. Extensive Lander, Rotors and Backshell force, torque or the canted thrust contributions canceled and adverse moment, and surface pressure data were obtained at over Lander suction increased.

13,000 conditions. In parallel, a Simcenter STAR-CCM+ 9. Although not a PPF rotor state, the A5 sequence with all CFD simulation of the as-built model in the test section was eight rotors active has a very large effect reducing or reversing developed. The rotors were modeled using Blade Element Backshell drag and increasing low frequency unsteady forces.

Momentum Theory (BEMT) to provide a time-averaged actuator disk representation of each rotor that was coupled Specific CFD observations include: into the overall Navier Stokes flow solution. 1833 RANS- 1. Mid-fidelity modeling with RANS-VDM correlates well VDM cases were simulated for the LRB configuration.

for the primary PPF objective: accurate LRB total M in z support of the despin maneuver. The mean average error for The experiment successfully overcame several challenges: Q1 and Q7 near the maximum M (+ or -17 Nm) was 2.1 Nm, z 1. Accurately measuring and maintaining low wind which indicates a 12% error.

velocities in the test section using upstream towers with ultrasonic anemometers.

2. Higher fidelity CFD is required in conditions that stress the RANS-VDM underlying assumptions. IDDES-VDM 2. Measuring low magnitude aerodynamic loads relative to significantly improves the correlation while still being less large gravitational and vibratory loads from structural modes computationally expensive than simulations resolving the and rotor harmonics. Acquiring data for 8 second blocks and discrete rotor blade geometry.

filtering provided focus on the low frequency aerodynamics.

Acta Astronautica, 2024.

ACKNOWLEDGMENTS doi.org/10.1016/j.actaastro.2024.07.046.

This work was conducted as part of the National Aeronautics 7. Gruber, K., et al. The Evolution of Dragonfly’s Design and Space Administration Dragonfly Phase B contract Using CFD at Titan. Virginia Beach, VA : Vertical Flight N00024-13-D-6400 to the Johns Hopkins University Applied Society 81st Annual Forum, 2025.

Physics Laboratory. Sikorsky’s experimental data analysis and CFD simulation activities were funded through a 8. Diaz, P.V., Edquist, C. and Yoon, S. High-Fidelity subcontract from APL to Lockheed Martin Space.

Computational Modeling of Dragonfly Lander during Preparation for Powered Flight. Virginia Beach, VA : Many people from each participating organization made Vertical Flight Society 81st Annual Forum, 2025.

essential contributions to the success of this effort. They include, but are not limited to, the following: 9. Zell, Peter T. Performance and Test Section Flow Characteristics of the National Full-Scale Aerodynamics NASA: Bill Tomek, Jared Fell (Backshell Model Design), Complex 80- by 120-Foot Wind Tunnel. s.l. : NASA, 1993.

Steve Geissinger (Backshell Model Fabrication) (LaRC), TM-103920.

Larry Young and Jason Cornelius (ARC).

10. Berg, H and Tijdeman, H. Theoretical and Experimental APL: Matt Misiorowski, Stephanie Lepchenske, John Results for the Dynamic Response of Pressure Measuring Samsock, Chris Ward, Don Burton.

Systems . Amsterdam, Netherlands : National Aerospace Lab Sikorsky: Kate Gruber, Antonio Rivera, Katarina Trubelja, NLR-TR F-238, Jan., 1965.

Maria Smerekanicz, William Welsh.

11. Cornelius, J and Schmitz, S. Coaxial Rotor CFD NFAC: Arturo Zamora, Jon Winegar, Daniel Brookbank, Validation and ML Surrogate Model Generation. Santa Clara, Johannes M. van Aken, Daniel Grieb, Emily Sayles, Chris CA : Vertical Flight Society Aeromeanics Specialists Nykamp, Jose Cabrales, Meliton Abenojar, Pat Goulding II, Conference, 2024.

Tyler Pearsall.

12. Leishman, J Gordon. Principles of Helicopter NAVAIR Applied Aerodynamics Branch: Mark Silva & Eric Aerodynamics. New York : Cambridge University Press, Hayden for loaning the anemometer arrays to the test effort.

2006.

13. Johnson, Wayne. Model for Vortex Ring State Influence on Rotorcraft Flight Dynamics. s.l. : NASA, 2005. TP-2005- Author Contacts: 213477.

Peter Lorber peter.f.lorber @lmco.com Karl Edquist karl.t.edquist @nasa.gov 14. Cornelius, J and Schmitz, S. Dragonfly Rotor Brian McGrath brian.mcgrath @jhuapl.edu Optimization using Machine Learning Applied to an Paul Gilles paul.gilles.ctr @us.af.mil OVERFLOW Generated Airfoil Database. Montreal, Quebec : Vertical Flight Society 80th Annual Forum & Technology Display, 2024.

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