Document
Comparing 3D and 2D CFD for Mars Helicopter
Ingenuity Rotor Performance Prediction
1, 2, 1, 1, * † ‡ § Witold J. F. Koning, Brian G. Allan, Ethan A. Romander, Wayne Johnson NASA Ames Research Center, Moffett Field, California 94035 NASA Langley Research Center, Hampton, Virginia 23681 S i ngle and coaxial rotor performance simulations for the Mars Helicopter Ingenuity rotor are performed for representative Mars atmospheric conditions. Analyses are presented using both a high - fidelity 3D CFD model of the rotor and 2D CFD models of the airfoil secti ons for comprehensive analyses that use CAMRADII (Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dynamics) .
When available , the airfoil performance calculations are generated using a numerical approach identical to that used in the high - fidelity 3D model, allowing for a direct comparison between the approaches.
Experimental data from a validation campaign to explore higher thrust from an Ingenuity rotor is provided to substantiate a discussion on the simulation fidelity required for both coaxial and single rotor performance predictions. The data is in support of the Sample Recovery Helicopter (SRH) element that serves as the primary backup for tube retrieval as part of the Mars Sample Ret urn (MSR) Campaign .
Insights on modeling turbulence at low Reynolds numbers and its influence on the rotor f igure of m erit are discussed. Key rotor performance metrics are compared . A detailed investigation into differences between 2D and 3D rotor performance predictions , spanwise loading, and rotor stall behavior is included .
Nomenclature 𝑡 = time , s 𝑡 = physical time, 𝑡𝑐 / 𝑉 𝑝 ℎ 𝑦𝑠 𝑎 = speed of sound , m s ⁄ 𝑇 = temperature, K ; rotor thrust, N 𝐴 = roto r disk area , m 𝑉 = section resultant velocity , m s ⁄ + 𝑐 = chord, m 𝑦 = dimensionless wall distance 𝐶 = section aerodynamic axial (chord) force , N m ⁄ 𝛼 = angle of attack, deg 𝑐 = sectional axial force coefficient , 𝐶 ( 0 . 5 𝜌 𝑉 𝑐 ) ⁄ 𝛾 = specific heat ratio 𝑐 𝑐 = sectional normal force coefficient , 𝑁 ( 0 . 5 𝜌 𝑉 𝑐 ) ⁄ 𝜃 = rotor collective angle , deg 𝑛 3 2 𝐶 = rotor power coefficient, 𝑃 ( 𝜌𝐴 ( Ω 𝑅 ) ) ⁄ 𝜇 = dynamic viscosity, Ns m ⁄ 𝑃 𝐶 = rotor thrust coefficient, 𝑇 ( 𝜌𝐴 ( Ω 𝑅 ) ) ⁄ 𝜓 = rotor azimuth angle , deg 𝑇 𝐹𝑀 = hover figure of merit , 𝑇 √ 𝑇 ( 2 𝜌𝐴 ) 𝑃 𝜌 = density, kg m ⁄ ⁄ ⁄ 𝜎 = rotor solidity (thrust - weighted) 𝑀 = blade section Mach number Ω = rotor rotational speed , rad s ⁄ 𝑁 = section aerodynamic normal force , N m ⁄ 𝑃 = rotorcraft power, W Subscripts 𝑟 = rotor radial coordinate , m 𝑐 = chord - based 𝑅 = gas constant, m ( s K ) ⁄ ; rotor radius, m 𝑡𝑖𝑝 = tip - based 𝑅𝑒 = chord - based Reynolds number, 𝜌𝑉𝑐 / 𝜇 * Aerospace Engineer, Aeromechanics Branch, and Science and Technology Corporation; witold.koning@nasa.gov.
† Aerospace Engineer, Flow Physics and Control Branch; brian.g.allan@nasa.gov.
‡ Aerospace Engineer, Aeromechanics Branch; ethan.romander@nasa.gov.
§ Aerospace Engineer, Aeromechanics Branch; wayne.johnson@nasa.gov.
including accuracy of rotor peak figure of merit (FM) I. Introduction predictions, rotor stall behavior, and compressibility effects.
Understanding where rotor p erformance discrepancies can The Mars Helicopter Ingenuity made history in April 2021 appear, identifying what the role of the numerical approach is, by being the first aircraft in history to make a powered, and comparing the influence of strict 2D versus full 3D controlled flight on another planet [1] . The N ational modeling are key to better understanding of CA - based rotor Aeronautics and Space Administration (N ASA ) Jet Propulsion performance predictions at compr essible low Reynolds number Laboratory (JPL) designed the Mars Helicopter (MH) in conditions.
collaboration with AeroVironment Inc. and other NASA The goal of this work is to compare 2D CFD as aerodynamic cen ters . Helicopter design for operation on Mars presents inputs for comprehensive analyses to 3D CFD of the isolated challenges generally not encountered for terrestr ial designs Ingenuity rotor in hover. Data from the recent experimental [2,3] : the low a tmospheric density on Mars, the communication validation campaign is provided, both for coaxial and single delays to Earth, and the space environment ( thermal, radiation ) rotor configurations, to further allow the comparison with are some of the key factors rapidly increasing design analytical methods. Rotor hover performance metrics, sectional complexity. The former is of particular importance to flight in and spanwise performance comparisons, and stall predictions the Mar tian atmosphere and presents many new challen ges for are compared and investigated.
the vehicle flight dynamics [4 – 7] and aerodynamics [8,9] .
Pioneering work on rotorcraft planetary exploration was performed by Young et al. [10 – 13] and Datta et al. [14] . Early II. Experimental D ata development o f Ingenuity started in 2013 and an early conceptual design was published the following year [15] . To support the increased lift off mass, a n increased blade Ingenuity features a coaxial rotor with a 1.21 m rotor diameter loading and increased tip Mach number s , amongst others, are and a total vehicle mass of 1.8 kg . The helicopter relies on solar par ameters being consi dered for SRH [16] . This prompted an cells and a battery system for power, demonstrating flight experimental validation campaign to increase blade loading and endurance of up to ~ 170 seconds that is conducted fully tip Mach number to validate predicted increases in rotor thrust autonomously due to the communication delay between Earth from an Ingenuity rotor. A coaxial test campaign and a single and Mars. The rotor design features two counter - rotating, rotor test were performed to identify stall char acteristics and hingeless, two - bladed rotors [4] . drag divergence effects, respectively, at representative Mars Recently, the Sample Recovery Helicopter (SRH) element atmosphere conditions. The experiments were conducted at the was announced [16] , serving as the primary backup for soil JPL Space Simulator (JPLSS) using CO as the driving gas. The sample tube retrieval as part of the Mars Sample Return (MSR) approximate operating conditions during the experimenta l * Campaign . The MSR program aims to bring Mars materials campaigns are shown in Table 1 , next to sea - level standard back to Earth for the f irst time. Under current planning, a (SLS) conditions for Earth.
Sample Retrieval Lander (SRL) will bring a small rocket, the Table 1 Approximate JPLSS Test Condit ions Mars Launch System (MLS) and two Sample Recovery Helicopters to Mars in 2030. The SRH mission leverages on the Variable Earth EDM1 TRT design heritage of Ingenuity: each helicopter c onsists of an (SLS) Ingenuity - like rotorcraft with the addition of ground mobility Density, ρ (kg/m ) 1.225 Varying 0.0100 and a manipulator. An experimental validation campaign to Temperature, T (K) 288.20 293.15 293.15 2 2 Gas constant, R (m /s /K) 287.10 188.9 188.9 explore higher thrust from an Ingenuity - like rotor was Specific heat ratio, γ 1.400 1.289 1.289 performed by the Jet Propulsion Laboratory (JPL) with support 2 - 5 - 5 - 5 Dynamic viscosity, μ (N ⋅ s/m ) 1.750 ⋅ 10 1.46 ⋅ 10 1.46 ⋅ 10 from AeroVironment, Inc. [16] .
Speed of sound, a (m/s) 340.35 267.17 267.17 The design of the Ingenuity rotor was performed by AeroVironment, Inc. using their PROP code and Mark Drela ’ s The Ingenuity design uses a 25 % rotor thrust margin to XROTOR [2,3,17] . Additional aerodynamic analyses were account for uncertainties in predicting rotor (stall) performance completed on Ingenuity’s rotor blade geometry in 2018 using in the Mars atmosphere. Next to that, the highest hover tip Mach 2D Computationa l Fluid Dynamics (CFD) to generate airfoil number flown on Mars is approxi mately 𝑀 = 0 . 72 , leaving 𝑡𝑖𝑝 tables to drive the Comprehensive Analysis (CA) code room for improve d performance if compressibility effects prove CAMRAD II [8,9] . CAMRAD II is a CA tool for rotorcraft [18] to be acceptable.
and has undergone extensive correlation of performance and Further understanding of rotor performance predictive loads measurements on rotorcraft, inc luding coaxial rotors [19] .
capabilities possibly allow for more accurate risk quantification Furthermore, for a select number of cases, high - fidelity 3D and increased performance figures in future Mars helicopter CFD was used to predict rotor performance .
designs. Experimental data from the two tests are included to Given the heavy usage of CA to guide the design of provide context to the two approaches to rotor performance Ingenuity, understanding the differences in rotor performance predictions presented herein.
predictio ns between 2D and 3D CFD aerodynamic modeling is key, as this can affect critical rotor performance parameters * The decision to implement Mars Sample Return will not be finalized until NASA’s completion of the National Environmental Poli cy Act (NEPA) process. This document is being made available for information purposes only.
A. The Transonic Rotor Test (TRT) A single Ingenuity rotor was used to investigate poss ible increases in tip Mach number. While h igher tip speeds could improve both dimensional thrust and efficiency (due to Reynolds number increase s ), decreas ing the tip speed margin necessitates that co mpressibility effects and eventually drag
T
divergence are well characteri zed . Figure 1 shows the experimental setup of the TRT , showing the bottom mounted motor ( ‘ M ’ ), the single rot or and the support structure on top.
Figure 2 The sc hematic experimental setup for the EDM1 test campaign in the JPL Space Sim ulator .
T
Table 3 EDM1 Test Campaign Conditions EDM1 condition 1 2 3 4 Density, ρ (kg/m ) 0.0100 0.0185 0.0185 0.0300 M tip 0.52 0.48 0.60 0.48
M
RPM 2,200 2,043 2,550 2,043 Figure 1 The sch ematic experimental setup for the TRT test III. Numerical Approach in the JPL Space Simulator .
The TRT primary rotor performance measurements are A irfoil and rotor performance for all CFD simulations are rotor thrust and torque (from which shaft power was derived ).
obtained using structured grids and solved using the implicit, Ingenuity’s highest hover tip Mach number is 𝑀 = 0 . 72 .
𝑡𝑖𝑝 compressible Navier - Stokes solver OVERFLOW 2.3d [20,21] .
The Transonic Rotor Test (TRT) showed that Ingenuity’s rotor Inviscid fluxes are computed using the HLLC or HLLE++ flux th can spin up to 𝑀 = 0 . 85 , corresponding to 𝑀 = 0 . 77 in 𝑡𝑖𝑝 𝑡𝑖𝑝 schemes with a 5 - order WENOM upwind reconstruction hover when taking cruise speed into consideration. The ground approach for high spatial accuracy with low numerical system equipment (GSE) prevented testing at higher Mach dissipation [22] . Viscous fluxes are computed using second - numbers. The tip Mach numbers and corresponding rotor RPM order central differencing, as are grid metric terms. Time values in the TRT are summarized in Table 2 .
advance uses a second - order backward differenci ng scheme, with a dual time - stepping approach as described in Table 2 TRT Test Conditions Refs. [23,24] .
CFD analyses for Ingenuity rotor conditions are complex TRT condition 1 2 3 4 5 because the modeling of turbulence at low Reynolds numbers M tip 0.65 0.70 0.75 0.80 0.85 is not trivial. A computationally efficient, Reynolds - Average d RPM 2,740 2,950 3,160 3,375 3,585 Navier - Stokes (RANS) method is the only affordable option for airfoil table generation (which requires approximately 1,500 B. The Engineering Design Model 1 Test Campaign simulations per set of C81 tables) and also for 3D rotating blade The Ingenuity Engineering Design Model 1 (EDM1) was CFD analyses. However, RANS approaches require special used to perform several tests to investigate the (coaxial) rotor attention when modeling transition and turbulence, particularly stall behavior in the EDM1 test campaign. Determining the at low Reynolds numbers.
usable thrust was key in evaluating current capabilities in A ‘fully turbulent’ approach was initially evaluated but is simulating rotor pe rformance. Figure 2 shows the experimental not advised because the Reynolds numbers are outside of the setup of the EDM1 test campaign in the JPLSS , showing the range of where the model should be used. The AFT2017 - b inverted Ingenuity airframe (lan ding legs, body and solar tran sition model [25] provided good comparison to panel), the coaxial rotor, and the support arm on top.
experimental test data at earlier representative conditions in the The EDM1 campaign primary rotor performance Space Simulator at the Jet Propulsion Laboratory (JPL) [8] .
measurements are system total thrust and e stimated m echanical A later study [26] showed satisfactory correlation for Eppler p ower of each motor. Testing of only one motor at a time and 387 airfoil performanc e at low Reynolds numbers to measurement of electrical power of the motor and motor torque experimental data when modeling laminar Unsteady Navier - allowed for computation of motor efficiency which allowed Stokes (UNS) equations , meaning no turbulence model is for an e stima ted m echanical p ower calculation of each rotor employed . The study showed that mean behavior of unsteady during the coaxial tests.
Laminar Separation Bubbles (LSB) can be captured accura tely The campaign found stall at lower co llective than initially using laminar UNS [26] , and transition to turbulence was expected from current best modeling practices. Qualitatively, governed by a separated shear layer instability resulting in the t he onset of stall occur red in a gradual bui ld up (‘soft’) rather shedding of large - scale coherent vortices, resulting in than immediate. The four rotor oper ating conditions are reattachment of the mean flow only.
summarized in Table 3 .
Similar shear layer instabilities are observed in the sectional G rids were generated using Chimera Grid Tools 2.2 (CGT) simulations for the Ingenuity rotor performance model [8] , [28] and the gridding guidelines from the American Institute of alluding to similar mechanisms at play and the relative Aeronautics and Astronautics (AIAA) CFD High Lift importance of large - scale coherent motion, when compared to Prediction Workshop were used where applicable [29 ] . The small - scale turbulence. (2D) grid size is based on the grid resolution study (GRS) at 𝛼 = 4° (approximate outboard angle of attack in hover for A. 2D Aerodynamic Airfoil P erformance Simulations Ingenuity [9] ) at conditions corresponding to radial stations CA conventionally uses sectional airfoil performance 𝑟 𝑅 ⁄ = 0 . 50 , 0 . 75 , 0 . 90 . Through independent halving of the organized in C81 lookup tables for angle of attack - Mach physic al time step and doubling the grid density in each combination s to model the rotor performance. Because the coordinate direction, it was ensured that finer grids in space and Ingenuity airfoil geometry was new and the aerodynamic time resulted in relative changes of the mean integrated en vironment unique, no such tables existed in 2018 befo re the aerodynamic coefficients comfortably below 0.1%, while first rotor model was generated . For this reason, 2D CFD was simultaneously ensuring at least 100 timesteps per shedding used to generate airfoil performance tables in C81 format at cycle of the boundary layer. This resulted in an O - grid with three representative Mars atmospheric conditions [8,9] . The chordwise spacing at the leading edge (LE) and trailing edge eight radial stations at which the current calculation s are ( TE ) set to 0 . 001% 𝑐 and 0 . 01% 𝑐 , respectively. The number of performed are identical to those found in Ref. [8] .
cells over the TE is monitored to ensure adequate grid ding. The All airfoil surfaces are subjected to a no - slip adiabatic maximum chordwise separation was fixed at 0 . 5% 𝑐 to provide boundary condition and the far field boundaries are modeled a reasonably uniform chordwise grid spacing in the using a freestream characteristic boundary condition. A ‘quick predominant region of unsteady separated flow.
start’ [27] procedure is performed by using a relatively coarse Simulations are performed between 𝛼 = [ − 15° , 20° ] in physical timestep (the time it takes the freestream velocity to steps of 1 degree for 8 radial stations and 6 Mach numbers on travel one chord length) 𝑡 = 0 . 16 and forcing only a 1 - 𝑝 ℎ 𝑦𝑠 average, resulting in around 5,000 time - accurate airfoil order drop in subiteration residual until the freestream has simulations for the three rotor models at the three density passed at least t he entire domain. Subsequently, the physical conditions .
timestep is reduced to 𝑡 = 0 . 0025 and subiterations are The viscous wall spacing is estimated for the first point of 𝑝 ℎ 𝑦𝑠 + continued until three orders of subiteration convergence are the airfoil surface at 10% 𝑐 and kept at 𝑦 < 1 for all Reynolds numbers studied. The initial wall spacing layer contains five achieved. After 25 passes of the flow over the chord, the following 50 airfoil flow passes a re used to extract a meaningful layers of constant cell spacing normal to the viscous walls. The cell stretching ratio (SR) for the normal and mean of the unsteady flow.
The CA model for Ingenuity’s rotor in hover is set up to use tangential/chordwi se layers is kept at 7% and the farfield is the generated C81 tables and predict the rotor performance. The located at 200 𝑐 for all grids. The number of cells normal to the CAMRADII aerodynamic model for the rotor blade is based on surface is obtained from the target stretching ratios.
lifting - line theory, using steady two - dimensional airfoil The grid is generated to anticipate thick boundary layers and characteristics and a vortex wake model, and additional models unsteady separated shear lay er behavior because of the low for unsteady flow (attached flow and dynamic stall) and Reynolds numbers experienced by the rotor. As such, the yawed/swept flow. Effects of compressibility (Mach numbers) maximum chordwise and off - body separation was fixed at and viscosity (Reynolds number, stall, and drag) enter through 0 . 5% 𝑐 in the predominant region of unsteady separated flow, as airfoil table data: lift, drag, and moment coefficients of two - shown in red in Figure 3 .
dimensional sections as function of angle of attack and Mach number, for the appropriate chord and atmosphere (density, temperature) to have correct Reynolds number v ariation with Mach number. In the paper, the term “CA cases” is used to refer to the same rotor model as that indicated by “2D OVERFLOW” or “2D CFD cases”.
1. Grid Generation for 2D Airfoils The Ingenuity airfoil coordinates [9] were interpolated to yield a high density set of coordinates. In contrast to the geometry in Ref. [8] , airfoil geometry for all eight radial stations was not based on the original airfoil geometry design , Figure 3 The near body grid for the clf5605 airfoil.
but on the as - built geometry and extracted from the out er mold This ‘maximum global separation’ is constrained up to line (OML) Computer Aided Design (CAD) model. This same 0 . 20 𝑐 normal to the airfoil surface, in order to approach geometry is used for the 3D CFD, to allow for a direct uniformly sized cells in the predominant region where large - comparison. The main difference with the profiles used in scale unsteady fl ow is expected (red in Figure 3 ) . After 0 . 20 𝑐 Ref. [8] is the constant thickness trailing edge on the actual normal to the airfoil surface, the regular hyperbolic stretching Ingenuity rot or geometry of around 0 . 5 mm.
is continued while ensuring a smooth tr ansition ( grey in Figure 3 ) .
Figure 4 shows the vorticity magnitude around the clf5605 Spalart - Allmaras (SA) turbulence model with a Detached Eddy Simulation (DES) approach: SA - DES [31] . As described above, airfoil for expected conditions at a spanwise distance of 𝑟 𝑅 ⁄ = best practices in modeling turbulence at low Reynolds number s 0 . 75 to illustrate the flowfields at different angles of attack .
are not fully defined. The advised SA - DES approach relies on Figure 5 and Figure 6 show increases in angle of attack to 6 and a fully turbulent SA model and is therefore not applicable for 8 degrees, respectively, showing the vast change in flow low Reynolds number studies. Furthermore, transition structure and complexity. The shear layer instability on the modeling, especially in unsteady flows, is still an active field of upper surface is clearly seen to progressively move upstream as study in RANS simulations and, therefore, l aminar UNS will be angle of attack is increased. These large - scale vortical dynamics evaluated for the current work.
are key to the performance of airfoils at these conditions.
The high - fidelity model uses the same numerical approach as the sectional simulations, but the timestep will be increased and the grid density will be decreased in order to keep the high - fidelity simulations practical. The same airfoil profiles are used to generate the 3D rotor blades, thereby minimizing discrepancies in airfoil geometry along the rotor between the two approaches.
1. Grid Generation for the 3D Rotor The wake grid resolution and time steps for the 3D hover simulations followed the grid and time step recommendations as described by Ref. [27] . Figure 7 shows the rotor wake grids Figure 4 Ingenuity airfoil r/R = 0.75, α = 4 ° , instantane ous where the Level 1 (L1) wake grid was defined to enclose the vorticity magnitude.
rotors and extends 0 . 75 𝑅 below the center of the two coaxial rotors with a grid spacing of 0.003m or 6.7% of a tip chord ( 𝑐 = 0 . 0 45 ), which is below the typical 10% tip chord used 𝑡𝑖𝑝 for hover performance. Adaptive Mesh Refinement (AMR) was used to capture the rotor wake 2 . 10 𝑅 below the center of the coaxial rotors using the same L1 wake grid resolution of 0.003m. This resulted in a computational cost savings because the rotor wake is only resolved where needed.
Figure 5 Ingenuity airfoil r/R = 0.75, α = 6 ° , instantaneous vorticity magnitude.
L1 0.75R R AMR 2.10 Figure 6 Ingenuity airfoil r/R = 0.75, α = 8 ° , instantaneous vorticity magnitude.
B. 3D Aerodynamic Rotor Performance Simulations Figure 7 Wake grids for 3D CFD hover calculations for For a select number of cases, high - fidelity 3D CFD coaxial rotors showing L1 and AMR zones with vorticity simulations were performed at fixed collective values for the magnitude contours.
upper and lower rotors . Accurate predictions of FM for high - The coaxial and single rotor simulations were discretized fidelity 3D rotor simulat ions operating at higher Reynolds with 15 million grid points per rotor blade with 5 overset grids.
numbers (in fully turbulent flow) are generally observed to The main blade grid con sisted of 258 grid points along the span require both higher order spatial differencing and adequate and 401 grid points at each blade station in the chordwise turbulence modeling [27,30] . To obtain results within direction and 91 grid points normal to the blade surface. The experimental error, the state - of - the - art solut ion is to use a coaxial rotor simulations had a total of 216 million grid points, hybrid RANS/Large Eddy Simulation (LES) model such as the 60 million for the roto r body grids, 76 million for the background grids and 80 million for the AMR. The single rotor simulation had a total of 186 million grid points with the same number of background and AMR grids but with 30 million fewer rotor body grids. 2. Timestep and solut ion procedure for the 3D rotor A physical time step of ¼ - degree blade rotation was used with a 2 - order drop in the L - norm. The calculations used an 2 adaptive number of subiterations until a 2 - order drop in the L 2 - norm was achieved. Typically, 13 to 17 subiterations were typically needed to obtain a 2 - order drop in the L 2 - norm.
A ‘ quick - start ’ , quasi time - accurate, procedure was used as described by Ref. [27] where a larger time step ( 1 degree for Figure 9 FM convergence using quick - start and time - this investiga tion ) was used with only 1 - order of convergence accurate procedure for coaxial rotor at a collective of 15 and no AMR. This results in a factor of 10 in cost saving per degrees showing the lower rotor.
revolution using the quick - start approach versus the time accurate ¼ degree, 2 - order L 2 - norm time - accurate simulation. A. S ingle Rotor Performance and TRT data For the coaxial rotor sim ulations, 40 rotor revolutions were An overview for the TRT results is pres ented for TRT performed using the quick - start approach to establish the rotor condition 3 ( 𝑀 = 0 . 75 ). Figure 10 presents rotor power 𝑡𝑖𝑝 wake and remove any transients due to starting the rotor versus thrust for the single TRT rotor conditions. The overall simulations. The simulation was then switched to the time - agreement is fair until a blade loading of around 𝐶 𝜎 > 0 . 15 ⁄ 𝑇 accurate approach using ¼ - degree blade ro tation and 2 - orders where the stall behavior of the computational methods predicts of convergence. The hover simulations at the ¼ - degree time higher efficiencies at stall (onset).
stepping were run for a total of 4 revolutions. Figure 8 and Figure 9 shows the convergence of the FM for a coaxial simulation using the quick start procedure for the 15 - degree collective for the upper and lower rotor, respectively.
Figure 10 Rotor power versus blade loading for TRT condition 3 ( M tip = 0.75 ).
Figure 11 shows the figure of merit distribution for the same dataset . The correlation between 2D CFD and the experimental Figure 8 FM convergence using quick - start and time - data is fair until peak FM is reached, albeit at an offset in blade accurate procedure for coaxial rotor at a collective of 15 loading. This offset seems to not be present in the 3D CFD degrees showing the upper rot or .
results, but the differences in figure of merit at the onset of stall are similar to 2D CFD .
IV. Results T o highlight the predictive capabilities for rotor thrust , the blade loading versus collective angle is presented in Figure 12 .
Rotor performance figures are presented for the TRT and The difference in slope between computational and EDM1 test results, and 2D and 3D CFD simulations . Due to the experimental results is clear.
high computational cost of the 3D CFD cases , cases near peak FM were prioritized to highlight performance at peak efficiency and the onset of stall . Next, select cases are highlighted to illustrate where the differences between 2D and 3D CFD predictions or iginate by examining the spanwise distributions of thrust and power . Lastly, t he flowfield at 𝑟 𝑅 ⁄ = 0 . 75 is compared to illustrate the effect of spanwise flow on the performance.
and landing legs during the experiment and were part of the measured vehicle thrust . The 2D CFD results did not include a manner to account for the effects of the body , solar panel or landing legs . Most of the 3D CFD simulations were performed without the body, solar panel and landing legs in order to compare directly to the CA results. However, 3D CFD was performed at two collective angles with the body and solar panel to quantify their effect on performance.
Figure 14 presents coaxial rotor power versus thrust at EDM1 condition 1 ( 𝜌 = 0 . 0100 kg m ⁄ ) . T he results show adequate agreement between the computational approaches a nd, similarly to Figure 10 , show increased power mismatch with experimental data at increasingly higher thrust levels.
Figure 11 Figure of merit versus blade loading for TRT conditi on 3 ( M = 0.75 ).
tip # !
" Figure 14 Rotor power versus blade loading for EDM1 condition 1 (ρ = 0.0100 kg/m ).
Figure 12 Blade loading versus collective for TRT Figure 15 shows the figure of merit distribution for EDM1 condition 3 ( M = 0.75 ).
tip condition 1. 2D CFD results at low blade loading are acceptable but exceed experimental results near peak FM and above. 3D Figure 13 shows the flowfield at TRT co ndition 3 ( 𝑀 = 𝑡𝑖𝑝 CFD results show slight increases in FM, but with a similar 0 . 75 ) for a single rotor at 𝜃 = 14° . The Q - criterion isosurface is peak FM blade loading .
shown, colored by vorticity magnitude, to highlight the complexity of the flow near the outboard sections of the rotor.
$ " #! Figure 15 Figure of merit versus blade l oading for EDM1 condition 1 (ρ = 0.0100 kg/m ).
Including the solar panel and body in the 3D CFD calculations did result in a 1.0% to 1.2% increase in total thrust of the entire vehicle resulting in a 1.5% increase in FM. The 3D CFD simulations did not include the landing legs, which would Figure 13 Q - criterion colored by vorticity magnitude, TRT increase the download on the vehicle, reducing thrust.
Condition 3 , θ = 14°.
B lade loading versus collect ive angle is shown in Figure 16 and highlights a similar mismatch in slope between B. Coaxial Rotor Performance and EDM1 data computational and experimental efforts to the TRT results in The EDM1 campaign was performed with the Ingenuity Figure 12 , albeit les pronounced. While the predicted slope is Engineering Design Model 1 , including the body , solar panel, similar for the computational approaches, the dissimilarity w ith T he blade loading versus collective curves are presented in the experimental results is evident . Figure 20 and show a similar slope between the computational analyses. The narrow thrust range of the EDM1 condition 4 data prevents an exhaustive comparison to experimental data.
! Figure 16 Blade loading versus collective for EDM1 condition 1 (ρ = 0.0100 kg/m ).
Figure 18 Rotor power versus blade loading for EDM1 For the computational results, the coaxial rotor performance condition 4 (ρ = 0.0 3 00 kg/m ).
can be split into separate predictions for upper and lower rotor performance. Figure 17 shows the same data as Figure 16 , but now split per upper and lower rotor. The results present a clear correlation for the lower rotor between the computational data.
However, the good lower rotor performance correlation is likely misle ading: taking the 3D CFD results as ground truth the increased upper rotor performance from 2D CFD would result in a decreased mean angle of attack over the lower rotor blades.
This would roughly correspond to a few percent change in lift coefficient which wo uld in turn make the correlation less favorable. Figure 19 Figure of merit versus blade loading for EDM1 condition 4 (ρ = 0.0 3 00 kg/m ).
Figure 17 Blade loading versus collective per rotor for EDM1 condition 1 (ρ = 0.0100 kg/m3).
Several 3D CFD cases were run for EDM1 condition 4 to evaluate if a change in operating conditions and Reynolds number would change the fundamental correlation challenges to the experimental data. Figure 18 presents co axial rotor power Figure 20 Blade loading versus collective for EDM1 3 3 condition 4 (ρ = 0.0 3 00 kg/m ).
versus thrust at EDM1 condition 4 ( 𝜌 = 0 . 0300 kg m ⁄ ) which bear s r esemblance to the curves for EDM1 condition 1.
Figure 19 shows the figure of merit distribution for the same C. TRT Rotor Disk Section Forces dataset . Overall, the trends of the computational analyses are While the agreement between 2D and 3D CFD in sections similar to the results for EDM1 condition 1. The 3D CFD A and B is favorable, differences are still exceeding desired predictions show a lower blade loading for identical collective, accuracy. Due to this, f urther analysis is presented to highlight but still increased figure of merit compared to the CA cases differences in spanwise loading for select datapoints to pinpoint because of the drop in rotor power. the origin of the discrepancies across the rotor disk . For the TRT test the collective angles of 𝜃 = 8° , 14° (see Figure 12 ) are selected for further analysis, corresponding to pre and post peak blade loading with azimuth that the 3D CFD can capture here , FM, respectively. To facilitate direct comparisons , the total in contrast to the CA .
thrust from the CA cases was trimmed to that for the 3D CFD cases. Since it is difficult to obtain lift and drag coefficient distributions from 3D CFD (due to the ambiguous value of the angle of attack along the span) , the airfoil normal and chord force coefficients are extract ed for both computational approaches. Spanwise distributions of thrust and power can then be extracted to examine the origin of thrust and power discrepancies along the span.
1. Case 1: 𝜃 = 8° , 𝐶 𝜎 ⁄ = 0 . 1054 .
𝑇 Figure 21 shows the ( azimuthal - mean) blade thrust distribution for both computational analyses, which highlights Figure 23 Rotor sectional normal for ce coefficient for 3D a small difference near the tip for case 1 . Figure 22 shows the CFD (left) and 2D CFD (right) , θ = 14° .
( azimuthal - mean) blade power distribution , showing a difference in power in a more outboard region than the thrust load. The combined thrust and power load clearly illustrate the higher FM of the 3D CFD case for this collective angle, but the overall correlation is fair .
Figure 24 Rotor sectional axial (chord) force coefficient for 3D CFD (left) and 2D CFD (right) , θ = 14° .
Despite the partial stall , the sectional normal force coefficient predictions are qualitatively similar, whereas the sectional axial ( chord ) force coefficient predictions show unsteady lower inboard forces that are not captured in the 2D CFD.
Figure 25 and Figure 26 show the blade thrust and power Figure 21 Mean b lade thrust distribution , θ = 8° .
distribution , respectively . The distributions show a similar correlation of the blade thrust and power distribution to the lower collective case as shown in Figure 21 and Figure 22 , respectively.
Figure 22 Mean b lade power distribution , θ = 8° .
2. Case 2 : 𝜃 = 14° , 𝐶 𝜎 ⁄ = 0 . 1683 .
𝑇 The collective for case 2 is beyond that for peak figure of merit , so as to investigate the correlation for a partially stalled Figure 25 Mean b lade thrust distribution , θ = 14° .
blade . Figure 23 and Figure 24 show a direct comparison of resulting sectional normal and axial (chord) force coefficients versus rotor azimuth for the high thrust case , respectively , for both 3D and 2D CFD . The figures highlight the variation in The cases highlight the relatively good agreement betwee n the computational approaches for a coaxial c onfi guration . Figure 26 Mean b lade power distribution, θ = 14°.
D. EDM1 Rotor Disk Section Forces Figure 29 Instantaneous blade thrust distribution, Ψ =90 ° , T wo collective values for the (coaxial) EDM1 cases are θ = 15° , lower rotor .
presented to further analyze discrepancies between the computational analyses , i n a similar vein to sec tion C showing spanwise load distributions for the TRT conditions. For the EDM1 test the collective angles of 𝜃 = 15° , 19° ( Figure 16 ) are selected for further analysis, corresponding to peak FM and early stall, respectively. To facilitate direct comparisons the total coaxia l thrust from the CA cases was trimmed to that for the 3D CFD cases.
1. Case 1: 𝜃 = 15° , 𝐶 𝜎 ⁄ = 0 . 1451 .
𝑇 Figure 27 and Figure 28 show the section al normal force coefficients for case 1 for the lower and upper rotor, respectively. Qualitatively, an agreement in azimuthal variation of the normal load is shown .
Figure 30 Instantaneous blade thrust distribution, Ψ =270 ° , θ = 15 °, upper rotor .
The agreement for the sectional axial (chord) forces is less favorable, showing a n unsteady component in the 3D CFD cases for both lower and upper rotor, as shown in Figure 31 and Figure 32 , respectively. Azimuthal variations are present in the 2D CFD cases in Figure 31 and Figure 32 , but with much lower magnitudes, and therefore less pronounced compared to their 3D CFD counterparts , due to the forced normalization between both computational analyses.
Figure 27 Lower rotor sectional normal force coefficient for 3D CFD (left) and 2D CFD (right) , θ = 15° .
Figure 31 Lower rotor sectional axial (chord) force coefficient for 3D CFD (left) and 2D CFD (right) , θ = 15° .
Figure 28 Upper rotor sectional normal force coefficient for The instantaneous blade power distribution for the lower 3D CFD (left) and 2D CFD (right) , θ = 15° .
and upper rotor is shown in Figure 33 and Figure 34 , The instantaneous blade thrust distribution for the lower and respectively. The lower rotor agreement is fair but is upper rotor is shown in Figure 29 and Figure 30 , respectively.
overshadowed by the mismatch across the span for the upper rotor , which shows a strong power offset between the analyses illustrated by the discontinu ity of the 3D CFD curves near the across the blades. tip ) further illustrates the distinct differences in predicted aerodynamic env ironment between the analyses .
Figure 32 Upper rotor sectional axial (chord) force coefficient for 3D CFD (left) and 2D CFD (right) , θ = 15° . Figure 35 Lower rotor sectional normal force coefficient for 3D CFD (left) and 2D CFD (right) , θ = 19° .
Figure 36 Upper rotor sectional normal force coefficient for 3D CFD (left) and 2D CFD (right) , θ = 19° .
Figure 33 Instantaneous blade power distribution, Ψ =90 ° , θ = 15° , lower rotor .
Fi gure 37 Instantaneous blade thrust distribution, Ψ =90 ° , θ = 19° , lower rotor .
Figure 34 Instantaneous blade power distribution, Ψ =270 ° , θ = 15° , upper rotor .
2. Case 2 : 𝜃 = 19° , 𝐶 𝜎 ⁄ = 0 . 1827 .
𝑇 Figure 35 and Figure 36 show the sectional normal force coefficients for case 2 for the lower a nd upper rotor, respectively. The qualitative agreement in azimuthal variation of the sectional normal force coefficient is reasonable, but the upper rotor shows a lower overall force. The instantaneous blade thrust distribution for lower and upper rotor i s shown in Fi gure 37 and Figure 38 , respectively.
The lower rotor agreement is ad e quate , though the upper rotor thrust shows the thrust rapid ly climbing towards the tip and then dropping off after about 𝑟 𝑅 ⁄ = 0 . 65 as the outboard sect ion of Figure 38 Instantaneous blade thrust distribution, Ψ =270 ° , the upper rotor begins to stall . The strong unsteadiness ( as θ = 19° , upper rotor .
Figure 39 and Figure 40 show the sectional ax ial (chord) force coefficients for case 2 for the lower and upper rotor, respectively. Both rotors show significantly lower airfoil chord forces for the 3D CFD case, compared to the CA (2D CFD ) case .
Figure 42 Instantaneous blade power distribution, Ψ =270 ° , θ = 19° , upper rotor .
Figure 39 Lower rotor sectional axial (chord) force E. Influence of Spanwise Flow coefficient for 3D CFD (left) and 2D CFD (right) , θ = 19° .
One key difference between the 3D CFD and CA analyses is the existence of spanwise flow in fluid dynamics input of the former . Figure 43 shows the Q - criterion iso - surface color ed by vorticity magnitude for a TRT case at 𝜃 = 16° .
Figure 40 Upper rotor sectional axial (chord) force coefficient for 3D CFD (left) and 2D CFD (right) , θ = 19° .
The instantaneous blad e power distribution for the lower and upper rotor is shown in Figure 41 and Figure 42 , respectively. The upper rotor stall in the 3D CFD case is visible here as the outboard section power ( 𝑟 / 𝑅 ≳ 0 . 70 ) starts to become very unsteady near the tip, directly correlated to the discontinuities observed for the corresponding thrust distributions in Fi gure 37 and Figure 38 .
Figure 43 Q - criterion color by vorticity magnitude for TRT condition 1, θ = 16° (slice at r/R = 0.75 ).
A slice at 𝑟 𝑅 ⁄ = 0 . 75 (perpendicular to the pitch axis) is shown too. Figure 44 shows the flowfield as velocity magnitude (normalized by freestream) at the slice for the 2D CFD (left) and the equivalent location in 3D CFD . This highlight s the strong influence of the spanwise component on the local flowfield , and hence the ae rodynamic performance predictions of the blade . However, when the spanwise components are removed from the 3D CFD flowfield , the flowfields are Figure 41 Instantaneous blade power distribution, Ψ =90 ° , qualitatively similar, as shown in Figure 45 .
θ = 19° , lower rotor .
CA analyses rely on C81 tables with mean flow values for the aerodynamic co efficients , but the 2D sectional stall predictions and/or the 3D flowfield around the blade are seen to alter the flowfield around the outer regions of the blade. The flowfield comparison at 𝑟 𝑅 ⁄ = 0 . 75 illustrates that removal of the spanwise component in 3 D CFD resembles the flowfield of the strictly 2D simulations. This could point to the 3D flow around the blade being the primary reason for differences in aerodynamic flow, rather than the strict 2D assumption in the Figure 44 Instantaneous velocity magnitude at r/R = 0.75 CA case 2D CFD input tables.
for 2D CFD (left) and 3D CFD (right), TRT, θ = 16° .
VI. Conclusions High - fidelity 3D CFD is used for performance predictions of the isolated Ingenuity rotor and compared to CA based on 2D CFD airfoil lookup tables. Computational analyses are presented for single and coaxial rotor setups and are compared to experimental single and coaxial rotor performance data at representative Mars conditions.
Rotor performance metrics are compared and show reasonable agreement between the computational analyses.
Figure 45 Instantaneous velocity magnitude , spanwise Correlation with experimental data shows consistent component removed, at r/R = 0.75 for 2D CFD (left) and 3D discrepancies at high blade loading (near or post peak figure of CFD (right), TRT, θ = 16° .
merit ) and shows a consist change in blade loading slope with rotor collective angle. The reason for the differe nces in rotor V. Discussion performance predictions between computational and experimental approaches is currently not known .
The reason for the differences between experimental and A nalyses of the spanwise distributions of thrust and power computational results present ed remains inconclusive at this show differences in stall, which first become ap parent at the point . The 2D CFD analyses of airfoils will show differences to outboard sections of the blade. Comparisons at lower collective finite - width airfoil simulations [26] , though this does not angles generally shows favorable agreement of blade thrust and explain why the slopes of the CA and 3D - based CFD power distributions with differences likely attributable to the simulations for blade loading as function of collective look significant difference s in fidelity of the computational similar for both the single and coaxial rotor pred ictions in approaches.
Figure 12 and Figure 16 . Despite differences that could be attributed due to the large differen ce in computational fidelity, Acknowledgments 3D CFD and CA cases ( 2D CFD) are showing similar trends in the figures presented in Sections A and B . A future study may The authors would like to acknowledge the support of also be performed in order to quantify the effect of the landing William Warmbrodt and Larry Hogle during this research.
legs on the total vehicle thrust and hover performance.
Resources supporting this work were provided by the NASA High - End Computing (HEC) Program through the NASA A. Modeling of Small - scale Turbulence Advanced Supercomputing (NAS) Division at Ames Research Differences in FM predictions between 2D and 3D CFD are Center.
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