Document
Paper 28
I mproved M ars H elicopter A erodynamic R otor M odel
f or C omprehensive A nalyses
Witold J. F. Koning Wayne Johnson Håvard F. Grip Science and Technology Corporation NASA Ames Resea rch Center Jet Propulsion Laboratory NASA Ames Research Center Moffett Field, California California Institute of Technology Moffett Field, California wayne.johnson@nasa.gov Pasadena, California witold.koning@nasa.gov havard.f.grip@jpl.nasa.gov ABSTRACT The Mars Helicopter is part of the NASA Mars 2020 rover mission scheduled to launch in July of 2020. Its goal is to demonstrate the viability and potential of heavier - than - air vehicles in the Martian atmosphere .
U ltimately , it aims to bridge the resolution gap between orbiters and the rover as well as allow access to otherwise inaccessible regions . The low density o f the Martian atmosphere an d the relatively small - scale rotor result in very low Reynolds number flows . The low density and low Reynolds numbers reduce the lifting force and lifting efficiency, respectively. This paper describes the generation of the impro ved Mars Helicopter aerodynamic rotor model. The goal is to generate a performance model for the Mars Helicopter rotor using a free wake analysis , since this has a low computational cost for design . The improvements in the analys i s are two - fold and are exp a nded on from two prior p ublications . First , the fidelity of the simulations is increased by performing higher - order two - dimensional time - accurate OVERFLOW simulations allowing for higher acc uracy aerodynamic coefficients and a better understanding of the boundary layer behavior as well as its transient features . Second , a version of the model is generated to duplicate the exact testing conditions in the 25 – ft .
diameter Space Simulator at the Jet Propulsion Laboratory , which allows for better correlation o f rotor performance figures . Previous work correlated performance with that test , but did not consider the higher temperature s in the experiment compared to th ose of the Martian atmosphere. T he higher temperature s in the experiment are expected t o give con servative performance estimates , as they g i ve rise to an increase in speed of sound and decrease in observed Reynolds numbers.
NOTATION airfoil c hord ma ximum chordwise spacing 𝑐 𝑠 ';< section drag coefficient chordwise spacing at trailing edge 𝑐 𝑠 " *0 section lift coefficient airfoil thickness 𝑐 𝑡 # 𝑐 absolute temperature maximum section lift coefficient 𝑇 # $%& + section moment coefficient dimensionless wall distance 𝑦 𝑐 ' angle of attack rotor power coefficient 𝐶 𝛼 ) specific heat ratio rotor thrust coefficient 𝛾 𝐶 * dynamic viscosity Figure of Merit 𝜇 𝐹𝑀 density gravitational acceleration 𝜌 𝑔 rotor solidity Mach number 𝜎 𝑀 amplification factor 𝑁 American Institute of Aeronautics and n umber of cells on trailing ed ge AIAA 𝑛 *0 Astronautics rotor radial coordinate 𝑟 Backward Difference Formula (2nd order) BDF2 gas constant , rotor radius 𝑅 B oundary L ayer Reynolds number BL 𝑅𝑒 C omprehensive A nalytical M odel of chord - based Reynolds number CAMRAD 𝑅𝑒 R otorcraft A erodynamics and D ynamics displacement thickness Reynolds number 𝑅𝑒 Computational Fluid Dynamics CFD at separation Chimera Grid Tools chordwise spacing at leading edge CGT 𝑠 :0 th Presented at the 44 European Rotorcraft F orum, Delft, t he Netherlands, 18 - 2 1 September, 2018. Page 1 of 14 This paper is a work of the U.S. Government and is not subject to copyright protection in the U.S.
Carbon Dioxide C O 2 1.1. Mars Helicopter Design DNS Direct Numerical Simulation The design of the MH , shown in Figure 1 , features a Grid Resolution Study GRS co - axial rotor with a ma ss of roughly 1.8 kg and a Jet Propulsion Laboratory JPL 1.21 m rotor diameter. The helicop ter relies on solar Kelvin - Helmholtz KH LE Leading Edge cells and a batter y system for power, allowing up to LSB Laminar Separation B ubble 90 s econd flight endurance that is conducted fully Mars Condition MC autonomously due to the communicati on delay Mars Helicopter MH between Earth and Mars .
Navier - Stokes NS RANS Reynolds - Averag ed Navier - Stokes Spalart - Allmaras SA Sea Level Standard SLS Stretching R atio SR SS Space Simulator Trailing Edge TE Turbulence I ntensity TI Tollmien - Schlichting TS Unmanned Aerial Vehicle UAV VTOL Vertical Take - Off and Landing Figure 1 . An Artistic depiction of th e Mars Helicopter 1. INTRODUCTION The rotor design features two counter - rotating, hingeless, two - bladed rotors. The rotors are spaced The NASA Jet Propulsion Laboratory designed the Mars Helicopter (MH) in collaboration with apart at approximately 8 % of th e rotor diameter and AeroVironment Inc., NASA Ames Research Center, are designed to operate at speeds up to 2,800 RPM.
and NASA Langley Research Center to explore the Flights are limited to favorable weather with low wind possibility of a Vertical Take - Off and Landing and gust speeds. The maximum airspeed is (VTOL) Unmanned Aerial Vehicle (UAV) for flight constrained to 10 m/s horizontally and 3 m/s on Mars. The helicopter join s the NASA Mars 2020 vertically .
mission, currently scheduled to launch in July of 2020 , to demonstra te the viability and potential of heavier - 2. MARS ATMOSPHERIC CONDITIONS than - air vehicles in the Martian atmosphere.
Development started late 2 013, and Balaram The Martian environment provides major challenges and Tokumaru published the initial conceptual design for the design of a UAV . The low density of the of the current MH in 2014 . Grip et al. more recently Martian atmo sphere and the relatively small MH published a paper describing the flight dynamics of rotor result in very low chord - based Reynolds number the MH and experimental testing in the 25 - ft.
3 4 flows with a range of 𝑅𝑒 ≈ 10 to 10 , see Figure 2 .
diameter Space Simulator (SS) at the Jet Propulsion Furthermore, the low density and low Re ynolds Laboratory (JPL) . Balaram et al. describe d the full - number reduce the lift force and lift efficiency, scale technology demonstrator . Ko ning et al.
respectively, which are only marginally compensated published performance predictions for the MH rotor , by a lower gravitational acceleration of around 𝑔 = and also evaluated the feasibility of cambered plates 3.71 m/s .
4, 5 as substitute airfoils for the rotor.
2.0 The helicopter is mounted on the bottom of the c Re Mars 2020 rover for its journey to Mars. The rover 1.5 places the helicopter on the ground after touch down , 1.0 starting a 30 - day flight test campaign, of up to five 0.5 flights and a few hundred meters.
Reynolds Number, 0.0 The present work describes the second 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 generation of the performance model for t he Mars radial station, r/R Figure 2 . Approximate span - wise Reynolds number distribution Helicopter rotor using a free wake analysis .
for the MH rotor in the Martian atmosphere , from Koning et al.
th Presented at the 44 European Rotorcraft F orum, Delft, t he Netherlands, 18 - 2 1 September, 2018. Page 2 of 14 This paper is a work of the U.S. Government and is not subject to copyright protection in the U.S.
-1 In addition, the low temperature and largely CO min based atmosphere result s in a low speed of sound, d c further constraining rotor operation in the Martian smooth cient, airfoils -2 laminar fl at 10 ffi atm osphere . plate ( 2C ) f minimum section turbulent fl at drag coe plate ( 2C ) f 3. LOW REYNOLDS NUMBER -3 2 3 4 5 6 7 8 10 10 10 10 10 10 10 AERODYNAMICS chord-based Reynolds Number, Re c Figure 4 . Minimum section drag coefficient versus Reynolds The very low chord - based Reynolds numbers of the number , reproduced from McMasters and Henderson Mars Helicopter rotor, around 𝑅𝑒 ≈ 10 , result in relatively poor lift - to - drag ratios when compared to 3.1. Subcritical Airfoil Performance conventional performance figures at higher Reynolds In the l ow Reynolds number regime, the boundary numbers . At these low Reynolds numbers , starting layer can still be laminar after the point of pressure below approximately 𝑅𝑒 ≈ 10 , the boundary layer recovery. T he laminar boundary layer at lower state can be subc ritical. The term critical is used here Reynolds numbers does not encounter sufficient to indicate the termination of low drag and amplification of disturbances in time to experience on - commencement of laminar separation from a body transition or turbulent flow reattachment after streamlined shape. The flow is only called subcritical laminar separation. The laminar boundary layer if the boundary layer flow is laminar for the range of carries much less momentum near the surface due to angles of attack. The corresponding Reynolds number the absence of the momentum exchanges found in a at which the boundary layer just begins to exhibit typical turbulent boundary layer, and therefore turbulent features is the critical Reynolds number.
cannot withstand a strong adverse pressure gradient McMa sters and Henderson provide an overview without separati ng . S eparation of the laminar of experimental airfoil performance over a wide boundary layer then gives rise to a large pressure drag Reynolds number spectrum. Figure 3 shows the c omponent. Furthermore, the relatively thick maximum section lift - to - drag ratio versus Reynolds boundary layer at low Reynolds numbers reduces the number. The aforementioned performance drop is effective camber of the airfoil, reducing the attainable visible aro und approximately 𝑅𝑒 ≈ 10 . Rough lift coefficient, especially if a separated shear - layer airfo ils exhibit higher performance u p to slightly lower fails to reattach.
Reynolds numbers , because of the roughness T he turbulent boundary layer exhibits higher contribution to boundary layer transition.
resultant losses and friction drag compared to laminar smooth boundary layer. However, the turbulent layer has airfoils max ) d higher near - w all velocity and momentum that allow s /c l (c for larger positive pressures (due to an adverse rough airfoils pressure gradient ) prior to separati on, resulting in Schmitz fl at higher airfoil performance of airfoils in supercritical maximum section plate lift to drag ratio, states.
2 3 4 5 6 7 8 10 10 10 10 10 10 10 chord-based Reynolds Number, Re 3.1.1. Mars Helicopter Boundary Layer State c Figure 3 . Maximum section lift - to - drag rati o versus Reynolds Analysis number , reproduced from McMasters and Henderson Koning, Johnson, and Allan performed an evaluation The dramatic performance drop at low Reynolds of the two - dimensional boundary layer state for the numbers is primarily attributed to the rise in drag MH airfoils in hover . The analyses were performed coefficient in the critical Rey nolds number range. This solely to obtain the boundary layer state, and not to is illustrated by the minimum section drag coefficient estimate a erodynamic coefficients.
versus Re ynolds numb er shown in Figure 4 .
The instability and laminar separation The low performance figures clearly indicate the location s were computed from the momentum - need for careful design and evaluation of airfoils and integral equation derived from the work of 9 10 rotors to be used in the low Reynolds number regime.
Schlichting , and Wazzan, Okamura, and Smith . A Karman - Tsien compressibility correction was performed on the potential flow velocity distribution th Presented at the 44 European Rotorcraft F orum, Delft, t he Netherlands, 18 - 2 1 September, 2018. Page 3 of 14 This paper is a work of the U.S. Government and is not subject to copyright protection in the U.S.
to account for first - order compressibility effects .
5 . 0 ∙ 10 the free shear - layer after lam inar sep aration Tollmien - Schlichting (TS) waves were assumed to be does not normally transition to turbulent flow in time the dominant transition - initiation mechanis m and to reattach to the airfoil surface.
we re computed using the meth od suggested by Smith T he two - dimensional boundary layer equations and Gamberoni using stability charts from represent only an approximation of the true three - Wazzan et al. T he airfoils were then analyzed for dim ensional flowfield , even though the aspect ratio of the expected angles of attack and Mach numbers at the rotor blades should warrant the use of blade various radial stations for the rotor in hover. The element models. The standard boundary layer analysis allow ed for the computation of disturbance equations also assume thin boundary layers, which at g ro wth over the airfoils and estimation of transition, increasingly lower Reynolds numbers become invalid .
I analogous to the 𝑒 method , based on linear stability A high er order boundary layer formulation for airfoil theory by van Ingen. performance evaluation , for example that presented The maximum amplification factor was by Drela, would therefore be instrumental in future computed over the contour length , and the largest airfoil design optimization at very low Reynolds total amplification factor at the point of laminar numbers.
separation was estimated . For the majority of the The approach is also limited in evaluating radial locations evaluated , the first most amplified compressibility features. A turbulence transition model is helpfu l to assess these features without frequency result s in an amplification fac tor 𝑁 ≤ 1 , not assuming ‘fully turbulent’ or fully laminar exceeding 𝑁 ≈ 2 at laminar separation . The likelihood simulations .
of boundary layer transition to turbulence at any airfoil station is deduced to be very low f or the rotor 3.1.2. Laminar Separation Bubbles and Shear - layer in hover .
Instability The method computes the amplitude ratio and not the ac tual disturbance am plitude since external The laminar separated shear - layer is susceptible to influences are not known. Freestream turbulence transition , and can undergo rapid transition to levels, vibrations, dust , or surface roughness can all turbulen t flow. The increased entrainment by the add to the actual disturbance amplitude. However, separated shear - layer can lead to reattachment of the evaluating the former is complicated due to the flow, creating a Laminar Separation Bubble importance of the distribution a cross the frequency 18 , 19 , 20 (LSB) . The low velocities inside the bubble are spectrum, besides the freestream turbulence level .
linked to the characteristic flat pressure distribution This is difficult to predict and model , and is therefore of an LSB.
not attempted. Freestream tu rbulence levels might be Periodic unsteadiness can be observed due to very low in the free atmosphere , but the lower rotor the unstable reattachment region caus ed by might experience increased turbulence levels from the fluctuating entrainment of the fluid in the shear - layer , upper rotor wake. Vibrations and dust require higher periodic stabilization of the reverse - flow boundary knowledge of the rotor system and atmospheric dust 21 layer, and possible developing eddy structures .
behavior in the Mart ian atmosphere , work that is Movement of the bubble over the airfoil can therefore † currently being pursued . It is concluded that flow 22 occur, as observed by Gaster .
conditions would have to be severe to cause transition In addition to TS instabilities, the shear - layer of the boundary layer prior to laminar separation of flow is also observed to oscillate due to Kelvin - the boundary layer .
Helmholtz (KH) instabilities , which could develop Lissaman observe s that complete laminar flow into KH vo rtices if the flow does not reattach, thus ca n occur for small angles of attack below 𝑅𝑒 ≈ 19 causing fluctuating forces on the airfoil . At high - 3 ∙ 10 with boundary layer reattachment unlikely subsonic Mach numbe rs, possible shock - induced 4 15 below 𝑅𝑒 ≈ 7 ∙ 10 . The absence of transition has separation and /or transition may cause additional also been observed by Mueller and DeLaurier who complexities in the flow.
state, aft er Carmichael , that for airfoils below 𝑅𝑒 ≈ † Work in progress on experimental dust studies and two - dimensional airfoil testing for low Reynolds numbers at NASA Ames Research Center.
th Presented at the 44 European Rotorcraft F orum, Delft, t he Netherlands, 18 - 2 1 September, 2018. Page 4 of 14 This paper is a work of the U.S. Government and is not subject to copyright protection in the U.S.
If an LSB occurs a t the low Reynolds number , the A thorough investigation on vortex shedding at low level of freestream turbulence intensity can alter Reynolds numbers was performed by Yarusevych, when , or if, reattachment occurs, and as such can Sullivan, and Kawall .
st rongly affec t expected airfoil performance . Angle The boundary layer investigation on the MH of attack changes and boundary layer receptivity, the rotor in hover predict s flow structure B to be process by which free - stream disturbances influence dominant in the linear regime.
or generate insta bilities in the boundary layer, can 3.2. Cambered Plate Performance greatly influence bubble formation and thus airfoil performance . This i s linked to the often significant Flat and ca mbered plates, especially with sharp hysteresis encountered in experimental low Reynolds leading edges, behave differently at low Reynolds 5 7, 24 number research around 𝑅𝑒 ≈ 10 .
numbers than conventional airfoils. The plate performance evaluation by Koning et al. observed 3.1.3. Low Reynolds Number Flow Structures different flow structures than those found 25 26 Wang et al. and Huang and Lin investigated f low experimentally for smooth shapes at low Reynolds numbers by Wang et al. (see Figure 5 ). This is due structures and characteristics of vortex shedding for to the vastly different geometry of the airfoils and an NACA 0012 airfoil. Eight distinct flow patterns are resulting transient flow structures. Hoerner presents identified based on angle of attack and Reynolds insight into differences in performance between a flat number. Figure 5 illus trates the different flow plate and an airfoil crossing the critic al Reynolds structures and stall modes for the NACA 0012 airfoil, number transition region. The section lift and drag showing more modes than the typical leading edge coefficient behavior near the critical Reynolds number stall, trailing edge stall, and thin - airfoil stall known 27, 28 for higher Reynolds number regimes . are shown in Figure 6 and Figure 7 , respectively.
The different flow modes in Figure 5 indicate 1.20 the characteristic differences observed in the low l c Reynolds number regime. Flow structure B ‘ Partially 1.00 cient, attached laminar boundary layer which separates near critical Reynolds number ffi transition region 0.80 the trailing edge and then roll s up and/or experiences transition further downstream ’, C ‘ Fully separated 0.60 laminar shear - layer near the leading edge with a section lift coe f/c = 4.0% N60 Airfoil, t/c = 12.4%, subsequent transition downstream but without cambered plate, t/c = 3.0%, f/c = 5.8% 0.40 reattachment ’, and D ‘ Laminar bubble, i.e., laminar 4 5 6 10 10 10 flow from separation to reattachmen t ’ are some of the chord-based Reynolds number, Re c flow structures only observed for the low Reynolds Figure 6 . Variation of section lift coefficient with Reynolds 25 7 num ber at constant angle of attack, reproduced from Hoerner number regime . Flow mode D in particular indicate s the necessity for time - accurate evaluation of the The cambered plates in the comparison have a boundary layer in order to be able to investigate the thickness ratio of 𝑡 𝑐 ⁄ = 3 . 0% . The low thickness ratio flow structure and behavior adequately.
30, 31 has a beneficial effect on the drag coefficient .
H The sharper the leading edge, the earlier C transition starts . For all positive angles of attack, G α the stagnation point m oves downstream on the lower F surface, creating a turbulent edge, essentially forcing E supercritical behavior up to very low Reynolds numbers. A sharp leading edge plate therefore does D angle of attack, Transition Laminar not exhibit a critical Reynolds number because the B Reattachment Turbulent point of breakaway is fixed. The t urbulent edge has Rolling Separation A both an immediate and a fixed transition location at ultra low low moderate high all non - zero angles of attack . Crompton indicates chord-based Reynolds number, Re c the high shear turbulent fluid feedback and n atural Figure 5 . Schematic of flow structures around NACA 0012 airfoil 25 21 for each Reynolds number regime , reproduced from Wang et al.
KH instability as main reasons for rapid transition .
He finds the transition to turbulence to be located at 4 5 21 𝑥 𝑐 ⁄ ≈ 2 . 5% for flat plates at 𝑅𝑒 ≈ 10 − 10 .
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Schmitz notes that beneficial turbulent time - accurate and time - averaged methods might skew reattachment occurs for plates up to angles of attack observations of the existence of an LSB.
4 4 around 𝛼 ≈ 7° to 10° , whereas Crompton indicates Schmitz says 𝑅𝑒 ≈ 1 . 0 ∙ 10 to 2 . 0 ∙ 10 is reattachment up to 𝛼 ≈ 5° . Laitone reports a similar enough for sharp leading edge boundary layer 4 32 range and observe d for 𝑅𝑒 < 4 . 0 ∙ 10 and 𝛼 < 8° transition . Werle shows a flat plate at 𝛼 ≈ 2 . 5 ° and that the large leading edge bubble (compared to blunt 𝑅𝑒 ≈ 1 . 0 ∙ 10 with laminar reattachme nt , whereas leading edges) is replaced by continuous shedding of at 𝑅𝑒 ≈ 5 . 0 ∙ 10 the shear - layer turns turbulent 34, 35 small vortices over the upper surface, thereby prior to reattachment .
mitigating the effects of total flow separation. Using Direct Numerical Simulation (DNS) Sampaio, Rezende , and Nieckele show the possibility 0.20 N60 Airfoil, t/c = 12.4%, f/c = 4.0% of a secondary separation bubble. This bubble was cambered plate, t/c = 3.0%, f/c = 5.8% d c 0.15 also observed by Crompton experimentally. A cient, sketch of the separation bubble on a flat plate is ffi 0.10 provided in Figure 8 . When the reattachment point critical Reynolds number reaches the trailing edge, the bubble effectively transition region 0.05 ‘bursts’, which is likely to generat e periodic vortex section drag coe 32, 40 25 shedding. Wang et al. observe that Gaster’s laminar fl at plate ( 2C ) f 0.00 bursting criterion for separation bubbles does not 4 5 6 10 10 10 hold in the low Reynolds number regime.
chord-based Reynolds number, Re c Koning et al. show that the addition of cambe r Figure 7 . Variation of section drag coefficient with R eynolds num ber at constant angle of attack, reproduced from Hoerner to a sharp leading edge plate can indeed have very competitive performance to the airfoils discussed in 23, 33 Neither the trailing edge shape nor freestream the present research. Transient Reynolds - Averaged turbulence levels seem to impact cambered or flat Navier - Stokes (RANS) computations showed both plate perfo rmance to any significance within the leading edge bubbles and transient upper surface evaluated low Reynolds number range . No hysteresis vortex shedding that decreased the separated flow.
occurs for thin plates, compared to that observed for This is attributed to the leading edge geometry as also thicker airfoils, because the nose turbulence increases ex perimentally observed by Laitone. At smaller 32 31 faster than the pressure increase . Okamoto et al. , angles of attack , the flow seems to reach a steady - 23 33 Laitone , and Pelletier and Mueller show the state by means of a separation bubble similar to that comparatively low influence of freestream turbulence .
36 37, 38 reported by Suwa et al. , Anyoji et al. , and However, a Reynolds number must exist at others.
which the boundary layer does not transition to separated shear layer dividing streamline turbulence, despite the sharp leading edge. Indeed, boundary layer edge flat plates at low Reynolds numbers around 𝑅𝑒 ≈ 10 have been shown to have laminar flows without primary leading edge bubble 34, 35 transition to turbulence .
stagnation reattachment Experimental results seem to contradict each secondary bubble other on whether turbulent reattachment of the separated shear - layer from the leading edge of a flat plate indeed occurs. Laitone does not mention an Figure 8 . Sket ch of leading edge separation bubble on a flat plate LSB, and Pelletier and Mueller do not observe an with sharp leading edge (not to scale), created referring to LSB for (cambe red) flat plates and airfoils around 39 Sampaio et al.
𝑅𝑒 ≈ 10 . In the experimental work by Suwa et al.
37, 38 The Reynolds number sensitivities of the flat plate and Anyoji et al. , however, the existence of an minimum drag coefficient a nd maximum lift - to - drag LSB is deduced from the pressure distribution ratio were in agreement with the results of Schmitz obtained via pressure sensitive p aint observations for and two dimensional laminar flat plate theory. The similar geometry and Reynolds numbers. Anyoji et al.
cambered plate was observed to obtain a higher lift - find the flat plate reattachment state to disappear 3 4 37 to - drag ratio than the flat plate, d espite the between 𝑅𝑒 ≈ 4 . 3 ∙ 10 and 1 . 1 ∙ 10 . It is unclear to unavoidable increase in minimum section drag.
what extent the eval uation of the flow field using th Presented at the 44 European Rotorcraft F orum, Delft, t he Netherlands, 18 - 2 1 September, 2018. Page 6 of 14 This paper is a work of the U.S. Government and is not subject to copyright protection in the U.S.
4. PRIOR ROTOR PERFORMANCE roughly a 1 3 % de crease in Mach number and 29 % PREDICTIONS de crease in Reynolds number ( due to th e temperature dependence of the viscosity for CO ) compared to Figure 9 shows the performance predictions from Mars atmospheric conditions. It is estimated that this Koning et al. for Figure of Merit versus blade results in conservative exp erimental performance loading. Performance is calculated by comprehensive numbers from the JPL SS test conditions .
analysis in CAMRADII using a free wake geometry, and airfoil ta bles are generated by Computational 5. COMPUTATIONAL APPROACH Fluid Dynamics (CFD). The three conditions in Figure 9 span expected operating conditions on Mars, Two - dimensional airfoil s ections are analyzed using and temperature varies along with density.
two - dimensional structured grids and solved using the 0.70 implicit compressible RANS solver OVERFLOW Mars Condition 1, ρ = 0.015 Mars Condition 2, ρ = 0.017 2.2n . All solutions presented are run time - accurate , 0.60 Mars Condition 3, ρ = 0.020 in an effort to quantify possible unsteady behavior, Measured data (JPL), ρ = 0.0175 th 0.50 and use 6 order central differencing of Euler terms nd 42 FM with 2 order BDF2 time marching. In total , over 0.40 6,000 simulations are performed on the Pleiades 0.30 Supercomputer at NASA Ames Research Center.
Figure of Merit, 0.20 5.1. Operating Conditions 0.10 Airfoil performance is evaluated for average Martian atmospheric conditions, MC 2 , as previous work 0.00 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 show s marginal performance differences with other blade loading, C / σ T variations . Oper ating conditions for MC 2 are Figure 9 . F igure of Merit versus blade loading for all Martian Conditions , from Koning et al. presented in Table 1 and compared to Earth Sea Level Standard (SLS) conditions.
The predictions show generally good agreement with Experiments in the 25 - ft. diameter Space experimental results from th e 25 - ft. Space Simulator S imulator at JPL are performed using CO at similar at JPL . However, t he CFD analysis was performed gas dens it y but at a different temperature range. The using a thi n - layer Navier - Stokes (NS) code and the temperature in the JPL SS varied between 𝑇 = measured data in Figure 9 obta ined at much higher 293 . 15 − 303 . 15 𝐾 during testing . The average temperature, leading to the need for a better CFD temperature was used from the JPL SS operating method and calculations performed at the correct conditions, an d the corresponding viscosity obtained temperature for proper comparison with from Sutherland’s equation with Sutherland’s measurements.
constants for CO .
Table 1 .
Operating c onditions for Mars Condition 2 4.1. Prediction Improvements Variable Earth SLS MC 2 JPL SS Compared to the previous work by Koning et a l. , the Density, 𝜌 [kg/m ] 1.225 0.017 0.0185 Temperature, T [K] 288.20 223.20 298.15 rotor model predictions in the present work have been 2 2 Gas constant, R [m /s /K] 287.10 188.90 188.90 impro ved on a couple of fronts. First , h igher fidelity , Specific heat ratio, 𝛾 1.400 1.289 1.289 time - accurate simulation s are employed in 2 - 5 - 5 - 5 Dynamic viscosity, 𝜇 [Ns/m ] 1.750·10 1.130·10 1.504 ·10 OVERFLOW to allow for higher accuracy Static pressure, p [kPa] 101.30 0.72 1.04 aerodynamic coefficients and better understanding of Fre e - stream turbulence and boundary layer t he f low structure . Second , airfoil files are re - de fined receptivity are generally important, but no further to allow for denser meshes, and trailing edge thickness information is known . Therefore , the free - stream is adjusted to reflect a realistic thickness . Third , a turbulence intensity is kept at the standard value rotor model is made separately for the JPL 𝑇𝐼 ≈ 0 . 082% .
experimental c onditions and MC 2.
However, Wang et al. experimentally show The main differe nce between JPL SS conditions that the influence of the turbulence intensity is and MC 2 is the operational temperature in the JPL greatly diminished when the Re ynolds number regime SS experiments , as shown in Table 1 . This causes th Presented at the 44 European Rotorcraft F orum, Delft, t he Netherlands, 18 - 2 1 September, 2018. Page 7 of 14 This paper is a work of the U.S. Government and is not subject to copyright protection in the U.S.
4 5 The evaluation of the upper rotor wake influence on is low ( 𝑅𝑒 ≈ 1 . 0 ∙ 10 to 3 . 0 ∙ 10 ) compared to the 4 25 transition locations of the lower rotor BL is not ultra - low regime ( 𝑅𝑒 < 1 . 0 ∙ 10 ).
attempted due to the complexity of the problem. A Compressibility effects are expected to be small three - dimensional model can provide more insight as shown by experimental work by Suwa et al. and in to the influence of upper rotor wake on l ower rotor Anyoji et al. for similar Mach - Reynolds number transition and perhaps quantify performance trends .
ranges. The (turbulent) Prandtl number is assumed to stay the same as for air.
5.3. Time - Accurate Solver The angle of attack and Mach number range for each radial station is presented in Table 2 . The angle The time - accurate solver allows for extraction of flow of attack range use s 1 - degree increments and the solutions over time and investigat ion of potential Mach range use s increments equal to 𝑀 = 0 . 1 . Each transient features for a better understanding of the radial station’s ( 𝑀 , 𝛼 ) pair provides the lift, drag, and flow , as was done by Koning et al .
moment coefficients for the C81 airfoil deck files A script detects whether the converged required for comprehensive analyses.
integrated forces over the airfoil are peri odic , and subsequently takes the mean and standar d deviation Table 2 . C81 alpha - Mach pair input parameters (MC 2) - 4 CFD s tation r/R α [deg] M Re/ M [ 10 ] over whole periods to ensure adequate averaging of Station 1 0.091 - 15 to 2 0 0.1 0 to 0.3 0 1.074 the aerodynamic coefficients.
Station 2 0.200 - 15 to 2 0 0.1 0 to 0.4 0 2.984 Station 3 0.295 - 15 to 2 0 0.1 0 to 0.5 0 4.176 Station 4 0.390 - 15 to 2 0 0.1 0 to 0.5 0 4.176 5.4. Geometry Definition and Grid Resolution Station 5 0.527 - 15 to 2 0 0.2 0 to 0.5 0 3.451 Stud y Stat ion 6 0.762 - 15 to 2 0 0.2 0 to 0.70 2.564 Station 7 0.924 - 15 to 2 0 0.2 0 to 0.85 1.825 The clf5605 airfoil is used for a Grid Resolution Study Station 8 0.991 - 15 to 2 0 0.2 0 to 0.90 0.724 (GRS). The G RS is p erformed for two limiting cases: 5.2. Turbulence and Transition Modeling the highest and lowest Reynolds number expected at 𝑟 / 𝑅 = 0 . 75 . Th e gridding guidelines from the third The p revi ous rotor models were generated using the American Institute of Aeronautics and Astronautics Spalart - Allmaras (SA) 1 - equation turbulence model ( AIAA ) CFD High Lift Prediction Workshop are used (SA - noft2) in ‘fully turbulent’ mode . In the linear to generate different grids in four levels: coarse, angle of attack range , the performance was fou nd to medium, fine, and extra - fine. A super - fine grid level be near ly equal to cases run fully laminar .
is added.
T ransition modeling is realized using the SA 1 - The chord wise spacing at the leading edge equation turbulence model (SA - neg - 1a) with the (LE) , 𝑠 , and trailing edge (TE) , 𝑠 , are varied Coder 2 - equation Amplification Factor Trans port :0 *0 between 1 and 0 . 001% 𝑐 . The maximum chord wise (AFT) transition model (SA - AFT2017b). The SA - spacing , 𝑠 , is limited between 0 . 5 and 1 . 0% 𝑐 . The AFT2017b model is referred to as the “ transition ';< + model ” from here on out. This allows for a direct 𝑦 values are calculated for the first point off the comparison to the flat plate model presented by airfoil surface at 10% 𝑐 . The initial wall spacing layer Koning et a l. , which uses the same turbulence and contain s 5 layers of constant cell spacing normal to transition model s . the viscous walls. The cell Stretching Ratio (SR) for The intermittency is deduced from the the normal and tangential/chordwise layers is kept transpo rt of the amplification factor in the flow . This identical and t he farfield is located at 100 𝑐 for all allows for a co m parison with the in i tial estimates of grids. The number of cells normal to the surface is the a mplification factor in the BL of the initial MH obtained from the target stretchi ng ratios. The rotor model . The general understanding of the MH number of cells over the trailing edge, 𝑛 , is *0 airfoil performance and flow conditions can therefore monitored to ensure adequate gridding near the TE .
be improved .
Table 3 shows the grid resolution parameters for the The initial mode l deduced the BL state from a various grid levels.
two - dimensional BL analysi s. Limitations include a Table 3 .
Grid resolution parameters for the GRS at 𝑅𝑒 = 18 , 000 crude compressibility evaluation and simple empirical + Grid level s / s [ c ] s [ c ] SR y n LE TE max TE evaluation of the shear - layer behavior after Coarse 1% / 1% 1.0% 1.25 1 .00 3 Medium 0.1% / 0.1% 1.0% 1.16 0.67 5 separation . The transition model allows for a more Fine 0.01% / 0.01% 0.5% 1.10 0.44 32 thorough evaluation of these features and estimation Extra - fine 0.001% / 0.005% 0.5% 1.0 7 0.30 46 Super - fine 0.001% / 0.001% 0.5% 1.05 0.25 102 of their effect on airfoil p erformance.
th Presented at the 44 European Rotorcraft F orum, Delft, t he Netherlands, 18 - 2 1 September, 2018. Page 8 of 14 This paper is a work of the U.S. Government and is not subject to copyright protection in the U.S.
All grids are generated using Chimera Grid Tools Figure 11 shows the amplification factor plot for (CGT) 2.3. The original airfoil contained a sharp station 7 at α = 3 . 00° , M = 0 . 60 .
trailing edge that re sulted in unrealistically thin TEs .
The airfoils have been adapted to utilize a 0.25% c thick rounded TE . An O - grid is preferred over a C - grid to remove the inherent bias in the wake resolution present in the latter.
The extra - fin e grid level is ultimately chosen since it is the first level at which the section drag Figure 11 . C omputed amplification factor in the flow at 𝑟 / 𝑅 = th coefficients are converged up to the 4 decimal point.
0 . 92 , 𝛼 = 3 . 00° , 𝑀 = 0 . 60 . Values of 𝑁 < 1 are solid blue (red is This is deemed sufficient as the C81 airfoil format 𝑁 ≈ 7 , time - accurate , with transition model ) only allow s 4 decimal numbers for the aerodyn amic The analysis by Koning et al. does not evaluate the coefficients.
amplification factor after laminar separation. The present results agree with the analysis from Koning et 5.5. Three - Dimensional Effe cts al. up until laminar separation and also indicate that All simulations performed are two - dimensional. The transition is unlikely in hover for the MH.
vast separation at moderate to high angles of attack c an yield three - dim ensional breakdown of the flow 6.2. Transition Model Influence on Turbulence 23, 37, 47 around 𝛼 ≈ 8° . Since the majority of the rotor Behavior Near Stall is expected to operate in the linear regime, this is not The SA turbulence model (SA - noft2) is run “fully pursued further at this time. With transition of the turbulent , ” meaning that production terms are act ive, BL to turbulence unlikely in the design thrust without a t rip line or a form of transition control.
coe ff icient range, cross - flow transition is as sumed not Koning et al. found that t he turbulence model to be critical for rotor performance.
produces near - identical results to a fully laminar solution in the linear angle of attack range. At h igher 6. SIMULATION RESULTS : angles of attack and higher Ma ch numbers, however, TRANSITION MODEL INFLUENCE the model produces some turbulent features leading to higher performance tha n that of the laminar Select airfoil station s are studied to investigate the solution , even at the low Reynolds numbers under flow structures simulated. Figure 10 shows the investigation . The transition model coupled with the velocity field around station 6 with a laminar BL SA turbulence model retains the laminar behavior up separating at the end of the airfoil. All flowfields to higher angles of attack . A t 𝑟 / 𝑅 = 0 . 75 , station 6 presented are simulated for MC 2 conditions.
conditions are compared to laminar simulations at two Mach numbers, 𝑀 = 0 . 20 ( Figure 12 , ‘ incompressible ’ ) and 𝑀 = 0 . 50 ( Figure 13 , approximate Mach number for station 6 in hover ).
0.20 0.18 0.16 Figure 10 . L aminar boundary layer with trailing edge sepa ration d 0.14 c and vortex shedding at 𝑟 / 𝑅 = 0 . 76 , 𝛼 = 0 . 00° , 𝑀 = 0 . 50 ( velocity ient, magnitude, time - accurate , with transition model ) 0.12 ffi 0.10 6.1. Transition Model Influence on Amplification 0.08 Factor in Hover 0.06 section drag coe 0.04 The amplification factor is monitored for expected SA-AFT2017b transition model SA turbulence model ‘fully turbulent’ angle of attack and Mach co mbinations over the 0.02 No turbulence model (laminar) radial stations as published in Koning et al. In 0.00 -1.00 -0.50 0.00 0.50 1.00 1.50 agreement with this paper , the amplification factor section lift coe ffi cient, c l prior to lamina r separation rarely exceeds 𝑁 = 1 .
Figure 12 . 𝑟 / 𝑅 = 0 . 76 , 𝑀 = 0 . 20 , dr ag polars for laminar, ‘ fully turbulent’ SA turbulence , and SA - AFT2017b transi tion model th Presented at the 44 European Rotorcraft F orum, Delft, t he Netherlands, 18 - 2 1 September, 2018. Page 9 of 14 This paper is a work of the U.S. Government and is not subject to copyright protection in the U.S.
Rumsey and Spalart discuss the use of the SA The simulations in Figure 14 and Figure 15 perform turbulence mo del at low Reynolds numbers and note: s imilar ly to laminar simulations. If the simulation is “ (…) a t low Re it is likely that the turbulence models time - averaged , the flowfield c ould average out to a c will not become activated over much of the airfoil bubble structure . Since the flow s tructure is similar to surface, and the higher the Mach number, the larger laminar cases , it is important to note that this w ould the laminar region is likely to be .” constitute a completely laminar bubble up to and The results at 𝑀 = 0 . 20 indeed show th at in including 𝛼 = 6° ( flow structure D in Figure 5 ).
the linear regime the performance of the airfoils is very similar between laminar, transition, and fully turbulent simulations.
0.20 SA-AFT2017b transition model 0.18 SA turbulence model ‘fully turbulent’ No turbulence model (laminar) 0.16 d Figure 16 . S eparated shear - layer at 𝑟 / 𝑅 = 0 . 76 , 𝛼 = 7 . 00° , 𝑀 = 0.14 c 0 . 50 ( velocity magnitude, time - accurate , transition model ) ient, 0.12 ffi 0.10 0.08 0.06 section drag coe 0.04 0.02 0.00 -1.00 -0.50 0.00 0.50 1.00 1.50 Figure 17 . S eparated shear - layer at 𝑟 / 𝑅 = 0 . 76 , 𝛼 = 7 . 00° , 𝑀 = section lift coe ffi cient, c l 0 . 50 ( vorticity magnitude, time - accurate , transition model ) Figure 13 . 𝑟 / 𝑅 = 0 . 76 , 𝑀 = 0 . 50 , drag polars for laminar, ‘fully turbulent ’ SA turbulence, and SA - AFT2017b transition model T he t ransition model influences the shear - layer roll up that results in a performance decrease at around 𝑐 ≈ " The polar in Figure 13 shows that turbulence model 0 . 06 and 𝑐 ≈ − 0 . 10 whe n compared to the laminar # produces higher efficiency at higher Mach numbers .
cases , in which the shear - layer keeps rolling up . This The sharp drop in lift - to - drag ratio of the turbulence - ‘stall’ process is similar to that observed by Wang transit ion model in Figure 13 around 𝑐 ≈ 0 . 10 and " et al. , as shown in Figure 5 (flow structure D to C) .
𝑐 ≈ 1 . 00 , is due to a simulated flow state change from # At lower angles of attack , the laminar boundary a partially attached laminar BL which separates with layer stays attached over the majority of the chord shear - layer roll up ( Figure 14 and Figure 15 ) to a fully length ( Figure 18 and Figure 19 ), similar to flow separated laminar shear - layer without ‘ reattachment ’ st ructure B in Figure 5 .
( Figure 16 and Figure 17 ) . These correspond roughly to state D and C in Figure 5 , respectively .
Figure 18 . A ttached laminar boundary layer with separation near trailing edge at 𝑟 / 𝑅 = 0 . 76 , 𝛼 = 1 . 00° , 𝑀 = 0 . 50 (v elocity Figure 14 . S hear - layer ro ll - up at 𝑟 / 𝑅 = 0 . 76 , 𝛼 = 6 . 00° , 𝑀 = 0 . 50 magnitude , time - accurate , with transition model ) ( v elocity magnitude, time - accurate , with transition model ) Figure 19 . A ttached laminar boundary layer with separation near Figure 15 . S hear - layer roll - up at 𝑟 / 𝑅 = 0 . 76 , 𝛼 = 6 . 00° , 𝑀 = 0 . 50 trailing edge at 𝑟 / 𝑅 = 0 . 76 , 𝛼 = 1 . 00° , 𝑀 = 0 . 50 ( vorticity ( vorticity magnitude, time - accurate , with transition model ) magnitude , time - acc urate , with transition model ) th Presented at the 44 European Rotorcraft F orum, Delft, t he Netherlands, 18 - 2 1 September, 2018. Page 10 of 14 This paper is a work of the U.S. Government and is not subject to copyright protection in the U.S.
The performance reduction on the negative lift the mutual interaction of the wake from the two coefficient side in Figure 13 shows similar coaxial rotors. The CAMRAD II blade structural characteristics. Figure 20 and Figure 21 show the model is based on nonlinear beam theory of rotating different flow structures before and after the finite elements.
performance decrease, respectively.
7.1. Rotor Performance Correlation to JPL Test Data Figure 22 shows rotor model performance predictions in terms of the FM versus thrust coefficient for JPL SS conditions.
0.70 Figure 20 . 𝑟 / 𝑅 = 0 . 76 , 𝛼 = − 2 . 00° , 𝑀 = 0 . 50 ( vorticity 0.60 magnitude, time - accurate , transition model ) 0.50 design thrust coe ffi cient range FM 0.40 0.30 Figure of Merit, 0.20 JPL 25–ft. diameter Space Simulator measurements Figure 21 . 𝑟 / 𝑅 = 0 . 76 , 𝛼 = − 3 . 00° , 𝑀 = 0 . 50 ( vorticity 0.10 Mars Helicopter (CAMRADII, ‘fully turbulent’) magnitude, time - accurate , transition model ) Mars Helicopter (CAMRADII, transition model) 0.00 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 thrust coe ffi cient, C T 7. ROTOR PERFORMANCE Figure 22 . Figure of Merit versus thrust for 𝜌 = 0 . 0175 𝑘𝑔 𝑚 ⁄ and 𝑇 = 20° 𝐶 (JPL SS test c onditions), including JPL 25 - ft.
All simulations are post - proce ssed into C81 airfoil diameter Space Simulator measurements format. In total , 4 rotor models are generated, two for JPL SS conditions, and two for MC 2 conditions, one Both rotor models are generated for JPL SS using the SA turbulence model and the other using conditions and perform similar ly up to around 𝐶 = * the AFT2017b transition model.
0 . 018 . Beyond this point the rotor mo del s with the The coaxial rotor performance was calculated transition model start predicting lower efficiencies using CAMRAD II, a comprehensive analysis tool for over the design thrust coefficient range.
rotorcraft . CAMRAD II has undergone extensive Apart from the outliers , the transition model correlation of performance and loads measurements curve matches the performance predictions well , even on rotorcra ft, includin g coaxial rotors . The after peak FM thrust . Figure 23 shows the same data CAMRAD II aerodynamic model for the rotor blade points , but expressed as power versus thrust curves.
is based on lifting - line theory, using steady two - -3 10.0 dimensional airfoil characteristics and a vortex wake JPL 25–ft. diameter Space Simulator measurements 9.0 model, plus models for unsteady flow (attached flow Mars Helicopter (CAMRADII, ‘fully turbulent’) Mars Helicopter (CAMRADII, transition model) 8.0 and dynamic stall) and yawed/swept flow. Effects of design thrust compressibility (Mach numbers) and viscosity 7.0 P coe ffi cient range C (Reynolds number, stall and drag) enter through 6.0 cient, airfoil table data: lift, drag, moment coefficients of ffi 5.0 two - dimensional sections as function of angle of 4.0 attack and Mach number, for the appropriate chord power coe 3.0 and atmosphere (density, temperature) so as to have 2.0 correct Reynolds number variation with Mach 1.0 number . The vortex wake consists of rolled - up tip 0.0 vortices and inboard vortex sheets, emanating from 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 thrust coe ffi cient, C T each blade. Second - order lifting - line theory gives the Figure 23 . Thrust versus power for 𝜌 = 0 . 0175 𝑘𝑔 𝑚 ⁄ and 𝑇 = vortex - induced loading on the blades well. Free wake 20° 𝐶 (JPL SS t est c onditions), including JPL SS measurements geometry calculations give the self - induced distortio n of the inter - twined, interacting tip vortices, including th Presented at the 44 European Rotorcraft F orum, Delft, t he Netherlands, 18 - 2 1 September, 2018. Page 11 of 14 This paper is a work of the U.S. Government and is not subject to copyright protection in the U.S.
Both performance comparisons show good agreement The reason for the difference in characteristic shape in the design thrust coefficient range of the MH. of the FM curve for the transition model between JPL Modeling of stall is difficult but seems to be SS and MC 2 conditions is no doubt related to reasonably captur ed in the transition model, w h ile the different predictions of stall characteristics, and turbulence model by itself produces an overestimate deserves further investigation.
of the efficiency metric , but a reduction of maximum thrust.
8. CONCLUSIONS 7.2. Rotor Performance Predictions in the Martian For both JPL SS and MC 2 conditions , the rotor Atmosphere model with transition and with a ‘fully turbulent’ model perform similar ly over the design thrust Figure 24 shows the FM versus thrust coefficient for coefficient range. At higher collective settings the rotor models generated for MC 2 conditions.
transitio n model predicts lower efficiencies , attributed 0.70 to the absence of transition in the fully turbulent 0.60 model. This re sult s in earlier separation and reduced performance .
0.50 T he rotor Figure of Merit is shown to be 1.3 % FM design thrust coe ffi cient range – 2.6% higher over the design thrust coeffi cient range 0.40 for M ars Condition 2, compared to experimental measurements . This implies a slight thrust m argin 0.30 Figure of Merit, over JPL measured performance when taking the 0.20 transition - based model as the conservative predictor Mars Helicopter (CAMRADII, ‘fully turbulent’) of estimated performance. Mars Helicopter (CAMRADII, transition model) 0.10 0.000 0.005 0.010 0.015 0.020 0.025 0.030 thrust coe ffi cient, C 8.1. Future Work T Figure 24 . Figure of Merit versus thrust for 𝜌 = 0 . 017 𝑘𝑔 𝑚 ⁄ and The sensit ivity of airfoil performance to freestream 𝑇 = − 50° 𝐶 (Mars Condition 2) turbulen ce intensity needs to be evaluated for this Reynolds number range .
The FM is slightly increased for MC 2 conditions Furthermore, differences between the two - relative to JPL SS conditions in the design thrust dimensional and thr ee - dimensional flow fields need to coefficient range. This is mos t likely a direct effect of be investigated to ensure that no first - or der flow Mach number and Reynolds number difference s due physics are overlooked using a comprehensive to the difference in temperature between the JPL SS analyses approach for performance estimations of the and MC 2 conditions, resulting in a c onservative MH .
estimate obtained from the experiments. Figure 25 shows power versus thrust curves for the two rotor models in MC 2 conditions.
9. ACKNOWLEDGEMENTS -3 8.0 Mars Helicopter (CAMRADII, ‘fully turbulent’) The authors would like to thank Ethan Romander , Mars Helicopter (CAMRADII, transition model) 7.0 Mark Potsdam, Pieter Buning , Natasha Schatzman, and Belen Veras - Alba for their i nsights for the 6.0 P design thrust OVERFLOW simulations and assistance with C coe ffi cient range 5.0 running the cases .
cient, ffi T he research of Håvard F. Grip was carried out 4.0 at the Jet Propulsion Laboratory, California Institute power coe of Technology, under a contract with the National 3.0 Aeronautics and Space Administration.
2.0 E duardo Solis and Patricia Ventura - Diaz are thanked for their assistance in preparing the airfoil 1.0 0.000 0.005 0.010 0.015 0.020 0.025 0.030 geometry and mesh.
thrust coe ffi cient, C T 3 Jason Cornelius, Haley Cummings, Kristen Figure 25 . Thrust versus power for 𝜌 = 0 . 017 𝑘𝑔 𝑚 ⁄ and 𝑇 = Kallstrom, Keiko Nagam i, Ethan Romander, Alan − 50° 𝐶 (Mars Condition 2) th Presented at the 44 European Rotorcraft F orum, Delft, t he Netherlands, 18 - 2 1 September, 2018. Page 12 of 14 This paper is a work of the U.S. Government and is not subject to copyright protection in the U.S.
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th Presented at the 44 European Rotorcraft F orum, Delft, t he Netherlands, 18 - 2 1 September, 2018. Page 14 of 14 This paper is a work of the U.S. Government and is not subject to copyright protection in the U.S.