Plume Impingement on a Dusty Lunar Surface

Transcription

1 Plume Impingement on a Dusty Lunar Surfae A. B. Morris, D. B. Goldstein, P. L. Varghese, L. M. Trafton ASE-EM Department, 1 University Station, C0600, Austin, TX 78712, USA Abstrat. A loosely oupled ontinuum-dsmc solver is used to simulate the interation between the exhaust from a roket engine with the lunar surfae. This problem is of partiular interest beause the high veloity dust spray an damage nearby strutures. The flow field is hallenging to simulate beause ontinuum assumptions are no longer valid in the far field, while in the near field DSMC beomes impratial beause of the high ollision rate. In the urrent work the high density ore of the roket plume is modeled with NASA's ontinuum flow solver, DPLR [1]. Sine the two solvers are loosely oupled, i.e. one-way oupling from the DPLR to the DSMC regimes, the interfae between the two solvers is plaed in the supersoni region above the surfae shok. At the lunar surfae, a boundary layer develops and the shear stress auses dust grains to slide and eventually enter the flow field. Robert s theory of dust entrainment [2,3] is used to predit how muh dust is lofted into the flow field by the near surfae flow onditions. In Robert s original theory the interation between entrained dust grains and the gas was negleted and the partiles were assumed to follow ballisti trajetories. In our urrent model, the dust grains are oupled with the DSMC gas model. Both the dust trajetories and the flow fields are omputed for various hovering altitudes and dust grain sizes. Comparisons are made to Robert s original preditions and Apollo photogrammetry [4]. Keywords: Plume Impingement, Hybrid Continuum-DSMC, Partile-Laden Flows PACS: Dt, Hv, Ka, Jd, Kf INTRODUCTION As a lunar lander approahes the surfae, the roket engine exhaust plume strikes the ground ausing dust and larger debris to be dispersed into the flow field. During the Apollo moon landings, the dust erosion posed several operational hazards, inluding obsuration of the pilot s vision and degradation of mehanial omponents, damage to spae suit seals, and logging of thermal rejetion systems. The Apollo 12 astronauts returned samples from the Surveyor III vehile, loated 163m from the lunar module, LM, landing site. Surveyor was found to be overed with dust produed by the LM roket blast and its surfae was found to have small pits due to blast abrasion [5]. Lunar dust is partiularly diffiult to handle beause it onsists of a fine powder that is exeptionally rough at the mirosopi sale. This ours beause the powdery dirt is formed by mirometeorite impats whih pulverize the soil into highly pitted and irregular grain shapes. The result of this ation is a dust that has the ability to ling to nearly any surfae it touhes. Upon return to the LM after moon walks, dust louds and respiratory problems in the rew abin were reported by Apollo astronaut Gene Cernan. The Apollo lunar module was powered by a 10,000 lb thrust desent engine with a speifi impulse of 311 s [6]. Aording to radio all outs during the Apollo 11 landing, lofted dust was first observed at an altitude of 20 m. After landing, the astronauts examined the area underneath the LM and found that the engine soured a shallow rater ~3 m deep [7]. In addition, video photogrammetry of the LM desent tapes indiates that the dust ejetion angle with respet to the surfae was approximately 2 degrees. Suh issues were reognized early in the lunar exploration program and have been investigated over the years. Modeling this proess is broken into three different phases: solving for the roket plume impinging on a solid surfae, prediting how muh dust is onsequently lofted into the flow field, and traking the resulting two phase dust spray. When the roket plume impinges on the lunar surfae, the expanded flow is proessed by a strong surfae shok. Downstream of the surfae shok, there is a stagnation region diretly under the engine bell and the strong favorable pressure gradient turns the flow outward reating a high veloity jet tangential to the surfae. To solve for the flow field, a loosely oupled ontinuum to DSMC flow solver was used. This approah has been implemented suessfully for 2D and 3D ases with surfae raters [8]. In [9], the flow field was simplified by

2 assuming free moleular flow from the roket engine. After solving for the flow field near the surfae an entrainment model was used to predit how muh dust is lofted into the flow field. Roberts developed a model to predit how muh dust and whih size grains would be lofted into the flow field [2]. He treated the roket engine as a point soure of momentum and alulated an erosion rate based on the shear stress on the surfae and ohesive strength of the soil. Roberts also estimated the veloity at whih the dust partiles are ejeted from the surfae based on the partile diameter, thrust level, and altitude. He did not solve for the aerodynami fores on the dust grains and alternatively assumed that the partiles followed ballisti trajetories. Reent improvements have been made to Roberts theory [3], and a number of different erosion mehanisms have been identified in [10, 11]. The dust spray is dominated by the aerodynami fores one dust is entrained into the flow field, and Lagrangian traking has been used to model the two phase flow in [12]. In the urrent work, dust grains are treated as a separate speies in DSMC in muh the same way that any other moleular speies is handled. METHOD In the urrent approah the flow field is first solved using a hybrid ontinuum and DSMC solver. From the resulting ontinuum flow field surfae shear fores are determined and the flux of dust partiles from the surfae is omputed using a slightly modified version of Roberts theory. These dust grains are subsequently injeted into the DSMC flow field and their trajetories and veloities are mapped. Plume Impingement The entire omputational domain is first solved to steady state with the ontinuum flow solver, DPLR. We onsider the senario where the roket engine hovers at a fixed altitude and is direted normal to the surfae, Fig. 1. The omputational domain is bounded by a speified inflow at the nozzle exit plane, a onstant temperature wall at the lunar surfae, a symmetry boundary ondition along the engine enterline, and supersoni exit onditions everywhere else. Although the marosopi properties at the exit plane of a real nozzle are non-uniform and a thin boundary layer exists, onstant properties aross the exit plane are assumed. A onstant lunar surfae temperature of 1000 K is used in the following simulations. The LM desent engine burned Aerozine-50 and nitrogen tetroxide and the exhausting gas mixture ontained many different speies, mainly NH 3, H 2 O, CO ; NO, O 2, CO 2, and NO 2 [6]. For our urrent simulations ammonia is used as the representative speies. V, ρ, T Engine Bell Vauum Axis of Sym. DPLR Region DSMC Region Surfae Shok Vauum Constant Temp. Wall FIGURE 1. Computational domain and boundary onditions. The hybrid interfae is marked by the dashed retangle. The DSMC and ontinuum solvers are oupled using volume reservoir ells [14]. An interfae between the DSMC and ontinuum alulations is drawn in the ylindrial shell from the nozzle exit plane to a height slightly above the surfae shok. At this loation the interfae normal Mah number is supersoni and the flow is largely ontinuum. Moleules are generated in reation ells along this presribed interfae with marosopi properties speified by the DPLR solution. The reation ells are populated at eah time step by DSMC partiles generated from the orresponding Maxwellian distribution funtions. A Maxwellian distribution is used instead of the Chapman-Enskog distribution beause in this region the flow is nearly invisid and the flow gradients are relatively small. One moved, the moleules that have not entered the omputational domain or reside inside of a reation ell

3 are deleted. One inside of the DSMC domain, the moleules are treated as traditional DSMC partiles that undergo translational and rotational energy exhange. Vibrational energy is ignored in the examples presented. Dust Generation and Transport Metzger has identified three possible erosion mehanisms: visous erosion, bearing apaity failure, and diffused gas eruption [10-11]. Visous erosion ours when the surfae shear exeeds the ohesive strength of the soil and small dust partiles begin to roll along the surfae. The rolling dust grains an ollide with neighboring partiles and may then be lofted into the flow field. Bearing apaity failure ours when the pressure exeeds the bearing apaity of the soil and a narrow up is formed. The walls of the narrow up are unstable and ollapse, releasing many dust grains into the flow field while forming a wider rater. The third mehanism is diffused gas eruption; this ours when the gas is driven into porous spaes and onsequently moves a slab of dust instead of a thin dust layer desribed by visous erosion. Due to the high paking density and bearing strength of lunar soil, bearing apaity failure is negleted as a dust generating mehanism. We do not onsider flow through porous media in our simulations and only onsider visous erosion as the dominant dust produing mehanism. This is the same mehanism that Roberts used when developing his theory. The mass flux of dust grains is omputed from eq. 1. The produt au is the fration of the loal gas veloity at the boundary layer edge that a dust partile is ejeted at, dm dt is the partile mass flux per unit area, and τ and τ are the shear stress and shear strength of the soil respetively. 1 dm au = τ τ (1) 2 dt The oeffiient a is obtained from: a = ζ 1 ( 4 + k ) 18µ h 1 1 h Cd F ζ = + 2 (3) σ RT ( 4 ) D D 72e 2RT + kh µ where µ and T are the roket hamber visosity and temperature, h is the altitude of the engine, k h is the hypersoni fator γ(γ 1)M 2 n, σ and D are the dust partile's density and diameter, F is the engine's thrust, and C d is a drag oeffiient (assumed 0.2 by Roberts) on an individual dust grain. The Mah number at the exit plane of the nozzle is M n and the ratio of speifi heats is γ. The shear strength of the soil is defined as τ = + P tanϕ (4) where is the ohesive stress, P is the pressure, and φ is the frition angle. Mehanial properties of the soil are obtained from [13], and in our simulation we assume that the ohesive stress is 100 Pa and the frition angle is 30. One an ompute the surfae shear stress by assuming a laminar or turbulent boundary layer if the surfae roughness is small relative to the boundary layer thikness. Alternatively, if the surfae roughness is not negligible ompared to the boundary layer height, the shear stress an be omputed by using the loal dynami pressure at the upper edge of the boundary layer and an assumed drag oeffiient. Using the dynami pressure to ompute the shear stress is the most onservative assumption and results in loads muh larger than laminar or turbulent shear stress. In our simulations, the loal dynami pressure and an assumed drag oeffiient of 1.0, suggesting roughness sales omparable to the boundary layer thikness, yields an erosion rate that agrees well with the observed Apollo landings. Roberts theory aounts for the aerodynami fores on the dust grains by omputing an initial ejetion veloity, au, assuming an ejetion angle and assuming ballisti trajetories. Sine dust grains in our model are oupled to the flow field and are aelerated by ollisions with the gas, the partiles are injeted with a zero initial veloity. The sensitivity of the solution to the initial partile veloity is disussed later in this report. To ouple the dust grains to the gas, we treat the grains as a hard sphere speies with a large moleular mass and diameter. The ollision ross setion between dust grains and the gas is relatively large and a ollision weighting sheme is implemented to redue the omputational effort. Without ollision weighting eah DSMC gas moleule may have to ollide thousands of times with eah dust grain. Alternatively, the number of ollisions an be redued by a fator N by temporarily saling the mass of the gas moleule by N. By inreasing the mass of the gas moleule, many ollisions with a less massive gas moleule are replaed with fewer ollisions with a heavier gas moleule. In addition, we are urrently assuming a low mass fration of dust grains and do not update the veloities of the gas during a ollision with a dust partile. When dust grains strike the surfae they impat other dust grains and an (2)

4 ause more dust partiles to enter the flow. This proess is alled saltation and is negleted in the urrent work. In our model the dust grains that strike the wall are diffusely refleted. NUMERICAL RESULTS We present results for a 10,000lb thrust engine with an exit plane diameter of 1m at three different altitudes: 5 m, 10 m, and 15 m. The density, temperature, and veloity at the exit plane of the nozzle are kg/m 3, 556 K, and 3008 m/s. The exhausting gas is ammonia and the exit Mah number is 5. Figure 2 shows number density and translational temperature ontours from pure DPLR and the hybrid solver when the roket engine is at an altitude of 5 m. (a) (b) FIGURE 2. (a) Number density for the hybrid ontinuum solution. The left half is pure DPLR and the right half is hybrid. The hybrid interfae is marked by the retangle surrounding the hash-marked region. (b) Translational temperature for the same ase. The hybrid solution and ontinuum solution are similar outside of the boundary layer and the shok stand-off distane agrees well. Although the boundary layer in the DSMC solution is under-resolved, this is not ritial beause the surfae shear stresses are omputed from the DPLR solution and the dust grain trajetories are dominated by the gas flow outside of the boundary layer. At a hovering altitude of 5 m, the impinging flow is largely ontinuum and the interfae in figure 2 is loated where the breakdown parameter is small, O(10 4 ), (see figure 3a). Beneath the surfae shok wave the flow is highly ollisional and onsequently very omputationally expensive. To redue the omputational effort, a ollision limiter that stops ollisions from ourring one the flow is in equilibrium is used. Although it is more omputationally effiient to use DPLR below the shok wave, problems arise due to the one-way oupling beause the normal flow is subsoni. Figures 3b and 3 shows two different hybrid interfaes when the roket engine is at an altitude of 10 m that yield glithes. In figure 3b, the interfae is a ylindrial shell that extends from the ground to the nozzle exit. In figure 3, the interfae is onstruted with two onentri ylindrial shells, one 3 m diameter shell near the surfae and a 1 m diameter shell slightly above the surfae shok wave. Even though the breakdown parameter indiates ontinuum flow at these interfaes, the inability of the DSMC simulation to feed bak into the DPLR simulation results in errors. (a) (b) () FIGURE 3. (a) Bird's breakdown parameter omputed using the DPLR solution. (b) Cylindrial hybrid interfae and flow streamlines. () A hybrid interfae onsisting of two onentri ylinders and the orresponding streamlines.

5 In figure 3b, the DSMC streamlines near the interfae non-physially deflet towards the axis of symmetry beause there is a disontinuity in the shok stand-off distane between the two solvers. DPLR predits a surfae shok that rests slightly loser to the surfae than the DSMC predition. Consequently the DSMC partiles immediately downstream of the shok see a low pressure boundary ondition at the ontinuum interfae and the streamlines are defleted inward. In figure 3, the shok stand-off distane in DPLR is larger than that for DSMC and the streamlines are defleted slightly to the right. The erosion rates were determined from the DPLR solution assuming a 30 miron dust diameter. Partile entrainment first ours at an altitude near 15 m and Apollo observations report dust entrainment at altitudes ranging from 18 m to 30 m. Better agreement is not expeted beause the LM axis was not oriented normal to a single point on the surfae and the loal surfae topography is not modeled. During the Apollo 11 landing, the astronauts observed that the LM desent engine exavated a shallow 3 m rater. An approximate desent trajetory was reonstruted from Buzz Aldrin's radio allouts. We further approximate the desent trajetory by using three different altitudes, 5 m, 10 m, and 15 m, with the LM spending 20 s at eah altitude. The shear stresses, partile mass fluxes, and predited rater depth are shown in figure 4. Shear Stress [Pa] =1.6 =4 5m 10m 15m 0 = x [m] Mass Flux [kg/m 3 -s] =1.75 5m 10m 15m 0.5 =4.40 = x [m] Crater Depth [m] Point Trajetory 20 15m 20 10m 20 5m x[m] (a) (b) () FIGURE 4. (a) Surfae shear stress distribution plotted at three different altitudes. (b) The partile mass flux plotted at three different altitudes. () The predited rater depth based on an assumed three point trajetory. Roberts theory predits maximum surfae shear stresses that are onsistently less than the values predited from DPLR, table 1. The disrepanies are larger at lower altitudes beause Roberts' density profiles assume a point soure of momentum and at low altitudes this assumption is far from valid. Additionally, Roberts theory predits the maximum shear stress on the surfae to be loated at a distane h from the axis of symmetry where h is the altitude of the roket engine. Our simulations indiate the maximum shear stress ours 1.6 m, 4 m, and 6.5 m from the axis of symmetry at altitudes of 5 m, 10 m, and 15 m: roughly h/2. The loation of peak mass flux is further from the axis than peak surfae shear beause at further distanes the pressure and soil shear strength diminish. TABLE 1. Maximum shear stress omputed from Robert's theory and DPLR. Altitude [m] Max. Shear Stress - Roberts [Pa] Max. Shear Stress - DPLR [Pa] (a) () FIGURE 5. (a) 30 miron diameter dust partiles overlaid upon the gas mean free path. (b) Horizontal veloity of gas and dust grains. The dust grains are initially at rest. () Dust grains are initially ejeted with a veloity determined by Roberts' theory.

6 From the omputed mass flux distribution, dust grains are generated at the surfae eah time step with a zero initial veloity, figure 5a. The dust grains have an assumed diameter of 30 mirons, partile density of 3000 kg/m 3, and a roundness of 0.1 [13]. The roundness is the ratio of the mean diameter of the dust grain to the diameter of the sphere that irumsribes the entire partile. Sine the dust grains are not spherial, the volume of the partile is omputed from the mean diameter and the ross setion is omputed from the maximum diameter of the partile. Near the surfae where the dust grains are first generated, the partile diameter is on the same order of magnitude or smaller than the mean free path of the gas. Consequently it is not valid to use Stokes drag approximations and a transitional or free moleular approah is neessary. At a distane 10 m from the axis of symmetry the dust partiles have a mean ejetion veloity of 1700 m/s and the spray is inlined at 2.8. The initial partile veloity does not affet the trajetories beause they are rapidly aelerated by the aerodynami fores, figures 5b and 5. CONCLUSIONS Roket plume impingement flow fields have been solved using a loosely oupled ontinuum DSMC model for roket altitudes of 5 m, 10 m, and 15 m. Qualitatively the ontinuum and hybrid solutions are similar, and good agreement is found in the shok stand-off distane. Visous erosion is assumed to be the dominant mehanism for dust entrainment beause the lunar soil has a high paking density and bearing apaity. Dust erosion rates were estimated by applying Roberts theory of dust entrainment in the ontinuum flow field. It is found that dust erosion for the LM desent engine ours at an approximate altitude of 15 m and based on a 3-point trajetory the exavated rater depth is approximately 2 m deep. These preditions agree with Apollo observations. When the roket engine is 5 m off the surfae, a high-veloity dust spray is inlined at 2.8. The 30 miron diameter dust spray has a mean veloity of 1700 m/s at a distane 10 m and the trajetories are insensitive to initial veloity. ACKNOWLEDGMENTS This work has been supported by NASA LASER grant NNX08AW08G. REFERENCES 1. M. J. Wright, G. V. Candler, and D. Bose, AIAA Journal, Vol. 36, No. 9, pp , Sep L. Roberts, The Interation of a Roket Exhaust With the Lunar Surfae, The Fluid Dynami Aspets of Spae Flight, AGARDograph 87, Vol. II, Gordon & Breah, , P. T. Metzger et al., Modifiation of Roberts Theory for Roket Exhaust Plumes Eroding lunar Soil, presented at the 11 th ASCE Aerospae Division International Conferene on Engineering, Siene, Constrution, and Operation in Challenging Environments, Long Beah, CA, 3-5 Marh C. Immer et al., Apollo Video Photogrammetry Estimation of Plume Impingement Effets, presented at the 11 th ASCE Aerospae Division International Conferene on Engineering, Siene, Constrution, and Operation in Challenging Environments, Long Beah, CA, 3-5 Marh J. R. Gaier, The Effets of Lunar Dust on EVA Systems During the Apollo Missions, NASA/TM , NASA Glenn Researh Center, Cleveland, OH B. R. Simoneit, et. al., "Apollo Lunar Module Engine Exhaust Produts", Siene, 166, No. 3906, pp , C. C. Mason, Comparison of Atual Versus Predited Lunar Surfae Erosion Caused by Apollo 11 Desent Engine, Geologial Soiety of Ameria Bulletin. 81, (1970). 8. F. Lumpkin et al., "Plume Impingement to the Lunar Surfae: A Challenging Problem for DSMC", presented at the Diret Simulation Monte Carlo, Theory, Methods, and Appliations Conferene, Santa Fe, NM, 30 Sept 3 Otober M. Woronowiz, Modeling of Lunar Dust Contamination Due to Plume Impingement, presented at the 6 th International Planetary Probe Workshop, Atlanta, GA, 25 June P. T. Metzger et al., J. Aero. Eng. 22, (2009). 11. P. T. Metzger et al., Craters Formed in Granular Beds by Impinging Jets of Gas in Powders and Grains-2009: Pro. of the 6 th Intern. Conf. on Miromehanis of Gran. Media, edited by M. Nakagawa et al., AIP Conf. Pro. 1145, (2009). 12. J. E. Lane et al., Lagrangian Trajetory Modeling of Lunar Dust Partiles, presented at the 11 th ASCE Aerospae Division International Conferene on Engineering, Siene, Constrution, and Operation in Challenging Environments, Long Beah, CA, 3 Marh G. Heiken, D. Vaniman, and B. M. Frenh, Lunar Sourebook, New York: Cambridge University Press, 1991, pp R. Roveda, D. Goldstein, P. Varghese, in Pro. of the 21st Rarefied Gas Dynamis Conferene, 2, pp , 1998.