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NASA NTRS1999

Computer Modeling of Sand Transport on Mars Using a Compart-Mentalized Fluids Algorithm (CFA)

It has been postulated that aeolian transport on Mars may be significantly different from that on Earth. From laboratory experiments simulating martian grain transport [2], it has been observed that (saltating) grains striking the bed can cause hundreds of secondary reptation trajectories when impact occurs at speeds postulated for Mars. Some of the ballistically induced trajectories "die ouf' and effectively join the ranks on the creep population that is merely nudged along by impact. Many of the induced reptation trajectories, however, are sufficiently high for the grains to become part of the saltation load (it is irrelevant to the boundary layer how a grain attained its initial lift force). When these grains, in turn, strike the surface, they too are capable of inducing more reptating grains. This cascading effect has been discussed in connection with terrestrial aeolian transport in an attempt to dispel the notion that sand motion is divisible only into creep and saltation loads. On Earth, only a few grains are splashed by impact. On Mars, it may be hundreds. We developed a computer model to address this phenomenon because there are some important ramifications: First, this ratio may mean that martian aeolian transport is dominated by reptation flux rather than saltation. On Earth, the flux would be a roughly balanced mixture between reptation/creep and saltation. On Venus, there would be no transport other than by saltation. In other words, an understanding of planetary aeolian processes may not be necessarily understood by extrapolating from the "Earth case", with only gravity and atmospheric density/viscosity being considered as variables. Second, the reptation flux on Mars may be self sustaining, so that little input is required by the wind once transport has been initiated. The number of grains saturating the boundary layer near the bed may mean that average grain speed on Mars might conceivably be less than that on Earth. This would say much for models of sand comminution on Mars. A multiple-grain transport model using just the equations of grain motion describing lift and drag is impossible to develop owing to stochastic effects --the very effects we wish to model. Also, unless we were to employ supercomputing techniques and extremely complex computer codes that could deal with millions of grains simultaneously, it would also be difficult to model grain transport if we attempted to consider every grain in motion. No existing computer models were found that satisfactorily used the equations of motion to arrive at transport flux numbers for the different populations of saltation and reptation. Modeling all the grains in a transport system was an intractable problem within our resources, and thus we developed what we believe to be a new modeling approach to simulating grain transport. The CFA deals with grain populations, but considers them to belong to various compartmentalized fluid units in the boundary layer. In this way, the model circumvents the multigrain problem by dealing primarily with the consequences of grain transport --momentum transfer between air and grains, which is the physical essence of a dynamic grain-fluid mixture. We thus chose to model the aeolian transport process as a superposition of fluids. These fluids include the air as well as particle populations of various properties. The prime property distinguishing these fluids is upward and downward grain motion. In a normal saltation trajectory, a grain's downwind velocity increases with time, so a rising grain will have a smaller downwind velocity than a failing grain. Because of this disparity in rising and falling grain proper-ties, it seemed appropriate to track these as two separate grain populations within the same physical space. The air itself can be considered a separate fluid superimposed within and interacting with the various grain-cloud "fluids". Additional informaiton is contained in the original.

Marshall, J.↗
NASA NTRS1999

Aeolian Sand Transport in the Planetary Context: Respective Roles of Aerodynamic and Bed-Dilatancy Thresholds

The traditional view of aeolian sand transport generally estimates flux from the perspective of aerodynamic forces creating the airborne grain population, although it has been recognized that "reptation" causes a significant part of the total airborne flux; reptation involves both ballistic injection of grains into the air stream by the impact of saltating grains as well as the "nudging" of surface grains into a creeping motion. Whilst aerodynamic forces may initiate sand motion, it is proposed here that within a fully-matured grain cloud, flux is actually governed by two thresholds: an aerodynamic threshold, and a bed-dilatancy threshold. It is the latter which controls the reptation population, and its significance increases proportionally with transport energy. Because we only have experience with terrestrial sand transport, extrapolations of aeolian theory to Mars and Venus have adjusted only the aerodynamic factor, taking gravitational forces and atmospheric density as the prime variables in the aerodynamic equations, but neglecting reptation. The basis for our perspective on the importance of reptation and bed dilatancy is a set of experiments that were designed to simulate sand transport across the surface of a martian dune. Using a modified sporting crossbow in which a sand-impelling sabot replaced the bolt-firing mechanism, individual grains of sand were fired at loose sand targets with glancing angles typical of saltation impact; grains were projected at about 80 m/s to simulate velocities commensurate with those predicted for extreme martian aeolian conditions. The sabot impelling method permitted study of individual impacts without the masking effect of bed mobilization encountered in wind-tunnel studies. At these martian impact velocities, grains produced small craters formed by the ejection of several hundred grains from the bed. Unexpectedly, the craters were not elongated, despite glancing impact; the craters were very close to circular in planform. High-speed photography showed them to grow in both diameter and depth after the impactor had ricochetted from the crater site. The delayed response of the bed was "explosive" in nature, and created a miniature ejecta curtain spreading upward and outward for many centimeters for impact of 100-300 micron-diameter grains into similar material. Elastic energy deposited in the bed by the impacting grain creates a subsurface stress regime or "quasi-Boussinesq" compression field. Elastic recovery of the bed occurs by dilatancy; shear stresses suddenly convert the grains from closed to open packing, and grains are consequently able to eject themselves forcefully from the impact site. Random jostling of the grains causes radial homogenization of stress vectors and a resulting circular crater. There is a great temptation to draw parallels with cratering produced by meteorite impacts, but a rigorous search for common modelling ground between the two phenomena has not been conducted at this time. For every impact of an aerodynamically energized grain, there are several hundred grains ejected into the wind for the high-energy transport that might occur on Mars. Many of these grains will themselves become subject to the boundary layer's aerodynamic lift forces (their motion will not immediately die and add to the creep population), and these grains will become indistinguishable from those lifted entirely by aerodynamic forces. As each grain impacts the bed, it will eject even more grains into the flow. A cascading effect will take place, but because it must be finite in its growth, damping will occur as the number of grains set in motion causes mid-air collisions that prevent much of the impact energy from reaching the surface of the bed -thus creating a dynamic equilibrium in a high-density saltation cloud. It is apparent that for a given impact energy, the stress field permits a smaller volume of grains to convert to open packing as the size of the bed grains increases, or as the energy of the "percussive" grain decreases (by decrease in velocity or mass). Thus, the mass of the "repercussive" grain population that is ejected from the impact site becomes a function of the scale of the stress field in relation to the scale of the bed material (self-similarity being applicable if both bed size and energy are simultaneously adjusted). In other words, in a very high energy aeolian system where an aerodynamically raised grain can ballistically raise many more grains, the amount of material lifted into the wind becomes largely a function of a dilatancy threshold. If this threshold is exceeded, grains are repercussively injected into the saltation cloud. The "dilatancy threshold" may be defined in terms of the saltation percussive force required to convert the bed, through elastic response, from a closed to an open packing system. If open packing cannot be created, the grains cannot escape from the impact site, even though the elastic deformation and percussive force may be able to reorganize the grains with respect to one another. As the crossbow experiments showed, for an ever-increasing bed grain size, a point is reached when no material can be moved because the energy of the percussive grain is insufficient to dilate the relatively coarse bed. Although this seems to be stating the obvious -- that too little energy will not cause the bed to splash -- the consequences of exceeding the "splash threshold" by dilatancy are not so obvious for high-energy aeolian transport. It is noted that the force required to elastically dilate the bed has to overcome Coulombic grain attractions such as dipole-dipole coupling, dielectric, monopole, contact-induced dipole attractions, van der Waals forces, molecular monolayer capillary forces, as well as the mechanical interlocking frictional resistance of the grains. On Mars, it is predicted that the dilatancy threshold may be the prime control of grain flux. Additional information is contained in the original.

Marshall, J. R.↗
NASA NTRS1999

The Enigmatic Longevity of Granular Materials on Mars: The Case for Geologically Episodic Dune Formation

Martian sand dunes are concentrated in vast sand seas in the circumpolar belt of the planet's northern hemisphere, but they are also pervasive over the whole planet. Their occurrence is to be expected on a super-arid planetary surface subjected to boundary layer drag from a continually active atmosphere. Whilst their occurrence is to be expected, their survival is enigmatic. But the enigma only arises if the martian system is considered similar to Earth's --where sand is moved highly frequently, more or less on a seasonal basis. Experimentally it is readily demonstrated that active sand will soon wear down to small grains and eventually diminish to below the critical sand size required to sustain dune formation. According to conventional wisdom, sand moves at higher speeds on Mars than on Earth, and if it were to move as frequently as it does on Earth, then the dune-forming sand population should have long since disappeared, given the great longevity of the martian aeolian system (Sagan coined the term "kamikaze" grains to express this disappearance). No supply of sand could keep pace with this depletion, especially in light of the fact that Mars does not have very active weathering, nor significant crustal differentiation. On Earth, plate tectonics, magmatic activity, and general crustal differentiation over geological time have produced great concentrations of quartz crystals in the continental crustal masses. Not only are these quartz grains chemically and mechanically resilient, they are about the right size for being transported by either wind or water. Add to this, the geologically recent contribution of glacial grinding, and it is easy to see why there are dune field on Earth. So what are the martian dunes composed of, and how does the material survive the eons of attrition? In addition to experimental demonstrations of sand comminution in laboratory aeolian simulations, the problem can be approached from first principles. Sagan showed that by simple considerations of material strength versus mechanical work applied to the material, comminution to sub-sand size would be inevitable. Another semi-analytical approach might be taken by considering that the archetypal aeolian sand surface texture is an irregularly pitted ("frosted") surface composed of chipping hollows approximately 10 microns in diameter, 5 microns deep. Their volume = about 250 cubic microns, or about 1/25000 of the volume of a 100 micron diameter dune grain. Because a saltating grain always strikes another grain, then two surfaces are impacted. Thus each grain undergoes two impacts for every one saltation leap, when the impact statistics are considered for a closed dune system (it can be calculated that a grain can never undergo <1 impact, and never >2 per saltation leap). Hence, if we conservatively assume that there is damage to a grain each time it bounces, but with the minimum damage of only 2 microscopic craters per impact, then approximately 12,500 impacts are required to completely eliminate the grain. Of course, it would require only a fraction of this amount to reduce the grain to below sand size. A grain will make only several tens of saltation leaps on the stoss side of a dune before becoming buried on the lee slope. The dune then has to move its full length before the grain is exhumed again for abrasion. Even with this hiatus in transport, it is easy to see that terrestrial dunes need resupplying with sand in order to survive. In recent theoretical work it has been shown that martian aeolian transport may be initiated with high-speed grains, but this converts to a lower energy dynamic transport equilibrium in which a reptation population dominates grain transport (on Earth, at least half of the flux is by reptation and creep). On Mars, therefore, average grain speeds may be lower than those on Earth, or at least comparable. This would permit greater longevity for martian sands, but it would not go far enough to solve the survival problem. It may, however, explain why martian dunes are about the same size as terrestrial dunes. If martian saltation leaps were significantly longer than on Earth (as usually assumed), then a dune's lee slope would have to be correspondingly longer in order to trap the sand; this would scale up the whole dune structure. But with shorter trajectories in a reptation population, larger dunes would be unnecessary. Additional information is contained in the original.

Marshall, J.↗
NASA NTRS2004

Undercut Rocks at the MER Gusev Landing Site

On January 3 2004, the NASA Spirit rover landed on the plains inside the Gusev Crater in the southern hemisphere of Mars, and has made observations of the landing site and nearby region in visual and infrared wavelengths, as well as making in-situ measurements of rocks and soil. A number of rocks at the Gusev site are perched, with a significant undercut above the surface; additional rocks show a feature of being eroded or etched at a height of one to three centimeters immediately above the soil line. Some rocks also show terracing, and others show a two-tone pattern of albedo, with a distinct dividing line between a lighter area near the surface and a darker color above the surface. In a small number of cases, the dividing line is correlated with a visible horizontal groove in the rock, most likely indicating an earlier location of burial of the rock. A number of explanations for this undercutting are possible. Perched rocks can be placed on the surface by deflation of the soil from underneath the rock. The surface etching may be abrasion due to reptation. Reptation, or surface creep, occurs as sand moves without leaving the surface, as small (100-200 micron particles) moved by saltation set larger particles in motion. These large particles are effective at abrading the rocks at the surface level. The structure of "ripple" features at the site is evidence to support reptation at the Gusev site. An alternate explanation is etching at the surface by chemically active grit.

Landis, Geoffrey A.↗
NASA NTRS1999

Unique Aeolian Transport Mechanisms on Mars: Respective Roles of Percussive and Repercussive Grain Populations in the Sediment Load

Experiments show that when sand-size grains impact a sediment surface with energy levels commensurate for Mars, small craters are formed by the ejection of several hundred grains from the bed. The experiments were conducted with a modified crossbow in which a sand-impelling sabot replaced the bolt-firing mechanism. Individual grains of sand could be fired at loose sand targets to observe ballistic effects unhindered by aerodynamic mobilization of the bed. Impact trajectories simulated the saltation process on dune surfaces. Impact craters were not elongated despite glancing (15 deg.) bed impact; the craters were very close to being circular. High-speed photography showed them to grow in both diameter and depth after the impactor had ricochetted from the crater site. The delayed response of the bed was "explosive" in nature, and created a miniature ejecta curtain spreading upward and outward for many centimeters for impact of 100-300 um-diameter grains into similar material. This behavior is explained by deposition of elastic energy in the bed by the "percussive" grain. Impact creates a subsurface stress regime or "quasi-Boussinesq" compression field. Elastic recovery of the bed occurs by dilatancy; shear stresses suddenly convert the grains to open packing and they consequently become forcefully ejected from the site. Random jostling of the grains causes radial homogenization of stress vectors and a resulting circular crater. A stress model based on repercussive bed dilatancy and interparticle adhesive forces (for smaller grains) predicts, to first order, the observed crater volumes for various impact conditions. On earth, only a few grains are mobilized by a percussive saltating grain; some grains are "knudged" along the ground, and some are partly expelled on short trajectories. These motions constitute reptation transport. On Mars, saltation and reptation become indistinct: secondary or "repercussive" trajectories have sufficient vertical impulse to create a dense saltation population of many tens or hundreds of grains for each single high-speed saltation percussion of the bed. Impact cascading will lead to near-surface distortion of the boundary layer, and choked flow formed by a dense "slurry" of sand, with the majority of grains mobilized by repercussive forces rather than by aerodynamic lift. This proceeds until a fully-matured transport layer imposes self-limitations as grain-population density constrains the free-path motion of individial grains.

Marshall, John R.↗
NASA NTRS1999

Behavior of Windblown Sand on Mars: Results from Single-Particle Experiments

Experiments are investigating the behavior of individual sand grains in the high-energy martian aeolian regime. Energy partitioning during impact of a saltating grain determines grain longevity, but it also influences the way in which the bed becomes mobilized by reptation. When single grains of sand are fired into loose beds, the bed can absorb up to 90% of the impact energy by momentum transfer to other grains; it has been discovered that the impacting grains cause circular craters even at low impact angles. Hundreds of grains can be splashed by a single high-velocity (100 m/s) impact causing more bed disturbance through reptation than previously thought. The research is supported by NASA's PG&G Program. Because the martian aeolian environment in both high energy and of long duration, the most mobile fractions of windblown sand should have eradicated themselves by attrition, unless sand supply has kept pace with destruction. It is therefore important to understand the rate of grain attrition in order to make sense of the existence of vast dune fields on Mars. Attrition, has been addressed in other studies, but precise data for a single saltating grain striking a loose bed of sand have not been acquired -- the quintessential case to be understood for dunes on Mars. To acquire these data, we are employing a compound crossbow which has the bolt-firing mechanism replaced with a pneumatically-automated sabot system. The sabot can launch individual grains of sand of any size between several millimeters and about 50 microns, at velocities up to 100m/s. This is around the maximum velocity expected for saltating grains on Mars. The sabot sled is equipped with photoelectric sensors for measuring shot velocity. Baffling of the grain's exit orifice has enabled projection of single grains without significant aerodynamic effects from the sabot. Grains are fired into loose beds of sand at about 15 degrees from the horizontal (typical saltation trajectory at impact) while being filmed on high-speed video. High-intensity pulse illumination for the grains is triggered by the solenoid-operated bow trigger. A 45 degree mirror over the impact site provides simultaneous horizontal and vertical images of the impact on each video frame. UV fluorescence is enabling grain and grain-fragment recovery. At 100 m/s, grains of all sizes shatter into many fragments when the sand is replaced with a solid target. Kinetic energy of the grains at this velocity exceeds the critical energy for catastrophic failure of minerals. Although probably exceptional as a grain speed, it suggests that conditions on Mars might elevate materials into an attrition regime not encountered on other planets; individual grains blown across rock pavements on Mars will have short lifespans. When experimental grains impact loose (dune) sand, much, if not most of the kinetic energy is converted into momentum of other grains. Using high-speed filming, the energy involved in splashing grains at the impact site can be derived from the size of the crater, the speed of the splashed grains, and the rebound speed of the impactor. The amount of energy partitioned into material failure (as opposed to momentum) is too small a fraction of the total to be calculated under these circumstances. This does not necessarily mean that little damage occurs to the grains (the full extent of the damage has yet to be determined) because only a small fraction of the impact energy is required for inducing brittle fracture. Damage is orders of magnitude less than during impact against solid surfaces.

Marshall, J. R.↗
NASA NTRS1999

Unique Aeolian Transport Mechanisms on Mars: Respective Roles of Percussive and Repercussive Grain Populations in the Sediment Load

Experiments show that when sand-size grains impact a sediment surface with energy levels commensurate for Mars, small craters are formed by the ejection of several hundred grains from the bed. The experiments were conducted with a modified crossbow in which a sand-impelling sabot replaced the bolt-firing mechanism. Individual grains of sand could be fired at loose sand targets to observe ballistic effects unhindered by aerodynamic mobilization of the bed. Impact trajectories simulated the saltation process on dune surfaces. Impact craters were not elongated despite glancing (15 deg.) bed impact; the craters were very close to being circular. High-speed photography showed them to grow in both diameter and depth after the impactor had ricochetted from the crater site. The delayed response of the bed was "explosive" in nature, and created a miniature ejecta curtain spreading upward and outward for many centimeters for impact of 100-300 micron-diameter grains into similar material. This behavior is explained by deposition of elastic energy in the bed by the "percussive" grain. Impact creates a subsurface stress regime or "quasi-Boussinesq" compression field. Elastic recovery of the bed occurs by dilatancy; shear stresses suddenly convert the grains to open packing and they consequently become forcefully ejected from the site. Random jostling of the grains causes radial homogenization of stress vectors and a resulting circular crater. A stress model based on repercussive bed dilatancy and interparticle adhesive forces (for smaller grains) predicts, to first order, the observed crater volumes for various impact conditions. On earth, only a few grains are mobilized by a percussive saltating grain; some grains are "knudged" along the ground, and some are partly expelled on short trajectories. These motions constitute reptation transport. On Mars, saltation and reptation become indistinct: secondary or "repercussive" trajectories have sufficient vertical impulse to create a dense saltation population of many tens or hundreds of grains for each single high-speed saltation percussion of the bed. Impact cascading will lead to near-surface distortion of the boundary layer, and choked flow formed by a dense "slurry" of sand, with the majority of grains mobilized by repercussive forces rather than by aerodynamic lift. This proceeds until a fully-matured transport layer imposes self- limitations as grain-population density constrains the free-path motion of individual grains.

Marshall, John R.↗
NASA NTRS1985

Thermoplastic matrix composite processing model

The effects the processing parameters pressure, temperature, and time have on the quality of continuous graphite fiber reinforced thermoplastic matrix composites were quantitatively accessed by defining the extent to which intimate contact and bond formation has occurred at successive ply interfaces. Two models are presented predicting the extents to which the ply interfaces have achieved intimate contact and cohesive strength. The models are based on experimental observation of compression molded laminates and neat resin conditions, respectively. Identified as the mechanism explaining the phenomenon by which the plies bond to themselves is the theory of autohesion (or self diffusion). Theoretical predictions from the Reptation Theory between autohesive strength and contact time are used to explain the effects of the processing parameters on the observed experimental strengths. The application of a time-temperature relationship for autohesive strength predictions is evaluated. A viscoelastic compression molding model of a tow was developed to explain the phenomenon by which the prepreg ply interfaces develop intimate contact.

Dara, P. H.↗
NASA NTRS2004

Sensitivity Studies for In-Situ Automated Tape Placement of Thermoplastic Composites

This modeling effort seeks to improve the interlaminate bond strength of thermoplastic carbon composites produced by the in-situ automated tape placement (ATP) process. An existing high productivity model is extended to lower values of the Peclet number that correspond to the present operating conditions of the Langley ATP robot. (The Peclet number is the dimensionless ratio of inertial to diffusive heat transfer.) In sensitivity studies, all of the process and material parameters are individually varied. The model yields the corresponding variations in the effective bonding time (EBT) referred to the glass transition temperature. According to reptation theory, the interlaminate bond strength after wetting occurs is proportional to the one-fourth power of EBT. The model also computes the corresponding variations in the thermal input power (TIP) and the mass and volumetric process rates. Process studies show that a 10 percent increase in the consolidation length results in a 20 percent increase in EBT and a 5 percent increase in TIP. A surprising result is that a 10 K decrease in the tooling temperature results in a 25 percent increase in EBT and an 8 percent increase in TIP. Material studies show that a 10 K decrease in glass transition temperature results in an 8 percent increase in EBT and a 8 percent decrease in TIP. A 20 K increase in polymer degradation temperature results in a 23 percent increase in EBT with no change in TIP.

Costen, Robert C.↗