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NASA NTRS2016

Bumper 3 Update for IADC Protection Manual

The Bumper code has been the standard in use by NASA and contractors to perform meteoroid/debris risk assessments since 1990. It has undergone extensive revisions and updates [NASA JSC HITF website; Christiansen et al., 1992, 1997]. NASA Johnson Space Center (JSC) has applied BUMPER to risk assessments for Space Station, Shuttle, Mir, Extravehicular Mobility Units (EMU) space suits, and other spacecraft (e.g., LDEF, Iridium, TDRS, and Hubble Space Telescope). Bumper continues to be updated with changes in the ballistic limit equations describing failure threshold of various spacecraft components, as well as changes in the meteoroid and debris environment models. Significant efforts are expended to validate Bumper and benchmark it to other meteoroid/debris risk assessment codes. Bumper 3 is a refactored version of Bumper II. The structure of the code was extensively modified to improve maintenance, performance and flexibility. The architecture was changed to separate the frequently updated ballistic limit equations from the relatively stable common core functions of the program. These updates allow NASA to produce specific editions of the Bumper 3 that are tailored for specific customer requirements. The core consists of common code necessary to process the Micrometeoroid and Orbital Debris (MMOD) environment models, assess shadowing and calculate MMOD risk. The library of target response subroutines includes a board range of different types of MMOD shield ballistic limit equations as well as equations describing damage to various spacecraft subsystems or hardware (thermal protection materials, windows, radiators, solar arrays, cables, etc.). The core and library of ballistic response subroutines are maintained under configuration control. A change in the core will affect all editions of the code, whereas a change in one or more of the response subroutines will affect all editions of the code that contain the particular response subroutines which are modified. Note that the Bumper II program is no longer maintained or distributed by NASA.

Christiansen, Eric L.↗
NASA NTRSDate not supplied

Thermal Protection System to Enable Ice Giant Aerocapture Mission for Delivering Both an Orbiter and an In Situ Probe

The Ice Giants have been identified as high priority science destinations in the last Decadal Survey [1] and could benefit from aerocapture as the primary method for orbit insertion [2]. A mass-efficient aerocapture system will enable the delivery of an orbiter along with an atmospheric probe (for in situ measurements to anchor global data collected by the orbiter) and possibly a lander at Triton [3]. Aerocapture could be executed either using low L/D rigid aeroshell with lift modulation (LMA) [4] or using deployable aeroshell using drag modulation (DMA) [3]. Nearly two decades ago, a NASA-funded team performed Neptune-Triton aerocapture studies with a mid-L/D lifting configuration [5] for achieving orbit using LMA. This study showed aerocapture challenges. Due to very high peak entry conditions combined with very high heat-load, a suite of TPS materials was required and this suite was deemed problematic from a qualification perspective, due test facility limitations. In the past 20 years, progress made in GN&C for lift-guided entry missions such as MSL, Orion EFT1, Mars 2020 and the upcoming Artemis missions, and the expertise in blunt body aerodynamics at large scale (~ 5m) has led the EDL community to conclude that aerocapture is a “go do” engineering activity and most technologies are in hand to propose missions with aerocapture [6] [7]. Aerocapture using DMA, currently in development, is an option for Ice Giant Missions. While DMA is simpler in some sense, due to ballistic entry and no need for lift-guided maneuvering, it has challenges and it’s maturity is lower. LMA and DMA both require one or more ablative Thermal Protection System (TPS) materials for the rigid aeroshell element. The ablative TPS needs to be robust and mass efficient due to the high heat loads and size of the rigid aeroshell. Currently, there are capable ablative thermal protection materials, e.g., Heatshield for Extreme Entry Environments Technology (HEEET), 3-D woven Mid-Density Carbon- Phenolic (3MDCP), and PICA (Phenolic-Impregnated Carbon Ablator) that are mature, i.e., at TRL 6 or higher. NASA also invested in Conformal PICA that was matured to TRL 5. Our goal is to evaluate the applicability of high TRL TPS and consider other design options. We first establish bounding aerocapture trajectories for a wide range of arrival conditions and the associated aerothermal environment. Based on the environments, we then determine the predicted TPS mass for the aeroshell [4]. In this presentation, we will outline the process by which we establish bounding aerocapture trajectories for hyperbolic excess velocities ranging from 27 km/s to 35 km/s, which are shown to be a range of velocities that can reduce the trip time from ~14 years to 8 years. The above velocity range translates to ~12 km/s to ~24 km/s arrival velocities at the planetary entry interface [2]. The velocity reduction required to achieve orbit ranges between ~2.5 km/s to 9.5 km/s for both Neptune and Triton. Propulsive insertion alone, due to the amount of fuel required to achieve the required velocity reduction, limits the science returned [2]. We establish the bounding aerocapture trajectories for a low L/D (~ 0.4) configuration for three different ballistic coefficients. The ballistic coefficient range is determined from three different aeroshell diameters of 3m, 4m and 5m and with an entry system mass of 2200 kg. With the above range of design parameters, we then determine conservative/bounding estimates of aerothermal environments by using a combination of CFD simulations and stagnation point heating estimates [7]. This engineering approach allows us to first assess the TPS need vs. TPS capability and determine the applicability of existing TPS. Once an applicable suite of TPS is determined, the TPS thickness and mass are computed. We show that the TPS mass fraction can be as low as 5% to as high as 20%, depending on total trip time reduction and other design parameters for a range of TPS. This is a large range for TPS mass fraction. We show PICA and HEEET can indeed enable aerocapture missions, but the missions incur a mass penalty. TPS mass savings, can be further reduced with the use of conformal PICA. Advancing the development of Conformal PICA to make it robust across the entire aerothermal environment (peak heat-flux, pressure and shear) range will result in TPS mass fractions of < 10% for Ice Giant aerocapture missions such as the Neptune-Triton mission. Aerocapture allows for not only shortening the trip time but enables larger mass to be placed in orbit. Furthermore, probes deployed from orbit will benefit in reduced entry environments allowing for a lower risk TPS implementation as compared to mission designs where the probe is released prior to orbit insertion. One of the challenges for the Ice Giant community is to ensure mission designs that maximize science and allow flexibility in the placement of the entry probe. The traditional approach to release the probe ahead of the orbiter may not optimize returned science. In this presentation, we will make the case for mature TPS such as HEEET and PICA. While these materials can enable aerocapture missions, completing the development of conformal PICA and extending Conformal PICA to be more robust, will have significant impact to TPS mass efficiency and significantly enhance science return for future Gas- and Ice-Giant missions.

E Venkatapathy↗
NASA NTRS1980

Analytic theory of orbit contraction and ballistic entry into planetary atmospheres

A space object traveling through an atmosphere is governed by two forces: aerodynamic and gravitational. On this premise, equations of motion are derived to provide a set of universal entry equations applicable to all regimes of atmospheric flight from orbital motion under the dissipate force of drag through the dynamic phase of reentry, and finally to the point of contact with the planetary surface. Rigorous mathematical techniques such as averaging, Poincare's method of small parameters, and Lagrange's expansion, applied to obtain a highly accurate, purely analytic theory for orbit contraction and ballistic entry into planetary atmospheres. The theory has a wide range of applications to modern problems including orbit decay of artificial satellites, atmospheric capture of planetary probes, atmospheric grazing, and ballistic reentry of manned and unmanned space vehicles.

Longuski, J. M.↗
NASA NTRS2014

A One-Dimensional Global-Scaling Erosive Burning Model Informed by Blowing Wall Turbulence

This paper makes no attempt to comprehensively review erosive burning models or the data collected in pursuit of them; the interested reader could begin with Landsbaum for a historical summary. However, a discussion and comparison to recent work by McDonald and Rettenmaier and Heister will be included, along with data generated by Strand, et. al. Suffice it to say that the search for a way to predict erosive burning in any size motor with formulas cleanly applicable to a typical 1D ballistics analysis has been long thwarted. Some models were based on testing that failed to adequately simulate the solid rocket motor environment. In most cases, no real‐time burn rate measurement was available. Two popular models, even when calibrated to recent motor‐like real‐time burn rate data obtained by Furfaro, were shown by McMillin to be inadequate at modeling erosive burning in the Space Shuttle Reusable Solid Rocket Motor (RSRM), the Space Launch Systems' Five‐Segment RSRM (RSRMV), and the five‐segment Engineering Test Motor (ETM)‐3. Subsequently to the data cited from Strand and Furfaro, additional motors of the same kind as Furfaro's were tested with RSRMV propellant, utilizing 7 segments per motor and 3 throat sizes. By measuring propellant web thickness with ultrasonic gages, the burn rate was determined at cross‐flow Mach numbers up to Mach 0.8. Furthermore, because of the different throat sizes in otherwise identical motors, this provides a unique look at the effect of pressure and base burn rate on the erosive response. Figure 1 shows example of the data pertaining to the high Mach motor, where the port area is initially less than the throat area. The burn rate data was processed using a smoothing method developed to reduce the noise without too severely introducing end effects that limit the range of useful data. Then, an empirical ballistics scheme was used to estimate the flow condition based on the burn rate measurements and pressure measured between each segment.

Kibbey, Timothy P.↗
NASA NTRS1994

Comment on 'Guidance for an Aerocapture Maneuver

It is stated that the aerodynamic forces on the vehicle being aerocaptured are controlled by "altering the angle of attack" and thereby controlling the lift coefficient. Furthermore, the resulting variation of drag coefficient with angle of attack was ignored. The purpose of this Comment is to point out that an aerodynamic control method that is much more effective than the pitch modulation has been studied and utilized during entries for many years. During aerocapture, it is desirable to have a large range of lift coefficients available, while keeping the vehicle's ballistic coefficients constant. This is accomplished by modulating the vehicle's bank angle, i.e., by rolling the vehicle about its velocity vector. By this method, the angle of attack can be held constant (at the trim angle, if desired), and the C(sub D) and the ballistic coefficient remain constant. Furthermore, the vertical component of the normal force vector (essentially the lift) can be varied over its entire range, from maximum positive to maximum negative values. Reaction controls, rather than aerodynamic ones, are usually utilized to change the bank angle of the vehicle, thus requiring the use of fuel. However, the fuel expenditure that is required to change the bank angle is far less than the amount that would have to be used to continuously hold the vehicle at pitch angles that differ significantly from its trim angle of attack. Also, it has been shown that bank angle modulation to vary the lift can enlarge the entry corridor by increasing the entry angle for the undershoot boundary, where both the heating rate and deceleration reach a maximum. Finally, the crew's deceleration tolerance can be increased somewhat when the bank angle is varied, as opposed to the pitch angle. For bank modulation, the deceleration force vector can be kept at a constant angle with respect to the occupants whose tolerance to g loads is highest when the force is applied in a direction normal to the upper torso. The advantages of bank angle variation to modulate the lift vector were recognized long ago, and this method of control was used successfully on the Apollo command module during lunar return' and, more recently, for the Space Shuttle Orbiter.

Tauber, Michael E.↗
NASA NTRS1991

Comparison of impact results for several polymeric composites over a wide range of low impact velocities

Static indentation, falling weight, and ballistic impact tests were conducted in clamped plates made of AS4/3501-6 and IM7/8551-7 prepreg tape. The transversely isotropic plates were nominally 7-mm thick. Pendulum and ballistic tests were also conducted on simply supported plates braided with Celion 12000 fibers and 3501-6 epoxy. The 20 degree braided plates were about 5-mm thick. The impactors had spherical or hemispherical shapes with a 12.7 mm diameter. Residual compression strength and damage size were measured. For a given kinetic energy, damage size was least for IM7/8551-7 and greatest for the braided material. Strengths varied inversely with damage size. For a given damage size, strength loss as a fraction of original strength was least for the braided material and greatest for AS4/3501-6 and IM7/8551-7. Strength loss for IM7/8551-7 and AS4/3501-6 was nearly equal. No significant differences were noticed between damage sizes and residual compression strengths for the static indentation, falling weight, and ballistic tests of AS4/3501-6 and IM7/8551-7. For the braided material, sizes of damage were significantly less and compression strengths were significantly more for the falling weight tests than for the ballistic tests.

Poe, C. C., Jr.↗
NASA NTRS2014

A One-Dimensional Global-Scaling Erosive Burning Model Informed by Blowing Wall Turbulence

A derivation of turbulent flow parameters, combined with data from erosive burning test motors and blowing wall tests results in erosive burning model candidates useful in one-dimensional internal ballistics analysis capable of scaling across wide ranges of motor size. The real-time burn rate data comes from three test campaigns of subscale segmented solid rocket motors tested at two facilities. The flow theory admits the important effect of the blowing wall on the turbulent friction coefficient by using blowing wall data to determine the blowing wall friction coefficient. The erosive burning behavior of full-scale motors is now predicted more closely than with other recent models.

Kibbey, Timothy P.↗
NASA NTRS1954

Analysis of Rocket, Ram-Jet, and Turbojet Engines for Supersonic Propulsion of Long-Range Missles. II - Rocket Missile Performance

The theoretical performance of a two-stage ballistic rocket mis having a centerbody and two parallel boosters was investigated for J oxygen and ammonia-fluorine propellants. Both power-plant and missi parameters were optimized to give minimum cost on-the basis of the analysis for a range of 5500 nautical miles. After optimum values were found, each parameter was varied independently to determine its effect on performance of the missile. The missile using the ammonia-fluorine propellant weighs about one half as much as a missile using JP4-oxygen. Based on an expected unit cost of fluorine in quantity production, the ammonia-fluorine missile has a substantially lower relative cost than a JP4-oxygen missile. Optimum chamber pressures for both propellant systems and for both the centerbody and boosters were between 450 and 600 pounds per square inch. High design altitudes for the exhaust nozzle are desirable for both the centerbody and boosters. For the centerbody, the design altitude should be between 45,000 and 60,000 feet, with the value for ammonia-fluorine lower than that for JP4-oxygen. For the boosters, the design altitude should be 20,000 to 30,000 feet, with the value for the ammonia-fluorine. missile higher.

Huff, Vearl N.↗
NASA NTRS1987

Variation in ejecta size with ejection velocity

The sizes and ranges of over 25,000 secondary craters around twelve large primaries on three different planets were measured and used to infer the size-velocity distribution of that portion of the primary crater ejecta that produced the secondaries. The ballistic equation for spherical bodies was used to convert the ranges to velocities, and the velocities and crater sizes were used in the appropriate Schmidt-Holsapple scaling relation of estimate ejecta sizes, and the velocity exponent was determined. The latter are generally between -1 and -13, with an average value of about -1.9. Problems with data collection made it impossible to determine a simple, unique relation between size and velocity.

Vickery, Ann M.↗
DOE OSTI2025

Along-Trajectory Acoustic Signal Variations Observed During the Hypersonic Re-Entry of the OSIRIS-REx Sample Return Capsule

The re-entry of the Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer (OSIRIS-REx) sample return capsule (SRC) on 24 September 2023 presented a rare opportunity to study atmospheric entry dynamics through a dense network of ground-based infrasound sensors. As the first interplanetary capsule to re-enter over the United States since Stardust in 2006, this event allowed for unprecedented observations of infrasound signals generated during hypersonic descent. We deployed 39 single-sensor stations across Nevada and Utah, strategically distributed to capture signals from distinct trajectory points. Infrasound data were analyzed to examine how signal amplitude and period vary with altitude and propagation path for a nonablating hypersonic object with well-defined physical and aerodynamic properties. Raytracing simulations incorporated atmospheric specifications from the ground-2-space model to estimate source altitudes for observed signals. Results confirmed ballistic arrivals at all stations, with source altitudes ranging from 44 to 62 km along the trajectory. Signal period and amplitude exhibited strong dependence on source altitude, with higher altitudes corresponding to lower amplitudes, longer periods, and reduced high-frequency content. Regression analysis demonstrated strong correlations between signal characteristics and both altitude and propagation geometry. Our results suggest, when attenuation is considered, the amplitude is primarily determined by the source, with the propagation path playing a secondary role over the distances examined. These findings emphasize the utility of controlled SRC re-entries for advancing our understanding of natural meteoroid dynamics, refining atmospheric entry models, and improving methodologies for planetary defense. The OSIRIS-REx SRC campaign represents the most comprehensive infrasound study of a hypersonic re-entry to date, showcasing the potential of coordinated geophysical observational networks for high-energy atmospheric phenomena, including space debris re-entries.

58 GEOSCIENCES↗
NASA NTRS2015

Mars Double-Flyby Free Returns

A subset of Earth-originating Mars double-flyby ballistic trajectories is documented. The subset consists of those trajectories that, after the first Mars flyby, perform a half-revolution transfer with Mars before returning to Earth. This class of free returns is useful for both human and robotic Mars missions because of its low geocentric energy at departure and arrival, and because of its extended stay time in the vicinity of Mars. Ballistic opportunities are documented over Earth departure dates ranging from 2015 through 2100. The mission is viable over three or four consecutive Mars synodic periods and unavailable for the next four, with the pattern repeating approximately every 15 years. Over the remainder of the century, a minimum Earth departure hyperbolic excess speed of 3.16 km/s, a minimum Earth atmospheric entry speed of 11.47 km/s, and a minimum flight time of 904 days are observed. The algorithm used to construct these trajectories is presented along with several examples.

Jesick, Mark↗
NASA NTRS2000

Earth Return Aerocapture for the TransHab/Ellipsled Vehicle

The current architecture being considered by NASA for a human Mars mission involves the use of an aerocapture procedure at Mars arrival and possibly upon Earth return. This technique would be used to decelerate the vehicles and insert them into their desired target orbits, thereby eliminating the need for propulsive orbital insertions. The crew may make the interplanetary journey in a large, inflatable habitat known as the TransHab. It has been proposed that upon Earth return, this habitat be captured into orbit for use on subsequent missions. In this case, the TransHab would be complimented with an aeroshell, which would protect it from heating during the atmospheric entry and provide the vehicle with aerodynamic lift. The aeroshell has been dubbed the "Ellipsled" because of its characteristic shape. This paper reports the results of a preliminary study of the aerocapture of the TransHab/Ellipsled vehicle upon Earth return. Undershoot and overshoot boundaries have been determined for a range of entry velocities, and the effects of variations in the atmospheric density profile, the vehicle deceleration limit, the maximum vehicle roll rate, the target orbit, and the vehicle ballistic coefficient have been examined. A simple, 180 degree roll maneuver was implemented in the undershoot trajectories to target the desired 407 km circular Earth orbit. A three-roll sequence was developed to target not only a specific orbital energy, but also a particular inclination, thereby decreasing propulsive inclination changes and post-aerocapture delta-V requirements. Results show that the TransHab/Ellipsled vehicle has a nominal corridor width of at least 0.7 degrees for entry speeds up to 14.0 km/s. Most trajectories were simulated using continuum flow aerodynamics, but the impact of high-altitude viscous effects was evaluated and found to be minimal. In addition, entry corridor comparisons have been made between the TransHab/Ellipsled and a modified Apollo capsule which is also being considered as the crew return vehicle; because of its slightly higher lift-to-drag ratio, the TransHab has a modest advantage with regard to corridor width. Stagnation-point heating rates and integrated heat loads were determined for a range of vehicle ballistic coefficients and entry velocities.

Muth, W. D.↗
NASA NTRS1991

Single wall penetration equations

Five single plate penetration equations are compared for accuracy and effectiveness. These five equations are two well-known equations (Fish-Summers and Schmidt-Holsapple), two equations developed by the Apollo project (Rockwell and Johnson Space Center (JSC), and one recently revised from JSC (Cour-Palais). They were derived from test results, with velocities ranging up to 8 km/s. Microsoft Excel software was used to construct a spreadsheet to calculate the diameters and masses of projectiles for various velocities, varying the material properties of both projectile and target for the five single plate penetration equations. The results were plotted on diameter versus velocity graphs for ballistic and spallation limits using Cricket Graph software, for velocities ranging from 2 to 15 km/s defined for the orbital debris. First, these equations were compared to each other, then each equation was compared with various aluminum projectile densities. Finally, these equations were compared with test results performed at JSC for the Marshall Space Flight Center. These equations predict a wide variety of projectile diameters at a given velocity. Thus, it is very difficult to choose the 'right' prediction equation. The thickness of a single plate could have a large variation by choosing a different penetration equation. Even though all five equations are empirically developed with various materials, especially for aluminum alloys, one cannot be confident in the shield design with the predictions obtained by the penetration equations without verifying by tests.

Hayashida, K. B.↗
NASA NTRS1958

A Comparative Analysis of the Performance of Long-Range Hypervelocity Vehicles

Long-range hypervelocity vehicles are studied in terms of their motion in powered flight. Powered flight is analyzed for an idealized propulsion system which approximates rocket motors. Unpowered flight is characterized by a return to earth along a ballistic, skip, or glide trajectory. Only those trajectories are treated which yield the maximum range for a given velocity at the end of powered flight. Aerodynamic heating is treated in a manner similar to that employed previously by the senior authors in studying ballistic missiles (NACA rep. 1381), with the exception that radiant as well as convective heat transfer is considered in connection with glide and skip vehicles. As a final performance consideration, it is shown that on the basis of equal ratios of mass at take-off to mass at the end of powered flight, the hypervelocity vehicle compares favorably with the supersonic airplane for ranges in the neighborhood of and greater than one half the circumference of the earth. In the light of this and previous findings, it is concluded that the ballistic and glide vehicles have, in addition to the advantages usually ascribed to great speed, the attractive possibility of providing relatively efficient long-range flight.

Eggers, Alfred J , Jr↗
NASA NTRS2006

Trajectory and Aeroheating Environment Development and Sensitivity Analysis for Capsule-shaped Vehicles

Recently, NASA's Exploration Systems Research and Technology Project funded several tasks that endeavored to develop and evaluate various thermal protection systems and high temperature material concepts for potential use on the crew exploration vehicle. In support of these tasks, NASA Langley's Vehicle Analysis Branch generated trajectory information and associated aeroheating environments for more than 60 unique entry cases. Using the Apollo Command Module as the baseline entry system because of its relevance to the favored crew exploration vehicle design, trajectories for a range of lunar and Mars return, direct and aerocapture Earth-entry scenarios were developed. For direct entry, a matrix of cases was created that reflects reasonably expected minimum and maximum values of vehicle ballistic coefficient, inertial velocity at entry interface, and inertial flight path angle at entry interface. For aerocapture, trajectories were generated for a range of values of initial velocity and ballistic coefficient that, when combined with proper initial flight path angles, resulted in achieving a low Earth orbit either by employing a full lift vector up or full lift vector down attitude. For each trajectory generated, aeroheating environments were generated which were intended to bound the thermal protection system requirements for likely crew exploration vehicle concepts. The trades examined clearly pointed to a range of missions / concepts that will require ablative systems as well as a range for which reusable systems may be feasible. In addition, the results clearly indicated those entry conditions and modes suitable for manned flight, considering vehicle deceleration levels experienced during entry. This paper presents an overview of the analysis performed, including the assumptions, methods, and general approach used, as well as a summary of the trajectory and aerothermal environment information that was generated.

Robinson, Jeffrey S.↗
NASA NTRS1987

On the simulation of ballistic shock loads

Blast or penetrator-impact induced shocks are characterized by high acceleration levels, particularily in the higher frequency range and for a short time duration. These shocks are dangerous for the equipment of ships, combat vehicles, airplanes or spacecraft structures. As ballistic shock loads are insufficiently simulated by laboratory test machines, researchers designed a ballistic shock simulator. The impact induced shocks are simulated by an explosive and the vehicle to be bombarded is replaced by a simplified structure. This structure is suitable to accommodate any equipment which can be tested up to their load limits.

Hollburg, Uwe↗
NASA NTRS1992

A comparative study between experimental results and numerical predictions of multi-wall structural response to hypervelocity impact

Over the last three decades, multiwall structures have been analyzed extensively, primarily through experiment, as a means of increasing the protection afforded to spacecraft structure. However, as structural configurations become more varied, the number of tests required to characterize their response increases dramatically. As an alternative, numerical modeling of high-speed impact phenomena is often being used to predict the response of a variety of structural systems under impact loading conditions. This paper presents the results of a preliminary numerical/experimental investigation of the hypervelocity impact response of multiwall structures. The results of experimental high-speed impact tests are compared against the predictions of the HULL hydrodynamic computer code. It is shown that the hypervelocity impact response characteristics of a specific system cannot be accurately predicted from a limited number of HULL code impact simulations. However, if a wide range of impact loadings conditions are considered, then the ballistic limit curve of the system based on the entire series of numerical simulations can be used as a relatively accurate indication of actual system response.

Schonberg, William P.↗
NASA NTRS2005

Length dependence of carbon nanotube thermal conductivity and the "problem of long waves"

We present the first calculations of finite length carbon nanotube thermal conductivity that extend from the ballistic to the diffusive regime, throughout a very wide range of lengths and temperatures. The long standing problem of vanishing scattering of the "long wavelength phonf dramatically here, making the thermal conductivity diverge as the nanotube length increases. We show that the divergence disappears if 3-phonon scattering processes are considered to second or higher order. Nevertheless, for defect free nanotubes, the thermal conductivity keeps increasing up to very large lengths (10 gm at 300 K). Defects in the nanotube are also able to remove the long wavelength divergence.

Evaluation Studies↗