Energy Deposition Rate Research Articles

Meteoroid Bombardment of Lunar Poles

Abstract While the floors of deep lunar craters are largely shielded from solar radiation and thus provide an ideal thermal environment for water-ice accumulation, meteoroids on highly inclined orbits can easily access permanently shadowed regions and alter the surface properties via hypervelocity impacts. Here we consider the detailed topography of the lunar poles and a dynamical model of meteoroids to quantify the meteoroid mass fluxes, energy deposition, and impact ejecta mass production rates. Our analysis of regions within 5° from the two lunar poles shows that the variations of the meteoroid mass flux, energy flux, and ejecta production rate are within 50% of their median values. We find that the lunar poles are easily accessible by meteoroid impacts, including the permanently shadowed regions. We find a positive correlation between the surface slope and the meteoroid ejecta production rate, a finding that suggests that a higher impact gardening rate on steep crater walls can facilitate mass wasting.

Concurrent Observations Of Magnetic Reconnection From Cluster, IMAGE and SuperDARN: A Comparison Of Reconnection Rates And Energy Conversion

AbstractAuroral emissions reflect energy dissipation in the atmosphere, while the energy mostly originates from the magnetospheric dynamics of the planet. In the Earth's magnetosphere, the interaction between the solar wind and the terrestrial magnetic field produces magnetic reconnection ultimately causing the appearance of auroras in the polar regions. In this study, we revisit two reconnection events previously identified using ESA Cluster observations during conditions of moderate geomagnetic activity, in the magnetotail. We compare these in situ detections with simultaneous global auroral images from the NASA‐IMAGE satellite and ionospheric convection measurements from SuperDARN. We show for the first time a direct correspondence between the electric voltage estimated at ionospheric altitude and the reconnection rate at the reconnection site. We compute the total auroral precipitation power and compare it to the energy released from the reconnection site. We deduce that the precipitated electron power of the aurora and the electron energy deposition rate from the reconnection site are of the same order of magnitude, which means that the thermal energy released by reconnection is primarily transferred to the ionosphere and contributes to the auroral activity.

A Novel Method for Predicting Power Transient CHF via the Heterogeneous Spontaneous Nucleation Trigger Mechanism

Using the Laplace transform for solving a two-region (cladding/liquid) conduction problem with an exponentially increasing heat flux boundary condition, an analytic temperature profile has been found. The rate of the temperature increase in the second region (liquid) is used to determine energy deposition in the thermal boundary layer of the liquid. Energy deposition rates are then compared to the latent heat capacity of the growing thermal boundary layer to create a condition for predicting transient critical heat flux (CHF) via the heterogeneous spontaneous nucleation (HSN) trigger mechanism. These analytic predictions are then compared to existing data for exponential power ramp transients with periods ranging from 5 ms up to 10 s. Comparison with experimental data show that the trends of the expected HSN-triggered CHF are in good agreement with the magnitude being controlled by the determination of the maximum boundary layer energy. This work presents the first known attempts to derive a mechanistic CHF prediction model for HSN. Though further work is necessary to develop the HSN model (and is being pursued in parallel to this research), this work will allow for a quantitative prediction of HSN-triggered CHF. Further developments of the HSN model will inform the boundary layer energy threshold that triggers CHF.

Effects of circuit inductance on electrical and shock wave characteristics at underwater wire explosion

Circuit inductance is an important parameter at underwater electrical wire explosion (UEWE) experiments as it closely relates to the energy deposition rate to the load wire. In this study, the circuit inductance was varied within a wide range from 1.55 μH to 93.2 μH by inserting inductive coils to study its effects on electrical and shock wave (SW) characteristics at UEWE. Experimental results showed that UEWEs using thinner wires were less affected by the increase of circuit inductance and the SW peak pressure several-cm away from the wire is not sensitive to the increase of circuit inductance if properly choosing the diameter of load wire: the maximum SW peak pressure obtained with varied diameter (constant energy storage and wire length) only saw a decrease of 30% as the circuit inductance increased by 60 times from 1.55 μH (0.3 mm diameter, 19 MPa) to 93.2 μH (0.2 mm diameter, 13 MPa). Hydrodynamic calculations were used to explain the experimental results. These results indicated that for a practical UEWE system, the energy storage can be far away from the load while keeping an acceptable loss of the capability of generating strong SWs, which greatly improves the flexibility of system designing for example by enabling much larger energy storage for certain harsh working environments.

Monte Carlo–Informed Decay Heat Model for Cermet LEU-NTP Systems

Two methodologies for performing decay heat analysis with Monte Carlo simulations were developed and implemented on a representative nuclear thermal propulsion (NTP) system. This paper presents the underlying theory, discusses the methodology, and states the key results. This work investigated the importance of utilizing a time-dependent Q-value for fission in NTP systems due to their short burn time. Two approaches for deriving the Q-value were taken: one based on deconvolving the fission rate from the reactor power to yield the rate of fission energy deposition, and the other based on the convergence of the fission product decay power during a long burn. The fission product decay power method is hypothesized to be the more accurate representation of an NTP system as it captures more of the underlying physics occurring during burnup, such as fission product transmutation. The calculated Q-values were employed to derive decay power profiles that were compared to the current state-of-the-art NTP decay power model. According to these new models, it is shown that the cooling requirements for decay heat removal calculated with the state-of-the-art model differ from the developed methods by as much as 23.3%. There exists a need to experimentally validate, and by extension improve, the proposed methods to better understand the nature of decay heat production in NTP systems.

Data-driven dimensional analysis of heat transfer in irradiated particle-laden turbulent flow

The study of thermal radiation interacting with particle-laden turbulence is of great importance in a wide range of scientific and engineering applications. The fundamental and applied study of such systems is challenging as a result of the large number of thermo-fluid mechanisms governing the underlying physics. This complexity is significantly reduced by transforming the problem of interest into its scale-free form by means of dimensional analysis techniques. However, the theoretical framework of classical dimensional analysis presents the limitations of not providing a unique set of dimensionless groups, and no support for measuring the relative importance between them. In the interest of addressing these shortfalls for multiphysics turbulent flow applications, we present a semi-empirical dimensional analysis approach to efficiently extract important dimensionless groups from data obtained by means of computational (or laboratory) experiments. The methodology presented is then used to characterize important dimensionless groups in irradiated particle-laden turbulence. The study concludes that two dimensionless groups are responsible for most of the variation in the system’s thermal response, with the absorption of radiation by particles, the radiative energy deposition rate and the turbulent flow mixing the most important thermo-fluid mechanisms. The generality of the results obtained can be leveraged to effectively reduce the dimensionality of irradiated particle-laden turbulent flows in research studies and in the design and optimization of similar systems.

Comparison of the Responses of New Reduced-Size Calorimetric Cells Made of Different Structure Materials for High Energy Deposition

This paper concerns experimental and numerical works on a new differential calorimeter called CALORRE and validated recently under irradiation conditions in MARIA reactor at low nuclear absorbed dose rate level. Works focus on a specific configuration of CALORRE which was designed especially for the measurement of high nuclear energy deposition rates inside Material Testing Reactors. Due to the high level, a new calibration system was fabricated in order to determine the response of the new configuration under laboratory conditions for a very wide range of electrical power never applied in the literature. The response of the new configuration can be considered linear for this very wide range of electrical power. An analytical calculation shows the contribution of each heat transfer in specific zones. 3D thermal simulations performed by means of COMSOL Multiphysics under irradiation conditions give the predictions of the calorimeter behavior under real conditions (up to 20W.g−1).

Calibration of a Single-Cell Calorimeter in a New Transient-state Test Bench

The nuclear radiation energy deposition rate is a key value for the thermal design of experiments, on materials and nuclear fuels, carried out in experimental channels of nuclear research reactors. Studies are led for two kinds of sensor currently dedicated to quantifying this value and corresponding to calorimeter. Development of new sensors but also improvement of their calibration and their associated interpretation methods are necessary. These aims are possible by many ways such as numerical simulations of sensor, characterizations under laboratory conditions and experimental campaign under irradiation conditions. The calibration step under non-irradiation conditions represents a crucial phase. This phase requires the development of specific benches. The present paper focuses on a new thermal-transient bench and its use to perform calibration of a polish single-cell calorimeter. The new bench is detailed. First studies of the influence of external conditions (temperature, velocity) on the calorimeter sensitivity are presented and discussed.

Compositionally-tailored steel-based materials manufactured by electron beam melting using blended pre-alloyed powders

The paper presents the prospects of additive manufacturing (AM) in metal, using the powder bed fusion (PBF) method Electron Beam Melting (EBM) in fabrication specific steel-based alloys for different applications. The proposed approach includes manufacturing of metals from blended pre-alloyed powders for achieving in situ alloying and the material microstructure tailoring by controlling electron beam energy deposition rate EBM tests were conducted with the blends of 316L stainless steel and Colferoloys 103 and 139, corrosion- and abrasion-resistant iron based materials commonly used for plasma spray coating. Thorough microstructure analysis of the manufactured sample was carried out using electron microscopy and measurements of microhardness and elastic modulus was carried out using nanoindentation. It is concluded that implementation of blended powder pathway in PBF AM allows to widen the scope of available materials through diminishing the dependence on the availability of pre-alloyed powders. Together with beam energy steering this pathway also allows for an effective sample microstructure control at different dimensional scales, resulting in components with unique properties. Therefore, the implementation of ‘blended powder pathway’ in PBF AM provides a possibility of manufacturing components with the composite-like and homogeneous zones allowing for the microstructure control and effectively adding a “4th dimension” to “3D printing".

Starburst and post-starburst high-redshift protogalaxies

Quenching of star-formation has been identified in many starburst and post-starburst galaxies, indicating burst-like star-formation histories (SFH) in the primordial Universe. Galaxies undergoing violent episodes of star-formation are expected to be rich in high energy cosmic rays (CRs). We have investigated the role of these CRs in such environments, particularly how they could contribute to this burst-like SFH via quenching and feedback. These high energy particles interact with the baryon and radiation fields of their host via hadronic processes to produce secondary leptons. The secondary particles then also interact with ambient radiation fields to generate X-rays through inverse-Compton scattering. In addition, they can thermalise directly with the semi-ionised medium via Coulomb processes. Heating at a rate of ∼10−25 erg cm−3 s−1can be attained by Coulomb processes in a star-forming galaxy with one core-collapse SN event per decade, and this is sufficient to cause quenching of star-formation. At high-redshift, a substantial amount of CR secondary electron energy can be diverted into inverse-Compton X-ray emission. This yields an X-ray luminosity of above 1041 erg s−1by redshiftz = 7 which drives a further heating effect, operating over larger scales. This would be able to halt inflowing cold gas filaments, strangulating subsequent star-formation. We selected a sample of 16 starburst and post-starburst galaxies at 7 ≲ z ≲ 9 and determine the star-formation rates they could have sustained. We applied a model with CR injection, propagation and heating to calculate energy deposition rates in these 16 sources. Our calculations show that CR feedback cannot be neglected as it has the strength to suppress star-formation in these systems. We also show that their currently observed quiescence is consistent with the suffocation of cold inflows, probably by a combination of X-ray and CR heating.

Molecular dynamics simulations on the effect of energy deposition rate on the electrical explosion of metal nanowires

We performed molecular dynamics simulations of the electrical explosion of aluminum nanowires in vacuum, and studied the effect of time rate of energy deposition on the exploding nanowires. The matched regime explosion was employed to eliminate the influence of the plasma corona layer. Our results showed that, under a given energy ratio of 0.45, all the four simulations with different specified energy deposition rates experienced surface evaporation and small cluster ejection processes. Production of large clusters can be observed only during the phase explosion period. When the energy deposition rates were reduced, phase explosions, however, became weak or even absent. If surface evaporation and small cluster ejection dominated the explosion, there would finally leave a residual liquid core.

Transient Reactor Test Facility Advanced Transient Shapes

The Transient Reactor Test (TREAT) facility restarted transient operations in 2018 and has met or exceeded expectations for reactor experiments. TREAT’s flexibility in power shaping provides the ability to prescribe a variety of operating conditions for test specimens, including shaped transients, steady-state irradiations, natural pulses, and clipped pulses, to deliver the necessary energy deposition and energy deposition rate. The initial operations following the TREAT restart were designed to mimic historical operations to confirm TREAT’s capability. Then, studies were performed to evaluate the minimum pulse width possible in the facility as well as reactor power profiles characteristic of a loss-of-coolant accident (LOCA); both were achieved with excellent results.This paper highlights the following:1. The TREAT facility has been restarted to resume nuclear fuel safety research.2. Initial reactor operations have mimicked historical operations.3. A minimum pulse width has been achieved by control rod reinsertion during pulse.4. Power profiles characteristic of a LOCA accident were performed.

MAVEN Case Studies of Plasma Dynamics in Low‐Altitude Crustal Magnetic Field at Mars 1: Dayside Ion Spikes Associated With Radial Crustal Magnetic Fields

AbstractWe report for the first time, simultaneous ion, electron, magnetic field vector and electric field wave measurements made possible by Mars Atmosphere and Volatile EvolutioN, during ion energy flux spikes in low‐altitude radial crustal magnetic fields on the Mars dayside. Observations show energetic electrons and ions (E > 25 eV) precipitating on magnetic field lines assumed as closed. Ions (E < 1.4 keV) display broad velocity distributions toward Mars, showing ions flowing from higher altitude possibly after magnetic reconnection or loss cone filling from pitch angle scattering effects. Precipitating ions (E < 1.4 keV) show nonadiabatic features depending on ion mass and energy and returning ions (E < 1.4 keV) show evidence of conserving the first adiabatic invariant in a mirror field. We observe magnetic field perturbations up to 60 nT, electric field wave amplitudes up to 38 mV/m, and brief periods of peaked electron spectra. At ∼175 km and at times Mars Atmosphere and Volatile EvolutioN is below the mirroring altitude of electrons, we observe mirroring and transverse heating of H+ ions alongside increased electric field wave amplitude fluctuations. It suggests field aligned potential drops result from different mirror altitudes of ions and electrons. Ions E > 1.4 keV (O+) occur as injected accelerated ion beams and ions heated after energization or deceleration. Energy dispersed kilo‐electron‐volt ions suggest a selection effect in radial magnetic fields for lower‐energy Marsward ions, compared to reflection of higher‐energy anti‐Sunward ions. Precipitating kilo‐electron‐volt ions show energy deposition rates of 3.6 ×10−6 W/m2 and sputtering escape rates from precipitating O+ ions of 1.5 ×105/(cm2.s) and 2.1 ×106/(cm2.s) are calculated.

The Near-ultraviolet Continuum Radiation in the Impulsive Phase of HF/GF-type dMe Flares. I. Data

Abstract We present near-UV (NUV) flare spectra from the Hubble Space Telescope (HST)/Cosmic Origins Spectrograph during two moderate-amplitude U-band flares on the dM4e star GJ 1243. These spectra are some of the first accurately flux-calibrated, NUV flare spectra obtained over the impulsive phase in M dwarf flares. We observed these flares with a fleet of nine ground-based telescopes simultaneously, which provided broadband photometry and low-resolution spectra at the Balmer jump. An increase in the broadband continuum occurred with a signal-to-noise ratio >20 in the HST spectra, while numerous Fe ii lines and the Mg ii lines also increased but with smaller flux enhancements than the continuum radiation. These two events produced the most prominent Balmer line radiation and the largest Balmer jumps that have been observed to date in dMe flare spectra. A T = 9000 K blackbody underestimates the NUV continuum flare flux by a factor of two and is a poor approximation to the white light in these types of flare events. Instead, our data suggest that the peak of the specific continuum flux density is constrained to U-band wavelengths near the Balmer series limit. A radiative-hydrodynamic simulation of a very high energy deposition rate averaged over times of impulsive heating and cooling better explains the properties of the λ > 2500 Å flare continuum. These two events sample only one end of the empirical color–color distribution for dMe flares, and more time-resolved flare spectra in the NUV, U band, and optical from 2000 to 4200 Å are needed during more impulsive and/or more energetic flares.

Laser-treated glass platform for rapid wicking-driven transport and particle separation in bio microfluidics.

In this work, we present a laser-based fabrication technique for direct patterning of micro-channels consisting of interconnected micro-cracks on soda-lime glass. Using a CO2 laser to deposit energy at a linear rate of 18.75 to 93.75 mJ mm−1, we were able to manipulate the micro-crack formation, while enabling rapid manufacturing and scalable production of cracked-glass microfluidic patterns on glass. At the higher end of the energy deposition rate (93.75 mJ mm−1), the laser fabricated microfluidic channels (1 mm wide and 20 mm long) had extremely fast wicking speeds (24.2 mm s−1, ×10 faster than filter paper) as a result of significant capillary action and laser-induced surface hydrophilization. At the lower end (18.75 mJ mm−1), 3–4 μm wide micro-cracked crevices resulted in an increased mesh/sieve density, hence, more efficiently filtering particle-laden liquid samples. The reproducibility tests revealed an averaged wicking speed of 10.6 ± 1.5 mm s−1 measured over 21 samples fabricated under similar conditions, similar to that of filter paper (∼85%). The micro-cracked channels exhibited a stable shelf life of at least 82 days with a wicking speed within 10–13 mm s−1.

The Electrothermal Instability on Pulsed Power Ablations of Thin Foils

Presented are results from the optical imaging of atmospheric ablations of thin aluminum foils. These experiments were performed to evaluate the growth of temperature perturbations attributed to the electrothermal instability (ETI). ETI has been shown to seed magnetohydrodynamic instabilities on pulsed power-driven ablations of initially solid metallic targets, a topic of interest to various programs in pulsed power-driven plasma physics that depend on stable liner implosions. Experimental observations presented herein demonstrate exponentially growing temperature perturbations perpendicular to the direction of current with growth rates consistent with the linear ETI theory. High-temperature regions were observed to enter the vapor phase before sufficient energy had been deposited in the bulk foil to overcome the latent heat of vaporization, indicating a significant spatial heterogeneity in energy deposition rates. The growth rates of these perturbations scale as the square of current density, the predicted behavior for long-wavelength ETI structures. The development of these structures was unchanged by physical deformation of the foil surface, but dramatically influenced by incorporating areas of local high resistance in the foil loads. Extending the observation window in time showed a transition from perpendicular to parallel filaments, which is significant because ETI is predicted to switch orientations when the bulk foil material transitions into the plasma state. Collectively, these results provide an experimental validation of many theoretical predictions regarding ETI.

Delayed gamma determination at the JSI TRIGA reactor by synchronous measurements with fission and ionization chambers

Well characterized neutron and gamma fields inside a nuclear reactor are of key importance for its safe operation and for successful utilization of various research reactor irradiation facilities. In case of high-flux research reactors such as BR2 in Belgium, Maria in Poland and the future Jules Horowitz Reactor in France, the gamma energy deposition rate in reactor structural components and irradiated samples reaches values well over 10W/g. To assure safe reactor operation, the gamma field and associated heating must therefore be thoroughly characterized in order to provide adequate component and sample cooling.The gamma field can be divided into two contributions: prompt gamma rays are emitted almost instantly after neutron interaction with nuclei, while the delayed gamma rays are emitted from nuclei, which become radioactive by neutron absorption, generated from fission and other processes. Most modern Monte-Carlo particle transport codes enable the transport of prompt gamma rays; a few support delayed gamma ray generation and transport as well. The latter have mostly been applied to fusion devices, where detailed shutdown dose-rate measurements have been performed. Although the delayed gamma field can also be simulated in fission devices, significant inaccuracy in the result is to be expected due to the computational complexity arising from the large number of radioactive fission products and incompleteness of nuclear data. Furthermore, the unavailability of experimental delayed gamma measurements in fission systems presents an important challenge for the validation of the experimental results.Previous measurements in several research reactors show that the delayed gamma flux amounts to around 30% of the total gamma flux. However, these evaluations were performed with measurement data obtained during rapid reactor shutdowns (SCRAMs), using a single measurement point per SCRAM.In this paper we propose a new technique to accurately determine the magnitude of the delayed gamma component and its time evolution, based on synchronous acquisition of fission and ionization chamber signals. The measurements were performed at the JSI TRIGA reactor, using fission and ionization chambers placed in several in-core measurement positions. Their signal was acquired synchronously and at the highest possible acquisition rate in order to distinguish between measurement noise and reactor transients. Using the novel delayed gamma extraction technique we were able to estimate the magnitude of the delayed gamma contribution to be: 18.9% ± 2.0% at the reactor core periphery, linearly increasing towards the reactor core center to 31.4% ± 2.8% of the total measured gamma flux signal after 10min of reactor operation.

DUAL- FREQUENCY FOCUSED ULTRASOUND- MEDIATED THROMBOLYTIC THERAPY ACCOMPANIED BY TISSUE PLASMINOGEN ACTIVATOR ADMINISTRATION REDUCE THROMBUS CONTENT IN THE ARTERIAL ATHEROTHROMBOTIC STENOSIS

Vascular disease arises through the complications of atherosclerosis, a complex chronic inflammatory condition affecting the arterial circulation. It leads to the development of vascular lesions or atherosclerotic plaques, which manifest as asymmetrical thickenings of the intima of medium to large sized elastic and muscular arteries. A plaque may rupture with high risk of subsequent thrombus mediated acute clinical events such as myocardial infarction and stroke. Focused ultrasound is one of the non- invasive methods to treat abnormal tissues. In pulsed- focused ultrasound with low duty cycle, which is used for thrombolysis, energy deposition rates are low that temperature rises are well below the threshold for thermal damage. The aim of this study was to generate a rabbit model of common carotid artery atherothrombotic stenosis and the subsequent investigating the feasibility of dual- frequency focused ultrasound - mediated thrombolytic therapy accompanied by tissue plasminogen activator (tPA) administration in this model. Briefly, New Zealand white rabbits were submitted to common carotid artery atherothrombotic stenosis by primary balloon injury followed 1.5% cholesterol- rich diet injury for 12 weeks and finally perivascular severe cold injury. Then treatment group underwent dual- frequency focused ultrasound (I= 3w, F= 3MHz, PD= 30 ms and I= 30 W/cm2, F= 150 KHz, PD= 150 ms) - mediated thrombolytic therapy accompanied by tPA (0.6 mg/kg) administration. Results from histopathology, B-mode and color Doppler ultrasonography, showed a significant reduction in the mean value for thrombus content, blood mean velocity and a significant increase in the mean value for blood volume flow at the stenotic region in the treatment group compared with the other groups (P<0.05). Focal thrombus disruption mechanism was partly clarified as originated from microjet formation upon bubble collapse. Enhanced anti- thrombotic effect of tPA, due to microjets- induced by dual- frequency focused ultrasound, can cause to reduce the thrombus content and significantly dilate the luminal cross-sectional area of stenosis and lower treatment time in comparison with conventional tPA thrombolytic therapy.

Interactions between ultra-high-energy particles and protogalactic environments

We investigate the interactions of energetic hadronic particles (cosmic ray protons) with photons and baryons in protogalactic environments, where the target photons are supplied by the first generations of stars to form in the galaxy and the cosmological microwave background, while the target baryons are the interstellar and circumgalactic medium. We show that pair-production and photo-pion processes are the dominant interactions at particle energies above $10^{19}\;\! {\rm eV}$, while ${\rm pp}$-interaction pion-production dominates at the lower energies in line with expectations from, for example $\gamma$-ray observations of star-forming galaxies and dense regions of our own galaxy's interstellar medium. We calculate the path lengths for the interaction channels and determine the corresponding rates of energy deposition. We have found that protogalactic magnetic fields and their evolution can significantly affect the energy transport and energy deposition processes of cosmic rays. Within a Myr after the onset of star-formation the magnetic field in a protogalaxy could attain a strength sufficient to confine all but the highest energy particles within the galaxy. This enhances the cosmic ray driven self-heating of the protogalaxy to a rate of around $10^{-24}\;\! {\rm erg} \;\!{\rm cm}^{-3}\;\! {\rm s}^{-1}$ for a galaxy with strong star-forming activity that yields 1 core collapse SN event per year. This heating power exceeds even that due to radiative emission from the protogalaxy's stellar populations. However, in a short window before the protogalaxy is fully magnetised, energetic particles could stream across the galaxy freely, delivering energy into the circumgalactic and intergalactic medium.

Superposition Method for Force Estimations on Bodies in Supersonic and Hypersonic Flows

Aerodynamic interactions of fragments of meteoroids and space debris during atmospheric entry influence the flight trajectories of the fragments and their strewn field on the Earth’s surface as well as the meteoroids’ airburst altitude and energy deposition rate in the atmosphere and thus the resulting ground damage. For the design of experiments in the Hypersonic Wind Tunnel H2K of DLR, German Aerospace Center in Cologne to investigate the interaction phenomena, a method is developed to estimate the forces on two interacting bodies in supersonic and hypersonic flows, which is more accurate than existing analytical and semi-analytical methods and more efficient than numerical simulations regarding the computational effort. It is based on the superposition of flowfields taken from a database of numerical simulations of a single body for a range of Mach numbers. Furthermore, three-dimensional computations of configurations of interacting bodies are carried out by NASA Ames Research Center. Results obtained with the superposition method are compared to the simulations by NASA and to results of computations that can be found in the literature. The results from the method show good agreement with the computations.