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At least 577 records · Page 32

The problem of cooling the cold Io torus

Two models are developed for the transport of ions inward from Io's orbit, the first using the assumption that radial diffusion is the dominant transport mechanism while the second uses a combination of diffusive and convective transport. The models include thermal and number density transport, radiation, ionization and pickup of local neutrals, recombination, charge exchange, and Coulomb interactions. It is found that pure diffusive transport can account for the dramatic inward depletion of the torus only by invoking recombination or by postulating a massive increase in the production rate of torus ions sometime prior to the Voyager mission. Recombination is determined to be far too slow to be the cause of the observed density decrease inside of Io. The model combining convection and diffusion is shown to reasonably match the data, but only if a diffusion coefficient 100 times less than that derived from Pioneer observations is used. In addition, it is shown that the Pioneer derived diffusion rate combined with Voyager temperature and density measurements indicate a large nonradiative sink of energy in the inner torus.

Richardson, J. D.↗

Attenuated direct and scattered wave propagation on simulated land mobile satellite service paths in the presence of trees

Measurements were made of direct path with no trees, attenuated direct, and tree scattered signal levels at 1.3 GHz. Signals were received in two small groves of mixed hardwood trees. In the groves studied, average total signal levels were about 13 dB below adjacent no-trees locations, with attenuated direct signal levels about 14.6 dB below the no-trees case and scattered signals about 17.3 dB below the no-trees case. A simple model for land mobile satellite service (LMSS) propagation in groves of trees is proposed. The model assumes a constant scattered signal contribution at 17 dB below no-trees levels added to an attenuated direct signal which varies, depending on the number and density of trees in the direct path. When total signal levels are strong, the attenuated direct signal dominates. When total signal levels are more than 15 dB below no-trees levels, the scattered signals dominate.

Campbell, Richard L.↗

Observations of molecular and atomic gas in photodissociation regions

Dense gas at the ionized/neutral boundaries of molecular clouds illuminated by far-UV photons plays an important role in the appearance of the neutral interstellar medium. It also is a laboratory for the study of UV-photochemistry and of a number of heating and cooling phenomena not seen elsewhere. Fine structure lines of neutral and low ionization potential species dominate the cooling in the outer part of the photodissociation regions. Observations of these lines show that the regions are dense and highly clumped. Observations of H2 and CO show that heating by UV photons plays a significant role in the excitation of molecular lines near the H II/neutral boundary. Warm CO is more abundant in these regions than predicted by the standard theoretical models. Optical reflection nebulas provide an ideal laboratory for the study of photodissocciation region phenomena.

Jaffe, D. T.↗

ISM stripping from cluster galaxies and inhomogeneities in cooling flows

Analyses of the x ray surface brightness profiles of cluster cooling flows suggest that the mass flow rate decreases towards the center of the cluster. It is often suggested that this decrease results from thermal instabilities, in which denser blobs of gas cool rapidly and drop below x ray emitting temperatures. If the seeds for the thermal instabilities are entropy perturbations, these perturbations must enter the flow already in the nonlinear regime. Otherwise, the blobs would take too long to cool. Here, researchers suggest that such nonlinear perturbations might start as blobs of interstellar gas which are stripped out of cluster galaxies. Assuming that most of the gas produced by stellar mass loss in cluster galaxies is stripped from the galaxies, the total rate of such stripping is roughly M sub Interstellar Matter (ISM) approx. 100 solar mass yr(-1). It is interesting that the typical rates of cooling in cluster cooling flows are M sub cool approx. 100 solar mass yr(-1). Thus, it is possible that a substantial portion of the cooling gas originates as blobs of interstellar gas stripped from galaxies. The magnetic fields within and outside of the low entropy perturbations can help to maintain their identities, both by suppressing thermal conduction and through the dynamical effects of magnetic tension. One significant question concerning this scenario is: Why are cooling flows seen only in a fraction of clusters, although one would expect gas stripping to be very common. It may be that the density perturbations only survive and cool efficiently in clusters with a very high intracluster gas density and with the focusing effect of a central dominant galaxy. Inhomogeneities in the intracluster medium caused by the stripping of interstellar gas from galaxies can have a number of other effects on clusters. For example, these density fluctuations may disrupt the propagation of radio jets through the intracluster gas, and this may be one mechanism for producing Wide-Angle-Tail radio galaxies.

Soker, Noam↗

Discreteness noise versus force errors in N-body simulations

A low accuracy in the force calculation per time step of a few percent for each particle pair is sufficient for collisionless N-body simulations. Higher accuracy is made meaningless by the dominant discreteness noise in the form of two-body relaxation, which can be reduced only by increasing the number of particles. Since an N-body simulation is a Monte Carlo procedure in which each particle-particle force is essentially random, i.e., carries an error of about 1000 percent, the only requirement is a systematic averaging-out of these intrinsic errors. We illustrate these assertions with two specific examples in which individual pairwise forces are deliberately allowed to carry significant errors: tree-codes on supercomputers and algorithms on special-purpose machines with low-precision hardware.

Hernquist, Lars↗

Diffuse X-ray emission from the NGC 2300 group of galaxies - Implications for dark matter and galaxy evolution in small groups

The discovery of diffuse X-ray emission from the NGC 2300 group of galaxies using the ROSAT Position Sensitive Proportional Counter is reported. The gas distributions is roughly symmetric and extends to a radius of at least 0.2/h(50) Mpc. A Raymond-Smith hot plasma model provides an excellent fit the X-ray spectrum with a best-fit value temperature of 0.9 + -/15 or - 0.14 keV and abundance 0.06 + 0/.12 or - 0.05 solar. The assumption of gravitational confinement leads to a total mass of the group of 3.0 + 0.4 or - 0.5 x 10 exp 13 solar. Baryons can reasonably account for 4 percent of this mass, and errors could push this number not higher than 10-15 percent. This is one of the strongest pieces of evidence that dark matter dominates small groups such as this one. The intragroup medium in this system has the lowest metal abundance yet found in diffuse gas in a group or cluster.

Mulchaey, John S.↗

Fingerprints of carbon, nitrogen, and silicon isotopes in small interstellar SiC grains from the Murchison meteorite

We report ion microprobe determinations of the carbon, nitrogen, and silicon isotopic compositions of small SiC grains from the Murchison CM2 chondrite. Analyses were made on samples containing variable numbers of grains and on 14 individual grains. In some cases the multiple-grain sample compositions were probably dominated by only one or two grains. Total ranges observed are given. Only a few grains show values near the range limits. Both the total ranges of carbon and nitrogen isotopic compositions, and even the narrower ranges typical for the majority of the grains, are similar to those observed for larger SiC grains. Two rare components appear to be present in the smaller-size fraction, one characterized by C-12/C-13 about 12-16 and the other by very heavy nitrogen. The carbon and nitrogen isotopic compositions qualitatively may reflect hydrostatic H-burning via the CNO cycle and He-burning in red giants, as well as explosive H-burning in novae. The silicon isotopic compositions of most grains qualitatively show what is the signature of He-burning. The silicon isotopic composition of one grain, however, suggests a different process.

Hoppe, Peter↗

A revised analysis of micron-sized particles detected near Saturn by the Voyager 2 plasma wave instrument

The impulsive noise that the plasma wave and radio astronomy instruments detected during the Voyager 2 swing by Saturn was attributed to dust grains striking the spacecraft. This report presents a reanalysis of the dust impacts recorded by the plasma wave instrument using an improved model for the response of the electric antenna to dust impacts. The fundamental assumption used in this analysis is that the voltage induced on the antenna is proportional to the mass of the impacting grain. Using the above assumption and the antenna response constants used at Uranus and Neptune, the following conclusions can be reached. The primary dust distribution consists of a 'disk' of particles that coincides with the equator plane and has a north-south thickness of 2-Delta zeta = 962 km. A less dense 'halo' with a north-south thickness of 2-Delta zeta = 3376 km surrounds the primary distribution. The dust particle sizes are of the order of 10 microns, assuming a mass density of 1 g/cu cm. The corresponding particle masses are of the order of 10(exp -9) g, and maximum number densities are of the order of 10(exp -2)/cu m. Most likely, the G ring is the dominate source since the particles were observed very close to that ring, namely at 2.86 R(sub S). Other sources, like nearby moons, are not ruled out especially when perturbations due to electromagnetic forces are included. The calculated optical depth differs by about a factor of 2 from photometric studies. The current particle masses, radii, and the effective north-south thickness of the particle distribution are larger than what Gurnett et al. (1983) reported by about 2, 1, and 1 orders of magnitude, respectively. This is attributed to the fact that the collection coefficient used in this study is smaller than what was used in Gurnett et al.'s earlier publication.

Tsintikidis, D.↗

Role of Turbulent Prandtl Number on Heat Flux at Hypersonic Mach Numbers

A new turbulence model suited for calculating the turbulent Prandtl number as part of the solution is presented. The model is based on a set of two equations: one governing the variance of the enthalpy and the other governing its dissipation rate. These equations were derived from the exact energy equation and thus take into consideration compressibility and dissipation terms. The model is used to study two cases involving shock wave/boundary layer interaction at Mach 9.22 and Mach 5.0. In general, heat transfer prediction showed great improvement over traditional turbulence models where the turbulent Prandtl number is assumed constant. It is concluded that using a model that calculates the turbulent Prandtl number as part of the solution is the key to bridging the gap between theory and experiment for flows dominated by shock wave/boundary layer interactions.

Gaffney, R. L., Jr.↗

Role of Turbulent Prandtl Number on Heat Flux at Hypersonic Mach Numbers

A new turbulence model suited for calculating the turbulent Prandtl number as part of the solution is presented. The model is based on a set of two equations: one governing the variance of the enthalpy and the other governing its dissipation rate. These equations were derived from the exact energy equation and thus take into consideration compressibility and dissipation terms. The model is used to study two cases involving shock wave/boundary layer interaction at Mach 9.22 and Mach 5.0. In general, heat transfer prediction showed great improvement over traditional turbulence models where the turbulent Prandtl number is assumed constant. It is concluded that using a model that calculates the turbulent Prandtl number as part of the solution is the key to bridging the gap between theory and experiment for flows dominated by shock wave/boundary layer interactions.

Xiao, X.↗

Local starburst galaxies and their descendants. Statistics from the Sloan Digital Sky Survey

Despite strong interest in the starburst phenomenon in extragalactic astronomy, the concept remains ill-defined. Here we use a strict definition of starburst to examine the statistical properties of starburst galaxies in the local universe. We also seek to establish links between starburst galaxies, post-starburst (hereafter postburst) galaxies, and active galaxies. Data were selected from the Sloan Digital Sky Survey DR7. We applied a novel method of treating dust attenuation and derive star formation rates, ages, and stellar masses assuming a two-component stellar population model. Dynamical masses are calculated from the width of the H-alpha line. These masses agree excellently with the photometric masses. The mass (gas+stars) range is approximately 10( exp 9) - 10(exp 11.5) solar mass. As a selection criterion for starburst galaxies, we use, the birthrate parameter, b = SFR/SFR, requiring that b is greater than 3. For postburst galaxies, we use, the equivalent width of Hdelta in absorption with the criterion EW (sub Hdelta_abs) is greater than 6 A. Results. We find that only 1% of star-forming galaxies are starburst galaxies. They contribute 3-6% to the stellar production and are therefore unimportant for the local star formation activity. The median starburst age is 70 Myr roughly independent of mass, indicating that star formation is mainly regulated by local feedback processes. The b-parameter strongly depends on burst age. Values close to b = 60 are found at ages approximately 10 Myr, while almost no starbursts are found at ages greater than 1 Gyr. The median baryonic burst mass fraction of sub-L galaxies is 5% and decreases slowly towards high masses. The median mass fraction of the recent burst in the postburst sample is 5-10%. A smaller fraction of the postburst galaxies, however, originates in non-bursting galaxies. The age-mass distribution of the postburst progenitors (with mass fractions is greater than 3%) is bimodal with a break at logM(solar mass ) 10.6, above which the ages are doubled. The starburst and postburst luminosity functions (LFs) follow each other closely until M(sub r ) (is) approximately -21, when active galactic nuclei (AGNs) begin to dominate. The postburst LF continues to follow the AGN LF, while starbursts become less significant. This suggests that the number of luminous starbursts is underestimated by about one dex at high luminosities, because of having large amounts of dust and/or being outshone by an AGN. It also indicates that the starburst phase preceded the AGN phase. Finally, we look at the conditions for global gas outflow caused by stellar feedback and find that massive starburst galaxies are susceptible to such outflows.

Statistical distributions↗

Validation of High-Resolution CFD Method for Slosh Damping Extraction of Baffled Tanks

Determination of slosh damping is a very challenging task as there is no analytical solution. The damping physics involve the vorticity dissipation which requires the full solution of the nonlinear Navier-Stokes equations. As a result, previous investigations and knowledge were mainly carried out by extensive experimental studies. A Volume-Of-Fluid (VOF) based CFD program developed at NASA MSFC was applied to extract slosh damping in a baffled tank from the first principle. First, experimental data using water with subscale smooth wall tank were used as the baseline validation. CFD simulation was demonstrated to be capable of accurately predicting natural frequency and very low damping value from the smooth wall tank at different fill levels. The damping due to a ring baffle at different liquid fill levels from barrel section and into the upper dome was then investigated to understand the slosh damping physics due to the presence of a ring baffle. Based on this study, the Root-Mean-Square error of our CFD simulation in estimating slosh damping was less than 4.8%, and the maximum error was less than 8.5%. Scalability of subscale baffled tank test using water was investigated using the validated CFD tool, and it was found that unlike the smooth wall case, slosh damping with baffle is almost independent of the working fluid and it is reasonable to apply water test data to the full scale LOX tank when the damping from baffle is dominant. On the other hand, for the smooth wall, the damping value must be scaled according to the Reynolds number. Comparison of experimental data, CFD, with the classical and modified Miles equations for upper dome was made, and the limitations of these semi-empirical equations were identified.

Yang, H. Q.↗

Wavenumber-frequency Spectra of Pressure Fluctuations on a Generic Space Vehicle Measured via Unsteady Pressure-Sensitive Paint

Time histories of pressure fluctuations on a generic, hammerhead space vehicle model were measured using unsteady Pressure-Sensitive Paint (uPSP). The test was conducted in the 11-foot transonic wind tunnel of NASA Ames Research Center over a Mach number range of 0.6 M 1.2, and angles of attack of -4 4. The model was coated with a porous binder and PtTFPP-based porous polymer paint. An elaborate system of four high-speed cameras, and forty LED lamps was used for image acquisition. Various steps for image registration, reduction of shot noise, photogrammetry procedure to map images from the four cameras on a grid for the model, and finally a calibration procedure to convert the measured fluctuations in light intensity to fluctuating pressure, are discussed in the paper. The calibration process using a set of unsteady pressure sensors mounted on the model, was found to overcome some of the inherent problems of the fast response paint, such as rapid photo-degradation, non-linearity in pressure response, and significant temperature sensitivity. Comparison of spectra of pressure fluctuations between UPSP and pressure sensors demonstrated the ability of the paint to faithfully follow fluctuations up to 10 kHz, the maximum attempted. It was also found that the camera bit-depth and the illumination level limited the lowest measurable levels of pressure fluctuations to around 140dB. The large data set exposed various critical transonic flow physics not seen before, such as a coupling of the shock motion on the Payload Fairing (PF) with the separated flow region on the upper stage of the launch vehicle, and upstream convection of pressure fluctuation on PF at certain Mach numbers. The data also confirmed the expectation of a general lowering of the coefficient of pressure fluctuation with Mach number. The availability of the data set on a dense, regularly-spaced, surface grid allowed for the calculation of wavenumber-frequency (k-) spectra via straightforward applications of Fourier transform. The k- spectra were compared for the separated flow regions on the Second Stage, and the shock-boundary layer interactions on PF. The former showed self-similarity with Mach number while the latter was distinctly different, and confirmed the upstream propagation of pressure fluctuations. The k- spectra were dominated by the convected fluctuations; the acoustic domain was not discernable. These data, valuable for the vibro-acoustics analysis of aerospace vehicles, are believed to be the first obtained for the transonic flight regime, and pave the path for application on production models of aerospace vehicles.

buffet↗

Hydrodynamics of Two-Phase Flows through Porous Media in Microgravity: Packed Bed Reactor Experiment onboard of the International Space Station

The objective of the Packed Bed Reactor Experiment was to develop a fundamental understanding of the hydrodynamics of two-phase flow with no phase transition through porous media in microgravity. This work describes two experimental campaigns flown on the International Space Station (ISS) that were designed to achieve the objective. This work presents the results on flow patterns observed, two-phase flow pressure drop in porous media, and the impact of capillary effects on pressure drop at various gas and liquid flow rates. This work is the first to present predictive correlations of the two-phase friction factor for the different regimes identified based on the superficial liquid and gas velocity in microgravity, the first to hypothesize the different regimes based on the change in slope of the pressure gradient versus flow rate plots, the first to address the effects of the capillarity on the pressure gradient and the first to measure column holdup and assess the effective porosity based on the packing and the trapped gas bubbles. Experimental data on pressure drop in gas (N2) – liquid (water) flow show the presence of four different flow regimes in microgravity. Dispersed bubble flow (DB) and pulse (P) flow regimes are detected at high liquid flow rates, whereas at low liquid flow rates “large bubble” or elongated bubble (LB) and “gas channeling” (GC) regimes are observed. For these different flow regimes, different two-phase flow friction factor and pressure gradient correlations are presented for the first time as a function of the gas and liquid modified Reynolds numbers and Suratman number. Within the viscous-capillary (V-C) regime, it is found that the capillary contribution is the dominant force that contributes to the pressure drop for the wetting case (glass). However, for the non-wetting packing (Teflon), the viscous contribution dominates. It was found that the gas hold-up and pressure drop are functions of bed history at low liquid and gas flow rates with the magnitude of the hysteresis decreasing with increasing flow rates. PBRE-2 results show that the capillary force is a strong function of the superficial liquid velocity but is a much weaker function of the superficial gas velocity and varies inversely with the particle diameter. Within the Viscous-Capillary (V-C) regime, over 90% of the pressure gradient is attributed to the capillary contribution in the gas continuous regime. However, in the large bubble regime, the viscous and capillary contributions were comparable. After the completion of PBRE-2 with glass spherical beads, another bed packed with alumina was installed. Pressure gradient data for the alumina packed bed (PBRE-Water Recovery) were transferred to the PI and were not analyzed by the authors of this work. The Packed Bed Reactor Experiment concluded its on-orbit operation after two successful campaigns of testing in 2017 and in 2021. The flight hardware was brought back from orbit and is being reconditioned for a series of future experiments referred to as PBRE-WRS in support of water recovery (WRS). The WRS series consists of testing different two-phase fluid system components and packed beds to assess their pressure gradient characteristics, which will be used for designing packed bed reactors for various applications relevant to life support. Although there is so much relevance of the experimental results obtained from the two PBRE campaign in microgravity to life support, these findings also apply to other applications that involve two phase flow in porous medium such as fuel cells, transport of nutrient to plants in space and other chemical and materials processing that involve two phase flows. These systems operate differently in microgravity because, due to the lack of buoyancy, the density difference between the phases becomes irrelevant and no longer leads to phase separation.

Packed Bed↗

Characterizing Signatures of Geothermal Exploration Data with Machine Learning Techniques: An Application to the Nevada Play Fairway Analysis

We are introducing machine learning methods to the play fairway analysis to generate geothermal potential maps to support the evaluation of geothermal resource potential and the exploration for undiscovered blind geothermal systems in the Nevada Great Basin region. Our project aims to identify new ways to combine the play fairway data and empirically organize relationships between feature weights and labels in an improved workflow. As a means of doing this, we introduce machine learning methods to evaluate the influence of certain geological and geophysical features/feature sets in predicting geothermal favorability. This report highlights promising approaches based on supervised and unsupervised learning methods. First, we demonstrate a filter method applied to supervised classification modeling. The supervised filter method is based on permutation analysis to evaluate every possible feature combination/drop out scenario and rank feature influence based on the performance variance of supervised classification models. Additionally, we present an unsupervised factor analysis based on principal component analysis coupled with a semi-supervised kmeans clustering algorithm. This analysis allows us to identify the optimal number of groups/clusters for training sites and structural settings to identify feature patterns including correlation, variance, and latent and dominant feature relationships. The results from these methods offer a promising avenue for identifying favorable sources of predictive information to identify the locations of blind geothermal systems and furthering our understanding of complex geothermal feature and label relationships in the Great Basin region and beyond.

15 GEOTHERMAL ENERGY↗

Toroidal phase of post-disruption runaway electron loss to wall in presence of applied 3-D fields in DIII-D

The toroidal distribution of runaway electrons (REs) striking the centre post in DIII-D post-disruption RE final loss events is simulated utilizing the MARS-F code combined with the REORBIT module, by tracing the guiding-centre drift orbits of test REs in the presence of external (applied) plus internal (intrinsic instability) 3-D fields. To better recover the experimental results, three different equilibria with different safety factor profiles are adopted. Dominant resistive magnetohydrodynamic instabilities are found to be m/n=2/1, 3/2 and 1/1 modes (where m and n are the poloidal and toroidal mode numbers). Externally applied n=1 resonant magnetic perturbations (RMPs), with both even and odd parity configuration, are considered in each equilibrium. Locking of MHD instability to the applied RMPs is simulated by minimizing the total perturbed magnetic energy in the plasma. Here, the simulated toroidal locations, where most REs strike in the presence of an edge m/n= 2/1 instability and the n=1 RMPs in even parity, are found to agree well with experiments. Modeling also captures the measured n = 2 RE loss pattern on the wall for experiments where an edge m/n=3/2 instability is dominant instead of the m/n=2/1 mode. The key overall findings include (a) the measured global RE toroidal impact pattern in experiments can be explained by a locked resistive kink instability, (b) the toroidal phase of the locked mode is well predicted by minimizing the total perturbed magnetic energy, and (c) this edge locked mode determines the toroidal phase of the peak RE wall impact.

Bai, Xue [University of California San Diego, La J↗

Transient Convection Due to Imposed Heat Flux: Application to Liquid-Acquisition Devices

A model problem is considered that addresses the effect of heat load from an ambient laboratory environment on the temperature rise of liquid nitrogen inside an enclosure. This model has applications to liquid acquisition devices inside the cryogenic storage tanks used to transport vapor-free propellant to the main engine. We show that heat loads from Q = 0.001 to 10 W, with corresponding Rayleigh numbers from Ra = 109 to 1013, yield a range of unsteady convective states and temperature rise in the liquid. The results show that Q = 1 to 10 W (Ra = 1012 to 1013) yield temperature distributions along the enclosure height that are similar in trend to experimental measurements. Unsteady convection, which shows selfsimilarity in its planforms, is predicted for the range of heat-load conditions. The onset of convection occurs from a free-convection-dominated base flow that becomes unstable against convective instability generated at the bottom of the enclosure while the top of the enclosure is convectively stable. A number of modes are generated with small-scale thermals at the bottom of the enclosure in which the flow selforganizes into two symmetric modes prior to the onset of the propagation of the instability. These symmetric vertical modes transition to asymmetric modes that propagate as a traveling-wave-type motion of convective modes and are representative of the asymptotic convective state of the flow field. Intense vorticity production is created in the core of the flow field due to the fact that there is shear instability between the vertical and horizontal modes. For the higher Rayleigh numbers, 1012 to 1013, there is a transition from a stationary to a nonstationary response time signal of the flow and temperature fields with a mean value that increases with time over various time bands and regions of the enclosure.

Duval, Walter M. B.↗

Molecular-gas-dynamics simulations of turbulent Couette flow over a mean-free-path-scale permeable substrate

Here we report flow statistics and visualizations from molecular-gas-dynamics simulations using the direct simulation Monte Carlo (DSMC) method for turbulent Couette flow in a minimal domain where the lower wall is replaced by an idealized permeable fibrous substrate representative of thermal-protection-system materials for which the Knudsen number is O(10 -1 ). Comparisons are made with smooth-wall DSMC simulations and smooth-wall direct numerical simulations (DNS) of the Navier-Stokes equations for the same conditions. Roughness, permeability, and noncontinuum effects are assessed. In the range of Reynolds numbers considered herein, the scalings of the skin friction on the permeable substrate and of the mean flow within the substrate suggest that they are dominated by viscous effects. While the regenerative cycle characteristic of smooth-wall turbulence remains intact for all cases considered, we observe that the near-wall velocity fluctuations are modulated by the permeable substrate with a wavelength equal to the pore spacing. Additionally, the flow within the substrate shows significant rarefaction effects, resulting in an apparent permeability that is 13% larger than the intrinsic permeability. In contrast, the smooth-wall DSMC and DNS simulations exhibit remarkably good agreement for the statistics examined, despite the Knudsen number based on the viscous length scale being as large as O(10 -1 ). This latter result is at variance with classical estimates for the breakdown of the continuum assumption and calls for further investigations into the interaction of noncontinuum effects and turbulence.

42 ENGINEERING↗