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At least 1,189 records · Page 66

Advanced development of the boundary element method for elastic and inelastic thermal stress analysis

The focus of this dissertation is on advanced development of the boundary element method for elastic and inelastic thermal stress analysis. New formulations for the treatment of body forces and nonlinear effects are derived. These formulations, which are based on particular integral theory, eliminate the need for volume integrals or extra surface integrals to account for these effects. The formulations are presented for axisymmetric, two and three dimensional analysis. Also in this dissertation, two dimensional and axisymmetric formulations for elastic and inelastic, inhomogeneous stress analysis are introduced. The derivatives account for inhomogeneities due to spatially dependent material parameters, and thermally induced inhomogeneities. The nonlinear formulation of the present work are based on an incremental initial stress approach. Two inelastic solutions algorithms are implemented: an iterative; and a variable stiffness type approach. The Von Mises yield criterion with variable hardening and the associated flow rules are adopted in these algorithms. All formulations are implemented in a general purpose, multi-region computer code with the capability of local definition of boundary conditions. Quadratic, isoparametric shape functions are used to model the geometry and field variables of the boundary (and domain) of the problem. The multi-region implementation permits a body to be modeled in substructured parts, thus dramatically reducing the cost of analysis. Furthermore, it allows a body consisting of regions of different (homogeneous) material to be studied. To test the program, results obtained for simple test cases are checked against their analytic solutions. Thereafter, a range of problems of practical interest are analyzed. In addition to displacement and traction loads, problems with body forces due to self-weight, centrifugal, and thermal loads are considered.

Henry, Donald P., Jr.↗

Modal Analysis and Model Correlation of the Mir Space Station

This paper will discuss on-orbit dynamic tests, modal analysis, and model refinement studies performed as part of the Mir Structural Dynamics Experiment (MiSDE). Mir is the Russian permanently manned Space Station whose construction first started in 1986. The MiSDE was sponsored by the NASA International Space Station (ISS) Phase 1 Office and was part of the Shuttle-Mir Risk Mitigation Experiment (RME). One of the main objectives for MiSDE is to demonstrate the feasibility of performing on-orbit modal testing on large space structures to extract modal parameters that will be used to correlate mathematical models. The experiment was performed over a one-year span on the Mir-alone and Mir with a Shuttle docked. A total of 45 test sessions were performed including: Shuttle and Mir thruster firings, Shuttle-Mir and Progress-Mir dockings, crew exercise and pushoffs, and ambient noise during night-to-day and day-to-night orbital transitions. Test data were recorded with a variety of existing and new instrumentation systems that included: the MiSDE Mir Auxiliary Sensor Unit (MASU), the Space Acceleration Measurement System (SAMS), the Russian Mir Structural Dynamic Measurement System (SDMS), the Mir and Shuttle Inertial Measurement Units (IMUs), and the Shuttle payload bay video cameras. Modal analysis was performed on the collected test data to extract modal parameters, i.e. frequencies, damping factors, and mode shapes. A special time-domain modal identification procedure was used on free-decay structural responses. The results from this study show that modal testing and analysis of large space structures is feasible within operational constraints. Model refinements were performed on both the Mir alone and the Shuttle-Mir mated configurations. The design sensitivity approach was used for refinement, which adjusts structural properties in order to match analytical and test modal parameters. To verify the refinement results, the analytical responses calculated using original and refined math models were compared with the measured responses. The results from this study show that the refined models predict more accurately the dynamics of the actual structure. The MiSDE test and analysis results provided the information and experience on test design, flight testing, and data analysis for the ISS and other future spacecraft, which are critical to the verification of analytical models and structural loads.

Kim, Hyoung M.↗

Ultraviolet line profiles of slowly rotating massive star winds using the ‘analytic dynamical magnetosphere’ formalism

Recent large-scale spectropolarimetric surveys have established that a small but significant percentage of massive stars host stable, surface dipolar magnetic fields with strengths on the order of kG. These fields channel the dense, radiatively driven stellar wind into circumstellar magnetospheres, whose density and velocity structure can be probed using ultraviolet (UV) spectroscopy of wind-sensitive resonance lines. Coupled with appropriate magnetosphere models, UV spectroscopy provides a valuable way to investigate the wind–field interaction, and can yield quantitative estimates of the wind parameters of magnetic massive stars. We report a systematic investigation of the formation of UV resonance lines in slowly rotating magnetic massive stars with dynamical magnetospheres. We pair the analytic dynamical magnetosphere (ADM) formalism with a simplified radiative transfer technique to produce synthetic UV line profiles. Using a grid of models, we examine the effect of magnetosphere size, the line strength parameter, and the cooling parameter on the structure and modulation of the line profile. We find that magnetic massive stars uniquely exhibit redshifted absorption at most viewing angles and magnetosphere sizes, and that significant changes to the shape and variation of the line profile with varying line strengths can be explained by examining the individual wind components described in the ADM formalism. Finally, we show that the cooling parameter has a negligible effect on the line profiles.

C Erba↗

Photophoretic Propulsion Enabling Mesosphere Exploration NIAC Phase I Final Report

This Phase I report presents a comprehensive study on photophoretic flyers—innovative, ultralight, solar-powered vehicles that harness photophoretic forces generated via Knudsen pumping to achieve sustained flight in the mesosphere (50–80 km altitude). By integrating advanced materials such as nanocardboard— characterized by its extremely low areal density (~1 g/m²) and high bending stiffness—with ultrathin light-absorbing coatings, the project converts incident solar radiation directly into a directed thrust. Extensive experimental investigations, coupled with high-fidelity computational fluid dynamics (CFD) simulations using ANSYS Fluent, validate the concept across various three-dimensional geometries, including spherical, conical, and rocket-shaped configurations. These simulations bridge the gap between free-molecular and continuum flow regimes, demonstrating that optimized designs can generate lift forces sufficient to support kilogram-scale payloads even in low-pressure environments. At the heart of this innovation is the use of Knudsen pumping, where temperature gradients across porous surfaces induce directional gas flow, creating a modest overpressure that provides lift. The report introduces an analytical framework that interpolates between the well-known low-Reynolds number drag regime and the high-Reynolds number momentum theory. This model accurately predicts lift based on design parameters such as microchannel dimensions, porous wall geometry, areal density, and nozzle exit area. For instance, simulations indicate that 10-meter-scale structures with carefully engineered porous walls can achieve the necessary pressure differential to support scientifically significant payloads (~1 kg). The study also explores a hybrid propulsion approach that combines solar buoyancy with photophoretic lift. Initially, solar heating creates a buoyant force that elevates the flyer to mesospheric altitudes. Once in the optimal pressure range, the photophoretic mechanism—powered by Knudsen pumping—takes over as the primary source of lift, ensuring stable, long-duration flight. This dual-mode operation not only facilitates the deployment of photophoretic flyers but also broadens the potential applications for mesospheric exploration. In addition to propulsion, the report investigates the integration of photophoretic thrusters for trajectory control of existing research balloons in the upper stratosphere. By dynamically adjusting the nozzle orientation and controlling the flow-through velocity, these thrusters provide precise maneuverability, enabling the flyers to counteract atmospheric disturbances and adjust their flight paths in real time. For example, a photophoretic thruster approximately 7.5 by 7.5 meters in size could be unfolded below a payload gondola of a 60 million-cubic-foot zero-pressure balloon. Such a thruster can provide horizontal speed control of approximately 1 m/s using only sunlight and no moving parts (except those needed to track the Sun and control the jet direction). Importantly, photophoretic thrusters operate more efficiently at higher altitudes, which is complementary to known trajectory control techniques, such as propellers and tethered wings, which are more effective at lower altitudes. Finally, the report identifies three scientific research thrusts where mesospheric aircraft technology can have a profound impact: atmospheric tides, characterization of gravity waves, and investigation of mesospheric instabilities. Overall, the findings of this Phase I project represent a significant advancement in photophoretic propulsion technology. By demonstrating that large-scale, ultralight structures can be powered solely by solar radiation—via carefully engineered Knudsen pumping—this work lays a robust foundation for scalable, near-space flight architectures. Future refinements in material fabrication, structural optimization, and integrated trajectory control are expected to further enhance performance, paving the way for operational demonstrations that could revolutionize atmospheric science, remote sensing, and communication networks.

Knudsen Pump↗

Reshaping of Truncated Pd Nanocubes: Energetic and Kinetic Analysis Integrating Transmission Electron Microscopy with Atomistic-Level and Coarse-Grained Modeling

Stability against reshaping of metallic fcc nanocrystals synthesized with tailored far-from-equilibrium shapes is key to maintaining optimal properties for applications such as catalysis. Yet Arrhenius analysis of experimental reshaping kinetics, and appropriate theory and simulation, is lacking. As such, we use TEM to monitor the reshaping of Pd nanocubes of ~25 nm side length between 410 °C (over ~4.5 h) and 440 °C (over ~0.25 h), extracting a high effective energy barrier of E eff ≈ 4.6 eV. We also provide an analytic determination of the energy variation along the optimal pathway for reshaping that involves transfer of atoms across the nanocube surface from edges or corners to form new layers on side {100} facets. The effective barrier from this analysis is shown to increase strongly with the degree of truncation of edges and corners in the synthesized nanocube. Theory matches experiment for the appropriate degree of truncation. In addition, we perform simulations of a stochastic atomistic-level model incorporating a realistic description of diffusive hopping for undercoordinated surface atoms, thereby providing a visualization of the initial reshaping process.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effect of control surface mass unbalance on the stability of a closed-loop active control system

The effects on stability of inertial forces arising from closed-loop activation of mass-unbalanced control surfaces are studied analytically using inertial energy approach, similar to the aerodynamic energy approach used for flutter suppression. The limitations of a single control surface like a leading-edge (LE) control or a trailing-edge (TE) control are demonstrated and compared to the superior combined LE-TE mass unbalanced system. It is shown that a spanwise section for sensor location can be determined which ensures minimum sensitivity to the mode shapes of the aircraft. It is shown that an LE control exhibits compatibility between inertial stabilization and aerodynamic stabilization, and that a TE control lacks such compatibility. The results of the present work should prove valuable, both for the purpose of flutter suppression using mass unbalanced control surfaces, or for the stabilization of structural modes of large space structures by means of inertial forces.

Nissim, E.↗

A hybrid perturbation-Galerkin technique for partial differential equations

A two-step hybrid perturbation-Galerkin technique for improving the usefulness of perturbation solutions to partial differential equations which contain a parameter is presented and discussed. In the first step of the method, the leading terms in the asymptotic expansion(s) of the solution about one or more values of the perturbation parameter are obtained using standard perturbation methods. In the second step, the perturbation functions obtained in the first step are used as trial functions in a Bubnov-Galerkin approximation. This semi-analytical, semi-numerical hybrid technique appears to overcome some of the drawbacks of the perturbation and Galerkin methods when they are applied by themselves, while combining some of the good features of each. The technique is illustrated first by a simple example. It is then applied to the problem of determining the flow of a slightly compressible fluid past a circular cylinder and to the problem of determining the shape of a free surface due to a sink above the surface. Solutions obtained by the hybrid method are compared with other approximate solutions, and its possible application to certain problems associated with domain decomposition is discussed.

Geer, James F.↗

Modeling of Kink-Shaped Carbon-Nanotube Schottky Diode with Gate Bias Modulation

A model is proposed for the recent gate-voltage (V(sub G)) modulation experiment of a kink-shaped carbon nanotube (NT) Schottky diode. Since larger V(sub G) increases both the forward and the reverse turn-on voltages of the diode in the experiment, we show that: (1) the rectification must occur at the kink where the metallic and the semiconducting NTs meet, and not at the electrode contact, and (2) the semiconducting NT must be n-type. The turn-on voltages are derived analytically as a function of V(sub G) with the electrode contact contribution and a good agreement is obtained with the experimental data.

Yamada, Toshishige↗

Issues and Strategies in Solving Multidisciplinary Optimization Problems

Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. The accumulated multidisciplinary design activity is collected under a testbed entitled COMETBOARDS. Several issues were encountered during the solution of the problems. Four issues and the strategies adapted for their resolution are discussed. This is followed by a discussion on analytical methods that is limited to structural design application. An optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. Optimum solutions obtained were infeasible for aircraft and airbreathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through a set of problems: Design of an engine component, Synthesis of a subsonic aircraft, Operation optimization of a supersonic engine, Design of a wave-rotor-topping device, Profile optimization of a cantilever beam, and Design of a cylindrical shell. This chapter provides a cursory account of the issues. Cited references provide detailed discussion on the topics. Design of a structure can also be generated by traditional method and the stochastic design concept. Merits and limitations of the three methods (traditional method, optimization method and stochastic concept) are illustrated. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions can be produced by all the three methods. The variation in the weight calculated by the methods was found to be modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliability traced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.

Patnaik, Surya↗

TPSAS-NF1676L-13539-DND

The performance of variable stiffness composite panels is characterized using experiments and structural analyses. Fabricated using a fiber placement system, the fiber angle in these panels varies continuously within each ply. Measured panel shapes and thermal responses are correlated with finite element analyses. Large geometric imperfections require unique fixtures to both straighten the panel edges and provide structural test boundary conditions. Panels show linear prebuckling and nonlinear postbuckling under applied end shortening, which occur at higher loads than a baseline panel. Panel responses to in-plane loading are computed using geometric and materially nonlinear analyses that include mechanical prestresses and measured imperfections. Analytical strains and displacements also correlate well with measured results.

Chauncey Wu↗

Standoff Detection of Chemical Plumes Using Swept-ECQCL Remote Detection Technology: Results from EMRTC Complex Terrain Dual Tracer Experiment

As part of the Complex Terrain Dual Tracer Experiments performed in support of the LYNM program, a swept-wavelength external cavity quantum cascade laser (swept-ECQCL) remote detection system was deployed to measure chemical plume propagation with high temporal resolution. The swept-ECQCL remote detection technology was initially developed at PNNL, and is now under further development at Opticslah, LLC under SBIR funding from DOE (DOE SBIR Phase I Project DE-SC0019855, Remote Detection Technologies, Program Manager Chris Ramos). The swept-ECQCL technology provides a single-frequency infrared laser source which is rapidly scanned over a large wavelength range to measure the infrared absorption of gases, liquids, or solids. Analysis of the measured infrared absorption spectrum is used to detect, identify, and quantify the chemical species which are present. While most previous laser-based techniques used small wavelength tuning ranges to measure only a few isolated spectral lines of a few species, the swept-ECQCL provides the large tuning range needed to measure multiple species simultaneously, and to detect broad absorption features from large molecules or condensed phase materials. In addition, the swept-ECQCL systems have high enough spectral resolution and sensitivity to measure narrow lines of small molecules and determine isotope ratios. The remote detection system for gas plumes is based on the swept-ECQCL technology, and consists of a swept-ECQCL source, infrared detector, control electronics, and beam transmitting and alignment optics. The remote detection system directs the infrared output of the swept-ECQCL to a target retro reflector typically located at ~10-10,000 m distance. The swept-ECQCL wavelength is varied continuously over a large wavelength range (>1000 nm) at rates up to 1000 Hz. The swept ECQCL light reflected from the remote target is collected and focused onto an infrared photodetector. By measuring the detector signal continuously as the swept-ECQCL wavelength is varied, a time-series of absorption spectra are measured for the gases along the beam line of-sight. Based on analysis and fitting of the measured absorption spectra, the time-dependent chemical concentrations of species are determined. Multiple species and mixtures can be detected simultaneously, for all species with absorption features above the sensor noise floor. The sensor output is thus a continuous, high-speed record of identified chemicals along with their concentrations and isotope ratios of interest. The high-speed operation enables low-noise operation in conditions of atmospheric turbulence and allows tracking of fluctuating concentrations in transient chemical plumes as needed for reliable remote detection applications. All components operate with minimal cooling requirements and no cryogens are needed. In addition, the output infrared light is invisible with an intensity below the maximum permissible exposure (MPE) threshold of 100 mW/cm2 for these infrared wavelengths and thus eye safe. The measurement concept for plume detection using the swept-ECQCL remote detection system is as follows. The ECQCL beam is directed toward a remote retro-reflector, which reflects the beam back to the ECQCL system where it is focused onto an infrared photodetector. The line-of-sight from the ECQCL system to the retro-reflector defines the measurement path. The detected infrared signal is recorded continuously and detects the absorption of molecular species along the measurement path. Before a plume release, the system measures absorption from atmospheric constituents, which in this LWIR band consist primarily of lines from H 2 O and CO 2 , with additional weaker absorption from N 2 O, NH 3 , and O 3 possibly contributing. The system then measures any changes in absorption due to the tracer compounds when they enter the measurement path. The shape of absorption features is used to distinguish and identify the different tracer compounds, and the strength of the absorption is used to determine the path-integrated concentration – also called the column density.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Tuning the Morphology and Electronic Properties of Single-Crystal LiNi 0.5 Mn 1.5 O 4-δ : Exploring the Influence of LiCl–KCl Molten Salt Flux Composition and Synthesis Temperature

Single-crystal materials have played a unique role in the development of high-performance cathode materials for Li batteries due to their favorable chemomechanical stability. The molten salt synthesis method has become one of the most prominent techniques used to synthesize single-crystal layered and spinel materials. In this work, the molten salt synthesis method is used as a technique to tune both the morphology and Mn 3+ content of high-voltage LiNi 0.5 Mn 1.5 O 4 (LNMO) cathodes. The resulting materials are thoroughly characterized by a suite of analytical techniques, including synchrotron X-ray core-level spectroscopy, which are sensitive to the material properties on multiple length scales. Furthermore, the multidimensional characterization allows us to build a materials library according to the molten salt phase diagram as well as to establish the relationship among synthesis, material properties, and battery performance. The results of this work show that the Mn 3+ content is primarily dependent on the synthesis temperature and increases as the temperature is increased. Additionally, the particle morphology is mostly dependent on the composition of the molten salt flux, which can be tailored to obtain well-defined octahedrons enclosed by (111) facets, plates with predominant ($11\tilde{2}$) facets, irregularly shaped particles, or mixtures of these. The electrochemical measurements indicate that the Mn 3+ content has a larger contribution to the battery performance of LNMO than do morphological characteristics and that a significant amount of Mn 3+ could become detrimental to the battery performance. However, with similar Mn 3+ contents, morphology still plays a role in influencing the battery cycle life and rate performance. The insights of molten salt synthesis parameters on the formation of LNMO, with deconvolution of the roles of Mn 3+ and morphology, are crucial to continuing studies in the rational design of LNMO cathode materials for high-energy Li batteries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Patterned crystal growth and heat wave generation in hydrogels

Abstract The crystallization of metastable liquid phase change materials releases stored energy as latent heat upon nucleation and may therefore provide a triggerable means of activating downstream processes that respond to changes in temperature. In this work, we describe a strategy for controlling the fast, exothermic crystallization of sodium acetate from a metastable aqueous solution into trihydrate crystals within a polyacrylamide hydrogel whose polymerization state has been patterned using photomasks. A comprehensive experimental study of crystal shapes, crystal growth front velocities and evolving thermal profiles showed that rapid growth of long needle-like crystals through unpolymerized solutions produced peak temperatures of up to 45˚C, while slower-crystallizing polymerized solutions produced polycrystalline composites and peaked at 30˚C due to lower rates of heat release relative to dissipation in these regions. This temperature difference in the propagating heat waves, which we describe using a proposed analytical model, enables the use of this strategy to selectively activate thermoresponsive processes in predefined areas.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Metasurfaces with Multipolar Resonances and Enhanced Light–Matter Interaction

Metasurfaces, composed of engineered nanoantennas, enable unprecedented control over electromagnetic waves by leveraging multipolar resonances to tailor light–matter interactions. This review explores key physical mechanisms that govern their optical properties, including the role of multipolar resonances in shaping metasurface responses, the emergence of bound states in the continuum (BICs) that support high-quality factor modes, and the Purcell effect, which enhances spontaneous emission rates at the nanoscale. These effects collectively underpin the design of advanced photonic devices with tailored spectral, angular, and polarization-dependent properties. This review discusses recent advances in metasurfaces and applications based on them, highlighting research that employs full-wave numerical simulations, analytical and semi-analytic techniques, multipolar decomposition, nanofabrication, and experimental characterization to explore the interplay of multipolar resonances, bound and quasi-bound states, and enhanced light–matter interactions. A particular focus is given to metasurface-enhanced photodetectors, where structured nanoantennas improve light absorption, spectral selectivity, and quantum efficiency. By integrating metasurfaces with conventional photodetector architectures, it is possible to enhance responsivity, engineer photocarrier generation rates, and even enable functionalities such as polarization-sensitive detection. The interplay between multipolar resonances, BICs, and emission control mechanisms provides a unified framework for designing next-generation optoelectronic devices. This review consolidates recent progress in these areas, emphasizing the potential of metasurface-based approaches for high-performance sensing, imaging, and energy-harvesting applications.

Kerker effect↗

Liquid-phase mixing of bipropellant doublets

Experimental results of unlike doublet mixing are correlated with an analytically derived equation predicting fluid cavitation. The correlation relates the minimum orifice pressure drop required to initiate cavitation, with the system back pressure, cold flow simulant vapor pressure, and the orifice flow discharge and contraction coefficients. Stream flow instabilities are also visually correlated with the onset of cavitation and orifice discharge coefficient measurements. The influence of cavitation on the characteristic phenomenon of hydraulic flip is observed for both circular and noncircular shaped orifices. For certain intermediate orifice lengths, some noncircular shapes are shown to produce more fully developed flows (shorter recovery lengths) and therefore a more cohesive jet, which in turn yields slightly higher cold flow mixing uniformities than circular shaped orifices of equal absolute length. The particular noncircular shaped elements evaluated are shown to be more sensitive to liquid stream misimpingement than the corresponding circular orifices.

Hoehn, F. W.↗

Predicting Wall Modifications for Adaptive Wind Tunnels

Wall shape changed iteratively until it matches streamlines. FLEXWAL predicts upper and lower wall modifications necessary to remove wall-interference effects in adaptive-wall wind tunnels. FLEXWAL aids in elimination of wall-interference effects on objects tested in typical two-dimensional wind tunnel with rigid sidewalls and flexible, solid floor and ceiling boundaries. Iterative procedure valid for subsonic and transonic test conditions, and convergence of method verified both analytically and experimentally. FLEXWAL written in FORTRAN IV for batch execution.

Everhart, J. L.↗

Investigation of hypersonic rarefied flow on a spherical nose of the AOTV

The Navier-Stokes (NS) equations were integrated numerically for investigating the flow characteristics on the forepart of the spherical nose of a space vehicle such as the AOTV or AFE by a modified Accelerated Successive Replacement (ASR) scheme under hypersonic rarefied conditions. Technical feasibility of the mathematical approach was demonstrated by computing the flowfield on a spherical nose under conditions that the AFE encounters at times t = 15 and 20 seconds after its reentry into the atmosphere. Local similar solutions for the merged layer flow along the stagnation line of the sphere were developed. These are correct to the same degree of accuracy as the NS equations. These solutions provided stagnation line boundary conditions for the domain of integration on the spherical noise. Also, a parametric study of the stagnation line solution was made with a view to understand the flow characteristics in tunnels with different ambient fluids. Analytical expressions for surface slip temperature, jump conditions, and concentration level in the presence of the real gas effects at the top of the Knudsen layer were derived and used to calculate the stagnation line flowfield with nonequilibrium dissociation and ionization. A number of graphics were drawn to illustrate the basic physics of the flowfields. The present analysis can be extended to include real gas effects and to bodies of arbitrary shapes. It can further provide boundary conditions for integrating the NS equations in the near wake region.

Jain, Amolak C.↗