Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “two-dimensional”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

Two-dimensional subsonic compressible flow past elliptic cylinders

The method of Poggi is used to calculate, for perfect fluids, the effect of compressibility upon the flow on the surface of an elliptic cylinder at zero angle of attack and with no circulation. The result is expressed in a closed form and represents a rigorous determination of the velocity of the fluid at the surface of the obstacle insofar as the second approximation is concerned. Comparison is made with Hooker's treatment of the same problem according to the method of Janzen and Rayleight and it is found that, for thick elliptic cylinders, the two methods agree very well. The labor of computation is considerably reduced by the present solution.

Kaplan, Carl↗

Performance comparison of three normal-shock position sensors for mixed-compression inlets

The performance of three types of normal shock position sensors for supersonic inlets is described. All three sensors determined the shock position from the presence of the large pressure gradient at the normal shock location. The logic means for the three sensors were: (1) electronic, using pressure transducers, (2) fluidic, and (3) direct-coupled pressure switches. The sensors were evaluated in a two-dimensional, Mach 2.7, supersonic inlet having 30-percent internal supersonic area contraction. Both dynamic (from 1 to 80 Hz) and static tests were conducted.

Dustin, M. O.↗

Predicted vortex shedding from noncircular bodies in supersonic flow

A method to predict nose vortex shedding from circular and noncircular bodies in supersonic flow at angles of attack and roll is presented. The body is represented by a supersonic panel method, and the lee side vortex wake is modeled by discrete vortices in crossflow planes. The three-dimensional steady flow problem is reduced to a two-dimensional, unsteady, separated flow problem for solution. Comparison of measured and predicted surface pressure distributions, flow field surveys, and aerodynamic characteristics are presented for circular and elliptic bodies.

Mendenhall, M. R.↗

A New Integrated Slot Element Feed Array for Multi-beam Systems

A feed array consisting of constant width slot antennas (CWSA's), fed from a block containing fin-line transitions, has been developed. The array has a two-dimensional configuration, with five elements each on five parallel substrates. Beam-widths are compatible with use in f/D-1.0 multi-beam systems, with optimum taper. Array element spacings are close to a factor of two smaller than for other typical arrays, and spill-over efficiency is about 65%.

Yngvesson, K. S.↗

Airfoil in sinusoidal motion in a pulsating stream

The forces and moments on a two-dimensional airfoil executing harmonic motions in a pulsating stream are derived on the basis of non-stationary incompressible potential flow theory, with the inclusion of the effect of the continuous sheet of vortices shed from the trailing edge. An assumption as to the form of the wake is made with a certain degree of approximation. A comparison with previous work applicable only to the special case of a stationary airfoil is made by means of a numerical example, and the excellent agreement obtained shows that the wake approximation is quite sufficient. The results obtained are expected to be useful in considerations of forced vibrations and flutter of rotary wing aircraft.

Greenberg, J Mayo↗

Airfoil section characteristics at high angles of attack

Information from the literature and from recent investigations is used herein to summarize briefly the effects of airfoil section parameters and flow variables on the aerodynamic characteristics of two-dimensional symmetrical airfoils at high angles of attack. The results presented indicate that airfoil thickness ratio, Reynolds number, Mach number, and surface roughness can all have an important effect on the maximum lift coefficient. The effect of surface roughness seems to be particularly important. Not only can surface roughness cause large decreases in maximum lift coefficient, but also the magnitudes of the effects of Reynolds number, Mach number, and airfoil thickness ratio are much reduced by surface roughness. Beyond the stall, changes in section thickness ratio appear to have little effect on the aerodynamic characteristics of airfoil sections. An investigation of one section through an angle-of-attack range of from 0° to 360° shows that the drag coefficient reaches a value of 2 at an angle of attack of 90°.

Laurence K Loftin, Jr↗

Thin airfoil theory based on approximate solution of the transonic flow equation

A method is presented for the approximate solution of the nonlinear equations transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.

WING-SECTION THEORY↗

Perforated Sheets as the Porous Material for a Suction-flap Application

Two-dimensional tests were made of an NACA 0006 airfoil with area suction applied to a porous region on a 0.3-chord trailing-edge flap deflected 50 degrees. The lift with suction approached the value computed from thin-airfoil theory. The lift gains and suction quantity requirements were unaffected by the perforation patterns of the surface over a wide range of hole sizes and spacings.

MATERIALS - TYPES↗

Air Flow in the Boundary Layer of an Elliptic Cylinder

The boundary layer of an elliptic cylinder of major and minor axis 11.78 and 3.98 inches, respectively, was investigated in air stream in which the turbulence could be varied. Conditions were arranged so that the flow was two-dimensional with the major axis of the ellipse parallel to the undisturbed stream. Speed distributions across the boundary layer were determined with a hot-wire anemometer at a number of positions about the surface for the lowest and highest intensities of turbulence, with the air speed in both cases sufficiently high to produce a turbulent boundary layer over the downstream part of the surface. The magnitude and the frequency of the speed fluctuations in the boundary layer were also measured by the use of the conventional type of hot-wire turbulence apparatus. Stream turbulence was found to affect both the nature of transition from laminar to turbulent flow in the layer and the position on the surface at which transition occurred. Transition was then investigated in detail with stream turbulence of several different scales and intensities.

Schubauer, G B↗

An analysis of supersonic aerodynamic heating with continuous fluid injection

An analysis of the steady-state aerodynamic heating problem at high-supersonic speeds is made for two-dimensional flows with laminar boundary layers. The aerodynamic heating is shown to be reduced substantially by injecting a small amount of coolant through a porous surface into the boundary layer. The analysis includes calculations of the cooling requirements and equilibrium surface temperatures for flat plates and for an equilibrium surface temperatures for flat plates and for flat porous surfaces with several rates of fluid injection at Mach numbers from 5 to 15 and altitudes from sea level to 200,000 feet. Some calculations of the skin friction are also included.

Klunker, E G↗

A Navier-Stokes boundary element solver

Using global interpolation functions (GIF's) boundary element solutions are obtained for two-dimensional laminar flows. Two schemes are proposed for handling the convective terms. The first treats convection as a forcing function, and converts the flow equations to pseudo-Poisson equations. In the second scheme, some convective effect is incorporated into the fundamental solution used in constructing the pertinent integral equations. The lid-driven cavity flow is selected as the benchmark problem.

Reddy, D. R.↗

Plane and Three-Dimensional Flow at High Subsonic Speeds

For two- and three-dimensional flow in a compressible medium, a simple relation is given by which, to a first approximation, the quantitative influence of compressibility upon the velocities and pressures can be understood in a clear manner. In the application of this relation the distinct behaviors of two-dimensional and axially symmetric three-dimensional flow with increasing Mach number are brought out. For slender elliptic cylinders and ellipsoids of revolution, calculations are made of the critical Mach number; that is, the Mach number at which local sonic velocity is achieved on the body. As a further example, the lifting wing of finite span is considered, and it is shown that the increase of wing lift with Mach number at a given angle of attack is greatly dependent upon the aspect ratio b(exp 2)/F.

Gothert, B.↗

Wind-Tunnel Investigation of an N.A.C.A. 23012 Airfoil with a Slotted Flap and Three Types of Auxiliary Flap

An investigation was made in the N.A.C.A. 7- by 10- foot wind tunnel to determine the aerodynamic section characteristics of an N. A. C. A. 23012 airfoil with a single main slotted flap equipped successively with auxiliary flaps of the plain, split, and slotted types. A test installation mas used in which an airfoil of 7-foot span was mounted vertically between the upper and the lower sides of the closed test section so that two-dimensional flow was approximated. On the basis of maximum lift coefficient, low drag at moderate and high lift coefficients, and high drag at high lift coefficients, the optimum combination of the arrangements was found to be the double slotted flap . All the auxiliary flaps tested, however, increased the magnitudes of the pitching moments over those of the main slotted flap alone.

Wenzinger, Carl J.↗

Analytical Model for Steady Flow through a Finite Channel with One Porous Wall with Arbitrary Variable Suction or Injection

This paper presents an exact solution of two-dimensional laminar flow through a finite length channel with one porous wall. It improves upon previous solutions by (1) satisfying the no-slip boundary condition at the channel dead end, (2) adding a turbulent term to the porous wall boundary condition, (3) allowing for arbitrary variable suction or injection across the porous wall, and (4) model validation against new cryogenic liquid hydrogen and oxygen experimental data. Of particular interest in the current work is the modeling of cryogenic propellant flow through a porous liquid acquisition device (LAD) screen and channel inside a propellant tank. First, a detailed review of the literature is presented for previously attempted solutions to channel flow with one porous wall. Next, the governing equations, boundary conditions, and model assumptions are used to derive the analytical flow solution and present general model results for pressure and velocity fields within the channel. Then, the model solution is compared with horizontal LAD channel flow data in liquid oxygen as well as vertical LAD channel flow data in an inverted outflow configuration in liquid hydrogen. Model results are used to update the static cryogenic bubble point pressure model with a dynamic bubble point term which factors in enhanced convection and cooling at the screen during propellant outflow. Convective heat transfer at the LAD screen during outflow is also quantified by comparing model and data. The new analytical flow solution with the dynamic bubble point model is shown to compare well with available cryogenic experimental data

Navier Stokes Equations↗

An Overview of Experiments and Modeling of Polysiloxane-Coated Thermal Protection Systems for Missions to Mars, Titan, and Beyond.

Phenolic Impregnated Carbon Ablator (PICA) gained heritage during the historic Stardust mission, where it successfully returned samples from a comet’s tail and has since been instrumental in delivering payloads to the surface of Mars [1-3]. Most recently, PICA enabled the safe return of samples collected from asteroid Bennu as part of the OSIRIS-REx mission. This rich legacy underscores PICA’s critical role in allowing NASA’s most ambitious exploration missions. However, the friable nature of its phenolic phase presents challenges during handling and pre-launch activities. To mitigate this issue, PICA is coated with a polysiloxane resin system, which serves to suppress particulate dispersion and thereby safeguard spacecraft components. A comprehensive understanding of the polysiloxane resin’s behavior is imperative, as it profoundly shapes the material response of PICA during atmospheric entry by influencing its thermal and oxidative stability. This influence extends to thermocouple plugs embedded within thermal protection systems. These plugs have demonstrated their significance in missions such as Mars Science Laboratory (MSL) and Mars 2020, where the MEDLI and MEDLI2 instrumentation suites delivered in-valuable insights into the performance of thermal protection systems during entry into the Martian atmosphere [4]. Looking ahead, missions such as Dragonfly, set to descend into Titan’s dense atmosphere, aim to leverage advanced sensor technologies to further refine our understanding of thermal protection response [5]. Moreover, thermocouple plugs play an essential role in validating cutting-edge material response models, such as those pioneered under NASA’s Entry Systems Modeling Project (ESM), designed, in-part, to predict the operational integrity of thermal protection systems under the extreme stresses of atmospheric entry. To achieve these modeling goals, ground-based experiments are crucial to provide the foundational data necessary for developing and refining these predictive tools. To this end, an extensive test campaign was conducted at the Hypersonic Materials Environmental Test System (HyMETS) to investigate the high-temperature behavior of the polysiloxane resin in an air environment [6]. These experiments revealed critical phenomena, including the formation of a silicon oxycarbide layer that enhances oxidation resistance, moderates surface temperatures, and alters in-depth thermal response. Building on these findings, subsequent tests were designed to simulate atmospheric entry conditions in reactive gases, such as CO2 and N2, to mimic the environments of Mars and Titan, respectively, as well as non-reactive gases representing the atmospheres of the Ice Giants (Neptune and Uranus). A heating rate dependent decomposition mechanism has been identified for the polysiloxane resin under oxidizing conditions (Fig. 1). In the initial stage, the resin and the underlying thermal protection system undergo pyrolysis, rapidly generating a thin amorphous silicon oxycarbide interwoven with carbonaceous char and residual fibers from PICA. During the second stage, the nascent oxide layer establishes a robust, oxidation-resistant thermal barrier coating, which significantly impedes heat transfer to the underlying carbonaceous char, resulting in a stagnation of the surface temperature. A key factor contributing to this thermal resistance is the low recombination efficiency of atomic oxygen (γ), which further diminishes the heat load on the material’s interior layers [7]. Moreover, as the surface temperature stagnates, the silicon oxycarbide phase separates into distinct regions of silica and free graphite. Ultimately, when the heat flux reaches a critical threshold, a third stage is triggered, leading to the breakdown of the coating through carbothermal reduction, exposing the underlying char layer. This exposure leads to a dramatic surface temperature spike, driven by highly exothermic reactions between atomic oxygen and the char layer, further accelerating material degradation. A detailed mass and heat transfer model of PICA coated with polysiloxane resin was implemented in the Porous material Analysis Toolbox based on OpenFOAM, PATO [8]. The initial stage was considered negligible in this model because the resin decomposition occurs rapidly within a thin surface layer. Instead, the coating was directly considered as an oxygen-resistant thermal barrier coating. For the second stage, the thin amorphous silicon oxycarbide was treated as a pure silica surface to simplify the thermochemical behavior. The model ac-counts for surface equilibrium processes using representative elements of the coating-environment system. For the third stage, specific boundary conditions were developed to estimate the onset and progression of the coating removal. Two-dimensional material response simulations were conducted to compare uncoated and coated PICA using boundary conditions calibrated with HyMETS data. Fig. 2 illustrates that the simulations closely align with experimental data, successfully reproducing measured temperature profiles. This work will include the latest advancements in the coating model, including the calibration of recombination of atomic oxygen at the surface during the second phase. These simulated results will be further validated against additional CO2 data points from HyMETS, reinforcing the models’ predictive capabilities. These mechanisms and their effects on thermal protection systems, including thermochemical behavior and thermocouple probe performance in extreme environments, provide crucial insights for optimizing spacecraft designs that safeguard scientific payload and ensure mission success in future planetary exploration endeavors.

Active Oxidation↗

Molecular Inventory and Comparative Organic Profiling of A Homogenized Aggregate Sample From Asteroid (101955) Bennu

Evaluating the distribution and diversity of solvent-soluble organic molecules in extraterrestrial materials provide information about the physicochemical environments where prebiotic chemistry occurred and is essential for assessing the inventory of prebiotic compounds available to the early Earth. In this work, we conducted a comprehensive molecular characterization of solvent-soluble organic compounds in a homogenized aggregate sample (ID: OREX-800107-128) of unsorted regolith from asteroid (101955) Bennu returned by NASA’s OSIRIS-REx mission. Using two-dimensional gas chromatography coupled with high-resolution time-of-flight mass spectrometry (GC×GC-HRMS), we identified 87 organic compounds across several molecular classes, including alkanes, polycyclic aromatic hydrocarbons, and nitrogen-, oxygen-, and sulfur-bearing species. Comparison with the organic inventory of CI (Orgueil), C2-ungrouped (Tagish Lake and Tarda), and CM2 (Murchison) carbonaceous chondrites revealed that Bennu sample OREX-800107-128 is most similar to Tagish Lake and Tarda yet compositionally distinct from all of these meteorites. This Bennu sample exhibits a relatively high abundance of low-molecular-weight aromatics (e.g., toluene), pyridine derivatives, and sulfur species such as dimethyl sulfite, consistent with episodic low-temperature aqueous alteration. The presence of these organic compounds suggests that this material experienced chemically diverse processes in the parent body conducive to complex organic synthesis, including aldol condensation reactions responsible for N- and O-bearing compounds. We also compared the molecular distributions of this Bennu sample and previously analyzed samples from (162173) Ryugu to assess potential common origins between these two carbonaceous asteroids. Bennu shows more chemically diverse and nitrogen-rich organic materials than Ryugu. While both asteroids share broadly similar primitive compositions, the observed chemical differences indicate distinct evolutionary histories within a likely common formation environment though whether Bennu and Ryugu derive from a single compositionally heterogeneous parent body or from multiple closely related progenitors remains unresolved. Further detailed comparative analyses of material from Bennu, Ryugu, and specific carbonaceous meteorites (e.g., Tagish Lake and Tarda) will provide new insights into how the N-rich molecular profile observed in Bennu samples was formed and evolved in the outer Solar System.

sample return↗

The Shape Effect: Influence of 1D and 2D Boron Nitride Nanostructures on the Radiation Shielding, Thermal, and Damping Properties of High-Temperature Epoxy Composites

In space exploration, lightweight multifunctional materials capable of shielding neutron radiation, dissipating heat, and providing damping are essential. Polymer composites reinforced with boron nitride (BN) nanomaterials—specifically one-dimensional boron nitride nanotubes (BNNTs) and two-dimensional boron nitride nanoplatelets (BNNPs)—offer promising solutions. This study investigates how BN nanomaterial morphology influences the performance of high-temperature (HT) epoxy composites. We developed ultralightweight, three-dimensional BN foams comprising 1D BNNTs, 2D BNNPs, and hybrid 1D BNNT/2D BNNP structures via freeze-drying, then infiltrated them with HT epoxy to form dense composites. The BNNT foam exhibited the highest neutron radiation shielding, with a mass absorption coefficient of 26.64 cm2 g −1 , outperforming the hybrid foam (18.18 cm 2 g −1 ) and the BNNP foam (11.12 cm 2 g −1 ). A similar trend was observed in the HT epoxy composites; incorporating these foams at least doubled the mass absorption coefficient compared to the neat polymer. In terms of thermal conductivity, the BNNT/BNNP foam-epoxy composite achieved the highest value of 0.34 W m −1 K −1 , a 2.13-fold increase over neat HT epoxy. The BNNT/BNNP foam-epoxy composites also improved by 1.88 and 1.75 times, respectively. Mechanical testing revealed that BNNP foams withstood the highest loads during nanoindentation (3.53 kN), followed by BNNT/BNNP foams (1.93 kN) and BNNT foams (1.56 kN). All BN foam-epoxy composites exhibited enhanced damping properties, with tan δ increasing by at least 30 % compared to neat HT epoxy. These findings elucidate the impact of BN nanomaterial morphology on the multifunctional performance of HT epoxy composites, offering insights for developing high-performance, tailorable materials for demanding environments.

Kazue Orikasa↗

Multidisciplinary Design Optimization and Analysis of an Open Rotor Stage: Part 1

Successful design of open rotor propulsors requires effective analysis across multiple disciplines, including aerodynamics, acoustics, and structures. A viable design must not only be efficient but must also produce an acceptable level of noise and meet all static and dynamic structural requirements. For design and optimization, this is especially challenging because running high fidelity analyses is resource-intensive, and optimizing a design may require many thousands of cases to be analyzed. For this reason, the NASA team has applied design methodology that utilizes low-cost aerodynamic methods, machine learning models, and high-fidelity analyses when necessary. This includes standard two-dimensional methods such as throughflow analysis and quasi-3D blade-to-blade CFD, as well as some newly developed methods. Optimization using 3D CFD is necessary to maximize performance, and this is considered as well. All optimizations are carried out subject to structural constraints evaluated using finite element analysis. Doing this accurately requires a robust trunnion design, capable of pitching the blade between cruise and takeoff conditions while maintaining acceptable factor of safety. Hot to cold analysis must also be applied in order to correctly determine the as-manufactured shape. For acoustics, the unsteady pressures on the blade surfaces must be predicted, and this can be done either through full-annulus unsteady CFD or through a nonlinear harmonic method (NLH). NLH can run much faster, allowing some acoustic considerations to be made earlier in the design process. The design process is ongoing, and this presentation will review the current status and planned next steps. This part of the talk will focus on aerodynamic performance and be followed by a talk on structures and acoustics.

Design↗