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All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Two-Dimensional Ffowcs Williams/Hawkings Equation Solver

FWH2D is a Fortran 90 computer program that solves a two-dimensional (2D) version of the equation, derived by J. E. Ffowcs Williams and D. L. Hawkings, for sound generated by turbulent flow. FWH2D was developed especially for estimating noise generated by airflows around such approximately 2D airframe components as slats. The user provides input data on fluctuations of pressure, density, and velocity on some surface. These data are combined with information about the geometry of the surface to calculate histories of thickness and loading terms. These histories are fast-Fourier-transformed into the frequency domain. For each frequency of interest and each observer position specified by the user, kernel functions are integrated over the surface by use of the trapezoidal rule to calculate a pressure signal. The resulting frequency-domain signals are inverse-fast-Fourier-transformed back into the time domain. The output of the code consists of the time- and frequency-domain representations of the pressure signals at the observer positions. Because of its approximate nature, FWH2D overpredicts the noise from a finite-length (3D) component. The advantage of FWH2D is that it requires a fraction of the computation time of a 3D Ffowcs Williams/Hawkings solver.

Lockard, David P.↗
NASA NTRS2001

Damage Tolerance of Sandwich Plates With Debonded Face Sheets

A nonlinear finite element analysis was performed to simulate axial compression of sandwich beams with debonded face sheets. The load - end-shortening diagrams were generated for a variety of specimens used in a previous experimental study. The energy release rate at the crack tip was computed using the J-integral, and plotted as a function of the load. A detailed stress analysis was performed and the critical stresses in the face sheet and the core were computed. The core was also modeled as an isotropic elastic-perfectly plastic material and a nonlinear post buckling analysis was performed. A Graeco-Latin factorial plan was used to study the effects of debond length, face sheet and core thicknesses, and core density on the load carrying capacity of the sandwich composite. It has been found that a linear buckling analysis is inadequate in determining the maximum load a debonded sandwich beam can carry. A nonlinear post-buckling analysis combined with an elastoplastic model of the core is required to predict the compression behavior of debonded sandwich beams.

Sankar, Bhavani V.↗
NASA NTRS2006

Computations of Viking Lander Capsule Hypersonic Aerodynamics with Comparisons to Ground and Flight Data

Comparisons are made between the LAURA Navier-Stokes code and Viking Lander Capsule hypersonic aerodynamics data from ground and flight measurements. Wind tunnel data are available for a 3.48 percent scale model at Mach 6 and a 2.75 percent scale model at Mach 10.35, both under perfect gas air conditions. Viking Lander 1 aerodynamics flight data also exist from on-board instrumentation for velocities between 2900 and 4400 m/sec (Mach 14 to 23.3). LAURA flowfield solutions are obtained for the geometry as tested or flown, including sting effects at tunnel conditions and finite-rate chemistry effects in flight. Using the flight vehicle center-of-gravity location (trim angle approx. equals -11.1 deg), the computed trim angle at tunnel conditions is within 0.31 degrees of the angle derived from Mach 6 data and 0.13 degrees from the Mach 10.35 trim angle. LAURA Mach 6 trim lift and drag force coefficients are within 2 percent of measured data, and computed trim lift-to-drag ratio is within 4 percent of the data. Computed trim lift and drag force coefficients at Mach 10.35 are within 5 percent and 3 percent, respectively, of wind tunnel data. Computed trim lift-to-drag ratio is within 2 percent of the Mach 10.35 data. Using the nominal density profile and center-of-gravity location, LAURA trim angle at flight conditions is within 0.5 degrees of the total angle measured from on-board instrumentation. LAURA trim lift and drag force coefficients at flight conditions are within 7 and 5 percent, respectively, of the flight data. Computed trim lift-to-drag ratio is within 4 percent of the data. Computed aerodynamics sensitivities to center-of-gravity location, atmospheric density, and grid refinement are generally small. The results will enable a better estimate of aerodynamics uncertainties for future Mars entry vehicles where non-zero angle-of-attack is required.

Edquist, Karl T.↗
NASA NTRS2016

Generalized Fluid System Simulation Program, Version 6.0

The Generalized Fluid System Simulation Program (GFSSP) is a general purpose computer program for analyzing steady state and time-dependent flow rates, pressures, temperatures, and concentrations in a complex flow network. The program is capable of modeling real fluids with phase changes, compressibility, mixture thermodynamics, conjugate heat transfer between solid and fluid, fluid transients, pumps, compressors, and external body forces such as gravity and centrifugal. The thermofluid system to be analyzed is discretized into nodes, branches, and conductors. The scalar properties such as pressure, temperature, and concentrations are calculated at nodes. Mass flow rates and heat transfer rates are computed in branches and conductors. The graphical user interface allows users to build their models using the 'point, drag, and click' method; the users can also run their models and post-process the results in the same environment. Two thermodynamic property programs (GASP/WASP and GASPAK) provide required thermodynamic and thermophysical properties for 36 fluids: helium, methane, neon, nitrogen, carbon monoxide, oxygen, argon, carbon dioxide, fluorine, hydrogen, parahydrogen, water, kerosene (RP-1), isobutene, butane, deuterium, ethane, ethylene, hydrogen sulfide, krypton, propane, xenon, R-11, R-12, R-22, R-32, R-123, R-124, R-125, R-134A, R-152A, nitrogen trifluoride, ammonia, hydrogen peroxide, and air. The program also provides the options of using any incompressible fluid with constant density and viscosity or ideal gas. The users can also supply property tables for fluids that are not in the library. Twenty-four different resistance/source options are provided for modeling momentum sources or sinks in the branches. These options include pipe flow, flow through a restriction, noncircular duct, pipe flow with entrance and/or exit losses, thin sharp orifice, thick orifice, square edge reduction, square edge expansion, rotating annular duct, rotating radial duct, labyrinth seal, parallel plates, common fittings and valves, pump characteristics, pump power, valve with a given loss coefficient, Joule-Thompson device, control valve, heat exchanger core, parallel tube, and compressible orifice. The program has the provision of including additional resistance options through User Subroutines. GFSSP employs a finite volume formulation of mass, momentum, and energy conservation equations in conjunction with the thermodynamic equations of state for real fluids as well as energy conservation equations for the solid. The system of equations describing the fluid network is solved by a hybrid numerical method that is a combination of the Newton-Raphson and successive substitution methods. The application and verification of the code has been demonstrated through 30 example problems.

Majumdar, A. K.↗
NASA NTRS1984

A model for chorus associated electrostatic bursts

The linear theory of the generation of electrostatic bursts of noise by electrons trapped in chorus wave packets is developed for a finite temperature electron beam and a Maxwellian elecron and ion background. The growth rates determined qualitatively in good agreement with those obtained by previous authors from a more idealized model. Two connected instability mechanisms seem to be occurring: a beam plasma (electron-ion two-stream) instability commonly associated with intensification of the chorus power levels, and a transitional or borderline resistive medium instability commonly associated with chorus hooks. The physical reasons for the two mechanisms is discussed. In the second case electron beams are difficult to identify in the particle data. An expression is obtained for the maximum growth rate in terms of the ratios of the beam and electron thermal velocities to the beam velocity, and of the beam density to plasma density. It is anticipated that this may allow the observed peak in the electrostatic noise spectrum to be used as a diagnostic for the beam characteristics. Previously announced in STAR as N84-12832

Grabbe, C. L.↗
NASA NTRS1992

Venus tectonic styles and crustal differentiation

Two of the most important constraints are known from Pioneer Venus data: the lack of a system of spreading rises, indicating distributed deformation rather than plate tectonics; and the high gravity/topography ratio, indicating the absence of an asthenosphere. In addition, the high depth/diameter ratios of craters on Venus indicate that Venus probably has no more crust than Earth. The problems of the character of tectonics and crustal formation and recycling are closely coupled. Venus appears to lack a recycling mechanism as effective as subduction, but may also have a low rate of crustal differentiation because of a mantle convection pattern that is more distributed, less concentrated, than Earth's. Distributed convection, coupled with the nonlinear dependence of volcanism on heat flow, would lead to much less magmatism, despite only moderately less heat flow, compared to Earth. The plausible reason for this difference in convective style is the absence of water in the upper mantle of Venus. We have applied finite element modeling to problems of the interaction of mantle convection and crust on Venus. The main emphasis has been on the tectonic evolution of Ishtar Terra, as the consequence of convergent mantle flow. The early stage evolution is primarily mechanical, with crust being piled up on the down-stream side. Then the downflow migrates away from the center. In the later stages, after more than 100 m.y., thermal effects develop due to the insulating influence of the thickened crust. An important feature of this modeling is the entrainment of some crustal material in downflows. An important general theme in both convergent and divergent flows is that of mixing vs. stratification. Models of multicomponent solid-state flow obtain that lower-density crustal material can be entrained and recycled, provided that the ration of low-density to high-density material is small enough (as in subducted slabs on Earth). The same considerations should apply in upflows; a small percent of partial melt may be carried along with its matrix and never escape to the surface. Models that assume melt automatically rising to the crust and no entrainment or other mechanism of recycling lower-density material obtain oscillatory behavior, because it takes a long time for heat to build up enough to overcome a Mg-rich low-density residuum. However, these models develop much thicker crust than consistent with estimates from crater depth/diameter ratios.

Kaula, W. M.↗
NASA NTRS2012

Energy-Based Tetrahedron Sensor for High-Temperature, High-Pressure Environments

An acoustic energy-based probe has been developed that incorporates multiple acoustic sensing elements in order to obtain the acoustic pressure and three-dimensional acoustic particle velocity. With these quantities, the user can obtain various energy-based quantities, including acoustic energy density, acoustic intensity, and acoustic impedance. In this specific development, the probe has been designed to operate in an environment characterized by high temperatures and high pressures as is found in the close vicinity of rocket plumes. Given these capabilities, the probe is designed to be used to investigate the acoustic conditions within the plume of a rocket engine or jet engine to facilitate greater understanding of the noise generation mechanisms in those plumes. The probe features sensors mounted inside a solid sphere. The associated electronics for the probe are contained within the sphere and the associated handle for the probe. More importantly, the design of the probe has desirable properties that reduce the bias errors associated with determining the acoustic pressure and velocity using finite sum and difference techniques. The diameter of the probe dictates the lower and upper operating frequencies for the probe, where accurate measurements can be acquired. The current probe design implements a sphere diameter of 1 in. (2.5 cm), which limits the upper operating frequency to about 4.5 kHz. The sensors are operational up to much higher frequencies, and could be used to acquire pressure data at higher frequencies, but the energy-based measurements are limited to that upper frequency. Larger or smaller spherical probes could be designed to go to lower or higher frequency range

Gee, Kent L.↗
NASA NTRS2009

Orion Landing Simulation Eight Soil Model Comparison

LS-DYNA finite element simulations of a rigid Orion Crew Module (CM) were used to investigate the CM impact behavior on eight different soil models. Ten different landing conditions, characterized by the combination of CM vertical and horizontal velocity, hang angle, and roll angle were simulated on the eight different soils. The CM center of gravity accelerations, pitch angle, kinetic energy, and soil contact forces were the outputs of interest. The simulation results are presented, with comparisons of the CM behavior on the different soils. The soils analyzed in this study can be roughly categorized as soft, medium, or hard, according to the CM accelerations that occur when landing on them. The soft group is comprised of the Carson Sink Wet soil and the Kennedy Space Center (KSC) Low Density Dry Sand. The medium group includes Carson Sink Dry, the KSC High Density In-Situ Moisture Sand and High Density Flooded Sand, and Cuddeback B. The hard soils are Cuddeback A and the Gantry Unwashed Sand. The softer soils were found to produce lower peak accelerations, have more stable pitch behavior, and to be less sensitive to the landing conditions. This investigation found that the Cuddeback A soil produced the highest peak accelerations and worst stability conditions, and that the best landing performance was achieved on the KSC Low Density Dry Sand.

Mark, Stephen D.↗
NASA NTRS1993

Transverse cracking and stiffness reduction in composite laminates

A study of transverse cracking mechanism in composite laminates is presented using a singular hybrid finite element model. The model provides the global structural response as well as the precise local crack-tip stress fields. An elasticity basis for the problem is established by employing Lekhnitskii's complex variable potentials and method of eigenfunction expansion. Stress singularities associated with the transverse crack are obtained by decomposing the deformation into the symmetric and antisymmetric modes and proper boundary conditions. A singular hybrid element is thereby formulated based on the variational principle of a modified hybrid functional to incorporate local crack singularities. Axial stiffness reduction due to transverse cracking is studied. The results are shown to be in very good agreement with the existing experimental data. Comparison with simple shear lag analysis is also given. The effects of stress intensity factors and strain energy density on the increase of crack density are analyzed. The results reveal that the parameters approach definite limits when crack densities are saturated, an evidence of the existence of characteristic damage state.

Yuan, F. G.↗
NASA NTRS1998

Computational Modeling of Vertical-Cavity Surface-Emitting Lasers

Vertical-Cavity Surface-Emitting Lasers (VCSELs) have become increasingly important for many applications, such as optical interconnects and optical data storages. In many applications, critical requirements are very often high beam quality and/or high output powers. To help the design and optimization of VCSELs for such applications, it is essential to have a simulation model that includes the time evolution of the transverse space dependence of the hewn. Such models allow arbitrary transverse profiles of laser intensity or carrier density to develop in time without any a priori assumption about the number and types of transverse modes. In addition, extensive research in the past has shown that many-body effects are important in influencing the optical gain and the refractive index of semiconductor quantum wells. It is thus important to include the key many-body effects in simulation models for semiconductor lasers. A computational model, called the Maxwell-Effective Bloch Equations (MEBE) was developed recently that simulates the above features and effects. This model combines the space-time resolution with microscopic many-body effects in a way that is both accurate enough and computationally manageable. This model has been used to simulate edge-emitting high power lasers recently. A new finite-difference algorithm has been developed for solving these equations and will be shown in the presentation. That algorithm will be used to calculate the detailed time evolution of the transverse mode profiles of VCSELs. The VCSELs are based on InGaAs/GaAs quantum well structures. Effects of pumping current and refractive index profiles will be investigated in detail. The simulation results will be compared with other results the use the rate-equation model.

Goorjian, Peter M.↗
NASA NTRS1998

Computational Nonlinear of Vertical-Cavity Surface-Emitting Lasers

Vertical-Cavity Surface-Emitting Lasers (VCSELs) have become increasingly important for many applications, such as optical interconnects and optical data storages. In many applications, critical requirements are very often high beam quality and/or high output powers. To help the design and optimization of VCSELs for such applications, it is essential to have a simulation model that includes the time evolution of the transverse space dependence of the beam. Such models allow arbitrary transverse profiles of laser intensity or carrier density to develop in time without any a priori assumption about the number and types of transverse modes. In addition, extensive research in the past has shown that many-body effects are important in influencing the optical gain and the refractive index of semiconductor quantum wells. It is thus important to include the key many-body effects in simulation models for semiconductor lasers. A computational model, called the Maxwell-Effective Bloch Equations (MEBE) was developed recently that simulates the above features and effects. This model combines the space-time resolution with microscopic many-body effects in a way that is both accurate enough and computationally manageable. This model has been used to simulate edge-emitting high power lasers recently. A new finite-difference algorithm has been developed for solving these equations and will be shown in the presentation. That algorithm will be used to calculate the detailed time evolution of the transverse mode profiles of VCSELs. The VCSELs are based on InGaAs/GaAs quantum well structures. Effects of pumping current and refractive index profiles will be investigated in detail. The simulation results will be compared with other results the use the rate-equation model.

Goorjian, Peter M.↗
NASA NTRS1998

An Integrated Tool for the Coupled Thermal and Mechanical Analysis of Pyrolyzing Heatshield Materials

Materials that pyrolyze at elevated temperature have been commonly used as thermal protection materials in hypersonic flight, and advanced pyrolyzing materials for this purpose continue to be developed. Because of the large temperature gradients that can arise in thermal protection materials, significant thermal stresses can develop. Advanced applications of pyrolytic materials are calling for more complex heatshield configurations, making accurate thermal stress analysis more important, and more challenging. For non-pyrolyzing materials, many finite element codes are available and capable of performing coupled thermal-mechanical analyses. These codes do not, however, have a built-in capability to perform analyses that include pyrolysis effects. When a pyrolyzing material is heated, one or more components of the original virgin material pyrolyze and create a gas. This gas flows away from the pyrolysis zone to the surface, resulting in a reduction in surface heating. A porous residue, referred to as char, remains in place of the virgin material. While the processes involved can be complex, it has been found that a simple physical model in which virgin material reacts to form char and pyrolysis gas, will yield satisfactory analytical results. Specifically, the effects that must be modeled include: (1) Variation of thermal properties (density, specific heat, thermal conductivity) as the material composition changes; (2) Energy released or absorbed by the pyrolysis reactions; (3) Energy convected by the flow of pyrolysis gas from the interior to the surface; (4) The reduction in surface heating due to surface blowing; and (5) Chemical and mass diffusion effects at the surface between the pyrolysis gas and edge gas Computational tools for the one-dimensional thermal analysis these materials exist and have proven to be reliable design tools. The objective of the present work is to extend the analysis capabilities of pyrolyzing materials to axisymmetric configurations, and to couple thermal and mechanical analyses so that thermal stresses may be efficiently and accurately calculated.

Pronchick, Stephen W.↗
NASA NTRS2004

Quantifying Square Membrane Wrinkle Behavior Using MITC Shell Elements

For future membrane based structures, quantified predictions of membrane wrinkling behavior in terms of amplitude, angle and wavelength are needed to optimize the efficiency and integrity of such structures, as well as their associated control systems. For numerical analyses performed in the past, limitations on the accuracy of membrane distortion simulations have often been related to the assumptions made while using finite elements. Specifically, this work demonstrates that critical assumptions include: effects of gravity. supposed initial or boundary conditions, and the type of element used to model the membrane. In this work, a 0.2 square meter membrane is treated as a structural material with non-negligible bending stiffness. Mixed Interpolation of Tensorial Components (MTTC) shell elements are used to simulate wrinkling behavior due to a constant applied in-plane shear load. Membrane thickness, gravity effects, and initial imperfections with respect to flatness were varied in numerous nonlinear analysis cases. Significant findings include notable variations in wrinkle modes for thickness in the range of 50 microns to 1000 microns, which also depend on the presence of an applied gravity field. However, it is revealed that relationships between overall strain energy density for cases with differing initial conditions are independent of assumed initial con&tions. In addition, analysis results indicate that the relationship between amplitude scale (W/t) and structural scale (L/t) is linear in the presence of a gravity field.

Jacobson, Mindy B.↗
NASA NTRS1997

Mechanical Characterization and Micromechanical Modeling of Woven Carbon/Copper Composites

The present investigation examines the in-plane mechanical behavior of a particular woven metal matrix composite (MMC); 8-harness (8H) satin carbon/copper (C/Cu). This is accomplished via mechanical testing as well as micromechanical modeling. While the literature is replete with experimental and modeling efforts for woven and braided polymer matrix composites, little work has been done on woven and braided MMC's. Thus, the development and understanding of woven MMC's is at an early stage. 8H satin C/Cu owes its existence to the high thermal conductivity of copper and low density and thermal expansion of carbon fibers. It is a candidate material for high heat flux applications, such as space power radiator panels. The experimental portion of this investigation consists of monotonic and cyclic tension, compression, and Iosipescu shear tests, as well as combined tension-compression tests. Tests were performed on composite specimens with three copper matrix alloy types: pure Cu, Cu-0.5 weight percent Ti (Cu-Ti), and Cu-0.7 weight percent Cr (Cu-Cr). The small alloying additions are present to promote fiber/matrix interfacial bonding. The analytical modeling effort utilizes an approach in which a local micromechanical model is embedded in a global micromechanical model. This approach differs from previously developed analytical models for woven composites in that a true repeating unit cell is analyzed. However, unlike finite element modeling of woven composites, the geometry is sufficiently idealized to allow efficient geometric discretization and efficient execution.

Bednarcyk, Brett A.↗
NASA NTRS1999

Effects of Gravity on the Double-Diffusive Convection during Directional Solidification of a Non-Dilute Alloy with Application to the HgCdTe

General 2-D and 3-D finite element model of non-dilute alloy solidification was used to simulate growth of HgCdTe in terrestrial and microgravity conditions. Parametric research was undertaken to investigate effects of gravity level, gravity vector orientation and growth velocity on the pattern of melt convection, shape of crystal/melt interface and radial thermal gradient. Verification of the model was undertaken by comparison with previously published results. For low growth velocities plane front solidification occurs. The location and the shape of the interface was determined using melting temperatures obtained from the HgCdTe liquidus curve. The low thermal conductivity of the solid HgCdTe causes thermal short circuit through the ampoule walls, resulting in curved isotherms in the vicinity of the interface. Double-diffusive convection in the melt is caused by radial temperature gradients and by material density inversion with temperature. Cooling from below and the rejection at the solid-melt interface of the heavier HgTe-rich solute each tend to reduce convection. Because of these complicating factors dimensional rather then non-dimensional modeling was performed. For gravity levels higher then 10(exp -7) of terrestrial one it was found that the maximum convection velocity is extremely sensitive to gravity vector orientation and can be reduced at least by 50% by choosing proper orientation of the ampoule. The predicted interface shape is in agreement with one obtained experimentally by quenching.

Bune, Andris↗
NASA NTRS1961

A Study of the Free Oscillations of the Earth

Published observations on the toroidal oscillations of the earth are critically reviewed. A supplementary analysis of the record obtained by the Lamont strain seismometer is presented. Eleven toroidal modes are identified, and it is concluded that the periods are known to within 1 per cent. A perturbation scheme involving the ratio of the angular velocity of the earth to the resonant frequency is used in calculating the effects due to the rotation of the earth on the resonant frequency. The free oscillations are viewed as a superposition of traveling waves. In a nonrotating system two traveling waves combine to produce a stationary standing wave. In a rotating system, the rotation distinguishes between waves that travel in the direction of rotation and those that travel in the opposite direction. Rotation removes a degeneracy and results in a splitting of a spectral peak of order l into 2 times l plus 1 peaks. The fractional displacement in frequency for the lowest-order toroidal oscillations is 1/206 and of the same order as the Q of the peak, so that splitting will probably not be observed in the toroidal oscillations. Viewed locally, rotation causes a particle to precess about a direction parallel to the axis of rotation. This precession will cause a variation of amplitude with time if the motion is recorded by an instrument with an anisotropic response function. Care is therefore needed in studying the time decay of a given spectral peak. Rotation also couples the normal coordinates so that a motion that is initially purely horizontal will develop a vertical component. It is expected that vertical seismometers should record particle motion with the toroidal frequencies. The perturbations of the toroidal oscillations due to core-mantle interaction are treated in detail. An exact expression is obtained for the rate of energy dissipated by a finitely conducting plate oscillating across a magnetic field. The energy dissipated at the core-mantle boundary due to viscous and hydromagnetic coupling is shown to be insignificant as compared with the energy dissipated within the mantle. The toroidal magnetic field leaking into the lower mantle combines with the dipole field, resulting in a stress on the mantle, tending to stiffen the lower boundary. The stress is of sufficient magnitude to produce a displacement toward higher frequency in the lower-order toroidal oscillations. Observations on the (sub 0) T (sub 2) oscillations lead to an estimate of the toroidal magnetic field in the lower mantle. A calculation of elastic energy in the low-order oscillations suggests a value of 10 (sup 18) ergs per cycles per hour for the energy density at low frequencies in the Chilean earthquake. Each mode of oscillation has a characteristic radial distribution of elastic energy associated with it. This distribution determines which parts of the earth contribute most heavily in determining a particular resonant frequency. The distribution of energy for the lower 17 modes for a homogeneous and a Gutenberg model earth is calculated. The resonant frequencies for models of the earth based on the Gutenberg and Lehmann distribution of elastic properties are presented. It is shown that the Gutenberg model earth fits the observations more closely than the Lehmann model and that a slight alteration of the Gutenberg model gives a significantly better fit to the observations. The alteration involves a lower shear-wave velocity in the lower mantle while the Gutenberg velocity distribution is maintained in the upper mantle. Various studies of the earth's oscillations coupled with surface-wave investigations substantiate Gutenberg's hypothesis of a layer of low velocity in the upper mantle. The physical conditions required for the formation of a region of low velocity are examined in detail. The results confirm Birch's earlier statement that a temperature gradient in excess of 6 degrees to 7 degrees per kilometer is needed to produce a decrease in velocity. The low-velocity layer does not require that the temperature approach or exceed the melting temperature. If tile upper mantle is homogeneous, the region of lower velocity should commence at the base of the crust and extend to 150 kilometers under the oceans and about 100 kilometers under continental regions. The distribution of thermal conductivity and radioactivity consistent with the low-velocity layer is also considered.

MacDonald, Gordon J. F.↗
NASA NTRS1939

Airfoil Theory at Supersonic Speed

A theory is developed for the airfoil of finite span at supersonic speed analogous to the Prandtl airfoil theory of 1918-1919 for incompressible flow. In addition to the profile and induced drags, account must be taken at supersonic flow of still another drag, namely, the wave drag, which is independent of the wing aspect ratio. Both wave and induced drags are proportional to the square of the lift and depend on the Mach number, that is, the ratio of flight to sound speed. In general, in the case of supersonic flow, the drag-lift ratio is considerably less favorable than is the case for incompressible flow. Among others the following examples are considered: 1) lifting line with constant lift distribution (horseshoe vortex); 2) computation of wave and induced drag and the twist of a trapezoidal wing of constant lift density; 3) computation of the lift distribution and drag of an untwisted rectangular wing.

Schlichting, H↗
NASA NTRS2010

Validation of a Polyimide Foam Model for Use in Transmission Loss Applications

The work described in this paper was focused on the use of a new polyimide foam in a double wall sound transmission loss application. Recall that polyimide foams are functionally attractive, compared to polyurethane foams, for example, owing to their fire resistance. The foam considered here was found to have a flow resistivity that was too high for conventional acoustical applications, and as a result, it was processed by partial crushing to lower the flow resistivity into an acceptable range. Procedures for measuring the flow resistivity and Young s modulus of the material have been described, as was an inverse characterization procedure for estimating the remaining Biot parameters based on standing wave tube measurements of transmission loss and absorption coefficient. The inverse characterization was performed using a finite element model implementation of the Biot poro-elastic material theory. Those parameters were then used to predict the sound transmission loss of a double panel system lined with polyimide foam, and the predictions were compared with full-scale transmission loss measurements. The agreement between the two was reasonable, especially in the high and low frequency limits; however, it was found that the SEA model resulted in an under-prediction of the transmission loss in the mid-frequency range. Nonetheless, it was concluded that the performance of polyimide foam could be predicted using conventional poro-elastic material models and that polyimide foam may offer an attractive alternative to other double wall linings in certain situations: e.g., when fire resistance is a key issue. Future work will concentrate on reducing the density of the foam to values similar to those used in current aircraft sidewall treatments, and developing procedures to improve the performance of the foam in transmission loss applications.

Hong, Kwanwoo↗