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Material Model Testing in the DYNA3D Code: Material Models 1 through 5

This report is the first volume in an effort to study the material model implementations in DYNA3D, using the latest developmental version of the code. Input files were derived from a template supplied by Jerry Lin to perform an equation-of-state study. Most of the simulations use 10 cubes, each 1 cm on a side with a density of 8.03 (steel). Each of the cubes tests a different aspect of the material model. The first three cubes are testing normal stresses and normal strains (uniaxial stresses and strains) placed on the cube parallel to the x-axis, y-axis and z-axis, respectively. The x (or y or z) = 1 face of the cube is moved along the x-axis (or y-axis or z-axis) to test the model, while the opposite side remains in the x (or y or z) = 0 plane. For some of the tests, the nodes are free to move perpendicular to the applied strain to allow the cross-sectional area of the cube to change in response to being placed under pressure or tension (to test Poisson’s Ratio), while in others the nodes are frozen to eliminate dynamic effects resulting from the code. The cube is placed in tension along the axis being tested and then released, followed by a cycle of compression and release. This tension/compression cycle is repeated 3 more times. The additional cycles allow for the model to be tested under different loads. For these calculations, the amount by which the cube is stretched and compressed is varied from cycle to cycle to allow testing of model features. Cubes number 4 and 5 are intended to test xy shear stresses/strains. This is done by sliding one face of the cube in its plane parallel to the axis of interest. For example, for cube 4, the upper face of the cube is slid in the y=1 plane in a direction parallel to the x-axis (so there are no changes in the y and z coordinates of the points in the plane) and then returned to its starting position. This preserves the volume of the cube, so there is no change in density or pressure. The cycle is repeated 8 times. For cube 5, the plane of the cube satisfying x=1 is slid in this plane in a direction parallel to the y-axis and then returned to its starting position. This preserves the volume of the cube, so there is no change in density or pressure. The cycle is repeated 8 times. Cubes number 6 through 9 repeat these tests for yz shear stresses/strains (Cubes 6 and 7) and zx shear stresses and strains (Cubes 8 and 9). For reasons discussed in the next paragraph, it is unclear if these tests represent a state of pure shear stress and shear strain in the code. Application of shear stresses and strains should not, in general, result in the appearance of normal stresses and strains in Cubes 4 - 9. In the infinitesimal limit, this result might be obtained. However, DYNA3D is a finite deformation code and in the real deformations used in the code, this result is not achieved and the individual components of the normal stresses and strains are non-zero during the cycling. However, the sums of the normal strains are zero in these tests and, except in the case of thermally dependent models, so are the sums of the normal stresses. Cube 10 tests the response of the material model to a hydrostatic loading of the cube. The load curve used for the first three tests is used again and applied to each of the 8 nodes in a manner causing the cube to be either compressed or expanded. This compression/tension cycle is repeated 4 times. The additional cycles allow for the model to be tested under different loads. The amount by which the cube is stretched and compressed is varied from cycle to cycle to allow testing of model features. This document will discuss the testing of Material Models 1 through 5. Relevant results from the test cubes will be discussed. A discussion of the results from all 10 test cubes will be presented only if necessary.

36 MATERIALS SCIENCE↗

NH 4 OH Looping with Membrane CO 2 Absorber and Distributed Stripper for Enhanced Algae Growth

The University of Kentucky Center for Applied Energy (UK CAER) has devised a unique, integrated CO2 capture and utilization technology. CO2 from coal-fired power generation flue gas is first captured at half the operating cost of a typical aqueous CO2 capture system (CCS), distributed in an aqueous stream and then fixed by algae in bioreactors where the algae production is increased by 50% over that with a typical intermittent nutrient feeding system. Lower CCS operating cost is achieved by eliminating the flue gas pretreatment step for cooling and SO2 removal, eliminating steam extraction from the power generation steam cycle for solvent regeneration, and eliminating CO2 compression. Higher algae production is achieved by continuous, just-in-time nutrient feed to the bioreactors directly from a distributed solvent regenerator, which maintains the bioreactor pH for optimum growth. The process starts with a uniquely configured membrane absorber, where the flue gas is indirectly contacted with an ammonium hydroxide (NH4OH) solvent. Dissolved NH3 is attractive for both CO2 capture and as an algae nutrient. For CO2 capture it is inexpensive, has a low regeneration energy, is thermally- and oxidatively-stable and has a viscosity near that of water, which makes is easy to transport. Numerous studies have shown that the scrubbing capacity of NH3 is approximately 0.9-1.2 kg of CO2/kg of NH3, with a CO2 removal efficiency of ~99% and half the solvent regeneration energy than that of 30 wt% MEA[1, 2, 3]. NH3 is attractive as an algae nutrient due to its low cost. The rich NH4OH solvent is pumped to a set of distributed regenerators which are co-located with the algae bioreactors. Solvent pumping, transport and distribution reduces the balance of plant (BOP) cost compared to a typical aqueous CCS related to the flue gas duct and boost fan required to transport the flue gas. The energy required for the distributed solvent regeneration is supplied by solar-thermal panels eliminating the need for steam extraction from the power generation steam cycle. After solvent regeneration, the product stream contains both the CO2 captured from the flue gas and volatized NH3 from the solvent. This product stream is fed directly to the bioreactors, eliminating the need for compression of the CO2 stream. The relative amounts of CO2 and NH3 in the product stream are adjusted and controlled by a controlling the regeneration conditions (pressure and temperature). The continuous feed of the right ratio of nutrients overcomes the typical inhibition of algae growth resulting from frequent pH swings in the bioreactor due to unbalanced (intermittent) feeding systems for CO2 and N. Also, because the regenerators will operate at pressure and be located in close proximity to the bioreactors, there is no worry about pressure drop when sparging the gas into the algae. Sparging produces small bubbles which is beneficial for mass transfer efficiency. One known challenge when using an NH4OH solvent is high NH3 emission. Hydrophobic membranes are used for CO2 capture using an aqueous NH3 solution[4, 5] without the direct contact between flue gas and aqueous solution. Additionally, UK CAER CO2 capture and utilization process manages NH3 slip in three extra measures. First, NH3 slip is minimized by working with minimal species partial pressure, which is proportional to the concentration in the liquid. Hence, lowering the capture solvent concentration will lower the NH3 partial pressure. Second, UK CAER’s previous work has demonstrated that the addition of Zn2+ into NH3 solutions to chelate the NH3 can reduce NH3 volatility. Third, the configuration of the membrane CO2 absorber utilizes condensed water from the flue gas to continually wash the gas-side of the membrane to reduce fouling and recapture NH3 slip. Additional details about the UK CAER unique, integrated CO2 capture and utilization technology will be presented along with technology development plans. Diao, N., Q. Li, and Z. Fang. 2004. Heat transfer in ground heat exchangers with groundwater advection. International Journal of Thermal Sciences. 43: 1203-1211, He, Q., M. Chen, L. Meng, K. Liu, and W. Pan. 2004. Study on Carbon Dioxide Removal from Flue Gas by Absorption of Aqueous Ammonia. Western Kentucky University. Yeh, A.C., and H. Bai. 1999. Comparison of ammonia and monoethanolamine solvents to reduce CO2 greenhouse gas emissions. The Science of the Total Environment. 228: 121-133, Villeneuve, K., D. Roizard, J.C. Remigy, M. Iacono, and S. Rode. 2018. CO2 capture by aqueous ammonia with hollow fiber membrane contactors: Gas phase reactions and performance stability. Separation and Purification Technology, 199: 189-197, Toro Molina, C., and C. Bouallou. 2016. Carbon dioxide absorption by ammonia intensified with membrane contactors. Clean Techn Environ Policy 18, 2133–2146 (2016)

20 FOSSIL-FUELED POWER PLANTS↗

Possible flow regimes of adiabatic one-dimensional compressible fluid flow with friction in convergent and divergent ducts.

An analytical solution for the compressible one-dimensional flow in convergent and divergent ducts with friction is obtained. It is found that a nondimensional parameter, N, can be formed using the friction factor, duct half-angle and the ratio of specific heats of the gas. Seven flow regimes are describable with the solution, based on certain bounds on the magnitude of N. The regimes are discussed and corollary data are presented graphically.

Shouman, A. R.↗

Effect of Subsonic Inlet Lip Geometry on Predicted Surface and Flow Mach Number Distributions

The effect of subsonic inlet lip geometry on predicted surface and flow Mach number distributions is illustrated. The theoretical results were obtained from incompressible potential flow calculations corrected for compressibility. The major emphasis of this investigation is on the low-speed (takeoff and landing) operating conditions. The low-speed results were obtained for a range of three geometric variables of interest: contraction ratio, defined as the ratio of highlight area to throat area; internal lip major - to minor-axis ratio; and internal lip shape. The low-speed results were obtained at both static conditions and a free-stream velocity of 42.6m/sec, with incidence angles ranging from 0 deg to 50 deg. The results indicate that of the three geometric variables considered, contraction ratio had the largest effect on the surface Mach number distributions. The effects of inlet diameter ratio and blunting of the external forebody on maximum external surface Mach numbers are illustrated at a cruise Mach number of 0.8.

Albers, J. A.↗

Hypersonic aerodynamic characteristics of a family of power-law, wing body configurations

The configurations analyzed are half-axisymmetric, power-law bodies surmounted by thin, flat wings. The wing planform matches the body shock-wave shape. Analytic solutions of the hypersonic small disturbance equations form a basis for calculating the longitudinal aerodynamic characteristics. Boundary-layer displacement effects on the body and the wing upper surface are approximated. Skin friction is estimated by using compressible, laminar boundary-layer solutions. Good agreement was obtained with available experimental data for which the basic theoretical assumptions were satisfied. The method is used to estimate the effects of power-law, fineness ratio, and Mach number variations at full-scale conditions. The computer program is included.

Townsend, J. C.↗

Buckling and Failure of Compression-Loaded Composite Cylindrical Shells With Geometric and Material Imperfections

The results of an experimental and numerical study of the effects of initial imperfections on the buckling response and failure of unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells are presented. The shells considered in the study have six different orthotropic or quasi-isotropic shell-wall laminates and two different shell-radius-to-thickness ratios. The numerical results include the effects of geometric shell-wall mid-surface imperfections, shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform end loads, and the effects of elastic boundary conditions. Selected cylinder parameter uncertainties were also considered. Results that illustrate the effects of imperfections and uncertainties on the nonlinear response characteristics, buckling loads and failure the shells are presented. In addition, a common failure analysis is used to predict material failures in the shells.

Hilburger, Mark W.↗

Effects of Different R ratios on Fatigue Crack Growth in Laser Peened Friction Stir Welds

The influence of laser peening on the fatigue crack growth behavior of friction stir welded (FSW) Aluminum Alloy (AA) 7075-T7351 sheets was investigated. The surface modification resulting from the peening process on the fatigue crack growth of FSW was assessed for two different R ratios. The investigation indicated a significant decrease in fatigue crack growth rates resulting from using laser shock peening compared with unpeened, welded and unwelded specimens. The slower fatigue crack growth rate was attributed to the compressive residual stresses induced by the peening.

Hatamleh, Omar↗

Probing the Energetic Particle Environment near the Sun

NASA’s Parker Solar Probe mission1 recently plunged through the inner heliosphere of the Sun to its perihelia, about 24 million kilometres from the Sun. Previous studies farther from the Sun (performed mostly at a distance of 1 astronomical unit) indicate that solar energetic particles are accelerated from a few kiloelectronvolts up to near-relativistic energies via at least two processes: ‘impulsive’ events, which are usually associated with magnetic reconnection in solar flares and are typically enriched in electrons, helium-3 and heavier ions2, and ‘gradual’ events3,4, which are typically associated with large coronal-mass-ejection-driven shocks and compressions moving through the corona and inner solar wind and are the dominant source of protons with energies between 1 and 10 megaelectronvolts. However, some events show aspects of both processes and the electron–proton ratio is not bimodally distributed, as would be expected if there were only two possible processes5. These processes have been very difficult to resolve from prior observations, owing to the various transport effects that affect the energetic particle population en route to more distant spacecraft6. Here we report observations of the near-Sun energetic particle radiation environment over the first two orbits of the probe. We find a variety of energetic particle events accelerated both locally and remotely including by corotating interaction regions, impulsive events driven by acceleration near the Sun, and an event related to a coronal mass ejection. We provide direct observations of the energetic particle radiation environment in the region just above the corona of the Sun and directly explore the physics of particle acceleration and transport.

D J Mccomas↗

Determining Compression Characteristics of Honeycomb Material - 19674

The objective is to determine compression test characteristics of stainless steel honeycomb material to be able to represent honeycomb structures accurately in analytical models used to simulate hypothetical accident scenarios of shipping packages. Honeycomb is a material used primary in the aerospace industry due to its high strength-to-weight ratio. Because it doesn't have a shelf life and can withstand high heats, it is an excellent candidate for a structural material in package designs. Honeycomb has orthotropic material properties. The honeycomb currently being evaluated is made of metal ribbons spot welded together to form hexagon pattern between metal plates. The hexagon ribbons are brazed to the metal plates. The complexity of the honeycomb significantly lengthens the simulation time, which is further complicated when the brazing, welding, and imperfections of the material is considered. This means to affectively represent the honeycomb in simulation programs, such as Abaqus, the material needs to be approximated as a uniform orthotropic material. This requires material properties in each of the three directions, T, W, and L. The T direction is defined as the 'strong' direction, perpendicular to the honeycomb sheet. The L direction is parallel the ribbon and the W direction is perpendicular to the ribbon. Honeycomb has 3 different compression stages. Stage 1 is the initial compression where the honeycomb maintains its structural integrity and does not permanently deform from loads from normal operations. Stage 2 is when the initial buckling causes irreversible damage to the honeycomb. Stage 2 is the one we are most interested in because it absorbs the most energy from a hypothetical accident scenario. During Stage 2, the honeycomb fails layer-by-layer, indicating that the more layers, the longer material crushing is sustained, and thus the more energy that is absorbed. Stage 3 is final compression, similar to compressing solid metal. During stage 3 the stress increases with a diminishing rate of elongation and the honeycomb is completely failed where the plates between the honeycomb core sandwich the crushed honeycomb ribbon. The stress-strain graph bellow shows compression test of 3 different samples in the T direction. The red lines divide the three stages. The far left is Stage 1, the middle stage 2, and the right stage 3. The data collected is displayed in the table below. The expressions in the table represent the regression formula that represents each stage of the compression on a stress-strain graph. Stage 1 is assumed to intersect with the origin; data for stage 3 for the crush in W and L directions where unable to be gathered due to the nature of failure for those directions. Stage 1 and 2 are linear regressions while stage 3 is a degree 2, to best match the curve. Linear regression is used on stage 2 because ultimately that represents the energy absorbed. With more data, a degree n x 2 regression would be a more appropriate regression for stage 2, where n is the number of layers. The table below is the approximation of each scenario and stage. Each stage starts and ends at the intersection of the next stage. There where two main objectives for these tests: firstly to understand how honeycomb performs under extreme compression, and secondly to be able to numerically represent the honeycomb structure. Both of these where completed to varying degrees. It is important understood how the honeycomb fails. If it is crushed in the T direction it retains its integrity even after being crushed, however when crushed in the L and W crush direction, if it fails, it disintegrates, and loses all integrity. Also, the more layers the more time the material spends in stage 2. Failure is started by buckling, thus if there is any imperfection, the stress will not spike but transition straight into stage 2. The data collected and aggregated can be used for initial simulation of honeycomb used in packages. The initial testing has set the ground work for more data to be collected in order to verify results and to allow more confidence in the simulation results. This is only the initial data collected. The next steps is to continue to collect more data to verify results and to test more variants of honeycomb, with different brazing, layers, and shape.

36 MATERIALS SCIENCE↗

A computational parametric study of three-dimensional sidewall compression scramjet inlets at Mach 10

A computational parametric study of three-dimensional sidewall compression scramjet inlets has been performed. The parameters considered for the study include the leading edge sweep angle, varied between 30 and 60 degrees, and the cowl position, located at the throat and at two forward positions. Additionally, the effects of laminar and turbulent boundary layers as well as adiabatic and cold wall boundary conditions are assessed. The parametric study is performed for a Mach number of 10 and a unit freestream Reynolds number of 2 x 10 to the 6th/ft at a geometric contraction ratio of 5. Comparisons among the various configurations are made in terms of the gross parameters of mass capture, throat Mach number, total pressure recovery, and area weighted internal pressure ratios, as well as more detailed flow field phenomena comparisons. The inclusion of one 0-deg sweep computation indicates that the leading edge may be swept by up to 30 deg before significant changes in the gross flow field parameters occur. It is found that a 45-deg sweep configuration provides a good compromise of mass capture, total pressure recovery, and internal compression.

Holland, Scott D.↗

Full load testing in the platform module prior to tow-out: A case history of subsynchronous instability

An electric motor driven centrifugal compressor to supply gas for further compression and reinjection on a petroleum production platform in the North Sea was examined. The compressor design, raised concerns about susceptibility to subsynchronous instability. Log decrement, aerodynamic features, and the experience of other compressors with similar ratios of operating to critical speed ratio versus gas density led to the decision to full load test. Mixed hydrocarbon gas was chosen for the test to meet discharge temperature restrictions. The module was used as the test site. Subsynchronous vibrations made the compressor inoperable above approximately one-half the rated discharge pressure of 14500 kPa. Modifications, which includes shortening the bearing span, change of leakage inlet flow direction on the back to back labyrinth, and removal of the vaned diffusers on all stages were made simultaneously. The compressor is operating with satisfactory vibration levels.

Fulton, J. W.↗

Failure modes for compression loaded angle-ply plates with holes

A combined theoretical-experimental investigation of failure in notched, graphite-epoxy, angle-ply laminates subjected to far-field compression loading indicates that failure generally initiates on the hole boundary and propagates along a line parallel to the fiber orientation of the laminate. The strength of notched laminates with specimen width-to-hole diameter ratios of 5 and 10 are compared to the strength of unnotched laminates. The experimental results are complemented by a three-dimensional finite element stress analysis that includes interlaminar stresses around holes in (+/- theta)s laminates. The finite element predictions indicate that failure is initiated by shear stresses at the hole boundary.

Burns, S. W.↗

Extrusion-based Additive Manufacturing of Regolith-Filled Shape Memory Vitrimer Composite for Lunar Construction

The National Aeronautics and Space Administration (NASA) is visiting the moon again. This time, the objective is to explore establishing a permanent lunar base. To achieve both longterm human habitation on the moon and future deep space travel, it is crucial to make the most of the in-situ resources and build autonomous systems on the moon to support the construction of a lunar habitat. NASA’s In-situ Resource Utilization (ISRU) program aims to minimize the need to ship heavy prefabricated structures, reducing cost and enhancing sustainability. Here, we developed an economical extrusion method for printing lunar regolith-based composites using shape memory vitrimer as a binder. A rheological study is conducted to determine the extrudability of the composite with different regolith weight percentages. Several characterizations were conducted on the composites. The as-printed composites exhibited compressive and flexural strengths of 73.32 MPa and 156.59 MPa, respectively, and good impact tolerance. The composite maintained 57.92% of its mechanical properties even after the second crack healing cycle. The composites also exhibit shape fixity ratio of 90.02% and shape recovery ratio of 83.46%. The simple synthesis method, sustainability, and good thermomechanical properties make the 3D printed composite an ideal material for lunar construction applications.

Kingsley Yeboah Gyabaah↗

Tailored Synthesis of the Narrowest Zigzag Graphene Nanoribbon Structure by Compressing the Lithium Acetylide under High Temperature

Scientists are searching for the goal-directed methods to synthesize graphene nanoribbons (GNRs) with a particular edge type and width, which determines their electronic transport properties. A series of Li zigzag GNRs (ZGNRs) with different widths were predicted under high pressure with a stoichiometric ratio of Li n +1 C 2 n , which indicates a route to prepare ultranarrow GNRs. Here, with thermodynamics and ab initio Gibbs free-energy calculations by quasi-harmonic approximation, we investigated the phase stabilities of the Li GNR compounds under high pressure and high temperature. We have also identified Li graphenide LiC 2 ( n = ∞) and Li polyacenide Li 3 C 4 (n = 2) experimentally at the predicted pressure and temperature conditions using in situ X-ray diffraction, which can be recognized as the two end members of Li n +1 C 2 n , with the widest and narrowest ZGNR structures. High temperature and the temperature gradient increased the degree of polymerization and facilitated the formation of wider GNR or carbon slices. Furthermore, this suggests that by controlling temperature and pressure, we may get ultranarrow Li ZGNRs composed of a limited number of parallel carbon chains, such as 3- or 4-zigzag GNR, which is ready to be protonated or functionalized to form atomically ordered ZGNRs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling and Characterization of Geometric Effects on the Performance of Rainbow and Thunder Actuators

Dome formation in Rainbow and Thunder actuators occurs to relieve thermal expansion mismatch stress between the metallic and piezoelectric layers during cooling from device fabrication temperatures. Accompanying this process is the generation of an internal stress profile within the devices and the development of significant tensile stresses within the surface region of the piezoelectric. These tensile stresses affect the domain configuration (ratio of c-to-a domains), and improve the 90 deg. domain wall movement response of the device in this region of the piezoelectric. This results in improved electromechanical performance compared to standard direct extensional and flextensional devices, presumably because of the contributions of stress to the non-linearity of the piezoelectric d-coefficients. 1 Interestingly, this improvement in response seems counterintuitive; a stress perpendicular to the direction of the applied electric field should impede, not contribute to 90' domain switching. Further consideration of the lower region of the piezoelectric that is under compressive stress thus appears warranted. The specified objectives of the research were to: 1. Conduct finite element and equivalent circuit simulation-based investigations to understand the effects of actuator geometry on internal stress distribution and actuator performance (displacement and load-bearing capabilities). 2. Use the results of the modeling studies to predict the processing conditions (geometry and thickness ratio) required for the fabrication of Rainbow ceramics with optimized performance.

Schwartz, Robert W.↗

Pulsating one-dimensional detonation in ammonia-hydrogen–air mixtures

In this study, one-dimensional detonations in ammonia/hydrogen-air mixtures are numerically investigated by solving the fully compressible Navier-Stokes equations with detailed chemistry. Pulsating instabilities with single-mode are observed during the detonation wave propagation, accompanied by periodic coupling and decoupling of the lead shock wave and the reactive front. The ratio between driver pressure and initial pressure determines the overdrive degree and thus the oscillatory mode of detonation for a premixture with certain composition. The effects of hydrogen dilution and mixture equivalence ratio on pulsating detonations are also examined under a constant driver pressure. The growing hydrogen fraction in fuel blends significantly increases the oscillation frequency. In addition, the pulsating detonation frequency rises with increasing equivalence ratio under fuel-lean conditions, peaks under stoichiometric conditions, and falls under fuel-rich conditions as the equivalence ratio increases further. Evolutions of reactants, main intermediate radicals, and products are analysed in both fuel-lean and fuel-rich conditions. A chemical explosive mode analysis further confirms the highly-autoignitive nature of the mixture in the induction zone between reaction front and shock front where thermal diffusion plays a negligible role.

08 HYDROGEN↗

Valley-Tunable Even-Denominator Fractional Quantum Hall State in the Lowest Landau Level of an Anisotropic System

Fractional quantum Hall states (FQHSs) at even-denominator Landau level filling factors (v) are of prime interest as they are predicted to host exotic, topological states of matter. Here, we report here the observation of a FQHS at v = 1/2 in a two-dimensional electron system of exceptionally high quality, confined to a wide AlAs quantum well, where the electrons can occupy multiple conduction-band valleys with an anisotropic effective mass. The anisotropy and multivalley degree of freedom offer an unprecedented tunability of the v = 1/2 FQHS as we can control both the valley occupancy via the application of in-plane strain, and the ratio between the strengths of the short- and long-range Coulomb interaction by tilting the sample in the magnetic field to change the electron charge distribution. Thanks to this tunability, we observe phase transitions from a compressible Fermi liquid to an incompressible FQHS and then to an insulating phase as a function of tilt angle. We find that this evolution and the energy gap of the v = 1/2 FQHS depend strongly on valley occupancy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Transonic flutter study of a 50.5 deg cropped-delta wing with two rearward-mounted nacelles

Transonic flutter characteristics of three geometrically similar delta-wing models were experimentally determined in the Langley transonic dynamics tunnel at Mach numbers from about 0.6 to 1.2. The models were designed to be simplified versions of an early supersonic transport wing design. The model was an aspect-ratio-1.28 cropped-delta wing with a leadingedge sweep of 50.5 deg. The flutter characteristics obtained for this wing configuration indicated a minimum flutter-speed index near a Mach number of 0.92 and a transonic compressibility dip amounting to about a 27-percent decrease in the flutter-speed index relative to the value at a Mach number of 0.6. Analytical studies were performed for one wing model at Mach numbers of 0.6, 0.7, 0.8, and 0.9 by using both doublet-lattice and lifting-surface (kernel-function) unsteady aerodynamic theory. A comparison of the analytical and experimental flutter results showed good agreement at all Mach numbers investigated.

Sandford, M. C.↗