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At least 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Analysis of JP-4 fire test data and development of a simple fire model

A series of field experiments involving JP-4 fires of 7.6m dia and 15.2m dia was conducted under the sponsorship of NASA. The temperature inside the fire, the specie composition and vertical axial velocity were measured at several height locations and radial positions. The peak temperature recorded is 1400-1500 K; the velocities at 6m height are 11-12 m/s. The oxygen-to-nitrogen mass ratio along the vertical axis was found to be nearly a constant at 0.05. Significant necking of the fire was observed. A simple theoretical model was developed that predicts the experimental data on the velocity and vertical temperature distribution well. The model is based on the partial combustion of entrained air and assumed top-hat distributions for various property and flow parameters inside the fire. Quantitative agreement is obtained by using a value of 0.15 for the entrainment coefficient and 0.45 for the mixing efficiency factor. The model also predicts the fire necking.

Raj, P. K.↗
NASA NTRS1990

Frequency response of a thermocouple wire: Effects of axial conduction

Theoretical expressions are derived for the steady-state frequency response of a thermocouple wire. In particular, the effects of axial heat conduction are demonstrated for both a uniform thermocouple wire and a nonuniform wire with unequal material properties and wire diameters across the junction. For the case of a uniform wire, the amplitude ratio and phase angle compare favorably with the series solution of Scadron and Warshawsky (1952) except near the ends of the wire. For the case of a non-uniform wire, the amplitude ratio at low frequency omega yields 0 agrees with the results of Scadron and Warshawsky for a steady-state temperature distribution. Moreover, the frequency response for a non-uniform wire in the limit of infinite length l yields infinity is shown to reduce to a simple expression that is analogous to the classic first order solution for a thermocouple wire with uniform properties.

Forney, L. J.↗
NASA NTRS2001

Development and Validation of High Performance Unshrouded Centrifugal Impeller

The feasibility of using a two-stage unshrouded impeller turbopump to replace the current three-stage reusable launch vehicle engine shrouded impeller hydrogen pump has been evaluated from the standpoint of turbopump weight reduction and overall payload improvement. These advantages are a by-product of the higher tip speeds that an unshrouded impeller can sustain. The issues associated with the effect of unshrouded impeller tip clearance on pump efficiency and head have been evaluated with one-dimensional tools and full three-dimensional rotordynamic fluid reaction forces and coefficients have been established through time dependent computational fluid dynamics (CFD) simulation of the whole 360 degree impeller with different rotor eccentricities and whirling ratios. Unlike the shrouded impeller, the unshrouded impeller forces are evaluated as the sum of the pressure forces on the blade and the pressure forces on the hub using the CFD results. The turbopump axial thrust control has been optimized by adjusting the first stage impeller backend wear ring seal diameter and diverting the second stage backend balance piston flow to the proper location. The structural integrity associated with the high tip speed has been checked by analyzing a 3D-Finite Element Model at maximum design conditions (6% higher than the design speed). This impeller was fabricated and tested in the NASA Marshall Space Flight Center water-test rig. The experimental data will be compared with the analytical predictions and presented in another paper. The experimental data provides validation data for the numerical design and analysis methodology. The validated numerical methodology can be used to help design different unshrouded impeller configurations.

Chen, Wei-Chung↗
NASA NTRS2007

Coronal Heating, Weak MHD Turbulence, and Scaling Laws

Long-time high-resolution simulations of the dynamics of a coronal loop in Cartesian geometry are carried out, within the framework of reduced magnetohydrodynamics (RMHD), to understand coronal heating driven by the motion of field lines anchored in the photosphere. We unambiguously identify MHD anisotropic turbulence as the physical mechanism responsible for the transport of energy from the large scales, where energy is injected by photospheric motions, to the small scales, where it is dissipated. As the loop parameters vary, different regimes of turbulence develop: strong turbulence is found for weak axial magnetic fields and long loops, leading to Kolmogorov-like spectra in the perpendicular direction, while weaker and weaker regimes (steeper spectral slopes of total energy) are found for strong axial magnetic fields and short loops. As a consequence we predict that the scaling of the heating rate with axial magnetic field intensity B, which depends on the spectral index of total energy for given loop parameters, must vary from B3/2 for weak fields to B2 for strong fields at a given aspect ratio. The predicted heating rate is within the lower range of observed active region and quiet-Sun coronal energy losses.

corona↗
NASA NTRS1999

MRI Measurements and Granular Dynamics Simulation of Segregation of Granular Mixture

A counter intuitive axial segregation phenomenon in a rotating horizontal cylinder has recently captured attention of many researchers in different disciplines. There is a growing consensus that the interplay between the particle dynamics and the evolution of the internal structure during the segregation process must be carefully investigated. Magnetic resonance imaging (MRI) has been used to non-invasively obtain much needed dynamic/static information such as velocity and concentration profiles, and it has proven to be capable of depicting the evolution of segregation processes. Segregation in a rotating cylinder involves two processes: the first is to transport small particles in the radial direction to form a radial core, and the second is to transform the radial core into axially segregated bands. Percolation and/or "stopping" have been proposed as mechanisms for the radial segregation. As to mechanisms for axial band formation, much less is known. The difference in the dynamic angle of repose has been proposed to segregate different components in the axial direction. Recently, Hill and Kakalios have reported that particles mix or demix depending upon the competition between diffusion and preferential drift whose order can be determined by the dynamic angle of repose through the adjustment of the rotation rate. We claim that the dynamic angle of repose could be one of the causes, however, it fails to offer reasonable explanations for certain aspects of the axial migration. For example, we always observe that the radial segregation precedes the axial segregation and small particles migrate in the radial direction to form an axially extended radial core. It then transforms into axially segregated bands. By definition, the effects of the dynamic angle of repose are restricted near the free surface where the flowing layer is present. However, during the process of transforming from the radially segregated core to axially segregated bands, small particles located in the deep core region, which is untouched by the flowing layer, also completely disappear. Usually, the dynamics angle of repose are uniquely defined for individual species to characterize particle properties, and the dynamic angle of repose thus defined provides little information for the dynamic angle of repose of the mixture since the concentration ratio and the internal packing structure do not remain the same during the segregation processes. Under microgravity environment, the dynamics angle of repose argument does not hold since there is simply no flowing layer to influence/determine the preferred directions of segregation. We have thus designed an experiment so that the effects of the dynamic angle of repose can be minimized by filling the cylinder almost completely full. Small particles still formed a radial core and also migrated to form axial bands. As ground based experiments we have designed and conducted both 2D and 3D segregation experiments. The 2D experiments are performed using a thin cylinder (the gap between two end caps is about 5 mm) filled with different combinations of particles. The 3D experiments are conducted with a long cylinder of its length and diameter of 27cm and 7cm, respectively. Results of 2D experiments indicate that different mechanisms govern particle motion in regions near and far from the axis of rotation. Results of 3D experiments indicate that a series of collapses of microstructures of particle packing (micro-collapses) may be responsible for the creation of voids for small particles to migrate through in the axial direction. We have successfully eliminated the dynamic angle of repose as a cause for segregation, however, by almost completely filling the cylinder with the particles, we have lost an opportunity to investigate a possibility of particle "mobility" being a cause for segregation which requires a flowing surface but not the difference in the angle of repose. This is currently being investigated.

Nakagawa, M.↗
NASA NTRS2012

Cassegrain Solar Concentrator System for ISRU Material Processing

A 0.5 m diameter Cassegrain concentrator was constructed as a means of providing highly concentrated sunlight for the demonstration processing of lunar simulated regolith and other NASA In-Situ Resource Utilization Project (ISRU) reaction processes. The concentrator is constructed of aluminum with a concentration ratio of approximately 3000 to 1. The concentrator focuses solar energy into a movable tray located behind the concentrator. This tray can hold simulated regolith or any other material and or device to be tested with concentrated solar energy. The tray is movable in one axis. A 2-axis extended optical system was also designed and fabricated. The extended optical system is added to the back of the primary concentrator in place of the moveable test tray and associated apparatus. With this optical system the focused sunlight can be extended from the back of the primary concentrator toward the ground with the added advantage of moving the focal point axially and laterally relative to the ground. This allows holding the focal point at a fixed position on the ground as the primary concentrator tracks the sun. Also, by design, the focal point size was reduced via the extended optics by a factor of 2 and results in a concentration ratio for the system of approximately 6,000 to 1.The designs of both optical systems are discussed. The results from simulated regolith melting tests are presented as well as the operational experience of utilizing the Cassegrain concentrator system.

Colozza, Anthony J.↗
NASA NTRS2017

Impact of Wake Dispersion on Axial Compressor Performance

Rotor wake dispersion in a low-speed, one and half stage axial compressor is investigated in detail with a Large Eddy Simulation (LES). The primary focus is to quantify the total pressure recovery due to wake stretching and the total pressure loss from the rotor wake interaction with the stator blade boundary layer. The relative magnitude of the aerodynamic loss due to these two effects is examined at several radial locations. The spacing between the rotor and the stator was varied from 29% to 112% of the rotor axial chord at the mid span to investigate the effects of rotor wake decay before entering the stator passage. The current analysis indicates that the efficiency through the compressor stage is increased about 0.5% when the spacing between the rotor and the stator is decreased from 112% to 29% of the rotor axial chord at mid-span. 22% of the efficiency gain from the narrower axial gap is due to the wake recovery and 63% is due to the stronger unsteady pressure field at the exit of the rotor due to stage interaction. Total pressure loss/recovery across the stator varies significantly in the radial direction for the current compressor, which has a much lower aspect ratio. The total pressure recovery due to wake stretching is larger than the total pressure loss due to the unsteady boundary layer development on the stator blade from 20% to 35% of the span from the hub for 29% spacing and from 35% to 55% of the span for 112% spacing. Above 50% of the span, rotor tip clearance flow affects wake dispersion and the overall wake recovery is less than expected.

Axial Compressor↗
DOE OSTI2023

Efficient Thermal Energy Storage with Radial Flow in Packed Beds

Thermal energy storage (TES) is a way to store excess heat in order to generate power later. These types of systems are valuable in the solar industry, where power production can still occur when sunlight is not available. This not only increases system flexibility, it drives down the cost of electricity. One option to store thermal energy is with a packed bed where the storage media resides in a cylindrical container. Flow from one end of the cylinder to the other deposits or recovers heat (axial flow). While a promising technology in terms of energy storage, it exhibits a high pressure drop that lowers overall system efficiency. This project seeks to flow the heat transfer fluid through the storage media in the radial direction. This system offers the potential to retain reasonable thermal performance while substantially lowering the pressure drop. The overall goal was to assess the performance of radial flow experimentally and numerically. Three main designs were considered in this work. The first system utilized a central pipe and four receiving pipes near the wall. The second system utilized a central pipe and an annulus with holes near the wall. The last approach considered segmenting the bed so only select zones would receive flow in the radial direction. In a high-aspect ratio system, the hole patterns in the piping are important for ensuring even flow into the bed, and a major design effort was testing holes patterns to promote even flow. The four pipe system was shown to be not feasible, as preferential flow paths occur that do not allow even and full heating of the packed bed. The annular system can lead to even flow, but the results show this is better accomplished through larger piping instead of considering variations in the hole pattern along the axial length of the pipe. Segmenting the bed can lead to similar exergetic performance when compared to axial or radial flow. However, the pressure drop in the segmented design is likely too high for practical implementation. A baseline commercial design showed exergetic efficiencies for axial, radial, and radial segments of 81.6%, 82.8%, and 80.2%, respectively. Pressure drop for the axial and radial results were 2.36 psi and 2.45 psi, respectively, with segments being nearly an order of magnitude higher. At these large scales, the aspect ratio of the system is important. From a baseline of 0.64, an aspect ratio of 0.32 for radial flow showed an exergetic efficiency of 86% but a pressure drop of 5.39 psi. All of these results provide new insights into packed bed thermal energy storage with radial flow. Competing effects must be considered when designing a radial system, and results show a radial design can show strong thermal results at the expense of system efficiencies from pressure drop. The COMSOL models used in this analysis are available to the public and other researchers. Public benefits include a potential increase in the efficiency of packed bed thermal energy storage. Higher efficiency in storage promotes green energy technologies while reducing costs.

14 SOLAR ENERGY↗
NASA NTRS1953

Analysis of Off-design Performance of a 16-stage Axial-flow Compressor with Various Blade Modifications

The over-all performance of a 16-stage axial-flow compressor was determined with various stator-blade resettings and a reduction in solidity of the rotor blades in the last three stages. It was shown that little control over the sudden change in slope of the surge-limit line at intermediate speeds was obtained with the blade modifications attempted, except that some change in speed at which the change in slope occurred could be effected by stator-blade resettings. Interstage data indicated that the severe surge limit at intermediate speeds was caused by stall of the inlet stage, which, because of stage interaction effects, resulted in a simultaneous decrease in performance of the following five or six stages. Stage data are presented which indicate the flow and pressure-ratio range over which each stage is required to operate at compressor speeds from 50 to 100 percent of design speed.

COMPRESSORS - AXIAL-FLOW↗
NASA NTRS1993

Damage tolerance of pressurized graphite/epoxy tape cylinders under uniaxial and biaxial loading

The damage tolerance behavior of internally pressurized, axially slit, graphite/epoxy tape cylinders was investigated. Specifically, the effects of axial stress, structural anisotropy, and subcritical damage were considered. In addition, the limitations of a methodology which uses coupon fracture data to predict cylinder failure were explored. This predictive methodology was previously shown to be valid for quasi-isotropic fabric and tape cylinders but invalid for structurally anisotropic (+/-45/90)(sub s) and (+/-45/0)(sub s) cylinders. The effects of axial stress and structural anisotropy were assessed by testing tape cylinders with (90/0/+/-45)(sub s), (+/-45/90)(sub s), and (+/-45/0)(sub s) layups in a uniaxial test apparatus, specially designed and built for this work, and comparing the results to previous tests conducted in biaxial loading. Structural anisotropy effects were also investigated by testing cylinders with the quasi-isotropic (0/+/-45/90)(sub s) layup which is a stacking sequence variation of the previously tested (90/0/+/-45)(sub s) layup with higher D(sub 16) and D(sub 26) terms but comparable D(sub 16) and D(sub 26) to D(sub 11) ratios. All cylinders tested and used for comparison are made from AS4/3501-6 graphite/epoxy tape and have a diameter of 305 mm. Cylinder slit lengths range from 12.7 to 50.8 mm. Failure pressures are lower for the uniaxially loaded cylinders in all cases. The smallest percent failure pressure decreases are observed for the (+/-45/90)(sub s) cylinders, while the greatest such decreases are observed for the (+/-45/0)(sub s) cylinders. The relative effects of the axial stress on the cylinder failure pressures do not correlate with the degree of structural coupling. The predictive methodology is not applicable for uniaxially loaded (+/-45/90)(sub s) and (+/-45/0)(sub s) cylinders, may be applicable for uniaxially loaded (90/0/+/-45)(sub s) cylinders, and is applicable for the biaxially loaded (90/0/+/-45)(sub s) and (0/+/-45/90)(sub s) cylinders. This indicates that the ratios of D(sub 16) and D(sub 26) to D(sub 11), as opposed to the absolute magnitudes of D(sub 16) and D(sub 26), may be important in the failure of these cylinders and in the applicability of the methodology. Discontinuities observed in the slit tip hoop strains for all the cylinders tested indicate that subcritical damage can play an important role in the failure of tape cylinders. This role varies with layup and loading condition and is likely coupled to the effects of structural anisotropy. Biaxial failure pressures may exceed the uniaxial values because the axial stress contributes to the formation of 0 deg ply splitting (accompanied by delamination) or similar stress-mitigating subcritical damage. The failure behavior of similar cylinders can also vary as a result of differences in the role of subcritical damage as observed for the case of a biaxially loaded (90/0/+/-45)(sub s) cylinder with a 12.7 mm slit. For this case, the methodology is valid when the initial coupon and cylinder fracture modes agree. However, the methodology underpredicts the failure pressure of the cylinder when a circumferential fracture path, suggestive of a 0 deg ply split, occurs at one slit tip. Thus, the failure behavior of some tape cylinders may be highly sensitive to the initial subcritical damage mechanism. Finite element analyses are recommended to determine how structural anisotropy and axial stress modify the slit tip stress states in cylinders from those found in flat plates since similarity of these stress states is a fundamental assumption of the current predictive methodology.

Priest, Stacy Marie↗
DOE OSTI2020

Neutron yield enhancement and suppression by magnetization in laser-driven cylindrical implosions

In inertial confinement fusion, an externally applied magnetic field can reduce heat losses in the compressing fuel thereby increasing neutron-averaged ion temperatures and neutron yields. Yet, magnetization is only beneficial if the magnetic pressure remains negligible compared to the fuel pressure. Experiments and three-dimensional magneto-hydrodynamic simulations of cylindrical implosions on the OMEGA laser show ion temperature and neutron yield enhancements of up to 44% and 67%, respectively. As the applied, axial magnetic field is increased to nearly 30T, both experiments and simulations show yield degradation. For magnetized, cylindrical implosions, there exists an optimal magnetic field that maximizes the increase in yield. Limiting the fuel convergence ratio by preheating the fuel can further increase the benefit of magnetization. The findings demonstrate that it is possible to create a plasma with a density of order 1 g/cm 3 and an ion temperature greater than 1 keV with a magnetic pressure comparable to the thermal pressure, a new regime for laser-produced plasmas on OMEGA.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Meissner-London Susceptibility of Superconducting Right Circular Cylinders in an Axial Magnetic Field

Analysis of magnetic susceptibility of nonellipsoidal samples is a long-standing problem in experimental studies of magnetism and superconductivity. Here the quantitative description of the Meissner-London response (no Abrikosov vortices) of right circular cylinders in an axial magnetic field is given. Three-dimensional adaptive finite-element modeling is used to calculate the total magnetic moment ( m ) in a wide range of London penetration depth ( λ ) to sample size ( a ) ratios, λ /a. Furthermore, by fitting numerical solutions, the closed-form empirical magnetic susceptibility is obtained involving only sample dimensions and λ, thus providing a recipe for determining the London penetration depth from the precision measurements of the magnetic susceptibility. Detailed protocols of the experimental data analysis using the developed approach are given. The results can be readily extended to the most frequently used cuboid-shaped samples.

3-dimensional systems↗
DOE OSTI2024

Large-Eddy Simulation Study of Flow and Combustion Dynamics in a Full-Scale Hydrogen–Air Rotating Detonation Combustor-Stator Integrated System

In the present work, a first-of-its-kind three-dimensional (3D) large-eddy simulation (LES) study is conducted to numerically investigate the combustion dynamics as well as aero-thermal phenomena in a full-scale nonpremixed hydrogen–air rotating detonation engine (RDE) (with a diverging-shaped lower-end wall), when integrated with nozzle guide vanes (NGV) acting as the turbine stator. The wall-modeled LES framework incorporates hydrogen–air detailed chemical kinetics and adaptive mesh refinement (AMR). A comparative analysis is carried out for two operating conditions with different fuel/air mass flow rates but global equivalence ratio of unity, and considering RDE configurations without and with stator. The LES model is validated against available experimental data for the low mass flux condition with respect to detonation wave speed/height, wave dynamics, and axial static pressure distribution. Numerical results indicate significant deflagrative combustion occurring in the fill region near the inner wall due to formation of recirculation zones in the injection near-field driven by the backward facing step. The leading detonation wave is found to be trailed by an azimuthal reflected-shock combustion (ARSC) wave, consistent with experimental observations, which consumes unburned vitiated reactants that leak through the main detonation wave. The main detonation wave characteristics, such as detonation wave speed/height and combustion efficiency, do not change appreciably with the presence of NGV. A novel combustion diagnostic technique based on chemical explosive mode analysis (CEMA) is employed to quantify the fraction of heat release occurring in the detonative mode versus deflagrative mode for the simulated conditions. The exit flow is found to be nearly fully subsonic and supersonic for the low and high mass flux conditions, respectively. Further analysis of the exit flow profiles shows that the presence of NGV renders the flow more axial and significantly impacts the exit Mach number and total pressure, while the total temperature shows negligible change. In addition, the low mass flux operating point, despite exhibiting more deflagrative losses within the combustor, yields overall lower pressure drop from plenum to exhaust, which is mainly attributed to lower pressure drop across the injectors. Lastly, the rotating detonation engine-nozzle guide vanes (RDE-NGV) configuration exhibits higher total pressure loss compared to rotating detonation engine (RDE) without stator across both the mass flux conditions. In conclusion, this study extends the state-of-the-art in numerical modeling of pressure gain combustion (PGC) systems by demonstrating high-fidelity 3D reacting LES of full-scale RDE-NGV systems relevant to RDE-turbine integration for stationary power generation.

Combustion↗
NASA NTRS1979

Low-turbulence high-speed wind tunnel for the determination of cascade shock losses

A low turbulence high-speed wind tunnel, using anti-turbulence screening and a 100:1 contraction ratio, has been found suitable for high-speed smoke flow visualization. The location and strength of normal, oblique, and curved shock waves generated by transonic or supersonic wind tunnel flow over airfoils or through axial compressor cascades is determined by combined shadowgraph and smokelines visualization techniques without the interference effects caused by intrusive probes. The Reynolds number based on chord varied between 50,000 and 1,000,000. Preliminary results are compared with the relevant theory and data gathered using a total pressure probe.

Slovisky, J. A.↗
NASA NTRS1990

Experimental and analytical study of close-coupled ventral nozzles for ASTOVL aircraft

Flow in a generic ventral nozzle system was studied experimentally and analytically with a block version of the PARC3D computational fluid dynamics program (a full Navier-Stokes equation solver) in order to evaluate the program's ability to predict system performance and internal flow patterns. For the experimental work a one-third-size model tailpipe with a single large rectangular ventral nozzle mounted normal to the tailpipe axis was tested with unheated air at steady-state pressure ratios up to 4.0. The end of the tailpipe was closed to simulate a blocked exhaust nozzle. Measurements showed about 5 1/2 percent flow-turning loss, reasonable nozzle performance coefficients, and a significant aftward axial component of thrust due to flow turning loss, reasonable nozzle performance coefficients, and a significant aftward axial component of thrust due to flow turning more than 90 deg. Flow behavior into and through the ventral duct is discussed and illustrated with paint streak flow visualization photographs. For the analytical work the same ventral system configuration was modeled with two computational grids to evaluate the effect of grid density. Both grids gave good results. The finer-grid solution produced more detailed flow patterns and predicted performance parameters, such as thrust and discharge coefficient, within 1 percent of the measured values. PARC3D flow visualization images are shown for comparison with the paint streak photographs. Modeling and computational issues encountered in the analytical work are discussed.

Mcardle, Jack G.↗
NASA NTRS1992

Aircraft ground test and subscale model results of axial thrust loss caused by thrust vectoring using turning vanes

The NASA-Dryden F/A-18 high alpha research vehicle was modified to incorporate three independently controlled turning vanes located aft of the primary nozzle of each engine to vector thrust for pitch and yaw control. Ground measured axial thrust losses were compared with the results from a 14.25 pct. cold jet model for single and dual vanes inserted up to 25 degs into the engine exhaust. Data are presented for nozzle pressure ratios of 2.0 and 3.0 and nozzle exit areas of 253 and 348 sq in. The results indicate that subscale nozzle test results properly predict trends but underpredict the full scale results by approx. 1 to 4.5 pct. in thrust loss.

Johnson, Steven A.↗
NASA NTRS1992

Investigation of three-dimensional flow field in a turbine including rotor/stator interaction. I - Design development and performance of the research facility

A description of the Axial Flow Turbine Research Facility (AFTRF) installed at the Turbomachinery Laboratory of the Pennsylvania State University is presented in this paper. The facility diameter is 91.66 cm (3 feet) and the hub-to-tip ratio of the blading is 0.73. The flow path consists of turbulence generating grid, 23 nozzle vane and 29 rotor blades followed by outlet guide vanes. The blading design, carried out by General Electric Company personnel, embody modern HP turbine design philosophy, loading and flow coefficient, reaction, aspect ratio, and blade turning angles; all within the current aircraft engine design turbine practice. State-of-the-art quasi-3D blade design techniques were used to design the vane and the blade shapes. The vanes and blades are heavily instrumented with fast response pressure, shear stress, and velocity probes and have provision for flow visualization and laser Doppler anemometer measurement. Furthermore, provision has been made for detailed nozzle wake, rotor wake and boundary layer surveys. A 150 channel slip ring unit is used for transmitting the rotor data to a stationary instrumentation system. All the design objectives have been met.

Lakshminarayana, B.↗
NASA NTRS1941

Tests on Stiffened Circular Cylinders

Compressive tests were made of two series of stiffened circular cylindrical shells under axial load. All the shells were 16 inches in diameter by 24 inches in length and were made of aluminum-alloy sheet curved to the proper radius and welded with one longitudinal weld. The ratios of diameter to thickness of shell wall in the two series of specimens were 258 and 572. Strains were measured with Huggenberger tensometers at a number of gage lines on the stiffeners and shell. The results of these tests indicate that a spacing of circumferential stiffeners equal to 0.67 times the radius is too great to strengthen the shell wall appreciably. The results are not inclusive enough to show the optimum in stiffeners. Plain cylinders without stiffeners developed ultimate strengths approximately half as great as the buckling strengths computed by the equation resulting from the classical theory and slightly greater than those computed by Donnell's large deflection theory.

Holt, Marshall↗