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All sources NASA NTRS DOE OSTI

NASA NTRS2017

Cause and Cure - Deterioration in Accuracy of CFD Simulations With Use of High-Aspect-Ratio Triangular Tetrahedral Grids

Traditionally high-aspect ratio triangular/tetrahedral meshes are avoided by CFD re-searchers in the vicinity of a solid wall, as it is known to reduce the accuracy of gradient computations in those regions and also cause numerical instability. Although for certain complex geometries, the use of high-aspect ratio triangular/tetrahedral elements in the vicinity of a solid wall can be replaced by quadrilateral/prismatic elements, ability to use triangular/tetrahedral elements in such regions without any degradation in accuracy can be beneficial from a mesh generation point of view. The benefits also carry over to numerical frameworks such as the space-time conservation element and solution element (CESE), where triangular/tetrahedral elements are the mandatory building blocks. With the requirement of the CESE method in mind, a rigorous mathematical framework that clearly identities the reason behind the difficulties in use of such high-aspect ratio triangular/tetrahedral elements is presented here. As will be shown, it turns out that the degree of accuracy deterioration of gradient computation involving a triangular element is hinged on the value of its shape factor Gamma def = sq sin Alpha1 + sq sin Alpha2 + sq sin Alpha3, where Alpha1; Alpha2 and Alpha3 are the internal angles of the element. In fact, it is shown that the degree of accuracy deterioration increases monotonically as the value of Gamma decreases monotonically from its maximal value 9/4 (attained by an equilateral triangle only) to a value much less than 1 (associated with a highly obtuse triangle). By taking advantage of the fact that a high-aspect ratio triangle is not necessarily highly obtuse, and in fact it can have a shape factor whose value is close to the maximal value 9/4, a potential solution to avoid accuracy deterioration of gradient computation associated with a high-aspect ratio triangular grid is given. Also a brief discussion on the extension of the current mathematical framework to the tetrahedral-grid case along with some of the practical results of this extension is also provided. Furthermore, through the use of numerical simulations of practical viscous problems involving high-Reynolds number flows, the effectiveness of the gradient evaluation procedures within the CESE framework (that have their basis on the analysis presented here) to produce accurate and stable results on such high-aspect ratio meshes is also showcased.

CESE Method↗

NASA NTRS1981

A study of high-altitude manned research aircraft employing strut-braced wings of high-aspect-ratio

The effect of increased wing aspect ratio of subsonic aircraft on configurations with and without strut bracing. Results indicate that an optimum cantilever configuration, with a wing aspect ratio of approximately 26, has a 19% improvement in cruise range when compared to a baseline concept with a wing aspect ratio of approximately 10. An optimum strut braced configuration, with a wing aspect ratio of approximately 28, has a 31% improvment in cruise range when compared to the same baseline concept. This improvement is mainly due to the estimated reduction in wing weight resulting from use of lifting struts. All configurations assume the same mission payload and fuel. The drag characteristics of the wings are enhanced with the use of laminar flow airfoils. A method for determining the extent of attainable natural laminar flow, and methods for preliminary structural design and for aerodynamic analysis of wings lifting struts are presented.

Smith, P. M.↗

NASA NTRS1988

High-aspect-ratio wings

High-aspect-ratio aircraft include most transport aircraft such as commercial and military transports, business aircraft, and cargo aircraft. Generally, these types of aircraft are designed to cruise over a narrow range of lift coefficients and Mach numbers in the performance of their mission. Emphasis is therefore placed on the cruise performance of transport aircraft and every effort is made to obtain accurate wind-tunnel data to use as a basis for prediction of full-scale cruise performance. However, off-cruise performance is also important and methods were developed for extrapolating wind-tunnel data on buffet and flutter at transonic speed. Transport-type aircraft were tested extensively in various wind tunnels around the world and many different test techniques were developed to simulate higher Reynolds numbers. Methods developed for one tunnel may not be applicable to another tunnel because of differences in size, Reynolds number capability, running time, and test objectives. Many of the methods of boundary-layer control developed in two-dimensional airfoil testing can be applied in tests of transport configurations, but sometimes the three-dimensional flow fields that develop on tranpsort aircraft can make application of the two-dimensional methods difficult or impossible. The discussion is intended to be a representative, but not exhaustive, survey of the various methods of high Reynolds number simulation in the testing of high-aspect-ratio aircraft.

Peterson, John B., Jr.↗

NASA NTRS2017

Cause and Cure - Deterioration in Accuracy of CFD Simulations with Use of High-Aspect-Ratio Triangular/Tetrahedral Grids

Traditionally high-aspect ratio triangular/tetrahedral meshes are avoided by CFD researchers in the vicinity of a solid wall, as it is known to reduce the accuracy of gradient computations in those regions. Although for certain complex geometries, the use of high-aspect ratio triangular/tetrahedral elements in the vicinity of a solid wall can be replaced by quadrilateral/prismatic elements, ability to use triangular/tetrahedral elements in such regions without any degradation in accuracy can be beneficial from a mesh generation point of view. The benefits also carry over to numerical frameworks such as the space-time conservation element and solution element (CESE), where simplex elements are the mandatory building blocks. With the requirement of the CESE method in mind, a rigorous mathematical framework that clearly identifies the reason behind the difficulties in use of such high-aspect ratio simplex elements is formulated using two different approaches and presented here. Drawing insights from the analysis, a potential solution to avoid that pitfall is also provided as part of this work. Furthermore, through the use of numerical simulations of practical viscous problems involving high-Reynolds number flows, how the gradient evaluation procedures of the CESE framework can be effectively used to produce accurate and stable results on such high-aspect ratio simplex meshes is also showcased.

CESE Method↗

NASA NTRS1959

Stability Characteristics of Two Missiles of Fineness Ratios 12 and 18 with Six Rectangular Fins of Very Low Aspect Ratio Over a Mach Number Range of 1.4 to 3.2

Two rocket-propelled missiles have been test flown by the Langley Pilotless Aircraft Research Division in order to study the stability characteristics of a body with six rectangular fins of very low aspect ratio. The fins, which had exposed aspect ratios of approximately o.o4 and 0.02 per fin, were mounted on bodies of fineness ratios of 12 and 18, respectively. Each body had a nose with a fineness ratio of 3.5 and a cylindrical afterbody. The body and the fin chord of the model having a fineness ratio of 12 were extended the length of 6 body diameters to produce the model with a fineness ratio of 18. The missiles were disturbed in flight by pulse rockets in order to obtain the stability data. The tests were performed over a Mach number range of 1.4 to 3.2 and a Reynolds number range of 2 x 10(exp 6) to 21 x l0(exp 6). The results of these tests indicate that these configurations with the long rectangular fins of very low aspect ratio showed little induced roll" with the missile of highest fineness ratio and longest fin chord exhibiting the least amount. Extending the body and fin chord of the shorter missile six body diameters and thereby increasing the fin area approximately 115 percent increased the lift-curve slope based on body cross-sectional area approximately 40 to 55 percent, increased the dynamic stability by a substantial amount, and increased the drag from 14 to 33 percent throughout the comparable Mach number range. The center-of-pressure location of both missiles remained constant over the Mach number range.

Henning, Allen B.↗

NASA NTRS1997

The Effect of Cooling Passage Aspect Ratio on Curvature Heat Transfer Enhancement

A series of electrically heated tube experiments was performed to investigate the effect of high aspect ratio on curvature heat transfer enhancement in uniformly heated rectangular cooling passages. Three hardware geometries were tested: a baseline straight aspect ratio 10 tube, an aspect ratio 1 (square) tube with a 45 deg. curve, and an aspect ratio 10 tube with a 45 deg. curve. Gaseous nitrogen with the following properties was used as the coolant: ambient inlet temperature, pressures to 8.3 MPa, wall-to-bulk temperature ratios less than two, and Reynolds numbers based on hydraulic diameter ranging from 250,000 to 1,600,000. The measured curvature enhancement factors were compared to values predicted by three previously published models which had been developed for low aspect ratio tubes. The models were shown to be valid for the high aspect ratio tube as well the low aspect ratio tube, indicating that aspect ratio had little impact on the curvature heat transfer enhancement in these tests.

Meyer, Michael L.↗

DOE OSTI2022

Finite orbit width effects in large aspect ratio stellarators

New orbit-averaged equations for low collisionality neoclassical fluxes in large aspect ratio stellarators with mirror ratios close to unity are derived. The equations retain finite orbit width effects by employing the second adiabatic invariant $J$ as a velocity-space coordinate and they have been implemented in the orbit-averaged neoclassical code KNOSOS (Velasco et al. , J. Comput. Phys. , vol. 418, 2020, 109512; Velasco et al. , Nucl. Fusion , vol. 61, 2021, 116013). The equations are used to study the $1/\nu$ regime and the lower collisionality regimes. For generic large aspect ratio stellarators with mirror ratios close to unity, as the collision frequency decreases, the $1/\nu$ regime transitions directly into the $\nu$ regime, without passing through a $\sqrt {\nu }$ regime. An explicit formula for the neoclassical fluxes in the $\nu$ regime is obtained. The formula includes the effect of particles that transition between different types of wells. While these transitions produce stochastic scattering independent of the value of the collision frequency in velocity space, the diffusion in real space remains proportional to the collision frequency. The $\sqrt {\nu }$ regime is only recovered in large aspect ratio stellarators close to omnigeneity: large aspect ratio stellarators with large mirror ratios and optimized large aspect ratio stellarators with mirror ratios close to unity. Neoclassical transport in large aspect ratio stellarators with large mirror ratios can be calculated with the orbit-averaged equations derived by Calvo et al. ( Plasma Phys. Control. Fusion , vol. 59, 2017, 055014). In these stellarators, the $\sqrt {\nu }$ regime exists in the collisionality interval $(a/R) \ln (R/a) \ll \nu _{ii} R a/\rho _i v_{ti} \ll R/a$ . In optimized large aspect ratio stellarators with mirror ratios close to unity, the $\sqrt {\nu }$ regime occurs in an interval of collisionality that depends on the deviation from omnigeneity $\delta$ : $\delta ^{2} |\ln \delta | \ll \nu _{ii} R a/\rho _i v_{ti} \ll 1$ . Here, $\nu _{ii}$ is the ion–ion collision frequency, $\rho _i$ and $v_{ti}$ are the ion gyroradius and thermal speed, and $a$ and $R$ are the minor and major radii.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2017

What Can We Conclude about the Real Aspect Ratios of Ice Particle Aggregates from Two-Dimensional Images?

Abstract A simple numerical experiment was performed to investigate the result published in many papers that measurements indicate that aggregates may be well represented as oblate spheroids with mean aspect ratio (semiminor axis to semimajor axis length) of 0.6. The aspect ratio measurements are derived from two-dimensional projections of complex three-dimensional aggregates. Here, aggregates were modeled as ellipsoids with semiprincipal axes of length a, b, and c, which include oblate spheroids (a = b) as a class, and the projected aspect ratios of large numbers of two-dimensional projections of them were sampled. When sampling oblate spheroids with aspect ratio 0.6 over random orientations, the mean projected aspect ratio is 0.746. A mean projected aspect ratio of 0.6 is obtained for an oblate spheroid with aspect ratio of 0.33. When sampling randomly oriented ellipsoids with semiminor axes (b, c) varying from 0.10 to 1.00 in steps of 0.01, representing many complex shapes, the mean projected aspect ratio is 0.595, close to the measured mean projected aspect ratio of aggregates of 0.6. These experiments demonstrate that the conclusion one may safely draw from the projected aspect ratio measurements is that the mean aspect ratio of aggregates is lower than 0.6. Moreover, the projected aspect ratio distributions from measurements suggest a mixture of aggregate shapes, rather than only oblate spheroids as is often assumed.

Jiang, Zhiyuan↗

NASA NTRS1959

Effect of Stator and Rotor Aspect Ratio on Transonic-Turbine Performance

The effect of stator and rotor aspect ratio on transonic-turbine performance was experimentally investigated. The stator aspect ratios covered were 1.6. 0.8, and 0.4, while the rotor aspect ratios investigated were 1.46 and 0.73. It was found that the observed variation in turbine design-point efficiency was negligible. Thus, within the range of aspect ratio investigated, these results verify for turbines operating in the transonic flow range the finding of a reference report, which showed analytically that, if blade shape and solidity are held constant, the aspect ratio may be varied over a wide range without appreciable change in turbine efficiency.

Wong, Robert Y.↗

NASA NTRS1992

An experimental investigation of high-aspect-ratio cooling passages

An experimental investigation was conducted to evaluate the effectiveness of using high-aspect-ratio cooling passenges to improve the life and reduce the colant pressure drop in high-pressure rocket thrust chambers. A plug-nozzle rocket-engine test apparatus was used to test two cylindrical chambers with low-aspect-ratio cooling passages and one with high-aspect-ratio cooling passages. The chambers were cyclically tested and data were taken over a wide range of coolant mass flows. The results showed that for the same coolant pressure drop, the hot-gas-side wall temperature of the high-aspect-ratio chamber was 30 percent lower than the baseline low-aspect-ratio chamber, resulting in no fatigue damage to the wall. The coolant pressure drop for the high-aspect-ratio chamber was reduced in increments to one-half that of the baseline chamber, by reducing the coolant mass flow, and still resulted in a reduction in the hot-gas-side wall temperature when compared to the low-aspect-ratio chambers.

Carlile, Julie A.↗

NASA NTRS1992

An experimental investigation of high-aspect-ratio cooling passages

An experimental investigation was conducted to evaluate the effectiveness of using high-aspect-ratio cooling passages to improve the life and reduce the coolant pressure drop in high-pressure rocket thrust chambers. A plug-nozzle rocket-engine test apparatus was used to test two cylindrical chambers with low-aspect-ratio cooling passages and one with high-aspect-ratio cooling passages. The chambers were cyclically tested and data were taken over a wide range of coolant mass flows. The results showed that for the same coolant pressure drop, the hot-gas-side wall temperature of the high-aspect-ratio chamber was 30 percent lower than the baseline low-aspect-ratio chamber, resulting in no fatigue damage to the wall. The coolant pressure drop for the high-aspect-ratio chamber was reduced in increments to one-half that of the baseline chamber, by reducing the coolant mass flow, and still resulted in a reduction in the hot-gas-side wall temperature when compared to the low-aspect-ratio chambers.

Carlile, Julie A.↗

NASA NTRS1990

Self-induced roll oscillations of low-aspect-ratio rectangular wings

Experimental investigation of small aspect ratio rectangular wings mounted on a free-to-roll sting balance indicated that self-induced roll oscillations are possible when the aspect ratio of such wings is less than 0.5. The oscillations are probably driven by the periodic changes in the location and strength of the side edge vortices, as it has been shown for the 'wing rock' motion of delta wings, where similar changes in the leading edge vortex strength and position cause the roll oscillations. During the roll oscillation cycle the roll angle, normal force, and the side force were recorded and presented for three wings with aspect ratios of 0.25, 0.35, and 0.47. This data indicates that the lift loss during roll oscillations of rectangular wings is less than what was measured for similar delta wings. Also, the flow field of such slender rectangular wings at high angles of attack is more complicated due to the additional leading edge vortex, when compared with the flow field over slender delta wings.

Levin, Daniel↗

DOE OSTI2018

Aspect ratio control and photocatalytic properties analysis of anatase TiO2 nanoparticles

Highlights: • TiO{sub 2} nanoparticles with different aspect ratio were prepared and characterized. • Their aspect ratio is tuned by varying surfactants molar ratio and concentration. • TiO{sub 2} nanoparticles show photocatalytic activities in degradation of methylene blue. - Abstract: Anatase TiO{sub 2} nanoparticles with tuning size and aspect ratio were successfully prepared by a simple solvothermal method, using ethanol as a solvent, titanium butoxide as a precursor, and oleic acid and oleylamine as anionic and cationic capping agents, respectively. The average size and aspect ratio of these nanoparticles can be greatly regulated by varying the oleic acid/oleylamine molar ratio while keeping their total molar content constant and finely adjusted by increasing the total capping agents molar concentration in solvent at constant molar ratio (oleic acid/oleylamine molar ratio = 1:1). The variation of molar ratio or molar concentration enables a manipulation of the growth rate along different facets of TiO{sub 2} nanoparticles and, consequently, a control of the aspect ratio of these nanoparticles. Moreover, the photocatalytic degradation rate of methyl blue for sample prepared with molar ratio of oleic acid to oleylamine at 6:24 is over 11% higher than that for the other samples.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

NASA NTRS1972

Required critical aspect ratio of fibers intended for stress rupture applications.

The observed critical aspect ratio for pullout specimens of tungsten wire in a copper matrix tested in stress rupture at 649 and 816 C was slightly greater than for tension tests at the same temperature. Time for failure of the stress rupture specimens was controlled by the properties of the fiber (tungsten) at aspect ratios greater than the critical aspect ratio and by the properties of the matrix (copper) at aspect ratios less than the critical ratio.

Jech, R. W.↗

NASA NTRS1993

Flow visualization study in high aspect ratio cooling channels for rocket engines

The structural integrity of high pressure liquid propellant rocket engine thrust chambers is typically maintained through regenerative cooling. The coolant flows through passages formed either by constructing the chamber liner from tubes or by milling channels in a solid liner. Recently, Carlile and Quentmeyer showed life extending advantages (by lowering hot gas wall temperatures) of milling channels with larger height to width aspect ratios (AR is greater than 4) than the traditional, approximately square cross section, passages. Further, the total coolant pressure drop in the thrust chamber could also be reduced, resulting in lower turbomachinery power requirements. High aspect ratio cooling channels could offer many benefits to designers developing new high performance engines, such as the European Vulcain engine (which uses an aspect ratio up to 9). With platelet manufacturing technology, channel aspect ratios up to 15 could be formed offering potentially greater benefits. Some issues still exist with the high aspect ratio coolant channels. In a coolant passage of circular or square cross section, strong secondary vortices develop as the fluid passes through the curved throat region. These vortices mix the fluid and bring lower temperature coolant to the hot wall. Typically, the circulation enhances the heat transfer at the hot gas wall by about 40 percent over a straight channel. The effect that increasing channel aspect ratio has on the curvature heat transfer enhancement has not been sufficiently studied. If the increase in aspect ratio degrades the secondary flow, the fluid mixing will be reduced. Analysis has shown that reduced coolant mixing will result in significantly higher wall temperatures, due to thermal stratification in the coolant, thus decreasing the benefits of the high aspect ratio geometry. A better understanding of the fundamental flow phenomena in high aspect ratio channels with curvature is needed to fully evaluate the benefits of this geometry. The fluid dynamic and conjugate heat transfer problem of high aspect ratio rocket engine coolant channels are being investigated numerically, but these efforts have been hampered by a lack of validating data. Wall temperature data is available for the conjugate problem for channels without curvature and aspect ratio = 5.0, and unheated fluid dynamic data are available for square and circular cross section channels with curvature at Reynold's numbers up to 40,000. But the effects of aspect ratio on secondary flow development have not been experimentally studied. To provide some insight into the effects of channel aspect ratio on secondary flow and to qualitatively provide anchoring for the numerical codes, a flow visualization experiment was initiated at the NASA Lewis Research Center.

Meyer, Michael L.↗

NASA NTRS1998

Comparison of High Aspect Ratio Cooling Channel Designs for a Rocket Combustion Chamber with Development of an Optimized Design

An analytical investigation on the effect of high aspect ratio (height/width) cooling channels, considering different coolant channel designs, on hot-gas-side wall temperature and coolant pressure drop for a liquid hydrogen cooled rocket combustion chamber, was performed. Coolant channel design elements considered were: length of combustion chamber in which high aspect ratio cooling was applied, number of coolant channels, and coolant channel shape. Seven coolant channel designs were investigated using a coupling of the Rocket Thermal Evaluation code and the Two-Dimensional Kinetics code. Initially, each coolant channel design was developed, without consideration for fabrication, to reduce the hot-gas-side wall temperature from a given conventional cooling channel baseline. These designs produced hot-gas-side wall temperature reductions up to 22 percent, with coolant pressure drop increases as low as 7.5 percent from the baseline. Fabrication constraints for milled channels were applied to the seven designs. These produced hot-gas-side wall temperature reductions of up to 20 percent, with coolant pressure drop increases as low as 2 percent. Using high aspect ratio cooling channels for the entire length of the combustion chamber had no additional benefit on hot-gas-side wall temperature over using high aspect ratio cooling channels only in the throat region, but increased coolant pressure drop 33 percent. Independent of coolant channel shape, high aspect ratio cooling was able to reduce the hot-gas-side wall temperature by at least 8 percent, with as low as a 2 percent increase in coolant pressure drop. ne design with the highest overall benefit to hot-gas-side wall temperature and minimal coolant pressure drop increase was the design which used bifurcated cooling channels and high aspect ratio cooling in the throat region. An optimized bifurcated high aspect ratio cooling channel design was developed which reduced the hot-gas-side wall temperature by 18 percent and reduced the coolant pressure drop by 4 percent. Reductions of coolant mass flow rate of up to 50 percent were possible before the hot-gas-side wall temperature reached that of the baseline. These mass flow rate reductions produced coolant pressure drops of up to 57 percent.

Wadel, Mary F.↗

DOE OSTI2016

Synthesis of high aspect ratio ZnO nanowires with an inexpensive handcrafted electrochemical setup

In this work, high aspect ratio zinc oxide nanowires are synthesized using templated one-step electrodeposition technique. Electrodeposition of the nanowires is done using a handcrafted electronic system. Nuclear track-etched polycarbonate membrane is used as a template to form the high aspect ratio nanowires. The result of X-ray diffraction and scanning electron microscopy shows that nanowires with a good crystallinity and an aspect ratio of more than 30 can be achieved in a suitable condition. The height of electrodeposited nanowires reaches to about 11 μm. Based on the obtained results, high aspect ratio ZnO nanowires can be formed using inexpensive electrodeposition setup with an acceptable quality.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Effect of aspect ratio on plasma response to resonant magnetic perturbations in tokamak devices

A systematic numerical study is carried out, computing and comparing the plasma response to the resonant magnetic perturbation (RMP) field, applied for controlling edge localized modes (ELMs), in a series of tokamak plasmas with varying aspect ratio and utilizing the MARS-F code. The aspect ratio is scanned either by varying the plasma major radius at a fixed minor radius or by varying the latter while fixing the former. Both approaches yield similar results when compared in terms of quantities with proper normalizations. In general, a non-monotonic dependence of the resonant response field (normalized by the vacuum counterpart) near the plasma edge is found with varying aspect ratio, indicating that a given ELM control coil current configuration strongly favors plasmas with a certain aspect ratio. This optimal aspect ratio, on the other hand, depends on the toroidal as well as poloidal (i.e., coil phasing) spectra of the applied RMP field. The equilibrium (edge) safety factor, the plasma shape, and the plasma toroidal flow are all fixed to ensure that the effects identified here are predominantly due to the plasma aspect ratio.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗