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

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1948

Tests of a Triangular Wing of Aspect Ratio 2 in the Ames 12-foot Pressure Wind Tunnel III : the Effectiveness and Hinge Moments of a Skewed Wing-tip Flap

Results of wind-tunnel tests of a semispan model of a triangular wing of aspect ratio 2 with a skewed wing-tip flap are presented. Lift, drag, pitching-moment, and hinge-moment data are included for subsonic Mach numbers up to 0.95. The flap showed extremely high hinge moments and low effectiveness as a longitudinal control. Although less affected by compressibility, this flap is indicated to be inferior to a constant-chord flap when applied to this triangular wing.

MACH NUMBER EFFECTS - COMPLETE WINGS↗
NASA NTRS1952

Longitudinal Stability and Drag Characteristics at Mach Numbers from 0.70 to 1.37 of Rocket-propelled Models Having a Modified Triangular Wing

A modified triangular wing of aspect ratio 2.53 having an airfoil section 3.7 percent thick at the root and 5.98 percent thick at the tip was designed in an attempt to improve the lift and drag characteristics of triangular wings. Free-flight drag and stability tests were made using rocket-propelled models equipped with the modified wing. The Mach number range of the test was from 0.70 to 1.37. Test results indicated the following: The lift-curve slope of wing plus fuselage approaches the theoretical value of wing alone at supersonic Mach numbers. The drag coefficient, based on total wing area, for wing plus interference was approximately 0.0035 at subsonic Mach numbers and 0.0080 at supersonic Mach numbers. The maximum shift in aerodynamic center for the complete configuration was 14 percent in the rearward direction from the forward position of 51.5 percent of mean aerodynamic chord at subsonic Mach numbers. The variation of lift and moment with angle of attack was linear at supersonic Mach numbers for the range of coefficients covered in the test. The high value of lift-curve slope was considered to be a significant result attributable to the wing modifications.

Chapman, Rowe, Jr↗
NASA NTRS1948

Aerodynamic Characteristics at Subsonic and Supersonic Mach Numbers of a Thin Triangular Wing of Aspect Ratio 2 II : Maximum Thickness at Midchord

The lift, drag, and pitching-moment characteristics of a triangular wing, having an aspect ratio of 2 and a symmetrical double-wedge profile of 5-percent-chord maximum thickness at midchord, have been evaluated from wind-tunnel tests at Mach numbers from 0.50 to 0.975 and from 1.09 to 1.49 and at Reynolds numbers ranging from 0.67 to 0.85 million. The lift, drag, and pitching-moment coefficients of the triangular wing with a leading-edge sweepback of approximately 63 degrees did not exhibit the irregular variations with Mach number at high subsonic and low supersonic Mach numbers that are characteristic of unswept wings. The lift-curve slope increased steadily with Mach number below unity and declined slowly beyond the Mach number of 1.13. A substantial rise in the minimum drag coefficient occurred between Mach numbers of 0.95 and 1.20 with an associated reduction in the maximum lift-drag ratio. The aerodynamic center shifted rearward toward the centroid of area of the wing with increasing Mach number below 0.975; whereas above 1.09 it coincided with the centroid.

Walker, Harold J↗
NASA NTRS1949

Theoretical characteristics in supersonic flow of two types of control surfaces on triangular wings

Methods based on the linearized theory for supersonic flow were used to find the characteristics of two types of control surfaces on thin triangular wings. The first type, the constant-chord partial-span flap, was considered to extend either outboard from the center of the wing or inboard from the wing tip. The second type, the full-triangular-tip flap, was treated only for the case in which the Mach number component normal to the leading edge is supersonic. For each type, expressions were found for the lift, rolling-moment, pitching-moment, and hinge-moment characteristics.

Tucker, Warren A↗
NASA NTRS1957

Linearized Lifting-Surface and Lifting-line Evaluations of Sidewash Behind Rolling Triangular Wings at Supersonic Speeds

The lifting-surface sidewash behind rolling triangular wings has been derived for a range of supersonic Mach numbers for which the wing leading edges remain swept behind the mark cone emanating from the wing apex. Variations of the sidewash with longitudinal distance in the vertical plane of symmetry are presented in graphical form. An approximate expression for the sidewash has been developed by means of an approach using a horseshoe-vortex approximate-lifting-line theory. By use of this approximate expression, sidewash may be computed for wings of arbitrary plan form and span loading. A comparison of the sidewash computed by lifting-surface and lifting-line expressions for the triangular wing showed good agreement except in the vicinity of the trailing edge when the leading edge approached the sonic condition. An illustrative calculation has been made of the force induced by the wing sidewash on a vertical tail located in various longitudinal positions.

Bobbitt, Percy J↗
NASA NTRS1954

Experimental investigation of the forces and moments due to sideslip of a series of triangular vertical and horizontal tail combinations at Mach numbers

An experimental investigation was made at Mach numbers of 1.62, 1.93, and 2.41 of a series of tail combinations consisting of triangular vertical tail attached symmetrically to a triangular horizontal tail to determine the lateral force, yawing moment, and rolling moment due to sideslip. The apex angles of both the vertical- and horizontal-tail surfaces were varied systematically in order to obtain results for an appreciable range of operating conditions. The results of the investigation indicated that, for tails having subsonic leading edges and supersonic trailing edges, the lateral-force derivative and the yawing-moment derivative were predicted satisfactorily by the method presented in NACA TN 3071 except when the leading edges approach a sonic condition. The theoretical rolling-moment derivative was in fair agreement with the experimental derivative. For the limited tests in which both the leading and trailing edges were supersonic, the prediction of the lateral-force derivative and the yawing-moment derivative obtained from NACA TN 2412 was in good agreement with the experimental derivatives, whereas the prediction of the rolling-moment derivative was fair.

Coletti, Donald E↗
NASA NTRS1959

The Effects of Streamwise-Deflected Wing Tips on the Aerodynamic Characteristics of an Aspect Ratio-2 Triangular Wing, Body, and Tail Combination

An investigation has been conducted on a triangular wing and body combination to determine the effects on the aerodynamic characteristics resulting from deflecting portions of the wing near the tips 900 to the wing surface about streamwise hinge lines. Experimental data were obtained for Mach numbers of 0.70, 1.30, 1.70, and 2.22 and for angles of attack ranging from -5 deg to +18 deg at sideslip angles of 0 deg and 5 deg. The results showed that the aerodynamic center shift experienced by the triangular wing and body combination as the Mach number was increased from subsonic to supersonic could be reduced by about 40 percent by deflecting the outboard 4 percent of the total area of each wing panel. Deflection about the same hinge line of additional inboard surfaces consisting of 2 percent of the total area of each wing panel resulted in a further reduction of the aerodynamic center travel of 10 percent. The resulting reductions in the stability were accompanied by increases in the drag due to lift and, for the case of the configuration with all surfaces deflected, in the minimum drag. The combined effects of reduced stability and increased drag of the untrimmed configuration on the trimmed lift-drag ratios were estimated from an analysis of the cases in which the wing-body combination with or without tips deflected was assumed to be controlled by a canard. The configurations with deflected surfaces had higher trimmed lift-drag ratios than the model with undeflected surfaces at Mach numbers up to about 1.70. Deflecting either the outboard surfaces or all of the surfaces caused the directional stability to be increased by increments that were approximately constant with increasing angle of attack at each Mach number. The effective dihedral was decreased at all angles of attack and Mach numbers when the surfaces were deflected.

Peterson, Victor L.↗
NASA NTRS1959

An Experimental Investigation of the Effect of a Canard Control on the Lift, Drag, and Pitching Moment of an Aspect-Ratio 2.0 Triangular Wing Incorporating a Form of Conical Camber

The results of an experimental investigation to determine the effect of a canard control on the lift, drag, and pitching-moment characteristics of an aspect-ratio-2.0 triangular wing incorporating a form of conical camber are presented. The canard had a triangular plan form of aspect ratio 2.0 and was mounted in the extended chord plane of the wing. The ratio of the area of the exposed canard panels to the total wing area was 6.9 percent, and the ratio of the total areas was 12.9 percent. Data were obtained at Mach numbers from 0.70 to 2.22 through an angle-of-attack range from -6 deg to +18 deg with the canard on, and with the canard off. To provide a basis for comparison, the canard was also tested with a symmetrical wing having the same plan form, aspect ratio, and thickness distribution as the cambered wing. The results of the investigation showed that at the high subsonic speeds the gain in maximum lift-drag ratio achieved by camber was considerably reduced by the addition of a canard. At the supersonic speeds, the addition of the canard did not change the effect of camber on the maximum lift-drag ratios.

Menees, Gene P.↗
NASA NTRS1959

An Experimental Investigation of a Triangular Wing of Aspect Ratio 2 and a Body Warped to be Trimmed at M = 2.24

A cambered and twisted triangular wing of aspect ratio 2 in combination with a cambered body was investigated experimentally to determine the effectiveness of the camber in reducing the drag due to lift at trim at supersonic speeds. Four arrangements were tested comprising all combinations of a symmetrical and a cambered wing with a symmetrical and a cambered body. The camber shape investigated was derived by linearized lifting surface theory for triangular wings with sonic leading edges and satisfied the requirement that the wing be trimmed at the design Mach number and lift coefficient. The experimental results for the cambered wing and cambered body showed that the drag coefficient at trim was always greater, at the same lift coefficient, than that for the untrimmed symmetrical wing and body. The trim lift coefficient was positive and decreased with increasing Mach number. At the design Mach number of 2.24, the trim lift coefficient was somewhat lower and the drag coefficient was higher than values predicted by linearized lifting surface theory for the wing alone. A comparison of the trim lift-drag ratio of the cambered wing and cambered body with values obtained by trimming the symmetrical wing and symmetrical body either with a canard or a trailing-edge flap showed that, at approximately the design Mach number the cambered configuration developed a somewhat higher value than the trailing-edge flap configuration but a lower value than the canard configuration.

Adams, Gaynor J.↗
NASA NTRS1959

Longitudinal Stability and Control Characteristics at Mach Numbers from 0.70 to 2.22 of a Triangular Wing Configuration Equipped with a Canard Control, a Trailing-Edge-Flap Control or a Cambered Forebody

Results of an investigation to determine the static longitudinal stability and control characteristics of an aspect-ratio-2 triangular wing and body configuration equipped with either a canard control, a trailing-edge-flap control, or a cambered forebody are presented without analysis for Mach numbers from 0.70 to 2.22. The canard surface had a triangular plan form and a ratio of exposed area to total wing area of 7.8 percent. The hinge line of the canard was in the extended wing chord plane, 0.83 wing mean aerodynamic chord ahead of the reference center of moments. The trailing-edge controls were constant-chord full-span flaps with exposed area equal to 10.7 percent of the total wing area. The cambered body was a modified Sears-Haack body with camber only ahead of the wing apex. Data are presented for various canard and flap deflections at angles of attack ranging from -6 deg to +18 deg.

Boyd, John W.↗
NASA NTRS1997

ASICs Approach for the Implementation of a Symmetric Triangular Fuzzy Coprocessor and Its Application to Adaptive Filtering

This paper discusses the implementation of a fuzzy logic system using an ASICs design approach. The approach is based upon combining the inherent advantages of symmetric triangular membership functions and fuzzy singleton sets to obtain a novel structure for fuzzy logic system application development. The resulting structure utilizes a fuzzy static RAM to store the rule-base and the end-points of the triangular membership functions. This provides advantages over other approaches in which all sampled values of membership functions for all universes must be stored. The fuzzy coprocessor structure implements the fuzzification and defuzzification processes through a two-stage parallel pipeline architecture which is capable of executing complex fuzzy computations in less than 0.55us with an accuracy of more than 95%, thus making it suitable for a wide range of applications. Using the approach presented in this paper, a fuzzy logic rule-base can be directly downloaded via a host processor to an onchip rule-base memory with a size of 64 words. The fuzzy coprocessor's design supports up to 49 rules for seven fuzzy membership functions associated with each of the chip's two input variables. This feature allows designers to create fuzzy logic systems without the need for additional on-board memory. Finally, the paper reports on simulation studies that were conducted for several adaptive filter applications using the least mean squared adaptive algorithm for adjusting the knowledge rule-base.

Starks, Scott↗
NASA NTRS1998

Self-Avoiding Walks over Adaptive Triangular Grids

In this paper, we present a new approach to constructing a "self-avoiding" walk through a triangular mesh. Unlike the popular approach of visiting mesh elements using space-filling curves which is based on a geometric embedding, our approach is combinatorial in the sense that it uses the mesh connectivity only. We present an algorithm for constructing a self-avoiding walk which can be applied to any unstructured triangular mesh. The complexity of the algorithm is O(n x log(n)), where n is the number of triangles in the mesh. We show that for hierarchical adaptive meshes, the algorithm can be easily parallelized by taking advantage of the regularity of the refinement rules. The proposed approach should be very useful in the run-time partitioning and load balancing of adaptive unstructured grids.

Heber, Gerd↗
NASA NTRS2003

Analysis and Improvement of Upwind and Centered Schemes on Quadrilateral and Triangular Meshes

Second-order accurate upwind and centered schemes are presented in a framework that facilitates their analysis and comparison. The upwind scheme employed consists of a reconstruction step (MUSCL approach) followed by an upwind step (Roe's flux-difference splitting). The two centered schemes are of Lax-Friedrichs (L-F) type. They are the nonstaggered versions of the Nessyahu-Tadmor (N-T) scheme and the CE/SE method with epilson = 1/2. The upwind scheme is extended to the case of two spatial dimensions (2D) in a straightforward manner. The N-T and CE/SE schemes are extended in a manner similar to the 2D extensions of the CE/SE scheme by Wang and Chang for a triangular mesh and by Zhang, Yu, and Chang for a quadrilateral mesh. The slope estimates, however, are simplified. Fourier stability and accuracy analyses are carried out for these schemes for the standard 1D and the 2D quadrilateral mesh cases. In the nonstandard case of a triangular mesh, the triangles must be paired up when analyzing the upwind and N-T schemes. An observation resulting in an extended N-T scheme which is faster and uses only one-third of the storage for flow data compared with the CE/SE method is presented. Numerical results are shown. Other improvements to the schemes are discussed.

Huynh, H. T.↗
NASA NTRS2004

A Six-Node Curved Triangular Element and a Four-Node Quadrilateral Element for Analysis of Laminated Composite Aerospace Structures

Mathematical development and some computed results are presented for Mindlin plate and shell elements, suitable for analysis of laminated composite and sandwich structures. These elements use the conventional 3 (plate) or 5 (shell) nodal degrees of freedom, have no communicable mechanisms, have no spurious shear energy (no shear locking), have no spurious membrane energy (no membrane locking) and do not require arbitrary reduction of out-of-plane shear moduli or under-integration. Artificial out-of-plane rotational stiffnesses are added at the element level to avoid convergence problems or singularity due to flat spots in shells. This report discusses a 6-node curved triangular element and a 4-node quadrilateral element. Findings show that in regular rectangular meshes, the Martin-Breiner 6-node triangular curved shell (MB6) is approximately equivalent to the conventional 8-node quadrilateral with integration. The 4-node quadrilateral (MB4) has very good accuracy for a 4-node element, and may be preferred in vibration analysis because of narrower bandwidth. The mathematical developments used in these elements, those discussed in the seven appendices, have been applied to elements with 3, 4, 6, and 10 nodes and can be applied to other nodal configurations.

Martin, C. Wayne↗
NASA NTRS2015

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.

Mazaheri, Alireza↗
NASA NTRS2016

High-Order Residual-Distribution Schemes for Discontinuous Problems on Irregular Triangular Grids

In this paper, we develop second- and third-order non-oscillatory shock-capturing hyperbolic residual distribution schemes for irregular triangular grids, extending our second- and third-order schemes to discontinuous problems. We present extended first-order N- and Rusanov-scheme formulations for hyperbolic advection-diffusion system, and demonstrate that the hyperbolic diffusion term does not affect the solution of inviscid problems for vanishingly small viscous coefficient. We then propose second- and third-order blended hyperbolic residual-distribution schemes with the extended first-order Rusanov-scheme. We show that these proposed schemes are extremely accurate in predicting non-oscillatory solutions for discontinuous problems. We also propose a characteristics-based nonlinear wave sensor for accurately detecting shocks, compression, and expansion regions. Using this proposed sensor, we demonstrate that the developed hyperbolic blended schemes do not produce entropy-violating solutions (unphysical stocks). We then verify the design order of accuracy of these blended schemes on irregular triangular grids.

Mazaheri, Alireza↗
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↗