On A. Raychaudhuri's Paper "Electric Energy Bands in Model Three-Dimensional Lattices"
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Schwed, Philip↗
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Lattice theory of three-dimensional cracks
The problem of the stability of a three-dimensional crack is analyzed within a lattice-statics approximation. The consequence of introducing a jog into the crack face as well as the effects of various nonlinear-force laws are studied. The phenomenon of lattice trapping (upper and lower bounds on the applied stress for an equilibrium crack of given length) is again obtained. It is possible to obtain some physical insight into which aspects of the force law are critical for crack stability. In particular, the inadequacy of a thermodynamic approach - which relates the critical stress to a surface energy corresponding to the area under the cohesive-force-vs-displacement curve - is demonstrated. Surface energy is a global property of the cohesive-force law. Crack stability is sensitive to much more refined aspects of the cohesive-force law. Crack healing is sensitive to the long-range portion of the cohesive force. Crack expansion is sensitive to the position of the maximum in the cohesive-force relation.
Esterling, D. M.↗
Dual wing, swept forward swept rearward wing, and single wing design optimization for high performance business airplanes
An investigation was performed to compare closely coupled dual wing and swept forward swept rearward wing aircraft to corresponding single wing 'baseline' designs to judge the advantages offered by aircraft designed with multiple wing systems. The optimum multiple wing geometry used on the multiple wing designs was determined in an analytic study which investigated the two- and three-dimensional aerodynamic behavior of a wide range of multiple wing configurations in order to find the wing geometry that created the minimum cruise drag. This analysis used a multi-element inviscid vortex panel program coupled to a momentum integral boundary layer analysis program to account for the aerodynamic coupling between the wings and to provide the two-dimensional aerodynamic data, which was then used as input for a three-dimensional vortex lattice program, which calculated the three-dimensional aerodynamic data. The low drag of the multiple wing configurations is due to a combination of two dimensional drag reductions, tailoring the three dimensional drag for the swept forward swept rearward design, and the structural advantages of the two wings that because of the structural connections permitted higher aspect ratios.
Rhodes, M. D.↗
A quasi-vortex-lattice method in thin wing theory
A quasi-continuous method is developed for solving thin-wing problems. For the purpose of satisfying the wing boundary conditions, the spanwise vortex distribution is assumed to be stepwise-constant, while the chordwise vortex integral is reduced to a finite sum through a modified trapezoidal rule and the theory of Chebyshev polynomials. Wing-edge and Cauchy singularities are acounted for. The total aerodynamic characteristics are obtained by an appropriate quadrature integration. The two-dimensional results for airfoils without flap deflection reproduce the exact solutions in lift and pitching moment coefficients, the leading edge suction, and the pressure difference at a finite number of points. For a flapped airfoil, the present results are more accurate than those given by the vortex-lattice method. The three-dimensional results also show an improvement over the results of the vortex-lattice method. Extension to nonplanar applications is discussed.
Lan, C. E.↗
Evaluation of Superalloy 718 Additively Manufactured Lattice Blocks
Lattice block structures made up of high temperature superalloys could offer advantages in density, efficiency, and tailored properties. Three candidate lattice designs were screened through additive manufacturing of superalloy 718. Laser powder bed fusion was applied with 718 powder to produce lattice blocks for three-dimensional octahedral unit cell designs of three heights. As-designed versus additively manufactured 718 lattices were compared, including structural dimensions, densities, defects, grain structures, crystallographic texture, and surface residual stresses. Manufactured lattice I diverged the most from its design, with both corner and center nodes merged into continuous columns. Manufactured lattice III came closest to its design, though the actual nodes and struts were still larger in cross section than in the design. Only modest grain coarsening and negligible chemical segregation were observed for all three designs, suggesting uniform thermo-physical and mechanical properties are possible. Significant tensile residual stresses were present at the surface of the manufactured blocks, with highest stresses in the building direction. Current findings indicate this concept could produce useful superalloy structures for high-temperature-capable static components requiring tailored density, and thermo-physical/mechanical properties.
super alloys↗
Evaluations of Additively Manufactured Superalloy Lattice Blocks
Cast lattice block structures made up of high-temperature superalloys were previously shown to offer advantages in density, efficiency, and tailored properties. However, inconsistencies in casting die-fill, composition, and microstructure were identified as persistent issues with the casting process path. Three candidate lattice designs were screened through additive manufacturing of a superalloy. Laser powder bed fusion was applied with superalloy powder to produce lattice blocks for three-dimensional octahedral unit-cell designs of three heights. Properties of the structural designs versus additively manufactured lattices were compared, including structural dimensions, densities, defects, grain structures, crystallographic texture, and surface residual stresses. Findings indicate this concept could produce useful superalloy structures for high-temperature-capable static components requiring tailored density, and thermophysical and mechanical properties.
superalloy↗
Optimization and design of three-dimensional aerodynamic configurations of arbitrary shape by a vortex lattice method
A new method based on vortex lattice theory has been developed which can be applied to the combined analysis, induced drag optimization, and aerodynamic design of three-dimensional configurations of arbitrary shape. Geometric and aerodynamic constraints can be imposed on both the optimization and the design process. The method is compared with several known analytical solutions and is applied to several different design and optimization problems, including formation flight and wingtip fins for the Boeing KC-135 tanker airplane. Good agreement has been observed between the theoretical predictions and the wind tunnel test results for the KC-135 modification.
Feifel, W. M.↗
A program to compute three-dimensional subsonic unsteady aerodynamic characteristics using the doublet lattice method, L216 (DUBFLEX). Volume 2: Supplemental system design and maintenance document
The information necessary for execution of the digital computer program L216 on the CDC 6600 is described. L216 characteristics are based on the doublet lattice method. Arbitrary aerodynamic configurations may be represented with combinations of nonplanar lifting surfaces composed of finite constant pressure panel elements, and axially summetric slender bodies composed of constant pressure line elements. Program input consists of configuration geometry, aerodynamic parameters, and modal data; output includes element geometry, pressure difference distributions, integrated aerodynamic coefficients, stability derivatives, generalized aerodynamic forces, and aerodynamic influence coefficient matrices. Optionally, modal data may be input on magnetic field (tape or disk), and certain geometric and aerodynamic output may be saved for subsequent use.
Harrison, B. A.↗
A program to compute three-dimensional subsonic unsteady aerodynamic characteristics using the doublet lattic method, L216 (DUBFLX). Volume 1: Engineering and usage
The program input presented consists of configuration geometry, aerodynamic parameters, and modal data; output includes element geometry, pressure difference distributions, integrated aerodynamic coefficients, stability derivatives, generalized aerodynamic forces, and aerodynamic influence coefficient matrices. Optionally, modal data may be input on magnetic file (tape or disk), and certain geometric and aerodynamic output may be saved for subsequent use.
Richard, M.↗
Calculation of aerodynamic characteristics of STOL aircraft with externally-blown jet-augmented flaps.
Analytical methods to predict the interference between lifting surfaces and high-bypass-ratio turbofan engines are described. A three-dimensional nonplanar vortex-lattice lifting surface method is used to predict the characteristics of a wing with leading-edge slat and multiple slotted trailing-edge flaps including effects of externally induced velocity fields. A flow model of the wake of a high-bypass-ratio turbofan is described which is capable of predicting the induced velocity field both inside and outside the jet wake. These methods are combined to predict the longitudinal characteristics of several STOL transport models utilizing externally-blown flaps and comparisons with data are shown. The results indicate good agreement between experiment and theory for various configurations under a wide range of power conditions.
Mendenhall, M. R.↗
Aerodynamic investigation of closely coupled lifting surfaces with positive and negative stagger for general aviation applications
Aerodynamic closely coupled lifting surfaces were investigated for both conventional tail aft configurations and canard configurations to determine whether positive stagger or negative stagger had more attractive aerodynamic characteristics. An inviscid multi-element vortex panel program was used in conjunction with a momentum integral boundary layer program to predict two-dimensional aerodynamic characteristics. A multi-element vortex lattice program was used for three-dimensional characteristics. Pressure distributions, transition location, momentum thickness, two- and three-dimensional drag, and boundary layer separation were compared for the positive and negative stagger case. For staggers less than six the results demonstrated that positive stagger configurations are aerodynamically superior.
Selberg, B. P.↗
Flow of Gas Through Turbine Lattices
This report is concerned with fluid mechanics of two-dimensional cascades, particularly turbine cascades. Methods of solving the incompressible ideal flow in cascades are presented. The causes and the order of magnitude of the two-dimensional losses at subsonic velocities are discussed. Methods are presented for estimating the flow and losses at high subsonic velocities. Transonic and supersonic flows in lattices are then analyzed. Some three-dimensional features of the flow in turbines are noted.
BOUNDARY LAYER - AIRFOILS - CASCADES↗
Models for the interaction of rarefied gas with a surface
Various theoretical models are discussed for the interaction of gaseous atoms with solids at energies of approximately 10 eV. The surface is modeled by a one- and three-dimensional aggregate of atoms with different initial conditions and lattice parameters. In calculating the accommodation coefficients, the direct integration of the equations of motion of gaseous molecules and atoms in the crystal lattice of the solid is used. An analysis of the advantages and the drawbacks of the models, as well as the possibilities of the analytical solutions in a one-dimensional case, is given. The dependence of the energy and the normal and the tangential momenta accommodation coefficients on the collision parameters is obtained.
Pyarnpuu, A. A.↗
An experimental investigation of olivine morphology
Results are reported for a morphological study of olivine and an experimental investigation performed to determine the degrees of supercooling and the cooling rates necessary to crystallize particular morphologies. Ten arbitrary categories of three-dimensional olivine crystal shape are identified: polyhedral, granular, hopper, chain, lattice, plate, branching, radiate, feather, and swallow-tail. The morphological study establishes that equant and tabular crystals are the common shapes of olivine, nonequant crystals are elongate parallel to the a or c axis, and skeletal crystals result when a particular form is missing or only partially developed. In the experiment, olivine crystals were grown by melting rock samples above their liquidus temperatures before initiating crystallization. The results show that olivine morphology changes systematically as a function of the degree of melt supercooling, the melt cooling rate, and the normative olivine and water contents of the melt. It is also found that each shape has a specific range of temperature stability which is essentially independent of melt composition.
Donaldson, C. H.↗
Aerodynamic canard/wing parametric analysis for general aviation applications
Vortex panel and vortex lattice methods have been utilized in an analytic study to determine the two- and three-dimensional aerodynamic behavior of canard and wing configurations. The purpose was to generate data useful for the design of general aviation canard aircraft. Essentially no two-dimensional coupling was encountered and the vertical distance between the lifting surfaces was found to be the main contributor to interference effects of the three-dimensional analysis. All canard configurations were less efficient than a forward wing with an aft horizontal tail, but were less sensitive to off-optimum division of total lift between the two surfaces, such that trim drag could be less for canard configurations. For designing a general aviation canard aircraft, results point toward large horizontal and vertical distance between the canard and wing, a large wing-to-canard area ratio, and with the canard at a low incidence angle relative to the wing.
Keith, M. W.↗
Computational technique for three-dimensional compressible flow past wings at high angles of attack
A computational technique, based on the integral solution of the full potential equation, has been developed for the solution of three-dimensional high-subsonic flows past wings at high angles of attack. The problem includes two sources of nonlinearities: a boundary oriented nonlinearity (separated flow roll up) and a region oriented nonlinearity (flow compressibility). The former is represented by a nonlinear vortex lattice while the latter is represented by a source distribution inside a finite volume. The solution is obtained by using double iteration cycles; a separated flow (wake) iteration cycle and a compressibility iteration cycle. The computational technique is applied to a delta wing. The results show that the technique is very promising and efficient.
Kandil, O. A.↗
Finite element solution theory for three-dimensional boundary flows
A finite element algorithm is derived for the numerical solution of a three-dimensional flow field described by a system of initial-valued, elliptic boundary value partial differential equations. The familiar three-dimensional boundary layer equations belong to this description when diffusional processes in only one coordinate direction are important. The finite element algorithm transforms the original description into large order systems of ordinary differential equations written for the dependent variables discretized at node points of an arbitrarily irregular computational lattice. The generalized elliptic boundary conditions is piecewise valid for each dependent variable on boundaries that need not explicitly coincide with coordinate surfaces. Solutions for sample problems in laminar and turbulent boundary flows illustrate favorable solution accuracy, convergence, and versatility.
Baker, A. J.↗
COMOC: Three dimensional boundary region variant, programmer's manual
The three-dimensional boundary region variant of the COMOC computer program system solves the partial differential equation system governing certain three-dimensional flows of a viscous, heat conducting, multiple-species, compressible fluid including combustion. The solution is established in physical variables, using a finite element algorithm for the boundary value portion of the problem description in combination with an explicit marching technique for the initial value character. The computational lattice may be arbitrarily nonregular, and boundary condition constraints are readily applied. The theoretical foundation of the algorithm, a detailed description on the construction and operation of the program, and instructions on utilization of the many features of the code are presented.
Orzechowski, J. A.↗