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Showing papers by "National Aerospace Laboratories published in 1995"


Journal ArticleDOI
TL;DR: In this article, a wurtzite boron nitride (wBN)-cBN composite tool was used to machine titanium alloys, and the mechanisms controlling the wear of the cutting tool have been found to be similar to those observed in polycrystalline diamond (PCD) and polyCrystalstalline cubic Boron Nitride (PCBN) tools.

113 citations


01 Jan 1995
TL;DR: In this paper, the National Research Council formed an international committee to examine the orbital debris issue, and the committee was asked to draw upon available data and analyses to characterize the current debris environment, project how this environment might change in the absence of new measures to alleviate debris proliferation, examine ongoing alleviation activities, explore measures to address the problem, and develop recommendations on technical methods to solve it.
Abstract: To acquire an unbiased technical assessment of (1) the research needed to better understand the debris environment, (2) the necessity and means of protecting spacecraft against the debris environment, and (3) potential methods of reducing the future debris hazard, NASA asked the National Research Council to form an international committee to examine the orbital debris issue. The committee was asked to draw upon available data and analyses to: characterize the current debris environment, project how this environment might change in the absence of new measures to alleviate debris proliferation, examine ongoing alleviation activities, explore measures to address the problem, and develop recommendations on technical methods to address the problems of debris proliferation.

77 citations


Journal ArticleDOI
TL;DR: In this paper, the underlying principles of electromagnetic analysis and design, fabrication and the trends in RAMs reviewed in this paper could lead to indigenisation, and even pioneering next generation of RAM technology.
Abstract: The research in the area of Radar Absorbing Materials (RAMs) has been actively pursued for at least four decades. Although resonant RAMs were originally designed by transmission line approach, and the broad band RAMs were obtained by multilayering, the quest for ultrawide band performance has led to novel approaches such as chirality and even exploring biochemical products. It is observed that radome materials are frequently used as RAMs. The understanding of the underlying principles of electromagnetic analysis and design, fabrication and the trends in RAMs reviewed in this paper could lead to indigenisation, and even pioneering next generation of RAM technology.

72 citations


Journal ArticleDOI
TL;DR: In this paper, an optical microscopy study of stress relief patterns in diamond-like carbon films is presented, which include the well-known sinusoidal type, branching pattern and string-of-beads pattern.

61 citations



Journal ArticleDOI
TL;DR: In this paper, the stability of boundary-layer flows in pressure gradients is presented, taking into account the spatial development of the flow and utilizing a special coordinate transformation, which is consistent with that of Bertolotti et al. (1992) to O(R(-1)) but simpler (i.e. has fewer terms).
Abstract: A new formulation of the stability of boundary-layer flows in pressure gradients is presented, taking into account the spatial development of the flow and utilizing a special coordinate transformation. The formulation assumes that disturbance wavelength and eigenfunction vary downstream no more rapidly than the boundary-layer thickness, and includes all terms nominally of order R(-1) in the boundary-layer Reynolds number R. In Blasius flow, the present approach is consistent with that of Bertolotti et al. (1992) to O(R(-1)) but simpler (i.e. has fewer terms), and may best be seen as providing a parametric differential equation which can be solved without having to march in space. The computed neutral boundaries depend strongly on distance from the surface, but the one corresponding to the inner maximum of the streamwise velocity perturbation happens to be close to the parallel flow (Orr-Sommerfeld) boundary. For this quantity, solutions for the Falkner-Skan flows show the effects of spatial growth to be striking only in the presence of strong adverse pressure gradients. As a rational analysis to O(R(-1)) demands inclusion of higher-order corrections on the mean flow, an illustrative calculation of one such correction, due to the displacement effect of the boundary layer, is made, and shown to have a significant destabilizing influence on the stability boundary in strong adverse pressure gradients. The effect of non-parallelism on the growth of relatively high frequencies can be significant at low Reynolds numbers, but is marginal in other cases. As an extension of the present approach, a method of dealing with non-similar flows is also presented and illustrated. However, inherent in the transformation underlying the present approach is a lower-order non-parallel theory, which is obtained by dropping all terms of nominal order R(-1) except those required for obtaining the lowest-order solution in the critical and wall layers. It is shown that a reduced Orr-Sommerfeld equation (in transformed coordinates) already contains the major effects of non-parallelism.

31 citations


Journal ArticleDOI
TL;DR: In this paper, the minimum total potential theorem and the Hu-Washizu theorem were used to derive the orthogonality condition for determining consistent, thermal stresses in a variationally correct manner.

29 citations


Journal ArticleDOI
TL;DR: In this article, the authors evaluated the performance of 3M riblets on a supercritical airfoil at transonic speeds covering an angle of attack range of -0.5 to 1 deg.
Abstract: Numerous studies have shown that viscous drag reduction of 4-8% at low speeds can be achieved in simple two-dimensional flows at wind-tunnel Reynolds numbers. Because of the encouraging benefits realized at low speeds, an evaluation of riblet effectiveness at subsonic and transonic speeds, both in wind tunnels and flight, has been reported. Realistic applications involve, among other factors, pressure gradient (eg, airfoil and wing) and three-dimensionality. Drag reductions under these conditions are being assessed currently. This paper presents recent results of drag reduction using 3M riblets on a supercritical airfoil at transonic speeds covering an angle of attack range of -0.5 to 1 deg, which is relevant to cruise conditions. (Authors)

28 citations


Journal ArticleDOI
TL;DR: In this article, an exact analytical solution of the governing biharmonic equation is derived which not only contains the leading term of the required singularities at the upper corners, but also approximately satisfies the boundary conditions at all four walls.
Abstract: The problem considered here is the steady, incompressible plane Stokes flow in a rectangular cavity generated by uniform translation of the upper wall. An exact analytical solution of the governing biharmonic equation is derived which not only contains the leading term of the required singularities at the upper corners, but also approximately satisfies the boundary conditions at all four walls. A standard numerical algorithm is employed to correct the small deviations in the boundary conditions satisfied by the analytical solution. This technique enables accurate computation of the solution uniformly throughout the domain; in particular, near the singular corners and in those regions where the flow is extremely weak, for example, in the secondary vortex regions of the deep cavity. The method is illustrated for the square cavity and also for a deep cavity with a depth-to-width ratio of five, and the results are compared with previous analytical and numerical solutions.

28 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated the flow field around a sphere with and without ventilation in a wind tunnel over a range of Reynolds numbers in an incompressible flow and found that at supercritical Re, the pressure drag of a sphere can be nearly nullified by venting only 2% of the frontal area of the sphere to the base through a smooth internal duct.
Abstract: The flowfield around a sphere with and without ventilation was investigated in a wind tunnel over a range of Reynolds numbers in an incompressible flow. At supercritical Re, the pressure drag of a sphere can be nearly nullified by venting only 2% of the frontal area of the sphere to the base through a smooth internal duct. The drag reduction is achieved by increased pressures in the separated flow region close to the base. At high Re, the vent flow breaks through the near wake and brings about symmetry in the global flowfield. When the internal shear is increased by using a rough internal duct, the base pressure is unchanged, but the external flow is accelerated to velocities beyond that achieved by the potential flow around the basic sphere. The findings can be explained by a flow model in which the near wake is aerodynamically streamlined by a pair of counterrotating vortex rings at the base. A roughness element can be made to partially destroy the vortex system at the base and result in a steady asymmetric wake. A 1.2 mm diameter wire placed at 70° was found to overtrip the boundary layer and completely destroy the vortex system. Simultaneously, the turbulent separation is advanced and the drag increased.

27 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated the evolution of the β phase in rapidly quenched Ti-2.8 pct Co and Ti-4.5 pct Cu alloys by electron microscopy, and found that the lamellar intermetallic compound Ti2Cu was found to evolve by a sympathetic nucleation process.
Abstract: The decomposition of the β phase in rapidly quenched Ti-2.8 at. pct Co, Ti-5.4 at. pct Ni, Ti-4.5 at. pct, and 5.5 at. pct Cu alloys has been investigated by electron microscopy. During rapid quenching, two compctitive phase transformations, namely martensitic and eutectoid transformation, have occurred, and the region of eutectoid transformation is extended due to the high cooling rates involved. The β phase decomposed into nonlamellar eutectoid product (bainite) having a globular morphology in Ti-2.8 pct Co and Ti-4.5 pct Cu (hypoeutectoid) alloys. In the near-eutectoid Ti-5.5 pct Cu alloy, the decomposition occurred by a lamellar (pearlite) type, whereas in Ti-5.4 pct Ni (hypereutectoid), both morphologies were observed. The interfaces between the proeutectoid α and the intermetallic compound in the nonlamellar type as well as between the proeutectoid α and the pearlite were often found to be partially coherent. These findings are in agreement with the Lee and Aaronson model proposed recently for the evolution of bainite and pearlite structures during the solid-state transformations of some titanium-eutectoid alloys. The evolution of the Ti2Cu phase during rapid quenching involved the formation of a metastable phase closely related to an “ω-type” phase before the equilibrium phase formed. Further, the lamellar intermetallic compound Ti2Cu was found to evolve by a sympathetic nucleation process. Evidence is established for the sympathetic nucleation of the proeutectoid a crystals formed during rapid quenching.

Journal ArticleDOI
TL;DR: In this article, the effects of fiber volume fraction and incident energy on the impact damage tolerance of composite laminates subjected to low13; velocity impacts at constant strike velocities were studied.
Abstract: An effort made to study the effects of fiber volume fraction and incident13; energy on the impact damage tolerance of composite laminates subjected to low13; velocity impacts at constant strike velocities. Repeated drop tests were conducted using an13; inhouse built drop weight impact-tester: Delamination-area was used as parameter for13; quantifying damage while the number of drops (impacts) to failure use to assess the13; damage tolerance limits. The delamination area was found to increase and then saturate13; after a certain number of drops. Impact fatigue studies showed the existence of a critical13; Incident energy (Ec) around which design of opmposite structures can be based. Also the13; minimum incident energy required to fracture the sample in a single impact (ESDT)was13; evaluated from the data. One of the interesting observations made was that for any given13; incident energy, the delamination area was found to be minimum at a certain fiber volume13; fraction (0.5 in this case) of the laminate. This was explained on lines of failure13; mechanisms reported earlier.13;

Journal ArticleDOI
TL;DR: In this article, the moisture diffusion characteristics of autoclave moulded T300-914C unidirectional composite specimens hygrothermally conditioned at 85% RH and 70'C till saturation to 1.5% moisture content were presented.
Abstract: This paper presents the moisture diffusion characteristics of autoclave moulded T300-914C unidirectional composite specimens hygrothermally conditioned at 85% RH and 70'C till saturation to 1.5% moisture content. In all, pin bearing strength test specimens of three different layup sequences viz. [45/03/ A 45/03/90/0],, [0/ 4 45/9012s and [45/02/45/03/45/0], were studied. All the test specimens exhibited Fickian Diffusion behaviour. It was further found that the Diffusion coefficient (D,) value of the composites increased with increase in the cut edge surface area and the values obtained compared well with those reported in literature. The difference in D, values obtained for different layup sequences was attributed to tortuousity caused by fibre orientations.

Journal ArticleDOI
TL;DR: In this article, the authors investigated features of vortex asymmetry and induced side forces on a family of three elliptic cones at subsonic speeds, and found that ellipticity progressively reduces the angle of attack for the onset of side force up to an ellipticity ratio (defined here as the ratio of major to minor axis) of 143.
Abstract: Experimental studies were carried out investigating features of vortex asymmetry and induced side forces on a family of three elliptic cones at subsonic speeds Measurements of forces, moments, and surface flow visualization studies were made up to an angle of attack of 45 deg over a wide range of Reynolds number Results show that ellipticity progressively reduces the angle of attack for the onset of side force up to an ellipticity ratio (defined here as the ratio of major to minor axis) of 143, beyond which there is a reversal in this trend for both horizontal as well as vertical orientations of the ellipse Interestingly, the (maximum) side force magnitudes are larger for the horizontal compared to the vertical ellipse orientation on each model A correlation of the angle of attack for the onset of asymmetry on pointed forebodies with elliptic cross section is suggested These results provide strong support to the hypothesis (often made in the literature) that inviscid mechanisms may play a key role in triggering asymmetry of vortex flows

Journal ArticleDOI
TL;DR: In this paper, a critical assessment of two vortex approaches (both two-dimensional) to the modelling of turbulent mixing layers is presented, paying due attention in both to the boundary conditions far downstream as well as those on the splitter plate from which the mixing layer issues.

Journal ArticleDOI
TL;DR: In this article, a finite element formulation based on the Fourier law of heat conduction is presented to analyze the transient temperature distribution in rectangular fiber-reinforced composite plates, where three-dimensional twenty-noded brick elements are used to discretize the spatial domain of the plate.
Abstract: A finite element formulation based on the Fourier law of heat conduction is presented to analyze the transient temperature distribution in rectangular fiber-reinforced composite plates. Three-dimensional twenty-noded brick elements are used to discretize the spatial domain of the plate. A Crank-Nicolson time marching scheme is used to solve the resulting time-dependent ordinary differential equations. The finite element solution is tested for convergence of results with mesh refinement. Further, the FEM is validated comparing the qualitative nature of results obtained for a plate made of aluminium and steel laminae with that of Tanigawa et al. Results are presented for graphite/epoxy and graphite-kevlar/epoxy plates subjected to different thermal boundary conditions. Laminae with fiber orientations of 0°, ±45°, and 90° are considered for the analysis. The results indicate that the temperature variation in the plane of the plate (x-y plane) is very much dependent on the boundary conditions. When the faces ...

Journal ArticleDOI
TL;DR: It is argued that cognitive models should be produced with an awareness of the possible form of the final computer model and the structure of these models would provide qualitative descriptions and explanations of behaviour which could be assimilated by non-specialists.
Abstract: Models of physical systems range from those of initial individual cognition to mathematical representations on a computer which are accepted as the developed final models. It is conjectured that a formalization of the qualitative cognitive models will help us to understand how they are formed and will eventually help us to produce better computer models. The structure of these models would provide qualitative descriptions and explanations of behaviour which could be assimilated by non-specialists. It is argued that cognitive models should be produced with an awareness of the possible form of the final computer model. To illustrate this, a case study of the development of the cognitive and computer models of a naturally parallel physical process is presented. This early work is part of the broader goal of producing an appropriate computing environment through which various models and techniques are combined for producing explanations. A procedure for developing models from the primitive stage to computer implementation is suggested. Theories in cognitive science and research on mental models are briefly discussed.

Journal ArticleDOI
TL;DR: In this article, the curing of triglycidyl para-aminophenol (TGPAP) epoxy resin with three aromatic amine hardeners, diaminodiphenye sulphone (DDS), pyridinediamine (PDA), and toluenediamine(TDA), has been investigated.
Abstract: The curing of triglycidyl para-aminophenol (TGPAP) epoxy resin with three aromatic amine hardeners, diaminodiphenye sulphone (DDS), pyridinediamine (PDA), and toluenediamine (TDA), has been investigated. A series of isothermal cures was conducted and analyzed by Fourier transform infrared spectrometry (FTIR) and differential scanning calorimetry (DSC). The chemical reactions occurring during cure were monitored at different temperatures by qualitative and quantitative estimation of different groups in the IR spectra, and the ratio of rate constants (k2/k1) were evaluated. Dynamic DSC analysis of TGPAP/TDA resulted in two exothermal peaks, indicating cure kinetics different from those of TGPAP/DDS and TGPAP/PDA systems, which gave a single exothermal peak. Various kinetic parameters such as total heat of reaction ?H?, activation energy Ea, Frequency factor z, and order of reaction n were evaluated for all the three systems. From the initial kick-off temperatures and activation energy values it was concluded that the rate of curing followed the order TDA amp;gt; PDA amp;gt; DDS. The reaction conversions during cure, evaluated from IR analysis, were exactly the same as those obtained from DSC Borchardt-Daniels kinetics. Using this model, the plots of time vs. temperature for different conversions were constructed for all the three systems; on the basis of these, the cure cycles can be fixed.

Journal ArticleDOI
TL;DR: In this paper, an upwind total variation diminishing formulation of the Roe Riemann solver within the cell-centered finite volume approach was used for three-dimensional supersonic and hypersonic inviscid blunt body flow computations.
Abstract: This paper discusses some aspects of three-dimensional supersonic and hypersonic inviscid blunt body flow computations. The method used is based on the solution of the Euler equations employing an explicit, upwind total variation diminishing formulation of the Roe Riemann solver within the cell-centered finite volume approach. A comparative study of various total variation diminishing limiters and entropy fixes is carried out to identify the most appropriate combination. The effect of using cell spacing in the total variation diminishing extrapolations is highlighted. Furthermore, a Mach number dependence and grid sensitivity study is carried out on various total variation diminishing limiters scaled with mesh spacing. Local time stepping and code parallelization has been employed to accelerate convergence in terms of effective wall clock times.

Journal ArticleDOI
TL;DR: In this paper, the use of the Jameson-Schmidt-Turkel (JST) dissipation scheme is successfully extended to compute hypersonic flows over an airfoil.
Abstract: In the present work, the use of the Jameson-Schmidt-Turkel (JST) dissipation scheme is successfully extended to compute hypersonic flows over an airfoil. It is shown that this scheme is not only capable of computing flows at speeds all the way up to Mach 50, but also the rate of convergence and the final results are as good as those obtained using the Swanson-Turkel modification of the JST scheme and better than the Yoon-Kwak flux limited dissipation specially designed to compute high-speed flows. The scheme is seen to be so robust that it does not require a well-prepared starting solution to compute flows with either strong shocks or with high incidence, or both.

Book ChapterDOI
01 Jan 1995
TL;DR: An explicit finite volume TVD (MUSCL) formulation of the Roe's Approximate Riemann Solver is presented for the solution of three-dimensional Euler and Navier-Stokes equations as mentioned in this paper.
Abstract: An explicit finite volume TVD (MUSCL) formulation of the Roe's Approximate Riemann Solver is presented for the solution of three-dimensional Euler and Navier-Stokes equations. It is shown to provide accurate solutions of 3D inviscid and viscous high speed flows past blunt body configurations of practical interest.

Journal ArticleDOI
TL;DR: In this paper, the authors re-examine the mechanics of the residual bending flexibility correction and show that it is an extravariational trick, which is an improvement over the conventional residual bending correction.
Abstract: In this paper I re-examine the mechanics of the residual bending flexibility correction and show that it is an extravariational trick.

Journal ArticleDOI
TL;DR: In this paper, a finite volume method based on the nodal point approach was used to develop an algebraic turbulence model for the computation of the transonic flows with shock-induced separation.
Abstract: A finite volume method based on the nodal point approach was used to develop an algebraic turbulence model for the computation of the transonic flows with shock-induced separation. Three examples were considered using a C type algebraic grid. Results of the study suggest that the flow between the wall and the minimum velocity line inside the bubble can be treated as laminar, and outside the minimum velocity line the flow behaves like attached flow.

Journal ArticleDOI
TL;DR: In this article, the preparation of high-purity silicon nitride powder (useful as high-temperature ceramic material) from silicon tetrachloride has been studied, which involved vapour reaction in a two-zone horizontal furnace.
Abstract: The preparation of high-purity silicon nitride powder (useful as high-temperature ceramic material) from silicon tetrachloride has been studied. Zinc was chosen for reduction to Si, which involved vapour reaction in a two-zone horizontal furnace. The silicon nitride whiskers formed were characterized by x-ray diffraction (XRD) and electron microscopy. The whiskers were very thin (approx 0.5 mu m, length gt; 1 cm) at low reaction temperature (950 deg C). In situ nitration with increased nitrogen flow was tried without success, although 0.1 mu m whisker thickness was obtained, and dry ammonia gas was then used for separate nitration at 1200-1300 deg C. XRD and infrared absorption data revealed alpha -Si sub 3 N sub 4 as the product (thickness 0.5, length approx 12 mu m). Such whisker-like particles with uniform aspect ratio may also be useful in ceramic composites.

Book ChapterDOI
TL;DR: In this paper, the authors presented an experimental program on fatigue crack growth in an interference fit lug joint and numerical estimation of relevant fracture parameters to correlate the experimental data, which resulted in a power law similar to the Paris equation.
Abstract: Results of an experimental program on fatigue crack growth in an interference fit lug joint and numerical estimation of relevant fracture parameters to correlate the experimental data are presented. Fatigue crack growth rates of naturally initiating cracks were estimated fractographically as a function of crack length for lug joints fitted with different levels of interference. The fracture parameters to correlate the crack growth behavior were estimated using a 2D materially nonlinear contact stress finite element analysis. A path-independent integral, computed for incremental loads and summed up during cyclic loading, was used as an elasto-plastic fracture parameter. Correlation of the experimental crack growth data and the evaluated range of Delta-T resulted in a power law similar to the Paris equation. Further, the fatigue crack growth rate was evaluated using the relationship between low cycle fatigue parameters and Delta-T, as estimated. These are in good agreement with the experimental results. (Author

01 Mar 1995
TL;DR: In this article, an elliptic grid generation method is presented which generates excellent boundary conforming grids in domains in 2D physical space based on the composition of an algebraic and elliptic transformation.
Abstract: An elliptic grid generation method is presented which generates excellent boundary conforming grids in domains in 2D physical space. The method is based on the composition of an algebraic and elliptic transformation. The composite mapping obeys the familiar Poisson grid generation system with control functions specified by the algebraic transformation. New expressions are given for the control functions. Grid orthogonality at the boundary is achieved by modification of the algebraic transformation. It is shown that grid generation on a minimal surface in 3D physical space is in fact equivalent to grid generation in a domain in 2D physical space. A second elliptic grid generation method is presented which generates excellent boundary conforming grids on smooth surfaces. It is assumed that the surfaces are parametrized and that the grid only depends on the shape of the surface and is independent of the parametrization. Concerning surface modeling, it is shown that bicubic Hermite interpolation is an excellent method to generate a smooth surface which is passing through a given discrete set of control points. In contrast to bicubic spline interpolation, there is extra freedom to model the tangent and twist vectors such that spurious oscillations are prevented.

Journal ArticleDOI
TL;DR: A computer code has been developed for estimating the aerodynamic characteristics of cruciform missile configurations at high angles of attack, with13; arbitrary control deflections and non-zero roll angle, which demonstrates the capability of the code for preliminary design of missile configurations.
Abstract: A computer code has been developed for estimating the aerodynamic characteristics of cruciform missile configurations at high angles of attack (upto 30xB0;), with13; arbitrary control deflections (xB1;25xB0;) and non-zero roll angle (0 xA3; 0 xA3; 90xB0;). The prediction code is based on the equivalent angle of attack technique. It combines semi-empirical methods, theoretical methods and correlated data bases. The code has been validated over a wide range of missile configurations and flight parameters. The overall capabilities of the code have been compared with nine other missile aeroprediction codes. These studies have demonstrated the capability of the code for preliminary design of missile configurations.

Journal ArticleDOI
TL;DR: In this paper, a review is made of efforts at the National Aerospace Laboratories in the development of fatigue crack growth prediction technology for airframe applications, focusing on extension of rainflow techniques for crack growth analysis and development of accelerated crack growth calculation methods for spectrum loading.
Abstract: A review is made of efforts at the National Aerospace Laboratories in the development of fatigue crack growth prediction technology for airframe applications. The research was focused on extension of rainflow techniques for crack growth analysis and development of accelerated crack growth calculation methods for spectrum loading. Fatigue crack closure forms a crucial element of modelling and fractographic techniques were developed for its study. These, combined with binary coded event registration enabled crack growth and closure mapping for part-through cracks in metallic materials. Experimental research on short cracks at notches led to discovery of the hysteretic nature of crack closure, which explains well-known history-sensitive local mean stress effects in notch root fatigue. Optical fractography of failures obtained under simulated service conditions revealed that short cracks do not exhibit any more scatter than long cracks at comparable growth rates. The nature of multi-site crack initiation and growth of small cracks at notches was investigated and the effort extended to lug joints that are widely used in airframe applications. Results from this work suggest the possibility of modelling crack growth from a size smaller than 50 microns through to failure, thereby accounting for a major fraction of total life.

Journal ArticleDOI
TL;DR: The paper describes the multigrid acceleration technique to compute numerical solutions of three equations of common fluid mechanical interest; Laplace equation, transonic full potential equation and Reynolds averaged Navier-Stokes equations, which offers these codes as designer's tools for evaluating the characteristics of the airfoils.
Abstract: The paper describes the multigrid acceleration technique to compute numerical solutions of three equations of common fluid mechanical interest; Laplace equation, transonic full potential equation and Reynolds averaged Navier-Stokes equations. Starting with the simple and illustrative multigrid studies on the Laplace equation, the paper discusses its application to the cases of full potential equation and the Navier-Stokes equations. The paper also discusses some elements of multigrid strategies like V- and W-cycles, their relative efficiencies, the effect of number of grid levels on the convergence rate and the large CPU time saving obtained from the multigrid acceleration. A few computed cases of transonic flows past airfoils using the full potential equations and the Navier-Stokes equations are presented. A comparison of these results with the experimental data shows good agreement of pressure distribution and skin friction. With the greatly accelerated multigrid convergence, the full potential code typically takes about 10 seconds and the Navier-Stokes code for turbulent flows takes about 5 to 15 min of CPU time on the Convex 3820 computer on a mesh which resolves the flow quantities to good levels of accuracy. This low CPU time demand, made possible due to multigrid acceleration, on one hand, and the robustness and accuracy on the other, offers these codes as designer’s tools for evaluating the characteristics of the airfoils.

Book ChapterDOI
01 Jan 1995
TL;DR: In this paper, a unified EMD is presented to model delaminated stiffened laminated composite shells, for synthesizing accurate multiple postbuckling solution paths under compressive loading, and for predicting delamination growth in an a posteriori sense with reference to finite element applications.
Abstract: In this paper, a unified ethod is presented to model delaminated stiffened laminated composite shells, for synthesizing accurate multiple post-buckling solution paths under comprssive loading, and for predicting delamination growth in an a posteriori sense with reference to finite element applications. A multi-domain modeling technique is presented for modeling the delaminated stiffened shell structures. Error-free formulations axe presented for a 2-noded curved stiffener element and a 3-noded shell element for geometrically nonlinear applications. An accurate and simple automated solution strategy based on Newton type iterations is presented for predicting the general geometrically nonlinear and postbuckling behaviour of structures. Finally, a simple method is derived for predicting the delamination growth in terms of pointwise energy release rate at the delamination front from the 3-dimensional J-integral.