Approximate factorization scheme for transonic potential flow computations

The implicit approximate factorization scheme known asaf2 is investigated here for the purpose of application to the solution of two-and three-dimensional transonic full potential equations in conservative form. The artificial viscosity used by different authors has been deduced, and is discussed in detail. A second-order correction to the implicit artificial viscosity is tested for transonic flow past a Korn aerofoil at both design and off-design conditions. The inviscid transonic flow past different aerofoils, wings and wing-body configurations has been computed using theaf2 scheme and the solutions are compared with experimental and other numerical results. It is shown that theaf2 scheme is fast, and is not sensitive to grid stretching. Modified version of the paper presented at CAARC (Commonwealth Advisory Aeronautical Research Council) Specialists Meeting on Computational Fluid Dynamics, held during 5–10 December, 1988, at National Aeronautical Laboratory, Bangalore.     

Current research in composite structures at NASA’s langley research center

Research on the mechanics of composite structures atnasa’s Langley Research Center is discussed. The advantages and limitations of special purpose and general purpose analysis tools used in research are reviewed. Future directions in computational structural mechanics are described to address analysis short-comings. Research results on the buckling and postbuckling of unstiffened and stiffened composite structures are presented. Recent investigations of the mechanics of failure in compression and shear are reviewed. Preliminary studies of the dynamic response of composite structures due to impacts encountered during crash-landings are presented. Needs for future research are discussed.     

CFD codes and applications at boeing

The use of computational methods for three-dimensional flow design and analysis at the Boeing Company is presented. A range of computational “tools” consisting of “production” tools for everyday use by project engineers, “expert user” tools for special applications by computational researchers, and a new “emerging” tool which may see considerable use in the near future is described. These methods include full potential and Euler solvers, some coupled to three-dimensional boundary layer analysis methods, for transonic flow analysis about nacelle, wing/body, wing/body/strut/nacelle, and complete airplane configurations. As the examples presented show, such a tool box of codes is necessary for the variety of applications typical of an industrial environment. Such a tool box of codes makes possible aerodynamic advances not previously achievable in a timely manner, if at all. With a few exceptions, this paper is a version of the paper entitled “TransonicCFD applications at Boeing”, by E N Tinoco, presented at the Transonic Symposium,nasa Langley, April 1988. The paper was presented at the Specialists’ meeting onCFD, held at National Aeronautical Laboratory, Bangalore, December 1988. This paper is based in part on work conducted for the Boeing Independent Research and Development Program.     

Turbulence/shock wave interactions in chemically reacting flows

Physical interactions between turbulence and shock waves are very complex phenomena. If these interactions take place in chemically reacting flows, the degree of complexity increases dramatically. Examples of applications may be cited in the area of supersonic combustion, in which the controlled generation of turbulence and/or large scale vortices in the mixing and flame-holding zones is crucial for efficient combustion. Equally important, shock waves interacting with turbulence and chemical reactions affect the combustor flowfield resulting in enhanced relaxation and chemical reaction rates. Chemical reactions in turn contribute to dispersion of shock waves and reduction of turbulent kinetic energies. Computational schemes to address these physical phenomena must be capable of resolving various length and time scales. These scales are widely disparate and the most optimum approach is found in explicit/implicit adjustable schemes for the Navier-Stokes solver. This is accomplished by means of the generalized Taylor-Galerkin (gtg) finite element formulations. Adaptive meshes are used in order to assure efficiency and accuracy of solutions. Various benchmark problems are presented for illustration of the theory and applications. Geometries of ducted rockets, supersonic diffusers, flame holders, and hypersonic inlets are included. Merits of proposed schemes are demonstrated through these example problems. This research was supported by the US Army Missile Command (daah01-91-D-R002) and National Science Foundation (asc-8918081) and contributions were made by a number of graduate students, notably by W S Yoon.     

On the computation of steady‐state compressible flows using a discontinuous Galerkin method

Computation of compressible steady‐state flows using a high‐order discontinuous Galerkin finite element method is presented in this paper. An accurate representation of the boundary normals based on the definition of the geometries is used for imposing solid wall boundary conditions for curved geometries. Particular attention is given to the impact and importance of slope limiters on the solution accuracy for flows with strong discontinuities. A physics‐based shock detector is introduced to effectively make a distinction between a smooth extremum and a shock wave. A recently developed, fast, low‐storage p‐multigrid method is used for solving the governing compressible Euler equations to obtain steady‐state solutions. The method is applied to compute a variety of compressible flow problems on unstructured grids. Numerical experiments for a wide range of flow conditions in both 2D and 3D configurations are presented to demonstrate the accuracy of the developed discontinuous Galerkin method for computing compressible steady‐state flows. Copyright © 2007 John Wiley & Sons, Ltd.     

Numerical analysis of aerodynamic performance of rotors with leading edge slats

A three dimensional compressible Navier-Stokes analysis capable of computing flows around wings and rotors with partial-span flaps or slats is described. This analysis is cast in a moving body-fitted coordinate system permitting arbitrary motion of the solid surfaces to be directly modeled. This methodology is validated through several single and multi-element rotor and wing configurations. The analysis is subsequently applied to two helicopter rotors. The effects of leading edge slats on the aerodynamic performance of these rotors in hover is studied. It is demonstrated that leading edge slats can significantly improve the hover performance at high pitch settings, with an increase in thrust and a reduction in torque. At low pitch settings, the slats were found to be detrimental to the rotor performance. Many practical issues such as surface imperfections, proper sealing of the slat during retraction, control loads and other implementation aspects should be carefully evaluated in the event of a practical design of a slat. However, in the present study only the aerodynamic effects of slats are addressed and no practical issues are considered.This work was supported by the U.S. Army Research Office under the Center of Excellence in Rotorcraft Technology (CERT) program. Dr. Thomas Doligalski was the technical monitor.     

Truncation Approximations for Gravity-capillary Free-surface Flows

Gravity-capillary free-surface flows past disturbances in a channel of finite depth are considered. These flows are usually assumed to extend from x = −∞ to x = ∞ where the x-axis is parallel to the bottom. Many numerical schemes truncate this infinite domain to the interval −B < x < A where A and B are large positive numbers. These truncations introduce inaccuracies, especially when the effect of surface tension is included. In this paper numerical methods are presented which remove these inaccuracies. This is achieved by taking into account the contributions from −∞ to −B and from A to ∞. Explicit computations are presented for a semi-circular obstacle at the bottom of the channel.     

Development of a shock-fitting field-panel method for 3D transonic flows

The paper presents the development of a shock-fitting field-panel method for three-dimension (3D) transonic flows. In this method, the full-potential equation, written in the form of the Poisson's equation, is solved by integral equation field-panel method. The solution consists of a wing surface source panel integral term, a field-volume panel integral term of compressibility over a small limited domain, and a shock panel integral term. Due to the non-linearity of flows, solutions are obtained through an iterative procedure. Instead of using a field-panel refinement procedure, a shock-fitting technique is used to fit the shock. Finally, numerical examples are provided to demonstrate the accuracy of the method.This work is supported by NASA-Langley Research Center under the Grant No. NAG-1-1170. Dr. E. Yates, Jr. and Mr. W. Silva were the technical monitors     

On a geometrically exact curved/twisted beam theory under rigid cross-section assumption

 A geometrically exact curved/ twisted beam theory, that assumes that the beam cross-section remains rigid, is re-examined and extended using orthonormal frames of reference starting from a 3-D beam theory. The relevant engineering strain measures with an initial curvature correction term at any material point on the current beam cross-section, that are conjugate to the first Piola-Kirchhoff stresses, are obtained through the deformation gradient tensor of the current beam configuration relative to the initially curved beam configuration. The stress resultant and couple are defined in the classical sense and the reduced strains are obtained from the three-dimensional beam model, which are the same as obtained from the reduced differential equations of motion. The reduced differential equations of motion are also re-examined for the initially curved/twisted beams. The corresponding equations of motion include additional inertia terms as compared to previous studies. The linear and linearized nonlinear constitutive relations with couplings are considered for the engineering strain and stress conjugate pair at the three-dimensional beam level. The cross-section elasticity constants corresponding to the reduced constitutive relations are obtained with the initial curvature correction term. Along with the beam theory, some basic concepts associated with finite rotations are also summarized in a manner that is easy to understand. Received: 17 June 2002 / Accepted: 21 January 2003 The work was partly sponsored by a grant (CDAAH04-95-1-0175) from the Army Research Office with Dr. Gary Anderson as the grant monitor. We would also like to thank Prof. Raymond Plaut of Dept. of Civil and Environmental Engineering at Virginia Polytechnic Institute and State University for his technical help.     

Fuzzy medial axis transformation (fmat): Image representation,skeleton extraction and uncertainty management in computer vision

The problem of extraction of medial axis transformation of a gray image with reference to skeletonization, image representation and uncertainty management in a vision system has been addressed. The Fuzzy Medial Axis Transformation (fmat) of a fuzzy setf is a set of fuzzy disks whose sup isf. Unfortunately, specifying thefmat sometimes requires more storage space than specifyingf itself. The present paper describes some techniques to improve the compact representation offmat; thereby making it practically useful to an image for its skeleton extraction and compact representation, for shape analysis and template matching, for representation and retrieval, for uncertainty management in recognition and for creating new images of various poses. The algorithms involve reduction of redundancy infmat, its approximation, and reduction of the searching spaces for its computation. Computational aspects for the convenience of writing an efficient program have been described. Some applications of thefmat have also been mentioned. This work was done while SKP held annrc-nasa Senior Research Associateship at the Lyndon B Johnson Space Center, Houston, Texas.     

Precise measurements of small gas flows—metrological basis for the calibration of leak detectors

This article discusses technical aspects of the calibration of leak detectors by using a series of artificial control flows. Results are presented from the calibration of several mass-spectrometric leak detectors. Procedures and methods of analyzing measurements obtained in the calibration of such flows are discussed, and several approaches to the metrological certification of halogen and electron-capture leak detectors are described. Translated from Izmeritel'naya Tekhnika, No. 2, pp. 20–23, February, 1997.     

Mathematical methods for physical layout of printed circuit boards: an overview

This article surveys mathematical models and methods used for the physical layout of printed circuit boards, in particular component placement and wire routing. The main concepts are briefly described together with relevant references. Work supported by the DFG Research Center Matheon in Berlin.     

The vortex liquid piston engine and some other vortex technologies

By exploiting three unique characteristics of confined swirling incompressible flows — centrifugal acceleration, internal separation or recirculation zones near the axis, andbistability (i.e. rarefied and condensed stable states) of multi-phase flows — we developed several innovativevortex machines which will revolutionize mechanical technologies in a variety of industries. The machines utilizing these features include:Vortex Engine, Vortex Thruster, Vortex Suction Device, Vortex Chemical Reactor, Bubbling Centrifuge andVortex Mill. As a specific example, we describe here in some detail the development of a liquid piston engine, including analysis of its hydrodynamic and thermodynamic features. We have designed a laboratory ‘cold’ model and performed detailed experimental, theoretical and numerical analyses to study the role of the controlling parameters and are now ready to test a ‘hot’ model. In addition, we mention a few other vortex technologies of interest to us. A list of symbols used appears at the end of the paper.     

On the use of conformal mapping for the computation of hydrodynamic forces acting on bodies of arbitrary shape in viscous flow. Part 1: simply connected body

Some aspects of the force and moment computations in incompressible and viscous flows are revisited. The basic idea was developed in Quartapelle and Napolitano (AIAA J. 21:991–913, 1983). They formulated the way to compute the force and moment without explicitly calculating the pressure. The principle is to project Navier–Stokes equations on a set of functions. Surprisingly these functions have a meaning in potential theory. They are precisely the solutions which give the added masses and added moment of inertia for potential flow. By revisiting this problem for two-dimensional flows in unbounded liquid, a general identity giving the added masses and added moment of inertia is formulated. To this end a conformal-mapping technique is used to transform the fluid domain. Once the potential solution has been obtained, the projection method by Quartapelle and Napolitano is implemented. In addition an a posteriori computation of the pressure is described. Applications illustrate the present study.     

Visualization and analysis of longitudinal vortices at curved walls of 2D laminar and turbulent channel flows

The three-dimensional structure of longitudinal vortices at the curved walls of both laminar and turbulent channel flows is visualized by the hydrogen bubble technique. Together with the conditional sampling of the turbulent characteristics at the wall processed by thevita method the dynamics of the near-wall structure is discussed.     

Computation of Inviscid Supersonic Flows Around Cylinders and Spheres with the SUPG Formulation and YZβ Shock-Capturing

Numerical experiments with inviscid supersonic flows around cylinders and spheres are carried out to evaluate the stabilization and shock-capturing parameters introduced recently for the Streamline–Upwind/Petrov–Galerkin (SUPG) formulation of compressible flows based on conservation variables. The tests with the cylinders are carried out for both structured and unstructured meshes. The new shock-capturing parameters, which we call “YZβ Shock-Capturing”, are compared to earlier SUPG parameters derived based on the entropy variables. In addition to being much simpler, the new shock-capturing parameters yield better shock quality in the test computations, with more substantial improvements seen for unstructured meshes with triangular and tetrahedral elements. Furthermore, the results obtained with YZβ Shock-Capturing compare very favorably to those obtained with the well established OVERFLOW code     

Studies in multigrid acceleration of some equations of interest in fluid dynamics

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. Various parts of this paper have been presented at the following conferences; (i) 5th Asian Cong. on Fluid Mech., Taejon, Korea, 1992, (ii) Int. Conf. on Methods of Aerophysical Research, Novosibirsk, 1992, (iii) Fluid Dyn. Symp. in honour of Prof. R Narasimha on his 60th birthday, 1993.     

International issues in remote sensing

Starting with the initial aim of reconnaissance technical developments in remote sensing have progressed sufficiently for the large-scale realisation of practical benefits. During the eighties a number of countries will have remote sensing satellite systems in operation. There are however a few technical, legal, political and economic issues that still remain unresolved. The resolution of these issues would facilitate practical applications especially in developing countries. Apart from the purely technical and economic issues such as the ability to compare data from two different satellites, the cost of the data etc one of the major hurdles in the application of this technology is the establishment of an international regime governing the activities of states in remote sensing. This is particularly important in view of the link between surveillance and remote sensing. Even though discussions have been going on for quite some time at the United Nations, the prospects of reaching agreement remain bleak. The main problems precluding agreement are national security, commercial and sovereignty concerns of the developed and developing countries. The key issues relate to the right of countries to conduct remote sensing over other countries, the right of countries collecting remote sensing data (over other countries) to distribute this data freely and the modalities of how the “sensitivity” aspects of remote sensing for surveillance and economic espionage can be reconciled with a legal regime that emphasises international cooperation. A critical analysis of existing international space law seems to indicate that there are two kinds of remote sensing—passive and active. In passive remote sensing the satellite sensor detects the sun-reflected or self-emitted radiation from objects on the ground. In active remote sensing a pulse of electromagnetic radiation is transmited from the satellite and its reflectance or scattering by objects on the earth’s surface is measured. A strict reading of existing legal principles on space seem to imply that passive sensing is legal while active sensing could be interpreted as violating the sovereignty of the sensed state. Agreement on remote sensing can be reached if a resolution or a range of resolutions can be defined to discriminate between “sensitive” and “non-sensitive” data. The only international agreement in this area between the USSR and a group of nine socialist countries uses a resolution limit of 50m. Available information on the subject seems to indicate that the range is from 25–50 m. One other aspect dealt with relates to the use of satellite data for verification of arms control measures, for crisis monitoring and the prospects of setting up an International Satellite Monitoring Agency (ISMA). It appears that the huge expense that this would entail would be justified only if theISMA can monitor the superpowers and the arms race between them.     

Design and performance of a Tesla transformer type relativistic electron beam generator

A relativistic electron beam generator driven by an air core Tesla transformer is described. The Tesla transformer circuit analysis is outlined and computational results are presented for the case when the coaxial water line has finite resistance. The transformer has a coupling coefficient of 0·56 and a step-up ratio of 25. The Tesla transformer can provide 800 kV at the peak of the second half cycle of the secondary output voltage and has been tested up to 600 kV. A 100–200 keV, 15–20 kA electron beam having 150 ns pulse width has been obtained. The beam generator described is being used for the beam injection into a toroidal devicebeta.     

A multigrid accelerated hybrid unstructured mesh method for 3D compressible turbulent flow

 A cell vertex finite volume method for the solution of steady compressible turbulent flow problems on unstructured hybrid meshes of tetrahedra, prisms, pyramids and hexahedra is described. These hybrid meshes are constructed by firstly discretising the computational domain using tetrahedral elements and then by merging certain tetrahedra. A one equation turbulence model is employed and the solution of the steady flow equations is obtained by explicit relaxation. The solution process is accelerated by the addition of a multigrid method, in which the coarse meshes are generated by agglomeration, and by parallelisation. The approach is shown to be effective for the simulation of a number of 3D flows of current practical interest. Sponsored by The Research Council of Norway, project number 125676/410 Dedicated to the memory of Prof. Mike Crisfield, a respected colleague