Quasilinear theory of general electromagnetic fluctuations including discrete particle effects for magnetized plasmas: General analysis
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R. Schlickeiser↗
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Introduction to Generalized Functions with Applications in Aerodynamics and Aeroacoustics
Generalized functions have many applications in science and engineering. One useful aspect is that discontinuous functions can be handled as easily as continuous or differentiable functions and provide a powerful tool in formulating and solving many problems of aerodynamics and acoustics. Furthermore, generalized function theory elucidates and unifies many ad hoc mathematical approaches used by engineers and scientists. We define generalized functions as continuous linear functionals on the space of infinitely differentiable functions with compact support, then introduce the concept of generalized differentiation. Generalized differentiation is the most important concept in generalized function theory and the applications we present utilize mainly this concept. First, some results of classical analysis, are derived with the generalized function theory. Other applications of the generalized function theory in aerodynamics discussed here are the derivations of general transport theorems for deriving governing equations of fluid mechanics, the interpretation of the finite part of divergent integrals, the derivation of the Oswatitsch integral equation of transonic flow, and the analysis of velocity field discontinuities as sources of vorticity. Applications in aeroacoustics include the derivation of the Kirchhoff formula for moving surfaces, the noise from moving surfaces, and shock noise source strength based on the Ffowcs Williams-Hawkings equation.
Farassat, F.↗
An introduction to generalized functions with some applications in aerodynamics and aeroacoustics
In this paper, we start with the definition of generalized functions as continuous linear functionals on the space of infinitely differentiable functions with compact support. The concept of generalization differentiation is introduced next. This is the most important concept in generalized function theory and the applications we present utilize mainly this concept. First, some of the results of classical analysis, such as Leibniz rule of differentiation under the integral sign and the divergence theorem, are derived using the generalized function theory. It is shown that the divergence theorem remains valid for discontinuous vector fields provided that the derivatives are all viewed as generalized derivatives. This implies that all conservation laws of fluid mechanics are valid as they stand for discontinuous fields with all derivatives treated as generalized deriatives. Once these derivatives are written as ordinary derivatives and jumps in the field parameters across discontinuities, the jump conditions can be easily found. For example, the unsteady shock jump conditions can be derived from mass and momentum conservation laws. By using a generalized function theory, this derivative becomes trivial. Other applications of the generalized function theory in aerodynamics discussed in this paper are derivation of general transport theorems for deriving governing equations of fluid mechanics, the interpretation of finite part of divergent integrals, derivation of Oswatiitsch integral equation of transonic flow, and analysis of velocity field discontinuities as sources of vorticity. Applications in aeroacoustics presented here include the derivation of the Kirchoff formula for moving surfaces,the noise from moving surfaces, and shock noise source strength based on the Ffowcs Williams-Hawkings equation.
Farassat, F.↗
Affine Generalized Inverse for Optimal Control Allocation
This research is a follow on to the "Optimal Control Prediction Method for Control Allocation" paper in which the Prediction Method iterative algorithm was introduced. Previously, the Prediction Method was shown to provide optimal control allocation solutions over the entire Attainable Moment Set for the Moore-Penrose and the generalized (weighted) inverse. As an extension to the Prediction Method, this paper introduces a family of Moore Penrose Affine Generalized Inverses, applicable for all moments, which compute control allocation solutions using a constant matrix and fixed null-space vector. The Moore-Penrose Affine Generalized Inverse is proven to yield equivalent solutions to those of the Prediction Method and therefore is guaranteed to yield Moore-Penrose optimal control allocation solutions. While the Prediction Method is applicable for any moment along an a priori specified moment direction, the Affine Generalized Inverse is shown to yield optimal control allocation solutions in a neighborhood of the given moment which is not restricted to a specified moment direction. Furthermore, the Affine Generalized Inverse is shown to provide the time derivative of optimal control allocation solutions and to facilitate maintaining solutions within control effector rate limitations. The Moore-Penrose Affine Generalized Inverse is broadened to encompass any arbitrary (weighted) Affine Generalized Inverse. Finally, a method of creating a moment lookup table is outlined to utilize the Affine Generalized Inverse as an offline control allocation solution for all moments in the Attainable Moment Set.
Acheson, Michael J.↗
Explanation-based generalization of partially ordered plans
Most previous work in analytic generalization of plans dealt with totally ordered plans. These methods cannot be directly applied to generalizing partially ordered plans, since they do not capture all interactions among plan operators for all total orders of such plans. We introduce a new method for generalizing partially ordered plans. This method is based on providing explanation-based generalization (EBG) with explanations which systematically capture the interactions among plan operators for all the total orders of a partially-ordered plan. The explanations are based on the Modal Truth Criterion which states the necessary and sufficient conditions for ensuring the truth of a proposition at any point in a plan, for a class of partially ordered plans. The generalizations obtained by this method guarantee successful and interaction-free execution of any total order of the generalized plan. In addition, the systematic derivation of the generalization algorithms from the Modal Truth Criterion obviates the need for carrying out a separate formal proof of correctness of the EBG algorithms.
Kambhampati, Subbarao↗
US general aviation: The ingredients for a renaissance. A vision and technology strategy for US industry, NASA, FAA, universities
General aviation today is a vital component in the nation's air transportation system. It is threatened for survival but has enormous potential for expansion in utility and use. This potential for expansion is fueled by new satellite navigation and communication systems, small computers, flat panel displays, and advanced aerodynamics, materials and manufacturing methods, and propulsion technologies which create opportunities for new levels of environmental and economic acceptability. Expanded general aviation utility and use could have a large impact on the nation's jobs, commerce, industry, airspace capacity, trade balance, and quality of life. This paper presents, in viewgraph form, a general overview of U.S. general aviation. Topics covered include general aviation shipment and billings; airport and general aviation infrastructure; cockpit, airplane, and airspace technologies; market demand; air traffic operations and aviation accidents; fuel efficiency comparisons; and general aviation goals and strategy.
Holmes, Bruce↗
A multi-ion generalized transport model of the polar wind
The higher-order generalizations of the equations of standard hydrodynamics, known collectively as generalized transport theories, have been used since the early 1980s to describe the terrestrial polar wind. Inherent in the structure of generalized transport theories is the ability to describe not only interparticle collisions but also certain non-Maxwellian processes, such as heat flow and viscous stress, that are characteristic of any plasma flow that is not collision dominated. Because the polar wind exhibits a transition from collision-dominated to collisionless flow, generalized transport theories possess advantages for polar wind modeling not shared by either collision-dominated models (such as standard hydrodynamics) or collisionless models (such as those based on solving the collisionless Boltzmann equation). In general, previous polar wind models have used generalized transport equations to describe electrons and only one species of ion (H(+)). If other ion species were included in the models at all, it was in a simplified or semiempirical manner. The model described in this paper is the first polar wind model that uses a generalized transport theory (bi-Maxwellian-based 16-moment theory) to describe all of the species, both major and minor, in the polar wind plasma. In the model, electrons and three ion species (H(+), He(+), O(+)) are assumed to be major and several ion species are assumed to be minor (NO(+), Fe(+), O(++)). For all species, a complete 16-moment transport formulation is used, so that profiles of density, drift velocity, parallel and perpendicular temperatures, and the field-aligned parallel and perpendicular energy flows are obtained. In the results presented here, emphasis is placed on describing those constituents of the polar wind that have received little attention in past studies. In particular, characteristic solutions are presented for supersonic H(+) outflow and for both supersonic and subsonic outflows of the major ion He(+). Solutions are also presented for various minor ions, both atomic and molecular and both singly and multiply charged.
Demars, H. G.↗
General Aviation in Nebraska: Nebraska SATS Project Background Paper No. 1
The Nebraska SATS project is a state-level component of NASA's Small Aircraft Transportation System (SATS). During the next several years the project will examine several different factors affecting SATS implementation in Nebraska. These include economic and taxation issues, public policy issues, airport planning processes, information dissemination strategies, and systemic change factors. This background paper profiles the general aviation system in Nebraska. It is written to provide information about the "context" within which SATS will be pursued. The primary focus is thus on describing and providing background information about the current situation. A secondary focus is on drawing general conclusions about the ability of the current system to incorporate the types of changes implied by SATS. First, some brief information on the U.S. aviation system is provided. The next two sections profile the current general aviation aircraft and pilot base. Nebraska's system of general aviation airports is then described. Within this section of the paper, information is provided on the different types of general aviation airports in Nebraska, airport activity levels and current infrastructure. The fourth major section of the background paper looks at Nebraska's local airport authorities. These special purpose local governments oversee the majority of the general aviation airports in the state. Among the items examined are total expenditures, capital expenditures and planning activities. Next, the paper provides background information on the Nebraska Department of Aeronautics (NDA) and recent Federal funding for general aviation in Nebraska. The final section presents summary conclusions.
Smith, Russell↗
Virginia Space Grant Consortium Management of National General Aviation Design Competition
This report summarizes the management of the National General Aviation Design Competition on behalf of NASA, the FAA and the Air Force by the Virginia Space Grant Consortium (VSGC) for the time period October 1, 2000 through September 30, 2001. This was the VSGC's seventh and final year of managing the Competition, which the Consortium originally designed, developed and implemented for NASA and the FAA. The competition is now being managed in-house by NASA. Awards to winning university teams were presented at a ceremony held at AirVenture 2001, the Experimental Aircraft Association's Annual Convention and Fly-In at Oshkosh, Wis. by NASA and FAA officials. The competition called for individuals or teams of undergraduate and graduate students from U.S. engineering schools to participate in a major national effort to rebuild the U.S. general aviation sector. Participants were challenged to meet the engineering goals of the Advanced General Aviation Transport Experiment (AGATE) project. For the purpose of the contest, general aviation aircraft are typically defined as single or twin engine (turbine or piston), single-pilot, fixed-wing aircraft for 2 - 6 passengers. The competition seeks to raise student awareness of the importance of general aviation by having students address design challenges for a small aircraft transportation system. NASA, AFRL and the FAA hope to stimulate breakthroughs in technology and their application in the general aviation marketplace. National goals for revitalizing the industry offer excellent, open-ended design challenges with real world applications for the Innovative Design Category. Both individual and team submissions were encouraged. University faculty advisors and students consistently cite the value of this kind of educational experience for their engineering students. Eight proposals were submitted for the 2001 Competition for the Innovative Design Category. Eleven faculty members and 124 students participated. Since inception, more than 785 students and 60 faculty members have participated in the Competition. A review panel comprised of general aviation experts from the FAA, EAA, NASA and industry representatives reviewed the design packages and selected the winners. The VSGC coordinated marketing of the competition to a mailing list which included selected deans and department chairs from ABET-accredited institutions, Space Grant affiliates, faculty who had previously participated in or expressed interest in the Competition, and others.
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Robust integration schemes for generalized viscoplasticity with internal-state variables. Part 1: Theoretical developments and applications
This two-part report is concerned with the development of a general framework for the implicit time-stepping integrators for the flow and evolution equations in generalized viscoplastic models. The primary goal is to present a complete theoretical formulation, and to address in detail the algorithmic and numerical analysis aspects involved in its finite element implementation, as well as to critically assess the numerical performance of the developed schemes in a comprehensive set of test cases. On the theoretical side, the general framework is developed on the basis of the unconditionally-stable, backward-Euler difference scheme as a starting point. Its mathematical structure is of sufficient generality to allow a unified treatment of different classes of viscoplastic models with internal variables. In particular, two specific models of this type, which are representative of the present start-of-art in metal viscoplasticity, are considered in applications reported here; i.e., fully associative (GVIPS) and non-associative (NAV) models. The matrix forms developed for both these models are directly applicable for both initially isotropic and anisotropic materials, in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). On the computational side, issues related to efficiency and robustness are emphasized in developing the (local) interative algorithm. In particular, closed-form expressions for residual vectors and (consistent) material tangent stiffness arrays are given explicitly for both GVIPS and NAV models, with their maximum sizes 'optimized' to depend only on the number of independent stress components (but independent of the number of viscoplastic internal state parameters). Significant robustness of the local iterative solution is provided by complementing the basic Newton-Raphson scheme with a line-search strategy for convergence. In the present first part of the report, we focus on the theoretical developments, and discussions of the results of numerical-performance studies using the integration schemes for GVIPS and NAV models.
Saleeb, Atef F.↗
Robust integration schemes for generalized viscoplasticity with internal-state variables. Part 2: Algorithmic developments and implementation
This two-part report is concerned with the development of a general framework for the implicit time-stepping integrators for the flow and evolution equations in generalized viscoplastic models. The primary goal is to present a complete theoretical formulation, and to address in detail the algorithmic and numerical analysis aspects involved in its finite element implementation, as well as to critically assess the numerical performance of the developed schemes in a comprehensive set of test cases. On the theoretical side, the general framework is developed on the basis of the unconditionally-stable, backward-Euler difference scheme as a starting point. Its mathematical structure is of sufficient generality to allow a unified treatment of different classes of viscoplastic models with internal variables. In particular, two specific models of this type, which are representative of the present start-of-art in metal viscoplasticity, are considered in applications reported here; i.e., fully associative (GVIPS) and non-associative (NAV) models. The matrix forms developed for both these models are directly applicable for both initially isotropic and anisotropic materials, in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). On the computational side, issues related to efficiency and robustness are emphasized in developing the (local) interative algorithm. In particular, closed-form expressions for residual vectors and (consistent) material tangent stiffness arrays are given explicitly for both GVIPS and NAV models, with their maximum sizes 'optimized' to depend only on the number of independent stress components (but independent of the number of viscoplastic internal state parameters). Significant robustness of the local iterative solution is provided by complementing the basic Newton-Raphson scheme with a line-search strategy for convergence. In the present second part of the report, we focus on the specific details of the numerical schemes, and associated computer algorithms, for the finite-element implementation of GVIPS and NAV models.
Li, Wei↗
Generalized Wall Function for Complex Turbulent Flows
A generalized wall function was proposed by Shih et al., (1999). It accounts the effect of pressure gradients on the flow near the wall. Theory shows that the effect of pressure gradients on the flow in the inertial sublayer is very significant and the standard wall function should be replaced by a generalized wall function. Since the theory is also valid for boundary layer flows toward separation, the generalized wall function may be applied to complex turbulent flows with acceleration, deceleration, separation and recirculation. This paper is to verify the generalized wall function with numerical simulations for boundary layer flows with various adverse and favorable pressure gradients, including flows about to separate. Furthermore, a general procedure of implementation of the generalized wall function for National Combustion Code (NCC) is described, it can be applied to both structured and unstructured CFD codes.
Shih, Tsan-Hsing↗
Control Effector Unsaturation Modification to the Cascading Generalized Inverse Control Allocation Algorithm
Control allocation has sufficiently progressed such that it is used in front-line fighter aircraft such as the F-18Superhornet and the F-35 Joint Strike Fighter. Published literature shows the F-35 utilizes Nonlinear Dynamic Inversion in conjunction with an Effector Blender that incorporates the Cascading Generalized Inverse control allocation algorithm. While the Cascading Generalized Inverse algorithm is one of the premier generalized inverse methods, it does suffer from three deficiencies. In particular, it suffers from an inability to achieve some desired outcomes, it intermittently provides non-optimal solutions and generally fails to preserve moment direction near maximal achievable moments. An effector unsaturation method based on a Scalar Difference Quadratic was first introduced and implemented on the iterative Prediction Method control allocation algorithm which was shown to consistently achieve optimal (weighted) control allocation solutions throughout the entire Attainable Moment Set while preserving desired moment direction. In this paper, the shortcomings of the Cascading Generalized Inverse algorithm are addressed by augmenting the baseline algorithm with Scalar Difference Quadratic unsaturation identification and location at each iteration. Numerical case studies demonstrate that the Modified Cascading Generalized Inverse algorithm resolves the aforementioned deficiencies.
Michael J Acheson↗
General aviation avionics equipment maintenance
Maintenance of general aviation avionics equipment was investigated with emphasis on single engine and light twin engine general aviation aircraft. Factors considered include the regulatory agencies, avionics manufacturers, avionics repair stations, the statistical character of the general aviation community, and owners and operators. The maintenance, environment, and performance, repair costs, and reliability of avionics were defined. It is concluded that a significant economic stratification is reflected in the maintenance problems encountered, that careful attention to installations and use practices can have a very positive impact on maintenance problems, and that new technologies and a general growth in general aviation will impact maintenance.
Parker, C. D.↗
Helicopter rotor wake geometry and its influence in forward flight. Volume 1: Generalized wake geometry and wake effect on rotor airloads and performance
An analytic investigation to generalize wake geometry of a helicopter rotor in steady level forward flight and to demonstrate the influence of wake deformation in the prediction of rotor airloads and performance is described. Volume 1 presents a first level generalized wake model based on theoretically predicted tip vortex geometries for a selected representative blade design. The tip vortex distortions are generalized in equation form as displacements from the classical undistorted tip vortex geometry in terms of vortex age, blade azimuth, rotor advance ratio, thrust coefficient, and number of blades. These equations were programmed to provide distorted wake coordinates at very low cost for use in rotor airflow and airloads prediction analyses. The sensitivity of predicted rotor airloads, performance, and blade bending moments to the modeling of the tip vortex distortion are demonstrated for low to moderately high advance ratios for a representative rotor and the H-34 rotor. Comparisons with H-34 rotor test data demonstrate the effects of the classical, predicted distorted, and the newly developed generalized wake models on airloads and blade bending moments. Use of distorted wake models results in the occurrence of numerous blade-vortex interactions on the forward and lateral sides of the rotor disk. The significance of these interactions is related to the number and degree of proximity to the blades of the tip vortices. The correlation obtained with the distorted wake models (generalized and predicted) is encouraging.
Egolf, T. A.↗
Crack tip field and fatigue crack growth in general yielding and low cycle fatigue
Fatigue life consists of crack nucleation and crack propagation periods. Fatigue crack nucleation period is shorter relative to the propagation period at higher stresses. Crack nucleation period of low cycle fatigue might even be shortened by material and fabrication defects and by environmental attack. In these cases, fatigue life is largely crack propagation period. The characteristic crack tip field was studied by the finite element method, and the crack tip field is related to the far field parameters: the deformation work density, and the product of applied stress and applied strain. The cyclic carck growth rates in specimens in general yielding as measured by Solomon are analyzed in terms of J-integral. A generalized crack behavior in terms of delta is developed. The relations between J and the far field parameters and the relation for the general cyclic crack growth behavior are used to analyze fatigue lives of specimens under general-yielding cyclic-load. Fatigue life is related to the applied stress and strain ranges, the deformation work density, crack nucleus size, fracture toughness, fatigue crack growth threshold, Young's modulus, and the cyclic yield stress and strain. The fatigue lives of two aluminum alloys correlate well with the deformation work density as depicted by the derived theory. The general relation is reduced to Coffin-Manson low cycle fatigue law in the high strain region.
Minzhong, Z.↗
Some fundamentals regarding kinematics and generalized forces for multibody dynamics
In order to illustrate the various forms in which generalized forces can arise from diverse subsystem analyses in multibody dynamics, intrinsic dynamical equations for the rotational dynamics of a rigid body are derived from Hamilton's principle. Two types of generalized forces are derived: (1) those associated with the virtual rotation vector in some orthogonal basis, and (2) those associated with varying generalized coordinates. As one physical or kinematical result (such as a frequency or a specific direction cosine) cannot rely on this selection, a 'blind' coupling of two models in which generalized forces are calculated in different ways would be wrong. Both types should use the same rotational coordinates and should denote the virtual rotation on a similar basis according to method 1, or in terms of common rotational coordinates and their diversifications as in method 2. Alternatively, the generalized forces and coordinates of one model may be transformed to those of the other.
Hodges, Dewey H.↗
Time-domain analysis of planar microstrip devices using a generalized Yee-algorithm based on unstructured grids
The generalized Yee-algorithm is presented for the temporal full-wave analysis of planar microstrip devices. This algorithm has the significant advantage over the traditional Yee-algorithm in that it is based on unstructured and irregular grids. The robustness of the generalized Yee-algorithm is that structures that contain curved conductors or complex three-dimensional geometries can be more accurately, and much more conveniently modeled using standard automatic grid generation techniques. This generalized Yee-algorithm is based on the the time-marching solution of the discrete form of Maxwell's equations in their integral form. To this end, the electric and magnetic fields are discretized over a dual, irregular, and unstructured grid. The primary grid is assumed to be composed of general fitted polyhedra distributed throughout the volume. The secondary grid (or dual grid) is built up of the closed polyhedra whose edges connect the centroid's of adjacent primary cells, penetrating shared faces. Faraday's law and Ampere's law are used to update the fields normal to the primary and secondary grid faces, respectively. Subsequently, a correction scheme is introduced to project the normal fields onto the grid edges. It is shown that this scheme is stable, maintains second-order accuracy, and preserves the divergenceless nature of the flux densities. Finally, for computational efficiency the algorithm is structured as a series of sparse matrix-vector multiplications. Based on this scheme, the generalized Yee-algorithm has been implemented on vector and parallel high performance computers in a highly efficient manner.
Gedney, Stephen D.↗