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A recently developed spatial operator algebra approach to modeling and analysis of multibody robotic systems is used to develop O(n) recursive algorithms that compute the operational space mass matrix and the operational space coriolis/centrifugal and gravity terms of an n-link serial manipulator. These algorithms enable an O(n) recursive implementation of operational space control.
It is shown that the mechanism of bolt loading for preloaded fasteners can be effectively portrayed through simple spring models and some algebraic manipulations. Understanding schematically what is involved in such joints provides insight into the distribution of loads. The developed equations confirm that for both symmetric and nonsymmetric joints the loading plane factor and the stiffness factor directly affect the load seen in preloaded fasteners. The manner in which an external loading is transferred through the joint can be explained as energy dissipated in the various springs of both the abutment and the bolt itself.
The ease of applicability of three scattering models is examined. This is accomplished by considering the time taken to numerically evaluate these models and by comparing their predictions as a function of surface roughness, frequency, incident angle and polarization with the moment-method solution in two dimensions. The complexity of the analytic models in three dimensions and their analytic reduction to high- and low-frequency regions are also compared. The selected models are an integral equation model (IEM), a full wave model (FWM), and the phase perturbation model (PPM). It is noted that in three dimensions, the full-wave model requires an evaluation of a tenfold integral and the phase perturbation model requires a fourfold and a twofold integral, whereas the integral equation model is an algebraic equation in like polarization under single scattering conditions. It is found that both the IEM and PPM agree with the moment-method solution from low to high frequencies numerically.
An explicit 2D Navier-Stokes code has been modified and used to analyze the aerodynamics and heat transfer of a transonic turbine cascade. This code is based on a four-stage Runge-Kutta scheme. An algebraic Reynolds stress model (ARSM) and two versions of low Reynolds number (LRN) two-equation turbulence models, Chien's (1982) LRN k-epsilon model and Coakley's (1983) LRN q-omega model, have been employed in the computations. The surface pressure distributions and wake profiles are predicted well by all the models. The k-epsilon model and the k-epsilon/ARSM model yield better predictions of heat transfer than the q-omega model. The k-epsilon/ARSM solutions show some significant, though not dramatic, differences in the predicted skin friction coefficients, heat transfer rates, and performance parameters, as compared to the k-epsilon model. The predicted semiwake width is consistent with the measurement and correlation.
The objective of the present investigation is to assess the effect of the spatial order of accuracy used for the evaluation of the inviscid fluxes on the resolution of higher order quantitites, such as velocity gradients. The viscous terms are computed as second-order accurate with central difference formulas, even though for the explicit part of the algorithm higher order approximations may be used. A viscous/inviscid method is used, and the outer part of the flowfield is computed with the inviscid flow equations. The viscous boundary-layer type flow region close to the body surface is computed with an algebraic eddy viscosity model. Results obtained with the conservative and nonconservative formulations and the viscous/inviscid approach are compared with available experimental data. The effect of grid refinement on the accuracy of the solution is also presented.
This paper describes our experience using parameterized algebraic specifications to model properties of software architectures. The goal is to model the decomposition of requirements independent of the style used to implement the architecture. We begin by providing an overview of the role of architecture specification in software development. We then describe how architecture specifications are build up from component and connector specifications and give an overview of insights gained from a case study used to validate the method.
A detailed experimental, theoretical, and computational study of separated nozzle flows has been conducted. Experimental testing was performed at the NASA Langley 16-Foot Transonic Tunnel Complex. As part of a comprehensive static performance investigation, force, moment, and pressure measurements were made and schlieren flow visualization was obtained for a sub-scale, non-axisymmetric, two-dimensional, convergent- divergent nozzle. In addition, two-dimensional numerical simulations were run using the computational fluid dynamics code PAB3D with two-equation turbulence closure and algebraic Reynolds stress modeling. For reference, experimental and computational results were compared with theoretical predictions based on one-dimensional gas dynamics and an approximate integral momentum boundary layer method. Experimental results from this study indicate that off-design overexpanded nozzle flow was dominated by shock induced boundary layer separation, which was divided into two distinct flow regimes; three- dimensional separation with partial reattachment, and fully detached two-dimensional separation. The test nozzle was observed to go through a marked transition in passing from one regime to the other. In all cases, separation provided a significant increase in static thrust efficiency compared to the ideal prediction. Results indicate that with controlled separation, the entire overexpanded range of nozzle performance would be within 10% of the peak thrust efficiency. By offering savings in weight and complexity over a conventional mechanical exhaust system, this may allow a fixed geometry nozzle to cover an entire flight envelope. The computational simulation was in excellent agreement with experimental data over most of the test range, and did a good job of modeling internal flow and thrust performance. An exception occurred at low nozzle pressure ratios, where the two-dimensional computational model was inconsistent with the three-dimensional separation observed in the experiment. In general, the computation captured the physics of the shock boundary layer interaction and shock induced boundary layer separation in the nozzle, though there were some differences in shock structure compared to experiment. Though minor, these differences could be important for studies involving flow control or thrust vectoring of separated nozzles. Combined with other observations, this indicates that more detailed, three-dimensional computational modeling needs to be conducted to more realistically simulate shock-separated nozzle flows.
A dynamic model of a high-power Stirling convertor has been developed for space nuclear power systems modeling. The model is based on the Component Test Power Convertor (CTPC), a 12.5-kWe free-piston Stirling convertor. The model includes the fluid heat source, the Stirling convertor, output power and heat rejection. The Stirling convertor model includes the Stirling cycle thermodynamics, heat flow, mechanical mass-spring damper systems, and the linear alternator. The model was validated against test data. Both nonlinear and linear versions of the model were developed. The linear version algebraically couples two separate linear dynamic models; one model of the Stirling cycle and one model of the thermal system, through the pressure factors. Future possible uses of the Stirling system dynamic model are discussed. A pair of commercially available 1-kWe Stirling convertors is being purchased by NASA Glenn Research Center. The specifications of those convertors may eventually be incorporated into the dynamic model and analysis compared to the convertor test data. Subsequent potential testing could include integrating the convertors into a pumped liquid metal hot-end interface. This test would provide more data for comparison to the dynamic model analysis.
A dynamic model of a high-power Stirling convertor has been developed for space nuclear power systems modeling. The model is based on the Component Test Power Convertor (CTPC), a 12.5-kWe free-piston Stirling convertor. The model includes the fluid heat source, the Stirling convertor, output power, and heat rejection. The Stirling convertor model includes the Stirling cycle thermodynamics, heat flow, mechanical mass-spring damper systems, and the linear alternator. The model was validated against test data. Both nonlinear and linear versions of the model were developed. The linear version algebraically couples two separate linear dynamic models; one model of the Stirling cycle and one model of the thermal system, through the pressure factors. Future possible uses of the Stirling system dynamic model are discussed. A pair of commercially available 1-kWe Stirling convertors is being purchased by NASA Glenn Research Center. The specifications of those convertors may eventually be incorporated into the dynamic model and analysis compared to the convertor test data. Subsequent potential testing could include integrating the convertors into a pumped liquid metal hot-end interface. This test would provide more data for comparison to the dynamic model analysis.
In this paper we use the Reynolds stress models (RSM) to derive algebraic expressions for the following variables: a) heat fluxes; b) J.l fluxes; and c) momentum fluxes. These relations, which are fully 3D, include: 1) stable and unstable stratification, represented by the Brunt-Vaislila frequency, N(exp 2) =-g/H(sub p_(del - del(sub ad))(1 - RI(sub mu)); 2) double diffusion, salt-fingers, and semi-convection, represented by the density ratio R(sub mu) = del(sub mu)/(del - del(sub ad)); 3) shear (differential rotation), represented by the mean squared shear Sigma(exp 2) or by the Richardson number, Ri =N(exp 2)Sigma(exp -2); 4) radiative losses represented by a Peclet number, Pe; 5) a complete analytical solution of the ID version of the model. In general, the model requires the solution of two differential equations for the eddy kinetic energy K and its rate of dissipation, epsilon. In the local and stationary cases, when production equals dissipation, the model equations are all algebraic.
The majority of the work on this grant involved formal modeling of human-computer integration. We conceptualize computer resources as a multiagent system so that these resources and human collaborators may be modeled uniformly. In previous work we had used modal for this uniform modeling, and we had developed a process-algebraic agent abstraction. In this work, we applied this abstraction (using CSP) in uniformly modeling agents and users, which allowed us to use tools for investigating CSP models. This work revealed the power of, process-algebraic handshakes in modeling face-to-face conversation. We also investigated specifications of human-computer systems in the style of algebraic specification. This involved specifying the common knowledge required for coordination and process-algebraic patterns of communication actions intended to establish the common knowledge. We investigated the conditions for agents endowed with perception to gain common knowledge and implemented a prototype neural-network system that allows agents to detect when such conditions hold. The literature on multiagent systems conceptualizes communication actions as speech acts. We implemented a prototype system that infers the deontic effects (obligations, permissions, prohibitions) of speech acts and detects violations of these effects. A prototype distributed system was developed that allows users to collaborate in moving proxy agents; it was designed to exploit handshakes and common knowledge Finally. in work carried over from a previous NASA ARC grant, about fifteen undergraduates developed and presented projects on multiagent motion planning.
This paper presents a method for calculating compressible adverse pressure gradient boundary layers by using an algebraic eddy viscosity turbulence model that has been modified for variable pressure gradient and turbulence memory effects. The pressure gradient corrections are based on previous incompressible data correlations. Several methods for including the effects of turbulence memory are evaluated. A new lag model, which gives good agreement with available experimental data, is developed. Finally, a correlation is developed for the lag length parameter employed in the model as a function of the known experimental flow variables.
The turbulence models available for the prediction of complex turbulent shear layers are reviewed in this paper, concentrating mainly on three-dimensional flows, flows subjected to curvature and body rotation, separated flows, and vortex flows. A critical review of zero-equation, one-equation, two-equation, algebraic Reynolds stress, and full Reynolds stress models are carried out, with a specific emphasis on their applicability to complex flows. It is concluded that algebraic eddy viscosity models and kappa-epsilon/kappa-omega models, with a constant value of coefficients, are not adequate for complex flows. The models which include a description of stresses, either through an algebraic Reynolds stress model or a full Reynolds stress model, are essential for adequate prediction of these flows. It is recommended that systematic experimental investigations be carried out to isolate various complex interactions in order to understand and model the various effects and to carry out an extension of the present models to include complex flows.
A combined theoretical and experimental study is presented for the interaction between crossing shock waves generated by (10 deg, 10 deg) sharp fins and a flat plate turbulent boundary layer at Mach 8.3. The theoretical model is the full 3D mean compressible Reynolds-averaged Navier-Stokes (RANS) equations incorporating the algebraic turbulent eddy viscosity model of Baldwin and Lomax (1978). A grid refinement study indicated that adequate resolution of the flow field has been achieved. Computed results agree well with experiment for surface pressure and surface flow patterns and for pitot pressure and yaw angle profiles in the flow field. The computations, however, significantly overpredict surface heat transfer. Analysis of the computed flow field results indicates the formation of complex streamline and wave structures within the interaction region.
The ability of the three-dimensional Navier-Stokes method, PAB3D, to simulate the effect of Reynolds number variation using non-linear explicit algebraic Reynolds stress turbulence modeling was assessed. Subsonic flat plate boundary-layer flow parameters such as normalized velocity distributions, local and average skin friction, and shape factor were compared with DNS calculations and classical theory at various local Reynolds numbers up to 180 million. Additionally, surface pressure coefficient distributions and integrated drag predictions on an axisymmetric nozzle afterbody were compared with experimental data from 10 to 130 million Reynolds number. The high Reynolds data was obtained from the NASA Langley 0.3m Transonic Cryogenic Tunnel. There was generally good agreement of surface static pressure coefficients between the CFD and measurement. The change in pressure coefficient distributions with varying Reynolds number was similar to the experimental data trends, though slightly over-predicting the effect. The computational sensitivity of viscous modeling and turbulence modeling are shown. Integrated afterbody pressure drag was typically slightly lower than the experimental data. The change in afterbody pressure drag with Reynolds number was small both experimentally and computationally, even though the shape of the distribution was somewhat modified with Reynolds number.
A 3D hypersonic crossing shock wave/turbulent boundary layer interaction is examined numerically. The test geometry consists of a pair of opposing sharp fins of angle alpha = 15 deg mounted on a flat plate. The freestream Mach number is 8.28. Two theoretical models are evaluated. The full 3D Reynolds-averaged Navier-Stokes equations are solved using the Baldwin-Lomax algebraic turbulent eddy viscosity model and the Rodi turbulence model. Computed results for both cases show good agreement with experiment for flat plate surface pressure and for pitot pressure and yaw angle profiles in the flowfield. General agreement is obtained for surface flow direction. Fair to poor agreement is obtained for surface heat transfer, indicating a need for more accurate turbulence models. The overall flowfield structure is similar to that observed in previous crossing shock interaction studies.
A second derivative frequency modification procedure is developed to iteratively change analysis modeling parameters for the more rapid convergence of analytically determined frequencies to those obtained by structural dynamic testing. A nonlinear system of algebraic equations in the modeling parameters is derived and a rapidly converging iterative method for their solution is presented. Numerical results obtained show that the higher order formulation and nonlinear predictor-corrector solution procedure yields results which are more rapidly convergent than those obtained using only the usual linear first-order parameter modification procedure. The proposed higher order theory also connverges in some cases when the ordinary linear theory does not.
Report shows how spatial-operator algebra developed by authors used to derive linearized mathematical models of dynamics of robotic manipulators. Aspects of spatial-operator algebra also described in "Robot Control Based On Spatial-Operator Algebra" (NPO-17918), "Unified Formulation Of Dynamics Of Robot Arms" (NPO-18040), and "Spatial-Operator Algebra For Robotic Manipulators" (NPO-17770).