Approximate calculation of turbulent boundary-layer development in compressible flow
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An efficient formulation of the coupled finite element-integral equation technique for solving large 3D scattering problems
It is often desirable to calculate the electromagnetic fields inside and about a complicated system of scattering bodies, as well as in their far-field region. The finite element method (FE) is well suited to solving the interior problem, but the domain has to be limited to a manageable size. At the truncation of the FE mesh one can either impose approximate (absorbing) boundary conditions or set up an integral equation (IE) for the fields scattered from the bodies. The latter approach is preferable since it results in higher accuracy. Hence, the two techniques can be successfully combined by introducing a surface that encloses the scatterers, applying a FE model to the inner volume and setting up an IE for the tangential fields components on the surface. Here the continuity of the tangential fields is used bo obtain a consistent solution. A few coupled FE-IE methods have recently appeared in the literature. The approach presented here has the advantage of using edge-based finite elements, a type of finite elements with degrees of freedom associated with edges of the mesh. Because of their properties, they are better suited than the conventional node based elements to represent electromagnetic fields, particularly when inhomogeneous regions are modeled, since the node based elements impose an unnatural continuity of all field components across boundaries of mesh elements. Additionally, our approach is well suited to handle large size problems and lends itself to code parallelization. We will discuss the salient features that make our approach very efficient from the standpoint of numerical computation, and the fields and RCS of a few objects are illustrated as examples.
Cwik, T.↗
Dynamic analysis of Space Shuttle/RMS configuration using continuum approach
The initial assembly of Space Station Freedom involves the Space Shuttle, its Remote Manipulation System (RMS) and the evolving Space Station Freedom. The dynamics of this coupled system involves both the structural and the control system dynamics of each of these components. The modeling and analysis of such an assembly is made even more formidable by kinematic and joint nonlinearities. The current practice of modeling such flexible structures is to use finite element modeling in which the mass and interior dynamics is ignored between thousands of nodes, for each major component. The model characteristics of only tens of modes are kept out of thousands which are calculated. The components are then connected by approximating the boundary conditions and inserting the control system dynamics. In this paper continuum models are used instead of finite element models because of the improved accuracy, reduced number of model parameters, the avoidance of model order reduction, and the ability to represent the structural and control system dynamics in the same system of equations. Dynamic analysis of linear versions of the model is performed and compared with finite element model results. Additionally, the transfer matrix to continuum modeling is presented.
Ramakrishnan, Jayant↗
Investigation of Low-Reynolds-Number Rocket Nozzle Design Using PNS-Based Optimization Procedure
An optimization approach to rocket nozzle design, based on computational fluid dynamics (CFD) methodology, is investigated for low-Reynolds-number cases. This study is undertaken to determine the benefits of this approach over those of classical design processes such as Rao's method. A CFD-based optimization procedure, using the parabolized Navier-Stokes (PNS) equations, is used to design conical and contoured axisymmetric nozzles. The advantage of this procedure is that it accounts for viscosity during the design process; other processes make an approximated boundary-layer correction after an inviscid design is created. Results showed significant improvement in the nozzle thrust coefficient over that of the baseline case; however, the unusual nozzle design necessitates further investigation of the accuracy of the PNS equations for modeling expanding flows with thick laminar boundary layers.
Hussaini, M. Moin↗
Preconditioning Operators on Unstructured Grids
We consider systems of mesh equations that approximate elliptic boundary value problems on arbitrary (unstructured) quasi-uniform triangulations and propose a method for constructing optimal preconditioning operators. The method is based upon two approaches: (1) the fictitious space method, i.e., the reduction of the original problem to a problem in an auxiliary (fictitious) space, and (2) the multilevel decomposition method, i.e., the construction of preconditioners by decomposing functions on hierarchical meshes. The convergence rate of the corresponding iterative process with the preconditioner obtained is independent of the mesh step. The preconditioner has an optimal computational cost: the number of arithmetic operations required for its implementation is proportional to the number of unknowns in the problem. The construction of the preconditioning operators for three dimensional problems can be done in the same way.
Nepomnyaschikh, S. V.↗
An Experimental Investigation of the Effects of Mach Number, Stabilizer Dihedral, and Fin Torsional Stiffness on the Transonic Flutter Characteristics of a Tee-Tail
A transonic flutter investigation was made of elastically and dynamically scaled models of the tee-tail of a patrol bomber. It was found that removal of the 15 deg. dihedral of the stabilizer used on the airplane raised the flutter boundary to higher dynamic pressures. The effect of Mach number on the flutter boundary was different for dihedral angles of 0 and 15 deg. The dynamic pressure at the flutter boundary increased approximately linearly with the torsional stiffness of the fin. High-speed motion pictures indicated that the flutter mode consisted primarily of fin bending and fin torsion.
Land, Norman S.↗
Analysis of Three-Dimensional, Nonlinear Development of Wave-Like Structure in a Compressible Round Jet
An analysis of the nonlinear development of the large-scale structures or instability waves in compressible round jets was conducted using the integral energy method. The equations of motion were decomposed into two sets of equations; one set governing the mean flow motion and the other set governing the large-scale structure motion. The equations in each set were then combined to derive kinetic energy equations that were integrated in the radial direction across the jet after the boundary-layer approximations were applied. Following the application of further assumptions regarding the radial shape of the mean flow and the large structures, equations were derived that govern the nonlinear, streamwise development of the large structures. Using numerically generated mean flows, calculations show the energy exchanges and the effects of the initial amplitude on the coherent structure development in the jet.
Dahl, Milo D.↗
Evaporation, Heat Transfer, and Velocity Distribution in Two-Dimensional and Rotationally Symmetrical Laminar Boundary-Layer Flow
The fundamental boundary layer equations for the flow, temperature and concentration fields are presented. Two dimensional symmetrical and unsymmetrical and rotationally symmetrical steady boundary layer flows are treated as well as the transfer boundary layer. Approximation methods for the calculation of the transfer layer are discussed and a brief survey of an investigation into the validity of the law that the Nusselt number is proportional to the cube root of the Prandtl number is presented.
Froessling, Nils↗
Upward And Downward Flame Spreading And Extinction In Partial Gravity Environments
The premise of this research effort has been to begin exploring the gap in the literature between studies of material flammability and flame spread phenomena in normal-gravity and those conducted in the microgravity environment, with or without forced flows. From a fundamental point of view, flame spreading in upward (concurrent) buoyant flow is considerably different from concurrent forced flow. The flow accelerates throughout the length of the buoyant flame bringing the streamlines and the flame closer to the fuel surface and strengthening the interaction between the flame and fuel. Forced flows are diverted around the flame and away from the fuel surface, except where the flow might be constrained by a finite duct. The differences may be most clearly felt as the atmospheric conditions, viz. pressure or oxygen content, approach the flammability limit. From a more practical point of view, flame spreading and material flammability behavior have not been studied under the partial gravity conditions that are the natural state in space exploration destinations such as the Moon and Mars. This effort constitutes the beginning of the research needed to engineer fire safety provisions for such future missions. In this program we have performed partial-gravity experiments (from 0.1 to 1 g/g(sub Earth)) considering both upward and downward flame spread over thin solid fuels aboard the NASA KC-135 aircraft. In those tests, the atmospheric pressure and the fuel sample width were varied. Steady flame spread rates and approximate extinction boundaries were determined. Flame images were recorded using video cameras and two-dimensional fuel surface temperature distributions were determined using an IR camera. These results are available, and complement our earlier work in downward spread in partial gravity varying oxygen content. In conjunction with the experiment, three-dimensional models of flame spreading in buoyant flow have been developed. Some of the computed results on upward spreading have been presented. A derivative three-dimensional model of downward spreading has been developed. It is currently being used to evaluate the standard limiting oxygen index (LOI) measuring device and its potential performance in different gravity levels.
Sacksteder, Kurt R.↗
X-ray digital imaging petrography of lunar mare soils: modal analyses of minerals and glasses
It is essential that accurate modal (i.e., volume) percentages of the various mineral and glass phases in lunar soils be used for addressing and resolving the effects of space weathering upon reflectance spectra, as well as for their calibration such data are also required for evaluating the resource potential of lunar minerals for use at a lunar base. However, these data are largely lacking. Particle-counting information for lunar soils, originally obtained to study formational processes, does not provide these necessary data, including the percentages of minerals locked in multi-phase lithic fragments and fused-soil particles, such as agglutinates. We have developed a technique for modal analyses, sensu stricto, of lunar soils, using digital imaging of X-ray maps obtained with an energy-dispersive spectrometer mounted on an electron microprobe. A suite of nine soils (90 to 150 micrometers size fraction) from the Apollo 11, 12, 15, and 17 mare sites was used for this study. This is the first collection of such modal data on soils from all Apollo mare sites. The abundances of free-mineral fragments in the mare soils are greater for immature and submature soils than for mature soils, largely because of the formation of agglutinitic glass as maturity progresses. In considerations of resource utilization at a lunar base, the best lunar soils to use for mineral beneficiation (i.e., most free-mineral fragments) have maturities near the immature/submature boundary (Is/FeO approximately or = 30), not the mature soils with their complications due to extensive agglutination. The particle data obtained from the nine mare soils confirm the generalizations for lunar soils predicted by L.A. Taylor and D.S. McKay (1992, Lunar Planet Sci. Conf. 23rd, pp. 1411-1412 [Abstract]).
NASA Discipline Exobiology↗
Standardization of a Volumetric Displacement Measurement for Two-Body Abrasion Scratch Test Data Analysis
A limitation has been identified in the existing test standards used for making controlled, two-body abrasion scratch measurements based solely on the width of the resultant score on the surface of the material. A new, more robust method is proposed for analyzing a surface scratch that takes into account the full three-dimensional profile of the displaced material. To accomplish this, a set of four volume- displacement metrics was systematically defined by normalizing the overall surface profile to denote statistically the area of relevance, termed the Zone of Interaction. From this baseline, depth of the trough and height of the plowed material are factored into the overall deformation assessment. Proof-of-concept data were collected and analyzed to demonstrate the performance of this proposed methodology. This technique takes advantage of advanced imaging capabilities that allow resolution of the scratched surface to be quantified in greater detail than was previously achievable. When reviewing existing data analysis techniques for conducting two-body abrasive scratch tests, it was found that the ASTM International Standard G 171 specified a generic metric based only on visually determined scratch width as a way to compare abraded materials. A limitation to this method was identified in that the scratch width is based on optical surface measurements, manually defined by approximating the boundaries, but does not consider the three-dimensional volume of material that was displaced. With large, potentially irregular deformations occurring on softer materials, it becomes unclear where to systematically determine the scratch width. Specifically, surface scratches on different samples may look the same from a top view, resulting in an identical scratch width measurement, but may vary in actual penetration depth and/or plowing deformation. Therefore, two different scratch profiles would be measured as having identical abrasion properties, although they differ significantly.
Street, K. W. Jr.↗
Numerical Investigation of Film Coefficient Approximation for Chemically Reacting Boundary-Layer Flows
Aerothermal analysis of spacecraft planetary entry is heavily dependent on heritage engineering models. The film coefficient heat transfer model examined in this paper estimates the convective heating to the vehicle for a laminar, dissociated, chemically reacting boundary layer for an Earth atmosphere. This model requires information about the vehicle and flowfield for a given trajectory point and estimates a proportional relationship between enthalpy potential and convective heat flux. In practice it is the aerothermal engineer who must decide which assumptions are appropriate for his/her application. This work looks at numerous CFD simulations for an arbitrary, axisymmetric flight vehicle to analyze the relative importance of both the mass and energy constraints imposed at the wall boundary, as well as the effect of various diffusion models. Within the subset of tested energy boundary conditions, it is found that the most desirable energy boundary condition is the radiative equilibrium boundary condition, which permits conservative estimates of convective heat flux, but also generates flowfield-dependent spatial thermal distributions along the surface. Other key findings are presented in an effort to make the film coefficient engineering model readily available to design engineers across industry.
Film coefficient↗
Developing Data-Driven Artificial Neural Network for A High Throughput Retrieval of Aerosol Optical Depth and Surface Temperature of Mars
In this work, we aim to developartificial neural network(ANN)techniquesto reproduce the retrieval results ofphysical quantities from spacecraft observations of solar system bodiesusing radiative transfer methods. The particular application here is the retrieval of dust optical depth, water-ice optical depth, and surface temperatureonMarsusingdaytime observationsobtained by the Thermal Emission Spectrometer (TES) onboard the Mars Global Surveyor.Compared against the results obtained from traditional radiative transfer retrieval techniques, our ANN successfully recoveredthe three quantitiesusingdaytime observations. The principal advantage of thesemachine learning(ML) algorithms istheir complete automation and highthroughput. Therefore, the algorithms presented here would be useful for very large datasets andwould make practical the sampling of many different approximations or boundary conditions related to a given observation dataset and retrieval problem.
Rafael Moreno↗
Model Predictive Control in the Three-body Problem Using Invariant Funnels As Terminal Sets
This paper describes a method for augmenting Model Predictive Control techniques using invariant funnels computed in the Circular Restricted Three-Body Problem. We use ellipsoids that roughly approximate the boundary of the invariant funnel as convex terminal sets for a short look-ahead optimization problem at each time step. We apply this method to a hypothetical low-thrust mission to land on Jupiter’s mooon Europa and show that including the invariant funnels as terminal sets reduces the amount of control effort required by almost an order of magnitude.
Close, Sigrid↗
Modelling Nuclear Thermal Propulsion Reactor Expander Cycle Startup Transients
As the interest in nuclear thermal propulsion grows, the need for high fidelity and comprehensive models of the system increases. An expander cycle model was developed using RELAP-7 for the thermal-hydraulic performance and Griffin to provide the power level using a point kinetics approximation, for a reference NTP system. The tank and pump are approximated using boundary conditions. Flow is split between the moderator cooling channels flow path and the regenerative cooling/reflector cooling channels flow path. The flow recombines before entering the turbine and the fuel cooling channels. The turbine pressure ratio is maintained at 1.44 using a PID controller. A startup transient was simulated and shows the capability of the model to run from low temperature and pressures to nominal conditions.
33 ADVANCED PROPULSION SYSTEMS↗
Modelling Nuclear Thermal Propulsion Reactor Expander Cycle Startup Transients
As the interest in nuclear thermal propulsion grows, the need for high fidelity and comprehensive models of the system increases. An expander cycle model was developed using RELAP-7 for the thermal-hydraulic performance and Griffin to provide the power level using a point kinetics approximation, for a reference NTP system. The tank and pump are approximated using boundary conditions. Flow is split between the moderator cooling channels flow path and the regenerative cooling/reflector cooling channels flow path. The flow recombines before entering the turbine and the fuel cooling channels. The turbine pressure ratio is maintained at 1.44 using a PID controller. A startup transient was simulated and shows the capability of the model to run from low temperature and pressures to nominal conditions.
33 ADVANCED PROPULSION SYSTEMS↗
A recurrence matrix method for the analysis of longitudinal and torsional vibrations in non-uniform multibranch beams with variable boundary conditions
An approximate method for calculating the longitudinal and torsional natural frequencies and associated modal data of a beamlike, variable cross section multibranch structure is presented. The procedure described is the numerical integration of the first order differential equations that characterize the beam element in longitudinal motion and that satisfy the appropriate boundary conditions.
Davis, R. B.↗
Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement
The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.
Gibson, J. S.↗