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NASA NTRS1980

Large space system control technology status and accomplishments

In the area of antenna modeling and control, preliminary structural models were defined for two representative parabolic reflectors. A control system design evolved for attitude control of the reflectors. The controller design was based on a lumped control concept where the control hardware (sensor and actuators) was mounted at the base of the antenna. In the area of distributed control, static shape control techniques were worked out to establish a prescribed vehicle shape. The corresponding estimation process for determination of vehicle shape from selected sensor measurements was also developed. A model order reduction study was conducted to find the best preflight dynamical models for on board controller design. The problems caused by truncation of the vehicle dynamics required to minimize on board computations were investigated. Estimator designs were developed for on board detection of large structure model errors.

Rodriguez, G.↗

NASA NTRS2009

Crashworthy Seats Would Afford Superior Protection

Seats to prevent or limit crash injuries to astronauts aboard the crew vehicle of the Orion spacecraft are undergoing development. The design of these seats incorporates and goes beyond crash-protection concepts embodied in prior spacecraft and racing-car seats to afford superior protection against impacts. Although the seats are designed to support astronauts in a recumbent, quasi-fetal posture that would likely not be suitable for non-spacecraft applications, parts of the design could be adapted to military and some civilian aircraft seats and to racing car seats to increase levels of protection. The main problem in designing any crashworthy seat is to provide full support of the occupant against anticipated crash and emergency-landing loads so as to safely limit motion, along any axis, of any part of the occupant s body relative to (1) any other part of the occupant s body, (2) the spacecraft or other vehicle, and (3) the seat itself. In the original Orion spacecraft application and in other applications that could easily be envisioned, the problem is complicated by severe limits on space available for the seat, a requirement to enable rapid egress by the occupant after a crash, and a requirement to provide for fitting of the seat to a wide range of sizes and shapes of a human body covered by a crash suit, space suit, or other protective garment. The problem is further complicated by other Orion-application-specific requirements that must be omitted here for the sake of brevity. To accommodate the wide range of crewmember body lengths within the limits on available space in the original Orion application, the design provides for taller crewmembers to pull their legs back closer toward their chests, while shorter crewmembers can allow their legs to stretch out further. The range of hip-support seat adjustments needed to effect this accommodation, as derived from NASA s Human Systems Integration Standard, was found to define a parabolic path along which the knees must be positioned. For a given occupant, the specific position along the path depends on the distance from the heel to the back of the knee. The application of the concept of parabolic adjustment of the hip-support structure caused the seat pan to also take on a parabolic shape, yielding the unanticipated additional benefit that the seat pan fits the occupant s buttocks and thighs more nearly conformally than do seat pans of prior design. This more nearly conformal fit effectively eliminates a void between the occupant s body and the seat pan, thereby helping to prevent what, in prior seat designs, was shifting of the occupant s body into that void during an impact.

Gohmert, Dustin↗

DOE OSTI2018

On the convergence and convergence order of finite volume gradient schemes for oblique derivative boundary value problems

This work is an improvement of the previous note (Bradji in: Fuhrmann et al., Finite volumes for complex applications VII–methods, theoretical aspects. Proceedings of the FVCA 7, Berlin, 2014) which dealt with the convergence analysis of a finite volume scheme for the Poisson’s equation with a linear oblique derivative boundary condition. The formulation of the finite volume scheme given in Bradji (in: Fuhrmann et al., Finite volumes for complex applications VII–methods, theoretical aspects. Proceedings of the FVCA 7, Berlin, 2014) involves the discrete gradient introduced recently in Eymard et al. (IMA J Numer Anal 30(4):1009–1043, 2010). In this paper, we consider the convergence analysis of finite volume schemes involving the discrete gradient of Eymard et al. (IMA J Numer Anal 30(4):1009–1043, 2010) for elliptic and parabolic equations with linear oblique derivative boundary conditions. Linear oblique derivative boundary conditions arise for instance in the study of the motion of water in a canal, cf. Lesnic (Commun Numer Methods Eng 23(12):1071–1080, 2007). We derive error estimates in several norms which allow us to get error estimates for the approximations of the exact solutions and its first derivatives. In particular, we provide an error estimate between the gradient of the exact solutions and the discrete gradient of the approximate solutions. Convergence of the family of finite volume approximate solutions towards the exact solution under weak regularity assumption is also investigated. In the case of parabolic equations with oblique derivative boundary conditions, we develop a new discrete a priori estimate result. The proof of this result is based on the use of a discrete mean Poincaré–Wirtinger inequality. Thanks to the stated a priori estimate and to a comparison with an appropriately chosen auxiliary finite volume scheme, we derive the convergence results. This work can be viewed as a continuation of the previous work (Bradji and Gallouët in Int J Finite Vol 3(2):1–35, 2006) where a convergence analysis for a finite volume scheme, based on the admissible mesh of Eymard et al. (In: Ciarlet and Lions, Handbook of numerical analysis, North-Holland, Amsterdam, 2000), for the Poisson’s equation with a linear oblique derivative boundary conditions is given. The obtained convergence results do not require any relation between the mesh sizes of the spatial and time discretizations. Some numerical tests are presented for both elliptic and parabolic equations. In particular, we present three methods to compute the discrete solution.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1980

Numerical solutions of transonic flows by parametric differentiation and integral equation techniques

The paper discusses results of an exploratory study of the advantages obtained by combining integral equation methods with the method of parametric differentiation in the treatment of transonic flow problems. In the proposed method, the nonlinear unsteady transonic flow equation for small perturbations is transformed into a linear equation by the use of the method of parametric differentiation. The linear equation is split into a pair of weakly coupled partial differential equations by writing the transformed perturbation potential as the sum of a steady component and an unsteady component. The solution of the steady equation as an integral equation is based on Ogana's treatment (1978). As a test case, the formulation is applied to predict the steady transonic flow over a nonlifting parabolic-arc airfoil.

Sivaneri, N. T.↗

NASA NTRS1990

Application of CFD to sonic boom near and mid flow-field prediction

A 3-D parabolized Navier-Stokes (PNS) code was used to calculate the supersonic overpressures from three different geometries at near- and mid-flow fields. Wind tunnel data is used for code validation. Comparison of the computed results with different grid refinements is shown. It is observed that a large number of grid points is needed to resolve the tail shock/expansion fan interaction. Therefore, an adaptive grid approach is employed to calculate the flow field. The agreement between the numerical results and the wind tunnel data confirms that computational fluid dynamics can be applied to the problem of sonic boom prediction.

Cheung, Samson H.↗

NASA NTRS1992

The semi-discrete Galerkin finite element modelling of compressible viscous flow past an airfoil

A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid which provides high resolution near the wall and automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes, through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past NACA 0012 and RAE 2822 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack. All results show good agreement with experiment, and the coupled code proved to be a computationally-efficient and accurate airfoil analysis tool.

Meade, Andrew J., Jr.↗

DOE OSTI2025

Osmotic control of the spacing of parallel shear cracks in shale growing subcritically in geologic past

The geological genesis of natural cracks in sedimentary rocks such as shale is a problem that needs to be understood to improve the technology of hydraulic fracturing as well as deep sequestration of harmful fluids. Why are the vertical natural cracks roughly parallel and equidistant, and why is the spacing roughly 10 cm rather than 1 cm or 100 cm? Fracture mechanics of critical cracks cannot answer this question. Neither can the material heterogeneity. The growth of critical parallel cracks is impossible because the relative crack face displacements would immediately localize into one crack, leading to an earthquake. The cracks must have formed, on the tectonic time scale, by a slow growth of subcritical shear cracks governed by the Charles-Evans law. The idea advanced here is that what controls the crack spacing is the balance between the reduction, due to shear dilatancy, of the concentration of ions such as Na + and Cl - in each fracture process zone (PFZ), which decelerates the cracks, and the restoration of ion concentration by diffusion of ions from the space between the cracks into the FPZ. This diffusion of water is driven mainly by the osmotic pressure gradient, which offsets the deceleration and depends strongly on the crack spacing. A simple analytical solution of the steady state is rendered possible by approximating the ion concentration profiles between adjacent cracks by parabolic arcs. Applying this theory to Woodford shale yields the approximate crack spacing of 10 cm, which is realistic. Furthermore, the stability of unlimited parallel mode II frictional crack growth is proven by examining the second variation of the free energy. Water concentration drop in the FPZ due to shear dilatancy and its restoration by water diffusion from the inter-crack space have similar effect, although probably much weaker.

42 ENGINEERING↗

DOE OSTI2018

A Fiber-Optic System Generating Pulses of High Spectral Density

A cascade fiber-optic system that generates pulses of high spectral density by using the effect of nonlinear spectral compression is proposed. It is demonstrated that the shape of the pulse envelope substantially influences the degree of compression of its spectrum. In so doing, maximum compression is achieved for parabolic pulses. The cascade system includes an optical fiber exhibiting normal dispersion that decreases along the fiber length, thereby ensuring that the pulse envelope evolves toward a parabolic shape, along with diffraction gratings and a fiber spectral compressor. Based on computer simulation, we determined parameters of cascade elements leading to maximum spectral density of radiation originating from a subpicosecond laser pulse of medium energy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1995

Status Of The UPS Space-Marching Flow Solver

The status of the three-dimensional parabolized Navier-Stokes solver UPS is described. The UPS code, initiated at NASA Ames Research Center in 1986, continues to develop and evolve through application to supersonic and hypersonic flow fields. Hypersonic applications have motivated enhancement of the physical modeling capabilities of the code, specifically real gas modeling, boundary conditions, and turbulence and transition modeling. The UPS code has also been modified to enhance robustness and efficiency in order to be practically used in concert with an optimization code for supersonic transport design. These developments are briefly described along with some relevant results for generic test problems obtained during verification of the enhancements. Included developments and results have previously been published and widely disseminated domestically.

Lawerence, Scott L.↗

NASA NTRS2006

Gas-Liquid Separation Strategies in Microgravity Environment

Bubble entrainment in liquids represents a serious problem in the microgravity environment. Whenever bubbles are entrained in a liquid,they tend to remain stationary in the liquid bulk in the absence of any external forcing. This is due to the reduction or complete absence of the buoyancy force in the microgravity environment, Thus the buoyancy force can not the be exploited to place the bubbles at the top of the liquid volume as in Ig(sub o) conditions. This situation represents a serious drawback in many space based engineering and scientific applications. We have demonstrated in a series of low gravity experiments conducted during parabolic flight on board aircraft that bubbles can be controlled in such a manner as to increase,the probability of their expulsion from a liquid bulk. In these tests the liquid'bulk was made either to be contained within, or to flow through specially designed containers using capillary force alone. Such containers appear to facilitate bubble removal, from the liquid bulk. Different successful liquid flow configurations will be discussed and the efficacy of the resulting bubble expulsion mechanisms will be demonstrated.

Antar, Basil N.↗

NASA NTRS1998

Combined Numerical/Analytical Perturbation Solutions of the Navier-Stokes Equations for Aerodynamic Ejector/Mixer Nozzle Flows

In spite of rapid advances in both scalar and parallel computational tools, the large number of variables involved in both design and inverse problems make the use of sophisticated fluid flow models impractical, With this restriction, it is concluded that an important family of methods for mathematical/computational development are reduced or approximate fluid flow models. In this study a combined perturbation/numerical modeling methodology is developed which provides a rigorously derived family of solutions. The mathematical model is computationally more efficient than classical boundary layer but provides important two-dimensional information not available using quasi-1-d approaches. An additional strength of the current methodology is its ability to locally predict static pressure fields in a manner analogous to more sophisticated parabolized Navier Stokes (PNS) formulations. To resolve singular behavior, the model utilizes classical analytical solution techniques. Hence, analytical methods have been combined with efficient numerical methods to yield an efficient hybrid fluid flow model. In particular, the main objective of this research has been to develop a system of analytical and numerical ejector/mixer nozzle models, which require minimal empirical input. A computer code, DREA Differential Reduced Ejector/mixer Analysis has been developed with the ability to run sufficiently fast so that it may be used either as a subroutine or called by an design optimization routine. Models are of direct use to the High Speed Civil Transport Program (a joint government/industry project seeking to develop an economically.viable U.S. commercial supersonic transport vehicle) and are currently being adopted by both NASA and industry. Experimental validation of these models is provided by comparison to results obtained from open literature and Limited Exclusive Right Distribution (LERD) sources, as well as dedicated experiments performed at Texas A&M. These experiments have been performed using a hydraulic/gas flow analog. Results of comparisons of DREA computations with experimental data, which include entrainment, thrust, and local profile information, are overall good. Computational time studies indicate that DREA provides considerably more information at a lower computational cost than contemporary ejector nozzle design models. Finally. physical limitations of the method, deviations from experimental data, potential improvements and alternative formulations are described. This report represents closure to the NASA Graduate Researchers Program. Versions of the DREA code and a user's guide may be obtained from the NASA Lewis Research Center.

DeChant, Lawrence Justin↗

NASA NTRS1980

Three-layer interactive method for computing supersonic laminar separated flows

An interactive model for numerical computation of complicated two-dimensional flowfields including regions of reversed flow is proposed. The present approach is one of dividing the flowfield into three regions, in each of which a simplified mathematical model is applied: (1) outer, supersonic flow for which the full potential equation (hyperbolic) is used; (2) viscous, laminar layer in which the compressible boundary-layer model (parabolic) is used; and (3) recirculating flow modeled by the incompressible Navier-Stokes equations (elliptic). For matching of the numerical solutions in the three layers, two interaction models are developed: one for pressure interaction, the other for interaction between the shear layer and the recirculating flow. The uniform solution for the whole flowfield is then obtained by iteration of the local solutions under the constraints imposed by matching. The three-layer interactive model is used for solution of the flowfield past an asymmetric cavity. The method is shown to be capable of dealing with backflow without encountering problems at separation, characteristic to the boundary-layer approach.

Brandeis, J.↗

NASA NTRS1987

Curved edge modification of compact range reflector

For many years, the compact range has successfully been used to design and evaluate many electromagnetic radiation and scattering systems. However, it has had limited use for large structures because of the large discrepancy between the reflector and target zone sizes. The limitation results from the large edge diffracted signal which emanates from the termination of the reflector. Previous attempts to solve this problem have involved using serrated edges to diffuse the diffracted field. While this reduces the edge diffracted field in the target zone, it is not eliminated. In addition, one has introduced many new corners which also diffract into the target zone. A curved edge modification is presented which reduces the edge diffraction by an order of magnitude or more and in the process does not create new mechanisms which perturb the plane wave in the target zone. Using this curved modification, one is able to design a compact range reflector whose target zone cross section approaches the size of the reflector parabolic surface. This makes the compact range ideal for scale model measurements since larger targets (antennas) can be measured. It also makes it more practical to consider systems which can measure full scale vehicles.

Burnside, Walter D.↗

NASA NTRS1990

Application of CFD to sonic boom near and mid flow-field prediction

A three-dimensional parabolized Navier-Stokes (PNS) code has been used to calculate the supersonic overpressures from three different geometries at near- and mid-flow fields. Wind-tunnel data is used for code validation. Comparison of the computed results with different grid refinements is shown in this paper. It is observed that a large number of grid points is needed to resolve the tail shock/expansion fan interaction. Therefore, an adaptive grid approach is employed to calculate the flow field. The agreement between the numerical results and the wind-tunnel data confirms that computational fluid dynamics can be applied to the problem of sonic boom prediction.

Cheung, Samson H.↗

NASA NTRS1988

A 3D-PNS computer code for the calculation of supersonic combusting flows

A computer code has been developed based on the three-dimensional parabolized Navier-Stokes (PNS) equations which govern the supersonic combusting flow of the hydrogen-air system. The finite difference algorithm employed was a hybrid of the Schiff-Steger algorithm and the Vigneron, et al., algorithm which is fully implicit and fully coupled. The combustion of hydrogen and air was modeled by the finite-rate two-step combustion model of Rogers-Chinitz. A new dependent variable vector was introduced to simplify the numerical algorithm. Robustness of the algorithm was considerably enhanced by introducing an adjustable parameter. The computer code was used to solve a premixed shock-induced combustion problem and the results were compared with those of a full Navier-Stokes code. Reasonably good agreement was obtained at a fraction of the cost of the full Navier-Stokes procedure.

Chitsomboon, Tawit↗

NASA NTRS1960

An Analysis of the Corridor and Guidance Requirements for Supercircular Entry into Planetary Atmospheres

An analysis is presented of supercircular entry into a planet's atmosphere giving particular attention to the corridor through which spacecraft must be guided in order to accomplish various maneuvers. A dimensionless parameter based on conditions at the conic perigee altitude is introduced for characterizing supercircular entries and conveniently pre-scribing corridor widths associated with elliptic, parabolic, or hyperbolic approach trajectories. The analysis applies to vehicles of arbitrary weight, shape, and size. Illustrative calculations are made for Venus, Earth, Mars, Jupiter, and Titan. For nonlifting vehicles having fixed aerodynamic coefficients, curves are presented of dimensionless parameters from which can be calculated the maximum deceleration, maximum rate of laminar convective heating, and total laminar heat absorbed during single-pass entry at velocities up to twice circular velocity. For lifting vehicles, curves are presented of the maximum deceleration and overshoot boundary of an entry corridor; equations are presented for estimating laminar aerodynamic heating from the maximum deceleration. It is shown that the corridor width is independent of vehicle weight, dimensions, and drag coefficient, provided these are the same at the overshoot boundary as at undershoot. The corridors of certain planets can be broadened markedly by the application of aerodynamic lift; for example, the 10-earth-g corridor width for single- pass, nonlifting, parabolic entry is increased from 0 miles for Jupiter, 7 for Earth, and 8 for Venus, to 52, 51, and 52 miles, respectively, by employing a lift-drag ratio of 1. The use of aerodynamic lift does not increase appreciably the corridors of Mars and Titan. All corridor widths decrease rapidly as the entry velocity is increased. Terminal guidance requirements on accuracy of velocity and flight path angle for successfully entering various corridors are compared with analogous requirements for putting a satellite into orbit, for hitting the moon from the earth, and for achieving ICBM accuracy. Consideration is given to the terminal guidance problem involved in using a planet's atmosphere-rather than rocket fuel-to effect orbital transfers from heliocentric to planetocentric motion, thereby converting a hyperbolic approach trajectory to an elliptic orbit about the target planet. This fuel saving maneuver appears technologically feasible for certain planetary voyages, and implies the possibility of achieving a large reduction in required Earth lift-off weight of chemical propulsion systems.

Chapman, Dean R.↗

NASA NTRS1986

The calculation of supersonic viscous flows using the parabolized Navier-Stokes equations

Solution of the parabolic Navier-Stokes (PNS) equations for supersonic flows is discussed, and compatibility of the PNS method with the triple-deck theory of Stewartson (1974) is demonstrated. Characteristic and stability analyses show that use of an appropriate filter on the pressure term in the x-momentum equation can suppress the departure solutions, giving the usual desired weak interaction solution. An Alternating Direction Explicit procedure, with minimal computer storage requirements compared to the full Navier-Stokes solvers, is proposed to calculate strongly interacting flows using a global iteration procedure for the PNS equations. The PNS equations are used to solve the hypersonic viscous interaction problem, and good agreement is found with experimental results.

Davis, R. T.↗

NASA NTRS1987

Strong convergence and convergence rates of approximating solutions for algebraic Riccati equations in Hilbert spaces

The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.

Ito, Kazufumi↗