SEARCH · Engineering Papers

Results for “hyperbolic”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,009 records · Page 56

All sources NASA NTRS DOE OSTI

NASA NTRS1992

The geocentric particulate distribution: Cometary, asteroidal, or space debris?

Definition of the Low Earth Orbit (LEO) particulate environment has been refined considerably with the analysis of data from NASA's Long Duration Exposure Facility (LDEF). Measurements of the impact rates from particulates ranging from sub-micron to millimetres in dimension and, especially, information on their directionality has permitted new scrunity of the sources of the particulates. Modelling of the dynamics of both bound (Earth orbital) and unbound (hyperbolic interplanetary) particulates intercepting LDEF's faces leads to the conclusion that the source is dominantly interplanetary for particle dimensions of greater than some 5 microns diameter; however the anisotropy below this dimension demands lower velocities and is compatible with an orbital component. Characteristics of the LDEF interplanetary component are compatible with familiar meteoroid sources and deep space measurements. Understanding of the orbital component which exceeds the interplanetary flux by a factor of 4 is less clear; although the very small particulates in orbit have been associated with space debris (Lawrance and Brownlee, 1986) this data conflicts with other measurements (McDonnell, Carey and Dixon, 1984) at the same epoch. By analysis of trajectories approaching the Earth and its atmosphere, we have shown that a significant contribution could be captured by aerocapture, i.e., atmospheric drag, from either asteroidal or cometary sources; such enhancement is unlikely however to provide the temporal and spatial fluctuations observed by the LDEF Interplanetary Dust Experiment (Mullholland et al. 1992). A further new mechanism is also examined, that of aerofragmentation capture, where an atmospheric grazing trajectory, which would not normally lead to capture, leads to fragmentation by thermal or mechanical shock; the microparticulates thus created can be injected in large numbers, but only into short-lifetime orbits. The concentration in one particular orbit plane, could explain the temporal fluctuations seen on LDEF; space debris could also explain the phenomenon.

Mcdonnell, J. A. M.↗

NASA NTRS1992

Research in computational fluid dynamics and analysis of algorithms

Recently, higher-order compact schemes have seen increasing use in the DNS (Direct Numerical Simulations) of the Navier-Stokes equations. Although they do not have the spatial resolution of spectral methods, they offer significant increases in accuracy over conventional second order methods. They can be used on any smooth grid, and do not have an overly restrictive CFL dependence as compared with the O(N(exp -2)) CFL dependence observed in Chebyshev spectral methods on finite domains. In addition, they are generally more robust and less costly than spectral methods. The issue of the relative cost of higher-order schemes (accuracy weighted against physical and numerical cost) is a far more complex issue, depending ultimately on what features of the solution are sought and how accurately they must be resolved. In any event, the further development of the underlying stability theory of these schemes is important. The approach of devising suitable boundary clusters and then testing them with various stability techniques (such as finding the norm) is entirely the wrong approach when dealing with high-order methods. Very seldom are high-order boundary closures stable, making them difficult to isolate. An alternative approach is to begin with a norm which satisfies all the stability criteria for the hyperbolic system, and look for the boundary closure forms which will match the norm exactly. This method was used recently by Strand to isolate stable boundary closure schemes for the explicit central fourth- and sixth-order schemes. The norm used was an energy norm mimicking the norm for the differential equations. Further research should be devoted to BC for high order schemes in order to make sure that the results obtained are reliable. The compact fourth order and sixth order finite difference scheme had been incorporated into a code to simulate flow past circular cylinders. This code will serve as a verification of the full spectral codes. A detailed stability analysis by Carpenter (from the fluid Mechanics Division) and Gottlieb gave analytic conditions for stability as well as asymptotic stability. This had been incorporated in the code in form of stable boundary conditions. Effects of the cylinder rotations had been studied. The results differ from the known theoretical results. We are in the middle of analyzing the results. A detailed analysis of the effects of the heating of the cylinder on the shedding frequency had been studied using the above schemes. It has been found that the shedding frequency decreases when the wire was heated. Experimental work is being carried out to affirm this result.

Gottlieb, David↗

NASA NTRS1993

Numerical computation of complex multi-body Navier-Stokes flows with applications for the integrated Space Shuttle launch vehicle

An enhanced grid system for the Space Shuttle Orbiter was built by integrating CAD definitions from several sources and then generating the surface and volume grids. The new grid system contains geometric components not modeled previously plus significant enhancements on geometry that has been modeled in the old grid system. The new orbiter grids were then integrated with new grids for the rest of the launch vehicle. Enhancements were made to the hyperbolic grid generator HYPGEN and new tools for grid projection, manipulation, and modification, Cartesian box grid and far field grid generation and post-processing of flow solver data were developed.

Chan, William M.↗

NASA NTRS1992

On essentially non-oscillatory schemes on unstructured meshes: Analysis and implementation

A few years ago, the class of Essentially Non-Oscillatory Schemes for the numerical simulation of hyperbolic equations and systems was constructed. Since then, some extensions have been made to multidimensional simulations of compressible flows, mainly in the context of very regular structured meshes. In this paper, we first recall and improve the results of an earlier paper about non-oscillatory reconstruction on unstructured meshes, emphasizing the effective calculation of the reconstruction. Then we describe a class of numerical schemes on unstructured meshes and give some applications for its third order version. This demonstrates that a higher order of accuracy is indeed obtained, even on very irregular meshes.

Abgrall, R.↗

NASA NTRS1993

High-order cyclo-difference techniques: An alternative to finite differences

The summation-by-parts energy norm is used to establish a new class of high-order finite-difference techniques referred to here as 'cyclo-difference' techniques. These techniques are constructed cyclically from stable subelements, and require no numerical boundary conditions; when coupled with the simultaneous approximation term (SAT) boundary treatment, they are time asymptotically stable for an arbitrary hyperbolic system. These techniques are similar to spectral element techniques and are ideally suited for parallel implementation, but do not require special collocation points or orthogonal basis functions. The principal focus is on methods of sixth-order formal accuracy or less; however, these methods could be extended in principle to any arbitrary order of accuracy.

Carpenter, Mark H.↗

NASA NTRS1992

A hybrid multigrid technique for computing steady-state solutions to supersonic flows

Recently, Li and Sanders have introduced a class of finite difference schemes to approximate generally discontinuous solutions to hyperbolic systems of conservation laws. These equations have the form together with relevant boundary conditions. When modelling hypersonic spacecraft reentry, the differential equations above are frequently given by the compressible Euler equations coupled with a nonequilibrium chemistry model. For these applications, steady state solutions are often sought. Many tens (to hundreds) of super computer hours can be devoted to a single three space dimensional simulation. The primary difficulty is the inability to rapidly and reliably capture the steady state. In these notes, we demonstrate that a particular variant from the schemes presented can be combined with a particular multigrid approach to capture steady state solutions to the compressible Euler equations in one space dimension. We show that the rate of convergence to steady state coming from this multigrid implementation is vastly superior to the traditional approach of artificial time relaxation. Moreover, we demonstrate virtual grid independence. That is, the rate of convergence does not depend on the degree of spatial grid refinement.

Sanders, Richard↗

NASA NTRS1992

Three-dimensional boundary layer calculation by a characteristic method

A numerical method for solving the three-dimensional boundary layer equations for bodies of arbitrary shape is presented. In laminar flows, the application domain extends from incompressible to hypersonic flows with the assumption of chemical equilibrium. For turbulent boundary layers, the application domain is limited by the validity of the mixing length model used. In order to respect the hyperbolic nature of the equations reduced to first order partial derivative terms, the momentum equations are discretized along the local streamlines using of the osculator tangent plane at each node of the body fitted coordinate system. With this original approach, it is possible to overcome the use of the generalized coordinates, and therefore, it is not necessary to impose an extra hypothesis about the regularity of the mesh in which the boundary conditions are given. By doing so, it is possible to limit, and sometimes to suppress, the pre-treatment of the data coming from an inviscid calculation. Although the proposed scheme is only semi-implicit, the method remains numerically very efficient.

Houdeville, R.↗

NASA NTRS1991

Small body mass determination from a flyby

This paper investigates the accuracy with which the mass of a small body can be determined from a flyby. Due to the nearly linear nature of hyperbolic flybys of small bodies, analytic solutions can be derived. Four analytic solutions are developed, each of increasing complexity with different applications. These solutions are compared to a complex computer simulation for accuracy. When these methods are applied to nearly linear trajectories, the analytic solutions agree with the computer simulation results to within 4.0 percent except in one boundary case which is discussed in the text. Also described is the linear range for which these equations are applicable. These solutions are then applied to the proposed asteroid flyby of the CRAF mission to predict the mass estimate accuracy.

Sybert, Catherine B.↗

NASA NTRS1993

Trajectory-based heating analysis for the ESA/Rosetta earth return vehicle

A coupled, trajectory based flowfield and material thermal response analysis is presented for the European Space Agency (ESA) proposed Rosetta comet nucleus sample return vehicle. The probe returns to Earth along a hyperbolic trajectory with an entry velocity of 16.5 km/sec and requires an ablative heat shield on the forebody. Combined radiative and convective, ablating flowfield analyses were performed for the significant heating portion of the shallow ballistic entry trajectory. Both quasi-steady ablation and fully transient analyses were performed for a heat shield composed of carbon-phenolic ablative material. Quasi-steady analysis was performed using the two-dimensional, axisymmetric codes RASLE and BLIMPK. Transient computational results were obtained from the one-dimensional ablation/conduction code, CMA. Results are presented for heating, temperature and ablation rate distributions over the probe forebody for various trajectory points. Comparison of transient and quasi-steady results indicates that, for the heating pulse encountered by this probe, the quasi-static approach is conservative from the standpoint of predicted surface recession.

Henline, William D.↗

NASA NTRS1993

A numerical treatment of geodynamic viscous flow problems involving the advection of material interfaces

Effective numerical treatment of multicomponent viscous flow problems involving the advection of sharp interfaces between materials of differing physical properties requires correction techniques to prevent spurious diffusion and dispersion. We develop a particular algorithm, based on modern shock-capture techniques, employing a two-step nonlinear method. The first step involves the global application of a high-order upwind scheme to a hyperbolic advection equation used to model the distribution of distinct material components in a flow field. The second step is corrective and involves the application of a global filter designed to remove dispersion errors that result from the advection of discontinuities (e.g., material interfaces) by high-order, minimally dissipative schemes. The filter introduces no additional diffusion error. Nonuniform viscosity across a material interface is allowed for by the implementation of a compositionally weighted-inverse interface viscosity scheme. The combined method approaches the optimal accuracy of modern shock-capture techniques with a minimal increase in computational time and memory. A key advantage of this method is its simplicity to incorporate into preexisting codes be they finite difference, element, or volume of two or three dimensions.

Lenardic, A.↗

NASA NTRS1993

Spectral solution of the viscous blunt-body problem

The viscous blunt-body problem is solved with a shock-fitted Chebyshev spectral method. No explicit artificial viscosity or filtering is needed to obtain smooth, converged solutions. The method is applied to two problems. First, results for the flow over a right circular cylinder in the Mach number range of 5.5-6.0 are compared with experimental data. Second, a solution for a Mach 25 flow over a hyperbolic cone is compared with a viscous shock-layer calculation.

Kopriva, David A.↗

NASA NTRS1991

A staggered mesh finite difference scheme for the computation of hypersonic Euler flows

A shock capturing finite difference method for systems of hyperbolic conservation laws is presented which avoids the need to solve Riemann problems while being competitive in performance with other current methods. A staggered spatial mesh is employed, so that complicated nonlinear waves generated at cell interfaces are averaged over cell interiors at the next time level. The full method combines to form a conservative version of the modified method of characteristics. The advantages of the method are discussed, and numerical results are presented for the two-dimensional double ellipse problem.

Sanders, Richard↗

NASA NTRS1990

On resonance in linear conservation laws without source terms

A phenomena is described occuring in wave propagation for systems of conservation laws which are not hyperbolic. The nature of the wave propagation for linear systems of conservation laws which are degenerate in the sense that they are not equivalent to diagonal systems is examined. It is concluded that in the degenerate case, 'resonance' occurs, that is, the solutions are combinations of traveling waves and 'resonance waves'. Here resonance means that the solution may become unbounded even if the initial values are bounded. The solutions (waves) can be described as a superposition of 'packets' (groups) of 'resonance waves' traveling with the same speed. These are linear systems with constant coefficients which are self-exciting, which is what one would expect to encounter in nonlinear systems.

Gingold, H.↗

NASA NTRS1993

A coarse-grid correction/nonlinear relaxation algorithm for the three-dimensional, compressible Navier-Stokes equations

A combined coarse-grid correction/upwind relaxation strategy to provide rapid convergence for 3D high-speed viscous flowfields is discussed an evaluated. The construction and analysis of a simple two-grid acceleration procedure based on 'hyperbolic' multigrid concepts is presented. Numerical simulations of a 2D compression-corner flowfield, a 3D crossing shock/turbulent boundary layer interaction, and a 3D scramjet inlet flowfield are presented to illustrate the benefits of the approach. Results indicate that the procedure generally converges two or more times faster than the baseline algorithm.

Edwards, Jack R.↗

NASA NTRS1993

Conservative high-order-accurate finite-difference methods for curvilinear grids

Two fourth-order-accurate finite-difference methods for numerically solving hyperbolic systems of conservation equations on smooth curvilinear grids are presented. The first method uses the differential form of the conservation equations; the second method uses the integral form of the conservation equations. Modifications to these schemes, which are required near boundaries to maintain overall high-order accuracy, are discussed. An analysis that demonstrates the stability of the modified schemes is also provided. Modifications to one of the schemes to make it total variation diminishing (TVD) are also discussed. Results that demonstrate the high-order accuracy of both schemes are included in the paper. In particular, a Ringleb-flow computation demonstrates the high-order accuracy and the stability of the boundary and near-boundary procedures. A second computation of supersonic flow over a cylinder demonstrates the shock-capturing capability of the TVD methodology. An important contribution of this paper is the dear demonstration that higher order accuracy leads to increased computational efficiency.

Rai, Man M.↗

NASA NTRS1993

Interaction of the sonic boom with atmospheric turbulence

Theoretical research has been carried out to study the effect of free-stream turbulence on sonic boom pressure fields. A new transonic small-disturbance model to analyze the interactions of random disturbances with a weak shock has been developed. The model equation has an extended form of the classic small-disturbance equation for unsteady transonic aerodynamics. An alternative approach shows that the pressure field may be described by an equation that has an extended form of the classic nonlinear acoustics equation that describes the propagation of sound beams with narrow angular spectrum. The model shows that diffraction effects, nonlinear steepening effects, focusing and caustic effects and random induced vorticity fluctuations interact simultaneously to determine the development of the shock wave in space and time and the pressure field behind it. A finite-difference algorithm to solve the mixed-type elliptic-hyperbolic flows around the shock wave has also been developed. Numerical calculations of shock wave interactions with various deterministic and random fluctuations will be presented in a future report.

Rusak, Z.↗

NASA NTRS1993

Atmospheric entry of Mars-return nuclear-powered vehicles due to accidental termination of operations

The entry of nuclear reactors into Earth's atmosphere resulting from an accidental or inadvertent abort of a space vehicle powered by nuclear-thermal rockets is investigated. The study is made for a typical piloted Mars mission vehicle incapacitated by an accident or malfunction during the Earth-arrival phase of the Mars-return journey due to simultaneous, multiple failures of its component systems. A single accident/abort scenario resulting in three entry possibilities is considered for a nominal hyperbolic in-bound approach velocity of 8 km/sec. The most severe case involving a direct entry is then analyzed over a broad range of approach velocities extending to 12 km/sec to include sprint-type missions. The results indicate that the severe surface heating, stagnation pressures, and g-loads are greater than 150 kW/sq cm, 300 atm, and 800-g, respectively. The wall heat transfer rate exceeds the value that can be accommodated by a carbon heatshield through radiation equilibrium prior to sublimation at 5500 K. These conditions are beyond our previous experience in crew safety, structural design, and thermal protection.

Menees, Gene P.↗

NASA NTRS1993

Monte Carlo analysis of the Titan III/Transfer Orbit Stage guidance system for the Mars Observer mission

An important part of space launch vehicle mission planning for a planetary mission is the integrated analysis of guidance and performance dispersions for both booster and upper stage vehicles. For the Mars Observer mission, an integrated trajectory analysis was used to maximize the scientific payload and to minimize injection errors by optimizing the energy management of both vehicles. This was accomplished by designing the Titan III booster vehicle to inject into a hyperbolic departure plane, and the Transfer Orbit Stage (TOS) to correct any booster dispersions. An integrated Monte Carlo analysis of the performance and guidance dispersions of both vehicles provided sensitivities, an evaluation of their guidance schemes and an injection error covariance matrix. The polynomial guidance schemes used for the Titan III variable flight azimuth computations and the TOS solid rocket motor ignition time and burn direction derivations accounted for a wide variation of launch times, performance dispersions, and target conditions. The Mars Observer spacecraft was launched on 25 September 1992 on the Titan III/TOS vehicle. The post flight analysis indicated that a near perfect park orbit injection was achieved, followed by a trans-Mars injection with less than 2sigma errors.

Bell, Stephen C.↗