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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.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Effect of Configuration Pitching Motion on Twin Tail Buffet Response

The effect of dynamic pitch-up motion of delta wing on twin-tail buffet response is investigated. The computational model consists of a delta wing-twin tail configuration. The computations are carried out on a dynamic multi-block grid structure. This multidisciplinary problem is solved using three sets of equations which consists of the unsteady Navier-Stokes equations, the aeroelastic equations, and the grid displacement equations. The configuration is pitched-up from zero up to 60 deg. angle of attack, and the freestream Mach number and Reynolds number are 0.3 and 1.25 million, respectively. With the twin tail fixed as rigid surfaces and with no-forced pitch-up motion, the problem is solved for the initial flow conditions. Next, the problem is solved for the twin-tail response for uncoupled bending and torsional vibrations due to the unsteady loads on the twin tail and due to the forced pitch-up motion. The dynamic pitch-up problem is also solved for the flow response with the twin tail kept rigid. The configuration is investigated for inboard position of the twin tail which corresponds to a separation distance between the twin tail of 33% wing chord. The computed results are compared with the available experimental data.

Sheta, Essam F.↗
NASA NTRS1991

Numerical simulation of transition in wall-bounded shear flows

The current status of numerical simulation techniques for the transition to turbulence in incompressible channel and boundary-layer flows is surveyed, and typical results are presented graphically. The focus is on direct numerical simulations based on the full nonlinear time-dependent Navier-Stokes equations without empirical closure assumptions for prescribed initial and boundary conditions. Topics addressed include the vibrating ribbon problem, space and time discretization, initial and boundary conditions, alternative methods based on the triple-deck approximation, two-dimensional channel and boundary-layer flows, three-dimensional boundary layers, wave packets and turbulent spots, compressible flows, transition control, and transition modeling.

Kleiser, Leonhard↗
NASA NTRS1978

Numerical experiments on the stability of disklike galaxies

It is noted that the stability properties of available galactic models are not consistent with presumptions based on observation and that axisymmetric disk systems with velocity dispersions like those of the Galaxy display major changes in form on a dynamical time scale. A report is given on a series of numerical experiments carried out as part of a systematic search for purely self-consistent disk galaxy models that might undergo little change over the time of several galactic rotations. The stability problem is reviewed, the method and calculations used are described, and initial conditions are outlined. The problem of estimating growth rates is discussed, and growth rates are evaluated for various disturbances. Experimental results are presented concerning growths of axisymmetric disturbances in 'cold' systems as well as disturbances with m = 1, 2, and 3. It is found that m = 2 disturbances are the most virulent and should dominate when all m values are allowed, but that the most rapidly growing disturbances are inhibited when several m values are allowed.

Miller, R. H.↗
NASA NTRS1973

High speed flow past wings

The analytical solution to the transonic small perturbation equation which describes steady compressible flow past finite wings at subsonic speeds can be expressed as a nonlinear integral equation with the perturbation velocity potential as the unknown function. This known formulation is substituted by a system of nonlinear algebraic equations to which various methods are applicable for its solution. Due to the presence of mathematical discontinuities in the flow solutions, however, a main computational difficulty was to ensure uniqueness of the solutions when local velocities on the wing exceeded the speed of sound. For continuous solutions this was achieved by embedding the algebraic system in an one-parameter operator homotopy in order to apply the method of parametric differentiation. The solution to the initial system of equations appears then as a solution to a Cauchy problem where the initial condition is related to the accompanying incompressible flow solution. In using this technique, however, a continuous dependence of the solution development on the initial data is lost when the solution reaches the minimum bifurcation point. A steepest descent iteration technique was therefore, added to the computational scheme for the calculation of discontinuous flow solutions. Results for purely subsonic flows and supersonic flows with and without compression shocks are given and compared with other available theoretical solutions.

Norstrud, H.↗
NASA NTRS1975

On the Navier-Stokes equations with constant total temperature

For various applications in fluid dynamics, it is assumed that the total temperature is constant. Therefore, the energy equation can be replaced by an algebraic relation. The resulting set of equations in the inviscid case is analyzed. It is shown that the system is strictly hyperbolic and well posed for the initial value problems. Boundary conditions are described such that the linearized system is well posed. The Hopscotch method is investigated and numerical results are presented.

Gottlieb, D.↗
NASA NTRS1976

On the Navier-Stokes equations with constant total temperature

For various applications in fluid dynamics, one can assume that the total temperature is constant. Therefore, the energy equations can be replaced by an algebraic relation. The resulting set of equations in the inviscid case is analyzed in this paper. It is shown that the system is strictly hyperbolic and well posed for the initial-value problem. Boundary conditions are described such that the linearized system is well posed. The hopscotch method is investigated and numerical results are presented.

Gottlieb, D.↗
NASA NTRS1987

Estimation of discontinuous coefficients in parabolic systems - Applications to reservoir simulation

Spline-based techniques for estimating spatially varying parameters that appear in parabolic distributed systems (typical of those found in reservoir simulation problems) are presented. In particular, the problem of determining discontinuous coefficients is discussed, estimating both the functional shape and points of discontinuity for such parameters. In addition, the ideas may also be applied to problems with unknown initial conditions and unknown parameters appearing in terms representing external forces. Convergence results and a summary of numerical performance of the resulting algorithms are given.

Lamm, Patricia K.↗
NASA NTRS1995

On the breakup of viscous liquid threads

A one-dimensional model evolution equation is used to describe the nonlinear dynamics that can lead to the breakup of a cylindrical thread of Newtonian fluid when capillary forces drive the motion. The model is derived from the Stokes equations by use of rational asymptotic expansions and under a slender jet approximation. The equations are solved numerically and the jet radius is found to vanish after a finite time yielding breakup. The slender jet approximation is valid throughout the evolution leading to pinching. The model admits self-similar pinching solutions which yield symmetric shapes at breakup. These solutions are shown to be the ones selected by the initial boundary value problem, for general initial conditions. Further more, the terminal state of the model equation is shown to be identical to that predicted by a theory which looks for singular pinching solutions directly from the Stokes equations without invoking the slender jet approximation throughout the evolution. It is shown quantitatively, therefore, that the one-dimensional model gives a consistent terminal state with the jet shape being locally symmetric at breakup. The asymptotic expansion scheme is also extended to include unsteady and inerticial forces in the momentum equations to derive an evolution system modelling the breakup of Navier-Stokes jets. The model is employed in extensive simulations to compute breakup times for different initial conditions; satellite drop formation is also supported by the model and the dependence of satellite drop volumes on initial conditions is studied.

Papageorgiou, Demetrios T.↗
NASA NTRS2003

Preliminary Planar Formation: Flight Dynamics Near Sun-Earth L2 Point

NASA's Goddard Space Flight Center is planning a series of missions in the vicinity of the Sun-Earth L2 libration point. Some of these projects will involve a distributed space system of telescope spacecraft acting together as a single telescope for high-resolution. The individual telescopes will be configured in a plane, surrounding a hub, where the telescope plane can be aimed toward various astronomical targets of interest. In preparation for these missions, it is necessary to develop an improved understanding of the dynamical behavior of objects in a planar configuration near L2. The classical circular restricted three body problem is taken as the basis for the analysis. At first order, the motion of such a telescope relative to the hub is described by a system of linear second order differential equations. These equations are identical to the circular restricted problem's linear equations describing the hub motion about L2. Therefore, the fundamental frequencies, both parallel to and normal to the ecliptic plane, are the same for the relative telescope motion as for the hub motion. To maintain the telescope plane for the duration necessary for the planned observations, a halo-type orbit of the telescopes about the hub is investigated. By using a halo orbit, the individual telescopes remain in approximately the same plane over the observation duration. For such an orbit, the fundamental periods parallel to and normal to the ecliptic plane are forced to be the same by careful selection of the initial conditions in order to adjust the higher order forces. The relative amplitudes of the resulting oscillations are associated with the orientation of the telescope plane relative to the ecliptic. As in the circular restricted problem, initial conditions for the linearized equations must be selected so as not to excite the convergent or divergent linear modes. In a higher order analysis, the telescope relative motion equations include the effects of the position of the hub relative to L2. In this paper, the differential equations are developed through second order in the distance of the hub from the libration point. A modified Lindstedt-Poincad perturbation method is employed to construct the solution of these differential equations through that same order of magnitude. In the course of the solution process, relationships are determined between the initial conditions of the telescopes, selected in order to avoid resonance excitation. As the differential equations include the hub position, it is necessary to simultaneously develop the solution for the hub. As has been done in past analyses of the circular restricted problem, the hub position is written in a power series formulation in terms of its distance from L2. Then, in order to be included in the telescope equations, the hub solution is cast in terms of the nonlinear frequency of the relative telescope motion. In the course of the analysis, it is determined that the hub should also maintain a halo orbit - about L2. Additionally, relationships are formed between the initial conditions of the telescopes and the hub. These relationships may be used to associate sets of initial conditions with particular orientations of the telescope plane. The accuracy of the analytical solution is verified through various simulations and comparison to numerical integration of the differential equations. The results of the simulations are presented, along with a graphical representation of the relationships between the initial conditions of the telescopes and hub.

Segerman, Alan M.↗
NASA NTRSDate not supplied

Extending Explicit Guidance Methods to Higher Dimensions, Additional Conditions, and Higher Order Integration

Guidance functions play critical roles in autonomy to steer vehicles and aircraft to the intended target or destination. Explicit guidance (E Guidance) solves the two-point boundary value problem with initial and final conditions for position and velocity. The original formulation of E Guidance involves translational acceleration commands with a direct relationship to time, and it is possible to modify E Guidance for rotational acceleration. Other extensions for E Guidance include higher dimensions, additional conditions, and higher-order integration of the linearly independent E Guidance functions. The most promising extension involves higher-order integration of the E Guidance functions, but it may be physically impractical by initially moving away from the target. This paper provides a brief overview of some methods that extend E Guidance to higher dimensions, utilize additional conditions, or perform higher-order integration, and if they satisfy the two-point boundary value problem.

explicit guidance↗
NASA NTRSDate not supplied

Extending Explicit Guidance Methods to Higher Dimensions, Additional Conditions, and Higher Order Integration

Guidance functions play critical roles in autonomy to steer vehicles and aircraft to the intended target or destination. Explicit guidance (E Guidance) solves the two-point boundary value problem with initial and final conditions for position and velocity. The original formulation of explicit guidance involves translational acceleration commands with a direct relationship to time, and it is possible to modify E Guidance for rotational acceleration. Other extensions for E Guidance include higher dimensions, additional conditions, and higher-order integration of the linearly independent E Guidance functions. The most promising extension involves higher-order integration of the E Guidance functions, but it may be physically impractical by initially moving away from the target. This paper provides a brief overview of some methods that extend E Guidance to higher dimensions, utilize additional conditions, or perform higher-order integration, and if they satisfy the two-point boundary value problem.

explicit guidance↗
NASA NTRS1990

The CFL condition for spectral approximations to hyperbolic initial-boundary value problems

The stability of spectral approximations to scalar hyperbolic initial-boundary value problems with variable coefficients are studied. Time is discretized by explicit multi-level or Runge-Kutta methods of order less than or equal to 3 (forward Euler time differencing is included), and spatial discretizations are studied by spectral and pseudospectral approximations associated with the general family of Jacobi polynomials. It is proved that these fully explicit spectral approximations are stable provided their time-step, delta t, is restricted by the CFL-like condition, delta t less than Const. N(exp-2), where N equals the spatial number of degrees of freedom. We give two independent proofs of this result, depending on two different choices of approximate L(exp 2)-weighted norms. In both approaches, the proofs hinge on a certain inverse inequality interesting for its own sake. The result confirms the commonly held belief that the above CFL stability restriction, which is extensively used in practical implementations, guarantees the stability (and hence the convergence) of fully-explicit spectral approximations in the nonperiodic case.

Gottlieb, David↗
NASA NTRS1991

The CFL condition for spectral approximations to hyperbolic initial-boundary value problems

The stability of spectral approximations to scalar hyperbolic initial-boundary value problems with variable coefficients are studied. Time is discretized by explicit multi-level or Runge-Kutta methods of order less than or equal to 3 (forward Euler time differencing is included), and spatial discretizations are studied by spectral and pseudospectral approximations associated with the general family of Jacobi polynomials. It is proved that these fully explicit spectral approximations are stable provided their time-step, delta t, is restricted by the CFL-like condition, delta t less than Const. N(exp-2), where N equals the spatial number of degrees of freedom. We give two independent proofs of this result, depending on two different choices of approximate L(exp 2)-weighted norms. In both approaches, the proofs hinge on a certain inverse inequality interesting for its own sake. The result confirms the commonly held belief that the above CFL stability restriction, which is extensively used in practical implementations, guarantees the stability (and hence the convergence) of fully-explicit spectral approximations in the nonperiodic case.

Gottlieb, David↗
NASA NTRS1999

Autolanding Trajectory Design for the X-34

An Autolanding I-load Program (ALIP) is developed to design unpowered autolanding trajectories for the X-34 Mach 8 vehicle. The trajectory is comprised of geometric flight segments that are based on the shuttle approach and landing design (steep glideslope, circular flare, exponential flare to shallow glideslope). Enforcing physical constraints such as loads, vertical descent rate, continuity and smoothness reduces the design problem to a two point boundary value problem with conditions on the initial and final dynamic pressure. Finding a solution required the development of trajectory simulation techniques that constrained the flight profile to a prescribed geometry. The design methodology can be extended beyond the autolanding flight regime by repeating the series of geometric segments and solving multiple two-point boundary values problems (one for each series). The techniques described in this paper facilitate rapid design of reference trajectories.

Barton, Gregg H.↗
NASA NTRS1975

Spherical means of solutions of partial differential equations in a conical region

The spherical means of the solutions of a linear partial differential equation Lu = f in a conical region are studied. The conical region is bounded by a surface generated by curvilinear xi lines and by two truncating xi surfaces. The spherical mean is the average of u over a constant xi surface. Conditions on the linear differential operator, L, and on the orthogonal coordinates xi, eta, and zeta are established so that the problem for the determination of the spherical mean of the solution subjected to the appropriate boundary and initial conditions can be reduced to a problem with only one space variable. Conditions are then established so that the spherical mean of the solution in one conical region will be proportional to that of a known solution in another conical region. Applications to various problems of mathematical physics and their physical interpretations are presented.

Ting, L.↗
NASA NTRS1975

Generalized Du Fort-Frankel methods for parabolic initial boundary value problems

The Du Fort-Frankel difference scheme is generalized to difference operators of arbitrary high order accuracy in space and to arbitrary order of the parabolic differential operator. Spectral methods can also be used to approximate the spatial part of the differential operator. The scheme is explicit, and it is unconditionally stable for the initial value problem. Stable boundary conditions are given for two different fourth order accurate space approximations.

Gottlieb, D.↗
NASA NTRS1976

Generalized Du Fort-Frankel methods for parabolic initial-boundary value problems

The Du Fort-Frankel difference scheme is generalized to difference operators of arbitrary high order accuracy in space and to arbitrary order of the parabolic differential operator. Spectral methods can also be used to approximate the spatial part of the differential operator. The scheme is explicit, and it is unconditionally stable for the initial value problem. Stable boundary conditions are given for two different fourth order accurate space approximations.

Gottlieb, D.↗
NASA NTRS1990

Minimum fuel trajectory for the aerospace-plane

An overall trajectory for a single-stage-to-orbit vehicle with an initial weight of 234 tons is calculated, and four different propulsion models including turbojet, ramjet, scramjet, and rocket are considered. First, the atmospheric flight in the thicker atmosphere is discussed with emphasis on trajectory optimization, optimization problem, aerodynamic problem, propulsion model, and initial conditions. The performance of turbojet and ramjet-scramjet engines is analyzed; and then the flight to orbit is assessed from the optimization point of view. It is shown that roll modulation saves little during the trajectory, and the combined application of airbreathing propulsion and aerodynamic lift is suggested.

Breakwell, John V.↗