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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

A perturbation solution for transverse pressure-sensitive combustion instability in an annulus

A method for analysis of combustion instability in rocket motors based on a combination of the Galerkin method and the two-variable (or multiple-scales) perturbation method is developed. The method is illustrated by applying it to the problem of pressure-sensitive combustion instability in a liquid-fuel annular combustion chamber. To the order of approximation inherent in the method it is found that the complete linear stability analysis and most of the nonlinear stability analysis can be carried out in closed form. The results thus obtained are used to clarify several aspects of the interpretation of numerical solutions obtained by previous investigators.

Googerdy, A.↗
NASA NTRS1979

Perturbation solutions of combustion instability problems

A method involving approximate modal analysis using the Galerkin method followed by an approximate solution of the resulting modal-amplitude equations by the two-variable perturbation method (method of multiple scales) is applied to two problems of pressure-sensitive nonlinear combustion instability in liquid-fuel rocket motors. One problem exhibits self-coupled instability while the other exhibits mode-coupled instability. In both cases it is possible to carry out the entire linear stability analysis and significant portions of the nonlinear stability analysis in closed form. In the problem of self-coupled instability the nonlinear stability boundary and approximate forms of the limit-cycle amplitudes and growth and decay rates are determined in closed form while the exact limit-cycle amplitudes and growth and decay rates are found numerically. In the problem of mode-coupled instability the limit-cycle amplitudes are found in closed form while the growth and decay rates are found numerically. The behavior of the solutions found by the perturbation method are in agreement with solutions obtained using complex numerical methods.

Googerdy, A.↗
NASA NTRS1975

SSME turbopump technology improvements via transient rotordynamic analysis

The rotordynamic behavior of the high pressure oxygen turbopump and high pressure fuel pump was analyzed for the Space Shuttle Main Engine. The identification of potential rotordynamic problem areas which might arise during operation of these units prior to their testing was accomplished. Alternative procedures for correcting potential rotordynamic problems should they occur were investigated. An adequate analytic and physical understanding of the turbopump rotordynamics was developed to improve the probability of a correct diagnosis of rotordynamic problems from test data. Transient rotordynamic models were developed for both turbopumps. The transient models model the hydrodynamic forces of the turbopump seals. A linear stability analysis was performed for the turbopump rotordynamics models, which included gyroscopic effects, seal forces, speed-dependent bearing characteristics, and internal rotor damping. Results are presented and discussed.

Childs, D. W.↗
NASA NTRS1972

On the stability and pointing of an attached double-gimbal experiment package

The pointing capability of a double gimbal experiment isolation and control system of the Apollo telescope mount (ATM) type was investigated. Three composite structural models of an experiment package connected through frictionless gimbals to a carrier vehicle (including a rigid package-rigid carrier model, a rigid package-flexible carrier model, and a flexible package-flexible carrier model) were used, and a linear model of the nominal ATM gimbal control system is considered. A linear stability analysis was performed to verify stability of the control system with nominal gains. Transform techniques were used to compute pointing errors onboard the experiment package due to random crew motions input into the carrier vehicle. Results of the investigation indicate that there is no stability problem due to flexible coupling of the experiment package and the carrier, and that the ATM-type system is capable of pointing accuracies better than 0.1 arc second.

Groom, N. J.↗
NASA NTRS1972

The stability of tangential discontinuities

Intuition regarding the stability of MHD tangential discontinuities of solar wind has been borne out by a linear stability analysis of the MHD equations. In performing the calculation, the model used had no plasma flow and thus corresponded to the solar wind rest frame. The method calculated the change in total energy, plasma plus magnetic, due to the perturbation. This type of stability analysis is analogous to the test of the stability of an equilibrium point in a mechanical potential.

Birmingham, T.↗
NASA NTRS1972

Application of multivariable search techniques to structural design optimization

Multivariable optimization techniques are applied to a particular class of minimum weight structural design problems: the design of an axially loaded, pressurized, stiffened cylinder. Minimum weight designs are obtained by a variety of search algorithms: first- and second-order, elemental perturbation, and randomized techniques. An exterior penalty function approach to constrained minimization is employed. Some comparisons are made with solutions obtained by an interior penalty function procedure. In general, it would appear that an interior penalty function approach may not be as well suited to the class of design problems considered as the exterior penalty function approach. It is also shown that a combination of search algorithms will tend to arrive at an extremal design in a more reliable manner than a single algorithm. The effect of incorporating realistic geometrical constraints on stiffener cross-sections is investigated. A limited comparison is made between minimum weight cylinders designed on the basis of a linear stability analysis and cylinders designed on the basis of empirical buckling data. Finally, a technique for locating more than one extremal is demonstrated.

Jones, R. T.↗
NASA NTRS1972

Hydrodynamic stability of viscoelastic fluids - Importance of fluid model, overstability, and form of disturbance.

A linearized stability analysis has been applied to a fluid flowing in a gravity field between horizontal planes in Couette flow under conditions such that the temperature of the bottom plane exceeds that of the top. It is shown that, under conditions likely to be encountered with polymer solutions, oscillatory instabilities will not be controlling. Criteria are offered for ascertaining when an analysis based upon a second-order fluid model may be expected to yield physically meaningful results. It is also shown that, for the fluid model considered, critical conditions for stability are not changed when disturbances which vary in the flow direction are substituted for those which are a function of the coordinate transverse to the flow.

Mcintire, L. V.↗
NASA NTRS1977

Nonlinear Alfven waves in high-speed solar wind streams

A nonlinear proton distribution function that is an exact stationary solution of the nonlinear Vlasov equation and Maxwell's equations and which supports a single nonlinear transverse Alfven (ion cyclotron) wave that is circularly polarized and nondispersive is proposed for most of the observations during high-speed solar wind streams. This nonlinear distribution removes the strong Alfven wave instability, inconsistent with the persistence of the observed proton distribution functions in high-speed streams, found by the linear stability analysis. Model temperature anisotropies and drift velocities of the two spatially inhomogeneous bi-Maxwellian components are consistent with typical proton velocity distributions measured in high-speed streams at 1 AU. Two derived relations for each of the wave number and the phase velocity of the wave are obeyed within experimental uncertainties by two typical proton measurements. Our model also predicts that the alpha particle bulk flow velocity exceeds the proton particle bulk flow velocity, as is observed.

Abraham-Shrauner, B.↗
NASA NTRS1978

The effects of curvature and viscosity on baroclinic instability: A two-layer model

A linear stability analysis of a baroclinic zonal current contained between two parallel rigid boundaries is presented. Curvature is included by performing the analysis on a beta b-plane and viscosity by allowing for the effects of Ekman layers on the rigid boundaries. A two-layer model is used. This calculation was carried out to assist in the design of a spherical model of the general circulation of the earth's atmosphere for Spacelab. In the low-gravity environment on an orbiting vehicle, a dominant radial dielectric body force, analogous to planetary gravity, can be achieved over a volume of liquid held between two concentric spheres. The results show the Eady short wavelength cutoff, and long wavelength cutoffs due to Ekman damping and curvature.

Fowlis, W. W.↗
NASA NTRS1979

Some Problems of Nonlinear Waves in Solid Propellant Rocket Motors

This paper is concerned with analyses of nonlinear waves in solid propellant rockets. Most attention is given to an approximate technique which inexpensively provides results which appear to be quite accurate at least up to amplitudes of ten percent. The connection with linear stability analysis is shown. Primarily to study nonlinear stability, or triggering, the method is extended to third order in the amplitude of wave motion; no explicit results have been obtained. Application of the approximate method to the behavior of pulses is described.

F E C Culick↗
NASA NTRS1980

Attitude stability of spinning satellites

Some problems of attitude stability of spinning satellites are treated in a rigorous manner. With certain restrictions, linearized stability analysis correctly predicts the attitude stability of spinning satellites, even in the critical cases of the Liapunov-Poincare stability theory.

Caughey, T. K.↗
NASA NTRS1980

Stability of the stratifield cylindrical annulus flow

The linear stability analysis for the stratified flow between two rotating circular cylinders is formulated. Two approaches for the stability analysis are presented. The first approach results in an algebraic eigenvalue problem, while the second results in an initial value problem for the perturbation function. The advantages and disadvantages of both approaches are discussed and a preferable numerical solution technique is outlined.

Antar, B. N.↗
NASA NTRS1979

Convective instability when the temperature gradient and rotation vector are oblique to gravity. I - Fluids without diffusion

A linear stability analysis of fluid layers under uniform rotation (generally oblique to gravity) which possess both vertical and horizontal temperature gradients is made by considering ideal fluids without diffusion within a Boussinesq approximation. This simplified configuration is used to assess the preferred convective modes as a function of latitude on a planet like Jupiter. The tilted rotation vector introduces a preference for roll-like disturbances with north-south orientations, while the horizontal temperature gradient produces a thermal wind shear which favors convective rolls oriented parallel to the flow in an east-west direction. It is found that the horizontal temperature gradient needed to produce a preference for the axisymmetric or east-west rolls increases with an increasing rotation rate and a decreasing latitude. The parameter values for Jupiter are estimated with the use of a simple radiative convective model, indicating a preference for axisymmetric rolls at nearly all latitudes if the convection zone depth is greater than about 200 km below the one atmosphere pressure level and convective roll characteristics which contribute to an equatorial acceleration.

Hathaway, D. H.↗
NASA NTRS1980

Convective instability when the temperature gradient and rotation vector are oblique to gravity. II - Real fluids with effects of diffusion

The linear stability analysis of Hathaway et al. (1979) is repeated for Boussinesq fluids with viscous and thermal diffusion. The fluid is confined between plane parallel boundaries and the rotation vector is oblique to gravity; this tilted rotation vector introduces a preference for roll-like disturbances whose axes are oriented north-south. The presence of a latitudinal temperature gradient produces a thermal wind shear which favors axisymmetric convective rolls if the gradient exceeds some critical value. The axisymmetric rolls are similar in many respects to the cloud bands on Jupiter provided they extend to a depth of about 15,000 km.

Hathaway, D. H.↗
NASA NTRS1981

Subcritical transition to turbulence in planar shear flows

The two-dimensional steady and time dependent properties of plane Poiseuille and plane Couette flows are analyzed using iterative techniques and full numerical simulation of the Navier-Stokes equations. It is shown that the finite-amplitude two-dimensional states investigated are strongly unstable to very small three-dimensional perturbations. It is also shown, through full numerical simulation, that this explosive secondary instability can explain the subcritical transitions that occur in real flows. Finally, it is shown that the three-dimensional instability can be analyzed by a linear stability analysis of a two-dimensional flow consisting of the basic parallel flow and a steady (or quasi-steady) finite-amplitude two-dimensional cellular motion.

Orszag, S. A.↗
NASA NTRS1982

On stability of premixed flames in stagnation - Point flow

A quantitative description of flame stabilization in stagnation-point flow is proposed. Asymptotic and stability analyses are made for a flame model where the density of the gas is assumed to be constant and the reaction zone is assumed to be narrow and concentrated over the flame front. It is shown that, if blowing is sufficiently strong, the corrugations disappear and a plane flame results. The phenomena cannot be fully described by means of classical linear stability analysis.

Sivashinsky, G. I.↗