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At least 739 records · Page 41

Detailed Multidimensional Simulations of the Structure and Dynamics of Flames

Numerical simulations in which the various physical and chemical processes can be independently controlled can significantly advance our understanding of the structure, stability, dynamics and extinction of flames. Therefore, our approach has been to use detailed time-dependent, multidimensional, multispecies numerical models to perform carefully designed computational experiments of flames on Earth and in microgravity environments. Some of these computational experiments are complementary to physical experiments performed under the Microgravity Program while others provide a fundamental understanding that cannot be obtained from physical experiments alone. In this report, we provide a brief summary of our recent research highlighting the contributions since the previous microgravity combustion workshop. There are a number of mechanisms that can cause flame instabilities and result in the formation of dynamic multidimensional structures. In the past, we have used numerical simulations to show that it is the thermo-diffusive instability rather than an instability due to preferential diffusion that is the dominant mechanism for the formation of cellular flames in lean hydrogen-air mixtures. Other studies have explored the role of gravity on flame dynamics and extinguishment, multi-step kinetics and radiative losses on flame instabilities in rich hydrogen-air flames, and heat losses on burner-stabilized flames in microgravity. The recent emphasis of our work has been on exploring flame-vortex interactions and further investigating the structure and dynamics of lean hydrogen-air flames in microgravity. These topics are briefly discussed after a brief discussion of our computational approach for solving these problems.

Patnaik, G.↗

The dynamics of spin stabilized spacecraft with movable appendages, part 2

The dynamics and stability of a spin stabilized spacecraft with a hinged appendage system are treated analytically and numerically. The hinged system consists of a central hub with masses attached to (assumed) massless booms of fixed length whose orientation relative to the main part can change. The general three dimensional deployment dynamics of such a hinged system is considered without any restriction on the location of the hinge points. The equations of motion for the hinged system, with viscous damping at both hinge points, are linearized about the nominal equilibrium position where the booms are orthogonal to the nominal spin axis for the case of two dimensional and three dimensional motion. Analytic stability criteria are obtained from the necessary condition on the sign of all the coefficients in the system characteristic equation.

Bainum, P. M.↗

The Effects of Dissipation and Coarse Grid Resolution for Multigrid in Flow Problems

The objective of this paper is to investigate the effects of the numerical dissipation and the resolution of the solution on coarser grids for multigrid with the Euler equation approximations. The convergence is accomplished by multi-stage explicit time-stepping to steady state accelerated by FAS multigrid. A theoretical investigation is carried out for linear hyperbolic equations in one and two dimensions. The spectra reveals that for stability and hence robustness of spatial discretizations with a small amount of numerical dissipation the grid transfer operators have to be accurate enough and the smoother of low temporal accuracy. Numerical results give grid independent convergence in one dimension. For two-dimensional problems with a small amount of numerical dissipation, however, only a few grid levels contribute to an increased speed of convergence. This is explained by the small numerical dissipation leading to dispersion. Increasing the mesh density and hence making the problem over resolved increases the number of mesh levels contributing to an increased speed of convergence. If the steady state equations are elliptic, all grid levels contribute to the convergence regardless of the mesh density.

Eliasson, Peter↗

Hydrostatic calculations of axisymmetric flow and its stability for the AGCE model

Baroclinic waves in the atmospherics general circulation experiment (AGCE) apparatus by the use of numerical hydrostatic primitive equation models were determined. The calculation is accomplished by using an axisymmetric primitive equation model to compute, for a given set of experimental parameters, a steady state axisymmetric flow and then testing this axisymmetric flow for stability using a linear primitive equation model. Some axisymmetric flows are presented together with preliminary stability calculations.

Miller, T. L.↗

A mathematical model of the UH-60 helicopter

This report documents the revisions made to a ten-degree-of-freedom, full-flight envelope, generic helicopter mathematical model to represent the UH-60 helicopter accurately. The major modifications to the model include fuselage aerodynamic force and moment equations specific to the UH-60, a canted tail rotor, a horizontal stabilator with variable incidence, and a pitch bias actuator (PBA). In addition, this report presents a full set of parameters and numerical values which describe the helicopter configuration and physical characteristics. Model validation was accomplished by comparison of trim and stability derivative data generated from the UH-60 math model with data generated from a similar total force and moment math model.

Hilbert, K. B.↗

Stability analysis of cylinders with circular cutouts

The stability of axially compressed cylinders with circular cutouts is analyzed numerically. An extension of the finite-difference method is used which removes the requirement that displacement components be defined in the directions of the grid lines. The results of this nonlinear analysis are found to be in good agreement with earlier experimental results.

Almroth, B. O.↗

Partial implicitization

The steady-state solution to the full Navier-Stokes equations for complicated flows is generally difficult to obtain. The Burgers (1948) equation is used as a model of the Navier-Stokes equations. The steady-state solution is obtained by a one-step explicit technique resulting from a partial implicitization of the difference equation. Stability analysis shows that the technique is unconditionally stable, and numerical tests show the technique to be accurate.

Graves, R. A., Jr.↗

Dynamics of spin stabilized spacecraft during deployment of telescoping appendages

The dynamics of a spin stabilized spacecraft with telescoping appendages are treated both analytically and numerically. Two types of telescoping appendages are considered: (a) where an end mass is mounted at the end of an (assumed) massless boom; and (b) where the appendage is assumed to consist of a uniformly distributed homogeneous mass throughout its length. For the telescoping system Eulerian equations of motion are developed. During all deployment sequences it is assumed that the transverse component of angular momentum is much smaller than the component along the major spin axis. Closed form analytical solutions for the time response of the transverse components of angular velocities are obtained when the spacecraft hub has a nearly spherical mass distribution. For the more general case, a series solution is obtained and this solution is limited by its radius of convergence. The comparison of the different approximate analytical methods with numerical integration results are studied and it is observed that the oscillatory nature of the responses of the transverse angular velocity components reduces rapidly with faster extension rates.

Sellappan, R.↗

A numerical analysis for a comparative study of the pointing accuracy of flexible satellites

The analytical models for flexible satellites have been reported earlier. Numerical results comparing the pointing accuracy of three-axes stabilized, spinning, and dual-spin satellites are presented here. The responses are compared for deterministic and random models with and without external torques. The performances of a uniform control system have been compared to a time-optimal control system for the same base-line configurations.

Huang, T. C.↗

Spherical models: Basic states and stability

Steady axisymmetric basic states in a spherical cap and their stability to azimuthally varying perturbations of different wave numbers were numerically investigated. The main features of the planned computer code and numerical methods are outlined.

Roberts, G. O.↗

An unsteady lifting surface method for single rotation propellers

The mathematical formulation of a lifting surface method for evaluating the steady and unsteady loads induced on single rotation propellers by blade vibration and inflow distortion is described. The scheme is based on 3-D linearized compressible aerodynamics and presumes that all disturbances are simple harmonic in time. This approximation leads to a direct linear integral relation between the normal velocity on the blade (which is determined from the blade geometry and motion) and the distribution of pressure difference across the blade. This linear relation is discretized by breaking the blade up into subareas (panels) on which the pressure difference is treated as approximately constant, and constraining the normal velocity at one (control) point on each panel. The piece-wise constant loads can then be determined by Gaussian elimination. The resulting blade loads can be used in performance, stability and forced response predictions for the rotor. Mathematical and numerical aspects of the method are examined. A selection of results obtained from the method is presented. The appendices include various details of the derivation that were felt to be secondary to the main development in Section 1.

Williams, Marc H.↗

Analytical model for orbital debris environmental management

A differential equation, also referred to as the PIB (particle-in-a-box) model, expressing the time rate of change of the number of objects in orbit, is developed, and its applicability is illustrated. The model can be used as a tool for the assessment of LEO environment stability, and as a starting point for the development of numerical evolutionary models. Within the context of the model, evolutionary scenarios are examined, and found to be sensitive to the growth rate. It is determined that the present environment is slightly unstable to catastrophic growth, and that the number of particles on orbit will continue to increase until approximately 2250-2350 AD, with a maximum of 2,000,000. The model is expandable to the more realistic (complex) case of multiple species in a multiple-tier system.

Talent, David L.↗

Centralized, decentralized, and independent control of a flexible manipulator on a flexible base

The dynamics and control of a flexible manipulator arm with payload mass on a flexible base in space are considered. The controllers are provided by one torquer at the center of the base and one torquer at the connection joint of the robot and the base. The nonlinear dynamics of the system is modeled by applying the finite element method and Lagrangian formula. Three control strategies are considered and compared, i.e., centralized control, decentralized control, and independent control. All these control designs are based on the linear quadratic regulator theory. A mathematical decomposition is used in the decentralization process so that the coupling between the subsystems is weak, while a physical decomposition is used in the independent control design process. For both the decentralized and the independent controls, the stability of the overall linear system is checked before a numerical simulations is initiated. Two numerical examples show that the response of the independent control system are close to those of the centralized control system, while the responses of the decentralized control system are not.

Li, Feiyue↗

The influence of bulges on boundary-layer instability

Local disturbances caused by a spanwise surface corrugation affect the position of the boundary-layer transition, and so the drag, of an object. This premature transition from laminar to turbulent flow is often associated with a separation of the laminar boundary-layer from its surface. Also the roughness-induced separation bubble provides an important link between the pressure and velocity fluctuations in the environment and the development of the disturbance in the laminar boundary-layer, i.e., the receptivity problem. To investigate the influence of a laminar separation bubble on boundary-layer instability, a separated flow generated by a velocity gradient over a flat plate was analyzed by direct numerical simulation using finite-difference solutions of the Navier-Stokes equations. The bubble acts as a strong amplifier of the instability waves and a highly nonlinear flow field is shown to develop downstream of the bubble. Consequently, the results of the direct numerical simulation differ noticeably from those of the classical linear stability theory proving the fact that the nonparallel effects together with the nonlinear interactions are crucial to this flow development. In the present paper, the effect of physical perturbations such as humps and hollows on boundary-layer instability is analyzed. This problem has been considered theoretically by several researchers (e.g., Nayfeh et al., 1987 and 1990; Cebeci et al., 1988). They used linear stability theory in their approach which does not include the nonparallel nor the nonlinear effects. Therefore, to account for these important effects in studying flow over humps and hollows the direct simulation technique is being implemented in generalized coordinates.

Elli, S.↗

On the structure of cellular solutions in Rayleigh-Benard-Marangoni flows in small-aspect-ratio containers

Multiple steady flow patterns occur in surface-tension/buoyancy-driven convection in a liquid layer heated from below (Rayleigh-Benard-Marangoni flows). Techniques of numerical bifurcation theory are used to study the multiplicity and stability of two-dimensional steady flow patterns (rolls) in rectangular small-aspect-ratio containers as the aspect ratio is varied. For pure Marangoni flows at moderate Biot and Prandtl number, the transitions occurring when paths of codimension 1 singularities intersect determine to a large extent the multiplicity of stable patterns. These transitions also lead, for example, to Hopf bifurcations and stable periodic flows for a small range in aspect ratio. The influence of the type of lateral walls on the multiplicity of steady states is considered. 'No-slip' lateral walls lead to hysteresis effects and typically restrict the number of stable flow patterns (with respect to 'slippery' sidewalls) through the occurrence of saddle node bifurcations. In this way 'no-slip' sidewalls induce a selection of certain patterns, which typically have the largest Nusselt number, through secondary bifurcation.

Dijkstra, Henk A.↗

Viscous and inviscid instabilities of a trailing vortex

The linear stability of the trailing line vortex model of Batchelor (1964) is studied using a spectral collocation and matrix eigenvalue method. The entire unstable region in the swirl/axial wavenumber parameter space is mapped out for various azimuthal wavenumbers for both the inviscid and viscous stability problem. The results of the study provide a direct numerical validation of the large-azimuthal-wavenumber asymptotic analysis of Leibovich and Stewartson (1983). It is shown that accurate results are obtained up to azimuthal wavenumbers of 10,000 and greater, and the agreement with the asymptotic theory is excellent.

Mayer, Ernst W.↗

Comparison of Graphite Fabric Reinforced PMR-15 and Avimid N Composites After Long Term Isothermal Aging at Various Temperatures

Extensive effort is currently being expended to demonstrate the feasibility of using high-performance, polymer-matrix composites as engine structural materials over the expected operating lifetime of the aircraft, which can extend from 18,000 to 30,000 hr. The goal is to develop light-weight, high-strength, and high-modulus materials for use in higher temperature sections of advanced 21 st century aircraft propulsion systems. To accomplish this goal, it is necessary to pursue the development of thermal and mechanical durability models for graphite-fiber-reinforced, polymer-matrix composites. Numerous investigations have been reported regarding the thermo-oxidative stability (TOS) of the polyimide PMR-15 (1-5). A significant amount of this work has been directed at edge and geometry effects, reinforcement fiber influences, and empirical modeling of high-temperature weight loss behavior. It is yet to be determined if the information obtained from the PMR-15 composite tests is applicable to other polyimide-matrix composites. The condensation-curing polymer Avimid N is another advanced composite material often considered for structural applications at high temperatures. Avimid N has better thermo-oxidative stability than PMR-15 (6), but the latter is more easily processed. The most comprehensive study of the thermo-oxidative stability of Avimid N neat resin and composites at 371 (infinity)C is found in Salin and Seferis (7). The purposes of the work described herein were to compare the thermal aging behavior of these two matrix polymers and to determine the reasons for and the consequences of the difference in thermal durability. These results might be of some use in improving future polymer development through the incorporation of the desirable characteristics of both polyimides.

Bowles, Kenneth J.↗

Studies of Premixed Laminar and Turbulent Flames at Microgravity

Several topics relating to combustion limits in premixed flames at reduced gravity have been studied. These topics include: (1) flame balls; (2) numerical simulation of flame ball and planar flame structure and stability; (3) experimental simulation of buoyancy effects in premixed flames using aqueous autocatalytic reactions; and (4) premixed flame propagation in Hele-Shaw cells.

Abid, M.↗