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At least 37 records · Page 2

Protostellar rotation - Turbulence and heating of molecular clouds

The formation of rapidly rotating protostellar objects in turbulent and clumpy molecular clouds is analyzed. It is shown that the early dissipation of the protostellar rotational energy via a rotationally driven wind can keep their parent molecular clouds at the observed temperatures and in the observed turbulent state. The model requires a low space density of protostellar shells in order to provide the energy requirements to stabilize molecular clouds against gravitational collapse in regions of star formation. The dependence of this mechanism on the star formation rate suggests that the star formation is self-regulated.

Franco, J.↗

A numerical simulation of barotropic instability. I Wave-mean flow interaction

A numerical model is used to study the evolution of the barotropic point jet instability as it interacts with the mean flow. The linearized instability solution agrees well with the recent analytical solutions of Lindzen. Stabilization of the point jet instability occurs as the mean flow is modified by wave vorticity transport. Assuming stabilization occurs when the meridional gradient of the zonal mean vorticity is no longer negative, the maximum integrated wave enstrophy can be predicted. In addition, an estimate of the integrated wave enstrophy at steady state can be made by balancing the generation of vorticity against dissipation. These limits are found to be in good agreement with the numerical results.

Schoeberl, M. R.↗

The effects of oppositely sloping boundaries with Ekman dissipation in a nonlinear baroclinic system

The present analytical and numerical examination of the effect of the slope Delta with dissipation delta on baroclinic flows in linear and nonlinear systems uses a modified Eady channel model with oppositely sloping top and bottom Ekman layers, and truncates the spectral wave solution up to six components. Comparisons are made wherever possible with results from beta-plane dissipative systems. In the linear system, the combined effect of Delta and delta strongly stabilizes long waves. In a nonlinear system without wave-wave interaction, Delta stabilizes the flow even for small delta and reduces the domain of vacillation while enlarging the domain of single-wave steady state.

Weng, H.-Y.↗

Convergence Acceleration of the Navier-Stokes Equations Through Time-Derivative Preconditioning

Chorin's method of artificial compressibility is extended to both compressible and incompressible fluids by using physical arguments to define artificial fluid properties that make up a local preconditioning matrix. In particular, perturbation expansions are used to provide appropriate temporal derivatives for the equations of motion at both low speeds and low Reynolds numbers. These limiting forms are then combined into a single function that smoothly merges into the physical time derivatives at high speeds so that the equations are left unchanged at transonic, high Reynolds number conditions. The effectiveness of the resulting preconditioning procedures for the Navier-Stokes equations is demonstrated for a wide speed and Reynolds number ranges by means of stability results and computational solutions. Nevertheless, the preconditioned equations sometimes fail to provide a solution for applications for which the non-preconditioned equations converge. Often this is because the reduced dissipation in the preconditioned equations results in an unsteady solution while the more dissipative non-preconditioned equations result in a steady state. Problems of this type represent a computational challenge; it is important to distinguish between non-convergence of algorithms, and the non-existence of steady state solutions.

Merkle, Charles L.↗

Modeling Whitecaps on Global Scale

Whitecaps play an important role in the surface-atmosphere interactions across the ocean. They are directly linked to the energy dissipation rate during wave breaking and transfer of heat, momentum, and gas/aerosol exchange from the wind to the sea surface. Although the first models of W were dependent only on wind speeds, a large number of diverse models based on wind and sea state which include wave height, wave age, friction velocity, and stability effects have been proposed since then. However, it is recognized that most of the proposed W models have strong systematic (e.g., zonal bias) and random errors when compared against observations. This is partly due to the differences in environmental conditions, measurement techniques, and geographical locations among these studies. But, some of these biases are linked to the inability of the proposed models to capture the variability in W in certain wind/wave regimes. Despite the knowledge of existing biases, W residual relationships from the models with wind and wave fields remain highly uncertain, with residual trends varying between the published studies. Here, we take advantage of the availability of relatively dense observations of W from WindSat microwave satellite retrievals in combination with the University of Miami wave model which was recently incorporated within the NASA GMAO/GEOS system (GEOS-UMWM). We use Windsat W retrievals to assess and constrain the previously published W models and understand the relationships of residuals from models in different wind/wave regimes. We link these unexplained residual variations to additional factors such as swell index, drag coefficient etc and add information to the existing whitecap models. Since Windsat retrievals cover wide range of environmental conditions, it helps to reduce the uncertainties associated with differences in measurement techniques. Regression of wind-wave fields against all Windsat data points (CTL) results in larger residuals for lower wave age and W is overestimated upto ~4% for wave age < 10 and underestimated by upto ~2% as wave age increases. We attest to this bias by considering two approaches. One is to perform regression separately for different stages of wave development such as developing sea, fully developed, and wind sea regimes thereby understanding the sensitivity of regression coefficients to sea state (EXP1). Another is to derive coefficients of W models in EXP1 as a function of additional wind/wave factors such as swell index, drag coefficient, and mean squared slope, deriving more nonlinear W models (EXP2). EXP2 provides reduction in Root Mean Squared Error (RMSE) by 0.1-0.3%. Sea surface drag has a stronger relationship with regression coefficients compared to swell index.These additional factors provide improved parameterizations in different wind and wave age regimes, with smaller unexplained/residual variations in W that has been a major concern in the W community.

Raman, Aishwarya↗

Relaminarization of turbulent flow on a flat plate by localized surface heating

Relaminarization of a turbulent boundary layer in air on a flat plate is demonstrated experimentally using localized surface heating. Localized heating is achieved by electrically heating a wire embedded in a thermally insulated substrate (Space Shuttle Tile) on the surface. The stability of the flow downstream of the applied control point increases with decreasing stream temperature in the flow direction. The mean and perturbation velocity profiles without control show that the flow is turbulent. With control, these profiles sequentially change from intermittently turbulent to a fully laminar state. In the relaminarization stage, the turbulent energy is dissipated by molecular transport due to viscous and conductivity mechanisms. The new profile adjusts to a lower Reynolds number based on the momentum thickness than that of the previous turbulent state.

Maestrello, Lucio↗

On the Stability Analysis of Astrophysical Cooling Functions

To model the temperature evolution of optically thin astrophysical environments at MHD scales, radiative and collisional cooling rates are typically either pretabulated or fit into a functional form and then input into MHD codes as a radiative loss function. Thermal balance requires estimates of the analogous heating rates, which are harder to calculate, and due to uncertainties in the underlying dissipative heating processes these rates are often simply parameterized. The resulting net cooling function defines an equilibrium curve that varies with density and temperature. Such cooling functions can make the gas prone to thermal instability (TI), which will cause departures from equilibrium. There has been no systematic study of thermally unstable parameter space for nonequilibrium states. Motivated by our recent finding that there is a related linear instability, catastrophic cooling instability, that can dominate over TI, here we carry out such a study. We show that Balbus instability criteria for TI can be used to define a critical cooling rate, Λc, that permits a nonequilibrium analysis of cooling functions through the mapping of TI zones. We furthermore illustrate how thermal conduction modifies the shape of TI zones. Upon applying a Λc-based stability analysis to coronal loop simulations, we find that loops undergoing periodic episodes of coronal rain formation are linearly unstable to catastrophic cooling instability, while TI is stabilized by thermal conduction.

Amanda Stricklan↗

Transport processes in the upper atmosphere

Studies of transport mechanisms in the upper atmosphere (diffusion, turbulence, large-scale circulation) are reviewed. A normally turbulent state of the lower thermosphere is inferred from direct observations of tracers and from thermal and composition structure. Viscous dissipation in the thermosphere and energy dissipation in turbulence working against buoyancy are discussed in relation to a critical Richardson number for initiation of turbulence (0.25, as in the stratosphere). But the usefulness of the Richardson criterion is limited when static stability is low, as is the case when strong shear-generated turbulence prevails.

Johnson, F. S.↗

Dissipative compensators for flexible spacecraft control

The problem of controller design for flexible spacecraft is addressed. Model-based compensators, which rely on the knowledge of the system parameters to tune the state estimator, are considered. The instability mechanisms resulting from high sensitivity to parameter uncertainties are investigated. Dissipative controllers, which use collocated actuators and sensors, are also considered, and the robustness properties of constant-gain dissipative controllers in the presence of unmodeled elastic-mode dynamics, sensor/actuator nonlinearities, and actuator dynamics are summarized. In order to improve the performance without sacrificing robustness, a class of dissipative dynamic compensators is proposed and is shown to retain robust stability in the presence of second-order actuator dynamics if acceleration feedback is employed. A class of dissipative dynamic controllers is proposed which consists of a low-authority, constant-gain controller and a high-authority dynamic compensator. A procedure for designing an optimal dissipative dynamic compensator is given which minimizes a quadratic performance criterion. Such compensators offer the promise of better performance while still retaining robust stability.

Joshi, S. M.↗

Internal Dynamics and Crustal Evolution of Mars

The objective of this work is to improve understanding of the internal structure, crustal evolution, and thermal history of Mars by combining geophysical data analysis of topography, gravity and magnetics with results from analytical and computational modeling. Accomplishments thus far in this investigation include: (1) development of a new crustal thickness model that incorporates constraints from Mars meteorites, corrections for polar cap masses and other surface loads, Pratt isostasy, and core flattening; (2) determination of a refined estimate of crustal thickness of Mars from geoid/topography ratios (GTRs); (3) derivation of a preliminary estimate of the k(sub 2) gravitational Love number and a preliminary estimate of possible dissipation within Mars consistent with this value; and (4) an integrative analysis of the sequence of evolution of early Mars. During the remainder of this investigation we will: (1) extend models of degree-1 mantle convection from 2-D to 3-D; (2) investigate potential causal relationships and effects of major impacts on mantle plume formation, with primary application to Mars; (3) develop exploratory models to assess the convective stability of various Martian core states as relevant to the history of dynamo action; and (4) develop models of long-wavelength relaxation of crustal thickness anomalies to potentially explain the degree-1 structure of the Martian crust.

Zuber, Maria↗

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

Improved algorithms for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration shceme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. The paper presents a description of the Euler solvers along with results and comparisons which assess the capability.

Batina, John T.↗

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

Improved algorithm for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. A description of the Euler solvers is presented along with results and comparisons which assess the capability.

Batina, John T.↗

Algorithm For Hypersonic Flow In Chemical Equilibrium

Implicit, finite-difference, shock-capturing algorithm calculates inviscid, hypersonic flows in chemical equilibrium. Implicit formulation chosen because overcomes limitation on mathematical stability encountered in explicit formulations. For dynamical portion of problem, Euler equations written in conservation-law form in Cartesian coordinate system for two-dimensional or axisymmetric flow. For chemical portion of problem, equilibrium state of gas at each point in computational grid determined by minimizing local Gibbs free energy, subject to local conservation of molecules, atoms, ions, and total enthalpy. Major advantage: resulting algorithm naturally stable and captures strong shocks without help of artificial-dissipation terms to damp out spurious numerical oscillations.

Palmer, Grant↗

A detailed study of mean-flow solutions for stability analysis of transitional flows

A finite-volume upwind-difference parabolized Navier-Stokes code is utilized to obtain laminar mean-flow solutions at Mach 3.5 on a half-angle cone of 5 deg at an angle-of-attack of 2 deg. A detailed study is conducted on this configuration; the main focus is the velocity profiles in the leeward and windward symmetry planes at various axial locations. Comparisons of the solution profiles are made with both a central-difference code that incorporates scalar and matrix dissipation models and another state-of-the-art upwind-difference finitevolume code. The results obtained emphasize the importance of using matrix dissipation models for schemes that require explicit artificial dissipation. These results also illustrate the accuracy and efficiency of the planeby-plane marching procedure for computing mean-flow solutions for predicting the onset of transition with linear instability.

Ramakrishnan, R.↗

Gravitational instability in two-phase disks and the origin of the moon

Two-phase disks may be gravitationally unstable at temperatures or surface densities at which a disk composed of either single phase would be highly stable. It is argued that two-phase disks can achieve a marginally unstable state (in addition to a highly unstable state that leads to fragmentation), limited by the ability of the photosphere to radiate the energy dissipated in the disk. A self-consistent prescription for the viscosity induced by the slow instabilities is provided. Two-phase disks are more centrally condensed than single-phase disks, and their secular cooling time may be comparable to their spreading time. A circumterrestrial disk of sufficient mass to form the moon provides a detailed example of all the preceding points. Its stability, structure, and dynamical evolution are investigated, and it is concluded that its spreading time is short (about 100 yr); the moon is formed molten, or partially molten; the moon's initial orbit lies in the earth's equatorial plane; and only a small fraction of the disk mass is lost in a wind, although this may represent a substantial fraction of volatiles. Most of these conclusions are independent of how the disk was formed, e.g., from a giant impact.

Thompson, Christopher↗

Solid Rocket Motor Combustion Instability Modeling in COMSOL Multiphysics

Combustion instability modeling of Solid Rocket Motors (SRM) remains a topic of active research. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process, acoustics, and steady-state gas dynamics. Recent advances in defining the energy transport of disturbances within steady flow-fields have been applied by combustion stability modelers to improve the analysis framework [1, 2, 3]. Employing this more accurate global energy balance requires a higher fidelity model of the SRM flow-field and acoustic mode shapes. The current industry standard analysis tool utilizes a one dimensional analysis of the time dependent fluid dynamics along with a quasi-three dimensional propellant grain regression model to determine the SRM ballistics. The code then couples with another application that calculates the eigenvalues of the one dimensional homogenous wave equation. The mean flow parameters and acoustic normal modes are coupled to evaluate the stability theory developed and popularized by Culick [4, 5]. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The current study employs the COMSOL multiphysics finite element framework to model the steady flow-field parameters and acoustic normal modes of a generic SRM. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluates the gas flow inside of a SRM using St. Robert's law to model the solid propellant burn rate, no slip boundary conditions, and the hybrid outflow condition. Results from the HMNF model are verified by comparing the pertinent ballistics parameters with the industry standard code outputs (i.e. pressure drop, thrust, ect.). These results are then used by the coefficient form of the mathematics module to determine the complex eigenvalues of the Acoustic Velocity Potential Equation (AVPE). The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. The results of the steady-state CFD and AVPE analyses are used to calculate the linear acoustic growth rate as is defined by Flandro and Jacob [2, 3]. In order to verify the process implemented within COMSOL we first employ the Culick theory and compare the results with the industry standard. After the process is verified, the Flandro/Jacob energy balance theory is employed and results displayed.

Fischbach, Sean R.↗

Modeling and control of flexible space platforms with articulated payloads

The first steps in developing a methodology for spacecraft control-structure interaction (CSI) optimization are identification and classification of anticipated missions, and the development of tractable mathematical models in each mission class. A mathematical model of a generic large flexible space platform (LFSP) with multiple independently pointed rigid payloads is considered. The objective is not to develop a general purpose numerical simulation, but rather to develop an analytically tractable mathematical model of such composite systems. The equations of motion for a single payload case are derived, and are linearized about zero steady-state. The resulting model is then extended to include multiple rigid payloads, yielding the desired analytical form. The mathematical models developed clearly show the internal inertial/elastic couplings, and are therefore suitable for analytical and numerical studies. A simple decentralized control law is proposed for fine pointing the payloads and LFSP attitude control, and simulation results are presented for an example problem. The decentralized controller is shown to be adequate for the example problem chosen, but does not, in general, guarantee stability. A centralized dissipative controller is then proposed, requiring a symmetric form of the composite system equations. Such a controller guarantees robust closed loop stability despite unmodeled elastic dynamics and parameter uncertainties.

Graves, Philip C.↗

Multi-Agent Control Approach to the Stability of Linear Deployable Systems

Collisions and undesired dynamic responses may occur during the expansion phase of deployable elements on a spacecraft. This problem is more pronounced in large and complex deployable elements where characterization of transient dynamics using testing and simulation can be challenging. This paper introduces a multi-agent control theory approach to address the problem of collisions and transient behavior in deployable lattice systems. We introduce the graph theoretic and relative error vector-based state-space structures to represent the geometry of a lattice-based deploy system. We show that under the assumption of almost-strict dissipativity, the closed-loop feedback gains of the relative error dynamics are the spring and damper constants in the structure. Moreover, we introduce the control perspective of shaping transient dynamics using eigenstructure assignment and balanced coordinate transformation.

Pablos, Juan L. de↗