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Results for “Linear stability analysis”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Linear Stability of Binary Alloy Solidification for Unsteady Growth Rates

An extension of the Mullins and Sekerka (MS) linear stability analysis to the unsteady growth rate case is considered for dilute binary alloys. In particular, the stability of the planar interface during the initial solidification transient is studied in detail numerically. The rapid solidification case, when the system is traversing through the unstable region defined by the MS criterion, has also been treated. It has been observed that the onset of instability is quite accurately defined by the "quasi-stationary MS criterion", when the growth rate and other process parameters are taken as constants at a particular time of the growth process. A singular behavior of the governing equations for the perturbed quantities at the constitutional supercooling demarcation line has been observed. However, when the solidification process, during its transient, crosses this demarcation line, a planar interface is stable according to the linear analysis performed.

Mazuruk, K.↗
NASA NTRS2004

Buoyancy Effects on Flow Structure and Instability of Low-Density Gas Jets

A low-density gas jet injected into a high-density ambient gas is known to exhibit self-excited global oscillations accompanied by large vortical structures interacting with the flow field. The primary objective of the proposed research is to study buoyancy effects on the origin and nature of the flow instability and structure in the near-field of low-density gas jets. Quantitative rainbow schlieren deflectometry, Computational fluid dynamics (CFD) and Linear stability analysis were the techniques employed to scale the buoyancy effects. The formation and evolution of vortices and scalar structure of the flow field are investigated in buoyant helium jets discharged from a vertical tube into quiescent air. Oscillations at identical frequency were observed throughout the flow field. The evolving flow structure is described by helium mole percentage contours during an oscillation cycle. Instantaneous, mean, and RMS concentration profiles are presented to describe interactions of the vortex with the jet flow. Oscillations in a narrow wake region near the jet exit are shown to spread through the jet core near the downstream location of the vortex formation. The effects of jet Richardson number on characteristics of vortex and flow field are investigated and discussed. The laminar, axisymmetric, unsteady jet flow of helium injected into air was simulated using CFD. Global oscillations were observed in the flow field. The computed oscillation frequency agreed qualitatively with the experimentally measured frequency. Contours of helium concentration, vorticity and velocity provided information about the evolution and propagation of vortices in the oscillating flow field. Buoyancy effects on the instability mode were evaluated by rainbow schlieren flow visualization and concentration measurements in the near-field of self-excited helium jets undergoing gravitational change in the microgravity environment of 2.2s drop tower at NASA John H. Glenn Research Center. The jet Reynolds number was varied from 200 to 1500 and jet Richardson number was varied from 0.72 to 0.002. Power spectra plots generated from Fast Fourier Transform (FFT) analysis of angular deflection data acquired at a temporal resolution of 1000Hz reveal substantial damping of the oscillation amplitude in microgravity at low Richardson numbers (~0.002). Quantitative concentration data in the form of spatial and temporal evolutions of the instability data in Earth gravity and microgravity reveal significant variations in the jet flow structure upon removal of buoyancy forces. Radial variation of the frequency spectra and time traces of helium concentration revealed the importance of gravitational effects in the jet shear layer region. Linear temporal and spatio-temporal stability analyses of a low-density round gas jet injected into a high-density ambient gas were performed by assuming hyper-tan mean velocity and density profiles. The flow was assumed to be non parallel. Viscous and diffusive effects were ignored. The mean flow parameters were represented as the sum of the mean value and a small normal-mode fluctuation. A second order differential equation governing the pressure disturbance amplitude was derived from the basic conservation equations. The effects of the inhomogeneous shear layer and the Froude number (signifying the effects of gravity) on the temporal and spatio-temporal results were delineated. A decrease in the density ratio (ratio of the density of the jet to the density of the ambient gas) resulted in an increase in the temporal amplification rate of the disturbances. The temporal growth rate of the disturbances increased as the Froude number was reduced. The spatio-temporal analysis performed to determine the absolute instability characteristics of the jet yield positive absolute temporal growth rates at all Fr and different axial locations. As buoyancy was removed (Fr . 8), the previously existing absolute instability disappeared at all locations establhing buoyancy as the primary instability mechanism in self-excited low-density jets.

Pasumarthi, Kasyap Sriramachandra↗
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.↗
DOE OSTI2021

Electroconvection near an ion-selective surface with Butler–Volmer kinetics

We study the effects of interfacial kinetics on the electro-hydrodynamics of ion transport near an ion-selective surface using a combination of linear stability analysis and numerical simulation. The finite kinetics of the electrolyte–electrode interface affects the ion transfer and electroconvection in many ways. On a surface of fixed topography, such as a metal surface of slow and stable ion deposition or covered by a polymer membrane, the finite kinetics reduces the current in one-dimensional ion diffusion/migration, increases the critical voltage for the onset of the electroconvective instability, changes the dynamics of the electroconvection and the overlimiting current, and enhances the lateral ion diffusion within the interfacial layer. The first three effects are indirectly caused by the reaction kinetics and can be characterized by an effective voltage difference across the liquid electrolyte. In comparison, the last effect is controlled by a direct interplay between kinetics and nonlinear electroconvection. Scaling laws for ion transport and features of electroconvection are proposed. We also analyse the linear stability of a surface which evolves under ion deposition and find that the finite kinetics decreases the growth rate of both electroconvective and morphological instabilities and therefore modifies the wavenumber of the most unstable mode.

Mechanics↗
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.↗
DOE OSTI2022

Microstructural pattern formation during liquid metal dealloying: Phase-field simulations and theoretical analyses

In recent years, liquid metal dealloying has emerged as a promising material processing method to generate micro- and nanoscale bicontinuous or porous structures. Most previous studies focused on the experimental characterization of the dealloying process and on the properties of the dealloyed materials, leaving the theoretical study incomplete to fully understand the fundamental mechanisms of the liquid metal dealloying process. In this paper, we use theoretical models and phase-field simulations to clarify the kinetics and pattern formation during liquid metal dealloying. Our investigation starts from a theoretical analysis of the 1D dissolution of a binary precursor alloy, which reveals that the 1D dissolution process involves two regimes. In the first regime, due to the low solubility of one of the elements in the melt, it accumulates at the solid-liquid interface, which reduces the dissolution kinetics. In the second regime, the interface kinetics reaches a stationary regime where both elements of the precursor alloy dissolve into the melt. Previous works revealed that in the early dealloying stage, the dealloying front is destabilized by an interfacial spinodal decomposition, which triggers the formation of interconnected ligaments. Here we extend this line of work by proposing a linear stability analysis able to predict the initial length scale of the ligaments formed in the initial stage of the dealloying. Combining this analysis with the 1D dissolution model proposed here enables us to better understand the initial conditions (composition of the precursor alloy and the melt) leading to a planar dissolution without interface destabilization. Finally, we report a strong influence of solid-state diffusion on dealloying. Although the solid-state diffusivity is four to five orders of magnitude smaller than in the liquid phase, it is found to affect both dissolution kinetics and ligament morphologies.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Impact of equilibrium radial electric field on energy loss process after pedestal collapse

An impact of the equilibrium radial electric field on energy loss processes after pedestal collapse is numerically investigated using the BOUT++ framework. Using linear stability analysis, the resistive ballooning mode is shown to be stabilized by the radial shear of the equilibrium radial electric field. On the other hand, the energy loss level after the pedestal collapse increases if the equilibrium radial electric field is taken into account. The spatio-temporal and phase diagram analyses show that the equilibrium radial electric field partially cancels the fluctuation-driven toroidally axisymmetric radial electric field and weakens the E × B shearing rate after pedestal collapse, weakening the turbulence suppression by vortex shearing. Finally, the equilibrium radial electric field therefore increases turbulence intensity in nonlinear cyclic oscillations among pressure gradient, E × B shearing rate, and turbulence intensity, which gives rise to subsequent bursts of turbulent transport and increases the energy loss level.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

IMEX Runge-Kutta Parareal for Non-diffusive Equations

Parareal is a widely studied parallel-in-time method that can achieve meaningful speedup on certain problems. However, it is well known that the method typically performs poorly on non-diffusive equations. This paper analyzes linear stability and convergence for IMEX Runge-Kutta Parareal methods on non-diffusive equations. By combining standard linear stability analysis with a simple convergence analysis, we find that certain Parareal configurations can achieve parallel speedup on non-diffusive equations. These stable configurations all posses low iteration counts, large block sizes, and a large number of processors. Numerical examples using the nonlinear Schrodinger equation demonstrate the analytical conclusions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Migration of inclusions in a matrix due to a spatially varying interface energy

An interfacial energy can be a function of a bulk field such as temperature or electric field. Here we find that in a system with a gradient in temperature or electric potential, the resulting variation in interfacial energy can induce a particle to migrate by either surface or bulk diffusion. For a circular particle under a constant unidirectional gradient in the bulk field, the field dependence of the interfacial energy induces a circular particle to move as a circle at a constant velocity along the direction from higher to lower interfacial energy. A linear stability analysis of this steady state migration suggests that perturbations will damp out as time evolves, and thus under these conditions a migrating circular particle is morphologically stable. Other spatial distributions of interface energy can lead to the distortion of an initially circular shaped particle during migration. A phase field model is developed that captures these distortions and verifies the theoretical results mentioned above.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Destabilization of binary mixing layer in supercritical conditions

Compressible mixing layer instabilities are of importance to a wide range of environmental and industrial applications. Past studies have focused on either ideal-gas or real-fluid thermodynamic regimes of single-species mixing layers. However, mixing layers of binary mixtures at supercritical conditions, commonly encountered in fuel injection systems, introduce additional complexities due to the added compositional degree-of-freedom. Moreover, the effect of strong variations in thermodynamic response functions across the Widom line on the binary mixing layer stability remains poorly understood. Thus, the objective of this study is to examine the coupling between the hydrodynamic instability and the real-fluid thermodynamics across the Widom line and its effects on the overall binary mixing layer dynamics. To this end, we develop a linear stability analysis of the full binary-species compressible transport equations coupled with the PC-SAFT equation of state. Analysis shows the existence of a novel instability mechanism that arises from juxtapositioning of the Widom-line transition and the hydrodynamic inflection point. This novel thermodynamically induced instability mechanism has the net effect of destabilizing the binary mixing layer at lowering supercritical conditions towards the critical pressure point. This is in contrast to previous stability analyses of supercritical single-species mixing layers, where increasing pressure destabilizes the flow due to its effect on reducing the density stratification. The discovered thermodynamically induced instability mechanism of binary mixing flows highlights the need for an extension of classical instability criteria to incorporate the effect of strong variations in the thermodynamic response functions across the Widom line on mixing layer instability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Simulating ice-shelf extent using damage mechanics

Abstract Inaccurate representations of iceberg calving from ice shelves are a large source of uncertainty in mass-loss projections from the Antarctic ice sheet. Here, we address this limitation by implementing and testing a continuum damage-mechanics model in a continental scale ice-sheet model. The damage-mechanics formulation, based on a linear stability analysis and subsequent long-wavelength approximation of crevasses that evolve in a viscous medium, links damage evolution to climate forcing and the large-scale stresses within an ice shelf. We incorporate this model into the BISICLES ice-sheet model and test it by applying it to idealized (1) ice tongues, for which we present analytical solutions and (2) buttressed ice-shelf geometries. Our simulations show that the model reproduces the large disparity in lengths of ice shelves with geometries and melt rates broadly similar to those of four Antarctic ice shelves: Erebus Glacier Tongue (length ~ 13 km), the unembayed portion of Drygalski Ice Tongue (~ 65 km), the Amery Ice Shelf (~ 350 km) and the Ross Ice Shelf (~ 500 km). These results demonstrate that our simple continuum model holds promise for constraining realistic ice-shelf extents in large-scale ice-sheet models in a computationally tractable manner.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Multimode theory of electron hole transverse instability

We present Vlasov–Poisson three-dimensional linear stability analysis of an initially planar electron hole structure, solving for the distribution function by integration along unperturbed orbits. The non-sinusoidal potential perturbation shape (parallel to $B$ ) is expanded in eigenfunctions of the adiabatic Poisson operator, generalizing the prior assumption of a rigid shift of the equilibrium. We show that the shiftmode is then modified by a second discrete mode plus an integral over a continuum of wave-like modes. A rigorous treatment shows that the continuum can be approximated effectively by a single mode that satisfies the external wave dispersion relation, thus making the perturbation a weighted sum of three modes. We find numerically the solution for the complex instability frequency, and the corresponding three mode amplitudes determining the perturbation eigenmode. This multimode analysis refines the accuracy of the prior single-mode results, giving slightly higher growth rates at most parameters, as expected from the extra mode shape freedom. Oscillating modes near stability boundaries have larger mode distortions which help explain particle-in-cell simulations that observe instability up to ${\sim }20$ % beyond the prior shiftmode thresholds, and narrowing of the perturbation. At high magnetic field, the multimode analysis predicts a reduction of the already small growth rate.

Physics↗
DOE OSTI2021

Simultaneous Decomposition and Dewetting of Nanoscale Alloys: A Comparison of Experiment and Theory

In this work, we consider the coupled process of phase separation and dewetting of metal alloys of nanoscale thickness deposited on solid substrates. The experiments involve applying nanosecond laser pulses that melt the Ag40Ni60 alloy films in two setups: either on thin supporting membranes or on bulk substrates. These two setups allow for extracting both temporal and spatial scales on which the considered processes occur. The theoretical model involves a longwave version of the Cahn–Hilliard formulation used to describe spinodal decomposition, coupled with an asymptotically consistent longwave-based description of dewetting that occurs due to destabilizing interactions between the alloy and the substrate, modeled using the disjoining pressure approach. Careful modeling, combined with linear stability analysis and fully nonlinear simulations, leads to results consistent with the experiments. In particular, we find that the two instability mechanisms occur concurrently, with the phase separation occurring faster and on shorter temporal scales. The modeling results show a strong influence of the temperature dependence of relevant material properties, implying that such a dependence is crucial for the understanding of the experimental findings. The agreement between theory and experiment suggests the utility of the proposed theoretical approach in helping to develop further experiments directed toward formation of metallic alloy nanoparticles of desired properties.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Velocity Dependence of Rate‐And‐State Friction in Granular Fault Gouge and Implications for Slow‐Slip Events

Abstract The standard rate‐and‐state friction (RSF) has extensively captured frictional behaviors, but it fails to explain the velocity dependence of frictional stability transition and widespread slow‐slip events (SSEs) in experiments and nature adequately. An alternative microphysical Chen‐Niemeijer‐Spiers (CNS) model can well describe the velocity dependence of frictional behaviors of granular gouges. Using the original CNS model, standard RSF parameters can be quantified microphysically. However, some micro‐parameters are not easy to estimate quantitatively, making it difficult to extrapolate to natural and experimental conditions. Here, we simplify the microphysically‐derived RSF parameters including direct effect a , evolution effect b , and critical slip distance D c , as well as equivalent values ( a eq , b eq , and D eq ). The simplified friction parameters directly illustrate their velocity dependence, namely the essentially constant a , a eq , and D c , negatively velocity‐dependent b and b eq , as well as varying D eq for different laws. They are roughly consistent with experimental results in various fault gouges. A modified CNS model is further derived from the original CNS model, establishing a direct link between the standard RSF and CNS models. The modified CNS model exhibits virtually identical frictional behaviors to the original CNS, but differs from the standard RSF at large velocity perturbations. Moreover, the linearized stability analysis indicates that the critical stiffness for the modified CNS model is velocity‐dependent. Compared with the standard RSF, the modified CNS model not only explains the velocity dependence of frictional stability transition, but also exhibits a more gradual transition for SSEs with a broader range of stiffness ratios.

Geochemistry & Geophysics↗
DOE OSTI2022

Droplet formation simulation using mixed finite elements

Droplet formation happens in finite time due to the surface tension force. The linear stability analysis is useful to estimate the size of a droplet but fails to approximate the shape of the droplet. This is due to a highly nonlinear flow description near the point where the first pinch-off happens. A one-dimensional axisymmetric mathematical model was first developed by Eggers and Dupont [“Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] using asymptotic analysis. This asymptotic approach to the Navier–Stokes equations leads to a universal scaling explaining the self-similar nature of the solution. Numerical models for the one-dimensional model were developed using the finite difference [Eggers and Dupont, “Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] and finite element method [Ambravaneswaran et al., “Drop formation from a capillary tube: Comparison of one-dimensional and two-dimensional analyses and occurrence of satellite drops,” Phys. Fluids 14, 2606–2621 (2002)]. The focus of this study is to provide a robust computational model for one-dimensional axisymmetric droplet formation using the Portable, Extensible Toolkit for Scientific Computation. The code is verified using the Method of Manufactured Solutions and validated using previous experimental studies done by Zhang and Basaran [“An experimental study of dynamics of drop formation,” Phys. Fluids 7, 1184–1203 (1995)]. The present model is used for simulating pendant drops of water, glycerol, and paraffin wax, with an aspiration of extending the application to simulate more complex pinch-off phenomena.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

3D pattern formation of a protein–membrane suspension

Many essential cellular processes, including cell division and the establishment of cell polarity during embryogenesis, are regulated by pattern-forming proteins. These proteins often need to bind to a substrate, such as the cell membrane, onto which they interact and form two-dimensional (2D) patterns. It is unclear how the membrane’s continuity and dimensionality impact pattern formation. Here, we address this gap using the MinDE system, a prototypical example of pattern-forming membrane proteins. We show that when the lipid substrate is fragmented into submicrometer-sized diffusive liposomes, adenosine triphosphate-driven protein–protein interactions generate three-dimensional (3D) spatially extended patterns, despite the complete loss of membrane continuity. Remarkably, these 3D patterns emerge at scales four orders of magnitude larger than the individual liposomes. By systematically varying protein concentration, liposome size, and density, we observed and characterized a variety of 3D dynamical patterns not seen on continuous 2D membranes, including traveling waves, dynamical spirals, and a coexistence phase. Simulations and linear stability analysis of a coarse-grained model revealed that the physical properties of the dispersed membrane effectively rescale both the protein–membrane binding rates and diffusion, two key parameters governing pattern formation and wavelength selection. These findings highlight the robustness of Min’s pattern-forming ability, suggesting that protein–membrane suspensions could serve as an adaptable template for studying out-of-equilibrium self-organization in 3D, beyond in vivo contexts.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Logarithmic potential with super-super-exponential kink profiles and tails

In this work, we consider a novel one dimensional model of a logarithmic potential which has super-super-exponential kink profiles as well as kink tails. We provide analytic kink solutions of the model—it has 3 kinks, 3 mirror kinks and the corresponding antikinks. While some of the kink tails are super-super-exponential, some others are super-exponential whereas the remaining ones are exponential. The linear stability analysis reveals that there is a gap between the zero mode and the onset of continuum. Finally, we compare this potential and its kink solutions with those of very high order field theories harboring seven degenerate minima and their attendant kink solutions, specifically φ 14 , φ 16 and φ 18 .

97 MATHEMATICS AND COMPUTING↗