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Linear Stability Analysis (linear + stability_analysis)

Distribution by Scientific Domains
Engineering42%

Selected Abstracts

Linear stability analysis of flow in a periodically grooved channel

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2003
T. Adachi1
Abstract We have conducted the linear stability analysis of flow in a channel with periodically grooved parts by using the spectral element method. The channel is composed of parallel plates with rectangular grooves on one side in a streamwise direction. The flow field is assumed to be two-dimensional and fully developed. At a relatively small Reynolds number, the flow is in a steady-state, whereas a self-sustained oscillatory flow occurs at a critical Reynolds number as a result of Hopf bifurcation due to an oscillatory instability mode. In order to evaluate the critical Reynolds number, the linear stability theory is applied to the complex laminar flow in the periodically grooved channel by constituting the generalized eigenvalue problem of matrix form using a penalty-function method. The critical Reynolds number can be determined by the sign of a linear growth rate of the eigenvalues. It is found that the bifurcation occurs due to the oscillatory instability mode which has a period two times as long as the channel period. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Linear stability analysis of two-layer rectilinear flow in slot coating

AICHE JOURNAL, Issue 10 2010
Jaewook Nam
Abstract Two-layer coating occurs in many products. Ideally, the liquids are deposited onto the substrate simultaneously. In the case of two-layer slot coating, the interlayer between the coating liquids is subjected to enormous shearing. This may lead to flow instabilities that ruin the product. It is important to map the regions of the parameter space at which the flow is unstable. Most of the stability analyses of two-layer rectilinear flow consider the position of the interlayer as an independent parameter. Classical results cannot be applied directly in coating flows. We present a linear stability analysis of two-layer rectilinear flow considering the flow rates as an independent parameter. The predicted neutral-stability curves define the region of stable flow as a function of the operating parameters. The range of coating operating conditions is restricted further, when the condition for the desirable interlayer separation point location are considered together with the stability condition. © 2010 American Institute of Chemical Engineers AIChE J, 2010 [source]

Linear stability analysis and fourth-order approximations at first time level for the two space dimensional mildly quasi-linear hyperbolic equations

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2001
R. K. Mohanty
Abstract In 1996, Mohanty et al. [1] presented a fourth-order finite difference solution of a two space dimensional nonlinear hyperbolic equation with Dirichlet boundary conditions. In 1998, Mohanty et al. [2] discussed a fourth-order approximation at first time level for the numerical solution of the one space dimensional hyperbolic equation. In both the cases, they have discussed the stability analysis for the linear hyperbolic equation having first-order space derivative terms. Recently, Mohanty et al. [3] have developed fourth-order difference formulas for the three space dimensional quasi-linear hyperbolic equations and obtained fourth-order approximation at first time level. In this article, we extend our strategy for solving the two space dimensional quasi-linear hyperbolic equation. An operator splitting method for a linear hyperbolic equation having a time derivative term is proposed. Linear stability analysis and fourth-order approximation at first time level for the two space dimensional quasi-linear hyperbolic equation are also discussed. The results of the numerical experiments are compared with the exact solution. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 607,618, 2001 [source]

Linear stability analysis of oscillating Ekman boundary layers

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009
Martin Withalm
The analysed Ekman layer is generated in a fluid layer rotating around an axis normal to its two bounding rigid plates. One of the plates is stationary, the other moving at certain Reynolds numbers. An additional oscillation is added to the moving plate at different amplitudes and frequencies. The linear stability of this system is determined via a Floquet analysis and a Galerkin-approximation of the corresponding Navier-Stokes-Equations. If the frequencies of the oscillations are small the critical Reynolds numbers of the Type I and Type II instabilities do not differ much from steady Ekman layers. Also for a purely oscillating system the critical values of the instabilities are almost consistent with those for a steady system. Interestingly, for higher frequencies the Type II instability does not appear any more. Instead the boundary layer becomes unstable only in terms of a Type I instability. In comparison with findings of other authors these results seem to be quite reasonable. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

A nonlinear atomization model for computation of drop size distributions and spray simulations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2005
Hongbok Park
Abstract A model has been developed to provide a comprehensive simulation of a spray formed by a high-speed liquid jet. The primary atomization process is simulated in a completely nonlinear fashion using the boundary element method under the assumption of axisymmetric, inviscid flow. The presence of the orifice boundary layer is simulated with a ring vortex whose strength and location are uniquely determined from boundary layer properties at the orifice exit plane. Droplet and axisymmetric ligament tracking models have been developed to provide more comprehensive spray simulations. The breakup of the axisymmetric ligaments shed from the parent surface is assessed both in a nonlinear fashion as well as using the linear stability analysis of Ponstein. Using this latter approach, drop size distributions have been generated from first principles and compared with the popular Rosin,Rammler model. Copyright © 2005 John Wiley & Sons, Ltd. [source]

On Marangoni effects in a heated thin fluid layer with a monolayer surfactant.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2005
Part I: model development, stability analysis
Abstract We develop a model for surface tension driven flow induced by an insoluble surfactant monolayer on a heated thin fluid layer. The mathematical model is based on a perturbation analysis for a thin fluid layer. The resulting model involves coupling of flow and heat transfer to an additional transport equation for surfactant concentration on the surface. We develop the stability analysis of this coupled system. We characterize the stability behaviour and induced wave motion into four parametric regions based on linear stability analysis. A finite element formulation and numerical studies of the behaviour in the various stability regimes are given in Part II. Copyright © 2004 John Wiley & Sons, Ltd. [source]

On Marangoni effects in a heated fluid layer with a monolayer surfactant.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2005
Part II: finite element formulation, numerical studies
Abstract In this part we consider the dilute surfactant model developed in Part I and construct a variational formulation and mixed finite element scheme to obtain approximate solutions. In particular, we consider the stability regimes identified in the linear stability analysis of Part I and conduct numerical experiments to explore the nature of stability for the approximate solutions in these regimes. Both 1D and 2D simulation results are provided to illustrate the behaviour. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Linear stability analysis of flow in a periodically grooved channel

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2003
T. Adachi1
Abstract We have conducted the linear stability analysis of flow in a channel with periodically grooved parts by using the spectral element method. The channel is composed of parallel plates with rectangular grooves on one side in a streamwise direction. The flow field is assumed to be two-dimensional and fully developed. At a relatively small Reynolds number, the flow is in a steady-state, whereas a self-sustained oscillatory flow occurs at a critical Reynolds number as a result of Hopf bifurcation due to an oscillatory instability mode. In order to evaluate the critical Reynolds number, the linear stability theory is applied to the complex laminar flow in the periodically grooved channel by constituting the generalized eigenvalue problem of matrix form using a penalty-function method. The critical Reynolds number can be determined by the sign of a linear growth rate of the eigenvalues. It is found that the bifurcation occurs due to the oscillatory instability mode which has a period two times as long as the channel period. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Linear stability analysis of two-layer rectilinear flow in slot coating

AICHE JOURNAL, Issue 10 2010
Jaewook Nam
Abstract Two-layer coating occurs in many products. Ideally, the liquids are deposited onto the substrate simultaneously. In the case of two-layer slot coating, the interlayer between the coating liquids is subjected to enormous shearing. This may lead to flow instabilities that ruin the product. It is important to map the regions of the parameter space at which the flow is unstable. Most of the stability analyses of two-layer rectilinear flow consider the position of the interlayer as an independent parameter. Classical results cannot be applied directly in coating flows. We present a linear stability analysis of two-layer rectilinear flow considering the flow rates as an independent parameter. The predicted neutral-stability curves define the region of stable flow as a function of the operating parameters. The range of coating operating conditions is restricted further, when the condition for the desirable interlayer separation point location are considered together with the stability condition. © 2010 American Institute of Chemical Engineers AIChE J, 2010 [source]

Gas-solid flow distribution through identical vertical passages: Modeling and stability analysis

AICHE JOURNAL, Issue 8 2010
Mohammad S. Masnadi
Abstract As previous evidence shows, the distribution of gas-solid flow traveling through identical parallel paths can be significantly nonuniform, often with harmful operating consequences in practice. A fundamental analytical and numerical study is performed on the distribution of gas-solid pneumatic flow passing through a "Y branch". While many steady-state gas-solid distribution solutions, including a uniform distribution, satisfy the governing equations, linear stability analysis indicates that the uniform distribution is stable the most likely solution of the system. Both 2-D (two-dimensional) and 3-D multiphase computational fluid dynamic simulations and stability analyses confirm the analytical conclusions. © 2010 American Institute of Chemical Engineers AIChE J, 2010 [source]

Draw ratio enhancement in nonisothermal melt spinning

AICHE JOURNAL, Issue 3 2009
Balram Suman
Abstract Nonisothermal melt spinning of materials having a step-like viscosity variation with temperature is studied in this work. A set of nonlinear equations is used to describe the fiber behavior and to obtain the draw ratio, the square of the ratio of the fiber diameter at the entrance to that at the exit of the fiber-spinning device. The fluid-flow equation is based on a slender-jet approximation, and external heating and cooling have been accounted for with a one-dimensional model in order to obtain the fiber temperature and viscosity along the fiber length. The model is similar to that used by Wylie et al. (J Fluid Mech. 2007;570:1,16) but accounts for inertia, shear stress at the fiber surface, surface tension, gravity, cooling, and larger heating rates. Steady-state analysis reveals that the draw ratio increases with an increase in the pulling force, passes through a maximum, and then starts increasing again, resulting in three possible pulling forces for the same draw ratio. However, linear stability analysis reveals that depending on the strength of heating and/or cooling, at most two of the steady states are stable. The stability analysis also predicts complicated oscillatory and nonoscillatory dynamical behavior as the pulling force varies. Nonlinear simulations reveal that an unstable system always tends to limit-cycle behavior. Systems predicted as stable by the linear stability analysis are also stable for large-amplitude perturbations. External heating is found to dramatically enhance the draw ratio of the melt-spinning process. The addition of a cooling section suppresses the draw ratio, but this can be compensated for with a higher heating strength. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source]

Simulations of instability in fiber spinning of polymers

POLYMER ENGINEERING & SCIENCE, Issue 7 2010
Atanas Gagov
This work determines the critical regimes beyond which the melt fiber spinning for noncrystallizable polymeric liquids becomes unstable. The critical draw ratio of the process is established using linear stability analysis for both isothermal and nonisothermal fiber spinning regimes. In addition, nonlinear isothermal analysis describes the complete range of the stable and unstable conditions for fiber spinning. Unlike previous studies, this research uses quite realistic viscoelastic constitutive equations extensively tested for five polymer liquids, which provides a good comparison of our calculations with available experimental data. POLYM. ENG. SCI., 2010. © 2010 Society of Plastics Engineers [source]

Influence of Ohmic diffusion on the excitation and dynamics of MRI

ASTRONOMISCHE NACHRICHTEN, Issue 1 2010
M.J. Korpi
Abstract In this paper we make an effort to understand the interaction of turbulence generated by the magnetorotational instability (MRI) with turbulence from other sources, such as supernova explosions (SNe) in galactic disks. First we perform a linear stability analysis (LSA) of non-ideal MRI to derive the limiting value of Ohmic diffusion that is needed to inhibit the growth of the instability for different types of rotation laws. With the help of a simple analytical expression derived under first-order smoothing approximation (FOSA), an estimate of the limiting turbulence level and hence the turbulent diffusion needed to damp the MRI is derived. Secondly, we perform numerical simulations in local cubes of isothermal nonstratified gas with external forcing of varying strength to see whether the linear result holds for more complex systems. Purely hydrodynamic calculations with forcing, rotation and shear are made for reference purposes, and as expected, non-zero Reynolds stresses are found. In the magnetohydrodynamic calculations, therefore, the total stresses generated are a sum of the forcing and MRI contributions. To separate these contributions, we perform reference runs with MRI-stable shear profiles (angular velocity increasing outwards), which suggest that the MRI-generated stresses indeed become strongly suppressed as function of the forcing. The Maxwell to Reynolds stress ratio is observed to decrease by an order of magnitude as the turbulence level due to external forcing exceeds the predicted limiting value, which we interpret as a sign of MRI suppression. Finally, we apply these results to estimate the limiting radius inside of which the SN activity can suppress the MRI, arriving at a value of 14 kpc (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]