Fluid Dynamic Instabilities in Drawn Fibers

1989 ◽  
Vol 172 ◽  
Author(s):  
Charles Thompson ◽  
Arun Mulpur
Keyword(s):  
Stability Analysis ◽  
Numerical Solution ◽  
Linear Stability ◽  
Nonlinear Equations ◽  
Viscoelastic Fluid ◽  
Nonlinear Stability ◽  
Linear Stability Analysis ◽  
Fluid Dynamic ◽  
Nonlinear Stability Analysis ◽  
Zeroth Order

AbstractThe nonlinear stability analysis of viscoelastic fibers is presented. The molten fiber is modeled as a Maxwellian viscoelastic fluid and the zeroth order equations governing its behavior given. Linear stability analysis is performed to determine the influence of winder speed and impedance as well as viscosity and elasticity. The results of numerical solution of the nonlinear equations are given.

scholarly journals Nonlinear stability analysis of Darcy’s flow with viscous heating

2016 ◽  
Vol 472 (2189) ◽  
pp. 20160036 ◽  
Author(s):  
Michele Celli ◽  
Leonardo S. de B. Alves ◽  
Antonio Barletta
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Viscous Dissipation ◽  
Nonlinear Stability ◽  
Linear Stability Analysis ◽  
Integral Transform ◽  
Internal Heat ◽  
Neutral Stability ◽  
Nonlinear Stability Analysis ◽  
Rate Analysis

The nonlinear stability of a rectangular porous channel saturated by a fluid is here investigated. The aspect ratio of the channel is assumed to be variable. The channel walls are considered impermeable and adiabatic except for the horizontal top which is assumed to be isothermal. The viscous dissipation is acting inside the channel as internal heat generator. A basic throughflow is imposed, and the nonlinear convective stability is investigated by means of the generalized integral transform technique. The neutral stability curve is compared with the one obtained by the linear stability analysis already present in the literature. The growth rate analysis of different unstable modes is performed. The Nusselt number is investigated for several supercritical configurations in order to better understand how the system behaves when conditions far away from neutral stability are considered. The patterns of the neutrally stable convective cells are also reported. Nonlinear simulations support the results obtained by means of the linear stability analysis, confirming that viscous dissipation alone is indeed capable of inducing mixed convection. Low Gebhart or high Péclet numbers lead to a transient overheating of the originally motionless fluid before it settles in its convective steady state.

scholarly journals Linear and nonlinear stability analysis of binary viscoelastic fluid convection

2013 ◽  
Vol 37 (16-17) ◽  
pp. 8162-8178 ◽  
Author(s):  
Mahesha Narayana ◽  
Precious Sibanda ◽  
Pradeep G. Siddheshwar ◽  
G. Jayalatha
Keyword(s):  
Stability Analysis ◽  
Viscoelastic Fluid ◽  
Nonlinear Stability ◽  
Nonlinear Stability Analysis ◽  
Fluid Convection ◽  
Linear And Nonlinear

Rayleigh–Bénard instability in a vertical cylinder with a vertical magnetic field

2002 ◽  
Vol 469 ◽  
pp. 189-207 ◽  
Author(s):  
B. C. HOUCHENS ◽  
L. MARTIN WITKOWSKI ◽  
J. S. WALKER
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Numerical Solution ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Hartmann Number ◽  
Critical Rayleigh Number ◽  
Vertical Wall ◽  
Vertical Cylinder ◽  
Vertical Magnetic Field

This paper presents two linear stability analyses for an electrically conducting liquid contained in a vertical cylinder with a thermally insulated vertical wall and with isothermal top and bottom walls. There is a steady uniform vertical magnetic field. The first linear stability analysis involves a hybrid approach which combines an analytical solution for the Hartmann layers adjacent to the top and bottom walls with a numerical solution for the rest of the liquid domain. The second linear stability analysis involves an asymptotic solution for large values of the Hartmann number. Numerically accurate predictions of the critical Rayleigh number can be obtained for Hartmann numbers from zero to infinity with the two solutions presented here and a previous numerical solution which gives accurate results for small values of the Hartmann number.

Linear and Nonlinear Stability of Melt Flows in Induction Channels

2003 ◽  
Author(s):  
X. Ai ◽  
B. Q. Li
Keyword(s):  
Stability Analysis ◽  
Finite Difference ◽  
Numerical Solution ◽  
Linear Stability ◽  
Nonlinear Stability ◽  
Linear Analysis ◽  
High Order ◽  
Reynolds Stresses ◽  
Linear And Nonlinear ◽  
High Order Finite Difference

A linear and nonlinear stability analysis is presented of melt flows in induction channels, which are induced by traveling electromagnetic waves. The problem formulation within the framework of magnetodynamics for flow stability studies is discussed. The linear analysis entails the numerical solution of the Orr-Summerfield equation, which is solved by using the high order finite difference technique and combined with the QR method for eigenvalue solutions. The eigenvalue spectrum, the linear stability characteristics and time average Reynolds stresses are obtained from the linear stability analysis. Based on the linear analysis, the nonlinear stability is studied by direct numerical solution of the magnetohydrodynamic equations using the high order finite difference method. Starting from the linear critical Reynolds number, the weakly nonlinear analysis is performed to determine the nonlinear bifurcation phenomena associated with the induction channel flows. Results show that the flow exhibits the typical Hopf bifurcation behavior and the subcritical instability occurs with high perturbation amplitudes.

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